Mathematical Model of the Left Ventricle of the Human Heart and the Effect of Aortic Stenosis on Hemodynamics

One of the most common acquired heart defects is aortic stenosis, a continuously progressive disease characterized by limited mobility of the valves, their fusion, and a decrease in valve opening. With increasing life expectancy, the incidence of this disease increases, which makes it necessary to predict the valve’s operability and timely surgical treatment before complications occur. Objective, to develop a mathematical model of left ventricular function with varying degrees of aortic stenosis. The team of authors presents a mathematical model of the mechanics of the left ventricle of the heart, taking into account aortic stenosis, based on a geometric description of the cavity and separate consideration of the passive and active properties of the myocardium. The passive component of pressure is determined by a nonlinear exponential dependence on the deformation of the wall, the active component is a function of temporal activation describing the contraction cycle. The dynamics of the aortic valve is modeled by changing the effective area of the opening, taking into account the degree of stenosis. The blood flow through the valve is described by a zero-dimensional model that includes the contribution of pressure gradient, viscous drag, and inertia of the blood. The proper lumen area of the aortic valve is assumed to be 2.0 cm 2 , which corresponds to 0% stenosis. Numerical simulations were performed for degrees of stenosis of 0, 30, 50, and 70%. It has been shown that an increase in the degree of stenosis is accompanied by an increase in systolic pressure in the left ventricle (up to 210 mm Hg), an increase in the final systolic volume and a decrease in stroke volume by more than 50% in severe stenosis. The dependence corresponds qualitatively to the clinical concepts of the progression of aortic stenosis. The model can be used for parametric analysis of the influence of the mechanical properties of the myocardium and the degree of valvular obstruction on the pumping function of the heart, to decide on the need for surgery and the selection of an aortic valve prosthesis, taking into account the individual anatomical characteristics of the patient.