Interaction between Conformational Features and Hemodynamic Flows affecting Progression of Aortic Aneurysm and Dissection Disorders

Abstract

Hemodynamic flows are subjected to quasi-periodic velocity modulations. Currently, there is no methodology to predict the rate of progression of aortic aneurysm and dissection disorders. In this paper, the association between conformational features of the vessel wall and intra-luminal hemodynamic flows is explored to understand shear forces affecting the structural integrity of the vessel wall. The infinitesimal component of the vessel wall with cystic medial necrosis in tunica media is considered as nonlinear ballooning in the aorta with aortic aneurysm and dissection disorders. Assuming the hemodynamic system as a finite dissipative system, we frame the equation of the vessel wall of the aorta as well as lesion related to aortic aneurysm and dissection disorders. We introduce the main results for the generalized (3+1)-dimensional nonlinear evolution equation, using the Lie group of transformations method. Furthermore, we discuss the implications of traveling wave solutions and the shape, height, and width of the aneurysm to describe the impact of ballooning on hemodynamic flow in the aorta with aortic aneurysm and dissection disorders. We find that cumulative accretion of potential energy contributes to the creation of bright soliton in non-ballooned regions. The wave speed is minimum at the center of the ballooned region and maximum at the center of the non-ballooned region of the aorta. Interactions of topological defects and multi-breathers cause thrombus formation and/or turbulent flow. Interaction between breathers and standing waves is associated with thrombus formation.