Constitutive Modeling of Cardiac Tissue Growth

Long term responses of the heart to e.g. infarction or surgical intervention are related to response of the tissue to changes in the mechanical environment. The tissue response is likely to involve (local) change of mass. Implementation of the associated inhomogeneous change in volume for a complex geometry is cumbersome. In the present study, we propose a computational framework for finite volumetric growth. The local stimulus for growth is determined from a simulation of beat to beat cardiac mechanics, assuming the tissue to be incompressible. The related local volumetric growth is translated in a global change of cardiac shape through a simulation of long term cardiac mechanics, assuming the tissue to be compressible. We illustrate the model by simulating growth in response to a deviation of end-diastolic sarcomeric strain from a set optimal value assumed to be preferred by the tissue. Inhomogeneity in the stimulus was reduced after inhomogeneous growth of up to 25%. The transmural redistribution of mass due to growth was found to alter an initially unphysiological linear transmural course in myofiber orientations to a more physiological course. We conclude that the model enables simulation of locally inhomogeneous growth in a realistic left ventricular geometry.