Efficient probabilistic model personalization integrating uncertainty on data and parameters: Application to Eikonal-Diffusion models in cardiac electrophysiology

Biophysical models are increasingly used for medical applications at the organ scale. However, model predictions are rarely associated with a confidence measure although there are important sources of uncertainty in computational physiology methods. For instance, the sparsity and noise of the clinical data used to adjust the model parameters (personalization), and the difficulty in modeling accurately soft tissue physiology. The recent theoretical progresses in stochastic models make their use computationally tractable, but there is still a challenge in estimating patient-specific parameters with such models. In this work we propose an efficient Bayesian inference method for model personalization using polynomial chaos and compressed sensing. This method makes Bayesian inference feasible in real 3D modeling problems. We demonstrate our method on cardiac electrophysiology. We first present validation results on synthetic data, then we apply the proposed method to clinical data. We demonstrate how this can help in quantifying the impact of the data characteristics on the personalization (and thus prediction) results. Described method can be beneficial for the clinical use of personalized models as it explicitly takes into account the uncertainties on the data and the model parameters while still enabling simulations that can be used to optimize treatment. Such uncertainty handling can be pivotal for the proper use of modeling as a clinical tool, because there is a crucial requirement to know the confidence one can have in personalized models.     

The Noble cardiac ventricular electrophysiology models in CellML

We present a review of the cardiac ventricular cell electrophysiology models developed by Prof. Denis Noble and colleagues as an example of how models may be published using a web-based CellML publication framework. The models reviewed have been marked-up in CellML and then used to compute all results presented here. The models are freely available from a website as are the specific numerical experiments discussed in this review and the tools used to perform the simulations.     

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology.     

Cardiac survival in anoxia-tolerant vertebrates: An electrophysiological perspective

Certain vertebrates, such as freshwater turtles of the genus Chrysemys and Trachemys and crucian carp (Carassius carassius), have anoxia-tolerant hearts that continue to function throughout prolonged periods of anoxia (up to many months) due to successful balancing of cellular ATP supply and demand. In the present review, we summarize the current and limited understanding of the cellular mechanisms underlying this cardiac anoxia tolerance. What emerges is that cold temperature substantially modifies cardiac electrophysiology to precondition the heart for winter anoxia. Intrinsic heart rate is slowed and density of sarcolemmal ion currents substantially modified to alter cardiac action potential (AP) characteristics. These changes depress cardiac activity and reduce the energetic costs associated with ion pumping. In contrast, anoxia per se results in limited changes to cardiac AP shape or ion current densities in turtle and crucian carp, suggesting that anoxic modifications of cardiac electrophysiology to reduce ATP demand are not extensive. Additionally, as knowledge of cellular physiology in non-mammalian vertebrates is still in its infancy, we briefly discuss the cellular defense mechanisms towards the acidosis that accompanies anoxia as well as mammalian cardiac models of hypoxia/ischemia tolerance. By examining if fundamental cellular mechanisms have been conserved during the evolution of anoxia tolerance we hope to have provided a framework for the design of future experiments investigating cardiac cellular mechanisms of anoxia survival.     

Models of cardiac excitation-contraction coupling in ventricular myocytes

Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable.     

基于心脏电生理模型的心律失常机制研究进展

揭示发病机制是心律失常诊断、治疗、药物研发和设备设计的关键.整合当前在心脏分子生物学、生物化学、生理学及解剖学方面的最新成果,构建从离子通道、心肌细胞、心肌纤维、心肌组织、心脏器官到躯体各个层次的多尺度多模态心脏电生理模型,用于系统研究微观局部变化发生、发展、转化为宏观心律失常表现的过程,将彻底改变传统从基因突变、蛋白质表达、细胞电生理、临床表现单独研究心律失常的方式,实现微观与宏观研究的统一,使心脏电生理模型成为系统研究心律失常发病机制的有力手段.本文综述了心脏电生理模型的构建方法和研究进展,讨论了多尺度心脏电生理模型在揭示心律失常机制研究中的作用和地位,给出了基于心脏电生理模型心律失常研究的挑战和重要发展方向.     

Electromechanical models of the ventricles

Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.     

Computational biology in the study of cardiac ion channels and cell electrophysiology

The cardiac cell is a complex biological system where various processes interact to generate electrical excitation (the action potential, AP) and contraction. During AP generation, membrane ion channels interact nonlinearly with dynamically changing ionic concentrations and varying transmembrane voltage, and are subject to regulatory processes. In recent years, a large body of knowledge has accumulated on the molecular structure of cardiac ion channels, their function, and their modification by genetic mutations that are associated with cardiac arrhythmias and sudden death. However, ion channels are typically studied in isolation (in expression systems or isolated membrane patches), away from the physiological environment of the cell where they interact to generate the AP. A major challenge remains the integration of ion-channel properties into the functioning, complex and highly interactive cell system, with the objective to relate molecular-level processes and their modification by disease to whole-cell function and clinical phenotype. In this article we describe how computational biology can be used to achieve such integration. We explain how mathematical (Markov) models of ion-channel kinetics are incorporated into integrated models of cardiac cells to compute the AP. We provide examples of mathematical (computer) simulations of physiological and pathological phenomena, including AP adaptation to changes in heart rate, genetic mutations in SCN5A and HERG genes that are associated with fatal cardiac arrhythmias, and effects of the CaMKII regulatory pathway and beta-adrenergic cascade on the cell electrophysiological function.     

Model reduction using a posteriori analysis

Mathematical models in biology and physiology are often represented by large systems of non-linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the functional of interest. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell-level cardiac electrophysiology model.     

Computer simulations of in vitro morphogenesis

One of the most important challenges of contemporary biology is understanding how cells assemble into tissues. The complexity of morphogenesis calls for computational tools able to identify the dominant mechanisms involved in shaping tissues. This narrative review presents individual-based computational models that proved useful in simulating phenomena of interest in tissue engineering (TE), a research field that aims to create tissue replacements in the laboratory. First, we briefly describe morphogenetic mechanisms. Then, we present several computational models of cellular and subcellular resolution, along with applications that illustrate their potential to address problems of TE. Finally, we analyze experiments that may be used to validate computational models of tissue constructs made of cohesive cells. Our analysis shows that the models available in the literature are not exploited to their full potential. We argue that, upon validation, a computational model can be used to optimize cell culture conditions and to design new experiments.     

Uncovering physiologic mechanisms of circadian rhythms and sleep/wake regulation through mathematical modeling

Mathematical models of neurobehavioral function are useful both for understanding the underlying physiology and for predicting the effects of rest-activity-work schedules and interventions on neurobehavioral function. In a symposium titled "Modeling Human Neurobehavioral Performance I: Uncovering Physiologic Mechanisms" at the 2006 Society for Industrial and Applied Mathematics/Society for Mathematical Biology (SIAM/SMB) Conference on the Life Sciences, different approaches to modeling the physiology of human circadian rhythms, sleep, and neurobehavioral performance and their usefulness in understanding the underlying physiology were examined. The topics included key elements of the physiology that should be included in mathematical models, a computational model developed within a cognitive architecture that has begun to include the effects of extended wake on information-processing mechanisms that influence neurobehavioral function, how to deal with interindividual differences in the prediction of neurobehavioral function, the applications of systems biology and control theory to the study of circadian rhythms, and comparisons of these methods in approaching the overarching questions of the underlying physiology and mathematical models of circadian rhythms and neurobehavioral function. A unifying theme was that it is important to have strong collaborative ties between experimental investigators and mathematical modelers, both for the design and conduct of experiments and for continued development of the models.     

Modelling the Effect of Gap Junctions on Tissue-Level Cardiac Electrophysiology

When modelling tissue-level cardiac electrophysiology, a continuum approximation to the discrete cell-level equations, known as the bidomain equations, is often used to maintain computational tractability. Analysing the derivation of the bidomain equations allows us to investigate how microstructure, in particular gap junctions that electrically connect cells, affect tissue-level conductivity properties. Using a one-dimensional cable model, we derive a modified form of the bidomain equations that take gap junctions into account, and compare results of simulations using both the discrete and continuum models, finding that the underlying conduction velocity of the action potential ceases to match up between models when gap junctions are introduced at physiologically realistic coupling levels. We show that this effect is magnified by: (i) modelling gap junctions with reduced conductivity; (ii) increasing the conductance of the fast sodium channel; and (iii) an increase in myocyte length. From this, we conclude that the conduction velocity arising from the bidomain equations may not be an accurate representation of the underlying discrete system. In particular, the bidomain equations are less likely to be valid when modelling certain diseased states whose symptoms include a reduction in gap junction coupling or an increase in myocyte length.     

Mapping cardiac surface mechanics with structured light imaging

Cardiovascular disease often manifests as a combination of pathological electrical and structural heart remodeling. The relationship between mechanics and electrophysiology is crucial to our understanding of mechanisms of cardiac arrhythmias and the treatment of cardiac disease. While several technologies exist for describing whole heart electrophysiology, studies of cardiac mechanics are often limited to rhythmic patterns or small sections of tissue. Here, we present a comprehensive system based on ultrafast three-dimensional (3-D) structured light imaging to map surface dynamics of whole heart cardiac motion. Additionally, we introduce a novel nonrigid motion-tracking algorithm based on an isometry-maximizing optimization framework that forms correspondences between consecutive 3-D frames without the use of any fiducial markers. By combining our 3-D imaging system with nonrigid surface registration, we are able to measure cardiac surface mechanics at unprecedented spatial and temporal resolution. In conclusion, we demonstrate accurate cardiac deformation at over 200,000 surface points of a rabbit heart recorded at 200 frames/s and validate our results on highly contrasting heart motions during normal sinus rhythm, ventricular pacing, and ventricular fibrillation.     

Beyond spider personality: The relationships between behavioral,physiological, and environmental factors

Spiders are useful models for testing different hypotheses and methodologies relating to animal personality and behavioral syndromes because they show a range of behavioral types and unique physiological traits (e.g., silk and venom) that are not observed in many other animals. These characteristics allow for a unique understanding of how physiology, behavioral plasticity, and personality interact across different contexts to affect spider''s individual fitness and survival. However, the relative effect of extrinsic factors on physiological traits (silk, venom, and neurohormones) that play an important role in spider survival, and which may impact personality, has received less attention. The goal of this review is to explore how the environment, experience, ontogeny, and physiology interact to affect spider personality types across different contexts. We highlight physiological traits, such as neurohormones, and unique spider biochemical weapons, namely silks and venoms, to explore how the use of these traits might, or might not, be constrained or limited by particular behavioral types. We argue that, to develop a comprehensive understanding of the flexibility and persistence of specific behavioral types in spiders, it is necessary to incorporate these underlying mechanisms into a synthesized whole, alongside other extrinsic and intrinsic factors.     

Inter-model consistency and complementarity: learning from ex-vivo imaging and electrophysiological data towards an integrated understanding of cardiac physiology

Computational models of the heart at various scales and levels of complexity have been independently developed, parameterised and validated using a wide range of experimental data for over four decades. However, despite remarkable progress, the lack of coordinated efforts to compare and combine these computational models has limited their impact on the numerous open questions in cardiac physiology. To address this issue, a comprehensive dataset has previously been made available to the community that contains the cardiac anatomy and fibre orientations from magnetic resonance imaging as well as epicardial transmembrane potentials from optical mapping measured on a perfused ex-vivo porcine heart. This data was used to develop and customize four models of cardiac electrophysiology with different level of details, including a personalized fast conduction Purkinje system, a maximum a posteriori estimation of the 3D distribution of transmembrane potential, the personalization of a simplified reaction-diffusion model, and a detailed biophysical model with generic conduction parameters. This study proposes the integration of these four models into a single modelling and simulation pipeline, after analyzing their common features and discrepancies. The proposed integrated pipeline demonstrates an increase prediction power of depolarization isochrones in different pacing conditions.     

Effect of input resistance voltage-dependency on DC estimate of membrane capacitance in cardiac myocytes

The measure of membrane capacitance (C(m)) in cardiac myocytes is of primary importance as an index of their size in physiological and pathological conditions, and for the understanding of their excitability. Although a plethora of very accurate methods has been developed to access C(m) value in single cells, cardiac electrophysiologists still use, in the majority of laboratories, classical direct current techniques as they have been established in the early days of cardiac cellular electrophysiology. These techniques are based on the assumption that cardiac membrane resistance (R(m)) is constant, or changes negligibly, in a narrow potential range around resting potential. Using patch-clamp whole-cell recordings, both in current-clamp and voltage-clamp conditions, and numerical simulations, we document here the voltage-dependency of R(m), up to -45% of its resting value for 10-mV hyperpolarization, in resting rat ventricular myocytes. We show how this dependency makes classical protocols to misestimate C(m) in a voltage-dependent manner (up to 20% errors), which can dramatically affect C(m)-based calculations on cell size and on intracellular ion dynamics. We develop a simple mechanistic model to fit experimental data and obtain voltage-independent estimates of C(m), and we show that accurate estimates can also be extrapolated from the classical approach.     

Chaste: An Open Source C++ Library for Computational Physiology and Biology

Chaste — Cancer, Heart And Soft Tissue Environment — is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high-performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to ‘re-invent the wheel’ with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials.

This is a PLOS Computational Biology Software Article

     

Conservation physiology in practice: how physiological knowledge has improved our ability to sustainably manage Pacific salmon during up-river migration

Despite growing interest in conservation physiology, practical examples of how physiology has helped to understand or to solve conservation problems remain scarce. Over the past decade, an interdisciplinary research team has used a conservation physiology approach to address topical conservation concerns for Pacific salmon. Here, we review how novel applications of tools such as physiological telemetry, functional genomics and laboratory experiments on cardiorespiratory physiology have shed light on the effect of fisheries capture and release, disease and individual condition, and stock-specific consequences of warming river temperatures, respectively, and discuss how these findings have or have not benefited Pacific salmon management. Overall, physiological tools have provided remarkable insights into the effects of fisheries capture and have helped to enhance techniques for facilitating recovery from fisheries capture. Stock-specific cardiorespiratory thresholds for thermal tolerances have been identified for sockeye salmon and can be used by managers to better predict migration success, representing a rare example that links a physiological scope to fitness in the wild population. Functional genomics approaches have identified physiological signatures predictive of individual migration mortality. Although fisheries managers are primarily concerned with population-level processes, understanding the causes of en route mortality provides a mechanistic explanation and can be used to refine management models. We discuss the challenges that we have overcome, as well as those that we continue to face, in making conservation physiology relevant to managers of Pacific salmon.