Cardiac Mechanics Solvers

This page contains information on mechanics solvers for cardiac Chaste.

Mechanics solvers#

There are (as of the time of writing, Nov 2011) two mechanics solvers, an incompressible nonlinear elasticity solver and a compressible nonlinear elasticity solver, with the following hierarchy:

       AbstractNonlinearElasticitySolver
         ^                          ^
         |                          |
IncompressibleSolver        CompressibleSolver

(Here and throughout this page we shorten class names - for example CompressibleSolver is actually called CompressibleNonlinearElasticitySolver). See mechanics tutorials for more information on these classes.

Cardiac mechanics solvers#

Cardiac mechanics solvers solve mechanics problems for which the forcing comes from active tension developed in the tissue. Both incompressible and compressible versions are required, and the cardiac-specific part of a CardiacMechanicsSolver doesn’t really care whether it is a compressible or incompressible problem.

To complicate matters, there are two types of CardiacMechanicsSolver, an implicit solver and an explicit solver. The explicit solver basically uses active tensions computed at the previous timestep, whereas the implicit solver uses the current solution in computing the active tensions. (The appropriate choice of solver depends on the types of contraction model used). For more details on all of this see [1].

There are therefore four combinations: {incompressible,compressible} x {implicit,explicit}. The cardiac mechanics solvers are templated over the solver they should inherit from.

                IncompressibleSolver or CompressibleSolver
                                     ^
                                     |
                     template<class SOLVER>
                     AbstractCardiacMechanicsSolver : public SOLVER
                      ^                    ^
                      |                    |
  template<class SOLVER>                  template<class SOLVER>
  ExplicitSolver                          ImplicitSolver

To avoid CardiacElectroMechanicsProblem (the class used by a user) also having to be templated over the solver to use, which would be a pain for a user, all declarations of the methods in AbstractCardiacMechanicsSolver<SOLVER,DIM> are in AbstractCardiacMechanicsSolverInterface<DIM>, so that the problem class can just hold a pointer to the latter:

           AbstractNonlinearElasticitySolver
                           ^
                           |
      IncompressibleSolver or CompressibleSolver       AbstractCardiacMechanicsSolverInterface
                           ^                               ^
                           |                               |
                template<class SOLVER>                     |
                AbstractCardiacMechanicsSolver ____________|
                  ^                    ^
                  |                    |
template<class SOLVER>                template<class SOLVER>
ExplicitSolver                        ImplicitSolver

CardiacElectroMechanicsProblem<DIM> holds pointer to AbstractCardiacMechanicsSolverInterface<DIM> and allocates this to be one of

• ExplicitSolver<IncompressibleSolver,DIM>
• ExplicitSolver<CompressibleSolver,DIM>
• ImplicitSolver<IncompressibleSolver,DIM>
• ImplicitSolver<CompressibleSolver,DIM>

depending on whether the user wants compressible or incompressible, and based on which contraction model is used.

References#

[1] Pathmanathan, Pras, et al. “Cardiac electromechanics: the effect of contraction model on the mathematical problem and accuracy of the numerical scheme.” The Quarterly Journal of Mechanics & Applied Mathematics 63.3 (2010): 375-399. link