Whole-heart modeling: applications to cardiac electrophysiology and electromechanics

Submillimeter diffusion tensor imaging and late gadolinium enhancement cardiovascular magnetic resonance of chronic myocardial infarction

BACKGROUND

Knowledge of the three-dimensional (3D) infarct structure and fiber orientation remodeling is essential for complete understanding of infarct pathophysiology and post-infarction electromechanical functioning of the heart. Accurate imaging of infarct microstructure necessitates imaging techniques that produce high image spatial resolution and high signal-to-noise ratio (SNR). The aim of this study is to provide detailed reconstruction of 3D chronic infarcts in order to characterize the infarct microstructural remodeling in porcine and human hearts.

METHODS

We employed a customized diffusion tensor imaging (DTI) technique in conjunction with late gadolinium enhancement (LGE) cardiovascular magnetic resonance (CMR) on a 3T clinical scanner to image, at submillimeter resolution, myofiber orientation and scar structure in eight chronically infarcted porcine hearts ex vivo. Systematic quantification of local microstructure was performed and the chronic infarct remodeling was characterized at different levels of wall thickness and scar transmurality. Further, a human heart with myocardial infarction was imaged using the same DTI sequence.

RESULTS

The SNR of non-diffusion-weighted images was >100 in the infarcted and control hearts. Mean diffusivity and fractional anisotropy (FA) demonstrated a 43% increase, and a 35% decrease respectively, inside the scar tissue. Despite this, the majority of the scar showed anisotropic structure with FA higher than an isotropic liquid. The analysis revealed that the primary eigenvector orientation at the infarcted wall on average followed the pattern of original fiber orientation (imbrication angle mean: 1.96 ± 11.03° vs. 0.84 ± 1.47°, p = 0.61, and inclination angle range: 111.0 ± 10.7° vs. 112.5 ± 6.8°, p = 0.61, infarcted/control wall), but at a higher transmural gradient of inclination angle that increased with scar transmurality (r = 0.36) and the inverse of wall thickness (r = 0.59). Further, the infarcted wall exhibited a significant increase in both the proportion of left-handed epicardial eigenvectors, and in the angle incoherency. The infarcted human heart demonstrated preservation of primary eigenvector orientation at the thinned region of infarct, consistent with the findings in the porcine hearts.

CONCLUSIONS

The application of high-resolution DTI and LGE-CMR revealed the detailed organization of anisotropic infarct structure at a chronic state. This information enhances our understanding of chronic post-infarction remodeling in large animal and human hearts.

Parallelization and High-Performance Computing Enables Automated Statistical Inference of Multi-scale Models

Mechanistic understanding of multi-scale biological processes, such as cell proliferation in a changing biological tissue, is readily facilitated by computational models. While tools exist to construct and simulate multi-scale models, the statistical inference of the unknown model parameters remains an open problem. Here, we present and benchmark a parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm, tailored for high-performance computing clusters. pABC SMC is fully automated and returns reliable parameter estimates and confidence intervals. By running the pABC SMC algorithm for ∼10⁶ hr, we parameterize multi-scale models that accurately describe quantitative growth curves and histological data obtained in vivo from individual tumor spheroid growth in media droplets. The models capture the hybrid deterministic-stochastic behaviors of 10⁵-10⁶ of cells growing in a 3D dynamically changing nutrient environment. The pABC SMC algorithm reliably converges to a consistent set of parameters. Our study demonstrates a proof of principle for robust, data-driven modeling of multi-scale biological systems and the feasibility of multi-scale model parameterization through statistical inference.

3D Finite Element Electrical Model of Larval Zebrafish ECG Signals

Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace's equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions.

The Cardiac Electrophysiology Web Lab

Computational modeling of cardiac cellular electrophysiology has a long history, and many models are now available for different species, cell types, and experimental preparations. This success brings with it a challenge: how do we assess and compare the underlying hypotheses and emergent behaviors so that we can choose a model as a suitable basis for a new study or to characterize how a particular model behaves in different scenarios? We have created an online resource for the characterization and comparison of electrophysiological cell models in a wide range of experimental scenarios. The details of the mathematical model (quantitative assumptions and hypotheses formulated as ordinary differential equations) are separated from the experimental protocol being simulated. Each model and protocol is then encoded in computer-readable formats. A simulation tool runs virtual experiments on models encoded in CellML, and a website (https://chaste.cs.ox.ac.uk/WebLab) provides a friendly interface, allowing users to store and compare results. The system currently contains a sample of 36 models and 23 protocols, including current-voltage curve generation, action potential properties under steady pacing at different rates, restitution properties, block of particular channels, and hypo-/hyperkalemia. This resource is publicly available, open source, and free, and we invite the community to use it and become involved in future developments. Investigators interested in comparing competing hypotheses using models can make a more informed decision, and those developing new models can upload them for easy evaluation under the existing protocols, and even add their own protocols.

Diffusion Tractography of the Entire Left Ventricle by Using Free-breathing Accelerated Simultaneous Multisection Imaging

Purpose To develop a clinically feasible whole-heart free-breathing diffusion-tensor (DT) magnetic resonance (MR) imaging approach with an imaging time of approximately 15 minutes to enable three-dimensional (3D) tractography. Materials and Methods The study was compliant with HIPAA and the institutional review board and required written consent from the participants. DT imaging was performed in seven healthy volunteers and three patients with pulmonary hypertension by using a stimulated echo sequence. Twelve contiguous short-axis sections and six four-chamber sections that covered the entire left ventricle were acquired by using simultaneous multisection (SMS) excitation with a blipped-controlled aliasing in parallel imaging readout. Rate 2 and rate 3 SMS excitation was defined as two and three times accelerated in the section axis, respectively. Breath-hold and free-breathing images with and without SMS acceleration were acquired. Diffusion-encoding directions were acquired sequentially, spatiotemporally registered, and retrospectively selected by using an entropy-based approach. Myofiber helix angle, mean diffusivity, fractional anisotropy, and 3D tractograms were analyzed by using paired t tests and analysis of variance. Results No significant differences (P > .63) were seen between breath-hold rate 3 SMS and free-breathing rate 2 SMS excitation in transmural myofiber helix angle, mean diffusivity (mean ± standard deviation, [0.89 ± 0.09] × 10^-3 mm²/sec vs [0.9 ± 0.09] × 10^-3 mm²/sec), or fractional anisotropy (0.43 ± 0.05 vs 0.42 ± 0.06). Three-dimensional tractograms of the left ventricle with no SMS and rate 2 and rate 3 SMS excitation were qualitatively similar. Conclusion Free-breathing DT imaging of the entire human heart can be performed in approximately 15 minutes without section gaps by using SMS excitation with a blipped-controlled aliasing in parallel imaging readout, followed by spatiotemporal registration and entropy-based retrospective image selection. This method may lead to clinical translation of whole-heart DT imaging, enabling broad application in patients with cardiac disease. ^© RSNA, 2016 Online supplemental material is available for this article.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Myofiber Architecture of the Human Atria as Revealed by Submillimeter Diffusion Tensor Imaging

BACKGROUND

Accurate knowledge of the human atrial fibrous structure is paramount in understanding the mechanisms of atrial electric function in health and disease. Thus far, such knowledge has been acquired from destructive sectioning, and there is a paucity of data about atrial fiber architecture variability in the human population.

METHODS AND RESULTS

In this study, we have developed a customized 3-dimensional diffusion tensor magnetic resonance imaging sequence on a clinical scanner that makes it possible to image an entire intact human heart specimen ex vivo at submillimeter resolution. The data from 8 human atrial specimens obtained with this technique present complete maps of the fibrous organization of the human atria. The findings demonstrate that the main features of atrial anatomy are mostly preserved across subjects although the exact location and orientation of atrial bundles vary. Using the full tractography data, we were able to cluster, visualize, and characterize the distinct major bundles in the human atria. Furthermore, quantitative characterization of the fiber angles across the atrial wall revealed that the transmural fiber angle distribution is heterogeneous throughout different regions of the atria.

CONCLUSIONS

The application of submillimeter diffusion tensor magnetic resonance imaging provides an unprecedented level of information on both human atrial structure, as well as its intersubject variability. The high resolution and fidelity of this data could enhance our understanding of structural contributions to atrial rhythm and pump disorders and lead to improvements in their targeted treatment.

Rabbit models of cardiac mechano-electric and mechano-mechanical coupling

Cardiac auto-regulation involves integrated regulatory loops linking electrics and mechanics in the heart. Whereas mechanical activity is usually seen as 'the endpoint' of cardiac auto-regulation, it is important to appreciate that the heart would not function without feed-back from the mechanical environment to cardiac electrical (mechano-electric coupling, MEC) and mechanical (mechano-mechanical coupling, MMC) activity. MEC and MMC contribute to beat-by-beat adaption of cardiac output to physiological demand, and they are involved in various pathological settings, potentially aggravating cardiac dysfunction. Experimental and computational studies using rabbit as a model species have been integral to the development of our current understanding of MEC and MMC. In this paper we review this work, focusing on physiological and pathological implications for cardiac function.

Modeling Current Density Maps Using Aliev-Panfilov Electrophysiological Heart Model

Most existing studies of cardiac arrhythmia rely on surface measurements through optical or electrical mapping techniques. Current density imaging (CDI) is a method which enables us to study current pathways inside the tissue. However, this method entails implementation complexities for beating ex vivo hearts. Hence, this work presents an approach to simulate and study the current distributions in different cardiac electrophysiological states. The results are corroborated by experimental data, and they indicate that different states were distinguishable. The CDI simulations can be used for studying cardiac arrhythmias under simulation conditions which are otherwise impossible or difficult to be implemented experimentally.

A Mathematical Model of Neonatal Rat Atrial Monolayers with Constitutively Active Acetylcholine-Mediated K+ Current

Atrial fibrillation (AF) is the most frequent form of arrhythmia occurring in the industrialized world. Because of its complex nature, each identified form of AF requires specialized treatment. Thus, an in-depth understanding of the bases of these arrhythmias is essential for therapeutic development. A variety of experimental studies aimed at understanding the mechanisms of AF are performed using primary cultures of neonatal rat atrial cardiomyocytes (NRAMs). Previously, we have shown that the distinct advantage of NRAM cultures is that they allow standardized, systematic, robust re-entry induction in the presence of a constitutively-active acetylcholine-mediated K⁺ current (I_KACh-c). Experimental studies dedicated to mechanistic explorations of AF, using these cultures, often use computer models for detailed electrophysiological investigations. However, currently, no mathematical model for NRAMs is available. Therefore, in the present study we propose the first model for the action potential (AP) of a NRAM with constitutively-active acetylcholine-mediated K⁺ current (I_KACh-c). The descriptions of the ionic currents were based on patch-clamp data obtained from neonatal rats. Our monolayer model closely mimics the action potential duration (APD) restitution and conduction velocity (CV) restitution curves presented in our previous in vitro studies. In addition, the model reproduces the experimentally observed dynamics of spiral wave rotation, in the absence and in the presence of drug interventions, and in the presence of localized myofibroblast heterogeneities.

A fundamentally important element in cardiac in silico research is a model for the cardiac cell. It provides a link between measurable characteristics at the subcellular level and biological processes at the whole cell level, thereby allowing the researcher to study mechanisms of cardiac arrhythmias from a molecular cell biological perspective. Such studies are of vast importance for the advancement of understanding of living systems from cells to patient populations. This paper is a joint in silico-experimental study in which we propose the first model for the action potential of an NRAM. To develop this model, we fitted patch-clamp data from recent literature, while additionally performing specific measurements of I_KACh-c in NRAMs. I_KACh-c is an important factor in atrial arrhythmogenesis and a promising target for pharmacological AF-management. The model reproduces in vitro results such as standard characteristics of AP morphology, restitution, and spiral wave dynamics in monolayers, with effects of a subsequent drug-intervention and in the presence of localized myofibroblast heterogeneities. Thus it can be used as a tool to provide computational support to a variety of systematic experimental studies that investigate the mechanisms underlying atrial fibrillation (AF) in NRAM cultures.

Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia

Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.

Uncertainty and variability in computational and mathematical models of cardiac physiology

KEY POINTS

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community.

ABSTRACT

The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for predictive model outputs. We propose that the future of the Cardiac Physiome should include a probabilistic approach to quantify the relationship of variability and uncertainty of model inputs and outputs.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

Extensions to a manifold learning framework for time-series analysis on dynamic manifolds in bioelectric signals

This paper addresses the challenge of extracting meaningful information from measured bioelectric signals generated by complex, large scale physiological systems such as the brain or the heart. We focus on a combination of the well-known Laplacian eigenmaps machine learning approach with dynamical systems ideas to analyze emergent dynamic behaviors. The method reconstructs the abstract dynamical system phase-space geometry of the embedded measurements and tracks changes in physiological conditions or activities through changes in that geometry. It is geared to extract information from the joint behavior of time traces obtained from large sensor arrays, such as those used in multiple-electrode ECG and EEG, and explore the geometrical structure of the low dimensional embedding of moving time windows of those joint snapshots. Our main contribution is a method for mapping vectors from the phase space to the data domain. We present cases to evaluate the methods, including a synthetic example using the chaotic Lorenz system, several sets of cardiac measurements from both canine and human hearts, and measurements from a human brain.

Myocyte-fibroblast communication in cardiac fibrosis and arrhythmias: Mechanisms and model systems

Development of cardiac fibrosis and arrhythmias is controlled by the activity of and communication between cardiomyocytes and fibroblasts in the heart. Myocyte-fibroblast interactions occur via both direct and indirect means including paracrine mediators, extracellular matrix interactions, electrical modulators, mechanical junctions, and membrane nanotubes. In the diseased heart, cardiomyocyte and fibroblast ratios and activity, and thus myocyte-fibroblast interactions, change and are thought to contribute to the course of disease including development of fibrosis and arrhythmogenic activity. Fibroblasts have a developing role in modulating cardiomyocyte electrical and hypertrophic activity, however gaps in knowledge regarding these interactions still exist. Research in this field has necessitated the development of unique approaches to isolate and control myocyte-fibroblast interactions. Numerous methods for 2D and 3D co-culture systems have been developed, while a growing part of this field is in the use of better tools for in vivo systems including cardiomyocyte and fibroblast specific Cre mouse lines for cell type specific genetic ablation. This review will focus on (i) mechanisms of myocyte-fibroblast communication and their effects on disease features such as cardiac fibrosis and arrhythmias as well as (ii) methods being used and currently developed in this field.

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

Mechano-electric heterogeneity of the myocardium as a paradigm of its function

Myocardial heterogeneity is well appreciated and widely documented, from sub-cellular to organ levels. This paper reviews significant achievements of the group, led by Professor Vladimir S. Markhasin, Russia, who was one of the pioneers in studying and interpreting the relevance of cardiac functional heterogeneity.

Optogenetics-enabled assessment of viral gene and cell therapy for restoration of cardiac excitability

Multiple cardiac pathologies are accompanied by loss of tissue excitability, which leads to a range of heart rhythm disorders (arrhythmias). In addition to electronic device therapy (i.e. implantable pacemakers and cardioverter/defibrillators), biological approaches have recently been explored to restore pacemaking ability and to correct conduction slowing in the heart by delivering excitatory ion channels or ion channel agonists. Using optogenetics as a tool to selectively interrogate only cells transduced to produce an exogenous excitatory ion current, we experimentally and computationally quantify the efficiency of such biological approaches in rescuing cardiac excitability as a function of the mode of application (viral gene delivery or cell delivery) and the geometry of the transduced region (focal or spatially-distributed). We demonstrate that for each configuration (delivery mode and spatial pattern), the optical energy needed to excite can be used to predict therapeutic efficiency of excitability restoration. Taken directly, these results can help guide optogenetic interventions for light-based control of cardiac excitation. More generally, our findings can help optimize gene therapy for restoration of cardiac excitability.

A New MRI-Based Model of Heart Function with Coupled Hemodynamics and Application to Normal and Diseased Canine Left Ventricles

A methodology for the simulation of heart function that combines an MRI-based model of cardiac electromechanics (CE) with a Navier–Stokes-based hemodynamics model is presented. The CE model consists of two coupled components that simulate the electrical and the mechanical functions of the heart. Accurate representations of ventricular geometry and fiber orientations are constructed from the structural magnetic resonance and the diffusion tensor MR images, respectively. The deformation of the ventricle obtained from the electromechanical model serves as input to the hemodynamics model in this one-way coupled approach via imposed kinematic wall velocity boundary conditions and at the same time, governs the blood flow into and out of the ventricular volume. The time-dependent endocardial surfaces are registered using a diffeomorphic mapping algorithm, while the intraventricular blood flow patterns are simulated using a sharp-interface immersed boundary method-based flow solver. The utility of the combined heart-function model is demonstrated by comparing the hemodynamic characteristics of a normal canine heart beating in sinus rhythm against that of the dyssynchronously beating failing heart. We also discuss the potential of coupled CE and hemodynamics models for various clinical applications.

High-order finite element methods for cardiac monodomain simulations

Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.

Towards Personalized Cardiology: Multi-Scale Modeling of the Failing Heart

BACKGROUND

Despite modern pharmacotherapy and advanced implantable cardiac devices, overall prognosis and quality of life of HF patients remain poor. This is in part due to insufficient patient stratification and lack of individualized therapy planning, resulting in less effective treatments and a significant number of non-responders.

METHODS AND RESULTS

State-of-the-art clinical phenotyping was acquired, including magnetic resonance imaging (MRI) and biomarker assessment. An individualized, multi-scale model of heart function covering cardiac anatomy, electrophysiology, biomechanics and hemodynamics was estimated using a robust framework. The model was computed on n=46 HF patients, showing for the first time that advanced multi-scale models can be fitted consistently on large cohorts. Novel multi-scale parameters derived from the model of all cases were analyzed and compared against clinical parameters, cardiac imaging, lab tests and survival scores to evaluate the explicative power of the model and its potential for better patient stratification. Model validation was pursued by comparing clinical parameters that were not used in the fitting process against model parameters.

CONCLUSION

This paper illustrates how advanced multi-scale models can complement cardiovascular imaging and how they could be applied in patient care. Based on obtained results, it becomes conceivable that, after thorough validation, such heart failure models could be applied for patient management and therapy planning in the future, as we illustrate in one patient of our cohort who received CRT-D implantation.

Fast Simulation of Mechanical Heterogeneity in the Electrically Asynchronous Heart Using the MultiPatch Module

Cardiac electrical asynchrony occurs as a result of cardiac pacing or conduction disorders such as left bundle-branch block (LBBB). Electrically asynchronous activation causes myocardial contraction heterogeneity that can be detrimental for cardiac function. Computational models provide a tool for understanding pathological consequences of dyssynchronous contraction. Simulations of mechanical dyssynchrony within the heart are typically performed using the finite element method, whose computational intensity may present an obstacle to clinical deployment of patient-specific models. We present an alternative based on the CircAdapt lumped-parameter model of the heart and circulatory system, called the MultiPatch module. Cardiac walls are subdivided into an arbitrary number of patches of homogeneous tissue. Tissue properties and activation time can differ between patches. All patches within a wall share a common wall tension and curvature. Consequently, spatial location within the wall is not required to calculate deformation in a patch. We test the hypothesis that activation time is more important than tissue location for determining mechanical deformation in asynchronous hearts. We perform simulations representing an experimental study of myocardial deformation induced by ventricular pacing, and a patient with LBBB and heart failure using endocardial recordings of electrical activation, wall volumes, and end-diastolic volumes. Direct comparison between simulated and experimental strain patterns shows both qualitative and quantitative agreement between model fibre strain and experimental circumferential strain in terms of shortening and rebound stretch during ejection. Local myofibre strain in the patient simulation shows qualitative agreement with circumferential strain patterns observed in the patient using tagged MRI. We conclude that the MultiPatch module produces realistic regional deformation patterns in the asynchronous heart and that activation time is more important than tissue location within a wall for determining myocardial deformation. The CircAdapt model is therefore capable of fast and realistic simulations of dyssynchronous myocardial deformation embedded within the closed-loop cardiovascular system.

Under normal conditions, the electrical activation of the heart is almost synchronous, leading to uniform contraction. Due to either pathology or electrical pacing, the heart can be activated asynchronously. The result is discoordinated contraction and a reduction in the ability to pump blood. There is considerable interest in using computer simulations to understand how asynchronous electrical activation affects cardiac deformation, and how pathologies of the cardiac conduction system can be treated by pacing the heart. We present the MultiPatch module for simulating the effects of asynchronous electrical activation on cardiac contraction in the relatively simple CircAdapt model of the heart and circulation. We quantitatively compare model simulations to deformation patterns recorded during an experimental study of pacing-induced electrical asynchrony. We then demonstrate a ‘patient-specific’ simulation of deformation in a patient with a conduction disorder called left bundle-branch block. We use timings from endocardial mapping of electrical activation in a patient as an input for the model, and compare the resulting simulated deformation patterns to tagged magnetic resonance imaging recordings from the same patient. The model qualitatively reproduces deformation as observed in the patient. We conclude that the MultiPatch module makes CircAdapt appropriate for simulation of dyssynchronous heart failure in patients.

A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells

Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.

Modeling Pathologies of Diastolic and Systolic Heart Failure

Chronic heart failure is a medical condition that involves structural and functional changes of the heart and a progressive reduction in cardiac output. Heart failure is classified into two categories: diastolic heart failure, a thickening of the ventricular wall associated with impaired filling; and systolic heart failure, a dilation of the ventricles associated with reduced pump function. In theory, the pathophysiology of heart failure is well understood. In practice, however, heart failure is highly sensitive to cardiac microstructure, geometry, and loading. This makes it virtually impossible to predict the time line of heart failure for a diseased individual. Here we show that computational modeling allows us to integrate knowledge from different scales to create an individualized model for cardiac growth and remodeling during chronic heart failure. Our model naturally connects molecular events of parallel and serial sarcomere deposition with cellular phenomena of myofibrillogenesis and sarcomerogenesis to whole organ function. Our simulations predict chronic alterations in wall thickness, chamber size, and cardiac geometry, which agree favorably with the clinical observations in patients with diastolic and systolic heart failure. In contrast to existing single- or bi-ventricular models, our new four-chamber model can also predict characteristic secondary effects including papillary muscle dislocation, annular dilation, regurgitant flow, and outflow obstruction. Our prototype study suggests that computational modeling provides a patient-specific window into the progression of heart failure with a view towards personalized treatment planning.

Computational modeling of cardiac optogenetics: Methodology overview & review of findings from simulations

Cardiac optogenetics is emerging as an exciting new potential avenue to enable spatiotemporally precise control of excitable cells and tissue in the heart with low-energy optical stimuli. This approach involves the expression of exogenous light-sensitive proteins (opsins) in target heart tissue via viral gene or cell delivery. Preliminary experiments in optogenetically-modified cells, tissue, and organisms have made great strides towards demonstrating the feasibility of basic applications, including the use of light stimuli to pace or disrupt reentrant activity. However, it remains unknown whether techniques based on this intriguing technology could be scaled up and used in humans for novel clinical applications, such as pain-free optical defibrillation or dynamic modulation of action potential shape. A key step towards answering such questions is to explore potential optogenetics-based therapies using sophisticated computer simulation tools capable of realistically representing opsin delivery and light stimulation in biophysically detailed, patient-specific models of the human heart. This review provides (1) a detailed overview of the methodological developments necessary to represent optogenetics-based solutions in existing virtual heart platforms and (2) a survey of findings that have been derived from such simulations and a critical assessment of their significance with respect to the progress of the field.

Computer Modelling for Better Diagnosis and Therapy of Patients by Cardiac Resynchronisation Therapy

Mathematical or computer models have become increasingly popular in biomedical science. Although they are a simplification of reality, computer models are able to link a multitude of processes to each other. In the fields of cardiac physiology and cardiology, models can be used to describe the combined activity of all ion channels (electrical models) or contraction-related processes (mechanical models) in potentially millions of cardiac cells. Electromechanical models go one step further by coupling electrical and mechanical processes and incorporating mechano-electrical feedback. The field of cardiac computer modelling is making rapid progress due to advances in research and the ever-increasing calculation power of computers. Computer models have helped to provide better understanding of disease mechanisms and treatment. The ultimate goal will be to create patient-specific models using diagnostic measurements from the individual patient. This paper gives a brief overview of computer models in the field of cardiology and mentions some scientific achievements and clinical applications, especially in relation to cardiac resynchronisation therapy (CRT).

Comparison of diffusion tensor imaging by cardiovascular magnetic resonance and gadolinium enhanced 3D image intensity approaches to investigation of structural anisotropy in explanted rat hearts

BACKGROUND

Cardiovascular magnetic resonance (CMR) can through the two methods 3D FLASH and diffusion tensor imaging (DTI) give complementary information on the local orientations of cardiomyocytes and their laminar arrays.

METHODS

Eight explanted rat hearts were perfused with Gd-DTPA contrast agent and fixative and imaged in a 9.4T magnet by two types of acquisition: 3D fast low angle shot (FLASH) imaging, voxels 50 × 50 × 50 μm, and 3D spin echo DTI with monopolar diffusion gradients of 3.6 ms duration at 11.5 ms separation, voxels 200 × 200 × 200 μm. The sensitivity of each approach to imaging parameters was explored.

RESULTS

The FLASH data showed laminar alignments of voxels with high signal, in keeping with the presumed predominance of contrast in the interstices between sheetlets. It was analysed, using structure-tensor (ST) analysis, to determine the most (v1(ST)), intermediate (v2(ST)) and least (v3(ST)) extended orthogonal directions of signal continuity. The DTI data was analysed to determine the most (e1(DTI)), intermediate (e2(DTI)) and least (e3(DTI)) orthogonal eigenvectors of extent of diffusion. The correspondence between the FLASH and DTI methods was measured and appraised. The most extended direction of FLASH signal (v1(ST)) agreed well with that of diffusion (e1(DTI)) throughout the left ventricle (representative discrepancy in the septum of 13.3 ± 6.7°: median ± absolute deviation) and both were in keeping with the expected local orientations of the long-axis of cardiomyocytes. However, the orientation of the least directions of FLASH signal continuity (v3(ST)) and diffusion (e3(ST)) showed greater discrepancies of up to 27.9 ± 17.4°. Both FLASH (v3(ST)) and DTI (e3(DTI)) where compared to directly measured laminar arrays in the FLASH images. For FLASH the discrepancy between the structure-tensor calculated v3(ST) and the directly measured FLASH laminar array normal was of 9 ± 7° for the lateral wall and 7 ± 9° for the septum (median ± inter quartile range), and for DTI the discrepancy between the calculated v3(DTI) and the directly measured FLASH laminar array normal was 22 ± 14° and 61 ± 53.4°. DTI was relatively insensitive to the number of diffusion directions and to time up to 72 hours post fixation, but was moderately affected by b-value (which was scaled by modifying diffusion gradient pulse strength with fixed gradient pulse separation). Optimal DTI parameters were b = 1000 mm/s(2) and 12 diffusion directions. FLASH acquisitions were relatively insensitive to the image processing parameters explored.

CONCLUSIONS

We show that ST analysis of FLASH is a useful and accurate tool in the measurement of cardiac microstructure. While both FLASH and the DTI approaches appear promising for mapping of the alignments of myocytes throughout myocardium, marked discrepancies between the cross myocyte anisotropies deduced from each method call for consideration of their respective limitations.

A new classifier-based strategy for in-silico ion-channel cardiac drug safety assessment

There is currently a strong interest in using high-throughput in-vitro ion-channel screening data to make predictions regarding the cardiac toxicity potential of a new compound in both animal and human studies. A recent FDA think tank encourages the use of biophysical mathematical models of cardiac myocytes for this prediction task. However, it remains unclear whether this approach is the most appropriate. Here we examine five literature data-sets that have been used to support the use of four different biophysical models and one statistical model for predicting cardiac toxicity in numerous species using various endpoints. We propose a simple model that represents the balance between repolarisation and depolarisation forces and compare the predictive power of the model against the original results (leave-one-out cross-validation). Our model showed equivalent performance when compared to the four biophysical models and one statistical model. We therefore conclude that this approach should be further investigated in the context of early cardiac safety screening when in-vitro potency data is generated.

A brief history of tissue models for cardiac electrophysiology

The last four decades have produced a number of significant advances in the developments of computer models to simulate and investigate the electrical activity of cardiac tissue. The tissue descriptions that underlie these simulations have been built from a combination of clever insight and careful comparison with measured data at multiple scales. Tissue models have not only led to greater insights into the mechanisms of life-threatening arrhythmias but have been used to engineer new therapies to treat the consequences of cardiac disease. This paper is a look back at the early years in the cardiac modeling and the challenges facing the field as models move toward the clinic.

Robust image-based estimation of cardiac tissue parameters and their uncertainty from noisy data

Clinical applications of computational cardiac models require precise personalization, i.e. fitting model parameters to capture patient's physiology. However, due to parameter non-identifiability, limited data, uncertainty in the clinical measurements, and modeling assumptions, various combinations of parameter values may exist that yield the same quality of fit. Hence, there is a need for quantifying the uncertainty in estimated parameters and to ascertain the uniqueness of the found solution. This paper presents a stochastic method to estimate the parameters of an image-based electromechanical model of the heart and their uncertainty due to noise in measurements. First, Bayesian inference is applied to fully estimate the posterior probability density function (PDF) of the model. To that end, Markov Chain Monte Carlo sampling is used, which is made computationally tractable by employing a fast surrogate model based on Polynomial Chaos Expansion, instead of the true forward model. Then, we use the mean-shift algorithm to automatically find the modes of the PDF and select the most likely one while being robust to noise. The approach is used to estimate global active stress and passive stiffness from invasive pressure and image-based volume quantification. Experiments on eight patients showed that not only our approach yielded goodness of fits equivalent to a well-established deterministic method, but we could also demonstrate the non-uniqueness of the problem and report uncertainty estimates, crucial information for subsequent clinical assessments of the personalized models.

Left Ventricular Diastolic and Systolic Material Property Estimation from Image Data: LV Mechanics Challenge

Cardiovascular simulations using patient-specific geometries can help researchers understand the mechanical behavior of the heart under different loading or disease conditions. However, to replicate the regional mechanics of the heart accurately, both the nonlinear passive and active material properties must be estimated reliably. In this paper, automated methods were used to determine passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Two different approaches were used to model systole. In the first, a physiologically-based active contraction model [1] coupled to a hemodynamic three-element Windkessel model of the circulation was used to simulate ventricular ejection. In the second, developed active tension was directly adjusted to match ventricular volumes at end-systole while prescribing the known end-systolic pressure. These methods were tested in four normal dogs using the data provided for the LV mechanics challenge [2]. The resulting end-diastolic and end-systolic geometry from the simulation were compared with measured image data.

A smoothed finite element method for analysis of anisotropic large deformation of passive rabbit ventricles in diastole

The smoothed FEM (S-FEM) is firstly extended to explore the behavior of 3D anisotropic large deformation of rabbit ventricles during the passive filling process in diastole. Because of the incompressibility of myocardium, a special method called selective face-based/node-based S-FEM using four-node tetrahedral elements (FS/NS-FEM-TET4) is adopted in order to avoid volumetric locking. To validate the proposed algorithms of FS/NS-FEM-TET4, the 3D Lame problem is implemented. The performance contest results show that our FS/NS-FEM-TET4 is accurate, volumetric locking-free and insensitive to mesh distortion than standard linear FEM because of absence of isoparametric mapping. Actually, the efficiency of FS/NS-FEM-TET4 is comparable with higher-order FEM, such as 10-node tetrahedral elements. The proposed method for Holzapfel myocardium hyperelastic strain energy is also validated by simple shear tests through the comparison outcomes reported in available references. Finally, the FS/NS-FEM-TET4 is applied in the example of the passive filling of MRI-based rabbit ventricles with fiber architecture derived from rule-based algorithm to demonstrate its efficiency. Hence, we conclude that FS/NS-FEM-TET4 is a promising alternative other than FEM in passive cardiac mechanics.

Systems approaches in integrative cardiac biology: illustrations from cardiac heterocellular signalling studies

Understanding the complexity of cardiac physiology requires system-level studies of multiple cardiac cell types. Frequently, however, the end result of published research lacks the detail of the collaborative and integrative experimental design process, and the underlying conceptual framework. We review the recent progress in systems modelling and omics analysis of the heterocellular heart environment through complementary forward and inverse approaches, illustrating these conceptual and experimental frameworks with case studies from our own research program. The forward approach begins by collecting curated information from the niche cardiac biology literature, and connecting the dots to form mechanistic network models that generate testable system-level predictions. The inverse approach starts from the vast pool of public omics data in recent cardiac biological research, and applies bioinformatics analysis to produce novel candidates for further investigation. We also discuss the possibility of combining these two approaches into a hybrid framework, together with the benefits and challenges. These interdisciplinary research frameworks illustrate the interplay between computational models, omics analysis, and wet lab experiments, which holds the key to making real progress in improving human cardiac wellbeing.

In Silico Organ Modelling in Predicting Efficacy and Safety of New Medicines

The development of new medicines faces important challenges due to difficulties in the assessment of their efficacy and their safety in the targeted human population. In silico approaches through the use of mathematical modelling and computer simulations are increasingly being used to overcome some of the limitations of current experimental methods used in the development of new medicines. This chapter describes state-of-the-art in silico approaches for the evaluation of the safety and efficacy of medicines targeting important causes of mortality such as cardiovascular disease. Firstly, we describe the in silico multi-scale mathematical models and simulation techniques required to describe drug-induced effects on physiological systems such as the heart from the subcellular to the whole organ level. Then we illustrate the power of in silico approaches used to augment experimental and clinical investigations, by providing the framework to unravel multi-scale mechanisms underlying variability in the response to medicines and to focus on effects in human rather than animal models. We devote the last part of the chapter to discussing the process of validation of in silico models and simulations, which is key in building up their credibility.

Data analysis in cardiac arrhythmias

Cardiac arrhythmias are an increasingly present in developed countries and represent a major health and economic burden. The occurrence of cardiac arrhythmias is closely linked to the electrical function of the heart. Consequently, the analysis of the electrical signal generated by the heart tissue, either recorded invasively or noninvasively, provides valuable information for the study of cardiac arrhythmias. In this chapter, novel cardiac signal analysis techniques that allow the study and diagnosis of cardiac arrhythmias are described, with emphasis on cardiac mapping which allows for spatiotemporal analysis of cardiac signals.Cardiac mapping can serve as a diagnostic tool by recording cardiac signals either in close contact to the heart tissue or noninvasively from the body surface, and allows the identification of cardiac sites responsible of the development or maintenance of arrhythmias. Cardiac mapping can also be used for research in cardiac arrhythmias in order to understand their mechanisms. For this purpose, both synthetic signals generated by computer simulations and animal experimental models allow for more controlled physiological conditions and complete access to the organ.

Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach

Under diseased conditions, remodeling of the cardiac tissue properties (“passive properties”) takes place; these are aspects of electrophysiological behavior that are not associated with active ion transport across cell membranes. Remodeling of the passive electrophysiological properties most often results from structural remodeling, such as gap junction down-regulation and lateralization, fibrotic growth infiltrating the myocardium, or the development of an infarct scar. Such structural remodeling renders atrial or ventricular tissue as a major substrate for arrhythmias. The current review focuses on these aspects of cardiac arrhythmogenesis. Due to the inherent complexity of cardiac arrhythmias, computer simulations have provided means to elucidate interactions pertinent to this spatial scale. Here we review the current state-of-the-art in modeling atrial and ventricular arrhythmogenesis as arising from the disease-induced changes in the passive tissue properties, as well as the contributions these modeling studies have made to our understanding of the mechanisms of arrhythmias in the heart. Because of the rapid advance of structural imaging methodologies in cardiac electrophysiology, we chose to present studies that have used such imaging methodologies to construct geometrically realistic models of cardiac tissue, or the organ itself, where the regional remodeling properties of the myocardium can be represented in a realistic way. We emphasize how the acquired knowledge can be used to pave the way for clinical applications of cardiac organ modeling under the conditions of structural remodeling.

Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study

In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. Fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies.

The Living Heart Project: A robust and integrative simulator for human heart function

The heart is not only our most vital, but also our most complex organ: Precisely controlled by the interplay of electrical and mechanical fields, it consists of four chambers and four valves, which act in concert to regulate its filling, ejection, and overall pump function. While numerous computational models exist to study either the electrical or the mechanical response of its individual chambers, the integrative electro-mechanical response of the whole heart remains poorly understood. Here we present a proof-of-concept simulator for a four-chamber human heart model created from computer topography and magnetic resonance images. We illustrate the governing equations of excitation-contraction coupling and discretize them using a single, unified finite element environment. To illustrate the basic features of our model, we visualize the electrical potential and the mechanical deformation across the human heart throughout its cardiac cycle. To compare our simulation against common metrics of cardiac function, we extract the pressure-volume relationship and show that it agrees well with clinical observations. Our prototype model allows us to explore and understand the key features, physics, and technologies to create an integrative, predictive model of the living human heart. Ultimately, our simulator will open opportunities to probe landscapes of clinical parameters, and guide device design and treatment planning in cardiac diseases such as stenosis, regurgitation, or prolapse of the aortic, pulmonary, tricuspid, or mitral valve.

Multiscale computational analysis of the bioelectric consequences of myocardial ischaemia and infarction

Ischaemic heart disease is considered as the single most frequent cause of death, provoking more than 7 000 000 deaths every year worldwide. A high percentage of patients experience sudden cardiac death, caused in most cases by tachyarrhythmic mechanisms associated to myocardial ischaemia and infarction. These diseases are difficult to study using solely experimental means due to their complex dynamics and unstable nature. In the past decades, integrative computational simulation techniques have become a powerful tool to complement experimental and clinical research when trying to elucidate the intimate mechanisms of ischaemic electrophysiological processes and to aid the clinician in the improvement and optimization of therapeutic procedures. The purpose of this paper is to briefly review some of the multiscale computational models of myocardial ischaemia and infarction developed in the past 20 years, ranging from the cellular level to whole-heart simulations.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Effects of L-type calcium channel and human ether-a-go-go related gene blockers on the electrical activity of the human heart: a simulation study

Aims

Class III and IV drugs affect cardiac human ether-a-go-go related gene (I_Kr) and L-type calcium (I_CaL) channels, resulting in complex alterations in repolarization with both anti- and pro-arrhythmic consequences. Interpretation of their effects on cellular and electrocardiogram (ECG)-based biomarkers for risk stratification is challenging. As pharmaceutical compounds often exhibit multiple ion channel effects, our goal is to investigate the simultaneous effect of I_CaL and I_Kr block on human ventricular electrophysiology from ionic to ECG level.

Methods and results

Simulations are conducted using a human body torso bidomain model, which includes realistic representation of human membrane kinetics, anatomy, and fibre orientation. A simple block pore model is incorporated to simulate drug-induced I_CaL and I_Kr blocks, for drug dose = 0, IC₅₀, 2× IC₅₀, 10× IC₅₀, and 30× IC₅₀. Drug effects on human ventricular activity are quantified for different degrees and combinations of I_CaL and I_Kr blocks from the ionic to the body surface ECG level. Electrocardiogram simulations show that I_CaL block results in shortening of the QT interval, ST elevation, and reduced T-wave amplitude, caused by reduction in action potential duration and action potential amplitude during the plateau phase, and in repolarization times. In contrast, I_Kr block results in QT prolongation and reduced T-wave amplitude. When I_CaL and I_Kr blocks are combined, the degree of I_CaL block strongly determines QT interval whereas the effect of I_Kr block is more pronounced on the T-wave amplitude.

Conclusion

Our simulation study provides new insights into the combined effect of I_CaL and I_Kr blocks on human ventricular activity using a multiscale computational human torso model.

Optical mapping of optogenetically shaped cardiac action potentials

Light-mediated silencing and stimulation of cardiac excitability, an important complement to electrical stimulation, promises important discoveries and therapies. To date, cardiac optogenetics has been studied with patch-clamp, multielectrode arrays, video microscopy, and an all-optical system measuring calcium transients. The future lies in achieving simultaneous optical acquisition of excitability signals and optogenetic control, both with high spatio-temporal resolution. Here, we make progress by combining optical mapping of action potentials with concurrent activation of channelrhodopsin-2 (ChR2) or halorhodopsin (eNpHR3.0), via an all-optical system applied to monolayers of neonatal rat ventricular myocytes (NRVM). Additionally, we explore the capability of ChR2 and eNpHR3.0 to shape action-potential waveforms, potentially aiding the study of short/long QT syndromes that result from abnormal changes in action potential duration (APD). These results show the promise of an all-optical system to acquire action potentials with precise temporal optogenetics control, achieving a long-sought flexibility beyond the means of conventional electrical stimulation.

Methodology for image-based reconstruction of ventricular geometry for patient-specific modeling of cardiac electrophysiology

Patient-specific modeling of ventricular electrophysiology requires an interpolated reconstruction of the 3-dimensional (3D) geometry of the patient ventricles from the low-resolution (Lo-res) clinical images. The goal of this study was to implement a processing pipeline for obtaining the interpolated reconstruction, and thoroughly evaluate the efficacy of this pipeline in comparison with alternative methods. The pipeline implemented here involves contouring the epi- and endocardial boundaries in Lo-res images, interpolating the contours using the variational implicit functions method, and merging the interpolation results to obtain the ventricular reconstruction. Five alternative interpolation methods, namely linear, cubic spline, spherical harmonics, cylindrical harmonics, and shape-based interpolation were implemented for comparison. In the thorough evaluation of the processing pipeline, Hi-res magnetic resonance (MR), computed tomography (CT), and diffusion tensor (DT) MR images from numerous hearts were used. Reconstructions obtained from the Hi-res images were compared with the reconstructions computed by each of the interpolation methods from a sparse sample of the Hi-res contours, which mimicked Lo-res clinical images. Qualitative and quantitative comparison of these ventricular geometry reconstructions showed that the variational implicit functions approach performed better than others. Additionally, the outcomes of electrophysiological simulations (sinus rhythm activation maps and pseudo-ECGs) conducted using models based on the various reconstructions were compared. These electrophysiological simulations demonstrated that our implementation of the variational implicit functions-based method had the best accuracy.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

Mathematical modeling of physiological systems: an essential tool for discovery

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?"

Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This article aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention.

Microstructural impact of ischemia and bone marrow-derived cell therapy revealed with diffusion tensor magnetic resonance imaging tractography of the heart in vivo

BACKGROUND

The arrangement of myofibers in the heart is highly complex and must be replicated by injected cells to produce functional myocardium. A novel approach to characterize the microstructural response of the myocardium to ischemia and cell therapy, with the use of serial diffusion tensor magnetic resonance imaging tractography of the heart in vivo, is presented.

METHODS AND RESULTS

Validation of the approach was performed in normal (n=6) and infarcted mice (n=6) as well as healthy human volunteers. Mice (n=12) were then injected with bone marrow mononuclear cells 3 weeks after coronary ligation. In half of the mice the donor and recipient strains were identical, and in half the strains were different. A positive response to cell injection was defined by a decrease in mean diffusivity, an increase in fractional anisotropy, and the appearance of new myofiber tracts with the correct orientation. A positive response to bone marrow mononuclear cell injection was seen in 1 mouse. The response of the majority of mice to bone marrow mononuclear cell injection was neutral (9/12) or negative (2/12). The in vivo tractography findings were confirmed with histology.

CONCLUSIONS

Diffusion tensor magnetic resonance imaging tractography was able to directly resolve the ability of injected cells to generate new myofiber tracts and provided a fundamental readout of their regenerative capacity. A highly novel and translatable approach to assess the efficacy of cell therapy in the heart is thus presented.