Model Order Reduction via POD-DEIM for the Estimation of Cardiac Conductivities

Huanhuan Yang, Alessandro Veneziani

Published 2016-03-17Version 1

Cardiac conductivity estimation in the monodomain model for electrocardiology is crucial for its use in patient-specific settings, because the model is strongly sensitive to the conductivity parameter. Efficient and reliable estimation of this parameter is challenging due to the high computational cost from the monodomain solver and to the difficulty on model reduction resulted from the specific features of potential propagation in cardiac tissues (including wave-front propagation dynamics). This paper aims at applying model reduction techniques to dramatically decrease the computational cost of solving the inverse problem of cardiac conductivity estimation. The Proper Orthogonal Decomposition (POD) approach is taken for forward model reduction, along with the Discrete Empirical Interpolation Method (DEIM) for tackling nonlinearity. A derivative-based optimization is then employed on the reduced model for conductivity estimation. In the application of this POD-DEIM combination, we effectively sample the parameter space based on polar coordinates and densify the appropriate region of the sample space utilizing Gaussian nodes. The computational effort is eventually reduced by at least 90%.