Obesity, diabetes, and hypertension affect millions of people and are associated with cardiovascular mor- bidity and mortality. While blood vessel remodeling occurs under healthy conditions, and is modulated by cellular responses to hemodynamic and biochemical stimuli, this responsiveness to stimuli is reduced in many diseases. In fact, pathological structural remodeling of small blood vessels has emerged as a key contributor to the effect of these diseases, including driving high blood pressure, organ damage, and tis- sue ischemia. In particular, the abberrant remodeling of blood vessels observed in disease states is likely driven by the loss of normal function in endothelial cells, which are responsible for sensing hemodynamic and metabolic changes. Over the last decade, Pries, Secomb, and colleagues have developed a dynamic model of microvascular remodeling that is conceptually simple, yet based on biologically observed stimuli such as wall shear stress, circumferential stress, and metabolic demand. This elegant model captures key aspects of vascular remodeling by healthy vessels and has provided biological insight about the role of certain previously less appreciated factors influencing remodeling. We will mathematically model the effect of endothelial dysfunction on microvascular remodeling in obesity, diabetes, and hypertension, using the Pries-Secomb model as a basis. To do this, we will use a cellular-level biological understanding of endothelial dysfunc- tion in obesity, diabetes, and hypertension to guide development of mathematical descriptions of changes in endothelial function. These will be incorporated into the existing framework of the Pries-Secomb model for validation against experimental results. In this work, we will move between consideration of single vessel models, which allow thorough mathematical analysis of equilibrium solutions and remodeling dy- namics, and numerical simulation of small or large networks, which may capture more physiologically relevant phenomena. Multiple approaches will help to maximize our understanding of mathematical modeling results and how they capture experimental observations of microvascular remodeling. The overall goal of this work is to create a deeper link between mathematical modeling and experimental work in order to gain insight into the underlying biology of various disease states in order to work to- wards more effective interventions to treat diseases.
Changes in blood vessel remodeling that occur in prevalent diseases such as obesity, diabetes, and hy- pertension are thought to cause some of the morbidity associated with these diseases including organ damage and tissue ischemia. The proposed work aims to use experimentally-motivated, mathematical models of vessel remodeling to gain understanding of this process that would be difficult to obtain exper- imentally. Increasing our knowledge about the remodeling process will ultimately lead to more effective clinical interventions.
