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Dynamic Mode Decomposition for the Monodomain Equation in the Neuro-Muscular System
Bearbeiter Moritz Widmayer
Betreuer Dr.-Ing. Nehzat Emamy
Prüfer Prof. Dr. rer. nat. habil. Miriam Mehl

The neuro-muscular system is a complex multiscale coupled system, for which some chemo-electro-mechanical models are available. Realistic simulations of such models are computationally extremely demanding. The 3D continuum mechanics problem, which describes the deformation of the muscle is coupled with the 1D problem, which describes the propagation of the action potential along muscle fibers. This propagation is well described by the monodomain partial differential equation (PDE). The PDE is coupled with a set of nonlinear ordinary differential equations (ODEs), which resemble ionic currents at the cell membrane. The ODEs result from either the Hodgkin and Huxley (1952) model or the more complex Shorten model. To achieve an accurate and stable solution of the ODEs, one requires very small time steps. On the other hand, the coupled simulations undergo large physical time intervals with frequent activation of the muscle fibers.

In order to accelerate the whole coupled simulation, we would like to extrapolate the solution of the monodomain equation in time instead of solving each activation period and find the activation parameter, which is required by the 3D continuum mechanics problem. The purpose of this project is to apply the higher order dynamic mode decomposion (HODMD) for the extrapolation in time.