Date of Award

Summer 5-31-2021

Document Type

Dissertation/Thesis

Degree Name

B.S. Mathematics

Department

Mathematics

First Advisor

Brooks Emerick

Abstract

Certain congenital heart defects can lead to the development of only a single pumping chamber, or ventricle, in the heart instead of the usual two ventricles. Individuals with this defect undergo a corrective, three-part surgery, the third step of which is the Fontan procedure, but as the patients age, their cardiovascular health will likely deteriorate. Using computational fluid dynamics and differential equations, Fontan circulation can be modeled to investigate why the procedure fails and how Fontan failure can be maximally prevented. Borrowing from well-established literature on RC circuits, the differential equation models simulate systemic blood flow in a piecewise, switch-like fashion [Chugunova et al., 2019]. Here, we develop numerical solvers for both ordinary and partial differential equations to model Fontan circulation, with a special focus on system stability and parameter analysis. We also develop a numerical model that simulates Fontan circulation for patients with cardiovascular conditions, such as high blood pressure, that modify vessel area. Overall, our goal is to accurately model blood flow and determine parameters of interest to decrease the diagnosis time of Fontan failure and/or improve the surgical technique to prevent the failure from occurring.

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

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