title: Mechanics of left ventricular aneurysm.
abstract: When a coronary artery is significantly occluded, the left ventricular myocardial segment, which is perfused by that coronary artery, will become ischaemic and even irreversibly infarcted. An acute infarct has very low stiffness and if it involves the entire wall there is a risk of rupture; however, in the absence of such a critical situation, fibrous tissue is laid into the infarcted myocardial segment. Such an infarcted fibrotic myocardial segment will not be able to contract, and so generate tensile stress. The surrounding intact myocardium will contract and generate wall stress, thereby developing a high intra-chamber systolic pressure; the chronically infarcted and fibrotic segment will have to sustain this high chamber pressure. Its loss of contractility and the resulting reduced systolic stiffness relative to the intact segment, will cause it to deform into a bulge; this is an aneurysm. When a left ventricular chamber with an aneurysm contracts during the systolic phase, some blood also goes into the aneurysm, and this decreases the stroke volume; since the aneurysm wall is passive, stagnant blood flow prevails in the aneurysm itself, which in turn can give rise to the formation of a mural thrombus. These serious consequences provide a justification for the analysis of an infarcted left ventricular chamber, in order to predict the size of the aneurysmic bulge. Such an analysis is presented in this paper. To determine the left ventricular wall deformation, and the stress arising from infarction of a wall segment (which leads to a ventricular aneurysm) the left ventricle is modelled here as a pressurized ellipsoidal shell. Deformations of infarcted wall segments are computed for several damaged wall-thicknesses in left ventricles of different shapes. The analysis involves a derivation of equations for wall-stress equilibrium with the chamber pressure, and myocardial incompressibility before and after infarct formation. The equations are solved by the Newton-Raphson method (using elliptical integrals of the first and second kind). Of significance are the prognostic implications of the results, presented in the form of graphs, showing the dependence of tensile stress and the bulge of infarcted wall-segments, on the extent of damaged wall-thickness and the angle of infarct. Scaled illustrations of the bulge shapes, for various degrees of infarcts, are provided. The results indicate that for rupture of the ventricle, the percentage of infarcted wall-thickness and the shape of the ellipsoidal left ventricular chamber play more dominant roles than the angle-of-damage, or the extent of the infarct.
mesh_terms: D001696:Biomechanical Phenomena; D006322:Heart Aneurysm / Q000503:physiopathology*; D006352:Heart Ventricles / Q000503:physiopathology; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D013314:Stress, Mechanical