A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

Abstract

Cardiac electrophysiology modelling deals with a complex network of excitable cells forming an intricated syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modelling and simulation incorporating spatially non-local couplings within a physiological reactiondiffusion scenario. We formulate, in particular, a space-fractional Bidomain electrophysiological framework, extending and generalising similar works conducted for the Monodomain model. We characterise one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra-and extra-cellular conductivities combinations. Our numerical study demonstrates that: (i) symmetry properties occur in the conductivity parameters space following the proposed theoretical framework; (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics; (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.

Sensitivity Analysis of Cardiac Alternans and Tachyarrhythmia to Ion Channel Conductance Using Population Modeling

“…We only considered the APD alternans occurring in the single-cell level. APD alternans can occur at the tissue level, and anisotropy plays an important role in the development of APD alternans by affecting the occurrence of APD alternans [ 31 , 32 , 33 ]. In addition, the ventricular tissue has heterogeneous characteristics: the myocyte of each tissue, such as the endocardium, mid-myocardium, and epicardium; and different conductances of ion channels [ 29 , 33 ].…”

Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach

“…The action potential model can take the form of highly detailed and physically based ionic models 4–6 or simplified phenomenological models 7–9 . In addition, for the sake of improving the accuracy of the excitation model, the diffusion can also be treated in a nonlinear manner 10,11 and made dependent on the stress 12 …”

“…The action potential model can take the form of highly detailed and physically based ionic models [4][5][6] or simplified phenomenological models. [7][8][9] In addition, for the sake of improving the accuracy of the excitation model, the diffusion can also be treated in a nonlinear manner 10,11 and made dependent on the stress. 12 Many research efforts have been dedicated to tackling the large computational burden required for electrophysiology problems and solving the bidomain equations.…”

Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation

“…Innovative multiscale and multiphysics formulations of cell-cell couplings aim at filling this gap. Nonlinear, stress-assisted, and fractional diffusion (Lin and Keener, 2010;Hurtado et al, 2016;Cherubini et al, 2017;Cusimano et al, 2020;Cusimano et al, 2021), ephaptic and gap junction-mediated couplings (Lenarda et al, 2018;Weinberg, 2017), cellular automata, and coarse-grained homogenized gap junction approaches (Treml et al, 2021;Irakoze and Jacquemet, 2021) represent the state-of-the-art in this direction. Furthermore, within the specific context of cardiac electrophysiology, recent studies are proposing novel methods of data estimation, data assimilation, and uncertainty quantification (Barone et al, 2020a;Barone et al, 2020b;Pathmanathan et al, 2020;Marcotte et al, 2021) to reproduce complex cardiac dynamics with a reduced computational cost.…”