This study aims to identify the significance of different blood viscosity models along with different Reynolds numbers in the simulation of blood flow in a multi-stenosed Left Coronary Artery (LCA) model. Computational fluid dynamics techniques were implemented to derive the hemodynamic outcomes of the diseased three-dimensional Left Coronary Artery (LCA) models comprising of multiple stenoses. The three-dimensional LCA model was reconstructed using the angiographic images of a healthy person, and three viscosity models, i.e., Carreau, Quemada, and Modified Cross, were considered for carrying out blood flow simulation through it. In this work, the behavior of blood velocity was analyzed by increasing the level of blockage in each of the considered blood viscosity model. It is noticed that the increase in velocity is in proportion with the rise in Reynolds number. This study shows that the Quemada model records the maximum velocity magnitude with the other two rheological models for higher Reynolds numbers. In this work, the area-averaged wall shear stress (AAWSS) along the left anterior descending segment between the areas of double stenoses for different Reynolds numbers was also analyzed. Two peaks of AAWSS were seen for all the Reynolds numbers indicating the two sections of constrictions. The obtained highest peak reflects the primary blockage. Also, an emphasis is laid to prefer the Carreau model over the Quemada and Modified Cross model. This work is purely computational based that might be helpful in providing an insightful understanding of blood flow conduct at the diseased stage in the cardiovascular system.

Introduction: Artery blockage is the most prevailing cause of Coronary Artery Disease (CAD). The presence of blockage inside the artery breaks the continuity of blood supply to the other part of the body and therefore causes for heart attack. Objective: Two different three-dimensional models namely; normal and 50% plaque are used for the numerical studies. Five inlet velocities 0.10, 0.20, 0.50, 0.70 and 0.80 m/s are considered corresponding to different blood flow conditions to study the effect of velocity on the human heart. Methods: Finite Volume Method (FVM) based Computational Fluid Dynamics (CFD) technique is executed for the numerical simulation of blood flow. Hemodynamic factors are computed and compared for the two geometrical models (Normal Vs. Blockage model). Results: Blood hemodynamic factor i.e. Area Average Wall Shear Stress (AAWSS) ranges from 4.1-33.6 Pa at the façade of the Left Anterior Descending (LAD) part of the Left Coronary Artery (LCA) for the constricted artery. Conclusion: The predominantly low WSS index is analogous to the normal artery affirms the existence of plaque. From the medical point of view, this can prove as an excellent factor for early diagnosis of CAD. Therefore, a hindrance can be created in the increasing frequency of Myocardial Infarction (MI). In future research we will adopt the unsteady flow with both rigid and elastic arterial wall.

Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean Value Theorem in Extended Generalized Mean Value Theorem then what would the new theorem look like. A sincere effort is done to develop this theorem. This theorem is named as Extended Generalized Flett's Mean Value Theorem.