Refinements in Mathematical Models to Predict Aneurysm Growth and Rupture

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Abstract
The growth of aneurysms and eventually their likelihood of rupture depend on the determination of the stress and strain within the aneurysm wall and the exact reproduction of its geometry. A numerical model is developed to analyze pulsatile flow in abdominal aortic aneurysm (AAA) models using real physiological resting and exercise waveforms. Both laminar and turbulent flows are considered. Interesting features of the flow field resulting from using realistic physiological waveforms are obtained for various parameters using finite element methods. Such parameters include Reynolds number, size of the aneurysm (D/d), and flexibility of the aneurysm wall. The effect of non-Newtonian behavior of blood on hemodynamic stresses is compared with Newtonian behavior, and the non-Newtonian effects are demonstrated to be significant in realistic flow situations. Our results show that maximum turbulent fluid shear stress occurs at the distal end of the AAA model. Furthermore, turbulence is found to have a significant effect on the pressure distribution along AAA wall for both physiological waveforms. Related experimental work in which a bench top aneurysm model is developed is also discussed. The experimental model provides a platform to validate the numerical model. This work is part of our ongoing development of a patient-specific tool to guide clinician decision making and to elucidate the contribution of blood flow-induced stresses to aneurysm growth and eventual rupture. These studies indicate that accurately modeling the physiologic features of real aneurysms and blood is paramount to achieving our goal.