A brief history of tissue models for cardiac electrophysiology

Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges

Intracellular calcium (Ca) cycling in the heart plays key roles in excitation-contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach

Conduction velocity error is often the main culprit behind the need for very fine spatial discretizations and high computational effort in cardiac electrophysiology problems. In light of this, a novel approach for simulating an accurate conduction velocity in coarse meshes with linear elements is suggested based on a modified quadrature approach. In this approach, the quadrature points are placed at arbitrary offsets of the isoparametric coordinates. A numerical study illustrates the dependence of the conduction velocity on the spatial discretization and the conductivity when using different quadrature rules and calculation approaches. Additionally, examples using the modified quadrature in coarse meshes for wave propagation demonstrate the improved accuracy of the conduction velocity with this method. This novel approach possesses great potential in reducing the computational effort required but remains limited to specific linear elements and experiences a reduction in accuracy for irregular meshes and heterogeneous conductivities. Further research can focus on developing an adaptive quadrature and extending the approach to other element formulations in order to make the approach more generally applicable.

Image-Driven Modeling of Nanoscopic Cardiac Function: Where Have We Come From, and Where Are We Going?

Complementary developments in microscopy and mathematical modeling have been critical to our understanding of cardiac excitation–contraction coupling. Historically, limitations imposed by the spatial or temporal resolution of imaging methods have been addressed through careful mathematical interrogation. Similarly, limitations imposed by computational power have been addressed by imaging macroscopic function in large subcellular domains or in whole myocytes. As both imaging resolution and computational tractability have improved, the two approaches have nearly merged in terms of the scales that they can each be used to interrogate. With this review we will provide an overview of these advances and their contribution to understanding ventricular myocyte function, including exciting developments over the last decade. We specifically focus on experimental methods that have pushed back limits of either spatial or temporal resolution of nanoscale imaging (e.g., DNA-PAINT), or have permitted high resolution imaging on large cellular volumes (e.g., serial scanning electron microscopy). We also review the progression of computational approaches used to integrate and interrogate these new experimental data sources, and comment on near-term advances that may unify understanding of the underlying biology. Finally, we comment on several outstanding questions in cardiac physiology that stand to benefit from a concerted and complementary application of these new experimental and computational methods.

Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons

The bidomain model is considered to be the gold standard for numerical simulation of the electrophysiology of cardiac tissue. The model provides important insights into the conduction properties of the electrochemical wave traversing the cardiac muscle in every heartbeat. However, in normal resolution, the model represents the average over a large number of cardiomyocytes, and more accurate models based on representations of all individual cells have therefore been introduced in order to gain insight into the conduction properties close to the myocytes. The more accurate model considered here is referred to as the EMI model since both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model. Here, we show that the bidomain model can be derived from the cell-based EMI model and we thus reveal the close relation between the two models, and obtain an indication of the error introduced in the approximation. Also, we present numerical simulations comparing the results of the two models and thereby highlight both similarities and differences between the models. We observe that the deviations between the solutions of the models become larger for larger cell sizes. Furthermore, we observe that the bidomain model provides solutions that are very similar to the EMI model when conductive properties of the tissue are in the normal range, but large deviations are present when the resistance between cardiomyocytes is increased.

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Initiation and entrainment of multicellular automaticity via diffusion limited extracellular domains

Electrically excitable cells often spontaneously and synchronously depolarize in vitro and in vivo preparations. It remains unclear how cells entrain and autorhythmically activate above the intrinsic mean activation frequency of isolated cells with or without pacemaking mechanisms. Recent studies suggest that cyclic ion accumulation and depletion in diffusion-limited extracellular volumes modulate electrophysiology by ephaptic mechanisms (nongap junction or synaptic coupling). This report explores how potassium accumulation and depletion in a restricted extracellular domain induces spontaneous action potentials in two different computational models of excitable cells without gap junctional coupling: Hodgkin-Huxley and Luo-Rudy. Importantly, neither model will spontaneously activate on its own without external stimuli. Simulations demonstrate that cells sharing a diffusion-limited extracellular compartment can become autorhythmic and entrained despite intercellular electrical heterogeneity. Autorhythmic frequency is modulated by the cleft volume and potassium fluxes through the cleft. Additionally, inexcitable cells can suppress or induce autorhythmic activity in an excitable cell via a shared cleft. Diffusion-limited shared clefts can also entrain repolarization. Critically, this model predicts a mechanism by which diffusion-limited shared clefts can initiate, entrain, and modulate multicellular automaticity in the absence of gap junctions.

From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

Automated Localization of Focal Ventricular Tachycardia From Simulated Implanted Device Electrograms: A Combined Physics-AI Approach

Background: Focal ventricular tachycardia (VT) is a life-threating arrhythmia, responsible for high morbidity rates and sudden cardiac death (SCD). Radiofrequency ablation is the only curative therapy against incessant VT; however, its success is dependent on accurate localization of its source, which is highly invasive and time-consuming. Objective: The goal of our study is, as a proof of concept, to demonstrate the possibility of utilizing electrogram (EGM) recordings from cardiac implantable electronic devices (CIEDs). To achieve this, we utilize fast and accurate whole torso electrophysiological (EP) simulations in conjunction with convolutional neural networks (CNNs) to automate the localization of focal VTs using simulated EGMs. Materials and Methods: A highly detailed 3D torso model was used to simulate ∼4000 focal VTs, evenly distributed across the left ventricle (LV), utilizing a rapid reaction-eikonal environment. Solutions were subsequently combined with lead field computations on the torso to derive accurate electrocardiograms (ECGs) and EGM traces, which were used as inputs to CNNs to localize focal sources. We compared the localization performance of a previously developed CNN architecture (Cartesian probability-based) with our novel CNN algorithm utilizing universal ventricular coordinates (UVCs). Results: Implanted device EGMs successfully localized VT sources with localization error (8.74 mm) comparable to ECG-based localization (6.69 mm). Our novel UVC CNN architecture outperformed the existing Cartesian probability-based algorithm (errors = 4.06 mm and 8.07 mm for ECGs and EGMs, respectively). Overall, localization was relatively insensitive to noise and changes in body compositions; however, displacements in ECG electrodes and CIED leads caused performance to decrease (errors 16-25 mm). Conclusion: EGM recordings from implanted devices may be used to successfully, and robustly, localize focal VT sources, and aid ablation planning.

Cardiac tissue conductivity estimation using confirmatory factor analysis

Impaired electrical conduction has been shown to play an important role in the development of heart rhythm disorders. Being able to determine the conductivity is important to localize the arrhythmogenic substrate that causes abnormalities in atrial tissue. In this work, we present an algorithm to estimate the conductivity from epicardial electrograms (EGMs) using a high-resolution electrode array. With these arrays, it is possible to measure the propagation of the extracellular potential of the cardiac tissue at multiple positions simultaneously. Given this data, it is in principle possible to estimate the tissue conductivity. However, this is an ill-posed problem due to the large number of unknown parameters in the electrophysiological data model. In this paper, we make use of an effective method called confirmatory factor analysis (CFA), which we apply to the cross correlation matrix of the data to estimate the tissue conductivity. CFA comes with identifiability conditions that need to be satisfied to solve the problem, which is, in this case, estimation of the tissue conductivity. These identifiability conditions can be used to find the relationship between the desired resolution and the required amount of data. Numerical experiments on the simulated data demonstrate that the proposed method can localize the conduction blocks in the tissue and can also estimate the smoother variation in the conductivities. The conductivity values estimated from the clinical data are in line with the values reported in literature and the EGMs reconstructed based on the estimated parameters match well with the clinical EGMs.

Strategies to Refine Gastric Stimulation and Pacing Protocols: Experimental and Modeling Approaches

Gastric pacing and stimulation strategies were first proposed in the 1960s to treat motility disorders. However, there has been relatively limited clinical translation of these techniques. Experimental investigations have been critical in advancing our understanding of the control mechanisms that innervate gut function. In this review, we will discuss the use of pacing to modulate the rhythmic slow wave conduction patterns generated by interstitial cells of Cajal in the gastric musculature. In addition, the use of gastric high-frequency stimulation methods that target nerves in the stomach to either inhibit or enhance stomach function will be discussed. Pacing and stimulation protocols to modulate gastric activity, effective parameters and limitations in the existing studies are summarized. Mathematical models are useful to understand complex and dynamic systems. A review of existing mathematical models and techniques that aim to help refine pacing and stimulation protocols are provided. Finally, some future directions and challenges that should be investigated are discussed.

Approaches for determining cardiac bidomain conductivity values: progress and challenges

Modelling the electrical activity of the heart is an important tool for understanding electrical function in various diseases and conduction disorders. Clearly, for model results to be useful, it is necessary to have accurate inputs for the models, in particular the commonly used bidomain model. However, there are only three sets of four experimentally determined conductivity values for cardiac ventricular tissue and these are inconsistent, were measured around 40 years ago, often produce different results in simulations and do not fully represent the three-dimensional anisotropic nature of cardiac tissue. Despite efforts in the intervening years, difficulties associated with making the measurements and also determining the conductivities from the experimental data have not yet been overcome. In this review, we summarise what is known about the conductivity values, as well as progress to date in meeting the challenges associated with both the mathematical modelling and the experimental techniques. Graphical abstract Epicardial potential distributions, arising from a subendocardial ischaemic region, modelled using conductivity data from the indicated studies.

In-silico pace-mapping using a detailed whole torso model and implanted electronic device electrograms for more efficient ablation planning

BACKGROUND

Pace-mapping is a commonly used electrophysiological (EP) procedure which aims to identify exit sites of ventricular tachycardia (VT) by matching ventricular activation patterns (assessed by QRS morphology) at specific pacing locations with activation during VT. However, long procedure durations and the need for VT induction render this technique non-optimal. To demonstrate the potential of in-silico pace-mapping, using stored electrogram (EGM) recordings of clinical VT from implanted devices to guide pre-procedural ablation planning.

METHOD

Six scar-related VT episodes were simulated in a 3D torso model reconstructed from computed tomography (CT) imaging data, including three different infarct anatomies mapped from infarcted porcine imaging data. In-silico pace-mapping was performed to localise VT exit sites and isthmuses by using 12-lead electrocardiogram (ECG) signals and different combinations of EGM sensing vectors from implanted devices, through the creation of conventional correlation maps and reference-less maps.

RESULTS

Our in-silico platform was successful in identifying VT exit sites for a variety of different VT morphologies from both ECG correlation maps and corresponding EGM maps, with the latter dependent upon the number of sensing vectors used. We also showed the added utility of both ECG and EGM reference-less pace-mapping for the identification of slow-conducting isthmuses, uncovering the optimal algorithm parameters. Finally, EGM-based pace-mapping was shown to be more dependent upon the mapped surface (epicardial/endocardial), relative to the VT origin.

CONCLUSIONS

In-silico pace-mapping can be used along with EGMs from implanted devices to localise VT ablation targets in pre-procedural planning.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.

Fast uncertainty quantification of activation sequences in patient-specific cardiac electrophysiology meeting clinical time constraints

We present a fast, patient-specific methodology for uncertainty quantification in electrophysiology, aimed at meeting the time constraints of clinical practitioners. We focus on computing the statistics of the activation map, given the uncertainties associated with the conductivity tensor modeling the fiber orientation in the heart. We use a fast parallel solution method implemented on a graphics processing unit for the eikonal approximation, in order to compute the activation map and to sample the random fiber field with correlation on the basis of geodesic distances. While this enables to perform uncertainty quantification studies with a manageable computational effort, the required time frame still exceeds clinically suitable time expectations. In order to reduce it further by 2 orders of magnitude, we rely on Bayesian multifidelity methods. In particular, we propose a low-fidelity model that is patient-specific and free from the additional training cost associated with reduced models. This is achieved by a sound physics-based simplification of the full eikonal model. The low-fidelity output is then corrected by the standard multifidelity framework. In practice, the complete procedure only requires approximately 100 new runs of our eikonal graphics processing unit solver for producing the sought estimates and their associated credible intervals, enabling a full online analysis in less than 5 minutes.

Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

Realistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity.

Modeling dynamics in diseased cardiac tissue: Impact of model choice

Cardiac arrhythmias have been traditionally simulated using continuous models that assume tissue homogeneity and use a relatively large spatial discretization. However, it is believed that the tissue fibrosis and collagen deposition, which occur on a micron-level, are critical factors in arrhythmogenesis in diseased tissues. Consequently, it remains unclear how well continuous models, which use averaged electrical properties, are able to accurately capture complex conduction behaviors such as re-entry in fibrotic tissues. The objective of this study was to compare re-entrant behavior in discrete microstructural models of fibrosis and in two types of equivalent continuous models, a homogenous continuous model and a hybrid continuous model with distinct heterogeneities. In the discrete model, increasing levels of tissue fibrosis lead to a substantial increase in the re-entrant cycle length which is inadequately reflected in the homogenous continuous models. These cycle length increases appear to be primarily due to increases in the tip path length and to altered restitution behavior, and suggest that it is critical to consider the discrete effects of fibrosis on conduction when studying arrhythmogenesis in fibrotic myocardium. Hybrid models are able to accurately capture some aspects of re-entry and, if carefully tuned, may provide a framework for simulating conduction in diseased tissues with both accuracy and efficiency.

Ephaptic coupling rescues conduction failure in weakly coupled cardiac tissue with voltage-gated gap junctions

Electrical conduction in cardiac tissue is usually considered to be primarily facilitated by gap junctions, providing a pathway between the intracellular spaces of neighboring cells. However, recent studies have highlighted the role of coupling via extracellular electric fields, also known as ephaptic coupling, particularly in the setting of reduced gap junction expression. Further, in the setting of reduced gap junctional coupling, voltage-dependent gating of gap junctions, an oft-neglected biophysical property in computational studies, produces a positive feedback that promotes conduction failure. We hypothesized that ephaptic coupling can break the positive feedback loop and rescue conduction failure in weakly coupled cardiac tissue. In a computational tissue model incorporating voltage-gated gap junctions and ephaptic coupling, we demonstrate that ephaptic coupling can rescue conduction failure in weakly coupled tissue. Further, ephaptic coupling increased conduction velocity in weakly coupled tissue, and importantly, reduced the minimum gap junctional coupling necessary for conduction, most prominently at fast pacing rates. Finally, we find that, although neglecting gap junction voltage-gating results in negligible differences in well coupled tissue, more significant differences occur in weakly coupled tissue, greatly underestimating the minimal gap junctional coupling that can maintain conduction. Our study suggests that ephaptic coupling plays a conduction-preserving role, particularly at rapid heart rates.

Evaluation of a Rapid Anisotropic Model for ECG Simulation

State-of-the-art cardiac electrophysiology models that are able to deliver physiologically motivated activation maps and electrocardiograms (ECGs) can only be solved on high-performance computing architectures. This makes it nearly impossible to adopt such models in clinical practice. ECG imaging tools typically rely on simplified models, but these neglect the anisotropic electric conductivity of the tissue in the forward problem. Moreover, their results are often confined to the heart-torso interface. We propose a forward model that fully accounts for the anisotropic tissue conductivity and produces the standard 12-lead ECG in a few seconds. The activation sequence is approximated with an eikonal model in the 3d myocardium, while the ECG is computed with the lead-field approach. Both solvers were implemented on graphics processing units and massively parallelized. We studied the numerical convergence and scalability of the approach. We also compared the method to the bidomain model in terms of ECGs and activation maps, using a simplified but physiologically motivated geometry and 6 patient-specific anatomies. The proposed methods provided a good approximation of activation maps and ECGs computed with a bidomain model, in only a few seconds. Both solvers scaled very well to high-end hardware. These methods are suitable for use in ECG imaging methods, and may soon become fast enough for use in interactive simulation tools.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

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.

Noninvasive Imaging of Human Atrial Activation during Atrial Flutter and Normal Rhythm from Body Surface Potential Maps

Background

Knowledge of atrial electrophysiological properties is crucial for clinical intervention of atrial arrhythmias and the investigation of the underlying mechanism. This study aims to evaluate the feasibility of a novel noninvasive cardiac electrical imaging technique in imaging bi-atrial activation sequences from body surface potential maps (BSPMs).

Methods

The study includes 7 subjects, with 3 atrial flutter patients, and 4 healthy subjects with normal atrial activations. The subject-specific heart-torso geometries were obtained from MRI/CT images. The equivalent current densities were reconstructed from 208-channel BSPMs by solving the inverse problem using individual heart-torso geometry models. The activation times were estimated from the time instant corresponding to the highest peak in the time course of the equivalent current densities. To evaluate the performance, a total of 32 cycles of atrial flutter were analyzed. The imaged activation maps obtained from single beats were compared with the average maps and the activation maps measured from CARTO, by using correlation coefficient (CC) and relative error (RE).

Results

The cardiac electrical imaging technique is capable of imaging both focal and reentrant activations. The imaged activation maps for normal atrial activations are consistent with findings from isolated human hearts. Activation maps for isthmus-dependent counterclockwise reentry were reconstructed on three patients with typical atrial flutter. The method was capable of imaging macro counterclockwise reentrant loop in the right atrium and showed inter-atria electrical conduction through coronary sinus. The imaged activation sequences obtained from single beats showed good correlation with both the average activation maps (CC = 0.91±0.03, RE = 0.29±0.05) and the clinical endocardial findings using CARTO (CC = 0.70±0.04, RE = 0.42±0.05).

Conclusions

The noninvasive cardiac electrical imaging technique is able to reconstruct complex atrial reentrant activations and focal activation patterns in good consistency with clinical electrophysiological mapping. It offers the potential to assist in radio-frequency ablation of atrial arrhythmia and help defining the underlying arrhythmic mechanism.

In vivo Electrophysiological Study of Induced Ventricular Tachycardia in Intact Rat Model of Chronic Ischemic Heart Failure

OBJECTIVE

The objective of this study was to define the clinical relevance of in vivo electrophysiologic (EP) studies in a rat model of chronic ischemic heart failure (CHF).

METHODS

Electrical activation sequences, voltage amplitudes, and monophasic action potentials (MAPs) were recorded from adult male Sprague-Dawley rats six weeks after left coronary artery ligation. Programmed electrical stimulation (PES) sequences were developed to induce sustained ventricular tachycardia (VT). The inducibility of sustained VT was defined by PES and the recorded tissue MAPs.

RESULTS

Rats in CHF were defined ( 0.05) by elevated left ventricular (LV) end-diastolic pressure (5 ± 1 versus 18 ± 2 mmHg), decreased LV + d P/dt (7496 ± 225 versus 5502 [Formula: see text] s), LV - dP/dt (7723 ± 208 versus 3819 [Formula: see text]), LV ejection fraction (79 ± 3 versus [Formula: see text]), peak developed pressure (176 ± 4 versus 145 ± 9 mmHg), and prolonged time constant of LV relaxation Tau (18 ± 1 versus 29 ± 2 ms). The EP data showed decreased ( 0.05) electrogram amplitude in border and infarct zones (Healthy zone (H): 8.7 ± 2.1 mV, Border zone (B): 5.3 ± 1.6 mV, and Infarct zone (I): 2.3 ± 1.2 mV), decreased MAP amplitude in the border zone (H: [Formula: see text] 1.0 mV, B: 9.7 ± 0.5 mV), and increased repolarization heterogeneity in the border zone (H: 8.1 ± 1.5 ms, B: 20.2 ± 3.1 ms). With PES we induced sustained VT (>15 consecutive PVCs) in rats with CHF (10/14) versus Sham (0/8).

CONCLUSIONS

These EP studies establish a clinically relevant protocol for studying genesis of VT in CHF.

SIGNIFICANCE

The in vivo rat model of CHF combined with EP analysis could be used to determine the arrhythmogenic potential of new treatments for CHF.

Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study

Cardiac electrical dynamics are governed by cellular-level properties, such as action potential duration (APD) restitution and intracellular calcium (Ca) handling, and tissue-level properties, including conduction velocity restitution and cell-cell coupling. Irregular dynamics at the cellular level can lead to instabilities in cardiac tissue, including alternans, a beat-to-beat alternation in the action potential and/or the intracellular Ca transient. In this study, we incorporate a detailed single cell coupled map model of Ca cycling and bidirectional APD-Ca coupling into a spatially extended tissue model to investigate the influence of sarcoplasmic reticulum (SR) Ca uptake and release properties on alternans and conduction block. We find that an intermediate SR Ca uptake rate and larger SR Ca release resulted in the widest range of stimulus periods that promoted alternans. However, both reduced SR Ca uptake and release promote arrhythmogenic spatially and electromechanically discordant alternans, suggesting a complex interaction between SR Ca handling and alternans characteristics at the cellular and tissue level.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Mechano-electric feedback in one-dimensional model of myocardium

We utilized our earlier developed 1D mathematical model of the heart muscle strand to study contribution of the bilateral interactions between excitation and contraction on the cellular and tissue levels to the local and global myocardium function. Numerical experiments on the model showed that an initially uniform strand, formed on the inherently identical cells, became functionally heterogeneous due to the asynchronous excitation via the electrical wave spread. Mechanical interactions between the cells and the mechano-electric feedback beat-to-beat affect the functional characteristics of coupled cardiomyocytes further, adjusting their electrical and mechanical heterogeneity to the activation timing. Model simulations showed that functional heterogeneity increases with an enlarged spatial extension of the myocardial strand (in terms of the longer slack length not a higher stretch of the strand), demonstrating a special role of the heart size in its function. Model analysis suggests that cooperative mechanisms of myofilament calcium activation contribute essentially to the generation of cellular functional heterogeneity in contracting cardiac tissue.

Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System

A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.

The virtual heart as a platform for screening drug cardiotoxicity

To predict the safety of a drug at an early stage in its development is a major challenge as there is a lack of in vitro heart models that correlate data from preclinical toxicity screening assays with clinical results. A biophysically detailed computer model of the heart, the virtual heart, provides a powerful tool for simulating drug–ion channel interactions and cardiac functions during normal and disease conditions and, therefore, provides a powerful platform for drug cardiotoxicity screening. In this article, we first review recent progress in the development of theory on drug–ion channel interactions and mathematical modelling. Then we propose a family of biomarkers that can quantitatively characterize the actions of a drug on the electrical activity of the heart at multi‐physical scales including cellular and tissue levels. We also conducted some simulations to demonstrate the application of the virtual heart to assess the pro‐arrhythmic effects of cisapride and amiodarone. Using the model we investigated the mechanisms responsible for the differences between the two drugs on pro‐arrhythmogenesis, even though both prolong the QT interval of ECGs. Several challenges for further development of a virtual heart as a platform for screening drug cardiotoxicity are discussed.

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This article is part of a themed section on Chinese Innovation in Cardiovascular Drug Discovery. To view the other articles in this section visit http://dx.doi.org/10.1111/bph.2015.172.issue-23

The cardiac muscle duplex as a method to study myocardial heterogeneity

This paper reviews the development and application of paired muscle preparations, called duplex, for the investigation of mechanisms and consequences of intra-myocardial electro-mechanical heterogeneity. We illustrate the utility of the underlying combined experimental and computational approach for conceptual development and integration of basic science insight with clinically relevant settings, using previously published and new data. Directions for further study are identified.