An anatomically-based computational study of cardiac mechanics and myocardial infarction

Abstract

An anatomically based computational model of the cardiac ventricles was developed. The model is based upon the pig ventricles, as the pig is now the principal large animal used experimentally. The model includes concise mathematical descriptions of the left and right ventricular walls and the basal skeleton geometries in rectangular cartesian coordinates. The non-homogeneous fibre and sheet microstructure is also incorporated. The finite element method for finite deformation elasticity was used to simulate the cardiac cycle and to investigate the global and regional mechanics. The deformation response showed good agreement with reported observations. For the physiological loading conditions chosen an ejection fraction of 48% was predicted with an apex-base shortening of approximately 4%. The large ejection fraction was achieved through an apex-base twist of 22.8 degrees and wall thickening of 33%. Predictions of the distributions of stress and strain in the ventricular myocardium are presented. A finite element model was used to interpret the results from a published experimental study of myocardial infarction. A nonlinear optimisation problem was solved to determine the parameters for a published proposal for an exponential constitutive law for infarcted myocardium. The suitability of the “pole-zero” constitutive law for myocardium to model infarcted myocardium was also investigated. The pole-zero formulation, which incorporates structural details of the myocardium, yielded strain distributions more similar to those measured experimentally. The effect of infarction upon the regional and global mechanics of the new porcine ventricular model was then examined. In order to accurately and efficiently represent the ventricular anatomy and the large spatial variations in the material properties and solution fields associated with myocardial infarction, several new techniques were developed. The hanging node method for high order cubic Hermite finite elements was developed to enable the use of localised mesh refinement. Mapping constraints, to enforce- continuity between high order elements with inconsistent parametric coordinates, were implemented to allow irregular mesh topology. Texture map evaluations were used to provide a method of prescribing the spatially varying constitutive parameters independent of mesh resolution . The new techniques and models have provided initial insights into the behaviour of infarcted myocardium, and a framework has been developed that can now be used for future studies of both physiologically normal and infarcted porcine hearts.