Multiscale Heart Simulation with Cooperative Stochastic Cross-Bridge Dynamics and Cellular Structures.

In this paper, we introduce a multiscale heart simulation method that integrates the three-scale phenomena from the microscopic stochastic sarcomere kinetics to the macroscopic heartbeat via the mesoscopic myocardial cell assembly. In sarcomere kinetics, the stochastic behavior of the myosin heads in the cooperative cross-bridge formation and the strain-dependent head rotations are directly simulated using a Monte Carlo (MC) method. This stochastic sarcomere model is coupled with contractile myofibril elements in a finite element (FE) cell assembly model. The cell assembly model is further coupled with a macroscopic FE heart model by means of the homogenization method. We bridge the large gap in the time step sizes between the MC and FE models with an idea based on impulse equilibrium between the sum of the stretches over the whole myosin arms and the contractile stress of the myofibril element. In the application of the homogenization method to the meso-macro coupling, a novel approach is introduced to deal with nearly incompressible material. In this approach, the mixed FE formulation is naturally extended to the homogenization method. The robustness and accuracy of our approach are verified through numerical experiments, and some interesting simulation results are given showing the benefit of such a multiscale simulation tool in physiological studies of hearts.