Mechanics and material properties of the heart using an anatomically accurate mathematical model

Abstract

Global and regional mechanics of the cardiac ventricles were investigated using an anatomicallyaccurate computational model formulated from concise mathematical descriptions ofthe left and right ventricular wall geometries and the non-homogeneous laminar microstructureof cardiac muscle. The finite element method for finite deformation elasticity was developedfor the analysis and included specialised coordinate systems, interpolation schemesand parallel processing techniques for greater computational efficiency.The ventricular mechanics model incorporated the fully orthotropic pole-zero constitutivelaw, based on the three-dimensional architecture of myocardium, to account for the nonlinearmaterial response of resting cardiac muscle, relative to the three anatomically relevant axes.A fibre distribution model was introduced to reconcile some of the pole-zero constitutiveparameters with direct mechanical properties of the tissue (such as the limiting strainsestimated from detailed physiological observations of the collagen helices that surroundmyofibres), whilst other parameters were estimated from in-vitro biaxial tension tests onthin sections of myocardium. A non-invasive approach to in-vivo myocardial materialparameter estimation was also developed, based on a magnetic resonance imaging techniqueto effectively tag ventricular wall tissue.The spatially non-homogeneous distribution of myocardial residual strain was accounted forin the ventricular mechanics model using a specialised growth tensor. A simple model of fluidshift was formulated to account for the changes in local tissue volume due to movement ofintramyocardial blood. Contractile properties of ventricular myofibres were approximatedusing a quasi-static relationship between the fibre extension ratio, intracellular calciumconcentration and active fibre stress, and the framework has been developed to include amore realistic model of active myocardial mechanics, which could be coupled to a realisticdescription of the time-varying spread of electrical excitation throughout the ventricularwalls. Simple volumetric cavity models were incorporated to investigate the effects of arterialimpedance on systolic wall mechanics.Ventricular mechanics model predictions of the cavity pressure versus volume relationships,longitudinal dimension changes, torsional wall deformations and regional distributions ofmyocardial strain during the diastolic filling, isovolumic contraction and ejection phasesof the cardiac cycle showed good overall agreement with reported observations derivedfrom experimental studies of isolated and in-vivo canine hearts. Predictions of the spatialdistributions of mechanical stress at end-diastole and end-systole are illustrated.