Cardiac Modeling: From Ion Channels and Protein Pathways to Integrative Cell, Tissue and Organ Function

Abstract

Models of ventricular mechanics have been developed over the last 20 years to include finite deformation theory, anisotropic and inhomogeneous material properties and an accurate representation of ventricular geometry using finite element methods. The sequence of electrical activation in the myocardium is also modeled using ionic current based cellular models and reaction-diffusion equations at the tissue level solved with multi-grid techniques on a fine resolution mesh defined in the material coordinates of the deforming finite element mechanics mesh. This talk will describe the development of a finite element model of the geometry and fibrous-sheet structure of the pig myocardium applied to the solution of the equations governing cardiac electro-mechanics. The finite element model of the left and right ventricular myocardium, using geometric measurements from potassium arrested pig hearts, is defined in rectangular Cartesian coordinates with tri-cubic Hermite basis functions1. Measurements of fibre and sheet orientations2,3 are obtained with a purpose-built instrument that combines a 3D confocal microscope with a precision mill4. Passive material properties are measured on tissue segments using purpose-built biaxial and shear testing rigs and are fitted with the "pole-zero" constitutive law parameters5. Active myofilament properties are measured using isolated trabeculae and fitted with the HMT model6. Stress and strain distributions throughout the cardiac cycle are determined by solving the governing equations from finite deformation elasticity theory, using the above anatomical model and constitutive parameters, and with ventricular pressure boundary conditions7.