Mathematics and Statistics
Mathematical models, Biomathematics, Cardiovascular system-Mathematical models, Differential equations, Mathematical modeling, Biomath, Cardiovascular system, ODEs, Applied mathematics
Cardiovascular diseases are the single largest cause of death worldwide. This study presents four ordinary differential equation models describing the cardiovascular system. The models reflect a realistic coupling between the dynamics of the heart and the properties of the vascular system. The first model describes the dynamics of the cardiovascular system in the absence of stress. The second model considers the neurovascular systems and the regulatory feedback responses to exercise. Using the systemic model in the absence of stress, we modeled the increase in resistance associated with atherosclerosis and the reduced valvular resistance associated with mitral valve prolapse. Each model illuminated theories surrounding underlying mechanisms in each disorder and posed prospects for future study. All four model results compare favorably with experimental observations. The models reproduce well-known phenomena corresponding to the cardiovascular system as a whole.
Cyr, Jamie Alexandra, "An investigative study of cardiovascular abnormalities using mathematical models of the cardiovascular system and its regulatory mechanisms" (2016). Theses, Dissertations, and Projects. 1626.