Bayesian inference and prediction in cardiac electrophysiology models with an application to representing variability

Many different techniques have been used for parameter estimation in cardiac electrophysiology models, from optimization algorithms to heuristic and frequentist statistical methods. However, the fixed parameter values obtained from such approaches cannot provide a complete description of variability within an individual or across a population. To overcome this shortcoming, in this work we adopt a Bayesian approach by applying the Hamiltonian Monte Carlo (HMC) algorithm to cardiac electrophysiology models and data for the first time through three studies. (i) Using HMC, we fit synthetic and experimental cardiac voltage data from different pacing rates and find the probability distributions of the parameters of two relatively low-dimensional models, the Mitchell-Schaeffer (MS) and Fenton-Karma (FK) models. We successfully fit synthetic and experimental voltage traces and build populations of action potentials with the posterior probability distributions of the parameters. (ii) We compare the performance of HMC with that of the main Bayesian approach used previously for similar applications, the Approximate Bayesian Computation Sequential Monte Carlo (ABC SMC) algorithm. Both techniques are able to describe the dynamics of synthetic and experimental voltage data using the MS and FK models, with HMC more consistent and ABC SMC more versatile and easier to implement. (iii) We study the variability of cardiac action potentials in space within an individual. We use HMC and a novel approach employing a Gaussian process prior for one spatially varying MS model parameter along with a hierarchical model for the remaining parameters, considered spatially invariant. Using this approach, we do inference and prediction on synthetic cardiac voltage data, exploiting the spatial correlations in cardiac tissue that arise from cellular coupling to use voltage information from a small number of sites to predict parameter value distributions and families of voltage data in other locations. Together these three studies show the potential of Bayesian inference and prediction in providing a framework to represent variability within cardiac electrophysiology modeling

Calibration of ionic and cellular cardiac electrophysiology models

© 2020 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc. Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models

Parameterization for in-silico modeling of ion channel interactions with drugs

Since the first Hodgkin and Huxley ion channel model was described in the 1950s, there has been an explosion in mathematical models to describe ion channel function. As experimental data has become richer, models have concomitantly been improved to better represent ion channel kinetic processes, although these improvements have generally resulted in more model complexity and an increase in the number of parameters necessary to populate the models. Models have also been developed to explicitly model drug interactions with ion channels. Recent models of drug-channel interactions account for the discrete kinetics of drug interaction with distinct ion channel state conformations, as it has become clear that such interactions underlie complex emergent kinetics such as use-dependent block. Here, we describe an approach for developing a model for ion channel drug interactions. The method describes the process of extracting rate constants from experimental electrophysiological function data to use as initial conditions for the model parameters. We then describe implementation of a parameter optimization method to refine the model rate constants describing ion channel drug kinetics. The algorithm takes advantage of readily available parallel computing tools to speed up the optimization. Finally, we describe some potential applications of the platform including the potential for gaining fundamental mechanistic insights into ion channel function and applications to in silico drug screening and development

Systems Modeling to Predict Mechano-Chemo Interactions In Cardiac Fibrosis

Cardiac fibrosis poses a central challenge in preventing heart failure for patients who have suffered a cardiac injury such as myocardial infarction or aortic valve stenosis. This chronic condition is characterized by a reduction in contractile function through combined hypertrophy and excessive scar formation, and although currently prescribed therapeutics targeting hypertrophy have shown improvements in patient outcomes, pathological fibrosis remains a leading cause of reduced cardiac function for patients long-term. Cardiac fibroblasts play a key role in regulating scar formation during heart failure progression, and interacting biochemical and biomechanical cues within the myocardium guide the activation of fibroblasts and expression of extracellular matrix proteins. While targeted experimental studies of fibroblast activation have elucidated the roles of individual pathways in fibroblast activation, intracellular crosstalk between mechanotransduction and chemotransduction pathways from multiple biochemical cues has largely confounded efforts to control overall cell behavior within the myocardial environment. Computational networks of intracellular signaling can account for complex interactions between signaling pathways and provide a promising approach for identifying influential mechanisms mediating cell behavior. The overarching goal of this dissertation is to improve our understanding of complex signaling in fibroblasts by investigating the role of mechano-chemo interactions in cardiac fibroblast-mediated fibrosis using a combination of experimental studies and systems-level computational models. Firstly, using an in vitro screen of cardiac fibroblast-secreted proteins in response to combinations of biochemical stimuli and mechanical tension, we found that tension modulated cell sensitivity towards biochemical stimuli, thereby altering cell behavior based on the mechanical context. Secondly, using a curated model of fibroblast intracellular signaling, we expanded model topology to include robust mechanotransduction pathways, improved accuracy of model predictions compared to independent experimental studies, and identified mechanically dependent mechanisms-of- ction and mechano-adaptive drug candidates in a post-infarction scenario. Lastly, using an inferred network of fibroblast transcriptional regulation and model fitting to patient-specific data, we showed the utility of model-based approaches in identifying influential pathways underlying fibrotic protein expression during aortic valve stenosis and predicting patient-specific responses to pharmacological intervention. Our work suggests that computational-based approaches can generate insight into influential mechanisms among complex systems, and such tools may be promising for further therapeutic development and precision medicine

Reproducible model development in the Cardiac Electrophysiology Web Lab

The modelling of the electrophysiology of cardiac cells is one of the most mature areas of systems biology. This extended concentration of research effort brings with it new challenges, foremost among which is that of choosing which of these models is most suitable for addressing a particular scientific question. In a previous paper, we presented our initial work in developing an online resource for the characterisation and comparison of electrophysiological cell models in a wide range of experimental scenarios. In that work, we described how we had developed a novel protocol language that allowed us to separate the details of the mathematical model (the majority of cardiac cell models take the form of ordinary differential equations) from the experimental protocol being simulated. We developed a fully-open online repository (which we termed the Cardiac Electrophysiology Web Lab) which allows users to store and compare the results of applying the same experimental protocol to competing models. In the current paper we describe the most recent and planned extensions of this work, focused on supporting the process of model building from experimental data. We outline the necessary work to develop a machine-readable language to describe the process of inferring parameters from wet lab datasets, and illustrate our approach through a detailed example of fitting a model of the hERG channel using experimental data. We conclude by discussing the future challenges in making further progress in this domain towards our goal of facilitating a fully reproducible approach to the development of cardiac cell models