Modeling and simulation of hypothermia effects on cardiac electrical dynamics

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.

Transcending Markov: non-Markovian rate processes of thermosensitive TRP ion channels

The Markov state model (MSM) is a popular theoretical tool for describing the hierarchy of time scales involved in the function of many proteins especially ion channel gating. An MSM is a particular case of the general non-Markovian model, where the rate of transition from one state to another does not depend on the history of state occupancy within the system, i.e. it only includes reversible, non-dissipative processes. However, an MSM requires knowledge of the precise conformational state of the protein and is not predictive when those details are not known. In the case of ion channels, this simple description fails in real (non-equilibrium) situations, for example when local temperature changes, or when energy losses occur during channel gating. Here, we show it is possible to use non-Markovian equations (i.e. offer a general description that includes the MSM as a particular case) to develop a relatively simple analytical model that describes the non-equilibrium behaviour of the temperature-sensitive transient receptor potential (TRP) ion channels, TRPV1 and TRPM8. This model accurately predicts asymmetrical opening and closing rates, infinite processes and the creation of new states, as well as the effect of temperature changes throughout the process. This approach therefore overcomes the limitations of the MSM and allows us to go beyond a mere phenomenological description of the dynamics of ion channel gating towards a better understanding of the physics underlying these processes.

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

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.

Modelling dendritic spines with the finite element method, investigating the impact of geometry on electric and calcic responses

Understanding the relationship between shape and function of dendritic spines is an elusive topic. Several modelling approaches have been used to investigate the interplay between spine geometry, calcium diffusion and electric signalling. We here use a second order finite element method to solve the Poisson-Nernst-Planck equations and describe electrodiffusion in dendritic spines. With this, we obtain relationships between dendritic geometry and calcic as well as electric responses to synaptic events. Our findings support the hypothesis that spine geometry plays a role shaping the electrical responses to synaptic events. Our method was also able to reveal the fine scale distribution of calcium in spines with irregular shapes.