Application of stochastic phenomenological modelling to cell-to-cell and beat-to-beat electrophysiological variability in cardiac tissue

An audit of uncertainty in multi-scale cardiac electrophysiology models

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Data-Driven Identification of Stochastic Model Parameters and State Variables: Application to the Study of Cardiac Beat-to-Beat Variability

OBJECTIVE

Enhanced spatiotemporal ventricular repolarization variability has been associated with ventricular arrhythmias and sudden cardiac death, but the involved mechanisms remain elusive. In this paper, a methodology for estimation of parameters and state variables of stochastic human ventricular cell models from input voltage data is proposed for investigation of repolarization variability.

METHODS

The proposed methodology formulates state-space representations based on developed stochastic cell models and uses the unscented Kalman filter to perform joint parameter and state estimation. Evaluation over synthetic and experimental data is presented.

RESULTS

Results on synthetically generated data show the ability of the methodology to: first, filter out measurement noise from action potential (AP) traces; second, identify model parameters and state variables from each of those individual AP traces, thus allowing robust characterization of cell-to-cell variability; and, third, replicate statistical population's distributions of input AP-based markers, including dynamic markers quantifying beat-to-beat variability. Application onto experimental data demonstrates the ability of the methodology to match input AP traces while concomitantly inferring the characteristics of underlying stochastic cell models.

CONCLUSION

A novel methodology is presented for estimation of parameters and hidden variables of stochastic cardiac computational models, with the advantage of providing a one-to-one match between each individual AP trace and a corresponding set of model characteristics.

SIGNIFICANCE

The proposed methodology can greatly help in the characterization of temporal (beat-to-beat) and spatial (cell-to-cell) variability in human ventricular repolarization and in ascertaining the corresponding underlying mechanisms, particularly in scenarios with limited available experimental data.

Generalized polynomial chaos-based uncertainty quantification and propagation in multi-scale modeling of cardiac electrophysiology

Uncertainty and physiological variability are ubiquitous in cardiac electrical signaling. It is important to address the uncertainty and variability in cardiac modeling to provide reliable and realistic predictions of heart function, thus ensuring trustworthy computer-aided medical decision-making and treatment planning. Statistical techniques such as Monte Carlo (MC) simulations have been applied to uncertainty quantification and propagation in cardiac modeling. However, MC simulation-based methods are computationally prohibitive for complex cardiac models with a great number of parameters and governing equations. In this paper, we propose to use the Generalized Polynomial Chaos (gPC) expansion in combination with Galerkin projection to analytically quantify parametric uncertainty in ion channel models of mouse ventricular cell, and further propagate the uncertainty across different organizational levels of cell and tissue. To identify the most significant parametric uncertainty in cardiac ion channel and cell models, variance decomposition-based sensitivity analysis was first performed. Following this, gPC was integrated with deterministic cardiac models to propagate uncertainty through ion current, ventricular cell, 1D cable, and 2D tissue to account for the stochasticity and cell-to-cell variability. As compared to MC, the gPC in this work shows the superior performance in terms of computational efficiency. In addition, the gPC models can provide a measure of confidence in model predictions, which can improve the reliability of computer simulations of cardiac electrophysiology for clinical applications.

Efficient parameterization of cardiac action potential models using a genetic algorithm

Finding appropriate values for parameters in mathematical models of cardiac cells is a challenging task. Here, we show that it is possible to obtain good parameterizations in as little as 30-40 s when as many as 27 parameters are fit simultaneously using a genetic algorithm and two flexible phenomenological models of cardiac action potentials. We demonstrate how our implementation works by considering cases of "model recovery" in which we attempt to find parameter values that match model-derived action potential data from several cycle lengths. We assess performance by evaluating the parameter values obtained, action potentials at fit and non-fit cycle lengths, and bifurcation plots for fidelity to the truth as well as consistency across different runs of the algorithm. We also fit the models to action potentials recorded experimentally using microelectrodes and analyze performance. We find that our implementation can efficiently obtain model parameterizations that are in good agreement with the dynamics exhibited by the underlying systems that are included in the fitting process. However, the parameter values obtained in good parameterizations can exhibit a significant amount of variability, raising issues of parameter identifiability and sensitivity. Along similar lines, we also find that the two models differ in terms of the ease of obtaining parameterizations that reproduce model dynamics accurately, most likely reflecting different levels of parameter identifiability for the two models.

Modeling an Excitable Biosynthetic Tissue with Inherent Variability for Paired Computational-Experimental Studies

To understand how excitable tissues give rise to arrhythmias, it is crucially necessary to understand the electrical dynamics of cells in the context of their environment. Multicellular monolayer cultures have proven useful for investigating arrhythmias and other conduction anomalies, and because of their relatively simple structure, these constructs lend themselves to paired computational studies that often help elucidate mechanisms of the observed behavior. However, tissue cultures of cardiomyocyte monolayers currently require the use of neonatal cells with ionic properties that change rapidly during development and have thus been poorly characterized and modeled to date. Recently, Kirkton and Bursac demonstrated the ability to create biosynthetic excitable tissues from genetically engineered and immortalized HEK293 cells with well-characterized electrical properties and the ability to propagate action potentials. In this study, we developed and validated a computational model of these excitable HEK293 cells (called “Ex293” cells) using existing electrophysiological data and a genetic search algorithm. In order to reproduce not only the mean but also the variability of experimental observations, we examined what sources of variation were required in the computational model. Random cell-to-cell and inter-monolayer variation in both ionic conductances and tissue conductivity was necessary to explain the experimentally observed variability in action potential shape and macroscopic conduction, and the spatial organization of cell-to-cell conductance variation was found to not impact macroscopic behavior; the resulting model accurately reproduces both normal and drug-modified conduction behavior. The development of a computational Ex293 cell and tissue model provides a novel framework to perform paired computational-experimental studies to study normal and abnormal conduction in multidimensional excitable tissue, and the methodology of modeling variation can be applied to models of any excitable cell.

One of the major challenges in trying to understand how arrhythmias can form in cardiac tissue is studying how the electrical activity of cardiac cells is affected by their surroundings. Current approaches have focused on studying cardiac cells in vitro and using computational models to elucidate the mechanisms behind experimental findings. However, tissue culture techniques are limited to working with neonatal, rather than adult, cells, and computational modeling of these cells has proven challenging. In this work, we have a developed a new approach for conducting paired experimental and computational studies by using a cell line engineered with the minimum machinery for excitability, and a computational model derived and validated directly from this cell line. In order to create a model that reproduces the diversity, rather than simply the average behavior, of experimental studies, we have incorporated a simple yet novel method of inherent variability, and explored what types of experimental variation must be incorporated into the model to recapitulate experimental findings. Using this new platform for paired experimental-computational studies with inherent variability, we will be able to study and better understand how changes in cardiac structure such as fibrosis and heterogeneity lead to conduction slowing, conduction failure, and arrhythmogenesis.

Experimentally-Based Computational Investigation into Beat-To-Beat Variability in Ventricular Repolarization and Its Response to Ionic Current Inhibition

Beat-to-beat variability in repolarization (BVR) has been proposed as an arrhythmic risk marker for disease and pharmacological action. The mechanisms are unclear but BVR is thought to be a cell level manifestation of ion channel stochasticity, modulated by cell-to-cell differences in ionic conductances. In this study, we describe the construction of an experimentally-calibrated set of stochastic cardiac cell models that captures both BVR and cell-to-cell differences in BVR displayed in isolated canine action potential measurements using pharmacological agents. Simulated and experimental ranges of BVR are compared in control and under pharmacological inhibition, and the key ionic currents determining BVR under physiological and pharmacological conditions are identified. Results show that the 4-aminopyridine-sensitive transient outward potassium current, I_to1, is a fundamental driver of BVR in control and upon complete inhibition of the slow delayed rectifier potassium current, I_Ks. In contrast, I_Ks and the L-type calcium current, I_CaL, become the major contributors to BVR upon inhibition of the fast delayed rectifier potassium current, I_Kr. This highlights both I_Ks and I_to1 as key contributors to repolarization reserve. Partial correlation analysis identifies the distribution of I_to1 channel numbers as an important independent determinant of the magnitude of BVR and drug-induced change in BVR in control and under pharmacological inhibition of ionic currents. Distributions in the number of I_Ks and I_CaL channels only become independent determinants of the magnitude of BVR upon complete inhibition of I_Kr. These findings provide quantitative insights into the ionic causes of BVR as a marker for repolarization reserve, both under control condition and pharmacological inhibition.

Variability in cardiac electrophysiology: Using experimentally-calibrated populations of models to move beyond the single virtual physiological human paradigm

Physiological variability manifests itself via differences in physiological function between individuals of the same species, and has crucial implications in disease progression and treatment. Despite its importance, physiological variability has traditionally been ignored in experimental and computational investigations due to averaging over samples from multiple individuals. Recently, modelling frameworks have been devised for studying mechanisms underlying physiological variability in cardiac electrophysiology and pro-arrhythmic risk under a variety of conditions and for several animal species as well as human. One such methodology exploits populations of cardiac cell models constrained with experimental data, or experimentally-calibrated populations of models. In this review, we outline the considerations behind constructing an experimentally-calibrated population of models and review the studies that have employed this approach to investigate variability in cardiac electrophysiology in physiological and pathological conditions, as well as under drug action. We also describe the methodology and compare it with alternative approaches for studying variability in cardiac electrophysiology, including cell-specific modelling approaches, sensitivity-analysis based methods, and populations-of-models frameworks that do not consider the experimental calibration step. We conclude with an outlook for the future, predicting the potential of new methodologies for patient-specific modelling extending beyond the single virtual physiological human paradigm.

Cardiovascular safety risk assessment for new candidate drugs from functional and pathological data: Conference report

This is a report on a 2-day joint meeting between the British Society of Toxicological Pathology (BSTP) and the Safety Pharmacology Society (SPS) held in the UK in November 2013. Drug induced adverse effects on the cardiovascular system are associated with the attrition of more marketed and candidate drugs than any other safety issue. The objectives of this meeting were to foster inter-disciplinary approaches to address cardiovascular risk assessment, improve understanding of the respective disciplines, and increase awareness of new technologies. These aims were achieved. This well attended meeting covered both 'purely functional' cardiovascular adverse effects of drugs (e.g., electrophysiological and haemodynamic changes) as well as adverse effects encompassing both functional and pathological changes. Most of the presentations focused on nonclinical safety data, with information on translation to human where known. To reflect the content of the presentations we have cited key references and review articles.