Neurodegenerative dementia often has multiple types of underlying pathology, for example, beta-amyloid, misfolded tau, chronic neuroinflammation and neurodegeneration may coexist in Alzheimer's disease. However, the relationship between them is often unclear, in other words, whether one pathology is upstream or downstream of others can be very difficult to investigate directly. This is partly because the underlying pathology in dementia may precede detectable symptoms by several years if not decades. The time scale associated with disease progression in dementia generally exceeds that in conventional longitudinal imaging studies in humans, so it is difficult to directly observe the temporal ordering of different pathologies. Also, animal studies are not always transferable to patients due to obvious differences between the two systems. To investigate the disease progression and relationships among underlying pathological changes, we propose a novel computational modeling approach for multimodal MRI and PET inspired by reaction rate equation in chemical kinetics. We also discuss the possibility and prerequisites to use cross-sectional data to generate preliminary hypothesis for future longitudinal studies. It has been shown that the rate of change in some biomarkers can be approximated by the average trajectory across patients at different stages of disease severity in cross-sectional studies. The relationship modeled in our approach is akin to that in the control theory, and can be assessed by demonstrating that the presence of one disease related biomarker predicts dynamics in another. We argue that the proposed framework has important implications for trials targeting different pathologies in dementia.