(D-157) Comparison of Simulated Electrogram Signals in Healthy and Fibrotic Tissue Using the Bidomain and Monodomain Models

Introduction:: Atrial fibrillation (AF) is the most common arrhythmia in both men and women. It remains a significant cause of morbidity and mortality, primarily because of the significant symptoms produced and the sequelae of stroke and heart failure. Persistent AF (PsAF) has proven to be difficult to treat and is associated with progressive changes to the underlying structural and ionic properties of the atrial tissue due to different types of fibrosis. The clinical identification of both type and degree of fibrosis remains challenging and could benefit from new clinical electro-biomarkers involving recorded electrograms (EGMs). We are developing both bidomain and monodomain computational models to improve understanding of the effects of fibrosis on EGMs seen in diseased hearts. Although both models have been used extensively to study the heart, bidomain models are better able to account for blood (bath) loading on propagation and signal morphology but are computationally expensive compared to monodomain models. In this study, we explored the differences in the EGMs generated in monodomain and bidomain models in both simulated healthy and fibrotic tissue. Using various metrics of similarity, we found that the EGMs generated by monodomain models can reproduce the EGMs of the bidomain model in fibrotic tissue with lower computational cost.


Materials and Methods:: Unipolar EGM signals were simulated in four idealized three-dimensional tissue slabs (6cm x 4cm x .3cm): 1) monodomain model without fibrosis; 2) bidomain model with blood bath without fibrosis; 3) monodomain model with fibrosis; and 4) bidomain model with blood bath with fibrosis. Fibrosis was modeled as compact type based on Jakes et. al. 2019 with a 38% fibrosis density. The governing equations were solved using the finite element method with trilinear (hexahedral) elements of 250 microns in size, and a first-order semi-implicit backwards differentiation technique with a time step size of .005ms. In bidomain preparations, the blood bath under the slab had a 3mm thickness, and the bottom plane was grounded. Simulation run times were 160ms, enough time for the action potential plane wave to propagate completely. Both bidomain with bath and monodomain conductivities were adjusted to produce a conduction velocity of approximately 58 cm/s longitudinally. The membrane potentials and activation times (and extracellular potentials in bidomain simulations) were visualized in ParaView. Extracellular signals were obtained at a 10 kHz rate on a grid of points .5mm away from the bottom of the tissue into the blood bath. Simulations were run in parallel (176-220 cores) on the Dogwood cluster at the University of North Carolina at Chapel Hill.


Results, Conclusions, and Discussions:: For healthy tissue, signals were obtained at random points close to where propagation began, ended, and towards the middle of the slab. For fibrotic tissue, the same start and end points were chosen but also four additional points were included: a random point under a transmural fibrotic obstacle; under non-transmural obstacles at the top and at the bottom of the tissue; and under a relatively fibrosis-free region. Transmural obstacles in this context refer to obstacles that start in the endocardial side and end in the epicardial side. For the resulting waveforms, signal power spectrum, cross-correlation, and non-linear energy (NLE) profiles of the signals, root-mean squared value (RMSE), and peak signal-to-noise ratio (PSNR) value were obtained to measure the similarity between bidomain and monodomain EGMs. Electrograms were also characterized by obtaining EGM duration, number of deflections, and peak-peak amplitude. In most healthy case, these metrics were very similar. Major differences are seen in points close to the ends of the tissue due to the differences in the extent of the bath. In the monodomain approach, the bath is assumed to be infinite. Fibrotic simulations produced similar trends, except that signals had more deflections. In general, the macro behavior is very similar, but there are fewer deflections with steeper slopes in the bidomain than in the monodomain signals. The monodomain approach appears to be more sensitive to heterogeneities. Figures 1 and 2 show a sample healthy analysis and a fibrotic one, respectively, and Table 2 shows the summary of the fibrotic metrics. Overall, the monodomain model in idealized geometries generates EGMs with similar features to those generated by the bidomain model even in the presence of fibrotic heterogeneities at a fraction of the computational cost. Simulations will be repeated in realistic geometries with more realistic fiber orientations. The reduced computational cost of the monodomain model will enable its use to generate signals to train classifier algorithms and obtain robust bioelectric-markers of fibrosis.


Acknowledgements (Optional): :

References (Optional): : 1. Alfio Quarteroni, Toni Lassila, Simone Rossi, Ricardo Ruiz-Baier, Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function, Computer Methods in Applied Mechanics and Engineering, Volume 314, 2017, Pages 345-407, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2016.05.031.
2. . Benjamin S. Kirk, John W. Peterson, Roy H. Stogner, and Graham F. Carey. libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations. Engineering with Computers, 22(3-- 4):237--254, 2006. https://doi.org/10.1007/s00366-006-0049-3.
3. Centers for Disease Control and Prevention. Underlying Cause of Death, 1999–2018. CDC WONDER Online Database. Atlanta, GA: Centers for Disease Control and Prevention; 2018. Accessed March 12, 2020
4. Colli Franzone P, Pavarino LF and Scacchi S (2018) A Numerical Study of Scalable Cardiac ElectroMechanical Solvers on HPC Architectures. Front. Physiol. 9:268. doi: 10.3389/fphys.2018.00268
5. Courtemanche M. (1996) Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity. Chaos 6: 579-600.
6. Henriquez CS. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit Rev Biomed Eng. 1993;21(1):1-77. PMID: 8365198.
7. Jakes, David & Burrage, Kevin & Drovandi, Christopher & Burrage, Pamela & Bueno-Orovio, Alfonso & Santos, Rodrigo & Rodriguez, Blanca & Lawson, Brodie. (2019). Perlin Noise Generation of Physiologically Realistic Patterns of Fibrosis. 10.1101/668848.
8. Jordi Heijman, Henry Sutanto, Harry J G M Crijns, Stanley Nattel, Natalia A Trayanova, Computational models of atrial fibrillation: achievements, challenges, and perspectives for improving clinical care, Cardiovascular Research, Volume 117, Issue 7, 15 June 2021, Pages 1682– 1699, https://doi.org/10.1093/cvr/cvab138
9. Pagani, S., Dede', L., Frontera, A., Salvador, M., Limite, L. R., Manzoni, A., Lipartiti, F., Tsitsinakis, G., Hadjis, A., Della Bella, P., & Quarteroni, A. (2021). A computational study of the electrophysiological substrate in patients suffering from atrial fibrillation. Frontiers in Physiology, 12. https://doi.org/10.3389/fphys.2021.673612