SUMMARY

Mathematical modeling, along with experimental tools, has demonstrated promising strategies in understanding, diagnosing, and treating pathophysiological conditions. Among different modeling approaches, wave propagation models, including 1-dimensional solid-fluid interaction models, have presented acceptable outcomes when compared to clinical or experimental data. In that regard, we will utilize a 1-D modeling approach along with other accepted paradigms, such as those applied in arterial wall mechanics, including growth and remodeling mechanisms and vasoactive responses, to study some aspects of three common human complications, including preeclampsia, lymphedema, and peripheral artery disease (PAD). The significance of this combined study is that these complications together affect more than 10% of the US population each year. For each physiological condition, a modeling framework will be developed based on fundamental physics laws and other governing equations, such as wall mechanics. Following the development of the model for each condition and based on the nature of the problem, available data sources, and accessibility of experimental methods, a practical technique or procedure will be used to validate the mathematical model. Thus, by the end of the study, three mathematical models that correspond to each physiological condition, along with the validation dataset, will be provided that most likely will shed light on the progression of each complication. For example, to develop the mathematical model of PAD, we will perform a ligation surgery on the femoral arteries of a mouse model and track the hemodynamic and vascular changes due to the controlled PAD conditions. This can be extrapolated to human studies to design better experiments to understand the PAD.