Modeling and Simulation with Higher-Order Finite Elements

Dr. Andrew McCulloch

The heart is a complex three-dimensional structure in which the biophysics of the cardiac action potential, and the mechanics of muscle cell contraction, interact to produce efficiently coordinated ventricular pumping. The aim of Dr. McCulloch's research is to develop and experimentally validate an accurate three-dimensional model of regional cardiac mechanics and electrophysiology and their mutual interactions. Three-dimensional finite element (FE) models of the heart are being developed by Dr. McCulloch's research group that include accurate descriptions of ventricular anatomy and myofiber architecture; the resting and contractile mechanical properties of myocardium; and the cellular dynamics of action potential propagation. To analyze the biological basis of electromechanical interactions in the intact heart, theoretical models of cardiac excitation-contraction coupling and mechanoelectric feedback are being incorporated by researchers into the continuum framework. The coupled models involve large-scale computations and are implemented on the IBM/SP Teraflop parallel supercomputer, Blue Horizon, by exploiting the structural parallelism of the underlying physical problem. These models will be used to investigate basic questions such as how stretch activated ion channels affect conduction patterns in the intact heart, and how altered pacing sequences affect ventricular pumping efficiency.

Dr. McCulloch's primary modeling tool is a large interactive finite element program, Continuity, that is specialized for three-dimensional problems in bioengineering and physiology, especially those in cardiac biology such as anatomic model fitting; active and passive ventricular mechanics; wall strain analysis from imaging; and action potential propagation. The program is written in FORTRAN and C with the high-level object-oriented scripting language Python used for component integration. We are currently working on a separate user interface client program for Continuity, including a graphical user interface, and integration of visualization tools developed by the Center investigators. Algorithms for wall stress analysis have been implemented for distributed memory parallel architectures and progress has been made by Dr. McCulloch's research group in parallelizing the collocation-Galerkin finite element methods for action potential propagation on the IBM/SP Teraflop parallel supercomputer, Blue Horizon at SDSC. Progress has also been made by their group in coupling electrical and mechanical models. A three-dimensional model of the left ventricle coupling FitzHugh-Nagumo membrane kinetics with a calcium activated model of systolic force development was recently described. When complete, this model will be deployed as a Continuity example on their web site, and will be useful for investigating the mechanical consequences of altered pacing sequences, an important problem in cardiac multichamber pacing. Parametric finite element anatomic models of the rabbit and dog ventricles and their 3D fiber architecture have been fitted to large data sets of morphological measurements. They have also been finely discretized into high-resolution regular grids suitable for finite difference modeling. These large data-sets are available from Dr. McCulloch's web server.