1-D Mathematical Modeling to Study the Mechanics of Pregnancy and Preeclampsia, Lymphatics, and Peripheral Artery Disease
Author(s)
Sedaghati, Farbod
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Abstract
The dissertation explores the critical role of mathematical modeling in understanding
complex biological systems. Despite extensive research, certain conditions such as preeclampsia
(PE), lymphedema, and peripheral arterial disease (PAD) remain insufficiently studied. These
disorders are intricately connected to the mechanical environment, involving factors like fluid
transport, solid mechanical responses, and growth and remodeling mechanisms. For example, in
PE, impaired vascular remodeling of the uterine vasculature leads to reduced blood flow to the
placenta, causing hypertension and associated complications. Hemodynamics, essential for normal
physiological function, is often examined through mathematical models. While simpler models
fail to capture axial wave behavior, higher-order models, such as 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 dissertation aims to evaluate the utility of 1-D mathematical models in investigating biological
phenomena influenced by wall phenotype, such as during pregnancy. The goal is to validate
whether these models, combined with established concepts like growth and remodeling, can
analyze biological events where the vascular system significantly affects fluid transport
mechanisms.
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Date
2024-07-22
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Text
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Dissertation