0 Biomechanical Modeling of the Arterial Fluid-Structure interaction in hemodynamic Mostafa Salehi [email protected] Fluid-Structure Interaction (ASEN 5519) Instructor: Professor Felipa Spring 20041 Introduction With regard to the properties of the arterial wall mechanics was established with the different kind of works and investigations. While most of these studies either theoretically and experimentally were shown that the mechanical behavior of arteries changed with age and disease, healthy human and animal arteries exhibited nonlinear inelastic, anisotropic behavior, radially heterogeneous, load-rate insensitive, expand upon cooling and shrink upon heating, However, very little work has been done specifically on the pulmonary artery and changes that occur due to pulmonary hypertension. For detailed discussion of the morphological structure or histology of arteries and relevant references are refer to Humphrey (1995) and Holzapfel et al. (2000). They are focus on the microscopic structure of arterial walls composed of three distinct layers. The Intima, the Media and the aventitia. They discuss the constituents of arterial wall from the mechanical perspective and emphasize those aspects, which are important to my research interested in constitutive issues. Histological, the media is an inhomogeneous material consisting of a highly organized three-dimensional network of elastin, vascular smooth muscle cells and collagen with extracelluar matrix protoglycans. As a recent study by Dorbrin (1999) has fund, it behaves mechanically as if its material properties were homogeneous. This is important to my research because the adventitia is composed of elastin and collagen fibrils that remain slack until higher levels of pressure are reached and at very high pressure it serves to reinforce the arterial wall and prevents the artery from overstretch and rupture. Most arterial wall models have assumed that the wall material is homogeneous and that the artery is a cylindrical membranes or a thick-walled tube. Associated material parameters are given for each layer base on a Fung-type Strain-energy function. Briefly those results show that the media and the adventitia are anisotropic; that the media is stiffer, more non-linear, and subjected to higher stresses than commonly assumed; and2 both layers are stiffer in the axial direction than in the tangential direction. My proposed is constitutive model materials parameters and implies to pulmonary arteries adventitia and media. Rachev (1998) have studied to propose a relatively simple but general mathematical model, which account for both the geometric and mechanical remodeling of arteries in response to induced hypertension. Theoretical predictions of the model are compared against available experimental data to assess the validity of certain new hypotheses concerning the driving stimuli and the interrelation between competing shear-dependent and wall stress-dependent. It is most likely that the compliance-dependent processes during arterial adaptation. The flow of a fluid in a compliant tube has received much attention because of its relevance in the applications, particularly in functioning in the mechanics of blood circulation; the fluid-structure interaction is of the primary interest in modeling blood flow, because of the arterial wall remodeling process and the subsequent altered flow pattern in pathological states. Wave propagation in arteries has been examined Experimentally, but in vivo studies in vascular flows are difficult, expensive and limited to easily accessible arteries. The fluid blood and the arterial structure constitute an intrinsically coupled system. Its dynamics is adequately described by a set of differential equations which Should be solved by a fully coupled method. Because of many physiological and clinical implications, several differential models of fluid-structure interaction have been developed and analyzed. Problem Statement and Research Objectives Study biomechanical properties of pulmonary arteries under normal and hypertensive conditions. The objectives of this research are: Analyze theory of biomechanics of the soft-tissue; Define pertinent function and relationships. Formulation for fluid-structure interaction in the mechanics of blood circulation. Main objective of this study is to get an insight of the3 complex relationship between arterial wall deformations, potential flow in a large arterial vessel and arterial pressure. Define pertinent function and relationships (Mechanical Mathematical computation) and apply theory to used for experimental measurements. Technical Background The artery is modeled as a two-layer thick-walled tube. The two layers are the media and the adventitia. The media is the middle layer of the artery, composed of smooth muscle cells a network of elastic and collagen fibrils and elastic laminae which separate the media into a number of fiber-reinforced layers. The adventitia is the outer layer composed primarily of thick bundles of collagen fibrils arranged in helical structures and fibroblast cells. A significant amount of prior work has been performed to elucidate the mechanical properties of the arterial wall. The general consensus of these studies is that the artery exhibits the following behavior: nonlinearly inelastic, anisotropic, radially heterogeneous, load-rate insensitive, expansion upon cooling and shrinkage upon heating. Other studies have shown that these properties can change significantly with age or disease. However, very little work has been done specifically on the pulmonary artery and changes that occur due to pulmonary hypertension. Pulmonary Hypertension Pulmonary arterial hypertension, a debilitating disease in which the blood pressure in the pulmonary artery rises above normal levels, leads to fatigue, shortness of breath, chest pain and fainting and may become life-threatening. The progressive disease is often misdiagnosed and can have a low survival rate. Hypertension either causes, or is induced by, morphological and functional changes in the vascular, which is include a thickening of the arterial wall and altered stiffness and contractile response. Liu and Fung (1989) reported that the primary distinguishing characteristic of hypertension is thickened vascular wall which is to say relations thickness to radius ratio .It is suggested that for analyze hypertensive and normotensive arteries we need