Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Brianna D. Bingham - Jackson State University
Co-Author(s): Tor A. Kwembe, Jackson State University, Jackson, MS
In 2009, the 15th leading cause of death in the United States was the aortic aneurysm. Aortic aneurysms are particularly dangerous because the aorta is the largest artery in the human body, and damage to the aorta can threaten vital bodily functions. The walls of the artery are able to endure a large amount of pressure due to their muscular structure, but occasionally, a segment of the artery wall can weaken, allowing the pressure of the blood flow within the artery to push outward forming a bulge, known as an aneurysm. In this study, we have modeled the evolution and development of an aneurysm using the Camenschi-Fung type system of equations to study the fluid and elastic behavior and stress factors that lead to defects in the membrane, causing an aneurysm. The technique of pulse wave propagation is utilized to solve the Camenschi-Fung system of equations to determine the influence of the various initial and boundary conditions on the displacement components of the membrane wall, blood pressure, and velocity. Conclusions are made from these results concerning the evolution and development of aneurysms and the conditions that may lead to the prediction of rupture potential. The benefit of these results is rested on the fact that they can be used to develop noninvasive means of detecting aneurysms, treatment, and management of ruptured aneurysms.
Regarding future work, the Womersley number, a dimensionless number in biofluid mechanics, is known for determining the thickness of boundary layers. We intend to investigate the role that Womersley numbers can play in understanding the evolution, growth and prediction of rupture potential of an aneurysm. Specifically, how can we use Womersley numbers to characterize the instability of aneurysm walls or fluid flow within aneurysm regions? Also, how do the Womersley numbers describe the behavior of pulsation of waveform within aneurysm geometry?Not Submitted
Funder Acknowledgement(s): I would like to thank Jackson State University's LSMAMP Bridge to the Doctorate Program. This project is also funded by the NSF Grant DMS: 1330801 and the PSC NIH Biomedical Research Subgrant.
Faculty Advisor: Tor A. Kwembe, firstname.lastname@example.org