SUMMARY

Mathematical modeling plays a pivotal role in unraveling complex biological systems, ranging from cellular to organ levels. Despite extensive research, certain conditions like preeclampsia (PE), lymphedema, and peripheral arterial disease (PAD) remain insufficiently explored. These disorders are intricately linked to the mechanical environment, encompassing factors such as fluid transport, solid mechanical responses, and growth and remodeling mechanisms. For instance, in PE, compromised vascular remodeling of the uterine vasculature leads to reduced blood flow to the placenta, resulting in hypertension and related complications. Hemodynamics, crucial for normal physiological function, is often studied using mathematical models. While simpler models lack the capacity to capture axial wave behavior, higher-order models like 1-D models offer a balance between complexity and computational efficiency. These models account for spatial variations along each vessel axis, providing insights into cardiovascular regions with valves or bifurcations. The study aims to assess the utility of employing 1-D mathematical models to investigate biological phenomena influenced by wall phenotype, such as during pregnancy. The objective is to validate whether these models, coupled with established concepts like growth and remodeling, can analyze biological events where the vascular system significantly impacts fluid transport mechanisms. Ultimately, leveraging established mathematical frameworks and paradigms, the study endeavors to provide valuable insights into the underlying mechanisms governing disease manifestations.