In vivo stresses in the human left ventricular wall: Analysis accounting for the irregular 3-dimensional geometry and comparison with idealised geometry analyses

Abstract

The in vivo stresses in the left ventricular wall are of interest to a cardiologist in evaluating the state of response or adjustment of the left ventricle to a heart disease. To determine the instantaneous in vivo stresses, we employ data consisting cineangiocardiographic determination (in single plane antero-posterior projection) of the instantaneous dimensions of the left ventricle and the left ventricular and chamber pressure. At each frame, an irregular planor outline of the LV is obtained from the X-ray film; each half of the frame is revolved into an irregular shell chamber of revolution, which is analysed for the wall stresses (due to the chamber pressure loading) by finite element procedure. The characteristic features of the finite element procedure are: (i) the left ventricular shell is divided into shell ring elements; the meridian of each element is represented by a 4th order polynomial passed through closely spaced points on the cineangiographically obtained single plane contour of the left ventricle, (ii) the geometrical properties of the shell are found from the derivatives of the equation of the meridional curve, (iii) the governing equilibrium equations of a shell ring element include effects of bending and transverse shear deformation, (iv) Displacement method of solution is employed; this is essentially an application of Ritz method utilizing the principle of minimum total potential energy, ( v) the high order displacement polynomials that are employed in the analysis, provide good approximations for the displacements as well as for the stresses. The wall stress results obtained from finite element analysis are compared with the ventricular wall stresses obtained by Mirsky and Ghista (thick shell and exact elasticity, respectively) idealised geometry (ellipsoidal shaped) models of the left ventricle. The peak stress states obtained from the two models are nearly the same, with the idealised geometry models underestimating the peak circumferential stress at the apex. So the finite element analysis of the left ventricle is effectively able to incorporate the effect of variations in the curvature of the left ventricular wall boundary on the stress distribution across the wall thickness and on, the level of stress concentrations.