Development of a novel uncovered stent 
system for the management of complex 
aortic aneurysms 
                    
 
 
Shuo Wang 
Department of Radiology 
University of Cambridge 
 
This dissertation is submitted for the degree of 
Doctor of Philosophy 
 
 
 
Christ’s College 28/09/2018 
  
Declaration 
I hereby declare that except where specific reference is made to the work of others, the contents 
of this dissertation are original and have not been submitted in whole or in part for consideration 
for any other degree or qualification in this, or any other University.  
The work was conducted in the Department of Radiology, University of Cambridge, under 
supervision of Dr Zhongzhao Teng and Professor Jonathan H Gillard. 
This dissertation is the result of my own work and includes nothing which is the outcome of 
work done in collaboration, except where specifically indicated in the text. This dissertation 
contains less than 65,000 words including appendices, bibliography, footnotes, tables and 
equations and has less than 150 figures. 
 
Shuo Wang 
28/09/2018 
  
Acknowledgements 
Firstly, I would like to express my very great appreciation and deep gratitude to my supervisors, 
Dr Zhongzhao Teng and Professor Jonathan H Gillard. They offered me the opportunity to start 
the doctoral degree in Cambridge and have been supporting me from the very first day. Dr 
Teng inspired me to purse the research of clinical biomechanics and provided me continuous 
guidance with great knowledge and patience. Professor Gillard has created such an open 
environment in our group, where the collaborations between clinicians and engineers are 
extremely close. He gave me enormous freedom to explore my interests and kept my progress 
on schedule. I feel incredibly privileged to have them as my supervisors. 
I wish to thank various people for their contribution to this project. I would like to thank Mr 
Aziz Tokgoz for the collaborations on material tests and enlightening discussions. I am very 
thankful to Dr Yuan Huang for his expertise on statistics and image processing. I would like to 
express my special thanks to Dr Yongxue Zhang, Dr Yanqing Chen, Dr Jiaxuan Feng, Professor 
Qingsheng Lu, Dr Adam Brown, Dr Umar Sadat, Dr Ammara Usman, Dr Priya Sastry for 
collecting the tissue samples and providing imaging data, as well as sharing their invaluable 
clinical insights. I am also thankful to Ms Nichola Figg and Professor Martin R Bennet for their 
guidance in histological analysis. I want to thank Mr Hao Li, Dr Jianmin Yuan, Mr Pascal 
Ruetten for their helpful suggestions in MRI. I am thankful to Mr Richard Black for the 
maintenance of computer clusters. 
I would like to acknowledge the China Scholarship Council for funding my PhD. I am thankful 
to Christ’s College and Cambridge Philosophical Society for travel grants.  
I want to express my thanks to college tutors, Professor David Newman and Professor Gábor 
Betegh, for their encouragements and suggestions. I wish to thank Dr Chao Li, Mr Xiaojian 
She, Mr Ran Guan, Dr Jing He, Ms Elyn Shen and all my friends for their help in the life.  
I would like to thank all my family for their love and support. I would like to give my deepest 
thanks to my wife Ms Xiaoyue Wang for her unconditional accompanying and support. 
  
Abstract 
Endovascular aortic repair (EVAR) is a minimally invasive alternative to open surgery for the 
treatment of aortic aneurysms (AA). However, standard EVAR is not applicable to complex 
AA with involvement of vital branches, which could be occluded by the endograft. As an 
emerging technique, the multiple overlapping uncovered stents (MOUS) have been proposed 
to manage complex lesions. MOUS was used to modulate the flow pattern inside the aneurysm 
sac, and promote the thrombus formation followed by the aneurysm shrinkage. In this 
dissertation, we sought to investigate the mechanism of MOUS-induced flow modulation and 
the key factors associated with the success of this novel technique: 
- The mechanical behaviour of AA was characterised by uniaxial material tests (Chapter 4). A 
Bayesian framework was proposed for material constants identification. They were found 
correlated to the microstructure of tissue fibre network and were capable in differentiating 
tissue types.  
- Solid-to-solid interaction and one-way fluid-solid interaction (FSI) analysis was performed 
based on patient-specific computer tomography angiography (Chapters 5&6). Structural stress 
concentrations were observed within the landing zones, which increased with the number of 
stents deployed. In the parameter studies (Chapter 6), the overall porosity was identified as the 
dominant factor of the flow-diverting outcome, while cross-stent structures of MOUS had 
limited influence. 
- The pathological effect of structural stress concentration induced by an implanted device was 
further studied in rabbit models (Chapter 7). The wall structural stress and fluid shear stress 
were obtained from FSI analysis based on magnetic resonance imaging (MRI), and correlated 
to plaque characteristics. Both high structural stress and low fluid shear stress were found 
correlated to plaque initialisation and increased inflammation. 
Overall, MOUS modulates the blood flow with robust performance under different overlapping 
patterns. Image-based biomechanical analysis can optimise MOUS design and can contribute 
to personalised pre-surgery planning.  
Contents 
Contents .............................................................................................................................. v 
List of Figures ......................................................................................................................... vii 
List of Tables ........................................................................................................................... xi 
List of Publications .............................................................................................................. xiii 
Glossary ............................................................................................................................ xv 
 
Chapter 1 Introduction ........................................................................................................ 2 
1.1 Overview of aortic aneurysms..................................................................................... 2 
1.2 Normal aorta ................................................................................................................ 3 
1.3 Pathophysiology .......................................................................................................... 6 
1.4 Biomechanical factors ............................................................................................... 12 
1.5 Clinical management ................................................................................................. 13 
1.6 Challenges in endovascular aortic repair .................................................................. 18 
1.7 Summary ................................................................................................................... 25 
Chapter 2 Imaging of aortic aneurysms........................................................................... 27 
2.1 Overview of imaging techniques............................................................................... 27 
2.2 X-ray imaging ........................................................................................................... 28 
2.3 Ultrasound imaging ................................................................................................... 32 
2.4 Magnetic resonance imaging ..................................................................................... 35 
2.5 Positron emission tomography .................................................................................. 40 
2.6 Clinical application ................................................................................................... 42 
Chapter 3 Biomechanical analysis .................................................................................... 45 
3.1 Description of internal deformation and forces ......................................................... 45 
3.2 Constitutive law for arteries ...................................................................................... 51 
3.3 Uniaxial tensile test ................................................................................................... 53 
3.4 Description of fluid dynamics of blood flow ............................................................ 54 
3.5 Haemodynamic variables on the wall ....................................................................... 57 
3.6 Finite element analysis .............................................................................................. 58 
3.7 Image-based biomechanical modelling ..................................................................... 60 
Chapter 4 Material properties of arterial tissues ............................................................ 63 
4.1 Introduction ............................................................................................................... 63 
4.2 Materials and methods .............................................................................................. 65 
4.3 Results ....................................................................................................................... 71 
4.4 Discussion ................................................................................................................. 79 
4.5 Appendix ................................................................... Error! Bookmark not defined. 
Chapter 5 Image-based finite element analysis of multiple overlapping uncovered  
 stents: a patient-specific study ........................................................................ 84 
5.1 Introduction ............................................................................................................... 84 
5.2 Materials and methods .............................................................................................. 85 
5.3 Results ....................................................................................................................... 93 
5.4 Discussion ............................................................................................................... 103 
Chapter 6 Influence of cross-stent structures: parameter studies of multiple 
 overlapping uncovered stents........................................................................ 108 
6.1 Introduction ............................................................................................................. 108 
6.2 Materials and methods ............................................................................................ 109 
6.3 Results ..................................................................................................................... 113 
6.4 Discussion ............................................................................................................... 122 
Chapter 7 Pathological effects of high structural stress concentrations ..................... 125 
7.1 Introduction ............................................................................................................. 125 
7.2 Materials and methods ............................................................................................ 127 
7.3 Results ..................................................................................................................... 134 
7.4 Discussion ............................................................................................................... 138 
Chapter 8 Conclusion ...................................................................................................... 143 
8.1 Limitations .............................................................................................................. 144 
8.2 Potential future directions ....................................................................................... 144 
Appendix 
References 
 List of Figures 
Figure 1.1 Types of aortic aneurysm ........................................................................................ 3 
Figure 1.2 Idealised architecture of a healthy human aorta. ..................................................... 4 
Figure 1.3 Histopathology of aortic aneurysms ........................................................................ 7 
Figure 1.4 Pathophysiological processes associated with the development of aneurysms ....... 9 
Figure 1.5 General pathogenesis of aortic aneurysm .............................................................. 11 
Figure 1.6 Open surgical repair of aortic aneurysm ................................................................ 15 
Figure 1.7 Endovascular aortic repair of aortic aneurysm ...................................................... 16 
Figure 1.8 Advanced endograft designs and chimney techniques .......................................... 19 
Figure 1.9 Fenestrated endograft and branched endograft ...................................................... 20 
Figure 1.10 Diverting effect of uncovered stents .................................................................... 22 
Figure 1.11 A photo of  Cardiatis Multilayer Flow Modulator .............................................. 23 
Figure 1.12 A photo of Sinus-XL stent and the schematic representation of the uniform 
overlapping pattern .................................................................................................................. 24 
Figure 2.1 Aortic aneruysms diagnosed by chest radiographs................................................ 28 
Figure 2.2 Compterised tomographic angiography of aortic aneruysm.................................. 30 
Figure 2.3  Digital subtraction angiography of aortic aneruysm ............................................ 31 
Figure 2.4 Ultrasonography of the aorta ................................................................................. 33 
Figure 2.5 Colour Doppler ultrasound of aortic aneurysm ..................................................... 33 
Figure 2.6 Intravascular ultrasound of a stent graft ................................................................ 34 
Figure 2.7 Illustration of the intraluminal thrombus on magnetic resonance imaging and 
compterised tomography angiography ..................................................................................... 36 
Figure 2.8 Comparison of compterised tomography angiography and magnetic resonance 
imaging in aortic aneruysm with intraluminal thrombus ......................................................... 37 
Figure 2.9 Magnetic resonance angiography of aortic aneruysm ........................................... 38 
Figure 2.10 Positron emission tomography of aortic aneurysm ............................................. 41 
Figure 3.1 Schematic drawing of the motion of a continuum body. ....................................... 46 
Figure 3.2 Schematic drawing of the deformation (right) of a continuum body. ................... 46 
Figure 3.3 Schematic drawing of stress vector ....................................................................... 49 
Figure 3.4 Schematic drawing of stress state .......................................................................... 50 
Figure 3.5 Schematic strain-stress curve of non-linear biological soft tissue ......................... 51 
Figure 3.6 Interpretation of rate of strain tensor components ................................................. 55 
Figure 3.7 Shearing stress and different types of viscosity..................................................... 56 
Figure 4.1 A representative sample of aortic aneurysm.......................................................... 66 
Figure 4.2 Overview of the testing equipment and an example of the testing process ........... 67 
Figure 4.3 A representative example showing the fitted results using ordinary least square  
method and Bayesian inference. .............................................................................................. 72 
Figure 4.4 The visualisation of material constants of different tissue strips from different 
types of samples. ...................................................................................................................... 74 
Figure 4.5 Representative EVG stained images showing the distribution of elastin in the 
thickened intima, media and adventitia of an aortic aneurysm ................................................ 76 
Figure 4.6 Representative Sirius Red stained images showing the collagen fibres in the media 
and adventitia of an aortic aneurysm ....................................................................................... 77 
Figure 4.7 Comparison of area percentage of elastin and collagen contents in the thickened 
intima, media and adventitia from eight aortic aneurysms ...................................................... 78 
Figure 4.8 The association between collagen fibre dispersion and waviness and D2. ............ 78 
Figure 4.9 The change of stress-stretch curves with the change of material constants .......... 80 
Figure 5.1 The configuration of a complex aortic aneurysm with vital side branches.. ......... 86 
Figure 5.2 Reconstruction of the uncovered stents ................................................................. 87 
Figure 5.3 Graphical User Interface of the aortic aneurysm segmentation platform .............. 88 
Figure 5.4 Surface processing and meshing of the aneruysm ................................................. 89 
Figure 5.5 The workflow chart of the one-way fluid-structure interaction analysis. .............. 90 
Figure 5.6 The computational model for haemodynamic simulation ..................................... 92 
Figure 5.7 Overall porosity of MOUS after stents deployment. ............................................. 94 
Figure 5.8 Structural stress level at different location changed after MOUS deployment. .... 95 
Figure 5.9 Band plots of effective stress before and after stents deployment. ....................... 96 
Figure 5.10 The change of mean sac time-averaged velocity before and after multiple stents 
deployment. .............................................................................................................................. 97 
Figure 5.11 Cross-sectional band plot of blood velocity at systole ........................................ 98 
Figure 5.12 Band plots of haemodynamic variables on the lumen wall before and after 
multiple stents deployment .................................................................................................... 100 
Figure 5.13 The change of peak stress and averaged stress in different regions with the 
number of stents deployed ..................................................................................................... 104 
Figure 6.1 The local view of two stents with different overlapping patterns in the 
circumferential direction ........................................................................................................ 110 
Figure 6.2 The local view of two stents with different overlapping patterns in the axial 
direction ................................................................................................................................. 110 
Figure 6.3 The 3D structure of a 4-stent MOUS and the corresponding compact model .... 112 
Figure 6.4 The probability density functions of MOUS porosity under random deployments
................................................................................................................................................ 113 
Figure 6.5 The overall porosity of no stent, 1-stent and 2-stent MOUS under different 
overlapping patterns ............................................................................................................... 114 
Figure 6.6 Structural stress level of a representative node in different location changed when 
two stents were overlapped differently .................................................................................. 115 
Figure 6.7 Influence of the 2D overlapping pattern on the velocity reduction inside the 
aneurysm sac .......................................................................................................................... 116 
Figure 6.8 Comparison of velocity reduction between the MOUS and compact models ..... 120 
Figure 6.9 Comparison of structural stress level at different location after the deployment of 
MOUS and corresponding compact models, with different number of stents. 121 
Figure 6.10 An example of aneurysm recurrence near the landing zone after MOUS 
treatment. ............................................................................................................................... 123 
Figure 7.1 In vivo magnetic resonance imaging showing rabbit carotid arteries with and 
without collar and corresponding blood velocity measurements ........................................... 128 
Figure 7.2 Reconstructed 3D geometry based on baseline MR images, images of arteries 
removed from the animals and corresponding Cluster of Differentiation 68 stain, and 
calculated flow parameters and mechanical loading within the structure. ............................ 129 
Figure 7.3 A representative image showing wall and plaque segmentation ......................... 133 
Figure 7.4 The comparison of plaque morphological and inflammatory features at different 
location ................................................................................................................................... 135 
Figure 7.5 The comparison of mechanical parameters among different regions .................. 136 
Figure 7.6 Wall thickness of both diseased and healthy section was associated with local 
vessel structural stress. ........................................................................................................... 139 
List of Tables 
Table 2.1 Typical HU values for different tissues. ................................................................. 29 
Table 4.1 Patient demographics. ............................................................................................. 65 
Table 4.2 Representative regressions using the ordinary method with different initial values 
and Bayesian inference procedure with different prior ranges. ............................................... 72 
Table 4.3 Bayesian inference-based estimations for different types of tissues (Median 
[Interquartile range]) ................................................................................................................ 73 
Table 5.1 Comparison of time-averaged flow rate in each side branch before and after 
MOUS deployment ................................................................................................................ 102 
Table 6.1 Comparison of mean TAWSS, OSI, RRT on the aneurysm sac after the 
deployment of 2-stent MOUS with different overlapping patterns. ...................................... 117 
Table 6.2 Comparison of time-averaged flow rate in each side branch after the deployment of 
2-stent MOUS with different overlapping patterns ............................................................... 118 
Table 6.3 Comparison of haemodyamicvariables averaged on the aneurysm wall, between 
MOUS and corresponding compact models. ......................................................................... 119 
Table 7.1 Weight and cholesterol levels after 16-week high fat diet .................................... 134 
List of Publications 
Peer-reviewed journal publications directly relevant to this thesis (* equal authorship): 
1. Shuo Wang*, Aziz Tokgoz*, Yuan Huang, Yongxue Zhang, Jiaxuan Feng, Priya Sastry, Chang 
Sun, Nichola Figg, Qingsheng Lu, Michael PF Sutcliffe, Zhongzhao Teng, Jonathan H Gillard. 
IEEE Transactions on Biomedical Engineering. 2018. 
2. Shuo Wang, Yongxue Zhang, Jiaxuan Feng, Yuan Huang, Aziz Tokgoz, Umar Sadat, Jonathan H 
Gillard, Qingsheng Lu, and Zhongzhao Teng. Influence of overlapping pattern of multiple 
overlapping uncovered stents on the local mechanical environment: A patient-specific parameter 
study. Journal of biomechanics. 2017. 
3. Zhongzhao Teng, Jianmin Yuan, Jiaxuan Feng, Yongxue Zhang, Adam J. Brown, Shuo Wang, 
Qingsheng Lu, and Jonathan H Gillard. The influence of constitutive law choice used to characterise 
atherosclerotic tissue material properties on computing stress values in human carotid plaques. 
Journal of biomechanics. 2015. 
Manuscripts under review/revision/in preparation (* equal authorship): 
1. Aziz Tokgoz*, Shuo Wang*, Priya Sastry, Chang Sun, Nichola Figg, Yuan Huang, Martin R. 
Bennett, Sanjay Sinha, Jonathan H Gillard, Michael PF Sutcliffe, Zhongzhao Teng. Journal of 
Thoracic and Cardiovascular Surgery. (under review). 
2. Shuo Wang, Yongxue Zhang, Jiaxuan Feng, Yuan Huang, Aziz Tokgoz, Umar Sadat, Jonathan H 
Gillard, Qingsheng Lu, and Zhongzhao Teng. Influence of cross-stent structure and optimised 
design of multiple overlapping uncovered stents. (in preparation) 
Conference presentation 
1. Shuo Wang, Yongxue Zhang, Jiaxuan Feng, Yuan Huang, Aziz Tokgoz, Umar Sadat, Jonathan H 
Gillard, Qingsheng Lu, and Zhongzhao Teng. Influence of multiple overlapping uncovered stents 
on the local mechanical environment: porosity and cross-stent structure. 8th World Congress of 
Biomechanics, Dublin, 2018 July. 
2. Aziz Tokgoz*, Shuo Wang*, Priya Sastry, Chang Sun, Nichola Figg, Yuan Huang, Martin R. 
Bennett, Sanjay Sinha, Jonathan H Gillard, Michael PF Sutcliffe, Zhongzhao Teng. Fracture 
behaviour and microstructure-mechanics relationship of human aortic aneurysms. 8th World 
Congress of Biomechanics, Dublin, 2018 July. 
3. Shuo Wang, Yongxue Zhang, Jiaxuan Feng, Yuan Huang, Umar Sadat, Jonathan H Gillard, 
Qingsheng Lu, and Zhongzhao Teng. MOUS: a novel management strategy for aortic aneurysms, 
Endovascology, Shanghai, 2016 October. (best oral presentation award) 
 
Other publications produced during the period of this thesis  
1. Chao Li, Shuo Wang, Jiun-Lin Yan, Rory J Piper, Hongxiang Liu, Turid Torheim, Hyunjin 
Kim et al. Intratumoral heterogeneity of tumor infiltration of glioblastoma revealed by joint 
histogram analysis of diffusion tensor imaging. Neurosurgery. 2018. 
2. Chao Li, Shuo Wang, Angela Serra, Turid Torheim, Jiun-Lin Yan, Natalie R. Boonzaier, Tomasz 
Matys, Mary A. McLean, Florian Markowetz, Stephen J. Price. Multi-parametric and multi-regional 
histogram analysis of MRI: revealing imaging phenotypes of glioblastoma correlated with patient 
Survival. European Radiology. 2018.  
Other conference presentations 
1. Hao Li, Shuo Wang, Andrew Priest, Martin M Graves and David Lomas. An optimised 
subtraction approach for subtractive NCE-MRA techniques based on robust regression 
using the deviation angle. 30th annual SMRA conference, Glasgow, 2018 August. (best 
poster presentation)  
2. Chao Li, Shuo Wang, Angela Serra, Turid Torheim, Jiun-Lin Yan, Natalie R Boonzaier, 
Tomasz Matys, Mary A McLean, Florian Markowetz, Stephen J Price. Multi-parametric 
and multi-regional histogram analysis of MRI: revealing imaging phenotypes of 
glioblastoma correlated with patient survival. ISMRM Annual Meeting, Paris, 2018 June. 
(Magna Cum Laude Merit)   
3. Chao Li, Shuo Wang, Turid Torheim, Florian Markowetz Stephen J Price, S. Mutual 
information: depicting the interdependence of perfusion and diffusion magnetic resonance 
imaging in glioblastoma patients. ISMRM Annual Meeting, Paris, 2018 June.  
4. Hao Li, Shuo Wang, Andrew Priest, Martin M Graves and David Lomas. An optimised 
subtraction approach for subtractive NCE-MRA techniques based on principal component 
analysis. ISMRM Annual Meeting, Paris, 2018 June.  
 
 
Glossary 
2D Two-dimensional 
3D Three-dimensional 
AA Aortic aneurysm  
AAA Abdominal aortic aneurysm  
CCA Common carotid artery 
CD68 Cluster of differentiation 68 
CE-MRA Contrast-enhanced magnetic resonance angiography 
CFD Computational fluid dynamics 
CT Computerised tomography  
CTA Computerised tomographic angiography  
CVD Cardiovascular disease 
ECG Electrocardiographic 
ECM Extracellular matrix 
EEL External elastic lamina  
EVAR Endovascular aneurysm repair  
EVG Verhoeff–van Geisen 
FC Fibrous cap  
18FDG-PET 18-fluorodeoxyglucose positron emission tomography 
FEM Finite element method  
FSE Fast spin echo 
FSI Fluid-structure interaction  
Gd Gadolinium  
HE Haematoxylin and Eosin 
HDL Low density lipoprotein 
HU Hounsfield unit 
IEL Internal elastic lamina 
ILT Intraluminal thrombus 
IPH/T Intraplaque haemorrhage/thrombus 
IVUS Intravascular ultrasound  
LDL Low density lipoprotein 
MCMC Markov Chain Monte Carlo  
MFM Multilayer flow modulator 
MMP Matrix metalloproteinase 
MOUS Multiple overlapping uncovered stents  
MRA Magnetic resonance angiography  
MRI Magnetic resonance imaging 
MTH Mean thickness of healthy section 
MWT Maximum wall thickness 
OLS Ordinary least square 
OSI Oscillatory shear index  
PAR Plaque area ratio 
PC Phase-contrast 
PDF Probability density function 
PET Positron emission tomography  
PSR Picrosirius Red 
RCT Randomised clinical trial 
RGD Arg-Gly-Asp  
ROI Region of interest  
ROS Reactive oxygen species 
RR Relative risk 
RRT Relative residence time  
𝐑𝐑𝐓̅̅ ̅̅ ̅̅  Normalised relative residence time  
SEDF Strain energy density function 
SNR Signal-to-noise ratio  
SSFP Steady-state free precession  
TAA Thoracic aortic aneurysm 
TAAA Thoracoabdominal aortic aneurysm  
TAWSS Time-averaged wall shear stress 
T Tesla 
TIMP Tissue inhibitor of metalloproteinase  
TOF Time-of-flight  
US Ultrasonography  
VSMC Vascular smooth muscle cells 
VSS Vascular structural stress 
WSS Wall shear stress 
 
 
 Chapter 1 Introduction 
In this chapter, the pathophysiology of aortic aneurysms is summarised, including the 
biological and biomechanical factors that may contribute to the formation and development of 
aortic aneurysms. The current clinical management and challenges of complex aortic 
aneurysms are reviewed. Moreover, as an emerging technique, the rationale and features of 
multiple overlapping uncovered stents are discussed. The purpose of this chapter is to discuss 
the underlying processes during the structural degradation of aortic aneurysm, providing an 
overview of the disease and treatment. 
1.1  Overview of aortic aneurysms 
The term aneurysm originates from the ancient Greek word aneurusma, which means “a 
widening/an opening” 1. Aortic aneurysm (AA) is defined as a permanent localised dilation of 
the aorta by more than 50% of its original diameter (Figure 1.1) 2. Aneurysm is the second most 
frequent disease of the aorta following atherosclerosis. It is estimated that 1-2% of the 
population have AAs with an increased prevalence of up to 10% in older age groups (>65 
years) 3. Risk factors for AA formation include increasing age, male sex, high blood pressure, 
smoking and family history. 
Most AAs are asymptomatic until catastrophic rupture, which causes life-threatening 
haemorrhage or sudden death without apparent prior warnings 4. The mortality rate of ruptured 
AAs is up to 90%, which is ranked as the 13th  most common cause of death 5. According to 
the latest statistics from Global Burden of Disease Study, AAs are the primary cause of 
approximately 8,000 deaths per year in the United Kingdom 6,7. A better understanding of the 
anatomy and structure of aorta, and the pathophysiology of AAs are crucial for their clinical 
management.  
1.2 Normal aorta 3 
 
1.2  Normal aorta 
The aorta is the largest artery of the human body (Figure 1.1A), which delivers about 200 
million litres of oxygenated blood throughout the body, with more than 3.0 billion heartbeats 
in a lifetime 8. The aorta expands and contracts repeatedly to help propel blood distally through 
the systemic circulation, while withstanding pulsatile loadings from the blood flow. Therefore, 
the structural integrity and durability are essential to maintain the normal pumping function. 
1.2.1 Aortic anatomy 
Anatomically, the aorta ascends from the left ventricle of the heart and extends inferiorly to the 
aortic bifurcation, where it diverges into the left and right common iliac arteries 4. The aorta is 
classically divided into two sections, namely the thoracic and abdominal aorta, by their relative 
locations to the diaphragm (Figure 1.1A). 
 
 
Figure 1.1 Types of aortic aneurysm: (A) A normal aorta. (B) A thoracic aortic aneurysm, 
which is located behind the heart. (C) An abdominal aortic aneurysm, which is located below 
the renal arteries. (Reproduced with permission from National Institutes of Health) 
1.2 Normal aorta 4 
 
Accordingly, aortic aneurysms can be generally classified as a thoracic aortic aneurysm (TAA) 
(Figure 1.1B) or as abdominal aortic aneurysm (AAA) (Figure 1.1C), involving different aortic 
segments. AAs that co-exist in both segments of the descending aorta and abdominal aorta are 
termed as thoracoabdominal aortic aneurysm (TAAA). Although aneurysms may arise at any 
site along the course of aorta, they most frequently occur in the abdominal aorta or at the 
descending portion of thoracic aorta. 
1.2.2  Structure of the aortic wall 
The healthy aorta is composed of three distinct layers: the intima, media and adventitia (Figure 
1.2). These three layers have different extracellular components and functions, separated by 
the internal elastic lamina (IEL) and the external elastic lamina (EEL) 9: 
 
 
Figure 1.2 Idealised architecture of a healthy human aorta. The healthy aorta is composed 
of three distinct layers: the intima, media and adventitia. (Reproduced from Gasser et. al 9, 
with permission from Elsevier)  
1.2 Normal aorta 5 
 
- Intima (I): the innermost layer consists of a monolayer of endothelial cells overlying a thin 
basal membrane and a subendothelial layer of collagen fibres. The intima is in direct contact 
with the blood providing a smooth non-thrombogenic surface for the blood flow 10. 
- Media (M): the middle layer is composed of extracellular connective elements including a 
network of elastin, collagen, proteoglycans and vascular smooth muscle cells (VSMCs). 
Multiple layers of elastic lamellae separate the media into several transversely isotropic 
medial units. The media is the main load-bearing layer which provides elasticity of the 
normal aorta under physiological conditions. 
- Adventitia (A): the outermost layer is primarily composed of thick collagen fibres which 
are arranged in helical structures. This outer layer is surrounded by loose connective tissue. 
The adventitia provides additional structure and support to the aorta. 
The three-layer composite structure provides the overall elasticity of the aorta. Elastin (elastic 
fibres) and collagen are two important structural components of the aortic wall, which however 
have different mechanical properties. Elastin is easily stretched (up to 70% of its original 
length), which helps the recoil process of the aorta by storing energy during cardiac contraction 
and releasing the energy during cardiac relaxation 11. Compared to elastin, collagen fibres have 
much higher stiffness and tensile strength (about 20 times more than elastin), but lower 
distensibility. Specifically, the collagen fibres are coiled up under a stress-free state, and are 
only engaged to bearing loadings when the stretch exceeds a threshold. In contrast, the elastin 
is engaged from the initial stretch. As a result, the elasticity of aortic wall is non-linear in the 
inflation test, with the transition pressure from distensible to stiff behaviour near 80 mmHg 8. 
A more distensible behaviour characterising elastin is observed at a lower blood pressure, 
whereas a stiffer behaviour characterising tensed collagen is observed at a higher pressure. In 
a normal aorta, only about 6-7% collagen fibres are engaged during physiological deformation 
12,13. Therefore, elastin is the principle load-bearing element for normal conditions, while the 
collagen acts as a stiff reinforcing ‘safety net’. 
The aortic architecture is not uniform along the aorta. The abdominal aorta is thinner with only 
about 28 layers of elastic lamellae, compared to 35-56 layers in the thoracic aorta 14. The greater 
concentration of elastin in the thoracic aorta leads to more compliance than the abdominal 
1.3 Pathophysiology 6 
 
aorta. These differences in wall structure may contribute to the susceptibility of aneurysm 
formation, which will be discussed in Section 1.4. 
1.2.3 Aging of the aorta 
Increasing age is a well-known risk factor for many aortic diseases including AAs 4. Vascular 
aging starts from infancy being “identifiable” at around 40 years of age. The morphological 
changes include the enlargement of diameter and the elongation of total length 10. Another 
significant change with increasing age is the stiffening of aorta, which is caused by 
microstructural changes within the aortic wall. A positive correlation between increasing age 
and arterial stiffness has been demonstrated in a series of studies by measuring pulse wave 
velocity 15–18.  
As mentioned above, the aortic compliance is dependent on the relative composition ratio of 
elastin and collagen. The decreasing compliance is caused by the fragmentation of elastin and 
alteration of the collagen. A fracture of the elastic lamella is estimated to occur after around 1 
billion cycles, equating to an age of approximately 40 years 10. Meanwhile, the regenerative 
potential of elastin diminishes: the expression of tropoelastin (the precursor of elastin) 
decreases by 50% in each age decade 19; the quantity of smooth muscle cells, where the elastin 
is synthesised, also decreases with increasing age 19. Moreover, following the disorganisation 
and loss of interlaminar cross-links, the elastic lamellae are further apart and filled with altered 
collagen – which becomes thicker and more linear in arrangement with increasing age. As a 
result, the age-related remodelling of aorta alters the biomechanical properties of the aortic 
wall, which may cause pathological changes.  
1.3  Pathophysiology 
Similarly to the aging process, the formation and development of AAs are closely related with 
remodelling of the aortic wall. The pathophysiology of AA is characterised by the extensive 
structural degradation, which is frequently observed in histological examinations (Figure 1.3). 
In 1987, Campa et al. reported thinning of the media, disruption of the connective tissue 
structure, and loss of elastin within AAs 20. Following studies reported that, collagen contents 
1.3 Pathophysiology 7 
 
are also decreased in aneurysmal walls, with increased ratio of collagen to elastin 21 and 
increased number of collagen cross-links 22. Along with the structural changes in ECM, the cell 
density of VSMCs is also reported to decrease 23. 
 
 
 
Figure 1.3 Histopathology of aortic aneurysms. Representative sections of aortic wall tissue 
stained with Verhoeff–van Geisen (EVG) for elastin (dark purple fibres). Extensive 
structural degradation is observed in both TAAs and AAAs. Compared with normal aorta, 
TAAs exhibited disruption, fragmentation and disorganisation of medial elastic fibres, and 
loss of nuclei (upper panels). AAAs exhibited more extreme destruction of medial elastin 
and replacement by fibrocollagenous extracellular matrix (pink), along with depletion of 
medial smooth muscle cells and mononuclear inflammatory cell infiltration in direct 
association with areas of elastic fibre degeneration (lower panels). (Reproduced from Absi 
et al. 24, with permission from Elsevier) 
Although the pathophysiology of different aortic segments may differ, the formation of AAs is 
well recognised as the consequence of structural degradation within the aortic wall. Below is 
an introduction of several important factors resulting in the structural degradation, including 
proteolytic degradation and inflammation 3. 
  
1.3 Pathophysiology 8 
 
 Proteolytic degradation 
Proteolytic degeneration is a well-known factor associated with AA formation and progression 
(Figure 1.4, left). The underlying biochemical process is the degradation of extracellular matrix 
(ECM), which is primarily catalysed by matrix metalloproteinases (MMPs). So far, about 30 
individual proteinases have been identified and classified into several categories of MMPs, 
including collagenases, gelatinases, stromelysins, matrilysins, membrane-type (MT)-MMPs 25. 
The most frequently overexpressed proteinase in aortic aneurysms are MMP-1 (collagenase), 
MMP-2 (gelatinase A), MMP-3 (stromelysin) and MMP-9 (gelatinase B), which catalyse the 
degradation of elastin and collagen 26. 
Since the first report of increased MMP production within aneurysms in 1991 27,28, the roles of 
different MMPs in the development of AAs have been extensively investigated, in both human 
and animal subjects. Expression of MMP-2 and MMP-9 are higher in human aneurysmal 
tissues than normal arterial tissues 29,30. Studies using animal aneurysm models also supported 
the role of MMP-2 and MMP-9 in aneurysm formation. In a previous study, MMP-2 and MMP-
9 knock-out mice models did not form aneurysms after the abluminal application of calcium 
chloride (CaCl2). By contrast, the increased level of MMP-2 and MMP-9 by reinfusing 
competent macrophages into above models enabled aneurysm formation 31. In other studies, 
increased production of MMP-1, MMP-8 and MMP-9 was found to associate with AA rupture 
risk 32,33. In addition to the increased expression of MMPs, the abnormal regulation of MMP 
levels has been found to be important for aneurysm formation. The activity of MMPs is 
primarily controlled by the tissue inhibitor of metalloproteinase (TIMP) at the molecular level. 
The imbalance between MMPs and TIMPs may contribute to AA formation, which is 
supported by the  decreased concentrations of TIMPs in human aneurysm tissues 34. Other 
pathways regulating MMPs include: augmented gene expression, post-translational activation 
by the cleavage of pro-MMP protein, by MMP-MMP interactions and by plasmin, thrombin 
and reactive oxygen species (ROS) 10,25,35,36. 
The contribution of MMPs to AA pathophysiology has been validated by the beneficial effect 
of medications reducing MMPs levels. In several small randomised phase 2 trials, doxycycline, 
a recognised inhibitor of MMPs, was related to a reduced expansion rate of AA 37. 
1.3 Pathophysiology 9 
 
 
Figure 1.4 The schematic depicts the pathophysiological processes associated with the 
development of aneurysms, which involve two different but connected key processes: the 
degradation of extracellular matrix proteins and the occurrence of inflammatory processes. 
(From the left) Degradation of the ECM, including elastin and collagen, catalysed by matrix 
metalloproteinases (MMPs) is shown. The imbalance between MMPs and their inhibitors 
(including /2-macroglobulin) results in aneurysm initiation and progression. (From the right) 
Proinflammatory cells (macrophages, neutrophils, lymphocytes, etc.) migrate from the 
vascular lumen into the aortic wall via adhesion molecules (e.g., P-selectin), secreting various 
factors including cytokines and growth factors. This leads to further recruitment of 
proinflammatory cells. Angioneogenesis occurs simultaneously with inflammatory processes 
in the vascular media, providing an additional route of entry for proinflammatory cells. The 
production of cytotoxic mediators leads to a reduction of smooth muscle cells density 
(apoptotic smooth muscle cells) and a thinning of the tunica media. Owing to the combination 
of inflammation and ECM degradation, as well as the biomechanical factors, the aortic 
diameter increases, ultimately resulting in the rupture of the aortic vessel wall with potentially 
lethal consequences. Abbreviations: EEM, external elastic membrane; IEM, internal elastic 
membrane. (Reproduced from Brangsch et al. 38, with permission from Elsevier) 
1.3 Pathophysiology 10 
 
 Inflammation 
The role of inflammation in different arterial diseases is well established, which is closely 
related to the degradation of ECMs 39. In 1981, Rose and Dent reported the inflammatory 
findings in AAAs, where they found mild inflammation in 73% and moderate inflammation in 
16% of resected AAAs 40. Subsequently, the quantities of lymphocytes and macrophages were 
found greater in AAAs than in normal aortas 41. Similarly, increased levels of various pro-
inflammatory cytokines were observed in aneurysms compared to normal control 42. In 
addition, increased levels of other acute-phase proteins were reported in the plasma and the 
aortic wall 43. The inflammatory response is also supported by the studies using 18-
fluorodeoxyglucose positron emission tomography imaging (18FDG-PET) with and advanced 
magnetic resonance imaging (MRI) with contrast media such as ultrasmall superparamagnetic 
iron oxide 25,44. 
Most of the inflammatory mediators derive from infiltrating macrophages; Lymphocytes, 
aortic endothelium cells and smooth muscle cells also contribute to the inflammatory milieu 3. 
These immune cells invade the aortic wall, become activated, and create an inflammatory 
environment through the release of a cascade of cytokines (Figure 1.4, right). This process 
results in the expression of cell adhesion molecules, increased protease expression, and the 
release of ROS causing degradation of the ECM through the activation of MMPs 34. Higher 
cytokine levels in ruptured AAs than asymptomatic AAs were reported in some studies 45. 
Several animal studies have also supported that increased inflammation promotes the 
development of AAs 34. However, the mechanism of molecular signalling pathways that 
modulate inflammatory cell recruitment in AAs remain unclear. 
 
1.3 Pathophysiology 11 
 
 
Figure 1.5 Chart showing the general pathogenesis of aortic aneurysm. (Reproduced from 
MacSweeney et al. 46, with permission from Elsevier John Wiley and Sons). 
As discussed above, the pathophysiology of AA is a chronic and multifactorial process that 
involves biological and biochemical factors. The general pathogenesis of an AA is 
demonstrated in Figure 1.5. In most cases, the initial degeneration is a reduction of elastin 
content as a result of proteolytic processes 47, regulated by genetic and environmental factors. 
Along with the elastin destruction, the collagen remodelling and the relative balance between 
elastin and collagen are critical for the development of AA. In earlier stages of the disease 
progression, production of collagen is up-regulated to compensate the loss of elastin 48, which 
leads to the expansion of aorta. In later stages, the degradation of collagen results in progressive 
dilation. In an in vitro study, collagen degradation was found to be the ultimate cause of AA 
rupture 48.  
1.4 Biomechanical factors 12 
 
1.4 Biomechanical factors 
The higher incidence of AA formation in the abdominal aorta compared with other aortic 
segments suggests a predisposition in this area. Adverse blood flow patterns and relative 
structural deficiencies in the abdominal aorta are considered as important biomechanical 
factors associated with the development of AA.  
 Wall shear stress 
The bifurcation of the aorta results in turbulence and areas of abnormal wall shear stress (WSS) 
49. In physiological conditions, optimal WSS is essential to maintain the survival, quiescence 
and alignment of endothelial cells in the direction of the blood flow. It is also central to the 
secretion of vasoactive substances that promote either vasodilatation or anticoagulation. In 
pathological conditions, however, both higher and lower WSSs than normal are reported to be 
associated with the development of AAs. In areas of high WSS, the production of endothelial 
nitric oxide, MMP-2 and MMP-9, and transforming growth factor-beta (TGF-β) are found to 
be up-regulated in endothelial cells 50. On the other hand, in areas of low wall shear stress, 
nuclear factor-κB (NF-κB) and endothelin-1 were found overexpressed in endothelial cells 51. 
The abnormal WSS can trigger the pathological remodelling of the aortic wall, leading to 
aneurysm formation. Vollmar et al. studied 329 subjects who lost a leg in World War II and 
702 war veterans 52. They observed AAAs in 6% of the amputees compared to 1% of the non-
amputees, concluding that the abnormal flow pattern caused a late damage to the aorta. With 
the expansion of AAs, the turbulent flow inside the aneurysm sac would cause separated 
regions of rotational flow with vertical structures, which may result in further aortic 
remodelling and disease progression 53,54. 
 Structural loading 
In addition to WSS, the structural loading within the aortic wall is also considered important 
to AA formation and development. As mentioned in Section 1.2.2, the physiological loading 
from blood pressure is mainly absorbed by the lamellar units within the aortic media. The 
abdominal aorta is more susceptible to the elastin breakdown, due to the higher structural 
loading withstood by each lamellar unit – there are more lamellar units in the abdominal aorta 
1.5 Clinical management 13 
 
compared with thoracic aorta 14, as well as the higher pulse pressure in the abdominal aorta. 
The structural loading also contributes to aneurysm progression. It can be approximately 
estimated by the Laplace’s Law 55: 
 
𝜎 =
𝑝𝐷
2ℎ
 (1.1) 
where 𝜎 is the averaged circumferential stress or wall tension; 𝑝 is the blood pressure; 𝐷 and 
ℎ denote the inner diameter and thickness of the vessel, respectively. The structural loading 
within the aortic wall was demonstrated to increase proportionally during the expansion of 
aorta, which accelerates the structural breakdown of elastin and collagen elements. Moreover, 
high wall tension was reported to up-regulate the MMP promoter activity, which could cause 
further degradation of the aortic wall 56,57. On the other hand, to maintain the structural 
integrity, vascular cells within the aortic wall attempt to produce more elastin to repair the 
degrading ECM, which is evidenced by a four to six-fold increase in tropoelastin level in 
resected aneurysm samples 58. However, the compensatory elastin deposition is not organised, 
as demonstrated by a nine-fold reduction of desmosine which is a marker for mature elastin 
cross-linking 58. Therefore, the disordered elastin does not restore the aortic elasticity. As a 
result, the imbalance between increasing structural loading and degrading aortic wall results in 
the progressive expansion of AAs. The ultimate rupture occurs when the structural loading 
exceeds the local strength of the aortic wall 59. 
1.5 Clinical management 
AA is clinically stratified and managed based on the characteristics of this disease – a history 
of progressive expansion with an increasing rupture risk 60. The expansion rate of AAs varies 
1-6 mm/year, depending on aetiological types and locations of the AA 61,62. Rupture risk 
increases rapidly when the aortic diameter exceeds a threshold (around 60 mm for the 
ascending aorta and 70 mm for the descending thoracic and abdominal aorta) 62. Therefore, the 
primary goal is to slow the expansion rate and reduce the risk of rupture.  
1.5 Clinical management 14 
 
According to the guidelines of the European Society of Cardiology 62, emergent aneurysm 
repair should be undertaken for ruptured AAs to achieve the best chance for survival. An urgent 
AA repair is also suggested for patients with non-ruptured but symptomatic AAs, if the risk of 
aortic repair is not prohibitive. For asymptomatic AAs, however, the decision for elective repair 
relies on the assessment of the rupture risk, compared to the expected risk of perioperative 
morbidity and mortality associated with aneurysm repair 60. Two randomised clinical trials 
(RCT), the Aneurysm Detection and Management (ADAM) and the UK Small Aneurysm Trial 
(UKSAT), have compared the benefits of early surgery for AAs against the surveillance 
strategy. Summarising the results, the annual risk of AA rupture was similar with, or lower 
than the repair risk for small- and medium-sized aneurysms (<55 mm in diameter) 63–67. 
Therefore, for patients with small AAs, it is regarded as a safe strategy to take conservative 
management with periodic imaging surveillance of the asymptomatic aneurysm until it reaches 
55 mm or becomes symptomatic or fast growing (> 10 mm/year). For good-risk surgical 
candidates with AA diameter >55 mm, elective repair (open or endovascular) is recommended. 
The threshold for AA repair is not absolute and depends on the patient’s status and the 
aneurysm location. Patients with syndromic AAs such as Marfan syndrome, should generally 
undergo elective repair at a smaller aortic diameter (>45 mm). Other factors that need to be 
accounted for include the patient's age and gender, expansion rates, and the presence of other 
peripheral aneurysms. 
The potential use of pharmacological therapies to suppress the growth rate of small AAs 
includes the use of beta-adrenergic receptor-blocking agents to diminish aortic stress, and the 
use of MMP inhibitors 68. However, none of these approaches have been demonstrated to 
provide benefits in RCTs 69,70.  
Currently, elective aneurysm repair remains the most effective management for preventing 
rupture. The purpose of aneurysm repair is to restore the biomechanical balance between the 
structural loading and the aortic wall structure. This can be accomplished by open surgery, 
which replaces the diseased segment with prosthetic graft, or by endovascular repair which 
occludes the diseased wall from the mechanical loading. 
1.5 Clinical management 15 
 
1.5.1 Open surgery 
Since it was first introduced by Dubost et al. in the 1950s, open surgery has been regarded as 
the default surgical intervention of AA 71. During the surgery, an open incision is made to enter 
the chest or abdomen. Then the surgeon incises the aorta and puts a synthetic graft connecting 
the two ends of healthy aorta by sutures, in order to bridge the affected segment of aorta, as 
shown in Figure 1.6. The diameter of the graft should match the diameter of the healthy aorta. 
To extent the patient life, the graft needs a good tensile strength and compliance to withstand 
mechanical loadings from blood pressure and flow. The common graft materials include 
polyethylene terephthalate (Dacron) and expanded polytetrafluoroethylene (ePTFE) 72,73. It can 
be expected that a successful surgical repair will be durable and protective from AA rupture 
throughout the lifetime of the patient 4.  
   
Figure 1.6 Open surgical repair showing the graft inside the aortic aneurysm. (Adapted from 
Eidt et al. 74 with permission from UpToDate) 
However, open surgical repair is a highly invasive technique. An operative mortality rate of 
2%-6% has been reported in elective repairs and over 15% in leaking or ruptured aneurysms 
75,76. The patients are required to be hospitalised typically for one week and to recuperate at 
home for several more weeks. Early complications include postoperative bleeding and 
ischaemic complications. Postoperative bleeding can lead to cardiac tamponade and 
1.5 Clinical management 16 
 
haemothorax, as well as shock, dilutional coagulopathy, and transfusion-related complications. 
Ischaemic complications are related with inadequate perfusion of the brain (stroke), spine 
(paraplegia, paraparesis), viscera (intestinal infarction, renal failure), and extremity (critical 
limb ischaemia). Life-threatening long-term complications include wound and graft material 
infections 77.  
1.5.2 Endovascular aortic repair 
To avoid invasive aortic surgery, the concept of endovascular aneurysm repair (EVAR) was 
first presented by Volodos in 1986 78 and performed by Parodi in 1991 79, where they used a 
Dacron graft sutured onto a balloon expandable Palmaz-Schatz stent. Since then, EVAR has 
become widely accepted as a safe alternative for AA treatment 75,80. EVAR involves the 
placement of an endograft across the aneurysm and its fixation to the aortic wall at both ends, 
as shown in Figure 1.6. The endograft is composed of fabric and metal stents and is deployed 
in a catheter system. Under fluoroscopic guidance, the delivery system is fed through the iliac 
arteries until the endograft is positioned and deployed correctly. Successful deployment of the 
endograft can exclude blood flow mechanically from the aneurysm sac and reduce structural 
loadings within the wall 5.   
   
Figure 1.7 Endovascular aortic repair showing the deployment of endograft inside the 
abdominal aortic aneurysm. (Reproduced with permission from National Institutes of Health) 
1.5 Clinical management 17 
 
Compared with open surgery, EVAR is associated with lower operative mortality risk, faster 
recovery time, and shorter hospital stays 81,82. The major complications with EVAR include 
device migration, kinking, occlusion, as well as endoleaks (a persistent blood flow leaking into 
the aneurysm sac outside the endograft) that can hamper the proper AA exclusion and lead to 
a state susceptible to secondary rupture 5,83.  
1.5.3 Comparative considerations between open surgery and EVAR 
There are certain exclusion criteria for open surgery due to its invasive nature, including: 
advanced age (>70 years), American Society of Anesthesiologists classification of IV or more, 
New York Heart Association classification (1994) of cardiac function of III/C or more, or 
dysfunction of other important organ systems (i.e. severe chronic obstructive pulmonary 
disease, renal or hepatic insufficiency) 84–86.  
Although EVAR provides a minimally invasive alternative for these patients, there are several 
anatomic criteria required for standard EVAR, including: (1) iliofemoral access vessels large 
enough to allow safe insertion of the device, (2) an aortic neck of adequate length (>15 mm) 
for endograft fixation, and (3) limited angulation (<60°) between the aorta and aneurysm 87.  
Considering the complex anatomy with involvement of important branches, open repair is still 
the standard of care for the AAs in the ascending thoracic aorta and the aortic arch. By contrast, 
EVAR is emerging as a preferred initial approach for the descending aorta and abdominal aorta 
88–90. 
To evaluate the treatment outcomes of open surgery and EVAR, several RCTs have been 
conducted for a head-to-head comparison. The first and largest RCT is the UK EndoVascular 
Aneurysm Repair (EVAR)-1 trial 91–94, which started in the United Kingdom from 1999. 
Similar trials were conducted in Netherlands: the Dutch Randomised Aneurysm Management 
(DREAM) trial 95–97. There was also the Open Vs. Endovascular Repair (OVER) trial in the 
United States 98,99 and the Anevrysme de l'aorte abdominale, Chirurgie versus Endoprothese 
(ACE) trial in France 100. A meta-analysis combined all of the RCTs mentioned above and two 
smaller trials 100, resulting in 1,470 patients being allocated to EVAR and 1,429 being patients 
allocated to open surgery. The results of short-term (30 days), intermediate-term (up to 2 years) 
1.6 Challenges in endovascular aortic repair 18 
 
and long-term (>3 years) were analysed. It was reported that 30-day all-cause mortality was 
significantly lower with EVAR than open surgery [relative risk (RR) 0.35; 95% CI 0.19-0.64]. 
However, the significance was gradually lost during follow-up due to secondary sac rupture 
after EVAR, yielding an RR of 0.78 (95% CI 0.57-1.08) for intermediate-term and 0.99 (95% 
CI 0.85-1.15) at long-term follow-up. Briefly, in patients with suitable AAA anatomy, EVAR 
is associated with a 66% reduction in operative mortality while the benefit is lost during long-
term follow-up due to an increased re-intervention rate. Given the need for lifelong surveillance 
after endovascular repair, younger patients with low operative risk may benefit more from open 
surgery, while older patients and those with high operative risk may benefit more from EVAR. 
 It should be noted that most of the endografts used in the above RCTs are early-generation 
endografts while optimised designs have been developed and more commonly used. Although 
the long-term durability of these later versions of endografts has not been evaluated yet, it is 
expected that they would be associated with lower rates of complications and reinterventions.  
In terms of the selection between open and endovascular techniques, personalised approaches 
to the patient are recommended by guidelines from major medical and surgical societies, taking 
into account the patient's age, risk factors for operative morbidity and mortality, anatomic 
factors, and experience of the surgeon 62,69,101. In particular, imaging is essential to achieve 
successful treatment and reduce therapeutic complications. As the deployment of endografts is 
irreversible during EVAR, precise imaging and thorough assessment of the morphology is 
crucial in pre-surgical plan. Moreover, post-operative lifelong imaging surveillance is required 
to monitor late complications including endoleaks, stent migration and rupture. The details of 
imaging technique will be discussed in Chapter 2. 
1.6  Challenges in endovascular aortic repair 
As discussed in Section 1.5, EVAR is an alternative for patients who are not suitable for open 
surgery. However, there are limitations for the application of standard EVARs. In a study with 
3,005 patients with AAs, it was estimated that 24% of the AAs were not suitable for standard 
EVAR, mostly due to a short neck length and an insufficient landing zone 102. Moreover, side 
branches of the aorta involved in complex AAs limit the use of standard EVAR, because the 
1.6 Challenges in endovascular aortic repair 19 
 
endograft may cover and occlude these branches. The side branches of the aorta include minor 
branches such as the segmental arteries, and major branches such as the superior mesenteric 
artery, coeliac artery, and the renal arteries. Occlusion of these vital side branches can lead to 
severe damage to important organs or even death. For example, spinal cord injury caused by 
side branch occlusion is the most dreaded potential complication after standard thoracic EVAR, 
with an overall risk reported to be between 2-10% 103,104.  
To preserve the vital side branches in EVAR, two different strategies have been proposed: (1) 
advanced endograft designs or techniques (Figure 1.8), including fenestrated and branched 
endografts, as well as the chimney technique; and (2) flow-diverting strategy with uncovered 
stents harnessing haemodynamic and rheological effects, such as flow-diverting stents and 
multiple overlapping uncovered stents. The implementations and differences of these strategies 
are discussed as follows. 
 
 
Figure 1.8  Examples of advanced endograft designs and chimney techniques treating 
juxarenal AAA. (A) fenestrated/branched endograft; (B) chimney technique. (Adapted from 
Buck et al. 105, with permission from Springer Nature) 
1.6.1 Fenestrated/branched endografts and chimney technique 
The principle of fenestrated or branched endografts is to integrate additional components and 
connect to the side branches, so as to preserve the blood supply. The first fenestrated endograft 
was reported in 1999 106. The technology in this area has advanced rapidly 107–114, and the first 
FDA-approved fenestrated endograft was available in 2012 115. The fenestrated endograft is 
featured by the fenestrations (holes) on the main endograft (Figure 1.9 left), which is 
1.6 Challenges in endovascular aortic repair 20 
 
individually customised based on the locations of target arteries from pre-operative imaging. 
The deployment of the main endograft must be precise to obtain a correct orientation. Smaller 
alignment stents for branch preservation are inserted to the side branches from the 
fenestrations, which can keep the patency and prevent the occlusion or stenosis. Fenestrated 
endovascular repairs have been used primarily to manage juxtarenal AAAs and showed lower 
operative morbidity and mortality than open surgery 116. Similar to fenestrated endografts, 
branched endografts have separate side-arm components to preserve the patency of target 
vessels (Figure 1.9 right). The cuffs are sutured to the main aortic endograft before intervention, 
which serve as a docking site for placement of side endografts connected to the main aortic 
component.  
Chimney grafting (Figure 1.8b) is an alternative to the fenestrated/branched endograft with 
challenging anatomy, which also preserves the perfusion of side branches. Instead of 
customising the main endograft, the chimney techniques include additional paralleled side 
endografts, which can be deployed via brachial or axillary access. Thus a conduit (chimney) is 
formed outside the main graft to preserves flow in the side branches. A systematic review 117 
 
Figure 1.9 An example of fenestrated endograft (left) and branched endograft (right).  
(Reproduced with permission from Mayo Clinic) 
1.6 Challenges in endovascular aortic repair 21 
 
involving data of 75 patients who had undergone EVAR using the chimney technique (96 
chimney grafts used) demonstrated a high technical success rate of 98.9%. During the follow-
up ranging from two days to 54 months, three deaths occurred as late complications and three 
chimney grafts occluded, necessitating two reinterventions 117. Long term follow-up is not 
available and FDA approval has not been attained yet. 
Although the application of EVAR is extended by the development of fenestrated endografts 
and the chimney technique, there are still many limitations. Target vessels <4 mm in diameter 
is a contraindication due to the increased risk of arterial complications 118. In addition, the 
number of side branches that can be preserved depends on the branches of endografts (usually 
<4). Due to the high degree of customisation, it can take up to 12 weeks for manufactured 
customisation at a high financial cost. Moreover, the complex procedure requiring advanced 
catheter skills is also a disadvantage. 
1.6.2 Flow-diverting strategy 
To preserve the side branches in EVAR, a distinct concept called flow-diverting strategy using 
uncovered stents has been proposed. This concept was first described about two decades ago, 
when Geremia et al 119 suggested that a low-mesh-porosity metallic bare stent bridging an 
intracranial aneurysm would lead to lesion occlusion by modulating the flow.  
 Principles 
As demonstrated in Figure 1.10, the successful deployment of flow-diverting stents can alter 
the flow pattern. Due to the rheological nature of blood, a reduction of flow velocity in the AA 
sac can accelerate the formation of intraluminal thrombus (ILT) 105. As an attached structural 
component, thrombus can change the geometry of the sac and therefore the mechanical loading 
within the aortic wall due to cushion-effect.  
The mechanical effect of stent-induced thrombus can be approximated by the Laplace’s law 
(Equation 1.1). The presence of thrombus decreases the luminal diameter 𝐷 and increases the 
wall thickness ℎ, resulting in the decrease of stress 𝜎. In 2002, Wang et al. showed that ILT 
changes the distribution of wall stress and reduces the peak wall stress 120. In that study, four 
1.6 Challenges in endovascular aortic repair 22 
 
patient-specific finite element models were analysed and all models showed a significant 
decrease in the wall stress under the presence of thrombus.  
 
Figure 1.10 The diverting effect of uncovered stents: (A) before intervention; (B) short-term 
outcome; (C) long-term outcome. (Adapted from Buck et al. 105, with permission from 
Springer Nature). 
Compared to endografts in standard EVAR, the concept of flow-diverting stents is based on a 
totally different mechanism: endografts provide a mechanical barrier between the aneurysm 
sac and normal blood flow, resulting in a reduced sac pressure immediately and therefore 
leading to a decreased aneurysm wall tension; but flow-diverting stents modulate the blood 
flow and promote the formation of thrombus, reducing the wall tension gradually with the 
thrombus growth. However, the thrombosis and endothelialisation process might take months 
to reach an effective level. Patients may remain exposed to the risk of AA rupture after the 
deployment of flow-diverting stents. This makes flow-diverting strategy not suitable for 
patients in emergency repair with a high risk of rupture.  
 Preliminary application in EVAR 
Cardiatis Multilayer Flow Modulator (MFM) (Cardiatis, Isnes, Belgium) is a flow-diverting 
uncovered stent used in most reported studies 121–124 for managing complex thoracoabdominal 
AAs. The stent is designed with self-expandable wire mesh interconnected in layers permitting 
a porosity of 65% (Figure 1.11).  
1.6 Challenges in endovascular aortic repair 23 
 
 
Figure 1.11 A photo of  Cardiatis Multilayer Flow Modulator. (Reproduced with permission 
from Cardiatis) 
A nonrandomised trial named the Evaluation of the Safety and Efficacy of the Multilayer Stent 
(STRATO), reported that MFM appears to be safe and effective in maintaining branch vessel 
patency 125. In this small cohort which included 23 patients with a 3-year follow-up, stable 
aneurysm thrombosis was achieved in 15 of 20 patients at 12 months, 12 of 13 patients at 24 
months, and 10 of 11 patients at 36 months. The rate of branch patency was 96% at 12 months 
(primary patency), 100% at 24 months, and 97% at 36 months. In a recent systematic review 
of MFM treatment including 171 patients, Hynes et al. reported an all-cause survival rate of 
97.1% (95% CI, 92.9%-98.9%) at 30 days and 53.7% (95% confidence interval, 46%-61.3%) 
at 1 year. It was suggested that MFM can be safely utilised in some patients with complex 
thoracoabdominal pathologies providing that operators adhere to the instructions for use. 
However, serious concerns have also been raised by several adverse reports about AAA rupture 
after MFM implantation 122,126. As MFM is interconnected and highly deformable, the 
significant longitudinal shorting and migration from the original target location could lead to 
insufficient coverage of the aneurysms or misuse of an undersized device. The mechanisms for 
delayed rupture should be investigated carefully and the instructions for use of MFM should 
be reviewed before this flow-modulator can be widely disseminated. RCTs, registries, and 
continued assessment are essential. 
1.6 Challenges in endovascular aortic repair 24 
 
1.6.3 Multiple overlapping uncovered stents 
Following the flow-diverting principle, Lu et al. proposed another implementation using 
multiple overlapping uncovered stents (MOUS) 85. The procedure includes the consecutive 
deployment of multiple uncovered stents, to achieve a lower porosity and better flow-diverting 
outcomes than a single aortic stent. The stents used are closed-cell, self-expandable stents 
(Sinus-XL stent, OptiMed, Ettlingen, Germany), providing strong fixation to landing zone, as 
shown in Figure 1.12.  
 
 
Figure 1.12  A photo of Sinus-XL stent and the schematic representation of the uniform 
overlapping pattern. (A) A photo of the aortic stent used in the MOUS technique; (B) The unit 
cell representation of the uniform overlapping pattern of four stents in different colours. 
The diameter of the stents is selected in conformity with the manufacturer’s instructions, with 
10% to 20% oversizing at the aneurysm neck. To conform to the deformation of the aorta, the 
MOUS technique is currently limited to the treatment of descending TAAs and AAAs. The 
advantages of MOUS includes: commercially available stents without customisation, flexible 
porosity controlled by the number of stent deployment, and firm fixation to the aortic wall. 
A pilot study of the MOUS procedure has been performed in a cohort of 42 patients who were 
judged neither suitable for open surgery nor standard EVAR. Encouraging short-term and mid-
term outcomes have been reported 85,127. On average, 3.3 stents were deployed for each patient 
in the MOUS procedure and the technical success rate was 40/42 (96%). During an average 
follow-up period of 20.9 ± 9.0 months, a significant shrinkage of mean aneurysm diameter 
(from 53.4 mm to 48.8 mm, P<0.001) and a significant increased sac thrombosis ratio (from 
18% to 94%, P<0.001) were observed. The patency of side branches was evaluated from the 
pre-operative and follow-up CTA imaging. It was reported that the majority of side branches 
1.7 Summary 25 
 
(74/76 (97%) major visceral branches, 237/244 (97%) minor segmental arteries) maintained 
their patency after stenting. The long-term follow-up is still ongoing. 
Although the short-term and mid-term outcomes of MOUS are encouraging, several important 
questions need to be addressed. Currently, the number of stents that should be deployed 
depends on the experience of the operator, while the optimised choice for a specific patient 
needs to be explored. Moreover, uncertainty during the deployment may result in different 
overlapping patterns of the multiple stents and their influence on the flow-diverting outcome 
is not clear. Furthermore, the increased structural loading in the loading zone induced by 
multiple stents deployment may cause wall damage that has not been assessed 
comprehensively. 
Mechanics theory plays an important role in the success of MOUS. Firstly, the material strength 
of the aortic wall is essential for the aneurysm rupture, which can be quantified by 
biomechanical testing. Secondly, biomechanics provides a framework to investigate the 
interaction between stents, blood flow and the aortic wall. In particular, imaged-based 
computational analysis provides a comprehensive assessment for personalised pre-surgical 
plan, which can be used to perform virtual MOUS deployment, visualise the flow-diverting 
effects and predict possible treatment outcome. 
1.7  Summary 
Formation of AAs is a complex and chronic process that results from the interaction of genetic 
and environmental factors. The progression of AA is a consequence of structural degeneration 
associated with multiple processes including proteolytic degradation, inflammation response, 
and tissue remodelling. These biochemical processes break the biomechanical balance between 
the structural loading and aortic wall structure. The elective repair of an aneurysm is based on 
the assessment of rupture risk compared to repair risk. EVAR is emerging as a preferred 
approach for suitable anatomies due to its minimally invasive nature. To solve the challenges 
of side branch involvement, fenestrated/branched endografts and the chimney technique have 
been proposed, while their application is limited by high costs and complex procedures. New 
therapeutic techniques with flow-diverting strategies have been proposed. The MOUS 
1.7 Summary 26 
 
procedure is an emerging technique with an encouraging clinical outcome in preliminary 
experiences. To achieve an improved outcome, several questions surrounding MOUS 
procedure remain unclear. They can be investigated by biomechanical methodologies. 
Aim of the study 
This dissertation seeks to investigate the mechanical behaviour of AA, characterise the 
interaction between the aorta and vascular stents, and provide a comprehensive assessment of 
the MOUS technique based on image-based biomechanical analysis.  
Structure of the thesis 
In Chapter 2, in vivo imaging techniques with their applications in clinical management and 
biomechanical modelling are discussed. In Chapter 3, the general methods of biomechanical 
modelling are introduced. In Chapter 4, the mechanical behaviours of AAs are characterised 
by uniaxial material tests. A Bayesian framework is proposed for material constants 
identification, and correlated to the microstructure of tissue fibre network. In the Chapter 5, 
biomechanical modelling of MOUS deployment is performed based on patient-specific images, 
and the mechanism of MOUS-induced flow modulation is investigated. In Chapter 6, the 
effects of cross-stent structure of MOUS are further investigated through parameter studies. In 
Chapter 7, the pathological effect of structural stress concentration induced by implanted 
device is further studied in rabbit models. In Chapter 8, the general conclusions and future 
directions are discussed. 
 
 Chapter 2 Imaging of aortic aneurysms 
The rapid development of imaging techniques has facilitated in vivo high-resolution evaluation 
of the vascular system, and revolutionised the clinical management of aortic aneurysms. High-
quality images of the AAs are of crucial importance for pre-surgical planning, intraoperative 
deployment, and follow-up assessment. In this chapter, commonly used vascular imaging 
techniques including anatomical and functional imaging, as well as their applications are 
discussed.  
2.1  Overview of imaging techniques 
Medical imaging techniques provide an in vivo visual representation of tissue and organs within 
the body for clinical assessment. In general, medical imaging techniques include anatomical 
imaging and functional imaging, according to the information they provide: 
Anatomical imaging. These techniques usually provide two-dimensional (2D) or three-
dimensional (3D) information on the geometry of tissues and dynamic changes in geometry 
with time. The morphology of the aortic vasculature with side branches is essential in both pre-
surgical planning of EVAR and follow-up surveillance. In addition, the structural information 
of tissue components within the aortic wall is of great importance for the assessment of 
aneurysm progression, such as calcification and intraluminal thrombus. The most frequently 
used anatomical imaging for AAs include computerised tomography (CT), magnetic resonance 
imaging (MRI) and ultrasound. 
Functional imaging. These techniques provide information related to physiology of living 
organisms. In contrast to anatomical imaging, functional imaging reveals physiological 
activities, usually by employing biomarkers. The biomarkers interact with target tissues and 
generate signals, which reflect the biological function and can be detected by the imaging 
2.2 X-ray imaging 28 
 
system. The most common molecular imaging technique used for AAs is positron emission 
tomography (PET), which can be used to reflect inflammation. Other modalities, including 
advanced MRI and ultrasound can also be used for functional purposes. 
2.2  X-ray imaging 
Since the discovery of X-rays by Rontgen in 1895, X-ray imaging has been widely used for 
medical diagnosis. The basic imaging system involves production of X-rays from a tube, 
passage of these X-rays through the target, and detection of their attenuation. At present, 
several types of X-ray imaging techniques have been well established. 
2.2.1 Conventional radiography 
 
Figure 2.1 TAAs diagnosed by chest plain X-rays. (A) Ascending; (B) Arch; (C) 
Descending. (Reproduced from Damberg et al. 52 with permission from Elsevier) 
Conventional radiography (also called plain X-rays) accounts for 75% of medical imaging 
examinations 128. Plain X-rays are 2D projection images made by an x-ray beam passing 
through and absorbed by various tissues in the body. Four basic densities are visible on plain 
X-rays: air, fat, water (blood and soft tissue) and bone 129. A chest radiography can be used to 
examine the contours of the aorta because of the contrast between the air-filled lungs and the 
fluid-filled aorta. As shown in Figure 2.1, the abnormalities of thoracic aortic aneurysms can 
be observed on conventional radiography, however lacking of many details. 
The advantages of conventional radiography include low costs, wide availability and short 
imaging time which is particularly useful for emergency diagnoses. However, it is neither 
2.2 X-ray imaging 29 
 
sufficient to make an accurate diagnosis or exclude aortic pathology, nor does it offer sufficient 
anatomical details for therapeutic planning 52. Another drawback of conventional radiography 
is the exposure to ionizing radiation (0.1 mSv for chest and 0.7 for abdominal radiographs) 130. 
2.2.2 Computerised tomography 
Computerised tomography (CT) is accomplished by passing a rotating fan beam of X-rays 
through the patient. The raw 2D cross-sectional images are acquired from thousands of 
projection angles, which are reconstructed using filtered back projections 131. The collection of 
2D slices enables production of a 3D volume, with each voxel assigned a grayscale value 
representing the local attenuation coefficient. The X-ray attenuation is quantified by 
Hounsfield Units (HU), named after Sir Godfrey N. Hounsfield for his pioneering work in the 
development of CT. The type of tissue can be inferred by the range of HU values, which 
provide more contrast beyond the four basic densities on conventional radiography. The HU 
values of the four common tissues prior to intravenous contrast is listed below (Table 2.1). 
Moreover, the 3D imaging volume provide more anatomical information for precise 
assessment of the aortic morphology. 
Table 2.1 Typical HU values for different tissues. 
Substance Hounsfield units (HU) 
Air -1,000 
Fat -100 
Water 0 
Muscle/soft tissue +40 
Contrast +130 
Bone +1,000 
 
On early CT machines, vascular imaging was limited due to slow acquisition time. The X-ray 
tube must finish a complete rotation to obtain a single slice before the table was moved 
incrementally for next slice. Until early 1990s, the development of helical scanning techniques 
and multi-detector row technology revolutionised the role of CT in vascular imaging 132,133. 
Slip-ring technology allows for the continuous rotation of the X-ray tube, and multiple detector 
2.2 X-ray imaging 30 
 
rows allow the simultaneous acquisition in a single rotation 134. The more detector rows used, 
the shorter imaging time and the less amount of intravenous contrast medias are required. A 
modern multi-detector CT machine can complete vascular interrogation from the aortic arch to 
the foot in less than 30 s 135. The helically acquired data can be reconstructed into traditional 
reformatted planes (Figure 2.2). Computerised tomographic angiography (CTA) is the contrast-
enhanced CT acquired after intravenously injecting contrast medias, to achieve a high 
radiodensity within the blood vessels. CTA normally consists of multiple imaging phases, 
including a pre-contrast image series and at least one contrast-enhanced series. 
 
Figure 2.2 CTA imaging of an AAA: (A) Axial view; (B) Sagittal view; (C) Coronal view; 
(D) 3D rendering. The aortic lumen is contrast-enhanced while the intensities of intraluminal 
thrombus and aortic wall are similar without a clear border. 
 
The advantages of CT for evaluating AAs include the short imaging time and detailed 3D 
anatomic information, allowing for accurate measurement of aneurysm diameters and 
evaluation of whole vessel morphology. For EVAR, a precise morphological assessment is 
vital in both pre-operative planning and follow-up surveillance, which has been extensively 
investigated based on CT images, including: aneurysm diameter 136–138, length 139–141, tortuosity 
2.2 X-ray imaging 31 
 
142,143 and volume 144–146. In addition, calcification with high HU values can be segmented and 
assessed 147–149, which alters the stiffness of aortic wall significantly. The main disadvantages 
of CT are the radiation burden (about 10-100 times more than conventional radiography) and 
use of potentially nephrotoxic contrast medias in CTA 150. Other limitations include weak soft-
tissue contrast making intraluminal thrombus segmentation difficult, and the susceptibility to 
blooming artefacts from calcium 151. 
2.2.3 Digital Subtraction Angiography 
Digital subtraction angiography is an X-ray fluoroscopy technique that is used to visualise the 
vasculature by masking the background tissues with digital subtraction 129. A catheter is 
inserted from the entry point (usually the femoral artery) and delivered into the targeted blood 
vessel for the injection of iodinated contrast. A series of 2D X-ray projections are acquired 
during the injection. The initial image without contrast is called the mask, which is digitally 
subtracted from later images with contrast. Therefore, only the contrast-enhanced vasculature 
is left in images (Figure 2.3). Compared to non-digital angiography, DSA provides superior 
contrast resolution with lower doses of intravenous contrast in dynamic imaging. 
The features of image magnification and real-time subtraction make DSA suitable for 
simultaneous EVAR. The intervention procedure of EVAR can be guided and monitored by 
    
Figure 2.3  DSA image of a thoracoabdominal aortic aneurysms before (A) and after (B) the 
deployment of MOUS. 
2.3 Ultrasound imaging 32 
 
DSA. The contrast change in the aneurysm sac is related to flow conditions, which can be used 
to indirectly assess aneurysm occlusion or the flow-diverting outcome 152–154. Although DSA 
can visualise the aorta with side branches, it has some major drawbacks. Since angiography 
only visualises the blood flow without the wall components, the actual vessel and aneurysm 
sizes may be underestimated, due to the presence of thrombus which is masked out in the 
subtraction. Moreover, DSA is an invasive procedure with exposure to iodinated contrast, 
which is related to complications such as arterial puncture and potential nephrotoxicity of the 
contrast medias. For those reasons, the primary role of DSA in pre-operative scan has been 
replaced by CT and MRI 150. 
2.3  Ultrasound imaging 
Differing from X-ray techniques, ultrasound imaging uses high-frequency sound waves 
(typically 2-18 MHz) without ionizing radiation 155. The transducer is the equipment to send 
out and receive the ultrasound waves, which transmit through and are reflected by internal 
structures of the body. The returning sound waves are categorised according to their intensity 
(referred to echogenicity) and reflection time.  
2.3.1 Ultrasonography 
Clinical ultrasonography (US) is a 2D imaging technique, reconstructed in real-time as the 
transducer moves across the body surface. Three-dimensional ultrasound images can be 
obtained by sequential collection of 2D images 156. The echogenicity of tissues varies greatly 
and result in different brightness, which can be used to distinguish the structures on the 
reconstructed images. In B-mode US, the aorta appears anechoic with hyperechoic walls 157. A 
rapid assessment of the aortic morphology from different planes can be achieved by rotating 
the orientations of the transducer. Ultrasound does not work well in imaging thoracic aorta due 
to the large chest cavity. Therefore, it is mainly used to screen the abdominal aorta. An example 
of abdominal US is shown in Figure 2.4. The diameter of aorta can be measured on cross-
sectional planes to identify AAs.  
2.3 Ultrasound imaging 33 
 
US is a non-invasive and inexpensive technique of high sensitivity and specificity, without 
ionizing radiation 158. However, the images are operator-dependent and provide less accuracy 
in measurement. The pathological findings on ultrasound should be further evaluated on more 
accurate anatomical modalities such as CT and MRI. 
2.3.2 Doppler ultrasound 
Doppler ultrasound can detect the motion of fluids based on the Doppler shift, which is a 
change in the frequency of the returning echo as it encounters a moving structure. With the 
information from the Doppler shift, images can be generated to visualise the speed and 
direction of the blood flow (Figure 2.5).  
 
 
Figure 2.4 Ultrasonography showing a transverse view of the distal aorta. (Reproduced from 
Buck et al. 105, with permission from Springer Nature) 
 
Figure 2.5 An aortic aneurysm is characterised by swirling flow on Colour Doppler 
ultrasound. (Reproduced from Prager et al. 157  with permission from Springer Nature)  
2.3 Ultrasound imaging 34 
 
Typical display formats include the time-velocity waveform form at an individual location, and 
a 2D real-time colour visualisation of the blood flow with velocity encoded. Doppler ultrasound 
is usually combined with traditional US providing the structural information, which is called 
duplex ultrasound. Doppler ultrasound is particularly useful in vascular imaging, providing a 
rapid and overall assessment of the blood flow condition. The duplex ultrasound can also be 
used for follow-up surveillance of EVAR, which helps monitor the aneurysm size and 
characterise the endoleak 159. The limitations include the aliasing noise and the poorer temporal 
resolution, especially at increased depths. 
2.3.3 Intravascular ultrasound 
Intravascular ultrasound (IVUS) is a recent development which provides a 360° cross-sectional 
view of the vessel wall (Figure 2.6), using a specially designed catheter with a miniaturised 
ultrasound probe attached to the distal end. 
Since no exogenous contrast is required, IVUS can be used in patients with renal insufficiency. 
Another advantage of IVUS is that the aortic diameter can be evaluated accurately in real time, 
which can be used to estimate aortic compliance 160. However, IVUS is susceptible to operator-
dependent error and the probe is required to be at the centre of lumen for accurate measurement, 
while it is increasingly difficult for the aorta with large diameter and tortuosity. Currently it 
still remains a costly and invasive procedure which is primarily used for research purposes 161. 
 
 
Figure 2.6 IVUS cross-sectional imaging demonstrating a stent graft in AAA. (Reproduced 
from Buck et al. 105, with permission from Springer Nature) 
2.4 Magnetic resonance imaging 35 
 
2.4  Magnetic resonance imaging 
MRI allows image the body by utilising a strong magnetic field (modern clinical machines 
function at 1.5-3.0 Tesla (T)) and radiofrequency (RF) pulses 162,163. The protons (or certain 
other nuclei) within patients are the primary source of signals. The net magnetization of protons 
can be deflected by the application of RF pulse, followed by a magnetic recovery process which 
emits signals. The spatial information can be encoded to the emitted signals by the design of 
RF pulses, and reconstructed to images via Fourier transforms 164. The magnetic recovery 
process after an RF pulse has two components: a longitudinal relaxation (T1 relaxation) and a 
transverse relaxation (T2 relaxation). Accordingly, the recovery times are termed as T1 and T2 
relaxation times, which characterise environments of protons and can be used to generate 
imaging contrast. The imaging contrast can be altered either by changing the properties of 
tissues (such as intravenous injection of Gadolinium-based media), or by acquisition protocols 
with RF sequence design highlighting different characteristics of tissues (such as black-blood 
technique). A wide spectrum of MRIs has been developed for different purposes, including the 
aortic wall imaging and magnetic resonance angiography (MRA). 
2.4.1 Aortic wall imaging 
MRI provides excellent soft-tissue contrast of the aortic wall, due to its intrinsic MR properties. 
In general, clinical MRI can be classified into two basic types – T1-weighted and T2-weighted 
images, highlighting different relaxation times. Example T1- and T2-weighted MRIs of aortic 
aneurysm wall from three different types of specimen are shown in Figure 2.8, along with their 
photos and CTA. MRI offers a significant advantage to CTA for characterising the 
morphological appearance of intraluminal thrombus 165, which can be integrated into the 
assessment of the aneurysm progression 166 and complications after EVAR 167. 
2.4 Magnetic resonance imaging 36 
 
Black-blood (also called dark-blood) imaging is a technique to suppress blood signals 169. This 
technique is particularly useful in wall imaging by applying double inversion recovery fast spin 
echo (FSE) sequences with electrocardiographic (ECG)-gating170. This technique provides 
contrast between mural morphology and the luminal signal-void, which is useful to depict 
suspected mural pathology such as intraluminal thrombus. FSE T1-weighted images can be 
used to provide accurate AA diameter measurements and to demonstrate the composition of 
the aortic wall (Figure 2.8, right) 171–173, providing more structural information than contrast-
enhanced CT (Figure 2.8, left). FSE T2-weighted images can be used to characterise oedema 
which may be visualised as a hyperintense intramural signal 170. To reduce the relatively long 
 
Figure 2.7 Illustration of the specimen categories and their appearance on MRI and CTA. 
(a) Photography, (b) T2-weighted image, (c) T1-weighted image, (d) CTA image. The 
specimen include different types of intraluminal thrombus with different apperances on 
MRIs. Type 1: organised thrombus (homogeneously low signal on both T1- and T2-weighted 
images); Type 2: unorganised thrombus (high signal on both T1- and T2-weighted images); 
Type 3: partially organzied thrombus (imhomogeneous signal with hyperintense areas on 
both T1- and T2-weighted images). (Reproduced from De La Motte et al. 168, with 
permission from  Elsevier) 
2.4 Magnetic resonance imaging 37 
 
acquisition time, some novel black-blood imaging techniques without ECG-gating are being 
developed including modified k-space reconstruction schemes and 3D high-spatial-resolution 
FSE sequences 174. 
In addition, paramagnetic contrast medias can be used to characterise the perfusion properties 
of wall components. Gradient-echo T1-weighted sequences with fat saturation technique are 
often employed to assess the enhancement of aneurysm wall, which is related to 
hypervascularity, suggesting the presence of inflammation 175,176. 
2.4.2 Magnetic resonance angiography 
The use of MRI in angiography is termed MRA. Unenhanced MRA was first introduced into 
clinical application more than 30 years ago 177. However, in early stages, the imaging time was 
long and image quality was low associated with artefacts. The clinical use of MRA became 
more popular after the introduction of gadolinium-based contrast medias and the subsequent 
development of contrast-enhanced magnetic resonance angiography (CE-MRA) 178. 
 
Figure 2.8 Comparison of CTA images (left) and FSE T1-weighted images (right) in an AAA 
patients with intraluminal thrombus (ILT). Coronal (a, d) and two axial slices (b-c, e-f) at 
identical locations are shown. (Reproduced from  Zhu et al. 171, with permission from  
Elsevier) 
2.4 Magnetic resonance imaging 38 
 
 Contrast-enhanced MRA 
Three-dimensional CE-MRA is acquired in a manner similar with CTA. The strong 
paramagnetic properties of gadolinium-based contrast media can shorten the T1 relaxation time 
and consequently produce enhanced intravascular signal (Figure 2.9 left). CE-MRA is typically 
performed using a rapid 3D T1-weighted spoiled gradient-echo sequence with short repetition  
and echo time 178. Different acquisition modes are available: the single-phase method that 
captures vascular images at a single time point; the time-resolved method that repeatedly 
acquire images as the contrast agent passes through the vasculature. Similarly to the DSA 
technique, image quality of MRA can be improved by image subtraction, where a pre-contrast 
image is subtracted from the later images. The application of higher-field strength (i.e., 3.0T 
versus 1.5T) MRI enables higher signal-to-noise ratio (SNR), which allows for higher spatial 
resolution, faster acquisition time, and less dose of contrast medias 180–182. Ultra-high-field (7T) 
MRA has been recently tested as a useful tool for microvascular imaging and functional 
angiography, although further studies are needed to assess its clinical feasibility and safety 183. 
The advantages of CE-MRA include intrinsically high SNR, high spatial resolution, and 
relative freedom from flow-related artefacts. Due to the excellent imaging quality and high 
speed of acquisition, CE-MRA has been widely used in routine clinical practice. However, 
multiple studies have raised safety concerns on gadolinium-based contrast medias in the last 
 
Figure 2.9 MR images in a 59-year-old patient suffering from aneurysm of the aorta root 
obtained with CE-MRA (left) and unenhanced MRA (right) sequence.  (Reproduced from  
Xu et al. 179, with permission from John Wiley & Sons) 
2.4 Magnetic resonance imaging 39 
 
decade. In 2006, Grobner described the link of nephrogenic systemic fibrosis with high dose 
of gadolinium (Gd) in patients with renal dysfunction 184. Since 2014, a number of publications 
also reported Gd deposition in the brain after administration of gadolinium-based contrast 
medias 185–187. In 2017, the European Medicine Agency released a report restricting the use of 
certain contrast medias due to safety concerns 188. Systematic studies to further delineate Gd-
induced symptoms are needed 189.  
 Unenhanced Magnetic Resonance Angiography 
Unenhanced MRA is a type of MRA without the injection of contrast medias (Figure 2.9 right). 
Although CE-MRA is widely regarded superior to unenhanced MRA for the diagnosis of 
vascular disease, in terms of imaging speed, accuracy and robustness, there has been a renewed 
interest in unenhanced MRA 190. Several factors contributed to the renaissance, including the 
aforementioned safety concerns regarding contrast medias, improvements in MR hardware, 
and advances in sequences design. In contrast to CE-MRA, unenhanced MRA techniques are 
entirely based on the MR properties of flowing blood, such as its intrinsic relaxation times, 
time-of-flight (TOF) effects, and spin-phase effects 191. Several different types of unenhanced 
MRA have been established: 
Time-of-flight (TOF) MRA: TOF-MRA refers to a category of unenhanced MRA using 
TOF effects with a flow-related enhancement 169. The advantages of TOF MRA include 
widespread availability on commercial MRI machines, and good opacification of arteries 
containing rapid or continuous flow191.  
Phase-contrast (PC) MRA: PC-MRA exploits the spin-phase effects, referred to the 
changes in precession angle (phase) of protons when moving within a gradient 192. One major 
advantage of PC-MRA is that the phase can be used to quantify the 3D velocity field of 
blood flow, which provides functional information of the vasculature 193.  
Steady-state Free Precession (SSFP) MRA: SSFP-MRA is emerging as an important 
method for unenhanced MRA of the chest and abdomen, which utilises the inherent T1/T2 
ratio of blood 194,195. The advantages of SSFP-MRA include its fast, high SNR readout with 
a high spatial resolution, and its ability to depict vessels containing very slow or stationary 
blood.  
2.5 Positron emission tomography 40 
 
Fast Spin Echo (FSE) MRA: FSE-MRA (or called fresh blood imaging, FBI) is a technique 
to obtain an arteriogram by subtraction of systolic from the diastolic images 191. The 
advantages of the FSE MRA include relatively short imaging time, sensitivity to slow flow, 
and less susceptible to field heterogeneities191. 
TOF-MRA and PC-MRA were the two most commonly used unenhanced MRA techniques 
while several novel methods have become more popular 196. Briefly, the primary benefit of 
unenhanced MRA is its non-invasiveness without the exposure to ionised irradiation or 
exogenous contrast medias 169. Another advantage of unenhanced MRA is that the angiograms 
can be repeated in the case of technical error, which is not immediately permissible in CE-
MRA. The main limitation of unenhanced MRA is the long acquisition time and artefacts in 
regions with complex blood flow, which is being improved by emerging techniques. 
2.5 Positron emission tomography 
PET uses radiolabelled molecules to create 3D tomographic images of biological processes in 
vivo 197,198. As a nuclear medicine imaging technique, PET is based on the detection of two 
photons emitted by the patient after administration of a radiolabel tracer. The image parameters 
measure the concentration of the tracers in the tissue. To reflect a wide variety of physiological 
and pathological processes at a molecular level, different isotopes (such as 18F, 11C, 13N, 15O) 
can be used to label compounds, including enzymes, receptor ligands, and neurotransmitters 
199. 
PET imaging was developed in mid-1970s, and has made major improvements in both 
diagnostic performance and practicality. Many standalone PET imaging systems have been 
replaced by hybrid systems such as PET-CT or PET-MR 200,201, which fuse PET with 
anatomical imaging to offer structural details and more accurate reconstruction. In routine 
clinical practice, the vast majority of PET studies are performed using fluorodeoxyglucose (18F-
FDG) which reflects glucose metabolism. 
2.5 Positron emission tomography 41 
 
2.5.1 18F-FDG PET 
18F-FDG is a glucose analogue, which enters cells using the same transporter as glucose 197. 
Once inside the cell, 18F-FDG is phosphorylated into 18F-FDG-6-phosphate which cannot be 
further metabolised or released and is thus trapped within cells. 18F-FDG PET can be used to 
image inflammation as glucose is the primary energy source for inflammatory cells such as 
macrophages 202. In previous studies, 18F-FDG demonstrates a high sensitivity for the detection 
of activated macrophages in PET 203. Therefore 18F-FDG PET could be potentially used to 
monitor inflammatory changes of the aorta, which might be linked to the development of AA 
204 (Figure 2.10). 
2.5.2 Integrin αVβ3 PET 
Integrin αVβ3 is a cell-surface adhesion receptor identified as a marker of angiogenesis, as it is 
up-regulated in vascular endothelial cells by angiogenesis 206. It has also been shown that 
vascular macrophages express high levels of integrin αVβ3. Arg-Gly-Asp (RGD) is an 
extensively studied short amino acid sequence binder to αVβ3, and radiolabelled RGD such as 
18F-labeled RGD agent (18F-FPPRGD2) can be used for PET imaging 
207. This technique has 
potential for clinical molecular imaging of AAs to quantify the inflammation and 
neoangiogenesis 38.  
 
Figure 2.10 In vivo PET-CT images of an abdominal aortic aneurysm: (A) contrast-
enhanced CT, sagittal view; (B) 18F-FDG PET, sagittal view; (C) contrast-enhanced CT, 
transverse view; (D) 18F-FDG PET, transverse view. (Adapted from Huang et al. 205,  with 
permission from Wolters Kluwer Health, Inc.) 
2.6 Clinical application 42 
 
2.6 Clinical application 
According to Clinical Practice Guidelines of the European Society 150, appropriate imaging 
modalities should be employed under different scenarios for different purposes. 
2.6.1 Aneurysm screening 
Diagnosis of AAs rely on aortic imaging to confirm the presence of the aneurysm 62,208. AAs 
are normally asymptomatic and are usually incidentally found after imaging studies such as 
chest X-rays and transabdominal ultrasound 209–214, which should be further evaluated using 
cross-sectional imaging such as CT and MRI.  
The guideline recommends chest radiography screening for first-degree relatives of patients 
with familial TAA 208, while ultrasound is recommended for screening AAAs in the population 
215. The utility of ultrasound has been validated in the large RCTs of AAA screening, with a 
sensitivity of 95-100% and a specificity of nearly 100% 216,217. One-time screening with 
ultrasound for AAA has been shown to be effective in reducing AAA-related mortality and 
AAA rupture in men over 65 years 218–221. In the United Kingdom, an ultrasound screening is 
offered to 65-year-old men, among whom diagnosed aneurysms are referred to a vascular 
surgeon for further management. 
2.6.2 Aneurysm surveillance 
Several randomised trials of intervention versus surveillance for small AAs (3.0 to 5.5 cm 
diameter) have shown no benefit from early intervention, as summarised in a recent systematic 
review 222. Therefore, patients with small AAs are suggested to undergo periodic imaging to 
assess AA growth. For AAA surveillance, ultrasound is the optimal imaging technique due to 
its sufficient accuracy and no irradiation. The recommended surveillance schedule depends on 
the disease history while the optimal frequency has not been defined by RCTs 223. For TAA 
surveillance, CT and MRI are recommended, ideally performed with contrast for accurate 
measurement. MRI has advantages to minimise patient’s radiation exposure during long-term 
2.6 Clinical application 43 
 
surveillance, particularly in younger individuals, where accumulated potential cancer risk from 
repeated imaging is important 208. 
2.6.3 Pre-operative assessment 
A thorough assessment of the aneurysm morphology is essential for the selection of appropriate 
endografts and pre-surgical plans. Three-dimensional angiography with high resolution is 
required to characterise the full extent of the aneurysm, assess the relationship to key branches, 
identify anomalous anatomy, and evaluate the adverse factors (such as excessive calcification) 
and surgery risks. Because of excellent image quality, relatively non-invasive nature and lower 
cost, CTA is the current standard for pre-operative AA assessment 150. However, MRA is 
emerging as a preferred alternative which provides the same details as CTA, and offer more 
information of the blood flow and aortic wall by advanced sequences as mention in Section 
2.4.2 62. In addition, PET has the potential to visualise and quantify the inflammatory response 
within the aneurysm wall, which is of clinical significance for risk evaluation 204. 
2.6.4 Endovascular aneurysm repair 
For EVAR, the fluoroscopic guidance is of great importance to deliver the catheter and to 
deploy endografts at the planned sites. DSA is recommended due to its real-time feature and 
dynamic imaging without the requirement of reconstruction. Novel methods that fuse pre-
operative imaging (such as CTA, MRA and ultrasound) with intraoperative fluoroscopy have 
been developed to provide 3D information with less dose of irradiation 224,225. 
2.6.5 EVAR follow-up 
The long-term efficacy of EVAR remains to be evaluated and subsequent lifelong imaging 
surveillance is currently required to monitor for late complications, which include endoleaks, 
aneurysm sac enlargement or rupture, migration or loss of integrity of the endograft 62. Spiral 
CTA has demonstrated advantages as the best imaging technique for endograft surveillance 
after EVAR 226,227. It is accurate for diameter measurement, the detection of endoleaks and 
other device-related complications 228,229. Duplex ultrasound is suggested as an alternative to 
2.6 Clinical application 44 
 
CTA in follow-up surveillance of AAA 230, to avoid ionising radiation or exposure to contrast 
media. In a recent meta-analysis evaluating surveillance outcomes after EVAR 231, MRI was 
reported to have a higher detection rate of endoleaks than CTA. However, the limitations of 
MRI in EVAR follow-up is the difficulty of evaluating device integrity due to artefact, and 
contraindication for stainless-steel-based grafts. 
 
 
 Chapter 3 Biomechanical analysis† 
This dissertation sought to provide a comprehensive assessment of the MOUS technique from 
a biomechanical perspective. Resected human samples are tested in vitro to characterise the 
material behaviour of aneurysm tissue, and image-based computational analyses are performed 
to investigate the interaction between the blood flow, stents and aortic wall. This chapter 
therefore describes the framework and methods used in the biomechanical modelling, including 
the basic mechanical concepts, experimental tests and computational simulations. 
3.1  Description of internal deformation and forces 
Since Fung et al. introduced finite deformation theory in 1960s, a comprehensive framework 
of continuum mechanics has been established to investigate the behaviour of arteries. In this 
theory, the arterial tissue is assumed as a continuum body, which deforms in a 3D space subject 
to loadings. The principal task is to model the internal deformation and forces within the vessel 
wall under external loadings. 
 Displacement 
When the body is in the reference state (undeformed configuration), a material particle 
occupies a place whose coordinate is X. At time t, the body deforms to the current state 
(deformed configuration), and the original material particle moves to a place with an updated 
coordinate x, as shown in Figure 3.1. The deformation history of the body can be described by 
the time-dependent deformation field 
𝐱 = 𝐱(𝐗, 𝑡) (3.1) 
                                                 
†More details on the concepts of stress, strain, constitutive law and the detailed finite element procedure can be found in Bathe 
Klaus-Jürgen, Finite element procedures, 2006. 
3.1 Description of internal deformation and forces 46 
 
 
Figure 3.1 Schematic drawing of the motion of a continuum body. 
The field functions of displacement of the material particle X at time t is expressed as 
𝐮(𝐗, 𝑡) = 𝐱(𝐗, 𝑡) − 𝐗 (3.2) 
 
 Deformation gradient 
Consider two nearby material particles P and Q. The vector dX connects the places occupied 
by P with coordinate X and Q with coordinate X+dX in the reference state (Figure 3.2). 
 
 
Figure 3.2 Schematic drawing of the deformation (right) of a continuum body. 
At time t, the two material particles move to new coordinates with x(X,t) and x(X+dX, t), which 
are two ends of a vector 𝑑𝐱 
3.1 Description of internal deformation and forces 47 
 
𝑑𝐱 = 𝐱(𝐗 + 𝑑𝐗, 𝑡) − 𝐱(𝐗, 𝑡) (3.3) 
Recall the one-order Taylor expansion of the function x(X, t) near X at time t 
𝐱(𝐗 + 𝑑𝐗, 𝑡) = 𝐱(𝐗, 𝑡) + 𝛁𝑿𝐱(𝐗, 𝑡)𝑑𝐗 (3.4) 
If the displacement is continuous and dX is infinitesimal, above Taylor expansion is accurate. 
Therefore, the Equation (1.4) can be rewritten as 
𝑑𝐱 =  𝛁𝑿𝐱(𝐗, 𝑡)𝑑𝐗 = 𝐅𝑑𝐗 
𝐹𝑖𝐾 =  
∂𝑥𝑖(𝐗, 𝑡)
∂𝑋𝐾
  
(3.5) 
where F is called the deformation gradient tensor, the linear map from dX in the reference state 
to dx in the current state. Similar to the deformation gradient tensor, the displacement gradient 
tensor H can be defined by 
𝑑𝐮 = 𝑑𝐱 − 𝑑𝐗 = (𝐅 − 𝐈)𝑑𝐗 = 𝐇𝑑𝐗 
𝐇 = 𝐅 − 𝐈 
𝐻𝑖𝐾 =  
∂𝑥𝑖(𝐗, 𝑡)
∂𝑋𝐾
− 𝛿𝑖𝐾 
(3.6) 
where δiK is the Kronecker delta, defined as δiK = 1 when i = K, δiK = 0 when i ≠ K. 
 Strain 
The strain is a normalised measure of deformation, which evaluates how much a given 
displacement differs locally from a rigid body displacement. Consider an infinitesimal line 
element dX in the reference state, the original length is 
𝑙𝑋
2 = 𝑑𝐗 ∙ 𝑑𝐗 (3.7) 
After the deformation onto dx, the length in the current state is 
𝑙𝑥
2 = 𝑑𝐱 ∙ 𝑑𝐱 =  𝐅𝑑𝐗 ∙ 𝐅𝑑𝐗 = 𝑑𝐗𝐅𝐓𝐅𝑑𝐗＝𝑑𝐗 ∙ 𝐂 ∙ 𝑑𝐗 (3.8) 
where C is called the right Cauchy-Green deformation tensor, defined as 
3.1 Description of internal deformation and forces 48 
 
𝐂 ≔ 𝐅𝐓 ∙ 𝐅 (3.9) 
Therefore, the change of element length is characterised by C. A spectral decomposition can 
be performed over C: 
𝐂 = ∑ 𝜆𝑖
2
𝟑
𝒊=𝟏
𝐍𝑖⨂𝐍𝑖 (3.10) 
where 𝜆𝑖 (𝑖 = 1,2,3) are the three principal stretches, with corresponding principal directions 
𝐍𝑖  (𝑖 = 1,2,3). Invariants of C are defined as 
𝐼1
𝐶 ≔ tr(𝐂) =  𝜆1
2 + 𝜆2
2 + 𝜆3
2 
𝐼2
𝐶 ≔
1
2
[tr(𝐂)2 − tr(𝐂𝟐)] =  𝜆1
2𝜆2
2 + 𝜆2
2𝜆3
2 + 𝜆3
2𝜆1
2 
𝐼3
𝐶 ≔ det(𝐂) =  𝜆1
2𝜆2
2𝜆3
2 = 𝐽2 
(3.11) 
which are useful for the expression of strain energy density function (SEDF). Recall the 
Equation 1.8, the right Cauchy-Green deformation tensor C can be expressed in terms of the 
displacement gradient H: 
𝐂 =  𝐇𝐓 + 𝐇 + 𝐇𝐓𝐇 + 𝐈 (3.12) 
There are different types of strain tensors to characterise the local deformation for different 
purposes. One of such strains for large deformation is the Lagrangian finite strain tensor, 
defined as 
𝐄 =
1
2
(𝐂 − 𝐈) =
1
2
(𝐇𝐓 + 𝐇 + 𝐇𝐓𝐇) (3.13) 
E is a measure of the difference between C and unit tensor I.  
Although the vessel wall undergoes big deformation, it is useful to understand the relationship 
between the displacement and strain under small deformation, which is fundamental to non-
linear analysis. The small-strain approximation assumes HiK << 1, therefore the quadratic term 
HTH can be neglected in Equation 1.14, and the Lagrangian finite strain tensor E can be 
simplified to the small strain tensor 𝛆:  
3.1 Description of internal deformation and forces 49 
 
𝛆 =
1
2
(𝐇𝐓 + 𝐇) 
𝜀𝑖𝑗 =
1
2
(
∂𝑢𝑖
∂𝑋𝑖
+
∂𝑢𝑗
∂𝑋𝑖
) 
(3.14) 
In brief, C (in the case of small deformation, 𝛆) is the strain tensor describing the local 
deformation of the continuum body. 
 Stress 
The concept of stress is to measure the internal forces existing in a deformed body. Image a cut 
plane inside the body and examine the force acting on the cut surface, as shown in Figure 3.3A. 
The limiting value of the force per unit area is called the stress vector or surface traction. In 
simple loading situations such as uni-axial tensile or simple shear test, the stress state within 
the body is uniform and therefore can be described by a single vector (Figure 3.3B&C). 
 
Figure 3.3 Schematic drawing of stress: (A) stress vector T on a cut surface with normal 
vector ν (B) normal stress vector σ (C) simple shear stress vector τ. 
In the example of a straight rod under uni-axial tension, the normal stress vector σ can be 
obtained by dividing the force F with the cross-sectional area A. The direction is perpendicular 
to the cut plane. Similarly, the shear stress vector can be calculated by dividing the shear force 
with the cross-sectional area, while the direction is parallel to the cut plane.  
However, under physiological conditions, a complex stress state exists within vessel wall. The 
magnitude and direction of local stress vector depend on the normal direction of the cut plane, 
and also vary at different locations. A higher order tensor is introduced to describe the stress 
3.1 Description of internal deformation and forces 50 
 
state, named Cauchy stress tensor. The Cauchy stress tensor σ can be expressed in terms of 
nine components 𝜎𝑖𝑗  (𝑖, 𝑗 = 1,2,3) on an orthonormal basis [e1, e2, e3] (Figure 3.4 left):  
𝛔 = 𝜎𝑖𝑗 = [
𝜎11 𝜎12 𝜎13
𝜎21 𝜎22 𝜎23
𝜎31 𝜎32 𝜎33
] (3.15) 
where 𝜎𝑖𝑗 represents the stress component acting on a plane normal to the xi-axis and along the 
direction of the xj-axis. The stress tensor completely defines the stress state at a point inside the 
deformed body: according to the Cauchy’s stress theorem, the stress vector 𝐓(𝐧) on an arbitrary 
cut plane with normal direction n can be obtained from the stress tensor (Figure 3.4 right) : 
𝐓(𝐧) =  𝐧 ∙ 𝛔 (3.16) 
 
 
Figure 3.4 Schematic drawing of stress tensor: the components of stress tensor (left) and the 
stress vector 𝐓(𝐧) on an arbitrary direction n (right) 
Similar to strain tensor, three principal normal stress 𝜎𝑖 (𝑖 = 1,2,3) and their corresponding 
principle directions 𝐍𝑖  (𝑖 = 1,2,3)  can be derived from the stress tensor, by solving the 
eigenvalue equation:  
 𝐍 ∙ 𝛔 = 𝜎𝐍 (3.17) 
The principle normal stresses can be used to calculate the effective stress (also called von Mises 
stress), which is defined as 
3.2 Constitutive law for arteries 51 
 
𝜎𝑒 = √
1
2
[(𝜎1 − 𝜎2)2 + (𝜎2 − 𝜎3)2 + (𝜎3 − 𝜎1)2] (3.18) 
In this dissertation, the effective stress is used to estimate the overall stress level within the 
vessel.  
3.2  Constitutive law for arteries 
Constitutive law, the relationship connecting strain/deformation and stress/force, is used to 
describe the inherent material properties. Typical engineering materials (e.g. steel and 
aluminium) usually exhibit linear and elastic properties, as reflected by a linear stress-strain 
curve (Figure 3.5 left). In contrast, arterial tissues often exhibit nonlinear behaviour due to their 
composite structures as discussed in Section 1.2 (Figure 3.5 right).  
 
Figure 3.5 Schematic strain-stress curve of linear metal material (left) and non-linear 
biological soft tissue (right). 
 Hyperelasticity 
Hyperelasticity is one type of non-linear elastic model which is commonly used to characterise 
the mechanical behaviour of biological tissues. Hyperelastic materials are truly elastic in the 
way that if external loadings are applied and removed later, the material returns to its original 
configuration without any energy loss. Therefore, a scalar-valued function can be defined as 
the energy stored within a unit volume due to deformation, which is called SEDF: 
𝑊 = 𝑊(𝐂) = ?̅?(𝐅T ∙ 𝐅) (3.19) 
3.2 Constitutive law for arteries 52 
 
As discussed in Section 1.3, the aorta is composed of three layers with reinforced fibres, which 
are anisotropic at the microscopic level. However, it is difficult to image the fibre structure in 
vivo due to the limited resolution of current imaging techniques. In this dissertation, the 
biological tissues are assumed to be isotropic materials. The principle of material frame 
indifference of an isotropic material leads to the conclusion that SEDF can be expressed in 
terms of the principle stretches or the invariants of C: 
𝑊 = ?̃?(𝜆1, 𝜆2, 𝜆3) = ?̂?(𝐼1, 𝐼2, 𝐼3) (3.20) 
The Cauchy stress tensor σ can be obtained from the derivative of SEDF with respect to the 
right Cauchy-Green deformation tensor C: 
𝝈 = 2𝐅 ∙
𝜕𝑊
𝜕𝐂
∙ 𝐅T (3.21) 
Accordingly, the principle normal stress can be expressed as 
𝜎𝑖 = 𝜆𝑖
𝜕?̃?
𝜕𝜆𝑖
 (3.22) 
 Modified Mooney-Rivlin model 
Different SEDFs have been developed to characterise hyperelastic materials. The modified 
Mooney-Rivlin model was initially proposed to model industrial materials such as rubber, and 
later was introduced into biomechanics to characterise the material behaviour of arteries. This 
phenomenon-based model has the capacity of capturing the linear response in lower stretch and 
non-linear response in higher stretch, and also showed excellent numerical stability for 
computational simulation. The SEDF of this model is expressed as  
?̂? = 𝐶1(𝐼1̅ − 3) + 𝐷1[𝑒
𝐷2(𝐼1̅−3) − 1] + 𝜅(𝐽 − 1) (3.23) 
where 𝐽 = 𝑑𝑒𝑡(𝐅) = 𝜆1𝜆2𝜆3, 𝐼1̅ = 𝐽
−
2
3(𝜆1
2 + 𝜆2
2 + 𝜆3
2), 𝐶1, 𝐷1 and 𝐷2 are material constants, 𝜅 
is the hydrostatic pressure as a Lagrangian multiplier to enforce the incompressibility (J=1). 
Considering Equation (1.23) and (1.24), the relationship between principle stress and the 
principle stretches is expressed as 
3.3 Uniaxial tensile test 53 
 
𝜎𝑖 = 𝜆𝑖 (
𝜕?̂?
𝜕𝐼1
𝜕𝐼1
𝜕𝜆𝑖
+
𝜕?̂?
𝜕𝐽
𝜕𝐽
𝜕𝜆𝑖
) = 2𝜆𝑖
2[𝑐1 + 𝐷1𝐷2𝑒
𝐷2(𝐼1̅−3)] + 𝜅 (𝑖 = 1,2,3) (3.24) 
where the hydrostatic pressure 𝜅 is determined by the boundary conditions. 
3.3  Uniaxial tensile test 
To determine the material constants, material tests on the tissue samples are required. The most 
common experimental method is the uniaxial tensile test with simple boundary conditions. 
Displacement loadings are exerted at two ends of the tissue strips, and the traction is measured 
to obtain the stress-strain relationship for estimation of material constants. The details of the 
equipment and experimental procedure are described in Chapter 4. This section gives the 
theoretical formula of the stress-stretch curve in uniaxial tensile tests. Considering the isotropy 
and incompressibility, the principle stretches under uniaxial test are expressed as 
𝜆1 = 𝜆11 = 𝜆, 𝜆2 = 𝜆3 =
1
𝜆1
=
1
√𝜆
 (3.25) 
where 𝜆 is the measured axial Cauchy stretch. As the sample is under uni-axial tensile stress, 
the principle stresses are expressed as 
𝜎1 = 𝜎11 = 𝜎, 𝜎2 = 0, 𝜎3 = 0 (3.26) 
where 𝜎 is the measured axial stress and the direction of 𝜎1 and 𝜆1 is the axial direction. Recall 
the Equation (1.25), the measured stress-stretch relationship can be expressed as 
𝜎 = 𝜎1 − 𝜎3 = 2 (𝜆
2 −
1
𝜆
) [𝑐1 + 𝐷1𝐷2𝑒
(𝜆2+
2
𝜆
−3)] (3.27) 
The ordinary least square (OLS) method is often used to fit experimental data to Equation (1.25) 
to determine the material constants 𝑐1, 𝐷1 and 𝐷2, by minimising the cost function 
Ψ(𝑐1, 𝐷1, 𝐷2) = ∑(𝜎
𝑗∗ − 𝜎𝑗 )
2
𝑁
𝑗=1
 (3.28) 
3.4 Description of fluid dynamics of blood flow 54 
 
where N is the number of experimental data points, 𝜎𝑗∗ is the jth directly measured stress value 
and 𝜎𝑗  is the fitted value at the jth stretch level. Due to the non-linearity of the cost function, 
the fitting result is usually not unique which limits the physical interpretation of the material 
constants. In Chapter 4, we introduce the Bayesian framework to infer the material constants 
to solve this challenge. 
3.4  Description of fluid dynamics of blood flow 
In fluid dynamics, a field approach is commonly used to describe the flow by Eulerian 
description. The individual fluid particle is not identified or tracked. Instead, a fixed control 
volume is defined and flow-related parameters are described as field functions within the 
control volume. 
 Velocity field 
A fluid is unable to retain an unsupported shape, and will flow to take up the shape of the 
container. Similar to the role of displacement in the solid analysis, velocity is a fundamental 
variable in the fluid analysis. The field of flow is described by the velocity vector field 
𝐯 = 𝐯(𝐗, 𝑡) = 𝐢 𝑢(𝑥, 𝑦, 𝑧, 𝑡)  +  𝐣 (𝑥, 𝑦, 𝑧, 𝑡)  +  𝐤 𝑤(𝑥, 𝑦, 𝑧, 𝑡) (3.29) 
where u, v, w are the velocity components along the basis vectors i, j and k, respectively.  
 
 Strain rate 
The strain rate tensor 𝐞 describes the rate of change of the deformation in the neighbourhood 
of a certain point (Figure 3.6), which can be defined as the derivative of the strain tensor with 
respect to time 
𝐞 =
∂𝛆
∂𝑡
=
1
2
(𝛁𝐯 + 𝐯𝛁) 
𝑒𝑖𝑗 =
1
2
(
∂𝑣𝑖
∂𝑥𝑗
+
∂𝑣𝑗
∂𝑥𝑖
) 
(3.30) 
3.4 Description of fluid dynamics of blood flow 55 
 
Note that Equation (3.25) is similar to Equation (3.15), where the displacement in strain tensor 
is replaced by velocity in the strain rate tensor. Therefore, their geometric interpretations are 
also similar: each diagonal term is the rate of stretching per unit in the direction of the 
corresponding basis vector, and the off-diagonal term is the rate of angular deformation which 
is called the rate of shear strain. 
 
Figure 3.6 Velocity gradients and interpretation of rate of strain tensor components: 
diagonal terms (left) and off-diagonal terms (right). (Adapted from Fung 232,  with 
permission from Springer Nature) 
 Stress 
As a continuum model, the stress state at any point in the fluid domain can be described by a 
second order stress tensor 𝛔, the same to Equation 3.16. The diagonal terms are the normal 
stress components and the off-diagonal terms are the shear stress components. 
𝛔 = 𝜎𝑖𝑗 = [
𝜎11 𝜎12 𝜎13
𝜎21 𝜎22 𝜎23
𝜎31 𝜎32 𝜎33
] 
𝛔 = −𝑝𝐈 +  𝛕 
(3.31) 
The stress tensor of fluid is usually written as the sum of a hydrostatic component −𝑝𝐈 (called 
hydrostatic pressure tensor where p is the pressure) and a deviatoric component 𝛕 (called 
viscous stress tensor). 
 
 
 
3.4 Description of fluid dynamics of blood flow 56 
 
 Viscosity 
The viscosity 𝜇 is an intrinsic property of a fluid, which connects the strain rate and stress 
within the fluid domain, similar to the role of elasticity in solid analysis. To illustrate this, 
consider two parallel plates each of cross-sectional arear A with fluid of viscosity 𝜇 (Figure 
3.7). The relationship between viscous shear stress 𝜏 and shear rate ∂𝑢/ ∂𝑦 for flow in the x-
direction is given as 
𝜏 = 𝜇
∂𝑢
∂𝑦
 (3.32) 
 
Figure 3.7 Fluid subjected to simple shearing stress (top) and different types of viscosity 
(bottom). 
The coefficient 𝜇 in the Equation (1.32) is known as the dynamic viscosity. If the viscosity is 
constant where shear stress increase linearly with shear rate (Figure 3.7), the fluid is known as 
a Newtonian fluid. Any fluid which does not have a linear stress-shear rate behaviour is called 
non-Newtonian, including Bingham plastic fluids, shear thinning fluids and shear thickening 
fluids. The viscosity of blood depends on the protein concentration of the plasma, the 
deformability of the blood cells, and the tendency of the blood cells to aggregate. In general, 
the viscosity increases when the shear strain rate decreases. Although the whole blood is non-
Newtonian, it is permissible to use Newtonian constitutive model to simplify the analysis. From 
3.5 Haemodynamic variables on the wall 57 
 
experiments 233, the shear strain rate of blood within human aorta exceeds 100 sec-1, so that the 
viscosity of blood may be regarded as a constant about 3.5 cP in aorta. The non-Newtonian 
effect is less important near the vessel wall compared to the centreline of the aorta because of 
higher strain rate. In this dissertation, the Newtonian fluid model for blood flow is assumed for 
the computational analysis. 
3.5  Haemodynamic variables on the wall 
As discussed in Section 1.4, the abnormal haemodynamics could trigger pathological 
remodelling of the aortic wall. Several haemodyamicvariables defined on the vessel wall have 
been demonstrated to be related to the development of aortic aneurysm formation and the 
thrombosis process. 
 Wall Shear Stress 
WSS is the shear force from blood flow that is exerted on the surface of endothelium cells. 
WSS is the stress vector tangential to the wall surface and varies with time, which can be 
obtained from the stress tensor 𝛔: 
𝛕𝐰(𝐗, 𝑡) =  𝐧(𝐗) ∙ 𝛔(𝐗, 𝑡) ∙ 𝐧(𝐗) (3.33) 
where 𝐧 is the normal direction of vessel wall. The time-averaged wall shear stress (TAWSS) 
is calculated by integrating WSS magnitude over the cardiac cycle: 
TAWSS =
1
𝑇
∫ |𝛕𝐰|𝑑𝑡
𝑇
0
 (3.34) 
 OSI 
Oscillatory shear index (OSI) is a dimensionless metric which characterises whether the WSS 
vector is aligned with the TAWSS vector throughout the cardiac cycle, defined as:  
OSI =
1
2
(1 −
|∫ 𝛕𝐰 𝑑𝑡
𝑇
0
|
∫ |𝛕𝐰|𝑑𝑡
𝑇
0
) (3.35) 
3.6 Finite element analysis 58 
 
The OSI is greater than zero if there is some direction change during the flow cycle, and the 
maximum value is 0.5 in the case of pure oscillatory flow without any net forward flow. 
 RRT 
Relative residence time (RRT) at a specific site is inversely proportional to the distance that a 
particle at that site travels during a single cardiac cycle, defined as 
RRT~ (
1 − 2 × 𝑂𝑆𝐼
𝑇
∫ |𝛕𝐰|𝑑𝑡
𝑇
0
)
−1
 (3.36) 
The expression on the right is used as the indicator of RRT to represent the average amount of 
time that a particle spent in a specific region.  
3.6  Finite element analysis 
In theory, based on detailed information about morphology, constitutive law and boundary 
conditions, the mechanical variables can be calculated by solving mathematical equations. 
However, due to the complex geometry of biological structures, non-linear material properties 
of biological tissues, as well as the complex governing equations, it is not feasible to find an 
analytical solution to the patient-specific problem. Instead, as a popular numerical technique, 
finite element method (FEM) can be used to find approximate solutions to partial differential 
and integral equations. If certain basic numerical requirements and standards of practice are 
satisfied, the solution from the finite element analysis (FEA) estimates the exact physical 
solution. As a general method, FEM can be used for both structural solid analysis and fluid 
analysis. 
3.6.1 Solid Analysis 
In solid mechanics, the mathematical equations include governing equations, constitutive law 
and boundary conditions that are written in differential forms and with the tensor notation: 
3.6 Finite element analysis 59 
 
 
Ω:                        𝛁 ∙ 𝛔 + 𝜌𝐛 = 𝜌𝐚 
                              𝝈 = 2𝐅 ∙
𝜕𝑊
𝜕𝐂
∙ 𝐅T 
𝑆𝑢:                            𝐮 = ?̅? 
𝑆𝑡:                          𝛔 ∙ 𝐧 = 𝐓 
(3.37) 
where 𝛔 is the Cauchy stress tensor; 𝐛 is the body force per unit mass; 𝜌 is the density; 𝐚 is the 
acceleration; 𝐅 is the deformation gradient; 𝐂 is the stiffness tensor; 𝐮 is the displacement; ?̅? is 
the prescribed displacement on boundary surface 𝑆𝑢; 𝐓 is the prescribed traction on boundary 
surface 𝑆𝑡  and 𝐧 is the normal direction. The detailed constitutive equation and boundary 
conditions in this study are described in Chapter 4.  
When performing solids analysis using FEM, the continuum (e.g. stent) is divided into a finite 
number of discrete regions, named elements. The mechanical variable (such as displacement, 
strain and stress) at any point within the continuum are interpolated with values at the nodes of 
these elements. An approximate solution of the entire continuum is solved from the assembly 
of the individual elements. Usually, the displacements of nodes are taken as fundamental 
unknown quantities. From the displacements, the strains are evaluated by taking the appropriate 
derivatives. The material properties provide the necessary basis for computing stress from these 
strains. Through FEM, the differential equations on continuous fields can be finally 
transformed to algebraic equations of discrete nodal quantities which can be solved efficiently. 
FEA is a reliable and efficient technique that a detailed stress analysis is required prior to 
approval of a new stent design by the regulatory agencies such as the U.S. Food and Drug 
Administration 234. 
3.6.2 Fluid Analysis 
The motion of a continuous fluid medium is governed by Navier–Stokes equations. Under the 
assumptions of incompressible and Newtonian fluid, the governing equations of blood flow 
can be expressed in non-conservative forms for mass and momentum, respectively: 
3.7 Image-based biomechanical modelling 60 
 
𝜕𝜌
𝜕𝑡
+ 𝜌𝛁 ∙ 𝐯 = 0 
𝜌
𝜕𝐯
𝜕𝑡
+ 𝜌𝐯 ∙ 𝛁𝐯 − 𝛁 ∙ 𝛕 = 𝟎 
𝐞 =
1
2
(𝛁𝐯 + 𝐯𝛁) 
𝛔 = −𝑝𝐈 + 2𝜇𝐞 
(3-38) 
where 𝑡  is the time, 𝜌  is the constant density, 𝐯  is the velocity vector, 𝜇  is the dynamic 
viscosity constant, 𝐞 is the strain rate tensor, 𝛔 is the stress tensor. The solve these equations, 
appropriate boundary conditions are applied, which are discussed in Chapter 4. 
For the FEM implementation in computational fluid dynamics (CFD), the flow domain is 
discretised into a set of small fluid elements. Similar to structural analysis, the equations are 
written into an appropriate form for each element, and the set of resulting algebraic equations 
for the whole domain are solved numerically. As numerical details of this method are 
mathematically sophisticated and are not the main focus of this dissertation, further information 
can be found in related textbooks 235.  
3.7  Image-based biomechanical modelling 
Although detailed morphology of an aneurysm can be obtained by means of advanced imaging 
techniques, in vivo measurements of the mechanical environment are not available yet. Image-
based FEA provides a non-invasive method to estimate the flow field and the deformation of 
aorta, which helps to predict the geometry and the biomechanical environment after EVAR. In 
industrial application of FEA, the computational model is usually generated from computer-
aided design software with standard geometry. Instead, models in biomechanical application 
come from in vivo images with complex geometry. Extra consideration and processing are 
required, as discussed below: 
 Pre-processing of medical images 
Clinical images are commonly stored in the DICOM file format, with 3D image volumes in 
greyscale values. As images may be generated from different machines with different 
3.7 Image-based biomechanical modelling 61 
 
parameters (e.g. resolution, contrast injection and orientation), the first step is to standardise 
the images, including processes of denoising, co-registration, resampling, and normalisation.  
 Image segmentation 
To extract the morphological information, the segmentation is performed to delineate the 
region of interest (ROI). The segmentation can be manually done by experienced radiologists 
or semi-automated by computer-aided algorithms such as thresholding and region growing. In 
recent years, the rapid development of machine learning algorithms makes the fully-automatic 
segmentation possible, given enough training data with manual annotations.  
 Pre-shrinkage 
Typically, the computational start shape in FEM solid simulation is stress-free. However, 
because the model was extracted from in vivo images, the aneurysm shape is pre-deformed 
under physiological loadings including blood pressure and axial stretch. Therefore, a shrinkage 
process should be applied to obtain the loading-free configuration. In mathematics, given the 
deformed shape and applied loading, the load-free configuration can be obtained by solving an 
inverse problem, which is time-consuming236. An approximate method was proposed by 
Raghavan237 motivated by the observation that patterns in displacement field for a given AAA 
are strikingly consistent under all physiological pressure. The basic principle is to recover the 
stress-free shape by subtracting the displacement caused by blood pressure from the in vivo 
shape. 
 
 
 Chapter 4 Material properties of arterial tissues† 
This chapter investigates the material behaviour of arterial tissues by uniaxial tensile material 
tests. A framework of Bayesian inference is proposed to estimate the material constants from 
the experimental data, which are further correlated to the microstructural fibre architecture on 
histological images. The material properties are compared among aortic aneurysm, normal 
aorta and atherosclerotic plaque. The experimental results of AAs in this chapter provide the 
material constants in constitutive equations for following computational analyses of this 
dissertation. 
4.1 Introduction 
Cardiovascular diseases (CVD) are the No.1 killer and responsible for an estimated 31% of all 
deaths worldwide 238. About 80% of all CVD deaths are due to heart attacks and strokes 239, 
which are induced by atherosclerotic plaques. AAs, occurring in approximately 8% of men 
aged >65 240, are another common cause of CVD deaths, with the mortality after aneurysm 
rupture being ~90% 241. In current clinical practice, luminal stenosis and maximum wall 
diameter are the only validated risk assessment criteria for atherosclerotic disease and 
aneurysm, respectively. However, such size-based criteria showed only limited sensitivity and 
specificity 66,242–244. Therefore, there is a clear need for novel risk-stratification biomarkers to 
estimate the risks of atherosclerosis and aneurysm in the hope of improving patient outcomes. 
                                                 
† The author of this dissertation carried out all of the work described in this chapter unless specified otherwise. The material 
test and histological analysis of eight aneurysms were performed together with Aziz Tokgoz from Department of Radiology, 
University of Cambridge. The other material tests of arterial tissues were performed by Dr Zhongzhao Teng from Department 
of Radiology, University of Cambridge. The main content of this chapter has been included in 
1. Wang S, Tokgoz A, Huang Y, Zhang Y, Feng J, Sastry P, Sun C, Figg N, Lu Q, Sutcliffe MPF, Teng Z, Gillard JH. Bayesian 
inference-based estimation of normal aortic, aneurysmal and atherosclerotic tissue mechanical properties: from material 
testing, modelling to histology. IEEE Transactions on Biomedical Engineering, 2018.  
4.1 Introduction 64 
 
Under physiological conditions, both types of lesion are subject to mechanical loading due to 
dynamic blood pressure and flow. It has been shown that mechanical loading within the arterial 
tissue structure has an association with biological activities within the lesion 56,205,245–247, which 
can promote its development 248–250, leading to both progression and rupture. Accurate 
characterisation of mechanical properties of atherosclerotic and aneurysmal tissues is required 
for reliable prediction of mechanical loading in the lesion structure. A reliable prediction 
process should follow the steps of: (1) direct measurement of tissue stress-stretch 251; (2) 
carefully selected SEDF 252; and (3) determination of material constants in SEDF with an 
optimisation method to minimise the objective function, which describes the difference 
between the predicted and measured stress-stretch curves. Several SEDFs have been used to 
characterize the tissue material, such as neo-Hookean 253–256, one-term Ogden 257, two-term 
Ogden  258–261, Yeoh 262,263, five-parameter Mooney-Rivlin 264,265, Demiray 266–268, and modified 
Mooney-Rivlin SEDF 269–271. 
It is challenging to obtain a robust estimation of material constants in these SEDFs with 
traditional least squares methods, which often converge to a local minimum of the objective 
function in a narrow region around the initial guesses. This yields different sets of constants 
that can all fit the experimental data well. Although these distinct sets of material constants can 
lead to very similar stress predictions 252, it is inappropriate to characterise the tissue 
mechanical behaviour by using regressed material constants, whose values are highly 
dependent on their initial guesses. In other words, it is incorrect to assign a physical meaning 
to these regressed constants. 
In this study, Bayesian inference was used to estimate the probability of each material constant 
across a wide range and the expectation was used to characterise the material constants for each 
tissue strip. This approach avoids non-uniqueness of parameter estimation associated with the 
least squares method. The capability of the determined material constants to differentiate 
tissues from normal aorta, carotid atherosclerotic plaque and AAs were assessed and the 
association between determined material constants and fibre architectures in the tissue was 
explored. 
4.2 Materials and methods 65 
 
4.2 Materials and methods 
4.2.1 Tissue collection and preparation 
In this study, stress-stretch curves from direct uniaxial material tests with 8 normal aortas 272, 
19 AAs 272 and 21 carotid atherosclerotic plaques 251 were collected from previous studies, 
except for 8 aneurysms. The eight aneurysmal samples (seven males, age 63.3±11.7 years) 
were collected from the Papworth Cambridge University Hospital during open surgical repair. 
The protocol was approved by the local ethics committee and written informed consent was 
obtained from all patients. Details of patient demographics and tissue preparation except for 
the eight from Papworth Hospital have been described in two previous studies 251,272. The 
overall patient demographics are listed in Table 4.1. 
 
Table 4.1 Patient demographics. 
 Normal aorta Aortic aneurysm Carotid atherosclerotic plaques 
Male, n (%) 7 (87.5) 16 (84.2) 18 (85.7) 
Age, 
(Mean±SD) 
34.1 ± 7.8 61.2 ± 7.3 68.2 ± 7.4 
 
 
 
Samples were banked in liquid nitrogen for <4 months prior to testing. Cryoprotectant solution 
(20% dimethylsulfoxide (DMSO) in 5% human albumin solution) added to a final 
concentration of 10% DMSO was utilised to prevent ice crystals from damaging the tissue. 
Prior to testing, the samples were immersed in phosphate buffered saline and defrosted in a 
37ºC tissue bath. The intact aneurysm rings were cut and open using a scalpel, and further 
dissected by a tweezer into three layers including intima, media and adventitia. Approximately 
10 rectangle tissue strips of 1-2 mm width were obtained, both longitudinal (the axial 
direction) and perpendicular (the circumferential direction) to the blood flow, as shown in 
Figure 4.1. 
4.2 Materials and methods 66 
 
 
Figure 4.1 A representative sample of aortic aneurysm. (A) The intact arterial ring; (B) Cut 
and opened arterial tissue; (C) Adventitia tissue strips; (D) Media tissue strips; (E) Intima 
tissue strips. 
4.2.2 Uniaxial tensile testing 
An in-house designed tester comprised of a stepper motor (Miniature Steel Linear Stages, 
Newport Corporation, USA), a load cell (custom designed), a camera (PixeLink PL-B776U 3.1 
MP USB2 Colour Camera, PixeLINK, Canada) and a controlling system developed in 
LabVIEW 2011 (National Instruments, USA) were used to perform the uniaxial extension test 
(Figure 4.2 A). The position resolution of the stepper motor was 0.1 μm; the precision of the 
4.2 Materials and methods 67 
 
load cell was 0.0005 N and the image size of each image frame is 2,048×1,536 pixels, with an 
80×60 mm2 field of view. The tissue strip was mounted on the tester using modified 6-cm 
straight haemostatic clamps (Shanghai Medical Instruments (Group) Ltd., Corp. China). The 
clamped section of each end was 1-1.5 mm.  
 
 
Figure 4.2 Overview of the testing equipment and an example of the testing process. (A) 
Different parts of the testing equipment; (B) Captured region of the camera; (C) An 
aneurysmal media strip at different stages of stretching; (D) The mass-displacement curve 
recorded during stretching and the unsmoothed steps along the curve representing tissue 
damage due to stretching; (E) The converted stress-stretch data points where stress≤400 kPa 
and the corresponding fitted curve. 
After five preconditioning cycles (by moving one of the clamps 2.5% of the total distance 
between the two clamp ends at a speed of 0.05 mm/s), the testing was performed with a speed 
of 0.01 mm/s immersed in a tissue bath with 37ºC saline solution. Black ink markers were 
placed on the surface to trace the local displacement (Figure 4.2C). Testing was stopped when 
the tissue strip failed under the applied strain. The centre of each marker was identified and the 
4.2 Materials and methods 68 
 
local stretch ratio was calculated from the distance between the marker centres. The Cauchy 
stress was converted from the measured force signal using the strip thickness, the width at rest 
and the stretch ratio with the assumption of incompressibility (Figure 4.2E). 
4.2.3 Strain energy density function 
As introduced in Section 3.2, the modified Mooney-Rivlin SEDF was used to characterise the 
mechanical behaviour of the tissue strips based on the consideration of material stability 252. 
Recall the Equation (3.27), the Cauchy stress 𝜎11 along the tensile direction is express as  
𝜎11(𝜆) = 2 (𝜆
2 −
1
𝜆
) [𝐶1 + 𝐷1𝐷2𝑒
𝐷2(𝜆
2+
2
𝜆
 −3)] (4.1) 
in which 𝜆 is the stretch ratio. 
4.2.4 Ordinary least square fitting method 
The ordinary least square (OLS) fitting method was used to determine the material constants 
in Equation (4.1) by finding the local minimum of the objective function around the initial 
guess of (𝐶10, 𝐷10, 𝐷20), 
𝑆(𝐶1, 𝐷1, 𝐷2) = ∑[𝜎11𝑘
𝑝 − 𝜎11𝑘
𝑚 ]
2
𝑁
𝑘=1
 (4.2) 
in which N is the number of data points, 𝜎11𝑘
𝑝
 and 𝜎11𝑘
𝑚  are the kth predicted and measured 
Cauchy stresses, respectively. All material constants were constrained to be positive to avoid 
any unphysical phenomenon. Relative error was used to assess the fitting quality, 
𝛾 =
∑ |𝜎11𝑘
𝑝 − 𝜎11𝑘
𝑚 |𝑁𝑖=𝑘
∑ |𝜎11𝑘
𝑚 |𝑁𝑖=𝑘
× 100% (4.3) 
4.2 Materials and methods 69 
 
4.2.5 Bayesian inference framework 
In the Bayesian inference, all unknown parameters are treated as random variables 𝜽. Given 
the experimental data 𝒟 , its aim is to estimate the conditional distribution of unknown 
parameters 𝑝(𝜽|𝒟), which is referred as the posterior distribution (posterior). First a prior 
distribution (prior) 𝑝(𝜽)  is assumed to represent the prior knowledge about unknown 
parameters. The prior distribution can be adapted from previous studies and/or from experts’ 
opinions. If there is no established prior distribution for a problem, a non-informative prior can 
be applied using the Principle of Maximal Entropy. 
An appropriate noise model and chosen constitutive equations are used to derive the likelihood 
function (likelihood) 𝑝(𝒟|𝜽). The posterior can be calculated by linking the prior and the 
likelihood using Bayes’ theorem, 
𝑝(𝜽|𝒟)  =  
𝑝(𝜽)  ×  𝑝(𝒟|𝜽)
𝑝(𝒟)
   (4.4) 
The denominator of Equation (4.4) is a constant referred to as the probability of the evidence 
(evidence) and given by, 
𝑝(𝒟) =  ∫ 𝑝(𝜽) × 𝑝(𝒟|𝜽)𝑑𝜽 (4.5) 
The multi-dimensional integral in Equation (4.5) is generally difficult to evaluate. If the 
unknown parameters are the only ones of interest, Equation (4.5) can be rewritten as, 
𝑝(𝜽|𝒟)  ∝  𝑝(𝜽) × 𝑝(𝒟|𝜽) (4.6) 
Sampling methods, e.g., Markov Chain Monte Carlo (MCMC), can be applied to explore the 
posterior without explicitly computing the evidence (Equation (4.6)). The strategy is to draw 
samples from a distribution similar to the posterior by using effective sampling methods. More 
details about Bayesian inference and different sampling methods can be found in references 
273–275. 
4.2 Materials and methods 70 
 
When Bayesian inference is used to estimate the material constants in Equation (4.1), a 
Gaussian noise model is introduced for the uncertainty, hoping that 𝜎11𝑘
𝑝 (𝜆) equals to 𝜎11𝑘
𝑚 (𝜆),  
𝜎11(𝜆) = 2 (𝜆
2 −
1
𝜆
) [𝐶1 + 𝐷1𝐷2𝑒
𝐷2(𝜆
2+
2
𝜆
 −3)] +  𝒩(0, 𝜀2) (4.7) 
 in which 𝒩(0, 𝜀2) is the Gaussian noise with zero mean and variance 𝜀2 . Therefore, the 
likelihood function can be written as,  
𝑝(𝒟|𝐶1, 𝐷1, 𝐷2, 𝜀) = ∏ 𝒩(𝜎11𝑘
𝑝 − 𝜎11𝑘
𝑚 |0, 𝜀2)
𝑁
𝑘=1
 (4.8) 
In this study, the prior for 𝐶1, 𝐷1, 𝐷2 and 𝜀 were assumed to be uniform distributions with 
ranges of [0, 5000 kPa], [0, 5000 kPa], [0, 5000 kPa] and [0, 5000 kPa], respectively. The 
sensitivity to the prior was tested. The MCMC with Gibbs sampling method was implemented 
in the software WinBUGS (MRC Biostatistics Unit, University of Cambridge) to estimate the 
posterior distribution of the parameters, i.e. 𝑝(𝜽|𝒟). The mean and standard deviation of the 
posterior was calculated for further analyses amongst tissues from different types of lesions 
and distinct morphological component. 
4.2.6 Quantitative histological analysis 
Twenty-four tissue strips adjacent to those used for mechanical testing from the 8 aneurysmal 
samples (3 strips from each sample), which were collected from Papworth Hospital were 
submitted for histological examination. Following a standard processing procedure, 4-µm 
tissue slices in were stained with Verhoeff–van Gieson (EVG) and Picrosirius Red (PSR) to 
visualise the elastin and collagen contents. Elastin appears dark in EVG stain, and collagen 
appears red in Sirius Red stain. Elastin and collagen percentage of each tissue slice, as well as 
the fibre dispersion (𝜅; a parameter describing the scatter of fibre orientations), and fibre 
waviness (𝜔) were quantified using an in-house designed MATLAB-based (MathWorks, Inc.) 
software, as described in the appedix at the end of this chapter. The software was optimised by 
using an expert pathologist to assess the results. In this study, the area percentage of elastin (= 
area with elastin/area of ROI; ROI stands for region of interest) and collagen (= area with 
collagen/area of ROI), 𝜅, and 𝜔 were used to characterise the fibre architecture in the structure. 
4.3 Results 71 
 
Perfectly parallel fibres correspond to κ=0 and an even scatter of fibre orientations has κ=1/3. 
Smaller values of 𝜔 correspond to wavier fibres, and 𝜔=1 indicates straight fibres. 
4.2.7 Statistical analysis 
The correlation between the percentage of collagens and the estimated material constants was 
assessed using Spearman correlation test. In this study, multiple samples were from a single 
tissue piece and the linear mixed effect model was constructed to assess the difference of 
parameters from different tissue types, considering both random and fixed effect. The statistical 
analysis was performed in MATLAB (MathWorks, Inc.). A significant difference was assumed 
if p<0.05. 
4.3 Results 
In this study, stress-stretch curves from 312 tissue strips in the circumferential direction 
(perpendicular to the direction of blood flow) were analysed using both OLS and Bayesian 
inference. In detail, the curves were from 15 media and 15 adventitial strips of 8 normal aortas; 
28 adventitial, 36 media, 8 thickened intima and 27 thrombus strips of 19 aortic aneurysms; 65 
media, 59 fibrous cap (FC), 38 lipid, and 21 intraplaque haemorrhage/thrombus (IPH/T) strips 
of 21 carotid atherosclerotic plaques.  
4.3.1 Case study on material constants’ uniformity 
Figure 4.3 provides a representative example showing the fitted results using OLS fitting 
method and Bayesian inference. The determined material constants were dependent on initial 
guesses when OLS method was used. In the cases shown in Figure 4.3, when the initial guesses 
of (1, 1, 1) and (10, 10, 10) were used, the fitting results were very different (Table 4.2). A 
certain choice of initial guesses, e.g., (100, 100, 100), might lead to a poor regression (Figure 
4.3). It is therefore inappropriate to use material constants determined by OLS to characterise 
the mechanical properties of arterial tissues. On the contrary, based on Bayesian inference, the 
determined material constants showed little changes (<5%) when the prior ranges of 𝐶1, 𝐷1 
and 𝐷2 all increased ten times from [0, 1000] to [0, 10000].  
4.3 Results 72 
 
 
Figure 4.3 A representative example showing the fitted results using ordinary least square 
(OLS) method and Bayesian inference (initially guessed values 1 of (𝐶1, 𝐷1, 𝐷2) are (1, 1, 
1), values 2 are (10, 10, 10), and values 3 are (100, 100, 100); the detailed fitted results are 
listed in Table 1; the experimental data were acquired from a media strip of a normal aorta). 
Table 4.2 Representative regressions using the ordinary method with different initial values 
and Bayesian inference procedure with different prior ranges.  
Fitting Method 𝑪𝟏 (kPa) 𝑫𝟏 (kPa) 𝑫𝟐 γ 
OLS - Initial values (1, 1, 1) 2.19 4.00 2.12 3.3% 
OLS - Initial values (10, 10, 10) 25.56 0.04 5.27 15.1% 
OLS - Initial values (100, 100, 100) 39.10 2.65×10-8 19.92 444.5% 
OLS - Initial values (0, 1, 0) 6.17 2.84 2.31 3.1% 
Bayesian inference (Prior [0, 1000]) 3.11 3.72 2.16 3.3% 
Bayesian inference (Prior [0, 5000]) 3.26 3.67 2.17 3.3% 
Bayesian inference (Prior [0, 10000]) 3.20 3.68 2.17 3.3% 
 
 
4.3 Results 73 
 
In general, if the initially guessed value is properly chosen, OLS can fit the experimental data 
well. The fitting quality 𝛾 was 8.5% [6.0, 12.1] (Median [Interquartile range]), which is slightly 
better than that of the Bayesian inference-based estimation (8.8% [6.0, 12.3], p<0.0001).  
4.3.2 Bayesian inference-based material constants of different tissues  
The values of 𝐶1, 𝐷1 and 𝐷2 for each type of tissue are provided in Figure 4.4 (the outliers that 
are out of 1.75 quartile range were not shown) with actual values listed in Table 4.3. In normal 
aorta, the media and adventitia have comparable 𝐶1  , 𝐷1  and 𝐷2  (p=0.18, 0.33, and 0.14, 
respectively). Samples from the aortic aneurysm, media and thickened intima showed a 
comparable 𝐶1 (p=0.50), which is higher than that in either adventitia or thrombus (p<0.05). 
Adventitia has the lowest value of 𝐷1 (p<0.005); intima has the highest value of 𝐷1 (p<0.01), 
but is comparable with the one of thrombus (p=0.21). Media has the highest 𝐷2 value compared 
with adventitia, thickened intima and thrombus (p<0.05); and thrombus has the lowest value 
of 𝐷2 (p<0.05), but is comparable with that of intima (p=0.29). 
 
Table 4.3 Bayesian inference-based estimations for different types of tissues (Median 
[Interquartile range]) 
 𝑪𝟏 (kPa) 𝑫𝟏 (kPa) 𝑫𝟐 𝜸 (%) 
Normal aorta Media 4.53 [0.88, 10.84] 3.68 [1.19, 9.21] 2.53 [1.74, 4.29] 3.3 [2.3, 4.5] 
Adventitia 1.04 [0.60, 3.46] 1.46 [0.75, 6.51] 3.57 [3.12, 5.26] 9.8 [5.5, 13.6] 
Aneurysm Media 1.81 [0.83, 6.31] 2.33 [0.79, 4.02] 16.77 [9.12, 25.71] 11.8 [8.8, 14.7] 
Adventitia 0.96 [0.30, 2.88] 0.79 [0.56, 3.40] 8.04 [5.60, 12.13] 12.0 [7.2, 14.8] 
Intima 3.27 [0.74, 20.91] 7.98 [3.82, 21.42] 6.05 [3.04, 10.44] 7.9 [5.6, 11.5] 
Thrombus 0.46 [0.12, 1.17] 5.34 [1.66, 9.90] 2.80 [0.59, 10.77] 8.3 [7.2, 14.1] 
Atherosclerosis Media 3.34 [1.44, 9.60] 2.27 [1.45, 3.62] 21.78 [16.16, 35.24] 7.7 [6.6, 9.6] 
FC 4.87 [2.50, 12.33] 2.21 [1.26, 4.16] 28.06 [17.95, 44.17] 9.2 [7.0, 11.5] 
Lipid 1.48 [0.71, 5.62] 1.40 [0.28, 4.15] 10.07 [6.42, 23.66] 8.4 [5.9, 11.4] 
IPH/T 0.79 [0.18, 1.47] 1.17 [0.44, 2.20] 10.58 [5.45, 13.63] 10.8 [8.2, 18.4] 
 
 
4.3 Results 74 
 
 
 
Figure 4.4 The visualisation of (𝐶1, 𝐷1, 𝐷2) of different tissue strips from different types of 
samples (A: tissue strips of media and adventitia from normal aortas; B: tissue strips of 
media, adventitia, thickened intima and thrombus from aortic aneurysms; C: tissues strips of 
media, fibrous cap, lipid and intraplaque haemorrhage/thrombus from carotid atherosclerotic 
plaques; Unit of 𝐶1 and 𝐷1 is kPa and 𝐷2 is dimensionless). 
 
4.3 Results 75 
 
In carotid atherosclerotic plaques, the media and FC have a comparable 𝐶1 (p=0.33), higher 
than those of lipid and IPH/T (p<0.05). Compared with IPH/T, 𝐶1 value of lipid is higher 
(p=0.03). The value of 𝐷1 for media, FC and lipid is comparable (p>0.05), and IPH/T has the 
lowest value of 𝐷1 compared with media and FC (p<0.01), but is comparable with that of lipid 
(p=0.87). Both media and FC have a comparable 𝐷2 (p=0.33), as do lipid and IPH/T (p=0.39); 
both media and FC have a significantly higher 𝐷2 than either lipid or IPH/T (p<0.005). 
The media is the only common tissue in all three types of samples. The 𝐶1 values of media 
from normal aorta, aortic aneurysm and carotid atherosclerotic plaque are comparable 
(p>0.05),  as is 𝐷1 (p>0.05). However, 𝐷2 has the capacity to differentiate all three types of 
tissue. The value of  𝐷2 for the media from both aneurysm and plaque is significantly larger 
than that from normal aorta (p<0.0001), and the 𝐷2 value of media from plaque is much larger 
than that from aneurysm (p=0.022). 
4.3.3 Material constants, elastin and collagen contents and architectures   
A tissue strip adjacent to the one used for the mechanical testing of each layer from each of the 
eight aneurysm samples from Papworth Hospital were submitted for histological examination, 
to investigate the elastin and collagen in the tissue microstructure (Figure.4.5 and Figure 4.6).  
As shown in Figure 4.7A, the area percentage of elastin in both thickened intima and media is 
higher than the adventitia (an example is shown in Figure 4.5), and thickened intima has the 
lowest area percentage of collagen (Figure 4.7B), followed by media, where the adventitia has 
the highest area percentage of collagen (an example is shown in Figure.4.6). The difference in 
elastin content in these three layers (Figure 4.7A) is consistent with the difference of 𝐶1 value 
as listed in Table 4.3.  
 
 
4.3 Results 76 
 
 
 
 
 
 
Figure 4.5 Representative EVG stained images showing the distribution of elastin in the thickened intima, media and adventitia of an aortic 
aneurysm (The elastin contents are segmented in black. The adventitia has much less elastin fibres than either the thickened intima or media.) 
4.3 Results 77 
 
 
 
Figure 4.6 Representative Sirius Red stained images showing the collagen fibres in the media and adventitia of an aortic aneurysm. (The collagen 
contents are segmented in black. Collagen fibres in the adventitia (B) is much wavier than those in the media (A). C: the stress-stretch curves of 
the tissue strips are shown in A and B.) 
 
4.3 Results 78 
 
 
Figure 4.7 Comparison of area percentage of elastin and collagen contents in the thickened 
intima, media and adventitia from eight aortic aneurysms. 
 
 
Figure 4.8 The association between collagen fibre dispersion (κ) and waviness (ω) and D2. 
 
4.4 Discussion 79 
 
Elastin fibres in the thickened intima and media are mostly well organised and straight while 
those in the adventitia are more fragmented (Figure.4.5). Similarly, the collagen fibres in the 
thickened intima and media are straight with a preferred direction, while in the adventitia, the 
collagen fibres are wavier and more disorganised. Compared with the media, the collagen fibre 
dispersion, 𝜅 , is much bigger (0.14 [0.13, 0.15] vs 0.23 [0.19, 0.25], p=0.008), and the 
waviness, 𝜔, is higher in the adventitia (0.07 [0.09, 0.12] vs 0.16 [0.15, 0.18], p=0.008). When 
𝜅, 𝜔, 𝐷1 and 𝐷2 of media and adventitia were pooled, 𝜅 was inversely associated with 𝐷2 (ρ=-
0.61, p=0.014) and 𝜔 was positively associated with 𝐷2 (ρ=0.73, p=0.002) (Figure 4.7); but no 
association was found between 𝐷1 and 𝜅 or 𝜔.  
4.4 Discussion 
Bayesian inference estimates the distribution of material parameters in the constitutive model 
rather than finding their point-based estimations. It is used in this study to avoid the sensitivity 
to initial guesses when the OLS method is used, allowing characterisation of the tissue through 
comparison of material constants. The obtained results indicate that 𝐶1 , 𝐷1 and 𝐷2 were tissue 
type dependent. In particular, 𝐷2 is the most sensitive parameter in differentiating tissues of 
distinct arterial layers from a single type of sample, or of the same layer between different type 
of samples; and 𝐷2  is also associated with tissue architectures, e.g., fibre dispersion and 
waviness. In general, atherosclerotic tissues have the largest 𝐷2 values, followed by those from 
aneurysms and then normal aortas. 
The proper choice of both SEDF and material constants is important for material stability and 
numerical convergence in computational studies that aim to predict stress distribution within 
the lesion 252,276. The robustness of the SEDF is reflected by its ability to reproduce several 
modes of deformation, including, but not limited to uniaxial, biaxial and pure shear 
deformation 17. In this study, stress-stretch data from uniaxial testing was used, since it is nearly 
impossible to perform biaxial and pure shear testing with atherosclerotic tissues, because of 
their non-homogeneity and irregularity. Regarding the material constants of the SEDF, using 
constraints on their values can make the SEDF convex to achieve material stability to a 
particular extent 277. Although a wide search with multiple initial guesses might alleviate the 
4.4 Discussion 80 
 
sensitivity of material constants to the initial guess, an exhausted try is not possible and 
moreover, different sets of material constants may all have a satisfactory regression. For 
example, the initial guess of (1, 1, 1) and (0, 1, 0) can both fit the experimental data points 
shown in Figure 4.3 well, but with very different material constants, in particular, 𝐶1 and 𝐷1 
(Table 4.2). The employment of Bayesian inference-based approach can eliminate such 
dependency.   
The material constants, 𝐶1 , 𝐷1 and 𝐷2 contribute differently to the stress when the tissue strip 
is subject to stretching as shown in Equation 4.7. Taking the results in Figure 4.3 as an example, 
when λ=1.2, the term with 𝐶1 contributes 21.2% to the total stress and the term with 𝐷1 and 𝐷2 
contributes the rest; when λ=1.6, the proportion from the term with 𝐶1 decreases to 6.3%, and 
that from 𝐷1 and 𝐷2 increases to 93.7%. The change of each constant also has a distinct effect 
on the calculated stress. Figure 4.9 shows the stress-stretch curves when 𝐶1 (=3.26 kPa), 
𝐷1(=3.67 kPa) and 𝐷2(=2.17) decrease by 50% and increase by 50% in intervals of 10%. 
 
 
Figure 4.9 The change of stress-stretch curves with the change of 𝐶1, 𝐷1, and 𝐷2 (all constants 
decrease and increase 50% from the baseline of (3.26, 3.67, 2.17) which are from the case shown 
in Figure 4.3). 
 
It can be seen that the change in curve is insensitive to the change of 𝐶1, more prominent with 
changes in 𝐷1, and very profound with changes in 𝐷2. The quantitative relationship between 
the stress change and the change of constants can be found through individual partial derivative, 
4.4 Discussion 81 
 
𝜕𝜎11(𝜆)
𝜕𝐶1
= 2 (𝜆2 −
1
𝜆
)   
𝜕𝜎11(𝜆)
𝜕𝐷1
= 2 (𝜆2 −
1
𝜆
) 𝐷2𝑒
𝐷2(𝜆
2+
2
𝜆
 −3)
 
𝜕𝜎11(𝜆)
𝜕𝐷2
= 2𝐷1 (𝜆
2 −
1
𝜆
) [1 + 𝐷2 (𝜆
2 +
2
𝜆
 − 3)] 𝑒𝐷2(𝜆
2+
2
𝜆
 −3)    
(4.9) 
The extracellular matrix components, specifically the mixture of elastin and collagen in the 
vessel wall, determine the passive mechanical properties of large arteries. 𝐶1, 𝐷1 and 𝐷2 might 
be used to characterise their mechanical behaviour under physiological and pathological 
conditions. In an unloaded healthy artery, both elastin and collagen appear undulated and wavy, 
where they straighten as the artery begins to bear load 278. Elastin is mostly straight at 
physiological pressures 278. Upon involvement of 𝐶1, the term in Equation (4.1) may reflect 
this procedure. In contrast to the elastin, less than 10% of the collagen fibres are straight and 
load-bearing at physiological pressures 13. As the pressure increases, more collagen fibres 
become load-bearing and their stiffness limits arterial distension, providing the classical 
nonlinear behaviour observed in arterial mechanics 279. This is characterised by the term in 
Equation (4.1) with 𝐷1 and 𝐷2 involvement, particularly, 𝐷2 dominates the rate of increase in 
stress. Elastin and collagen fibres can be degraded by several members of the matrix MMP 
family. Increased expression of MMP-1 and MMP-9, for example, have been reported in 
aneurysms, which are characterised by fragmentation of both elastin and collagen fibres 280, 
where the increased expression of MMP-2 is localised to the sites of fragmentation in the elastic 
lamellae 281. These pathological changes lead to a stiffer artery, that is, stress increases quicker 
during stretching. The bigger 𝐷2 value of aneurysmal and atherosclerotic tissues can be the 
consequence of these pathological changes. 
Of note, the modified Mooney-Rivlin SEDF is a phenomenological approximation of the 
material behaviour. Information from microstructure was not used, and therefore material 
parameters 𝐶1  , 𝐷1  and 𝐷2  can only loosely link to the fibre architecture. Moreover, the 
exponential term describing the toe region in the stress-stretch curve is oversimplified and 
unbounded, allowing the tangential stiffness to rise infinitely with increasing stretch. Such 
limitations can be overcome by employing a more microstructurally informed model, which 
4.4 Discussion 82 
 
takes gradual recruitment of collagen fibres into consideration 282–284. In their stress-free state, 
the collagen fibres rest in a crimped configuration with waviness following a right-skewed 
distribution 285,286. As a result, the likelihood of collagen fibres becoming newly recruited 
follows a Gamma distribution, 
Γ(𝐼1̅; 𝛼, 𝛽) =
𝛽𝛼(𝐼1̅ − 3)
𝛼−1𝑒−𝛽(𝐼1̅−3)
Γ(𝛼)
 (4.10) 
where  Γ𝛼 is a complete Gamma function, and α and β are the shape and rate parameters. Both 
parameters relate to the microstructure of the tissue, with 𝛼𝛽−1  and 𝛼𝛽−2  being the 
expectation and variance of 𝐼1̅ − 3 at which the collagen fibres become recruited. Integrating 
this probability density function gives the cumulative likelihood of collagen fibres contributing 
to stiffness. Thus, SEDF at a given stretch level can be obtained as follows, 
𝑊 = 𝐶1(𝐼1̅ − 3) + 𝐷1 ∫ Γ(𝑥;  𝛼, 𝛽)𝑑𝑥
𝐼1̅
0
 (4.11) 
where 𝐶1 and 𝐷1 reflect the contribution (incorporating fibre stiffness, alignment and relative 
volume fraction) of elastin and collagen fibres, respectively. Such a formulation offers more 
flexibility in fitting and better insights into the mechanical response 283,284, however the whole 
fitting procedure is much more complicated than either OLS or Bayesian inference-based 
estimations. Given that phenomenological models already lead to comparable goodness of fit 
49, we conducted the present study using modified Mooney-Rivlin models for conciseness.   
The obtained estimations listed in Table 4.3 can serve as priors for future studies to improve 
the accuracy of the estimation. Despite the interesting findings, limitations exist in this study: 
(1) the stress-stretch curve used in this study was from uniaxial tests and modified Mooney-
Rivlin SEDF is an isotropic model, so that the anisotropy was not considered. The anisotropic  
SEDF considering microstructures can be found in studies by Holzapfel et al 9; (2) the EVG 
and Sirius Red stains were used to visualise the gross elastin and collagen architectures and 
pathological features, e.g., inflammation, was not considered and might affect tissue 
mechanical properties and therefore the value of 𝐶1, 𝐷1 and 𝐷2; and (3) the modified Mooney-
Rivlin SEDF usually can fit the whole stress-stretch curve of the normal aorta well, but not for 
4.5 Conclusion 83 
 
all tissue strips of aneurysm and atherosclerotic plaque, in particular, in the region with a low 
stretch level. 
4.5 Conclusion 
Bayesian inference-based estimation robustly determines material constants in the modified 
Mooney-Rivlin SEDF and these constants can reflect the inherent physiological and 
pathological features of the tissue structure. The parameters from the experiments can be used 
for biomechanical simulation of arterial tissues.  
 Chapter 5 Image-based finite element analysis of 
multiple overlapping uncovered stents: a patient-
specific study† 
In this chapter, a patient-specific MOUS procedure is reproduced in silico through 
computational analysis based on pre-operative CTA images. The interaction between the stents 
and the aortic wall, as well as the flow-diverting effect, are investigated. The influence of 
multiple stents on the local mechanical environment is assessed. 
5.1 Introduction 
The flow diverter has been designed to induce thrombosis within intracranial aneurysm by 
altering blood flow 287–289. The underlying mechanism is thought to be related to the formation 
of mural thrombus, increasing the effective wall thickness and decreasing the lumen radius. 
This reduces the aneurysm wall tension resulting in a lower risk of arterial rupture 290. The 
primary aim of such a diverter is to treat intracranial lesions that are not effectively managed 
by traditional approaches, including coil embolization, conventional high porosity stents and 
coils, parent artery occlusion and neurosurgical procedures, e.g., aneurysm clipping, resection 
and bypass. Further technical developments have improved the cure rate with lower 
complication rates. This technique has transformed the management of intracranial aneurysms 
and has become the preferred treatment option for large or giant wide-necked lesions 291.  
                                                 
† Part of the content in this chapter has been published in 
1. Wang, S., Y. Zhang, J. Feng, Y. Huang, A. Tokgoz, U. Sadat, J. H. Gillard, Q. Lu, and Z. Teng. Influence of overlapping 
pattern of multiple overlapping uncovered stents on the local mechanical environment: A patient-specific parameter study. J. 
Biomech., 2017. 
5.2 Materials and methods 85 
 
The attractive advantages of this technology is its minimally invasive nature and the capacity 
to keep long-term patency of side branches 292. Encouraged by the success of flow diverter in 
treating intracranial aneurysms, researchers have attempted to use a similar strategy to manage 
complex aortic aneurysms by using MOUS. However, controversial findings were reported due 
to the differences in the haemodynamic environment and lesion size between intracranial and 
aortic aneurysms. Aneurysm expansion and rupture after uncovered metal stent deployment 
121,122,124 and longitudinal shortening of stents have been reported 293, while promising 
outcomes were also documented 294,295. This implies that there is a need for refined patient 
selection and further comprehensive studies to identify the key factors affecting the outcome 
of MOUS. 
This study is designed to quantify the MOUS deployment induced changes of local 
haemodynamic environment, including the flow velocity and rate in the sac and side branches, 
wall shear stress, oscillatory shear index, relative residence time and pressure in the sac and 
structural stress in the landing zone, by performing patient-specific FEA. The obtained results 
will help understand the mechanism of failure and success in different patient cohorts, and 
provide a framework to estimate the biomechanical environment for pre-surgical plan.   
5.2 Materials and methods 
5.2.1 The patient 
The patient involved in the analysis is from the previously reported cohort 294,295. This study 
was approved by the review board of Changhai Hospital, Shanghai, China. The patient was a 
68-year old male with a complex thoracoabdominal aortic aneurysm (maximum diameter was 
70.1 mm) (Figure 5.1). His medical history included pulmonary function impairment, grade II 
hypertension (146/92 mmHg) and coronary artery disease that had been previously treated by 
stenting. Given his multiple comorbid conditions and the risk of spinal cord ischaemia (at the 
level of T11-L1) and occlusion of coeliac arteries after stent-grafting, the patient was judged 
unfit for either open surgery or traditional endovascular aortic repair by the multidisciplinary 
surgical team consisting of vascular surgeons, cardio-thoracic surgeons, and anaesthetists. The 
5.2 Materials and methods 86 
 
MOUS strategy was therefore explained to the patient, who gave written informed consent for 
the procedure. Closed-cell, self-expandable and uncovered sinus-XL stents from OptiMed 
(Ettlingen, Germany) were used.  
 
 
 
Figure 5.1 The configuration of a complex aortic aneurysm with vital branches involvement. 
(A) 3D rendering of the lesion configuration before stent deployment; (B) 3D rendering of 
the configuration after 4-layer stents deployment; (C) A 2D axial slice; (D) A 2D sagittal 
slice. 
5.2.2 Stent reconstruction 
The diameter and length of the uncovered stents deployed in this patient were 28 mm and 100 
mm, respectively (Figure 5.2A). The geometry of the bare metal stent was reconstructed 
5.2 Materials and methods 87 
 
according to the parameters provided by the supplier in Creo2.0 (PTC, Needham, USA) (Figure 
5.2B) and exported to ICEM for meshing (Figure 5.2C). A single stent was meshed with 
119,592 hexahedron elements. The typical length of each element was approximately 0.15 mm. 
The same stent mesh was duplicated four times, generating the overall mesh of 4-stent MOUS. 
 
 
Figure 5.2 Reconstruction of the uncovered stents. (A) A photo of the stent product; (B) The 
geometry of the stent cell annotated with the measurements in CAD software; (C) 
Reconstructed stent model meshed with 3D hexahedral elements. 
5.2.3 Patient-specific aneurysm reconstruction 
Image Segmentation 
Segmentation was performed based on the pre-operative contrast-enhanced CTA images to 
identify aortic wall, calcium and thrombus using an in-house program developed in MATLAB 
R2016a (The MathWorks, Inc., USA). The surrounding tissues and organs, e.g., spine and liver, 
were not considered. In this study, the CTA resolution was 0.683×0.683×0.8 mm3, the aortic 
wall thickness was about 2.5 mm and the diameters of visible sub-branches ranged from 2.9 
mm to 6.0 mm, and the wall thickness of sub-branches was about 1.0 mm. To reduce the effect 
of smoothing operation during the 3D geometry reconstruction, CTA images were resampled 
with a voxel size of 0.1×0.1×0.1 mm3. The model reconstruction included the aorta 
5.2 Materials and methods 88 
 
reconstruction and sub-branches reconstruction. Firstly, the resampled CTA images were 
imported into an in-house MATLAB platform (Figure 5.3) to semi-automatically segment 
aortic lumen, calcium and aortic wall by trained operators 205.  
 
 
 
Figure 5.3 Graphical User Interface of the AAA segmentation platform. The contours of the 
lumen, calcium and aortic wall are annotated in red on axial slices. Adjacent slices are 
displayed on the middle panel for context reference. Segmentation tools are displayed on the 
right panel, including the options of region grow, threshold and contour smoothing. 
The segmented contour information was translated into a voxel-based label map then output to 
3D Slicer (http://www.slicer.org). The lumens of sub-branches were segmented using threshold 
algorithm and a uniform wall thickness of 1 mm for all sub-branches was applied by dilating 
the lumen label map. The voxel-based label maps of aortic components and sub-branches were 
then merged by Boolean operation and smoothed using the Gaussian Filter (Figure 5.4A). 
Surface Processing and 3D Meshing 
After completion of the final voxel-based label maps, the surfaces of each object were 
generated using fast marching method in 3D Slicer and imported to VMTK 
(http://www.vmtk.org/), followed by smoothing with Taubin's algorithm 296. Finally, surfaces 
5.2 Materials and methods 89 
 
of inlet and outlet of AAA and the outlet of each sub-branch were clipped (Figure 5.4B) and 
extended 15 times of the local diameter to eliminate the inlet and outlet effect.  
 
Figure 5.4 Surface processing and meshing of the aneruysm. (A) The 3D rendering (top 
panel) and cross-sectional views (bottom panel) of the lumen with side branches, where 
lumen is green and the aortic wall is blue. (B) Clipped and smoothed surfaces generated from 
voxel label map. (C) 3D meshing of the aortic wall and components after adding straight 
extension, where aortic wall is coloured in grey, thrombus in red and calcium in yellow. 
3D volumes enclosed by these surfaces were generated, and tetrahedron meshing was made 
based on local geometry curvature in ICEM (ANSYS Inc., USA) (Figure 5.4C). The ILT was 
first considered as part of aortic wall in the meshing procedure and further assigned to a 
separate element group. The distance to the outer wall surface was calculated for each element 
within the aortic wall. The average thickness of the aorta was assumed as 2.5 mm, and any 
5.2 Materials and methods 90 
 
element with a distance above 2.5 mm was assigned to the ILT group. For the baseline model 
(without any stent), 409,357 tetrahedron elements were generated for the solid part of the 
aneurysm model. 
5.2.4 Finite element analysis 
In this study, a one-way fluid-structure interaction (FSI) analysis was performed to re-predict 
the mechanical conditions before and after the deployment of the stents, to investigate the 
influence of stent deployment on critical mechanical conditions within the aneurysmal structure 
and blood flow in the sac and side branches. Detailed processes for the cases with stents 
deployment can be found in the flowchart shown in Figure 5.5. 
 
 
Figure 5.5 The workflow chart of the one-way fluid-structure interaction analysis. 
5.2 Materials and methods 91 
 
Virtual stent deployment 
Since the CTA images were acquired under pressurised condition, an inverse procedure with a 
pressure level of 110 mmHg (patient’s mean blood pressure) and axial stretch 2.5% at both 
ends was followed to obtain the computational starting shape 237. Each stent was assumed to 
be a linear material with Young’s modulus and Poison’s ratio of 75 GPa and 0.333, 
respectively. As discussed in Chapter 4, the modified Mooney-Rivlin model was used to 
describe the material properties of the aortic wall, thrombus and calcium. The material 
constants are adopted from the previous experimental results of AAA 272,297: aortic wall, 
𝐶1=0.07 kPa, 𝐷1=6.54 kPa and 𝐷2=5.88; thrombus, 𝐶1=0.24 kPa, 𝐷1=8.69 kPa and 𝐷2=0.61; 
and calcium, 𝐶1=1.147×10
5 kPa, 𝐷1= 7.673×10
4 kPa, and 𝐷2=2.838×10
-8. 
A static blood pressure of 110 mmHg was applied on the luminal surface and an axial stretch 
of 2.5% was prescribed at both aortic ends to restore the in-vivo configuration. The stents’ 
surface and lumen surface were defined as contact surfaces. Steps mimicking the deployment 
were as follows: (1) a gradually increased concentrated force from 0 to 350 N was applied at 
both ends of the stent along its axial direction to shrink the stent; (2) a rigid body displacement 
was prescribed to deliver the stents into the lumen to the target location, which were identified 
by the locations of radio-opaque markers on the post-operative CTA imaging; (3) the stent was 
released by gradually decreasing the concentrated force to 0. Multiple stents were deployed 
sequentially controlled by the phase-shifted time functions.  
Different degree of freedom (DOF) fixity policies were adopted to eliminate rigid 
displacements where appropriate for different parts. The displacement of both ends of the 
extended aorta was specified to maintain the axial stretch ratio, and the circumferential rotation 
of nodes on these two ends was not allowed. For each side branch, all DOFs at the end were 
fixed except for the local radial displacement. For stents, circumferential rotation and axial 
displacement at the proximal (close to the heart) were not allowed, while there was no 
constriction for the other end. The virtual deployment simulation was performed using ADINA 
9.0 in the implicit statics mode with the consideration of large strain and large displacement. 
An auto time step technique was used for the consideration of convergence. Finally, averaged 
and peak von Mises stress was extracted under the 99.5% criterion as the indicator of structural 
stress in the wall. 
5.2 Materials and methods 92 
 
Computational fluid dynamic simulation of blood flow before and after stent deployment 
The deformed lumen and struts surface after deployment were extracted to form the fluid 
domain (there was no struts surface before deployment). The stent struts in direct contact with 
the aortic wall were masked out to reduce computational costs. Then the fluid domain was 
imported into ICEM CFD (ANSYS Inc., USA) and meshed using the Octree method with 
tetrahedral elements. The thickness of the boundary layer was estimated to be 1.4 mm 
considering the Womersley number of about 18.2 in this study. Three prism thin boundary 
layers were therefore generated for a fine calculation in the region near the lumen surface with 
the first layer thickness being 0.4 mm and the third layer 0.8 mm 298,299. In total, the fluid 
domain without stents was meshed with 80,562 tetrahedral and 175,691 prism elements; a 
single stent with 518,988 tetrahedral and 99,037 prism elements; two stents with 832,072 
tetrahedral and 105,722 prism elements; three stents with 943,176 tetrahedral elements and 
114,642 prism elements; and four stents with 1,004,782 tetrahedral elements and 126,128 prism 
elements. 
 
 
Figure 5.6 The computational model for haemodynamic simulation. (A) The fluid domain 
was meshed with tetrahedron and prism elements after 4-stent MOUS deployment. 
Impendence units were added at the aortic outlet and ends of the side branches (pink). (B) 
The ‘plug’ velocity waveform was applied at the inlet over 4 cardiac cycles. 
5.3 Results 93 
 
A ‘plug’ velocity profile with a mean velocity of 66.7 mm/s, peak velocity 284 mm/s and period 
of 0.9 s was adopted from measurements by Olufsen et al. 300 as the loading condition at the 
aortic inlet (Figure 5.6B). At the outlets, a resistant unit was added at each outlet to mimic the 
afterload of the downstream circulation bed 301. The resistance of each unit was determined by 
the following steps: (1) a CFD simulation without resistance units was performed by assigning 
discharge ratio of each outlet according to Murray’s Law 302 and a pressure profile was applied 
at the outlet of the aorta; and (2) extract computed pressure at the outlet of each side branch 
and calculate the resistance by, resistance = (mean pressure)/(mean flow rate).  
The blood was assumed to be incompressible and Newtonian with a density of 1.06 g/cm3 and 
a constant viscosity of 0.035 poise, and the flow to be transient laminar. The Newton-Raphson 
iteration method was used for each time step with a convergence criterion for the relative 
residual of 0.001. Simulation was performed over 4 cardiac cycles. Results of the last cycle 
were extracted for analysis where the flow was fully developed.  
WSS 303,304, OSI 304 and RRT 305,306 have been widely suggested to be associated with 
atherosclerosis and aneurysm development and their clinical presentations. With this 
consideration, apart from flow velocity and rate, these parameters were also used to quantify 
the flow pattern modulated by the stent deployment. The calculation of these variables on the 
vessel wall were implemented using Equation (3.33-35), as discussed in Section 3.5. RRT was 
normalised (RRT̅̅ ̅̅ ̅̅ ) by the average value in the case before deployment at the proximal disease-
free region where the flow was fully developed.  
5.3 Results 
Nine side branches were located around the diseased region, including 7 intercostal arteries, 
superior mesenteric artery and the coeliac artery (Figure 5.4 B). Two intercostal arteries were 
ignored in this study due to their small size. The diameter at the proximal and distal were 25 
mm and 20 mm, respectively. In total, 4 uncovered stents were deployed in clinical treatment 
for this patient. After 12-month follow-up, one of the intercostal arteries was occluded and all 
others remained patency. The thrombus rate increased from 30% at the baseline to 97%, while 
the maximum aneurysm diameter decreased from 70.1 mm to 62.5 mm. 
5.3 Results 94 
 
5.3.1 Overall porosity of MOUS 
The deployment of multiple stents resulted in a periodic overlapping pattern. The 3D geometry 
of MOUS was projected to the outer cylinder surface, to quantify the porosity. A unit cell of 
the projection result was extracted (Figure 5.7A), and the overall porosity of MOUS was 
calculated as the relative area ratio of stent struts to the unit cell.  
 
 
Figure 5.7 Overall porosity of MOUS after stents deployment. (A) Unit cell representation 
of the projection of one stent, two stents, three stents and four stents; (B) The corresponding 
porosity calculated from the relative area ratio of the stent struts. 
The porosity of one single stent is 83%, which means a single stent covered 17% area of the 
corresponding cylinder surface. The subsequently deployed stents overlapped with previously 
deployed stents and decreased the overall porosity (Figure 5.7B). Under the overlapping pattern 
reconstructed from the post-operative CTA imaging, the 2nd, 3rd and 4th stents reduced the 
porosity to 69%, 56% and 46%, respectively. As more stents were deployed, the subsequent 
stent induced less reduction of the MOUS porosity, which was expected due to more 
overlapping coverage with previously deployed stents.  
5.3 Results 95 
 
5.3.2 Structural stress concentration induced by multiple stents 
Right after the first stent was deployed, the aneurysm configuration changed immediately due 
to the solid-solid interaction (Figure 5.9 A&B), and the structural stress increased accordingly 
depending on the location. The change of stress of the representative node at different regions 
was shown in Figure 5.8. At points in direct contact with the stent struts, particularly in the 
landing zone, the stress level could increase over 5 times (Node B&D, Figure 5.8). The stress 
increased more gently in the non-contact points, e.g., the stress could be doubled in the non-
contact landing zone (Node A, Figure 5.8); however, stress in the sac remained nearly 
unchanged (Node C, Figure 5.8).  
When subsequent stents were deployed, the configuration remained nearly unchanged (Figure 
5.9). The stress level in different regions however changed differently; regions in contact with 
stent struts experienced a much higher stress increase than the non-contact regions. In 
summary, the peak stress around the diseased region could increase 12 times from 143 kPa to 
1718 kPa after 4 stents were deployed and such stress elevation was only observed in the 
landing zone, not in the aneurysm sac.  
 
Figure 5.8 Structural stress level at different location changed after MOUS deployment. 
 
5.3 Results 96 
 
 
 
 
Figure 5.9 Band plots of effective stress within the wall before and after stents deployment. (A) The configuration and effective stress under static 
mean blood pressure before stent deployment; (B) The aneurysm configuration after one stent deployment, followed by effective stress after the 
deployment of the 2nd, 3rd and 4th stent). 
5.3 Results 97 
 
5.3.3 Flow velocity, WSS, OSI, RRT and pressure modulation by MOUS  
In general, the flow velocity inside the aneurysm sac was much slower than that in the main 
arterial lumen (Figure 5.11). After the deployment of the MOUS, the flow pattern in the sac 
was modulated significantly, resulting in the reduction of flow velocity (Figure 5.10).  
After the 1st stent was deployed, the mean sac time-averaged velocity decreased from 39.8 
mm/s to 25.3 mm/s (36.4% reduction). The deployment of 2nd, 3rd and 4th stents further reduced 
the velocity to 20.2 mm/s (49.3% reduction), 16.0 mm/s (59.8% reduction) and 14.8 mm/s 
(62.8% reduction), respectively. Similar to the change of overall porosity (Figure 5.7B), 
additional velocity reduction induced by the subsequent stent decreased after more stents 
deployed. In this patient-specific simulation, the 4-stent MOUS only induced about 3% further 
reduction of the original sac-averaged velocity, compared to the 3-stent MOUS. 
 
 
Figure 5.10 The change of mean sac time-averaged velocity before and after multiple stents 
deployment.  
Associated with changes of flow velocity, other haemodyamic parameters, including TAWSS, 
OSI and RRT, changed accordingly (Figure 5.12). The mean TAWSS on the sac wall decreased 
from 0.19 Pa to 0.15 Pa when the 1st stent was deployed, and further decreased to 0.13 Pa after 
subsequent stents were deployed. The flow became more disturbed after the 1st stent was 
deployed as OSI increased from 0.18 to 0.30, and the deployment of the subsequent stents 
further increased OSI to 0.40 (2nd stent), 0.44 (3rd stent) and 0.44 (4th stent). 
5.3 Results 98 
 
 
 
Figure 5.11 Cross-sectional band plot of blood velocity at systole (A) Band plot of velocity without stent deployment; (B) One stent deployment; 
(C) two stents deployment; (D) three stents deployment; (E) four stents deployment.  
5.3 Results 99 
 
   
5.3 Results 100 
 
 
Figure 5.12 Band plots of haemodynamic variables on the lumen wall before and after multiple stents deployment: (A) Time-averaged wall 
shear stress; (B) Oscillatory shear index; and (C) Normalised relative residence time.  
5.3 Results 102 
 
RRT at the proximal disease-free region where the flow fully developed was 8.5 Pa-1, and 
changed to be 8.4 Pa-1 after the first stent was deployed, while remained the same after 
subsequent stents deployment. When the first stent was deployed, the mean RRT̅̅ ̅̅ ̅̅  on the sac 
wall increased from 1.29 to 3.13; it further increased to 4.90 (2nd stent), 17.78 (3rd stent) and 
18.80 (4th stent). The mean time-averaged pressure in the sac decreased by 2.4% after the first 
stent was deployed, and decreased further by 4.2% (2nd stent), 5.4% (3rd stent) and 5.6% (4th 
stent) when the subsequent stents were deployed.  
5.3.4 Flow rate in side branches 
Keeping the side branch patency is one of the advantages of MOUS system. For this patient, 
only 1 of the intercostal arteries was lost after 1 year. Total flow rate of side branches was 6.0% 
of the whole flow rate. After stent deployment, the flow rate in each side branch changed 
differently depending on many factors, e.g., the location and relative position to the struts 
(Table 5.1).  
 
Table 5.1 Comparison of time-averaged flow rate in each side branch before and after 
MOUS deployment. (Unit: ×10-3ml/s; CA: coeliac artery; SMA: superior mesenteric artery; 
other side branches were intercostal arteries) 
Side branch No stent 1-stent 2-stent 3-stent 4-stent 
1† 111 119 120 119 118 
2† 119 117 113 110 109 
3† 116 122 117 115 115 
4 60 54 52 50 51 
5† 79 74 76 75 73 
CA 172 161 156 150 151 
SMA 574 578 572 570 569 
† The orifice of these side branches was partially covered by the stent strut.  
 
5.4 Discussion 103 
 
For this patient, CA originated from the sac and SMA originated right below the sac (Figure 
5.1). After the first stent was deployed, the flow rate decreased 6.4% in CA and increased 
slightly in SMA. Further decrease in both CA and SMA was observed after subsequent stents 
were deployed. In general, the flow rate change after the 4-stent MOUS deployment was less 
than 20% compared with the case before stent deployment.  
5.4 Discussion 
To the authors’ best knowledge, this is the first comprehensive study assessing the mechanical 
environments in both wall structure and fluid domains modulated by the MOUS system.   
The results obtained from this study indicate that MOUS introduce high structural stress 
concentrations around the diseased region. For a clear understanding of the change of stress 
with the number of stents deployed, the change of stress of a representative node was shown in 
Figure 5.8. In the landing zone, the stress increased with the number of stents deployed, while 
the stress level in the sac remained nearly constant. Further analysis indicated that either 
averaged stress or peak stress in different regions with stent contact increased similarly with 
the number of stents deployed (Figure 5.13). These two parameters remained nearly unchanged 
in regions away from stent struts, e.g., zone I (above or below the landing zone) and V (sac) in 
Figure 5.13. Elevated stress concentrations in the landing zone might have undesirable effects 
such as continued aneurysmal degeneration of the aortic wall. Long-term follow-up data is 
therefore required to assess this. 
The MOUS system decreased the flow velocity (Figure 5.11) and WSS (Figure 5.12A) in the 
sac, while increased OSI and RRT (Figure 5.12B&C). These results were in agreement with 
previous findings using CFD analysis with idealised geometry 290,307. Due to the rheological 
nature of blood, slow flow velocity increases its viscosity which is the primary driving force 
of thrombus formation and growth 308. In addition, low WSS promotes the adherence of discoid 
platelets contributing to the formation of thrombus 308. The developed thrombus appears to 
protect against aneurysm rupture through a ‘cushioning’ effect that reduces wall stress 120,309. 
However, such thrombus development may take time. In addition, MOUS system does not 
significantly reduce the blood pressure in the sac and thus structural stress in the sac wall 
5.4 Discussion 104 
 
(Figures 5.8 and 5.9). This technique therefore might not be suitable for lesions judged in a 
high risk of near-future rupture. On the other hand, the formation of thrombus might not be 
always protective in the long term. Inflammatory content might infiltrate the aneurysm wall 
beneath thrombus 310 and thick thrombus might lead to local hypoxia and neovascularization 
311. Such pathological effects might weaken the vessel wall leading to aneurysm expansion 312.  
 
 
Figure 5.13 The change of peak stress and averaged stress in different regions with the 
number of stents deployed. (A) The definition of different zones; (B) The change of peak 
stress in different zones with the number of stents deployed; (C) The change of averaged 
stress in different zone with the number of stents deployed. 
It is clear that one of the key functions of MOUS is to reduce the blood velocity and to increase 
RRT in the sac, promoting the formation and development of thrombus. The MOUS porosity 
has been identified as the main factor determining the velocity reduction associated with 
subsequent thrombosis, and literature suggested that optimal effect might be achieved with a 
5.4 Discussion 105 
 
porosity of 50-70% 313–316. The mesh porosity is 83% for a single stent used in this study, and 
MOUS resulted in a lower overall porosity. It is obvious that the velocity further reduces with 
the number of stents deployed, while the marginal velocity reduction is decreasing. 
Furthermore, more stents introduce higher structural stress concentrations in the landing zone 
(Figure 5.8). Two or three stents should be an optimal option considering the trade-off between 
velocity reduction and stress concentration. As demonstrated in this study, after two stents were 
deployed, the mean sac velocity reduced by nearly 50% and the peak structural stress was about 
1000kPa. If a third stent was added, the porosity might reduce to 56%, and the peak structural 
stress increased to about 1300kPa. According to direct material tests, the ultimate material 
strength of aneurysmal tissues was in a range of 500-2000kPa 245,272,317–321.  
Another key function of MOUS is to maintain the blood flow into side branches. The flow 
velocity in the side branch is determined by branch diameter, location, local configuration and 
the relative position with stent struts; predicting the flow rate in each side branch is difficult. 
However, according to the results obtained from the FEA (Table 5.1), there was subtle flow 
reduction for most of side branches, despite some side branches were partially covered by the 
stent strut. This finding explained the clinical observation that 311/320 side branches remained 
patency in 40 patients in a mean follow-up period of 21 months  295.  
In order to capture the temporal change of blood flow and obtain a stable result for an accurate 
calculation of flow parameters, e.g., OSI and RRT̅̅ ̅̅ ̅̅ , the time step has to be sufficiently small 
and simulation cycles should be enough. However, the finer time step or the more simulation 
cycles, the higher computational cost. In this study, the time step was set to be 9 milliseconds 
(ms). When the time step increased to be 18 ms or decreased to be 4.5 ms, the difference in 
flow parameter calculation was negligible, e.g., for the case with 1-stent, the OSI difference 
was less than 2% and the peak velocity different was less than 2.5%. Moreover, the result at 
the 4th cycle was extracted for analysis as the difference between the 3rd and 4th cycles was very 
small, e.g., the difference in peak velocity was less than 0.5%. Furthermore, in this study, blood 
was assumed to be Newtonian. This may introduce over-/under-estimation for flow parameters, 
e.g., WSS. An increase in mean WSS was observed in non-Newtonian fluid model compared 
to Newtonian model for a matched flow waveform 322. Perktold et al. reported WSS magnitude 
5.5 Conclusion 106 
 
difference only on the order of 10% between two models in carotid artery 323, but the difference 
in WSS could be up to 26.7% in AAAs 324.  
Despite the interesting findings, several limitations exist in the present study: (1) a one-way 
rather than fully coupled FSI analysis was performed (Figure 5.5) to re-predict the mechanical 
environment in this study. Due to the complexity in the geometry, interactions among 
aneurysmal wall, stents and blood flow, the non-linearity in material properties and governing 
equations, as well as big deformations, it is nearly impossible to perform a fully coupled FSI 
analysis using current numerical methodologies. However, it has been demonstrated that a one-
way FSI yielded a small deviation in predicting structural stress and flow parameters compared 
with those obtained from a fully coupled FSI in the carotid artery with atherosclerotic disease 
325; (2) tissue components, including wall, calcium and thrombus, were assumed to be piece-
wise homogenous and the inhomogeneity in each component was not considered; (3) The 
empirical Reynolds number for the transition to turbulence in pipe flow is 2000-2300. In this 
study, the Reynolds number was estimated to range from 532 to 2,256 when the mean and the 
peak velocity of 66.67 mm/s and 284 mm/s were considered. The ignorance of turbulence in 
this study should be reasonable. However turbulent flow might exist locally in the fluid domain 
298; (4) The flow discharged ratio into different side branches estimated from Murray’s Law 
might not reflect the real situation in diseased vasculature (5) residual stress that might exist in 
the aneurysmal wall was not considered. 
5.5 Conclusion 
In conclusion, the MOUS system may induce high structural stress concentrations in the 
landing zone, which increased linearly with the number of stents; MOUS system decreased the 
mean flow velocity and WSS, increased OSI and RRT in the sac, while maintained the blood 
supply to side branches; it had very little effect in pressure reduction in the sac. FEA based on 
pre-operative images could be used to predict the biomechanical environment and flow-
diverting outcome, which could aid surgeons in the decision of the optimal number of stents 
for personalised MOUS configuration. 
 
 Chapter 6  Influence of cross-stent structures: 
parameter studies of multiple overlapping uncovered 
stents† 
The uncertainty during the deployment of multiple stents may lead to different configurations 
of MOUS, while their influence on the treatment outcome remains unclear. This chapter 
conducts a series of parameter studies on the influence of cross-stent structures, including 2D 
overlapping patterns and 3D multi-layer structures. 
6.1 Introduction 
The principle of treating aneurysms with a flow-diverting strategy is to modulate the blood 
flow, which promotes the thrombosis and shrinkage of the aneurysm sac 85,105,326. Porosity has 
been identified as a key factor for the intracranial flow-diverters in previous experimental and 
computational studies 313–316. As an off-shelf implementation, MOUS are based on the 
sequential deployment of multiple stents, to achieve an efficient porosity 85,127. Different 
overlapping patterns could be generated from the uncertainty of deployment process, resulting 
in different cross-stent structures. The successful experience of treating giant intracranial 
aneurysms with overlapping stents have been described in a few clinical case reports 327–329. 
Several in vivo and in vitro studies reported the improved efficacy of overlapping intracranial 
stents on flow modulation 330–333. Previous computational studies also found the stent-in-stent 
                                                 
† Part of the content in this chapter has been included in 
1. Wang, S., Y. Zhang, J. Feng, Y. Huang, A. Tokgoz, U. Sadat, J. H. Gillard, Q. Lu, and Z. Teng. Influence of overlapping 
pattern of multiple overlapping uncovered stents on the local mechanical environment: A patient-specific parameter study. J. 
Biomech., 2017. 
2. Wang, S., Y. Zhang, J. Feng, Y. Huang, A. Tokgoz, U. Sadat, J. H. Gillard, Q. Lu, and Z. Teng. Influence of cross-stent 
structure and optimised design of multiple overlapping uncovered stents. (In preparation). 
6.2 Materials and methods 109 
 
technique promotes haemodynamic stasis in intracranial aneurysms 332,334,335. Most of previous 
studies focused on the haemodynamic comparison among different stents 331,334,335, however, a 
comprehensive study of the overlapping pattern is lacking. As an emerging area, only a few 
studies have investigated the application of MOUS in aortic aneurysms 336,337, which reported 
the flow modulation in the ideal models. The robustness of MOUS and influence of overlapping 
patterns are of great importance in clinical practice, which remains unknown yet. 
The study was designed to investigate the cross-stent structures after the deployment of MOUS, 
and their influence on the local biomechanical environment including both haemodyamic 
change inside the aneurysm and structural stress within the diseased wall.  
6.2 Materials and methods 
6.2.1 Patient-specific FEA of MOUS 
In this study, the same thoracoabdominal aortic aneurysm model was reconstructed from pre-
operative CTA images in Chapter 5 (Figure 5.1). The procedure of one-way FSI simulation 
was followed, where the fluid analysis was performed after the virtual deployment of stents, as 
described in Section 5.2 (Figure 5.5). The first stent was delivered to the real location as 
identified on the post-operative CTA image, while the delivered location of other stents were 
set different in the parameter studies, as described below. The structural stress and 
haemodynamic variables were calculated and compared, including sac-averaged flow velocity, 
pressure, TAWSS, OSI and RRT. 
6.2.2 2D overlapping patterns  
A parameter study of 2D overlapping patterns was performed in a 2-stent MOUS system. Once 
the first stent was deployed, the delivered position of the second stent before deployment was 
controlled by two parameters: the circumferentially overlapping angle, 𝜃, and the normalised 
axial overlapping displacement, D. The stent has a periodic configuration with 𝜃 = 18° in the 
circumferential direction and one cell unit in the axial direction. We therefore performed 
simulations with 𝜃 being 0º-15º with an interval of 3º, to investigate the influence of different 
6.2 Materials and methods 110 
 
overlapping angles in the circumferential direction (Figure 6.1). The parameter study on the 
axial displacement of -1 to 1 cell unit with an interval of 0.25 was also performed, to investigate 
the different overlapping patterns in the axial direction (Figure 6.2). For comparison, we also 
investigated the case without any stent and with only one stent. 
 
 
Figure 6.1 The local view of two stents with different overlapping patterns in the 
circumferential direction. The 1st stent is in green and the 2nd stent is in red. 𝜃 is the relative 
circumferential angle in the clockwise direction. 
 
Figure 6.2 The local view of two stents with different overlapping patterns in the axial 
direction. The 1st stent is in green and the 2nd stent is in red. 𝐷 is the relative axial displacement 
normalised by the cell length, along the blood flow direction. 
6.2 Materials and methods 111 
 
6.2.3 Monte Carlo Method  
As shown in Section 5.3.7, the overall porosity of the MOUS can be estimated from the 
geometry projection to the outer cylinder surface. Given the parameters of the relative 
circumferential angles and axial displacements for each stent, the overall porosity of MOUS 
can be determined. If the deployment processes of N stents are assumed independent and 
random, the overall porosity can be expressed as 
𝑝 = 𝑝(𝜃1, 𝐷1, 𝜃2, 𝐷2, … , 𝜃𝑁 , 𝐷𝑁) 
𝜃1 = 0, 𝐷1 = 0 
𝜃𝑘~𝑈[0,18°], 𝐷𝑘~𝑈[−1,1], 𝑘 = 2,3, … , 𝑁 
(6.1) 
where 𝜃𝑘 and 𝐷𝑘 are circumferential angle and normalised axial displacement of the kth stent, 
respectively. 𝑈[𝑎, 𝑏] is a uniform distribution between 𝑎 and 𝑏. The parameters of the 1st stent 
were set to 0, as the reference configuration for relative circumferential angles and axial 
displacements of subsequent stents. The irregular cell shape of the stent (Figure 5.2B) makes 
an analytical expression and analysis of the porosity function infeasible. Instead, the Monte 
Carlo method can be used to estimate the probability distribution of MOUS porosity after 
deployment, by repeated sampling of the porosity function. In this study, the porosity function 
𝑝 was sampled independently for 1,000,000 times for the deployment of 2-stent, 3-stent and 4-
stent MOUS, respectively. 
6.2.4 3D multi-layer structure  
In addition to 2D overlapping patterns, the deployment of multiple stents also generates 3D 
structures (Figure 6.3A&B). To investigate the influence of multi-layer structures, a compact 
model with a single layer was built for comparison (Figure 6.3C): the geometry of each stent 
was projected outwards to the surface of the first stent, after the virtual deployment of a MOUS 
system. MOUS had the same overall porosity as the corresponding compact model, while the 
multi-layer structure was transformed into a single layer. The 2-stent, 3-stent and 4-stent 
compact models were generated based on deployed geometry during patient-specific 
simulation, as discussed in Chapter 5. Then the compact models were imported to ICEM 
6.2 Materials and methods 112 
 
(ANSYS Inc., USA) for fluid domain meshing. The flow-diverting outcomes were compared 
between MOUS and compact models.  
 
 
Figure 6.3 The 3D structure of a 4-stent MOUS and the corresponding compact model. (A) 
The configuration of MOUS and lumen surface after the deployment of 4 stents. The four layers 
of stents were in different colours, while stent struts in contact of the lumen wall were masked 
out. (B) The local view of MOUS configuration. (C) The local view of corresponding compact 
model. 
A virtual deployment of the compact model of 4-stent MOUS was simulated by the similar 
procedure as described in Section 5.2.4. However, only contact pairs between the stents and 
the lumen wall were active while cross-stent contact pairs were inactive. This modified contact 
setting eliminated the internal interaction between stents and simulated an artificially ‘merged’ 
single-layer stent.  
6.3 Results 113 
 
6.3 Results 
6.3.1 Uncertainty of MOUS porosity 
The probability density functions (PDF) of MOUS porosity with different number of stents 
were estimated from Monto Carlo simulation results, as demonstrated in Figure 6.4.  
 
 
Figure 6.4 The probability density functions of MOUS porosity under random deployments. 
Mean ± standard deviation of sampling results from the Monto Carlo simulation are annotated 
for MOUS with different number of stents. 
The porosity of 1-stent MOUS is 83.2%, which was reduced by subsequently deployed stents. 
The porosity (mean±SD) of MOUS from random deployment was 69.3±1.5%, 57.7±2.1% and 
48.0±2.1% for 2-stent, 3-stent and 4-stent MOUS, respectively. For the parameter study of 
overlapping patterns, the porosity among different circumferential angles (Figure 6.5A) and 
axial displacements (Figure 6.5B) were similar (68.72%-69.51%), except for the cases with 
complete stents struts alignment (𝜃 = 0º, 18º; D = -1,0,1). 
6.3 Results 114 
 
 
Figure 6.5 The overall porosity of no stent, 1-stent and 2-stent MOUS under different 
overlapping patterns. (A) With different circumferential angles; (B) With different axial 
displacements. 
6.3.2 Influence of 2D overlapping patterns 
Structural stress within the aortic wall 
The different circumferential and axial overlapping patterns (Figure 6.1 & Figure 6.2) seem to 
have very little impact on the stress level in different regions (Figure 6.6). The stress variation 
was less than 2.5% when the two stents overlapped with each other in different circumferential 
angles (𝜃 changed from 0º to 18º, Figure 6.6A). When the second stent moved along the axial 
direction (D changed from -1 to 1, Figure 6.6B), significant stress decreases (~20%) were 
observed in the margin of the proximal landing zone (Figure 6.6B), but not in other regions. In 
general, the variation of peak stress around the diseased region was less than 5%, and stress 
level in the sac remained nearly unchanged when the stents were overlapped differently (Figure 
6.6).  
6.3 Results 115 
 
 
 
Figure 6.6 Structural stress level of a representative node in different location changed when 
two stents were overlapped differently in the circumferential (A) and axial (B) direction. 
Flow-diverting outcome  
After the first stent was deployed, the mean sac time-averaged velocity decreased from 39.8 
mm/s to 25.3 mm/s (36.4% reduction). The deployment of the second stent further reduced the 
mean sac time-averaged velocity. However, the reduction depended on the overlapping 
parameters in both circumferential and axial direction (Figure 6.7D&E). When cells of the two 
stents completely aligned with each other, e.g. the cases of 𝜃 being 0º and 18º, and D being -1, 
0 and 1, the further mean velocity reduction by the 2nd stent was ~10% (25.3 mm/s vs. 23.3±0.3 
mm/s). As long as there was separation between struts in the two stents, the further mean 
velocity reduction was prominent with further ~20% decrease (25.3 mm/s vs. 20.2±0.3 mm/s). 
Compared with the value before stent deployment, the mean sac velocity could be reduced by 
49.1%±0.7% under conditions with struts separation. 
  
6.3 Results 116 
 
 
 
Figure 6.7 Influence of the 2D overlapping pattern on the velocity reduction inside the aneurysm sac. Band plot of velocity without stent 
deployment (A); one stent deployment (B); and two stents deployment (C) at systole. The change of mean sac time-averaged velocity before 
and after two-stent MOUS deployment with different overlapping patterns in circumferential direction (D) and in axial direction (E). 
6.3 Results 117 
 
The mean time-averaged pressure in the sac decreased by 2.4% after the first stent was 
deployed and decreased by 5.1±0.9% when the second stent was deployed. Difference in stents 
overlapping had very minor influence on the pressure reduction. 
Also, the different 2D overlapping patterns had a little influence (~5%) on both mean TAWSS 
and OSI on the sac wall (Table 6.1). RRT at the proximal disease-free region where the flow 
fully developed was 8.5 Pa-1, changed to be 8.4 Pa-1 after the first stent was deployed and 
remained the same after the second deployment. When the first stent was deployed, RRT̅̅ ̅̅ ̅̅  in the 
sac increased from 1.29 to 3.13; it further increased to 4.90±0.75 after the second one was 
deployed; and the elevation (5.36±0.33) would be more prominent if the cases with complete 
stent cell alignment were excluded (Table 6.1).  
 
Table 6.1 Comparison of mean TAWSS, OSI, RRT̅̅ ̅̅ ̅̅  on the aneurysm sac after the deployment 
of 2-stent MOUS with different overlapping patterns. 
Variables  Overlapping parameters 
 𝜽 (º) 0 3 6 9 12 15 18   
TAWSS (Pa)  0.14 0.14 0.13 0.13 0.13 0.13 0.14   
OSI  0.32 0.34 0.35 0.35 0.35 0.35 0.32   
𝐑𝐑𝐓̅̅ ̅̅ ̅̅   3.81 4.92 5.55 5.40 5.61 5.57 3.81   
 D -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 
TAWSS (Pa)  0.14 0.13 0.14 0.13 0.14 0.14 0.13 0.14 0.14 
OSI  0.32 0.35 0.36 0.35 0.32 0.34 0.35 0.35 0.32 
𝐑𝐑𝐓̅̅ ̅̅ ̅̅   4.03 5.09 6.09 5.24 3.81 5.06 5.24 5.18 4.04 
 
The flow rates in side branches after the deployment of 2-stent MOUS under different 
overlapping patterns were listed in Table 6.2. The change of flow rate in the distal side branches 
(CA and SMA) were more prominent in the cases of large axial displacement (D=0.75 and D 
=1) than other overlapping patterns, because the orifices became partially covered by the 2nd 
6.3 Results 118 
 
stent. In general, the variation of flow rates in side branches is little (~1%) under different 
overlapping patterns. 
 
Table 6.2 Comparison of time-averaged flow rate in each side branch after the deployment 
of 2-stent MOUS with different overlapping patterns. (Unit: ×10-3ml/s; CA: coeliac artery; 
SMA: superior mesenteric artery; other side branches were intercostal arteries)  
Side branch   Overlapping parameters 
 𝜽 (º) 0 3 6 9 12 15 18   
1†  120 121 120 120 122 122 120   
2†  113 113 113 115 115 115 113   
3†  117 120 119 118 118 118 117   
4  52 53 52 52 52 53 52   
5†  76 75 78 77 77 75 76   
CA  156 157 156 157 157 157 156   
SMA  572 574 568 574 573 573 572   
 D -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 
1†  120 121 120 121 120 121 121 118 119 
2†  112 110 112 112 113 112 112 112 107 
3†  116 117 118 118 117 115 118 114 115 
4  52 53 52 52 52 51 52 50 49 
5†  76 75 73 73 76 74 73 68 70 
CA  156 156 158 157 156 156 157 154 151 
SMA  566 565 574 574 572 569 574 561 550 
† The orifice of these side branches was partially covered by the stent strut.  
 
6.3 Results 119 
 
6.3.3 Influence of 3D cross-stent structures 
Flow-diverting outcome  
The flow-diverting outcome after patient-specific virtual deployment of 1-stent, 2-stent, 3-stent 
and 4-stent MOUS have been reported in Section 5.3.3. Similar to the multi-layer MOUS, the 
single-layer compact models modulated the flow pattern and decreasing the flow velocity 
inside the aneurysm sac (Figure 6.8). After the deployment of 2-stent MOUS, the mean sac-
averaged velocity decreased from 39.8 mm/s to 20.2 mm/s, and the corresponding 2-stent 
compact model yield a similar mean velocity of 19.9 mm/s (Figure 6.8C). Compared to MOUS, 
the compact models led to slightly better performance (~5%) in flow velocity reduction (15.2 
vs. 16.0 mm/s for 3 stents, 13.7 vs 14.8 mm/s for 4 stents) (Figure 6.8C). 
In terms of the haemodynamics variables on the aneurysm wall (e.g. TAWSS, OSI and RRT̅̅ ̅̅ ̅̅ ), 
little difference (<5%) was observed between MOUS and compact models, as shown in Table 
6.3. The mean time-averaged pressure in the sac between MOUS and corresponding compact 
models were equivalent (relative difference <1%).  
Table 6.3 Comparison of haemodyamicvariables averaged on the aneurysm wall, between 
MOUS and corresponding compact models. 
Variables 2-stent 3-stent 4-stent 
  MOUS 
Compact 
model 
MOUS 
Compact 
model 
MOUS 
Compact 
model 
TAWSS 
(Pa) 
0.14 0.14 0.13 0.13 0.13 0.12 
OSI 0.40 0.40 0.44 0.43 0.44 0.44 
𝐑𝐑𝐓̅̅ ̅̅ ̅̅  4.90 4.82 17.77 17.79 18.80 18.91 
 
6.3 Results 120 
 
  
Figure 6.8 Comparison of velocity reduction between the MOUS and compact models. (A) Cross-sectional band plot of velocity without stent 
deployment at systole; (B) The local view of the flow velocity in the aneurysm sac before and after the deployment of the MOUS and 
corresponding compact models; (C) Comparison of the mean sac velocity between MOUS and corresponding compact models. 
 
6.3 Results 121 
 
Structural stress within aortic wall 
The structural stress level within the aortic wall after the deployment of corresponding compact 
models was lower than with MOUS, while varied on the different locations (Figure 6.9). In this 
study, the 2-stent compact model induced a peak structural stress about 14% lower than 2-stent 
MOUS, while the structural stress level within the sac wall (Figure 6.9, Node C) was about 6% 
lower. Similarly, after the virtual deployment of 3-stents compact models, the peak structural 
stress and sac wall stress were about 12% and 18% lower than MOUS, respectively. The 4-
stent compact model reduced the peak stress level about 14%, and 23% in the sac wall, 
compared to the 4-stent MOUS. 
 
 
 
Figure 6.9 Comparison of structural stress level at different location after the deployment of 
MOUS and corresponding compact models, with different number of stents. The results of 4 
different nodes are plotted in different colours, where MOUS is plotted with solid line and 
compact models are plotted with dash line. 
6.4 Discussion 122 
 
6.4 Discussion 
As discussed in Chapter 5, the overall porosity was considered as a key factor of the flow-
diverting outcome 313–316. The low-porosity MOUS induces significant flow velocity reduction 
inside the aneurysm sac and increased RRT on the sac wall, which promotes the formation and 
development of thrombus 295. The Monte Carlo simulation evaluated the uncertainty of the 
overall porosity of MOUS under random deployment (Figure 6.4). In average, the second stent 
reduced the porosity by 14% (from 69.3% to 83.2%), while the third and fourth stent led to a 
further reduction of overall porosity by 12% and 9%, respectively. The less reduction induced 
by the third and fourth stent was expected, as overlapping coverage between stents struts 
increased. Overlapping pattern has an influence on the overall porosity of MOUS (Figure 6.4), 
while the variation was small for most cases (standard deviation of PDF < 2.5%). In rare cases 
where the subsequent stent was aligned completely to previously deployed stents, the overall 
porosity remains the same. 
The parameter study of two-stent MOUS demonstrated the limited influence of 2D overlapping 
patterns on flow-diverting outcome. Apart from the cases with complete cells alignment (𝜃 
being 0º and 18º; and D being -1, 0 and 1), porosity (68.1±0.002%) varied very little with the 
change of 𝜃 or D. Despite of the difference in the resultant cell shape, different 𝜃 or D (except 
the cases of complete alignment) induced a negligible change in the velocity (Figure 6.7), 
pressure, OSI and RRT in the sac, which could be attributed to the fact that flow modulated by 
the stent strut was limited in a narrow region around the strut. Moreover, the difference in 
overlapping pattern also had limited influence on the stress concentration around the diseased 
region (Figure 6.6). These findings suggest that endovascular surgeries using MOUS can be 
performed with less attention to the overlapping pattern as the chance to achieve a complete 
cell alignment is low.  
Interestingly, the 3D multi-layer MOUS did not show better performance on the flow-diverting 
outcome compared to the corresponding single-layer structure (Table 6.3). Instead, a further 
velocity reduction (~5%) was observed in the 3-stent and 4-stent compact models than MOUS 
(Figure 6.9). This could be explained by the elimination of 3D ‘tunnels’ across the dimension 
6.4 Discussion 123 
 
of thickness, during the projection of multiple layers to single-layer structure, which reduced 
the effective porosity.  
The structural stress concentrations within landing zones after MOUS deployment might have 
undesirable effects, such as continued aneurysmal degeneration of the aortic wall  56,57. One 
case of aneurysm recurrence was observed in this cohort, which might be related to the 
structural stress concentrations. As demonstrated in Figure 6.10, the TAA was managed with 
a 4-stent MOUS and the aneurysm sac was thrombosed in 1 month. The aneurysm disappeared 
on 1-month and 12-month follow-up CTA (Figure 6.10B&C), however, recurrence near the 
proximal landing zone was observed on the 36-month follow-up images (Figure 6.10D). 
 
Figure 6.10 An example of aneurysm recurrence near the landing zone after MOUS treatment. 
(A) TAA identified on pre-operative CTA; (B) Full occlusion of aneurysm after 1 month; (C) 
Full occlusion of aneurysm after 12 months; (D) Recurrence of an aneurysm near the proximal 
landing zone. 
6.5 Conclusion 124 
 
To improve treatment outcome, the number of stents used for MOUS should be decided by 
considering the trade-off between the flow-modulation and the structural stress concentrations. 
The advanced imaging modalities such as PET have the potential to evaluate inflammation in 
the aorta and the risk of high stress concentrations 338. 
On the other hand, a better design of the stents used for the MOUS procedure is desirable to 
reduce the stress concertation. By comparing multi-layer MOUS to the single-layer compact 
model (Figure 6.9), it was observed that the artificially ‘merged’ structure could reduce the 
stress concentrations by more than 10%, while keeping equivalent flow-diverting outcome. 
This suggests that, the use of less number of stents with lower porosity could reduce the 
MOUS-induced structural stress concentrations, providing similar overall porosity. The 
material and size of the stents could also be optimised, to provide more compliance and achieve 
better conformity to the aorta. However, the stent should provide efficient fixation to the 
landing zones, avoiding the longitudinal shortening and displacement of stent which has been 
reported with aneurysm expansion and rupture 121,122,124. 
Despite these interesting findings, several limitations exist in the present study: (1) The 
limitations of patient-specific simulation as discussed in Chapter 5; (2) Considering the 
computational costs, only 16 representative overlapping patterns were investigated in the 
parameter study of 2-stent MOUS. However, it should be reasonable to infer the result of more 
complex overlapping patterns from the representative overlapping patterns. 
6.5 Conclusion 
In conclusion, porosity is the dominant factor for the flow-diverting outcome while cross-stent 
structures had limited influence. Better stent design with lower porosity and more material 
compliance might help reduce the structural stress concentrations and related adverse outcome. 
 
 Chapter 7 Pathological effects of high structural 
stress concentrations† 
As discussed in Chapter 6, MOUS may induce local high structural stress concentration within 
the landing zone, which might be related to adverse clinical outcomes. However, the correlation 
has not been validated in experiments. There was an animal study performed by our research 
group which studied the feasibility of creating atherosclerosis in rabbit models by collars. 
Similar to stents, the collars would induce high stress concentrations and trigger pathological 
remodelling of the arterial wall. In this chapter, a retrospective analysis of previous animal 
experiments was perform to investigates the pathological effects of abnormal environment 
induced by implanted device. 
7.1 Introduction 
Cardiovascular diseases (CVD) are the leading cause of death and disability worldwide 238. 
Atherosclerosis and aneurysms are the two most common forms of CVD, both of which share 
predisposing risk factors and exhibit similar inflammatory cell infiltrates at lesion sites 4. Under 
physiological conditions, arterial walls are subject to mechanical loading, which is considered 
important during the formation and development of these diseases 249,339. Mechanical loads can 
be classified into vascular structural stress (VSS) due to arterial expansion driven by blood 
pressure, and wall shear stress (WSS) acting on the lumen surface due to blood flow.  
                                                 
† The author of this dissertation carried out all of the work described in this chapter unless specified otherwise. The animal 
experiments were performed by Dr Joseph Bird from Department of Radiology, University of Cambridge. The MRI 
segmentation and biomechanical model reconstruction were performed by Dr Zhongzhao Teng from Department of Radiology, 
University of Cambridge. 
7.1 Introduction 126 
 
Blood flow at sites with bifurcation or bend is disturbed due to the irregular luminal geometry, 
leading to alterations in both the magnitude and direction of WSS. The association between 
supraphysiological WSS and the malfunctioning of endothelial cells, and therefore the 
initialisation and development of CVD has been extensively studied 249.  
Endothelial cells are actually subject to both WSS and VSS, while other cells within the 
extracellular matrix are subject to VSS only. The magnitude of VSS is much higher than that 
of WSS (100-1000 kPa vs. 0.01-0.10 kPa) 340. VSS is a complex mechanical stress state that 
acts in circumferential, axial and radial directions within the arterial wall, causing structural 
deformation of individual cells. VSMCs are capable of sensing pulsatile stretch through 
multiple mechanisms and transduce it into intracellular signals, resulting in the modulations of 
gene expression and cellular functions, such as proliferation, apoptosis, migration and 
remodelling 341,342. High VSS is also correlated with both increased MMP expression 343 and 
macrophage accumulation 344, which are associated with structural degradation of ECM. The 
role of VSS in atherogenesis was proposed more than half a century ago based on the fact that 
atherosclerosis is found in arteries and not in veins, and it is likely to develop at ostia of 
branches where high VSS concentration occurs 345,346. Experimental studies in rabbits showed 
that reduction of arterial intramural stress inhibited atherosclerosis 347,348. 
The deployment of stents will change the local geometry of lesion regions, as well as alter the 
biomechanical environment. Foreign body stent placement might lead to endothelium injury 
and inflammatory response, triggering pathological remodelling of the arterial wall 349. Most 
of previous studies focused on the role of WSS 350–352, while the role of VSS has been least 
explored 353.  
In this study, constrictions were created in rabbit carotid arteries by implantation of collars. In 
vivo MRI was performed to visualise the configuration and to reconstruct the 3D geometry. 
FSI analyses were performed to quantify both WSS and VSS near the constrictions. 
Histopathological stains were used to visualise the plaque distribution and the local 
inflammatory status. The association between WSS, VSS and presence of plaque is reported. 
7.2 Materials and methods 127 
 
7.2 Materials and methods 
7.2.1 Rabbit treatment protocol 
This study was performed according to Home Office animal welfare guidelines and had 
approval from the local ethics committee. Nine New Zealand White rabbits were put on a high 
fat diet that comprised of 0.3% cholesterol and 4.7% palm oil in standard rabbit chow for 16 
weeks. Drinking water was available all the time. A non-occlusive, silastic collar (ARK 
Therapeutics, Finland) was implanted on the left common carotid artery (CCA) after the 
animals had been on the high fat diet for two weeks (Figure 7.1A). The collar had two narrow 
points constricting to 2 mm external diameter (Figure 7.2A) and produced a partial occlusion 
of the artery. The proximal constriction was named Constriction 1# and the distal constriction 
was named Constriction 2#. 
7.2 Materials and methods 128 
 
 
 
Figure 7.1 In vivo magnetic resonance imaging showing rabbit carotid arteries with and without 
collar and corresponding blood velocity measurements. (A) Time of flight (TOF) image showing 
both arteries on the coronal plane; (B)&(C): T1-weighted image showing both arteries in the 
transverse plane at the location between two constrictions and above the Constriction 2#; (D)&(E): 
The magnitude and phase images obtained from phase contrast imaging; (F) The blood velocity 
profile on the collared side with a 20-ms interval between each frame; (G) The mean velocity on 
both sides. 
The collar was placed carefully using standard veterinary surgical and aseptic techniques. The 
right CCA was exposed at the same time during the operation but without collar deployment. 
Rabbit health status was assessed by serological analysis and body weight. Blood cholesterol, 
high density lipoprotein (HDL), low density lipoprotein (LDL) and triglyceride levels were 
measured to monitor the dietary intake of cholesterol and lipids.  
7.2 Materials and methods 129 
 
 
Figure 7.2 Reconstructed 3D geometry based on baseline MR images, images of arteries removed from the animals and corresponding Cluster 
of Differentiation 68 (CD68) stain, and calculated flow parameters and mechanical loading within the structure. (A) Schematic drawing showing 
the collar geometry and dimension; (B) MR-based 3D geometry reconstruction; (C) Artery with collar and the corresponding contralateral artery; 
(D) CD68 stain showing macrophages in brown; (E) Expanded view of TAWSS, OSI and RRT; (F) Peak VSS and Mean VSS in the artery wall. 
7.2 Materials and methods 130 
 
7.2.2 Magnetic resonance imaging 
MR imaging was performed on bilateral carotid arteries of all rabbits three days after 
implantation of collars with bespoke 3D time of flight (Figure 7.1A), T1-weighted spin echo 
(Figure 7.1B&C), T2*-weighted gradient echo and phase contrast (Figure 7.1D&E) sequences 
to visualise carotid artery structure and measure blood flow velocity (Figure 7.1F&G). The 
imaging was performed on a Bruker 4.7T system with a surface coil (Bruker 25-mm coil) with 
ECG-gating. The silastic does not produce any MR signal and the collar therefore appeared 
hypointense in both T1-weighted and T2
*-weighted images. Following implantation, the void 
within the collar became filled with interstitial fluid (Figure 7.1A&B) which was hyperintensed 
in both T1-weighted and T2
*-weighted images. The 3D TOF was performed with 0.3 mm 
isotropic resolution. T1-weighted and T2
*-weighted imaging were performed with a through 
plane resolution of 2.0 mm and an in-plane resolution of 0.13mm. 
7.2.3 Fluid-structure interaction analysis 
The lumen, outer wall, collar and interstitial fluid were identified manually with reviewing 
TOF, T1-weighted and T2*-weighted images using VascularView (Tenoke Ltd., Cambridge, 
UK). The 3D geometry was reconstructed and meshed using hexahedral elements.  
Determination of computational starting shape  
Since images were acquired at the pressurised condition with axial stretch 354, shrinkage was 
therefore necessary to recover the stretch-free configuration to generate the starting shape for 
the computational simulation 355. Axial shrinkage was set to be 15%, which was determined by 
the ratio of the arterial length before and after harvesting. The blood pressure (78-116 mmHg) 
and waveform were adopted from previous reports 356,357. Considering the constriction from 
the collar, radial shrinkages were different among the regions beyond the constrictions, at the 
constrictions and between the constrictions. The shrinkage for each section was determined 
such that when pressurised with mean blood pressure, the configuration matched with the one 
obtained from in vivo imaging. The radial shrinkage was 10.2±0.7%, 0.1±0.2%, 0.2±0.2% for 
each of the three sections, respectively. 
7.2 Materials and methods 131 
 
Fluid-structure interaction analysis 
After the shrinkage amounts were determined, the arterial lumen and outer wall contours and 
the slice thicknesses were updated accordingly. 3D geometry was reconstructed based on the 
updated configuration and meshed using hexahedral elements (Figure 2B). The Young 
modulus of silastic collar is 2.05 MPa and the Poisson's ratio is 0.35 as provided by the 
manufacturer. The arterial wall was assumed as a hyperelastic material and characterised by 
the modified Mooney-Rivlin model, and the material constants were fitted from previously 
reported experimental data 358. The interstitial fluid between the artery and collar was modelled 
as an incompressible gel with material constants set to be one-tenth of intraplaque haemorrhage 
(C1=0.02 kPa, D1=0.43 kPa and D2=0.53) 
359. The volume enclosed by the arterial lumen 
surface was defined as fluid domain, which was similarly meshed by hexahedral elements. 
Blood flow was assumed to be laminar, Newtonian, viscous, and incompressible. 
Incompressible Navier-Stokes equations with arbitrary Lagrangian-Eulerian formulation were 
used as the governing equations, 
 𝜌𝑏
𝜕𝒖
𝜕𝑡
+ [((𝒖 − 𝒖𝑔) ∙ ∇) 𝒖] = −𝜕𝑝 + 𝜇𝜕
2𝒖, ∇ ∙ 𝒖 = 0 (7.1) 
with loading conditions, 
 𝑝|𝑖𝑛𝑙𝑒𝑡 = 𝑝𝑖𝑛(𝑡), 𝑝|𝑜𝑢𝑡𝑙𝑒𝑡 = 𝑝𝑜𝑢𝑡(𝑡) (7.2) 
where u is the flow velocity, ug is the mesh velocity, p is the pressure, and  and 𝜌𝑏 stand for 
the blood viscosity and density, respectively. The motion of the arterial wall, collar and 
interstitial fluid was governed by,  
𝜌𝑤𝑣𝑖,𝑡𝑡 = 𝜎𝑖𝑗,𝑗     𝑖, 𝑗 = 1,2,3;  sum over 𝑗 (7.3) 
with boundary condition, 
 𝜎𝑖𝑗,𝑗 ∙ 𝑛𝑗|𝑜𝑢𝑡𝑡𝑒𝑟 𝑤𝑎𝑙𝑙 = 0 (7.4) 
in which 𝒗 is the displacement vector, 𝝈 is the stress tensor, and t denotes time. There was no 
relative displacement between collar, interstitial fluid and the arterial outer wall. No-slip 
condition between the flow-vessel interfaces was set as 
7.2 Materials and methods 132 
 
 𝒖|Γ =
∂𝒗
𝜕𝑡
|

 (7.5) 
and interaction actions between the fluid and solid was governed by 
 𝜎𝑖𝑗
𝑓 ∙ 𝑛𝑗|

= 𝜎𝑖𝑗
𝑠 ∙ 𝑛𝑗|

 (7.6) 
where  represents the inner wall of the vessel and the superscripts; f and s, stand for fluid part 
and solid part, respectively.  
The fully coupled FSI models were solved in ADINA 9.2.3 (ADINA R&D Inc.). It uses 
unstructured finite element methods for both fluid and solid models with nonlinear incremental 
iterative procedures. The governing finite element equations for both solid and fluid models 
are solved by the Newton-Raphson iteration method. The energy convergence criterion was 
used for solid domain during equilibrium iterations, with the relative energy tolerance being 
0.05 and relative force and moment tolerance being 0.01. For the fluid domain, the relative 
tolerances for velocities, pressure and displacements were set to be 0.06 for controlling the 
equilibrium. Both the displacements and velocities at the fluid-structure interface and the forces 
on the structure were checked for convergence. Relative displacement/velocity and force 
tolerances were both set to be 0.06. The 𝑝𝑜𝑢𝑡(𝑡) was adjusted such that the difference between 
the simulated flow rate and the one measured by phase contrast MR was less than 5%. Details 
of the models and methods are given by Bathe 235.  
Mechanical parameters for analysis 
In this study, effective stress was used to characterise the critical mechanical conditions within 
the arterial wall structure. WSS, OSI and RRT were used to characterise the haemodynamic 
environment, which have been widely suggested to be associated with atherosclerosis 
initialisation and development 303–306. 
7.2.4 Immunohistochemical processing and analysis 
All nine rabbits were sacrificed at the end of 16-week diet period. Carotid arteries on both sides 
of each animal were collected (Figure 7.2C). Implanted collars were carefully removed and 
constriction points were marked. Following the standard immunohistochemical procedure, 5-
7.2 Materials and methods 133 
 
μm slices were made for Haematoxylin and Eosin (H&E) and Cluster of Differentiation 68 
(CD68) stains, from three different regions: 1) Proximal: proximal to the Constriction #1 with 
a 1-mm gap on the collared side; 2) Distal: distal to the Constriction #2 with a 1-mm gap on 
the collared side; 3) Contralateral: similar levels on the contralateral side. Each histological 
slide was scanned and digitised using NanoZoomer (Hamamatsu Photonics, Hamamatsu, 
Japan) at x40 mode. 
 
 
Figure 7.3 A representative image showing wall and plaque segmentation (area marked in 
yellow showing the region with plaque and the one in grey is wall; MWT is the maximum wall 
thickness and MTH=( d1+d2+d3+d4+d5)/5 is the mean wall thickness of the healthy section) 
An in-house software developed in Matlab 2018a (The Mathworks, Inc., MA, USA) was used 
to perform quantitative histological analysis. Each CD68 image was processed with a semi-
automatic support vector machine classifier 360 to segment and detect macrophages. Density of 
macrophage within the arterial walls were quantified from the segmentation results. 
Segmentation parameters of the classifier were optimised with the help of Ms Nichola Figg, 
who has more than 15 years of experience in histopathological analysis of diseased arterial 
tissues. Moreover, plaque area ratio (PAR), maximum wall thickness (MWT) and the mean 
thickness of healthy (disease free) section (MTH) were measured manually in NDP Reviewer 
(Hamamatsu Photonics, Hamamatsu, Japan) (Figure 7.3). PAR is defined as the ratio between 
area in yellow (plaque) and the wall (area in grey and yellow). MWT is the largest thickness 
7.3 Results 134 
 
along the lumen and MTH is defined as the mean value of five sampling points d1, d2, d3, d4, 
and d5, as shown in Figure 7.3.  
7.2.5 Statistical analysis 
The normality was assessed by Shapiro Wilk test. The difference in plaque characteristics and 
mechanical variables at different regions were evaluated by Wilcoxon signed rank test. The 
correlations between plaque characteristics and mechanical variables were assessed using 
Spearman correlation test. The statistical analysis was performed in MATLAB (MathWorks, 
Inc.). A significant difference was assumed if p<0.05. 
7.3 Results 
The final weights, triglycerides, total cholesterol, LDL and HDL levels at the end of 16-week 
high fat diet were listed in Table 7.1. The stenosis caused by the collar at Constriction #1 was 
30.4±11.6% and 34.8±12.2% at Constriction #2. No significant difference was found between 
the two constrictions (p=0.324). 
 
Table 7.1 Weight and cholesterol levels after 16-week high fat diet 
Weight (kg) 5.04±0.20 
Total cholesterol (mmol/L) 1.525±0.465 
LDL (mmol/L) 0.525±0.222 
HDL (mmol/L) 0.665±0.157 
Triglycerides (mmol/L) 0.675±0.310 
 
7.3.1 Location-dependent histological features 
Presence of plaque was defined as plaque area ratio exceeding 5%. From the histological slides, 
15 plaques were found on the collared sides, eight from regions proximal to Constriction 1# 
and seven from regions distal to Constriction 2#. In comparison, only five plaques were found 
on the contralateral sides (p=0.003).  
7.3 Results 135 
 
Plaques on the collared side either proximal to Constriction 1# or distal to Constriction 2# 
tended to be bigger and more inflammatory than those on the contralateral side, with higher 
plaque area ratio (PAR), maximum wall thickness (MWT), mean thickness of healthy section 
(MTH) and density of macrophages (Figure 7.4). Plaques proximal to Constriction 1# were 
bigger than those distal to Constriction 2#, while with a similar level of inflammatory burden 
(Figure 7.4). 
 
 
Figure 7.4 The comparison of plaque morphological and inflammatory features at different 
location. (A) Plaque area ratio (PAR); (B) Maximum wall thickness (MWT); (C) Mean wall 
thickness of the healthy section (MTH); and (D) The density of CD68-positive macrophage.  
7.3 Results 136 
 
7.3.2 Location-dependent mechanical characteristics 
A representative case showing mechanical parameters on the collared side and corresponding 
contralateral side was illustrated in Figure 7.2E&F. The lumen surface was opened and mapped 
to a plain surface for visualisation. Quantitative comparison of the mechanical variables among 
different regions corresponding to the histological sites was demonstrated in Figure 7.5. 
 
 
Figure 7.5 The comparison of mechanical parameters among different regions. (A) Minimum 
time averaged wall shear stress (TAWSS); (B) Maximum oscillatory shear index (OSI); (C) 
Maximum relative residence time (RRT); (D) Peak vessel structural stress (VSS) during one 
cardiac cycle; (E) Mean VSS. 
 
  
7.3 Results 137 
 
Flow variables 
As shown in Figure 7.2E, flow parameters during one cardiac cycle, including TAWSS, OSI 
and RRT were all location-dependent. TAWSS was highest at the constriction points due to 
their narrowest dimension and it was lowest in the expanding region right after each 
constriction. The distributions of OSI and RRT were similar. Both of them were lowest at the 
sites with constriction, and highest in the expanding region right after each constriction. The 
values of WSS, OSI and RRT in the region proximal to Constriction 1# and in the middle 
region between the two constrictions were moderate.  
The minimum TAWSS, and maximum OSI and RRT in the region proximal to the Constriction 
1#, distal to Constriction 2# and on the contralateral side were quantitatively compared in 
Figure 7.5A-C. Minimum TAWSS in the region proximal to Constriction 1# was significantly 
higher than the one in the region distal to Constriction 2#. Both maximum OSI and RRT in the 
region proximal to Constriction 1# were significantly lower than the two in the region distal to 
Constriction 2#. The highest minimum TAWSS, and lowest maximum OSI and RRT appeared 
on the contralateral side.  
Structural stress within arterial wall 
The vessel structural stress was shown in Figure 7.2F. VSS is dependent on location (x, y, z) 
and time (t), that is, VSS=VSS(x, y, z, t). In this study, it was transformed into cylindrical 
coordinate system (r, θ, z). Both peak and mean values were used to characterise the structural 
loading, that is, 
Peak VSS = max
𝑡
{max
𝑟
[VSS(𝑟, 𝜃, 𝑧, 𝑡)]}  
Mean VSS = mean
𝑡
{max
𝑟
[VSS(𝑟, 𝜃, 𝑧, 𝑡)]} 
(7.7) 
As shown in Figure 7.2F, both of Peak VSS and mean VSS were lowest between the sites of 
constriction and highest near the constriction points. Arteries on the contralateral had the lowest 
Peak VSS and Mean VSS. In the quantitative analysis of the three regions, these two structural 
stress reached their highest level in the region proximal to Constriction 1#, while Peak VSS 
and Mean VSS were moderate in the other two regions (Figure 5D&E). 
7.4 Discussion 138 
 
7.3.3 Relations between local mechanical parameters and plaque features 
In the region distal to Constriction 2#, both maximum OSI and RRT were associated with PAR 
significantly with ρ being 0.76 (p=0.040) and 0.81 (p=0.025), respectively. Moreover, both of 
them were also associated with the density of macrophage with ρ being 0.85 (p=0.012) and 
0.83 (p=0.016), respectively. However, minimum TAWSS was not significantly correlated to 
neither PAR nor macrophage density. None of the flow parameters, including TAWW, OSI 
and RRT were associated with MWT or MTH. In the region proximal to Constriction 1#, none 
of the flow parameters were associated with PAR, MWT, MWH, or macrophage density. 
On the contrary, Peak VSS was associated with PAR, MWT and macrophage density with ρ 
being 0.88 (p=0.003), 0.72 (p=0.037), and 0.70 (p=0.043), respectively. Mean VSS was 
associated with PAR and macrophage density with ρ being 0.80 (p=0.014) and 0.75 (p=0.025), 
respectively. However, none of the Peak VSS and Mean VSS were associated with any plaque 
feature in the region distal to Constriction 2#. 
7.4 Discussion 
To the authors’ best knowledge, this is the first study to quantify the association between local 
mechanical loadings, including both WSS and VSS, and morphological and inflammatory 
features of atherosclerotic plaques, by deploying collars on rabbit carotid arteries to create two 
constrictions. Atherosclerotic plaques were found in the regions proximal to Constriction 1# 
and distal to Constriction 2#. Traditional WSS hypothesis could well explain the appearance 
of plaque in the region distal to Constriction 2# due to the turbulent flow. However, it failed 
for those found in the region proximal to Constriction 1#, where TAWSS was higher, and OSI 
and RRT were lower. Regression analysis demonstrated that high VSS associated well with 
lesion found in the region proximal to Constriction 1# (Figure 7.6). This study implied that 
both WSS and VSS could initialise atherosclerosis.  
7.4 Discussion 139 
 
 
Figure 7.6 Wall thickness of both diseased and healthy section was associated with local vessel 
structural stress. 
It has been reported that arteries tend to maintain a certain stress level within the wall by 
adjusting its thickness according to local intramural blood pressure 361,362. Following this 
principle and Laplace’s law (stress×thickness=pressure×radius), increased stress will stimulate 
wall thickening when pressure and radius remain constant, which is confirmed by this animal 
study. As shown in Figure 7.6 that VSS correlated very well with local wall thickness either at 
the location with plaque or free of plaque.     
In general, previous studies on the biomechanics of atherosclerosis focused largely on the 
pathological effects of abnormal flow environment on the vascular physiology. In contrast, 
there is a lack of comprehensive studies aimed to understand the effects of structural stresses 
and stretches on the pathophysiology of the vessel wall. The preferable appearance of 
atherosclerotic plaque at the location with bifurcation or bend has been thought to be mainly 
due to malfunctioned WSS. However, high VSS also appears in these locations. Only fluid-
structure interaction analysis can quantify WSS and VSS simultaneously. However, due to 
irregular wall geometry at these locations, nonlinear material properties and large 
deformations, it is challenging to obtain a successful FSI simulation due to convergence. 
7.5 Conclusion 140 
 
Perhaps this is one of the main reasons that major efforts have been spent on seeking the 
pathological impact of WSS, while the role of VSS has been ignored.     
The physiological stretch of the vessel wall ranges between 5-10%, while high magnitudes of 
stretches more than 20% are considered pathological363. Physiological stretch is beneficial for 
regulating the normal cellular processes such as angiogenesis364,365, cell proliferation366 and  
extracellular matrix (ECM) remodelling367. In contrast, pathological stretches as observed in 
hypertension, could activate pathways leading to CVD. Although hypertension is often 
associated with excessive levels of WSS, it is also equally responsible for elevated levels of 
structural stress, particularly at arterial regions with a highly tortuous shape and at bifurcations 
368. Increased structural loadings are known to cause phenotypic adaptations in vascular smooth 
muscle cells  that transform them to dedifferentiated states 341,349,369. This indicates that, 
structural loading has the capacity to modulate gene expression, as well as various functions of 
the VSMCs, such as proliferation, survival and ECM remodelling 339. In vivo experiments also 
demonstrated the role of pathological stretch in endothelial dysfunction and cell apoptosis370. 
Abnormal levels of stretch is known to promote expression of inflammatory genes, such as 
inducible nitric oxide synthase (iNOS) 371. Pathological stretch was reported to promote pro-
inflammatory response by cytokines (IL-8, IL-6) 372 and MCP-1373, resulting in the 
accumulation of inflammatory cells. It was also reported that pathological stretch could disturb 
the integrity of ECM by activating macrophage cells to produce MMPs such as MMP-1, MMP-
3 and MMP-9 371,374,375. 
Despite interesting finding in this study, there are several limitations: (1) The MRI sequences 
were susceptible to flow artefacts, which may induce error on the geometry reconstruction; (2) 
The FSI analysis did not consider residual stress within the arterial wall, which might 
overestimate the structural stress; (3) The computational model did not consider the biological 
reaction to the collar, which might also contribute to the inflammatory response.  
7.5 Conclusion 
In conclusion, this animal study confirmed the pathological role of structural stress induced by 
implanted device, which is associated with the arterial wall remodelling and inflammatory 
7.5 Conclusion 141 
 
response. Therefore, structural analysis is important for a comprehensive assessment of the 
biomechanical environment after the deployment of endovascular devices. 
 
 Chapter 8 Conclusion 
The pathological development of AA is a chronic and multifactorial process, characterised by 
the structural degradation of ECM within the aortic wall. The microstructural changes lead to 
weakening material properties, associated with an increased risk of AA rupture. The stretch-
stress curves from experimental tests can be parameterised into material constants of the 
hyperelastic model. Bayesian inference framework provides a robust estimation of these 
coefficients, reflecting the characteristics of tissue fibre network. The experimental results 
provide essential constitutive relations for a reliable assessment of the biomechanical factors. 
Image-based FEA provides a non-invasive method to simulate the virtual deployment of 
MOUS and predict the flow modulation, which is useful for understanding the mechanism of 
MOUS and making personalised pre-surgical plans. The MOUS provides an efficiently-low 
porosity, which modulates the flow patterns in the aneurysm, promoting the aneurysm 
thrombosis and shrinkage. The patency of side branches is preserved, as the stent struts 
coverage has minimal effects on the flow rate. The flow-diverting outcome is dominated by 
the overall porosity, while the various overlapping patterns have limited influence, providing 
a robust performance of MOUS. However, structural stress concentrations appear within the 
landing zones after the deployment of multiple stents. The elevated structural loading might 
lead to inflammatory response within the aortic wall, along with adverse pathological effects. 
Computational analysis showed that a more compact design of MOUS could reduce the 
structural stress concentrations, which provides insight into the design optimisation of next 
generation MOUS. More investigations and long-term follow-up are essential before this novel 
technique can be widely applied into clinical practice.  
8.1 Limitations 144 
 
8.1 Limitations 
Despite the interesting findings presented in this dissertation, there remains a few limitations 
that merit discussion.  
In the material tests, the uniaxial loading was applied, while biaxial loading conditions are 
more realistic in physiological conditions 285,376,377. However, useful information can be still 
obtained from uniaxial tests with appropriate data interpretation 378. The modified Mooney-
Rivlin SEDF is an isotropic model, where the microstructure was not explicitly included. The 
information of fibre distribution can be integrated into the SEDF with additional terms 379. 
The aneurysm model was reconstructed from CTA images, where the border between thrombus 
and vessel wall was not clear. A more accurate model could be established from MRA images 
with better soft-tissue contrast.  In the computational analysis, the virtual deployment of MOUS 
was simulated in a quasi-static style followed by the CFD with fixed wall conditions. The 
residual stress was not considered as it cannot be measured using current non-invasive 
approaches 380. The dynamic motion of stents after the deployment was not considered due to 
heavy computational cost. Flow rate waveform at the aortic inlet is adapted from literature, 
which could be replaced with patient-specific assessment, by in vivo measurement from 
Doppler ultrasound or PC-MRA 157,381. The patient-specific simulation and parameter studies 
were based on a representative aneurysm model. The findings should be further validated in 
more patient-specific models using the developed framework.  
8.2 Potential future directions 
Future work should focus on addressing the limitations mentioned above, as well as translating 
the image-based biomechanical analysis into clinical practice. 
The Bayesian framework can be extended to compare the performance of different constitutive 
models in describing the experimental data, and select the most suitable model 273. This 
provides more flexibility and accuracy in modelling different types of diseased tissue. Given a 
large amount of samples, Bayesian hierarchical modelling can be used to describe the change 
8.2 Potential future directions 145 
 
of mechanical behaviour during the disease process 382. This could provide a tool to evaluate 
the uncertainty of material property and the influence on biomechanical analysis at a population 
level. 
In addition to the pre-surgical planning, image-based biomechanical analysis could be also 
applied to real-time assessment during the intervention. The contrast concentration on the DSA 
images provides the information of the flow field, which has the potential to assess the 
haemodynamic environment within the aneurysm 383–385. This could help surgeons to optimise 
the surgical plan using the real-time assessment. 
Considering the possible structural stress concentrations within landing zones, the design 
optimisation is an essential step before MOUS is widely used. More compliant stents with 
better conformity to the aortic geometry should be preferred. On the other hand, the possible 
fretting corrosion between the struts of overlapping stents should be investigated, since it may 
enhance the incidence of stent rupture 114,386,387. 
 
  
Appendix 146 
 
Appendix 
Histology segmentation   
A semi-automatic MATLAB platform was developed to segment the collagen and elastin fibres 
on PSR stained and EVG stained images respectively. The histology slice was scanned using 
a NanoZoomer (Hamamatsu Photonics, Japan) and digitalised to RGB images for 
segmentation. First, a ROI was manually drawn and the pixels outside the ROI were removed. 
Then the cropped image was transformed into L-a-b colour space. A threshold was 
automatically selected to remove the white background by applying the Otsu’s method on the 
lightness channel 388,389. Next, the threshold for segmenting collagen from PSR stained image 
was chosen by applying the Otsu’s method on the green–red channel. The threshold for 
segmenting elastin from EVG stained image was chosen by applying the Otsu’s method on the 
green channel. An example of collagen segmentation by using the platform was demonstrated 
in Figure 4.10.  
The automatically segmented results of both PSR and EVG stained images were reviewed by 
NF, who has over 15 years of experience in histological analysis of diseased arterial tissues. 
 
Figure S1 The semi-automatic MATLAB platform that was used to compute the densities 
of all microstructural components. Left is the raw image with a yellow ROI drawn manually. 
Middle is the image after removing the white background. Right is the image with a green 
label masking the background tissue. 
Appendix 147 
 
Quantification of component percentages   
Based on above segmented results, the component percentage of each slice was computed as:  
𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝐴𝑟𝑒𝑎 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 =  
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑃𝑖𝑥𝑒𝑙𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑖𝑥𝑒𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑇𝑖𝑠𝑠𝑢𝑒 𝑅𝑒𝑔𝑖𝑜𝑛
× 100%  
Quantification of waviness and dispersion of collagen fibres 
Based on the segmented results from the PSR stained image, the waviness and dispersion were 
computed. Considering the heterogeneous distribution of collagen fibres, 16 square patches 
with 0.18 mm (200 pixels) in length were independently and randomly drawn in the ROI. The 
final waviness (𝜔) and dispersion (𝜅) of the overall image was computed as the average of 
results from the 16 patches. For each square patch, each disconnected collagen fibre was first 
recognised from the segmented mask.  
The major axis length and perimeter of each fibre was calculated using the function 
Regionprops in Matlab. The waviness of each fibre is computed as: 
𝑊𝑎𝑣𝑖𝑛𝑒𝑠𝑠 =  
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟
2 × 𝑀𝑎𝑗𝑜𝑟 𝑎𝑥𝑖𝑠 𝑙𝑒𝑛𝑔𝑡ℎ 
− 1  
The dispersion of collagen fibres was computed by using the previously proposed algorithm390. 
The distribution of the collagen fibre orientations were characterised with the 2D planar form 
of the transversely isotropic and -periodic von Misses distribution 391–393. The von Misses 
distribution with a probability density function of orientation, 𝜌(𝜃) was assumed: 
𝜌(𝜃) = 4√
𝑏
2𝜋
exp [𝑏(cos(2𝜃) + 1)]
erfi(√2𝑏)
  
Appendix 148 
 
where 𝑏 is the concentration parameter and erfi(𝑥) is the imaginary form of the error function, 
which were fitted from the orientations . The dispersion parameter 𝜅 was computed as: 
𝜅 =
1
4
∫ 𝜌(𝜃)𝑠𝑖𝑛3𝜃𝑑𝜃
180
0
  
The values of 𝜅 are between and including 0 and 1/3, where 0 means an isotropic distribution 
and 1/3 means a uniform distribution. 
 
 
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