Fluid-multi-layered-structure interaction problems

University Of Houston, Houston TX

Investigators

Abstract

Fluid-structure interaction (FSI) problems arise in many applications. The widely known examples are aeroelasticity and biofluids. In biofluidic applications, such as, e.g., the study of interaction between blood flow and cardiovascular tissue, the coupling between the fluid and the relatively light structure is highly nonlinear, requiring sophisticated ideas for the study of their solutions. In the blood flow application, the problems are further exacerbated by the fact that the walls of major arteries are composed of several layers, each with different mechanical characteristics. No results exist so far that analyze solutions to fluid-structure interaction problems in which the structure is composed of several different layers. The proposed research takes a first step in this direction by proposing a program to study the existence of solutions to a class of FSI problems describing the interaction between a multi-layered structure and the flow of an incompressible, viscous fluid, giving rise to a fully coupled, nonlinear moving boundary, fluid-multi-structure interaction problem. The analysis relies on a novel, loosely coupled, partitioned, time-marching numerical scheme, and on novel compactness arguments providing convergence of the numerical scheme to a weak solution of the nonlinear fluid-multi-layered structure interaction problem. The proposed program opens up a new field within the area of FSI problems. This work brings to light several features that have not been studied before. In particular, this work reveals a new regularizing mechanism in FSI problems that is due to the presence of a fluid-structure interface with mass. The inertia of the fluid-structure interface regularizes the evolution of the entire FSI solution. This is an exciting, novel study requiring the development of original mathematical techniques motivated by an important biological application: the interaction between blood flow and human arterial walls. It is well-known that arterial walls are composed of several layers, each with different mechanical characteristics and thickness. The healthy physiology and the pathophysiology of the human cardiovascular system are significantly affected by the pulsation of arterial walls during each cardiac cycle. However, the interaction between the different arterial wall layers and their interaction with blood flow is still not completely understood. For example, recent developments in ultrasound speckle tracking methods revealed significant shear strain between the different layers of arterial walls in high adrenaline situations. The consequences of this phenomenon on the initiation of cardiovascular disease are yet to be understood. The proposed research makes a step in this direction by designing mathematical models, and by analyzing solutions of the mathematical models that capture fluid-structure interaction between blood flow and arterial walls in the case when arterial walls are modeled as multi-layered structures. No mathematical results exist so far in this area, and the proposed research opens up a new area in the field of fluid-structure interaction problems. The work proposed here promises to develop a strong partnership between the University of Houston, the University of Pittsburgh, the University of Zagreb, and the Texas Medical Center in Houston. The PI is a woman, and active recruitment of minorities and women to participate in this research is proposed.