A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes

Mitochondrial oxidative stress during cardiac lipid overload causes intracellular calcium leak and arrhythmia

BACKGROUND

Diabetes and obesity are associated with an increased risk of arrhythmia and sudden cardiac death. Abnormal lipid accumulation is observed in cardiomyocytes of obese and diabetic patients, which may contribute to arrhythmia, but the mechanisms are poorly understood. A transgenic mouse model of cardiac lipid overload, the peroxisome proliferator-activated receptor-γ (PPARg) cardiac overexpression mouse, has long QT and increased ventricular ectopy.

OBJECTIVE

The purpose of this study was to evaluate the hypothesis that the increase in ventricular ectopy during cardiac lipid overload is caused by abnormalities in calcium handling due to increased mitochondrial oxidative stress.

METHODS

Ventricular myocytes were isolated from adult mouse hearts to record sparks and calcium transients. Mice were implanted with heart rhythm monitors for in vivo recordings.

RESULTS

PPARg cardiomyocytes have more frequent triggered activity and increased sparks compared to control. Sparks and triggered activity are reduced by mitotempo, a mitochondrial-targeted antioxidant. This is explained by a significant increase in oxidation of RyR2. Calcium transients are increased in amplitude, and sarcoplasmic reticulum (SR) calcium stores are increased in PPARg cardiomyocytes. Computer modeling of the cardiac action potential demonstrates that long QT contributes to increased SR calcium. Mitotempo decreased ventricular ectopy in vivo.

CONCLUSION

During cardiac lipid overload, mitochondrial oxidative stress causes increased SR calcium leak by oxidizing RyR2 channels. This promotes ventricular ectopy, which is significantly reduced in vivo by a mitochondrial-targeted antioxidant. These results suggest a potential role for mitochondrial-targeted antioxidants in preventing arrhythmia and sudden cardiac death in obese and diabetic patients.

Ryanodine receptor sensitivity governs the stability and synchrony of local calcium release during cardiac excitation-contraction coupling

Calcium-induced calcium release is the principal mechanism that triggers the cell-wide [Ca(2+)]i transient that activates muscle contraction during cardiac excitation-contraction coupling (ECC). Here, we characterize this process in mouse cardiac myocytes with a novel mathematical action potential (AP) model that incorporates realistic stochastic gating of voltage-dependent L-type calcium (Ca(2+)) channels (LCCs) and sarcoplasmic reticulum (SR) Ca(2+) release channels (the ryanodine receptors, RyR2s). Depolarization of the sarcolemma during an AP stochastically activates the LCCs elevating subspace [Ca(2+)] within each of the cell's 20,000 independent calcium release units (CRUs) to trigger local RyR2 opening and initiate Ca(2+) sparks, the fundamental unit of triggered Ca(2+) release. Synchronization of Ca(2+) sparks during systole depends on the nearly uniform cellular activation of LCCs and the likelihood of local LCC openings triggering local Ca(2+) sparks (ECC fidelity). The detailed design and true SR Ca(2+) pump/leak balance displayed by our model permits investigation of ECC fidelity and Ca(2+) spark fidelity, the balance between visible (Ca(2+) spark) and invisible (Ca(2+) quark/sub-spark) SR Ca(2+) release events. Excess SR Ca(2+) leak is examined as a disease mechanism in the context of "catecholaminergic polymorphic ventricular tachycardia (CPVT)", a Ca(2+)-dependent arrhythmia. We find that that RyR2s (and therefore Ca(2+) sparks) are relatively insensitive to LCC openings across a wide range of membrane potentials; and that key differences exist between Ca(2+) sparks evoked during quiescence, diastole, and systole. The enhanced RyR2 [Ca(2+)]i sensitivity during CPVT leads to increased Ca(2+) spark fidelity resulting in asynchronous systolic Ca(2+) spark activity. It also produces increased diastolic SR Ca(2+) leak with some prolonged Ca(2+) sparks that at times become "metastable" and fail to efficiently terminate. There is a huge margin of safety for stable Ca(2+) handling within the cell and this novel mechanistic model provides insight into the molecular signaling characteristics that help maintain overall Ca(2+) stability even under the conditions of high SR Ca(2+) leak during CPVT. Finally, this model should provide tools for investigators to examine normal and pathological Ca(2+) signaling characteristics in the heart.

Altered Left Ventricular Ion Channel Transcriptome in a High-Fat-Fed Rat Model of Obesity: Insight into Obesity-Induced Arrhythmogenesis

Introduction. Obesity is increasingly common and is associated with an increased prevalence of cardiac arrhythmias. The aim of this study was to see whether in obesity there is proarrhythmic gene expression of ventricular ion channels and related molecules. Methods and Results. Rats were fed on a high-fat diet and compared to control rats on a normal diet (n = 8). After 8 weeks, rats on the high-fat diet showed significantly greater weight gain and higher adiposity. Left ventricle samples were removed at 8 weeks and mRNA expression of ion channels and other molecules was measured using qPCR. Obese rats had significant upregulation of Ca_v1.2, HCN4, K_ir2.1, RYR2, NCX1, SERCA2a, and RYR2 mRNA and downregulation of ERG mRNA. In the case of HCN4, it was confirmed that there was a significant increase in protein expression. The potential effects of the mRNA changes on the ventricular action potential and intracellular Ca²⁺ transient were predicted using computer modelling. Modelling predicted prolongation of the ventricular action potential and an increase in the intracellular Ca²⁺ transient, both of which would be expected to be arrhythmogenic. Conclusion. High-fat diet causing obesity results in arrhythmogenic cardiac gene expression of ion channels and related molecules.

Semantics-Based Composition of Integrated Cardiomyocyte Models Motivated by Real-World Use Cases

Semantics-based model composition is an approach for generating complex biosimulation models from existing components that relies on capturing the biological meaning of model elements in a machine-readable fashion. This approach allows the user to work at the biological rather than computational level of abstraction and helps minimize the amount of manual effort required for model composition. To support this compositional approach, we have developed the SemGen software, and here report on SemGen's semantics-based merging capabilities using real-world modeling use cases. We successfully reproduced a large, manually-encoded, multi-model merge: the "Pandit-Hinch-Niederer" (PHN) cardiomyocyte excitation-contraction model, previously developed using CellML. We describe our approach for annotating the three component models used in the PHN composition and for merging them at the biological level of abstraction within SemGen. We demonstrate that we were able to reproduce the original PHN model results in a semi-automated, semantics-based fashion and also rapidly generate a second, novel cardiomyocyte model composed using an alternative, independently-developed tension generation component. We discuss the time-saving features of our compositional approach in the context of these merging exercises, the limitations we encountered, and potential solutions for enhancing the approach.

Modeling calcium regulation of contraction, energetics, signaling, and transcription in the cardiac myocyte

Calcium (Ca(2+)) plays many important regulatory roles in cardiac muscle cells. In the initial phase of the action potential, influx of Ca(2+) through sarcolemmal voltage-gated L-type Ca(2+) channels (LCCs) acts as a feed-forward signal that triggers a large release of Ca(2+) from the junctional sarcoplasmic reticulum (SR). This Ca(2+) drives heart muscle contraction and pumping of blood in a process known as excitation-contraction coupling (ECC). Triggered and released Ca(2+) also feed back to inactivate LCCs, attenuating the triggered Ca(2+) signal once release has been achieved. The process of ECC consumes large amounts of ATP. It is now clear that in a process known as excitation-energetics coupling, Ca(2+) signals exert beat-to-beat regulation of mitochondrial ATP production that closely couples energy production with demand. This occurs through transport of Ca(2+) into mitochondria, where it regulates enzymes of the tricarboxylic acid cycle. In excitation-signaling coupling, Ca(2+) activates a number of signaling pathways in a feed-forward manner. Through effects on their target proteins, these interconnected pathways regulate Ca(2+) signals in complex ways to control electrical excitability and contractility of heart muscle. In a process known as excitation-transcription coupling, Ca(2+) acting primarily through signal transduction pathways also regulates the process of gene transcription. Because of these diverse and complex roles, experimentally based mechanistic computational models are proving to be very useful for understanding Ca(2+) signaling in the cardiac myocyte.

Manipulation of KCNE2 expression modulates action potential duration and Ito and IK in rat and mouse ventricular myocytes

In heterologous expression systems, KCNE2 has been demonstrated to interact with multiple α-subunits of voltage-dependent cation channels and modulate their functions. However, the physiological and pathological roles of KCNE2 in cardiomyocytes are poorly understood. The present study aimed to investigate the effects of bidirectional modulation of KCNE2 expression on action potential (AP) duration (APD) and voltage-dependent K+ channels in cardiomyocytes. Adenoviral gene delivery and RNA interference were used to either increase or decrease KCNE2 expression in cultured neonatal and adult rat or neonatal mouse ventricular myocytes. Knockdown of KCNE2 prolonged APD in both neonatal and adult myocytes, whereas overexpression of KCNE2 shortened APD in neonatal but not adult myocytes. Consistent with the alterations in APD, KCNE2 knockdown decreased transient outward K+ current ( Ito) densities in neonatal and adult myocytes, whereas KCNE2 overexpression increased Ito densities in neonatal but not adult myocytes. Furthermore, KCNE2 knockdown accelerated the rates of Ito activation and inactivation, whereas KCNE2 overexpression slowed Ito gating kinetics in neonatal but not adult myocytes. Delayed rectifier K+ current densities were remarkably affected by manipulation of KCNE2 expression in mouse but not rat cardiomyocytes. Simulation of the AP of a rat ventricular myocyte with a mathematical model showed that alterations in Ito densities and gating properties can result in similar APD alterations in KCNE2 overexpression and knockdown cells. In conclusion, endogenous KCNE2 in cardiomyocytes is important in maintaining cardiac electrical stability mainly by regulating Ito and APD. Perturbation of KCNE2 expression may predispose the heart to ventricular arrhythmia by prolonging APD.

Computational analysis of the regulation of Ca(2+) dynamics in rat ventricular myocytes

Force-frequency relationships of isolated cardiac myocytes show complex behaviors that are thought to be specific to both the species and the conditions associated with the experimental preparation. Ca(2+) signaling plays an important role in shaping the force-frequency relationship, and understanding the properties of the force-frequency relationship in vivo requires an understanding of Ca(2+) dynamics under physiologically relevant conditions. Ca(2+) signaling is itself a complicated process that is best understood on a quantitative level via biophysically based computational simulation. Although a large number of models are available in the literature, the models are often a conglomeration of components parameterized to data of incompatible species and/or experimental conditions. In addition, few models account for modulation of Ca(2+) dynamics via β-adrenergic and calmodulin-dependent protein kinase II (CaMKII) signaling pathways even though they are hypothesized to play an important regulatory role in vivo. Both protein-kinase-A and CaMKII are known to phosphorylate a variety of targets known to be involved in Ca(2+) signaling, but the effects of these pathways on the frequency- and inotrope-dependence of Ca(2+) dynamics are not currently well understood. In order to better understand Ca(2+) dynamics under physiological conditions relevant to rat, a previous computational model is adapted and re-parameterized to a self-consistent dataset obtained under physiological temperature and pacing frequency and updated to include β-adrenergic and CaMKII regulatory pathways. The necessity of specific effector mechanisms of these pathways in capturing inotrope- and frequency-dependence of the data is tested by attempting to fit the data while including and/or excluding those effector components. We find that: (1) β-adrenergic-mediated phosphorylation of the L-type calcium channel (LCC) (and not of phospholamban (PLB)) is sufficient to explain the inotrope-dependence; and (2) that CaMKII-mediated regulation of neither the LCC nor of PLB is required to explain the frequency-dependence of the data.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

Titanium dioxide nanoparticles promote arrhythmias via a direct interaction with rat cardiac tissue

BACKGROUND

In light of recent developments in nanotechnologies, interest is growing to better comprehend the interaction of nanoparticles with body tissues, in particular within the cardiovascular system. Attention has recently focused on the link between environmental pollution and cardiovascular diseases. Nanoparticles <50 nm in size are known to pass the alveolar-pulmonary barrier, enter into bloodstream and induce inflammation, but the direct pathogenic mechanisms still need to be evaluated. We thus focused our attention on titanium dioxide (TiO₂) nanoparticles, the most diffuse nanomaterial in polluted environments and one generally considered inert for the human body.

METHODS

We conducted functional studies on isolated adult rat cardiomyocytes exposed acutely in vitro to TiO₂ and on healthy rats administered a single dose of 2 mg/Kg TiO₂ NPs via the trachea. Transmission electron microscopy was used to verify the actual presence of TiO₂ nanoparticles within cardiac tissue, toxicological assays were used to assess lipid peroxidation and DNA tissue damage, and an in silico method was used to model the effect on action potential.

RESULTS

Ventricular myocytes exposed in vitro to TiO₂ had significantly reduced action potential duration, impairment of sarcomere shortening and decreased stability of resting membrane potential. In vivo, a single intra-tracheal administration of saline solution containing TiO₂ nanoparticles increased cardiac conduction velocity and tissue excitability, resulting in an enhanced propensity for inducible arrhythmias. Computational modeling of ventricular action potential indicated that a membrane leakage could account for the nanoparticle-induced effects measured on real cardiomyocytes.

CONCLUSIONS

Acute exposure to TiO₂ nanoparticles acutely alters cardiac excitability and increases the likelihood of arrhythmic events.

Hypokalaemia induces Ca²⁺ overload and Ca²⁺ waves in ventricular myocytes by reducing Na⁺,K⁺-ATPase α₂ activity

KEY POINTS

Hypokalaemia is a risk factor for development of ventricular arrhythmias. In rat ventricular myocytes, low extracellular K(+) (corresponding to clinical moderate hypokalaemia) increased Ca(2+) wave probability, Ca(2+) transient amplitude, sarcoplasmic reticulum (SR) Ca(2+) load and induced SR Ca(2+) leak. Low extracellular K(+) reduced Na(+),K(+)-ATPase (NKA) activity and hyperpolarized the resting membrane potential in ventricular myocytes. Both experimental data and modelling indicate that reduced NKA activity and subsequent Na(+) accumulation sensed by the Na(+), Ca(2+) exchanger (NCX) lead to increased Ca(2+) transient amplitude despite concomitant hyperpolarization of the resting membrane potential. Low extracellular K(+) induced Ca(2+) overload by lowering NKA α2 activity. Triggered ventricular arrhythmias in patients with hypokalaemia may therefore be attributed to reduced NCX forward mode activity linked to an effect on the NKA α2 isoform.

ABSTRACT

Hypokalaemia is a risk factor for development of ventricular arrhythmias. The aim of this study was to determine the cellular mechanisms leading to triggering of arrhythmias in ventricular myocytes exposed to low Ko. Low Ko, corresponding to moderate hypokalaemia, increased Ca(2+) transient amplitude, sarcoplasmic reticulum (SR) Ca(2+) load, SR Ca(2+) leak and Ca(2+) wave probability in field stimulated rat ventricular myocytes. The mechanisms leading to Ca(2+) overload were examined. Low Ko reduced Na(+),K(+)-ATPase (NKA) currents, increased cytosolic Na(+) concentration and increased the Na(+) level sensed by the Na(+), Ca(2+) exchanger (NCX). Low Ko also hyperpolarized the resting membrane potential (RMP) without significant alterations in action potential duration. Experiments in voltage clamped and field stimulated ventricular myocytes, along with mathematical modelling, suggested that low Ko increases the Ca(2+) transient amplitude by reducing NKA activity despite hyperpolarization of the RMP. Selective inhibition of the NKA α2 isoform by low dose ouabain abolished the ability of low Ko to reduce NKA currents, to increase Na(+) levels sensed by NCX and to increase the Ca(2+) transient amplitude. We conclude that low Ko, within the range of moderate hypokalaemia, increases Ca(2+) levels in ventricular myocytes by reducing the pumping rate of the NKA α2 isoform with subsequent Na(+) accumulation sensed by the NCX. These data highlight reduced NKA α2 -mediated control of NCX activity as a possible mechanism underlying triggered ventricular arrhythmias in patients with hypokalaemia.

Species-dependent adaptation of the cardiac Na+/K+ pump kinetics to the intracellular Na+ concentration

The Na(+)/K(+) ATPase (NKA) plays a critical role in maintaining ionic homeostasis and dynamic function in cardiac myocytes, within both the in vivo cell and in silico models. Physiological conditions differ significantly between mammalian species. However, most existing formulations of NKA used to simulate cardiac function in computational models are derived from a broad range of experimental sources spanning many animal species. The resultant inability of these models to discern species-specific features is a significant obstacle to achieving a detailed quantitative and comparative understanding of physiological behaviour in different biological contexts. Here we present a framework for characterising the steady-state NKA current using a biophysical mechanistic model specifically designed to provide a mechanistic explanation of the NKA flux supported by self-consistent species-specific data. We thus compared NKA kinetics specific to guinea- pig and rat ventricular myocytes. We observe that the apparent binding affinity for sodium in the rat is significantly lower, whereas the overall pump cycle rate is doubled, in comparison to the guinea pig. This sensitivity of NKA to its regulatory substrates compensates for the differences in Na(+) concentrations between the cell types. NKA is thereby maintained within its dynamic range over a wide range of pacing frequencies in these two species, despite significant disparities in sodium concentration. Hence, by replacing a conventional generic NKA model with our rat-specific NKA formula into a whole-cell simulation, we have, for the first time, been able to accurately reproduce the action potential duration and the steady-state sodium concentration as functions of pacing frequency.

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.

Modeling of stochastic behavior of pacemaker potential in interstitial cells of Cajal

It is widely accepted that interstitial cells of Cajal (ICCs) generate pacemaker potentials to propagate slow waves along the whole gastrointestinal tract. Previously, we constructed a biophysically based model of ICCs in mouse small intestine to explain the pacemaker mechanism. Our previous model, however, could not explain non-uniformity of pacemaker potentials and random occurrence of unitary potentials, thus we updated our model. The inositol 1,4,5-trisphosphate (IP3)-mediated Ca(2+) mobilization is a key event to drive the cycle of pacemaker activity and was updated to reproduce its stochastic behavior. The stochasticity was embodied by simulating random opening and closing of individual IP3-mediated Ca(2+) channel. The updated model reproduces the stochastic features of pacemaker potentials in ICCs. Reproduced pacemaker potentials are not uniform in duration and interval. The resting and peak potentials are -75.5 ± 1.1 mV and -0.8 ± 0.5 mV, respectively (n = 55). Frequency of pacemaker potential is 14.3 ± 0.4 min(-1) (n = 10). Width at half-maximal amplitude of pacemaker potential is 902 ± 6 ms (n = 55). There are random events of unitary potential-like depolarization. Finally, we compared our updated model with a recently published model to speculate which ion channel is the best candidate to drive pacemaker depolarization. In conclusion, our updated mathematical model could now reproduce stochastic features of pacemaker activity in ICCs.

Systems approach to the study of stretch and arrhythmias in right ventricular failure induced in rats by monocrotaline

We demonstrate the synergistic benefits of using multiple technologies to investigate complex multi-scale biological responses. The combination of reductionist and integrative methodologies can reveal novel insights into mechanisms of action by tracking changes of in vivo phenomena to alterations in protein activity (or vice versa). We have applied this approach to electrical and mechanical remodelling in right ventricular failure caused by monocrotaline-induced pulmonary artery hypertension in rats. We show arrhythmogenic T-wave alternans in the ECG of conscious heart failure animals. Optical mapping of isolated hearts revealed discordant action potential duration (APD) alternans. Potential causes of the arrhythmic substrate; structural remodelling and/or steep APD restitution and dispersion were observed, with specific remodelling of the Right Ventricular Outflow Tract. At the myocyte level, [Ca(2+)]i transient alternans were observed together with decreased activity, gene and protein expression of the sarcoplasmic reticulum Ca(2+)-ATPase (SERCA). Computer simulations of the electrical and structural remodelling suggest both contribute to a less stable substrate. Echocardiography was used to estimate increased wall stress in failure, in vivo. Stretch of intact and skinned single myocytes revealed no effect on the Frank-Starling mechanism in failing myocytes. In isolated hearts acute stretch-induced arrhythmias occurred in all preparations. Significant shortening of the early APD was seen in control but not failing hearts. These observations may be linked to changes in the gene expression of candidate mechanosensitive ion channels (MSCs) TREK-1 and TRPC1/6. Computer simulations incorporating MSCs and changes in ion channels with failure, based on altered gene expression, largely reproduced experimental observations.

Electrophysiological and structural determinants of electrotonic modulation of repolarization by the activation sequence

Spatial dispersion of repolarization is known to play an important role in arrhythmogenesis. Electrotonic modulation of repolarization by the activation sequence has been observed in some species and tissue preparations, but to varying extents. Our study sought to determine the mechanisms underlying species- and tissue-dependent electrotonic modulation of repolarization in ventricles. Epi-fluorescence optical imaging of whole rat hearts and pig left ventricular wedges were used to assess epicardial spatial activation and repolarization characteristics. Experiments were supported by computer simulations using realistic geometries. Tight coupling between activation times (AT) and action potential duration (APD) were observed in rat experiments but not in pig. Linear correlation analysis found slopes of −1.03 ± 0.59 and −0.26 ± 0.13 for rat and pig, respectively (p < 0.0001). In rat, maximal dispersion of APD was 11.0 ± 3.1 ms but dispersion of repolarization time (RT) was relatively homogeneous (8.2 ± 2.7, p < 0.0001). However, in pig no such difference was observed between the dispersion of APD and RT (17.8 ± 6.1 vs. 17.7 ± 6.5, respectively). Localized elevations of APD (12.9 ± 8.3%) were identified at ventricular insertion sites of rat hearts both in experiments and simulations. Tissue geometry and action potential (AP) morphology contributed significantly to determining influence of electrotonic modulation. Simulations of a rat AP in a pig geometry decreased the slope of AT and APD relationships by 70.6% whereas slopes were increased by 75.0% when implementing a pig AP in a rat geometry. A modified pig AP, shortened to match the rat APD, showed little coupling between AT and APD with greatly reduced slope compared to the rat AP. Electrotonic modulation of repolarization by the activation sequence is especially pronounced in small hearts with murine-like APs. Tissue architecture and AP morphology play an important role in electrotonic modulation of repolarization.

Modeling the effects of the circadian clock on cardiac electrophysiology

An internal circadian clock regulates the electrical activity of cardiac myocytes controlling the expression of potassium channel interacting protein-2 (KChIP2), which is a key regulator of cardiac electrical activity. Here, we examine how the circadian rhythm of KChIP2 expression affects the dynamics of human and murine ventricular action potentials (APs), as well as the intervals in the equivalent electrocardiograms (ECGs) reflecting the duration of depolarization and repolarization phases of the cardiac ventricular APs (QRS and QT intervals), with mathematical modeling. We show how the internal circadian clock can control the shape of APs and, in particular, predict AP, QRS, and QT interval prolongation following KChIP2 downregulation, as well as shortening of AP, QRS, and QT interval duration following KChIP2 upregulation. Based on the circadian expression of KChIP2, we can accurately predict the circadian rhythm in cardiac electrical activity and suggest the transient outward potassium currents as the key current for circadian rhythmicity. Our modeling work predicts a smaller effect of KChIP2 on AP and QT interval dynamics in humans. Taken together, these results support the role of KChIP2 as the key regulator of circadian rhythms in the electrical activity of the heart; we provide computational models that can be used to explore circadian rhythms in cardiac electrophysiology and susceptibility to arrhythmia.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

Rotors and the dynamics of cardiac fibrillation

The objective of this article is to present a broad review of the role of cardiac electric rotors and their accompanying spiral waves in the mechanism of cardiac fibrillation. At the outset, we present a brief historical overview regarding reentry and then discuss the basic concepts and terminologies pertaining to rotors and their initiation. Thereafter, the intrinsic properties of rotors and spiral waves, including phase singularities, wavefront curvature, and dominant frequency maps, are discussed. The implications of rotor dynamics for the spatiotemporal organization of fibrillation, independent of the species being studied, are described next. The knowledge gained regarding the role of cardiac structure in the initiation or maintenance of rotors and the ionic bases of spiral waves in the past 2 decades, as well as the significance for drug therapy, is reviewed subsequently. We conclude by examining recent evidence suggesting that rotors are critical in sustaining both atrial and ventricular fibrillation in the human heart and its implications for treatment with radiofrequency ablation.

The force-frequency relationship: insights from mathematical modeling

The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by β-adrenergic stimulation, and, in a coordinated way, the neurohumoral state alters both frequency (acting on the sinoatrial node) as well as force generation (modifying ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Cardiac modelers have already linked mechanical and electrical activity in their formulations and showed how those activities feedback on each other. However, now it is necessary to include neurological control to have a complete description of heart performance, especially when changes in frequency are involved. Study of arrhythmias (or antiarrhythmic drugs) based on mathematical models should incorporate this effect to make useful predictions or point out potential pharmaceutical targets.

Cardiac fiber rotation distorts surface measurements of anisotropic propagation

Anisotropy is often determined experimentally from epicardial propagation measurements. We hypothesize that the direction of wave propagation on the epicardial surface is not aligned with the epicardial fiber orientation, due to intramural fiber rotation. In this paper, we modeled the effect of cardiac tissue fiber rotation on wave propagation. We used a three dimensional computer model of varying thickness with a 120 degree fiber rotation through the thickness. The angle difference between the direction of propagation and fiber orientation was most pronounced for thin tissue, and decreased with increasing tissue thickness. This angle also increased with the time elapsed since stimulation. Finally, we demonstrated that the fiber rotation from epicardium to endocardium results in inaccurate measurements of conduction velocities at the epicardium, particularly in thin tissues.

Cardiac dynamics: a simplified model for action potential propagation

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit's ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.

Rapid genetic algorithm optimization of a mouse computational model: benefits for anthropomorphization of neonatal mouse cardiomyocytes

While the mouse presents an invaluable experimental model organism in biology, its usefulness in cardiac arrhythmia research is limited in some aspects due to major electrophysiological differences between murine and human action potentials (APs). As previously described, these species-specific traits can be partly overcome by application of a cell-type transforming clamp (CTC) to anthropomorphize the murine cardiac AP. CTC is a hybrid experimental-computational dynamic clamp technique, in which a computationally calculated time-dependent current is inserted into a cell in real-time, to compensate for the differences between sarcolemmal currents of that cell (e.g., murine) and the desired species (e.g., human). For effective CTC performance, mismatch between the measured cell and a mathematical model used to mimic the measured AP must be minimal. We have developed a genetic algorithm (GA) approach that rapidly tunes a mathematical model to reproduce the AP of the murine cardiac myocyte under study. Compared to a prior implementation that used a template-based model selection approach, we show that GA optimization to a cell-specific model results in a much better recapitulation of the desired AP morphology with CTC. This improvement was more pronounced when anthropomorphizing neonatal mouse cardiomyocytes to human-like APs than to guinea pig APs. CTC may be useful for a wide range of applications, from screening effects of pharmaceutical compounds on ion channel activity, to exploring variations in the mouse or human genome. Rapid GA optimization of a cell-specific mathematical model improves CTC performance and may therefore expand the applicability and usage of the CTC technique.

Depolarization-induced automaticity in rat ventricular cardiomyocytes is based on the gating properties of L-type calcium and slow Kv channels

Depolarization-induced automaticity (DIA) of cardiomyocytes is the property of those cells to generate pacemaker cell-like spontaneous electrical activity when subjected to a depolarizing current. This property provides a candidate mechanism for generation of pathogenic ectopy in cardiac tissue. The purpose of this study was to determine the biophysical mechanism of DIA in terms of the ion conductance properties of the cardiomyocyte membrane. First, we determined, by use of the conventional whole-cell patch-clamp technique, the membrane conductance and DIA properties of ventricular cardiomyocytes isolated from adult rat heart. Second, we reproduced and analysed DIA properties by using an adapted version of the experimentally based mathematical cardiomyocyte model of Pandit et al. (Biophys J 81:3029-3051 2001, Biophys J 84:832-841 2003) and Padmala and Demir (J Cardiovasc Electrophysiol 14:990-995 2003). DIA in 23 rat cardiomyocytes was a damped membrane potential oscillation with a variable number of action potentials and/or waves, depending on the strength of the depolarizing current and the particular cell. The adapted model was used to reconstruct the DIA properties of a particular cardiomyocyte from its whole-cell voltage-clamp currents. The main currents involved in DIA were an L-type calcium current (I CaL) and a slowly activating and inactivating Kv current (I ss), with linear (I B) and inward rectifier (I K1) currents acting as background currents and I Na and I t as modulators. Essential for DIA is a sufficiently large window current of a slowly inactivating I CaL combined with a critically sized repolarizing current I ss. Slow inactivation of I ss makes DIA transient. In conclusion, we established a membrane mechanism of DIA primarily based on I CaL, I ss and inward rectifier properties; this may be helpful in understanding cardiac ectopy and its treatment.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

Early modelling of cardiac cells (1960-1980) was based on extensions of the Hodgkin-Huxley nerve axon equations with additional channels incorporated, but after 1980 it became clear that processes other than ion channel gating were also critical in generating electrical activity. This article reviews the development of models representing almost all cell types in the heart, many different species, and the software tools that have been created to facilitate the cardiac Physiome Project.

Evolution of CpG island promoter function underlies changes in KChIP2 potassium channel subunit gene expression in mammalian heart

Scaling of cardiac electrophysiology with body mass requires large changes in the ventricular action potential duration and heart rate in mammals. These changes in cellular electrophysiological function are produced by systematic and coordinated changes in the expression of multiple ion channel and transporter genes. Expression of one important potassium current, the transient outward current (I(to)), changes significantly during mammalian evolution. Changes in I(to) expression are determined, in part, by variation in the expression of an obligatory auxiliary subunit encoded by the KChIP2 gene. The KChIP2 gene is expressed in both cardiac myocytes and neurons and transcription in both cell types is initiated from the same CpG island promoter. Species-dependent variation of KChIP2 expression in heart is mediated by the evolution of the cis-regulatory function of this gene. Surprisingly, the major locus of evolutionary change for KChIP2 gene expression in heart lies within the CpG island core promoter. The results demonstrate that CpG island promoters are not simply permissive for gene expression but can also contribute to tissue-selective expression and, as such, can function as an important locus for the evolution of cis-regulatory function. More generally, evolution of the cis-regulatory function of voltage-gated ion channel genes appears to be an effective and efficient way to modify channel expression levels to optimize electrophysiological function.

Extracting surface activation time from the optically recorded action potential in three-dimensional myocardium

Optical mapping has become an indispensible tool for studying cardiac electrical activity. However, due to the three-dimensional nature of the optical signal, the optical upstroke is significantly longer than the electrical upstroke. This raises the issue of how to accurately determine the activation time on the epicardial surface. The purpose of this study was to establish a link between the optical upstroke and exact surface activation time using computer simulations, with subsequent validation by a combination of microelectrode recordings and optical mapping experiments. To simulate wave propagation and associated optical signals, we used a hybrid electro-optical model. We found that the time of the surface electrical activation (t(E)) within the accuracy of our simulations coincided with the maximal slope of the optical upstroke (t(F)*) for a broad range of optical attenuation lengths. This was not the case when the activation time was determined at 50% amplitude (t(F50)) of the optical upstroke. The validation experiments were conducted in isolated Langendorff-perfused rat hearts and coronary-perfused pig left ventricles stained with either di-4-ANEPPS or the near-infrared dye di-4-ANBDQBS. We found that t(F)* was a more accurate measure of t(E) than was t(F50) in all experimental settings tested (P = 0.0002). Using t(F)* instead of t(F50) produced the most significant improvement in measurements of the conduction anisotropy and the transmural conduction time in pig ventricles.

Quantitative comparison of cardiac ventricular myocyte electrophysiology and response to drugs in human and nonhuman species

Explanations for arrhythmia mechanisms at the cellular level are usually based on experiments in nonhuman myocytes. However, subtle electrophysiological differences between species may lead to different rhythmic or arrhythmic cellular behaviors and drug response given the nonlinear and highly interactive cellular system. Using detailed and quantitatively accurate mathematical models for human, dog, and guinea pig ventricular action potentials (APs), we simulated and compared cell electrophysiology mechanisms and response to drugs. Under basal conditions (absence of β-adrenergic stimulation), Na(+)/K(+)-ATPase changes secondary to Na(+) accumulation determined AP rate dependence for human and dog but not for guinea pig where slow delayed rectifier current (I(Ks)) was the major rate-dependent current. AP prolongation with reduction of rapid delayed rectifier current (I(Kr)) and I(Ks) (due to mutations or drugs) showed strong species dependence in simulations, as in experiments. For humans, AP prolongation was 80% following I(Kr) block. It was 30% for dog and 20% for guinea pig. Under basal conditions, I(Ks) block was of no consequence for human and dog, but for guinea pig, AP prolongation after I(Ks) block was severe. However, with β-adrenergic stimulation, I(Ks) played an important role in all species, particularly in AP shortening at fast rate. Quantitative comparison of AP repolarization, rate-dependence mechanisms, and drug response in human, dog, and guinea pig revealed major species differences (e.g., susceptibility to arrhythmogenic early afterdepolarizations). Extrapolation from animal to human electrophysiology and drug response requires great caution.

A computational investigation of cardiac caveolae as a source of persistent sodium current

Recent studies of cholesterol-rich membrane microdomains, called caveolae, reveal that caveolae are reservoirs of “recruitable” sodium ion channels. Caveolar channels constitute a substantial and previously unrecognized source of sodium current in cardiac cells. In this paper we model for the first time caveolar sodium currents and their contributions to cardiac action potential morphology. We show that the β-agonist-induced opening of caveolae may have substantial impacts on peak overshoot, maximum upstroke velocity, and ultimately conduction velocity. Additionally, we show that prolonged action potentials and the formation of potentially arrhythmogenic afterdepolarizations, can arise if caveolae open intermittently throughout the action potential. Our simulations suggest that caveolar sodium current may constitute a route, which is independent of channelopathies, to delayed repolarization and the arrhythmias associated with such delays.

Late phase of repolarization is autoregenerative and scales linearly with action potential duration in mammals ventricular myocytes: a model study

Scaling of action potential (AP) duration (APD) in mammals of different size is a rather complex phenomenon, dominated by a regulatory type mechanism of ion channels expression. By means of simulations performed on six published mathematical models of cardiac ventricular APs of different mammals, it is shown that AP repolarization is autoregenerative in its later phase (ARRP) and that the duration of such phase scales linearly with APD. For each AP, a 3-D instantaneous time-voltage-current surface is constructed, which has been recently described in a more simplified model. This representation allows us to measure ARRP and to study the contribution to it for different ion currents. It has been found that the existence of an ARRP is not intrinsic to cardiac models formulation; one out of the six models does not show this phase. A linear correlation between ARRP duration and APD in the remaining models is also found. It is shown that ARRP neither simply depend on AP shape nor on APD. Though I(K1) current seems to be the main responsible for determining and modulating this phase, the mechanism by which ARRP scales linearly with APD remains unclear and raises further questions on the scaling strategies of cardiac repolarization in mammals.

A computational model of cytosolic and mitochondrial [ca] in paced rat ventricular myocytes

We carried out a series of experiment demonstrating the role of mitochondria in the cytosolic and mitochondrial Ca(2+) transients and compared the results with those from computer simulation. In rat ventricular myocytes, increasing the rate of stimulation (1~3 Hz) made both the diastolic and systolic [Ca(2+)] bigger in mitochondria as well as in cytosol. As L-type Ca(2+) channel has key influence on the amplitude of Ca(2+)-induced Ca(2+) release, the relation between stimulus frequency and the amplitude of Ca(2+) transients was examined under the low density (1/10 of control) of L-type Ca(2+) channel in model simulation, where the relation was reversed. In experiment, block of Ca(2+) uniporter on mitochondrial inner membrane significantly reduced the amplitude of mitochondrial Ca(2+) transients, while it failed to affect the cytosolic Ca(2+) transients. In computer simulation, the amplitude of cytosolic Ca(2+) transients was not affected by removal of Ca(2+) uniporter. The application of carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone (FCCP) known as a protonophore on mitochondrial membrane to rat ventricular myocytes gradually increased the diastolic [Ca(2+)] in cytosol and eventually abolished the Ca(2+) transients, which was similarly reproduced in computer simulation. The model study suggests that the relative contribution of L-type Ca(2+) channel to total transsarcolemmal Ca(2+) flux could determine whether the cytosolic Ca(2+) transients become bigger or smaller with higher stimulus frequency. The present study also suggests that cytosolic Ca(2+) affects mitochondrial Ca(2+) in a beat-to-beat manner, however, removal of Ca(2+) influx mechanism into mitochondria does not affect the amplitude of cytosolic Ca(2+) transients.

Cardiac electromechanical models: from cell to organ

The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computational physiology and medicine. This review focuses on electromechanical (EM) models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single-cell models and the second half addresses organ models. At the subcellular level, myofilament models represent actin–myosin interaction and Ca-based activation. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered to be the cellular basis of the Frank–Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of the field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction–diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and defibrillation.

Intracellular [Na(+)] modulates synergy between Na(+)/Ca (2+) exchanger and L-type Ca (2+) current in cardiac excitation-contraction coupling during action potentials

Excitation-contraction coupling (ECC) in cardiac myocytes involves triggering of Ca(2+) release from the sarcoplasmic reticulum (SR) by L-type Ca channels, whose activity is strongly influenced by action potential (AP) profile. The contribution of Ca(2+) entry via the Na(+)/Ca(2+) exchanger (NCX) to trigger SR Ca(2+) release during ECC in response to an AP remains uncertain. To isolate the contribution of NCX to SR Ca(2+) release, independent of effects on SR Ca(2+) load, Ca(2+) release was determined by recording Ca(2+) spikes using confocal microscopy on patch-clamped rat ventricular myocytes with [Ca(2+)](i) fixed at 150 nmol/L. In response to AP clamps, normalized Ca(2+) spike amplitudes (ΔF/F (0)) increased sigmoidally and doubled as [Na(+)](i) was elevated from 0 to 20 mmol/L with an EC(50) of ~10 mmol/L. This [Na(+)](i)-dependence was independent of I (Na) as well as SR Ca(2+) load, which was unchanged under our experimental conditions. However, NCX inhibition using either KB-R7943 or XIP reduced ΔF/F (0) amplitude in myocytes with 20 mmol/L [Na(+)](i), but not with 5 mmol/L [Na(+)](i). SR Ca(2+) release was complete before the membrane repolarized to -15 mV, indicating Ca(2+) entry into the dyad (not reduced extrusion) underlies [Na(+)](i)-dependent enhancement of ECC. Because I (Ca,L) inhibition with 50 mmol/L Cd(2+) abolished Ca(2+) spikes, our results demonstrate that during cardiac APs, NCX enhances SR Ca(2+) release by synergistically increasing the efficiency of I (Ca,L)-mediated ECC.

High-throughput functional curation of cellular electrophysiology models

Effective reuse of a quantitative mathematical model requires not just access to curated versions of the model equations, but also an understanding of the functional capabilities of the model, and the advisable scope of its application. To enable this "functional curation" we have developed a simulation environment that provides high-throughput evaluation of a mathematical model's functional response to an arbitrary user-defined protocol, and optionally compares the results against experimental data. In this study we demonstrate the efficacy of this simulation environment on 31 cardiac electrophysiology cell models using two test cases. The S1-S2 response is evaluated to characterise the models' restitution curves, and their L-type calcium channel current-voltage curves are evaluated. The significant variation in the response of these models, even when the models represent the same species and temperature, demonstrates the importance of knowing the functional characteristics of a model prior to its reuse. We also discuss the wider implications for this approach, in improving the selection of models for reuse, enabling the identification of models that exhibit particular experimentally observed phenomena, and making the incremental development of models more robust.

Contribution of mechanical factors to arrhythmogenesis in calcium overloaded cardiomyocytes: model predictions and experiments

It is well-known that Ca²⁺ overload in cardiomyocytes may underlie arrhythmias. However, the possible contribution of mechanical factors to rhythm disturbances in Ca²⁺ overloaded myocytes has not been sufficiently investigated. We used a mathematical model of the electrical and mechanical activity of cardiomyocytes to reveal an essential role of the mechanisms of cardiac mechano-electric feedback in arrhythmogenesis in Ca²⁺ overloaded myocardium. In the model, the following mechanical factors increased Ca²⁺ overload in contracting cardiomyocytes and promoted rhythm disturbances: i) a decrease in the mechanical load for afterloaded contractions; and ii) a decrease in the initial length of sarcomeres for isometric twitches. In exact accordance with the model predictions, in experiments on papillary muscles from the right ventricle of guinea pigs with Ca²⁺ overloaded cardiomyocytes (using 0.5-1 μM of ouabain), we found that emergence of rhythm disturbances and extrasystoles depends on the mechanical conditions of muscle contraction.

Ca²⁺-induced delayed afterdepolarizations are triggered by dyadic subspace Ca2²⁺ affirming that increasing SERCA reduces aftercontractions

Ca(2+)-induced delayed afterdepolarizations (DADs) are depolarizations that occur after full repolarization. They have been observed across multiple species and cell types. Experimental results have indicated that the main cause of DADs is Ca(2+) overload. The main hypothesis as to their initiation has been Ca(2+) overflow from the overloaded sarcoplasmic reticulum (SR). Our results using 37 previously published mathematical models provide evidence that Ca(2+)-induced DADs are initiated by the same mechanism as Ca(2+)-induced Ca(2+) release, i.e., the modulation of the opening of ryanodine receptors (RyR) by Ca(2+) in the dyadic subspace; an SR overflow mechanism was not necessary for the induction of DADs in any of the models. The SR Ca(2+) level is better viewed as a modulator of the appearance of DADs and the magnitude of Ca(2+) release. The threshold for the total Ca(2+) level within the cell (not only the SR) at which Ca(2+) oscillations arise in the models is close to their baseline level (∼1- to 3-fold). It is most sensitive to changes in the maximum sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA) pump rate (directly proportional), the opening probability of RyRs, and the Ca(2+) diffusion rate from the dyadic subspace into the cytosol (both indirectly proportional), indicating that the appearance of DADs is multifactorial. This shift in emphasis away from SR overload as the trigger for DADs toward a multifactorial analysis could explain why SERCA overexpression has been shown to suppress DADs (while increasing contractility) and why DADs appear during heart failure (at low SR Ca(2+) levels).

Arrhythmogenic substrate in hearts of rats with monocrotaline-induced pulmonary hypertension and right ventricular hypertrophy

Mechanisms associated with right ventricular (RV) hypertension and arrhythmias are less understood than those in the left ventricle (LV). The aim of our study was to investigate whether and by what mechanisms a proarrhythmic substrate exists in a rat model of RV hypertension and hypertrophy. Rats were injected with monocrotaline (MCT; 60 mg/kg) to induce pulmonary artery hypertension or with saline (CON). Myocardial levels of mRNA for genes expressing ion channels were measured by real-time RT-PCR. Monophasic action potential duration (MAPD) was recorded in isolated Langendorff-perfused hearts. MAPD restitution was measured, and arrhythmias were induced by burst stimulation. Twenty-two to twenty-six days after treatment, MCT animals had RV hypertension, hypertrophy, and decreased ejection fractions compared with CON. A greater proportion of MCT hearts developed sustained ventricular tachycardias/fibrillation (0.83 MCT vs. 0.14 CON). MAPD was prolonged in RV and less so in the LV of MCT hearts. There were decreased levels of mRNA for K(+) channels. Restitution curves of MCT RV were steeper than CON RV or either LV. Dispersion of MAPD was greater in MCT hearts and was dependent on stimulation frequency. Computer simulations based on ion channel gene expression closely predicted experimental changes in MAPD and restitution. We have identified a proarrhythmic substrate in the hearts of MCT-treated rats. We conclude that steeper RV electrical restitution and rate-dependant RV-LV action potential duration dispersion may be contributing mechanisms and be implicated in the generation of arrhythmias associated with in RV hypertension and hypertrophy.

Construction and validation of anisotropic and orthotropic ventricular geometries for quantitative predictive cardiac electrophysiology

Reaction-diffusion computational models of cardiac electrophysiology require both dynamic excitation models that reconstruct the action potentials of myocytes as well as datasets of cardiac geometry and architecture that provide the electrical diffusion tensor D, which determines how excitation spreads through the tissue. We illustrate an experimental pipeline we have developed in our laboratories for constructing and validating such datasets. The tensor D changes with location in the myocardium, and is determined by tissue architecture. Diffusion tensor magnetic resonance imaging (DT-MRI) provides three eigenvectors e(i) and eigenvalues λ(i) at each voxel throughout the tissue that can be used to reconstruct this architecture. The primary eigenvector e(1) is a histologically validated measure of myocyte orientation (responsible for anisotropic propagation). The secondary and tertiary eigenvectors (e(2) and e(3)) specify the directions of any orthotropic structure if λ(2) is significantly greater than λ(3)-this orthotropy has been identified with sheets or cleavage planes. For simulations, the components of D are scaled in the fibre and cross-fibre directions for anisotropic simulations (or fibre, sheet and sheet normal directions for orthotropic tissues) so that simulated conduction velocities match values from optical imaging or plunge electrode experiments. The simulated pattern of propagation of action potentials in the models is partially validated by optical recordings of spatio-temporal activity on the surfaces of hearts. We also describe several techniques that enhance components of the pipeline, or that allow the pipeline to be applied to different areas of research: Q ball imaging provides evidence for multi-modal orientation distributions within a fraction of voxels, infarcts can be identified by changes in the anisotropic structure-irregularity in myocyte orientation and a decrease in fractional anisotropy, clinical imaging provides human ventricular geometry and can identify ischaemic and infarcted regions, and simulations in human geometries examine the roles of anisotropic and orthotropic architecture in the initiation of arrhythmias.

Alternans resonance and propagation block during supernormal conduction in cardiac tissue with decreased [K(+)](o)

Cardiac restitution is an important factor in arrhythmogenesis. Steep positive action potential duration and conduction velocity (CV) restitution slopes promote alternans and reentrant arrhythmias. We examined the consequences of supernormal conduction (characterized by a negative CV restitution slope) on patterns of conduction and alternans in strands of Luo-Rudy model cells and in cultured cardiac cell strands. Interbeat intervals (IBIs) were analyzed as a function of distance during S1S2 protocols and during pacing at alternating cycle lengths. Supernormal conduction was induced by decreasing [K(+)](o). In control [K(+)](o) simulations, S1S2 intervals converged toward basic cycle length with a length constant determined by both CV and the CV restitution slope. During alternant pacing, the amplitude of IBI alternans converged with a shorter length constant, determined also by the action potential duration restitution slope. In contrast, during supernormal conduction, S1S2 intervals and the amplitude of alternans diverged. This amplification (resonance) led to phase-locked or more complex alternans patterns, and then to distal conduction block. The convergence/divergence of IBIs was verified in the cultured strands, in which naturally occurring tissue heterogeneities resulted in prominent discontinuities of the spatial IBI profiles. We conclude that supernormal conduction potentiates alternans and spatial analysis of IBIs represents a powerful method to locate tissue heterogeneities.

Dual excitation wavelength epifluorescence imaging of transmural electrophysiological properties in intact hearts

BACKGROUND

Epifluorescence imaging using voltage-sensitive dyes has provided unique insights into cardiac electrical activity and arrhythmias. However, conventional dyes use blue-green excitation light, which has limited depth penetration.

OBJECTIVE

The aim of this study was to demonstrate that combining a short and a long excitation wavelength using near-infrared (NIR) dyes allows for epifluorescence imaging of transmural electrophysiological properties in intact hearts.

METHODS

Epifluorescence imaging was performed in rat hearts (N = 11) using DI-4-ANEPPS and the NIR dye DI-4-ANBDQBS. Activation and action potential duration (APD) patterns were investigated at 2 excitation wavelengths (530 and 660 nm) after epicardial stimulation at various cycle lengths (160 to 70 ms).

RESULTS

Optical action potential upstrokes acquired with 660-nm excitation of DI-4-ANBDQBS were significantly longer than upstrokes obtained with 530-nm excitation of DI-4-ANEPPS (P < .001). Comparison of activation maps showed counterclockwise rotation of isochrones consistent with a transmural rotation of myofibers. Pronounced APD modulation by the activation sequence was observed at both excitation wavelengths. Significantly prolonged APDs (P = .016) and steeper APD restitution curves were found with DI-4-ANBDQBS (660-nm excitation) when compared with DI-4-ANEPPS (530-nm excitation). Dual excitation wavelength experiments using solely DI-4-ANBDQBS yielded similar results. Monophasic action potential recordings showed prolonged APD and steeper APD restitution curves in the endocardium, indicating that 660-nm excitation provides a significant endocardial contribution to the signal. Three-dimensional computer simulations confirmed our findings.

CONCLUSION

Dual excitation wavelength epifluorescence allows detecting transmural heterogeneity in intact hearts. It therefore has the potential to become an important tool in experimental cardiac electrophysiology.

Integrative modeling of the cardiac ventricular myocyte

Cardiac electrophysiology is a discipline with a rich 50-year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage-gated ion channels, mitochondrial energy production, ATP-dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392-413 DOI: 10.1002/wsbm.122

Models of cardiac excitation-contraction coupling in ventricular myocytes

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

Stiffness analysis of cardiac electrophysiological models

The electrophysiology in a cardiac cell can be modeled as a system of ordinary differential equations (ODEs). The efficient solution of these systems is important because they must be solved many times as sub-problems of tissue- or organ-level simulations of cardiac electrophysiology. The wide variety of existing cardiac cell models encompasses many different properties, including the complexity of the model and the degree of stiffness. Accordingly, no single numerical method can be expected to be the most efficient for every model. In this article, we study the stiffness properties of a range of cardiac cell models and discuss the implications for their numerical solution. This analysis allows us to select or design numerical methods that are highly effective for a given model and hence outperform commonly used methods.

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.

Electrotonic effects on action potential duration in perfused rat hearts

Electrotonic interactions in cardiac tissue have been shown previously to modulate dynamical properties of the myocardium such as action potential duration (APD) and action potential duration restitution. A recent computational study indicated that these electrotonic effects may be strongest in small murine hearts. In the present study, we investigate experimentally how APD is modulated by activation sequence and pacing rate using optical mapping in Langendorff perfused rat hearts. Our results show that following an epicardial point stimulus, a strong correlation exists between epicardial APD and activation time, with decreasing APD for increasing activation time. This effect is preserved for all pacing frequencies (6-14 Hz) investigated in this study. Our experimental results are validated by detailed three-dimensional computer simulations. These simulations also demonstrate a strong transmural APD dependence on activation sequence, which, near the pacing site, is sufficient to mask the intrinsic transmural gradient.

A novel near-infrared voltage-sensitive dye reveals the action potential wavefront orientation at increased depths of cardiac tissue

Recently, novel near-infrared (NIR) voltage-sensitive dyes were developed for imaging electrical activity in blood-perfused hearts and for tomographic applications. However, their usefulness for conventional surface mapping is unclear. The spectral shift to the NIR range significantly increases the penetration depth of light into the tissue, thus increasing the intramural volume contributing to the optical action potential (OAP). Here, we characterize both computationally and experimentally the effect of increased penetration depth on the OAP upstroke, the OAP component most sensitive to optical scattering and absorption, and the activation maps. Optical imaging of cardiac electrical activity was performed in isolated rat hearts (n = 5) paced from the LV mid free wall. We used the NIR dye JPW-6033 (excitation at 660nm, acquisition at >695nm). The conventional dye DI-4-ANEPPS (excitation at 532nm, acquisition at 700 DF50nm) was used for comparison. To simulate OAP we utilized a hybrid model that couples light transport equations with the model of electrical propagation. As expected, the switch from DI-4-ANEPPS to JPW-6033 significantly increased the upstroke duration: from 3.95 + or - 0.69ms to 5.39 + or - 0.82 ms, respectively. However, activation maps were largely unaffected. The correlation between the shape of the optical upstroke, and the averaged subsurface wave front orientation was also preserved. The computer simulations are in excellent agreement with the experimental data. In conclusion, our analysis suggests that despite significant increase in upstroke duration, the novel NIR dyes can be a useful alternative to conventional dyes in surface mapping applications.

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.