Predicted effect of chronic apical aneurysms on the passive stiffness of the human left ventricle.

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Abstract
A theoretical analysis of the human left ventricle in diastole was performed to evaluate the quantitative effect of an aneurysm on local fiber elongation in the ventricular wall and to establish quantitative relationships between chronic aneurysm size and stiffness and overall ventricular stiffness. The myocardium was assumed to be a homogeneous, isotropic, essentially incompressible material which exhibits large, nonlinear, elastic deformation. A finite element procedure was used which allows explicit representation of aneurysms in the ventricular wall. Even when the myocardium near the aneurysm has normal elasticity, the restraining influence of the aneurysm results in a substantial reduction in end-diastolic length of normal muscle fibers located in this area. This reduction in length places these fibers at a less favorable position on the Starling curve for developing tension and shortening during systole. Given that the diastolic pressure-volume (P-V) relationship in the normal ventricle is of the form, dP/d(V/V0) = .alpha.P + .beta., (V0 = cavity volume at zero transmural pressure) it was found that, in the presence of fibrous and fibrous-muscular, apical, transmural aneurysms encompassing up to 20% of the wall volume, the parameter .alpha. increases linearly with aneurysm size. The ventricular secant modulus, .DELTA.P/(.DELTA.V/ESV) (.DELTA.P = difference between end-diastolic pressure and lowest observed diastolic pressure, .DELTA.V = angiographic stroke volume and ESV = end-systolic volume) remains normal with aneurysms encompassing up to approximately 10% of the wall volume, even though the diastolic P-V curve was shifted substantially to the left relative to the normal P-V curve. For larger aneurysms this modulus increases rapidly with aneurysm size.