Frank B. Sachse

Models of cardiac tissue electrophysiology: Progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

Heterogeneous three-dimensional anatomical and electrophysiological model of human atria

Investigating the mechanisms underlying the genesis and conduction of electrical excitation in the atria at physiological and pathological states is of great importance. To provide knowledge concerning the mechanisms of excitation, we constructed a biophysical detailed and anatomically accurate computer model of human atria that incorporates both structural and electrophysiological heterogeneities. The three-dimensional geometry was extracted from the visible female dataset. The sinoatrial node (SAN) and atrium, including crista terminalis (CT), pectinate muscles (PM), appendages (APG) and Bachmanns bundle (BB) were segmented in this work. Fibre orientation in CT, PM and BB was set to local longitudinal direction. Descriptions for all used cell types were based on modifications of the Courtemanche et al. model of a human atrial cell. Maximum conductances of , and were modified for PM, CT, APG and atrioventricular ring to reproduce measured action potentials (AP). Pacemaker activity in the human SAN was reproduced by removing , but including , , and gradients of channel conductances as described in previous studies for heterogeneous rabbit SAN. Anisotropic conduction was computed with a monodomain model using the finite element method. The transversal to longitudinal ratio of conductivity for PM, CT and BB was 1 : 9. Atrial working myocardium (AWM) was set to be isotropic. Simulation of atrial electrophysiology showed initiation of APs in the SAN centre. The excitation spread afterwards to the periphery near to the region of the CT and preferentially towards the atrioventricular region. The excitation extends over the right atrium along PM. Both CT and PM activated the right AWM. Earliest activation of the left atrium was through BB and excitation spread over to the APG. The conduction velocities were 0.6 m s−1 for AWM, 1.2 m s−1 for CT, 1.6 m s−1 for PM and 1.1 m s−1 for BB at a rate of 63 bpm. The simulations revealed that bundles form dominant pathways for atrial conduction. The preferential conduction towards CT and along PM is comparable with clinical mapping. Repolarization is more homogeneous than excitation due to the heterogeneous distribution of electrophysiological properties and hence the action potential duration.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Cardiac cell modelling: observations from the heart of the cardiac physiome project.

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Subcellular Structures and Function of Myocytes Impaired During Heart Failure Are Restored by Cardiac Resynchronization Therapy

Rationale: Cardiac resynchronization therapy (CRT) is an established treatment for patients with chronic heart failure. However, CRT-associated structural and functional remodeling at cellular and subcellular levels is only partly understood. Objective: To investigate the effects of CRT on subcellular structures and protein distributions associated with excitation-contraction coupling of ventricular cardiomyocytes. Methods and Results: Our studies revealed remodeling of the transverse tubular system (t-system) and the spatial association of ryanodine receptor (RyR) clusters in a canine model of dyssynchronous heart failure (DHF). We did not find this remodeling in a synchronous heart failure model based on atrial tachypacing. Remodeling in DHF ranged from minor alterations in anterior left ventricular myocytes to nearly complete loss of the t-system and dissociation of RyRs from sarcolemmal structures in lateral cells. After CRT, we found a remarkable and almost complete reverse remodeling of these structures despite persistent left ventricular dysfunction. Studies of whole-cell Ca2+ transients showed that the structural remodeling and restoration were accompanied with remodeling and restoration of Ca2+ signaling. Conclusions: DHF is associated with regional remodeling of the t-system. Myocytes undergo substantial structural and functional restoration after only 3 weeks of CRT. The finding suggests that t-system status can provide an early marker of the success of this therapy. The results could also guide us to an understanding of the loss and remodeling of proteins associated with the t-system. The steep relationship between free Ca2+ and contraction suggests that some restoration of Ca2+ release units will have a disproportionately large effect on contractility.

The molecular basis of chloroquine block of the inward rectifier Kir2.1 channel

Although chloroquine remains an important therapeutic agent for treatment of malaria in many parts of the world, its safety margin is very narrow. Chloroquine inhibits the cardiac inward rectifier K+ current IK1 and can induce lethal ventricular arrhythmias. In this study, we characterized the biophysical and molecular basis of chloroquine block of Kir2.1 channels that underlie cardiac IK1. The voltage- and K+-dependence of chloroquine block implied that the binding site was located within the ion-conduction pathway. Site-directed mutagenesis revealed the location of the chloroquine-binding site within the cytoplasmic pore domain rather than within the transmembrane pore. Molecular modeling suggested that chloroquine blocks Kir2.1 channels by plugging the cytoplasmic conduction pathway, stabilized by negatively charged and aromatic amino acids within a central pocket. Unlike most ion-channel blockers, chloroquine does not bind within the transmembrane pore and thus can reach its binding site, even while polyamines remain deeper within the channel vestibule. These findings explain how a relatively low-affinity blocker like chloroquine can effectively block IK1 even in the presence of high-affinity endogenous blockers. Moreover, our findings provide the structural framework for the design of safer, alternative compounds that are devoid of Kir2.1-blocking properties.

Novel Features of the Rabbit Transverse Tubular System Revealed by Quantitative Analysis of Three-Dimensional Reconstructions from Confocal Images

With scanning confocal microscopy we obtained three-dimensional (3D) reconstructions of the transverse tubular system (t-system) of rabbit ventricular cells. We accomplished this by labeling the t-system with dextran linked to fluorescein or, alternatively, wheat-germ agglutinin conjugated to an Alexa fluor dye. Image processing and visualization techniques allowed us to reconstruct the t-system in three dimensions. In a myocyte lying flat on a coverslip, t-tubules typically progressed from its upper and lower surfaces. 3D reconstructions of the t-tubules also suggested that some of them progressed from the sides of the cell. The analysis of single t-tubules revealed novel morphological features. The average diameter of single t-tubules from six cells was estimated to 448 +/- 172 nm (mean +/- SD, number of t-tubules 348, number of cross sections 5323). From reconstructions we were able to identify constrictions occurring every 1.87 +/- 1.09 microm along the principal axis of the tubule. The cross-sectional area of these constrictions was reduced to an average of 57.7 +/- 27.5% (number of constrictions 170) of the adjacent local maximal areas. Principal component analysis revealed flattening of t-tubular cross sections, confirming findings that we obtained from electron micrographs. Dextran- and wheat-germ agglutinin-associated signals were correlated in the t-system and are therefore equally good markers. The 3D structure of the t-system in rabbit ventricular myocytes seems to be less complex than that found in rat. Moreover, we found that t-tubules in rabbit have approximately twice the diameter of those in rat. We speculate that the constrictions (or regions between them) are sites of dyadic clefts and therefore can provide geometric markers for colocalizing dyadic proteins. In consideration of the resolution of the imaging system, we suggest that our methods permit us to obtain spatially resolved 3D reconstructions of the t-system in rabbit cells. We also propose that our methods allow us to characterize pathological defects of the t-system, e.g., its remodeling as a result of heart failure.

Structural basis of action for a human ether-a-go-go-related gene 1 potassium channel activator.

Activation of human ether-a-go-go-related gene 1 (hERG1) K+ channels mediates cardiac action potential repolarization. Drugs that activate hERG1 channels represent a mechanism-based approach for the treatment of long QT syndrome, a disorder of cardiac repolarization associated with ventricular arrhythmia and sudden death. Here, we characterize the mechanisms of action and the molecular determinants for binding of RPR260243 [(3R,4R)-4-[3-(6-methoxy-quinolin-4-yl)-3-oxo-propyl]-1-[3-(2,3,5-trifluoro-phenyl)-prop-2-ynyl]-piperidine-3-carboxylic acid] (RPR), a recently discovered hERG1 channel activator. Channels were heterologously expressed in Xenopus laevis oocytes, and currents were measured by using the two-microelectrode voltage-clamp technique. RPR induced a concentration-dependent slowing in the rate of channel deactivation and enhanced current magnitude by shifting the voltage dependence of inactivation to more positive potentials. This mechanism was confirmed by demonstrating that RPR slowed the rate of deactivation, but did not increase current magnitude of inactivation-deficient mutant channels. The effects of RPR on hERG1 kinetics and magnitude could be simulated by reducing three rate constants in a Markov model of channel gating. Point mutations of specific residues located in the S4–S5 linker or cytoplasmic ends of the S5 and S6 domains greatly attenuated or ablated the effects of 3 μM RPR on deactivation (five residues), inactivation (one residue), or both gating mechanisms (four residues). These findings define a putative binding site for RPR and confirm the importance of an interaction between the S4–S5 linker and the S6 domain in electromechanical coupling of voltage-gated K+ channels.

A Model of Electrical Conduction in Cardiac Tissue Including Fibroblasts

Fibroblasts are abundant in cardiac tissue. Experimental studies suggested that fibroblasts are electrically coupled to myocytes and this coupling can impact cardiac electrophysiology. In this work, we present a novel approach for mathematical modeling of electrical conduction in cardiac tissue composed of myocytes, fibroblasts, and the extracellular space. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added a description of fibroblasts, which are electrically coupled with each other and with myocytes. We applied the extended model in exemplary computational simulations of plane waves and conduction in a thin tissue slice assuming an isotropic conductivity of the intra-fibroblast domain. In simulations of plane waves, increased myocyte–fibroblast coupling and fibroblast–myocyte ratio reduced peak voltage and maximal upstroke velocity of myocytes as well as amplitudes and maximal downstroke velocity of extracellular potentials. Simulations with the thin tissue slice showed that inter-fibroblast coupling affected rather transversal than longitudinal conduction velocity. Our results suggest that fibroblast coupling becomes relevant for small intra-myocyte and/or large intra-fibroblast conductivity. In summary, the study demonstrated the feasibility of the extended bidomain model and supports the hypothesis that fibroblasts contribute to cardiac electrophysiology in various manners.

Knock-Out of the Potassium Channel TASK-1 Leads to a Prolonged QT Interval and a Disturbed QRS Complex

Background/Aims: The aim of the study was to characterize the whole cell current of the two-pore domain potassium channel TASK-1 (K2P3) in mouse ventricular cardiomyocytes (ITASK-1) and to analyze the cardiac phenotype of the TASK-1-/- mice. Methods and Results: We have quantified the ventricular ITASK-1 current using the blocker A293 and TASK-1-/- mice. Surface electrocardiogram recordings of TASK-1-/- mice showed a prolonged QTc interval and a broadened QRS complex. The differences in electrocardiograms between wild type and TASK-1-/- mice disappeared during sympathetic stimulation of the animals. Quantitative RT-PCR, patch clamp recordings and measurements of hemodynamic performance of TASK-1-/- mice revealed no major compensatory changes in ion channel transcription. Action potential recordings of TASK-1-/- mouse cardiomyocytes indicated that ITASK-1 modulates action potential duration. Our in vivo electrophysiological studies showed that isoflurane, which activates TASK-1, slowed heart rate and atrioventricular conduction of wild-type but not of TASK-1-/- mice. Conclusion: The results of an invasive electrophysiological catheter protocol in combination with the observed QRS time prolongation in the surface electrocardiogram point towards a regulatory role of TASK-1 in the cardiac conduction system.