Model Order Reduction of Cardiac Monodomain Model using Deep Autoencoder Based Neural Networks
Keywords:Autoencoder, Cardiac monodomain model, deep learning technique, dynamic mode decomposition, proper orthogonal decomposition, reduced order modeling, semi-implicit scheme
The numerical study of electrocardiology involves prohibitive computational costs because of its complex and nonlinear dynamics. In this paper, a lowdimensional model of the cardiac monodomain formulation has been developed by using the deep learning method. The restricted Boltzmann machine and deep autoencoder machine learning techniques have been used to approximate the cardiac tissue’s full order dynamics. The proposed reduced order modeling begins with the development of the low-dimensional representations of the original system by implementing the neural networks from the numerical simulations of the full order monodomain system. Consequently, the reduced order representations have been utilized to construct the lower-dimensional model, and finally, it has been reconstructed back to the original system. Numerical results show that, the proposed deep learning MOR framework gained computational efficiency by a factor of 85 with acceptable accuracy. This paper compares the accuracy of the deep learning based model order reduction method with the two different techniques of model reduction: proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The model order reduction deploying the deep learning method outperforms the POD and DMD concerning the modeling accuracy.
P. C. Franzone, L. F. Pavarino, and B. Taccardi, “Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models,” Mathematic Biosciences, vol. 197, pp. 35-66, 2005.
S. Gandhi and B. J. Roth, “A numerical solution of the mechanical bidomain model,” Computer Methods in Biomechanics and Biomedical Engineering, vol. 19, pp. 1099-1106, 2016.
C. F. Wang, “Efficient proper orthogonal decomposition for backscatter pattern reconstruction,” Progress in Electromagnetics Research, vol. 118, pp. 243-251, 2011.
C. Corrado, J. Lassoued, M. Mahjoub, and N. Zemzemi, “Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology,” Mathematical Biosciences, vol. 272, pp. 81-91, 2016.
R. Khan and K. T. Ng, “DMD-Galerkin model order reduction for cardiac propagation modeling,” Applied Computational Electromagnetics Society Journal, vol. 33, pp. 1096-1099, 2018.
X Geng, D. C. Zhan, and Z. H. Zhou, “Supervised nonlinear dimensionality reduction for visualization and classification,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 35, pp. 1098-1107, 2005.
M. K. Lee and D. S. Han, “A numerical solution of the mechanical bidomain model,” Electronics Letters, vol. 11, pp. 655–657, 2012.
Y. Wang, H. Yao, and S. Zhao, “Auto-encoder based dimensionality reduction,” Neurocomputing, vol. 184, pp. 232-242, 2016.
R. Khan and K. T. Ng, “Higher order finite difference modeling of cardiac propagation,” IEEE International Conference on Bioinformatics and Biomedicine (BIBM), Kansas City, MO, pp. 1945- 1951, 2017.
M. Ethier and Y. Bourgault, “Semi-implicit time discretization schemes for the bidomain model,” SIAM Journal on Numerical Analysis, vol. 46, pp. 2443-2468, 2008.