Abstract:

A modified mass-spring system for simulating the passive and active elastomechanical properties of the myocardial tissue was presented in a previous publication. The previously presented results are combined with the method also published earlier to use continuum mechanics calculate passive forces in a mass-spring system directly starting from the energy density function of the stress-strain relation. An efficient method for volume preservation is presented and the implementation of an implicit time integration method for solving the systems equations of motion is described. The computational complexity of the system is analyzed and shown to be of O(n). At the end several simulations are conducted to demonstrate the method.

Abstract:

A volumetric mass-spring system for simulating the passive and active elastomechanical properties of the myocardial tissue is presented. A 3D computer model containing information about the fiber, sheet, and sheet-normal directions and about the modeled objects physiological properties, is used to initialize the systems structure.Using an electrophysiology model and a force development model, contracting forces are introduced to the systems elements at each time step of the simulation loop.Using the methods of continuum mechanics, suitable springs functions were derived analytically from the energy density function of describing the hyperelastic properties of heart. That eliminated the need of springs parametrization. An efficient method for volume preservation is used to ensure the conservation of the model's volume under deformation.Implicit time integration is implemented to solve the equations of motion, that improves the stability of the simulation and allows larger simulation time steps. An iterative solver that take advantage of the sparsity of the system's matrices is used and the systems complexity is shown to be of O(n) where n is the the count of the models elements.