To access this work you must either be on the Smith College campus OR have valid Smith login credentials.

On Campus users: To access this work if you are on campus please Select the Download button.

Off Campus users: To access this work from off campus, please select the Off-Campus button and enter your Smith username and password when prompted.

Non-Smith users: You may request this item through Interlibrary Loan at your own library.

Publication Date

2016-5

Document Type

Honors Project

Department

Mathematics and Statistics

Keywords

Mathematical models, Biomathematics, Cardiovascular system-Mathematical models, Differential equations, Mathematical modeling, Biomath, Cardiovascular system, ODEs, Applied mathematics

Abstract

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.

Language

English

Comments

[185] pages : illustrations (some color). Honors project, Smith College, 2016. Includes bibliographical references (pages 92-96)

Download

Smith Only:
Off Campus Download

Share

COinS