Unsupervised stochastic learning and reduced order modeling for global sensitivity analysis in cardiac electrophysiology models.

BACKGROUND AND OBJECTIVE: Numerical simulations in electrocardiology are often affected by various uncertainties inherited from the lack of precise knowledge regarding input values including those related to the cardiac cell model, domain geometry, and boundary or initial conditions used in the mathematical modeling. Conventional techniques for uncertainty quantification in modeling electrical activities of the heart encounter significant challenges, primarily due to the high computational costs associated with fine temporal and spatial scales. Additionally, the need for numerous model evaluations to quantify ubiquitous uncertainties increases the computational challenges even further. METHODS: In the present study, we propose a non-intrusive surrogate model to perform uncertainty quantification and global sensitivity analysis in cardiac electrophysiology models. The proposed method combines an unsupervised machine learning technique with the polynomial chaos expansion to reconstruct a surrogate model for the propagation and quantification of uncertainties in the electrical activity of the heart. The proposed methodology not only accurately quantifies uncertainties at a very low computational cost but more importantly, it captures the targeted quantity of interest as either the whole spatial field or the whole temporal period. In order to perform sensitivity analysis, aggregated Sobol indices are estimated directly from the spectral mode of the polynomial chaos expansion. RESULTS: We conduct Uncertainty Quantification (UQ) and global Sensitivity Analysis (SA) considering both spatial and temporal variations, rather than limiting the analysis to specific Quantities of Interest (QoIs). To assess the comprehensive performance of our methodology in simulating cardiac electrical activity, we utilize the monodomain model. Additionally, sensitivity analysis is performed on the parameters of the Mitchell-Schaeffer cell model. CONCLUSIONS: Unlike conventional techniques for uncertainty quantification in modeling electrical activities, the proposed methodology performs at a low computational cost the sensitivity analysis on the cardiac electrical activity parameters. The results are fully reproducible and easily accessible, while the proposed reduced-order model represents a significant contribution to enhancing global sensitivity analysis in cardiac electrophysiology.

Efficiency of semi-implicit alternating direction implicit methods for solving cardiac monodomain model.

It is well known that numerical simulations of the cardiac monodomain model require fine mesh resolution, which increases the computational resources required. In this paper, we construct three operator-splitting alternating direction implicit (ADI) schemes to efficiently solve the nonlinear cardiac monodomain model. The main objective of the proposed methods is to reduce the computational time and memory consumed for solving electrocardiology models, compared to standard numerical methods. The proposed methods have second-order accuracy in both space and time while evaluating the ionic model only once per time-step. Several examples using regular wave, spiral wave reentry, and nonsymmetrical scroll wave are conducted, and the efficiency of the proposed ADI methods is compared to the standard semi-implicit Crank-Nicolson/Adams-Bashforth method. Large-scale two- and three-dimensional simulations are performed.

A Simulation Study of the Role of Mechanical Stretch in Arrhythmogenesis during Cardiac Alternans.

The deformation of the heart tissue due to the contraction can modulate the excitation, a phenomenon referred to as mechanoelectrical feedback (MEF), via stretch-activated channels. The effects of MEF on the electrophysiology at high pacing rates are shown to be proarrhythmic in general. However, more studies need to be done to elucidate the underlying mechanism. In this work, we investigate the effects of MEF on cardiac alternans, which is an alternation in the width of the action potential that typically occurs when the heart is paced at high rates, using a biophysically detailed electromechanical model of cardiac tissue. We observe that the transition from spatially concordant alternans to spatially discordant alternans, which is more arrhythmogenic than concordant alternans, may occur in the presence of MEF and when its strength is sufficiently large. We show that this transition is due to the increase of the dispersion of conduction velocity. In addition, our results also show that the MEF effects, depending on the stretch-activated channels' conductances and reversal potentials, can result in blocking action potential propagation.

Effects of mechano-electrical feedback on the onset of alternans: A computational study.

Cardiac alternans is a heart rhythm instability that is associated with cardiac arrhythmias and may lead to sudden cardiac death. The onset of this instability, which is linked to period-doubling bifurcation and may be a route to chaos, is of particular interest. Mechano-electric feedback depicts the effects of tissue deformation on cardiac excitation. The main effect of mechano-electric feedback is delivered via the so-called stretch-activated ion channels and is caused by stretch-activated currents. Mechano-electric feedback, which is believed to have proarrhythmic and antiarrhythmic effects on cardiac electrophysiology, affects the action potential duration in a manner dependent on cycle length, but the mechanisms by which this occurs remain to be elucidated. In this study, a biophysically detailed electromechanical model of cardiac tissue is employed to show how a stretch-activated current can affect the action potential duration at cellular and tissue levels, illustrating its effects on the onset of alternans. Also, using a two-dimensional iterated map that incorporates stretch-activated current effects, we apply linear stability analysis to study the stability of the bifurcation. We show that alternans bifurcation can be prevented depending on the strength of the stretch-activated current.

Modeling and simulation of hypothermia effects on cardiac electrical dynamics.

Previous experimental evidence has shown the effect of temperature on the action potential duration (APD). It has also been demonstrated that regional cooling of the heart can prolong the APD and promote the termination of ventricular tachycardia. The aim of this study is to demonstrate the effect of hypothermia in suppressing cardiac arrhythmias using numerical modeling. For this purpose, we developed a mathematical model that couples Pennes' bioheat equation and the bidomain model to simulate the effect of heat on the cardiac action potential. The simplification of the proposed heat-bidomain model to the heat-monodomain model is provided. A suitable numerical scheme for this coupling, based on a time adaptive mesh finite element method, is also presented. First, we performed two-dimensional numerical simulations to study the effect of heat on a regular electrophysiological wave, with the comparison of the calculated and experimental values of Q10. Then, we demonstrated the effect of global hypothermia in suppressing single and multiple spiral waves.

Mechanical perturbation control of cardiac alternans.

Cardiac alternans is a disturbance in heart rhythm that is linked to the onset of lethal cardiac arrhythmias. Mechanical perturbation control has been recently used to suppress alternans in cardiac tissue of relevant size. In this control strategy, cardiac tissue mechanics are perturbed via active tension generated by the heart's electrical activity, which alters the tissue's electric wave profile through mechanoelectric coupling. We analyze the effects of mechanical perturbation on the dynamics of a map model that couples the membrane voltage and active tension systems at the cellular level. Therefore, a two-dimensional iterative map of the heart beat-to-beat dynamics is introduced, and a stability analysis of the system of coupled maps is performed in the presence of a mechanical perturbation algorithm. To this end, a bidirectional coupling between the membrane voltage and active tension systems in a single cardiac cell is provided, and a discrete form of the proposed control algorithm, that can be incorporated in the coupled maps, is derived. In addition, a realistic electromechanical model of cardiac tissue is employed to explore the feasibility of suppressing alternans at cellular and tissue levels. Electrical activity is represented in two detailed ionic models, the Luo-Rudy 1 and the Fox models, while two active contractile tension models, namely a smooth variant of the Nash-Panfilov model and the Niederer-Hunter-Smith model, are used to represent mechanical activity in the heart. The Mooney-Rivlin passive elasticity model is employed to describe passive mechanical behavior of the myocardium.

Control of cardiac alternans in an electromechanical model of cardiac tissue.

Electrical alternations in cardiac action potential duration have been shown to be a precursor to arrhythmias and sudden cardiac death. Through the mechanism of excitation-contraction coupling, the presence of electrical alternans induces alternations in the heart muscle contractile activity. Also, contraction of cardiac tissue affects the process of cardiac electric wave propagation through the mechanism of the so-called mechanoelectrical feedback. Electrical excitation and contraction of cardiac tissue can be linked by an electromechanical model such as the Nash-Panfilov model. In this work, we explore the feasibility of suppressing cardiac alternans in the Nash-Panfilov model which is employed for small and large deformations. Several electrical pacing and mechanical perturbation feedback strategies are considered to demonstrate successful suppression of alternans on a one-dimensional cable. This is the first attempt to combine electrophysiologically relevant cardiac models of electrical wave propagation and contractility of cardiac tissue in a synergistic effort to suppress cardiac alternans. Numerical examples are provided to illustrate the feasibility and the effects of the proposed algorithms to suppress cardiac alternans.

Control of cardiac alternans by mechanical and electrical feedback.

A persistent alternation in the cardiac action potential duration has been linked to the onset of ventricular arrhythmia, which may lead to sudden cardiac death. A coupling between these cardiac alternans and the intracellular calcium dynamics has also been identified in previous studies. In this paper, the system of PDEs describing the small amplitude of alternans and the alternation of peak intracellular Ca(2+) are stabilized by optimal boundary and spatially distributed actuation. A simulation study demonstrating the successful annihilation of both alternans on a one-dimensional cable of cardiac cells by utilizing the full-state feedback controller is presented. Complimentary to these studies, a three variable Nash-Panfilov model is used to investigate alternans annihilation via mechanical (or stretch) perturbations. The coupled model includes the active stress which defines the mechanical properties of the tissue and is utilized in the feedback algorithm as an independent input from the pacing based controller realization in alternans annihilation. Simulation studies of both control methods demonstrate that the proposed methods can successfully annihilate alternans in cables that are significantly longer than 1 cm, thus overcoming the limitations of earlier control efforts.

Cardiac alternans annihilation by distributed mechano-electric feedback (MEF).

The presence of the electrical alternans induces, through the mechanism of the excitation-contraction coupling, an alternation in the heart muscle contractile activity. In this work, we demonstrate the cardiac alternans annihilation by applied mechanical perturbation. In particular, we address annihilation of alternans in realistic heart size tissue by considering ionic currents suggested by Luo-Rudy-1 (LR1) model, in which the control algorithm involves a combined electrical boundary pacing control and a spatially distributed calcium based control which perturbs the calcium in the cells. Complimentary to this, we also address a novel mechanism of alternans annihilation which uses a Nash Panfilov model coupled with the stress equilibrium equations. The coupled model includes an additional variable to represent the active stress which defines the mechanical properties of the tissue.

Towards accurate numerical method for monodomain models using a realistic heart geometry.

The simulation of cardiac electrophysiological waves are known to require extremely fine meshes, limiting the applicability of current numerical models to simplified geometries and ionic models. In this work, an accurate numerical method based on a time-dependent anisotropic remeshing strategy is presented for simulating three-dimensional cardiac electrophysiological waves. The proposed numerical method greatly reduces the number of elements and enhances the accuracy of the prediction of the electrical wave fronts. Illustrations of the performance and the accuracy of the proposed method are presented using a realistic heart geometry. Qualitative and quantitative results show that the proposed methodology is far superior to the uniform mesh methods commonly used in cardiac electrophysiology.

A time-dependent adaptive remeshing for electrical waves of the heart.

In this work, a time-dependent remeshing strategy and a numerical method are presented for the simulation of the action potential propagation of the human heart. The main purpose of these simulations is to accurately predict the depolarization-repolarization front position, which is essential to the understanding of the electrical activity in the myocardium. A bidomain model, which is commonly used for studying electrophysiological waves in the cardiac tissue, will be employed for the numerical simulations. Numerical results are enhanced by the introduction of an anisotropic remeshing strategy. The illustration of the performance and the accuracy of the proposed method are presented using a 2-D analytical solution and a test case with re-entrant waves.

An efficient computational method for simulation of the two-dimensional electrophysiological waves.

This work presents an efficient simulation for the two-dimensional bidomain model, a non-linear system of partial differential equations which is widely used for simulation of the electrical activity of the heart. The accuracy of the solution is obtained by using an anisotropic time-dependent adaptive method. The method reduces greatly the number of element and therefore the computational time. Two-dimensional numerical results are presented to illustrate the performance of the proposed method.

Numerical prediction of freezing fronts in cryosurgery: comparison with experimental results.

Recent developments in scientific computing now allow to consider realistic applications of numerical modelling to medicine. In this work, a numerical method is presented for the simulation of phase change occurring in cryosurgery applications. The ultimate goal of these simulations is to accurately predict the freezing front position and the thermal history inside the ice ball which is essential to determine if cancerous cells have been completely destroyed. A semi-phase field formulation including blood flow considerations is employed for the simulations. Numerical results are enhanced by the introduction of an anisotropic remeshing strategy. The numerical procedure is validated by comparing the predictions of the model with experimental results.