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

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

Dynamics of human atrial cell models: restitution, memory, and intracellular calcium dynamics in single cells

Mathematical models of cardiac cells have become important tools for investigating the electrophysiological properties and behavior of the heart. As the number of published models increases, it becomes more difficult to choose a model appropriate for the conditions to be studied, especially when multiple models describing the species and region of the heart of interest are available. In this paper, we will review and compare two detailed ionic models of human atrial myocytes, the Nygren et al. model (NM) and the Courtemanche et al. model (CM). Although both models include the same transmembrane currents and are largely based on the same experimental data from human atrial cells, the two models exhibit vastly different properties, especially in their dynamical behavior, including restitution and memory effects. The CM produces pronounced rate adaptation of action potential duration (APD) with limited memory effects, while the NM exhibits strong rate dependence of resting membrane potential (RMP), limited APD restitution, and stronger memory, as well as delayed afterdepolarizations and auto-oscillatory behavior upon cessation of rapid pacing. Channel conductance modifications based on experimentally measured changes during atrial fibrillation modify rate adaptation and memory in both models, but do not change the primary rate-dependent properties of APD and RMP for the CM and NM, respectively. Two sets of proposed changes to the NM that yield a spike-and-dome action potential morphology qualitatively similar to the CM at slow pacing rates similarly do not change the underlying dynamics of the model. Moreover, interchanging the formulations of all transmembrane currents between the two models while leaving calcium handling and ionic concentrations intact indicates that the currents strongly influence memory and the rate adaptation of RMP, while intracellular calcium dynamics primarily determine APD rate adaptation. Our results suggest that differences in intracellular calcium handling between the two human atrial myocyte models are responsible for marked dynamical differences and may prevent reconciliation between the models by straightforward channel conductance modifications.     

经颈静脉途径制备Beagle犬心脏记忆模型

目的经颈静脉途径应用心室起搏的方法制备心脏记忆犬模型。方法 8只普通级成年健康Beagle犬经腹腔麻醉后,Seldinger’s法穿刺颈外静脉成功后送入心内膜起搏电极,将电极头端固定于右室心尖部,近端连接于脉冲发生器。起搏频率设置较犬窦性心律时的基础心率快15%,保证起搏器连续起搏。结果连续起搏1周后所有动物均成功制备为心脏记忆模型。建模后犬的心率、呼吸、体重与建模前比较,无明显改变;所有模型组犬起搏前心电图均为窦性心律,起搏1周后出现心脏T波记忆,在下壁导联以及胸前导联均出现T波倒置,停止起搏后,心脏T波记忆逐渐消失;模型组犬与正常组犬心肌病理相比,无明显改变。结论经颈静脉途径应用心室起搏法建立心脏记忆犬模型的方法,具有手术简单,创伤小,诱发方式与临床相似等优点,为深入展开心脏记忆的机制研究奠定基础。     

The role of photon scattering in optical signal distortion during arrhythmia and defibrillation

Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitation of the technique is signal distortion due to photon scattering. The goal of this experimental/simulation study is to investigate the role of three-dimensional photon scattering in optical signal distortion during ventricular tachycardia (VT) and defibrillation. A three-dimensional realistic bidomain rabbit ventricular model was combined with a model of photon transport. Shocks were applied via external electrodes to induce sustained VT, and transmembrane potentials (V(m)) were compared with synthesized optical signals (V(opt)). Fluorescent recordings were conducted in isolated rabbit hearts to validate simulation results. Results demonstrate that shock-induced membrane polarization magnitude is smaller in V(opt) and in experimental signals as compared to V(m). This is due to transduction of potentials from weakly polarized midmyocardium to the epicardium. During shock-induced reentry and in sustained VT, photon scattering, combined with complex wavefront dynamics, results in optical action potentials near a filament exhibiting i), elevated resting potential, ii), reduced amplitude relative to pacing, and iii), dual-humped morphologies. A shift of up to 4 mm in the phase singularity location was observed in V(opt) maps when compared to V(m). This combined experimental/simulation study provides an interpretation of optical recordings during VT and defibrillation.     

Uniqueness and Stability of Action Potential Models during Rest, Pacing, and Conduction Using Problem-Solving Environment

Development and application of physiologically detailed dynamic models of the action potential (AP) and Ca²⁺ cycling in cardiac cells is a rapidly growing aspect of computational cardiac electrophysiology. Given the large scale of the nonlinear system involved, questions were recently raised regarding reproducibility, numerical stability, and uniqueness of model solutions, as well as ability of the model to simulate AP propagation in multicellular configurations. To address these issues, we reexamined ventricular models of myocyte AP developed in our laboratory with the following results. 1), Recognizing that the model involves a system of differential-algebraic equations, a procedure is developed for estimating consistent initial conditions that insure uniqueness and stability of the solution. 2), Model parameters that can be used to modify these initial conditions according to experimental values are identified. 3), A convergence criterion for steady-state solution is defined based on tracking the incremental contribution of each ion species to the membrane voltage. 4), Singularities in state variable formulations are removed analytically. 5), A biphasic current stimulus is implemented to completely eliminate stimulus artifact during long-term pacing over a broad range of frequencies. 6), Using the AP computed based on 1-5 above, an efficient scheme is developed for computing propagation in multicellular models.     

Ion fluxes,transmembrane potential,and osmotic stabilization: a new dynamic electrophysiological model for eukaryotic cells

Survival of mammalian cells is achieved by tight control of cell volume, while transmembrane potential has been known to control many cellular functions since the seminal work of Hodgkin and Huxley. Regulation of cell volume and transmembrane potential have a wide range of implications in physiology, from neurological and cardiac disorders to cancer and muscle fatigue. Therefore, understanding the relationship between transmembrane potential, ion fluxes, and cell volume regulation has become of great interest. In this paper we derive a system of differential equations that links transmembrane potential, ionic concentrations, and cell volume. In particular, we describe the dynamics of the cell within a few seconds after an osmotic stress, which cannot be done by the previous models in which either cell volume was constant or osmotic regulation instantaneous. This new model demonstrates that both membrane potential and cell volume stabilization occur within tens of seconds of changes in extracellular osmotic pressure. When the extracellular osmotic pressure is constant, the cell volume varies as a function of transmembrane potential and ion fluxes, thus providing an implicit link between transmembrane potential and cell volume. Experimental data provide results that corroborate the numerical simulations of the model in terms of time-related changes in cell volume and dynamics of the phenomena. This paper can be seen as a generalization of previous electrophysiological results, since under restrictive conditions they can be derived from our model.     

Systematic nocturnal atrial demand pacing results in high-output heart failure.

Beat-to-beat parameters of heart rate (HR), intra-arterial blood pressure (BP), central venous pressure, and derived indexes of cardiac output and total peripheral resistance were recorded 18 h/day (from 1800 to 1200 h the following day) in four monkeys (Macaca mulatta) during 20 control days followed by 20 days of atrial demand pacing. The pacing rate was set at approximately 10 beats/min above the fastest hourly average HR recorded during the control period, i.e., sufficient to prevent the normal nocturnal fall in HR. Nocturnal pacing resulted in progressive weekly increases in central venous BP and arterial BP. Analyses of levels and diurnal trends in hemodynamic parameters and cardiac function curves across consecutive 5-day periods of nocturnal pacing revealed a hemodynamic pattern characteristic of high-output heart failure, which progressively increased (week by week) during the early morning hours (0500-0700). Sustained elevated left ventricular work resulting from the prevention of a nocturnal fall in HR may have been responsible for the reduction in cardiac function seen in this experimental model.     

Metabolic, body temperature and hormonal responses to repeated periods of prolonged cycle-ergometer exercise in men.

This study was designed to find out whether rest intervals and prevention of dehydration during prolonged exercise inhibit a drift in metabolic rate, body temperature and hormonal response typically occurring during continuous work. For this purpose in ten healthy men the heart rate (fc), rectal temperature (Tre), oxygen uptake (VO2), as well as blood metabolite and some hormone concentrations were measured during 2-h exercise at approximately 50% maximal oxygen uptake split into four equal parts by 30-min rest intervals during which body water losses were replaced. During each 30-min exercise period there was a rapid change in Tre and fc superimposed on which, these values increased progressively in consecutive exercise periods (slow drift). The VO2 showed similar changes but there were no significant differences in the respiratory exchange ratio, pulmonary ventilation, mechanical efficiency and plasma osmolality between successive periods of exercise. Blood glucose, insulin and C-peptide concentrations decreased in consecutive exercise periods, whereas plasma free fatty acid, glycerol, catecholamine, growth hormone and glucagon concentrations increased. Blood lactate concentrations did not show any regular drift and the plasma cortisol concentration decreased during the first two exercise periods and then increased. In conclusion, in spite of the relatively long rest intervals between the periods of prolonged exercise and the prevention of dehydration several physiological and hormonal variables showed a distinct drift with time. It is suggested that the slow drift in metabolic rate could have been attributable in the main to the increased concentrations of heat liberating hormones.     

Arrhythmia and sudden death associated with elevated cardiac chloride channel activity

The identification and analysis of several cationic ion channels and their associated genes have greatly improved our understanding of the molecular and cellular mechanisms of cardiac arrhythmia. Our objective in this study was to examine the involvement of anionic ion channels in cardiac arrhythmia. We used a transgenic mouse model to overexpress the human cystic fibrosis transmembrane conductance regulator (CFTR) gene, which encodes a cAMP-regulated chloride channel. We used RNase protection and in situ hybridization assays to determine the level of CFTR expression, and radiotelemetry and in vivo electrophysiological study in combination with pharmacological intervention to analyse the cardiac function. Cardiac CFTR overexpression leads to stress-related sudden death in this model. In vivo intracardiac electrophysiological studies performed in anaesthetized mice showed no significant differences in baseline conduction parameters including atrial-His bundle (AH) or His bundle-ventricular (HV) conduction intervals, atrioventricular (AV) Wenckebach or 2:1 AV block cycle length and AV nodal functional refractory period. However, following isoproterenol administration, there was marked slowing of conduction parameters, including high-grade AV block in transgenic mice, with non-sustained ventricular tachycardia easily inducible using programmed stimulation or burst pacing. Our sudden death mouse model can be a valuable tool for investigation of the role of chloride channels in arrhythmogenesis and, potentially, for future evaluation of novel anti-arrhythmic therapeutic strategies and pharmacological agents.     

An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics

We present an integrated thermokinetic model describing control of cardiac mitochondrial bioenergetics. The model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca(2+) handling. The kinetic component of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH(2), which in turn are used by the electron transport chain to establish a proton motive force (Delta mu(H)), driving the F(1)F(0)-ATPase. In addition, mitochondrial matrix Ca(2+), determined by Ca(2+) uniporter and Na(+)/Ca(2+) exchanger activities, regulates activity of the TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase. The model is described by twelve ordinary differential equations for the time rate of change of mitochondrial membrane potential (Delta Psi(m)), and matrix concentrations of Ca(2+), NADH, ADP, and TCA cycle intermediates. The model is used to predict the response of mitochondria to changes in substrate delivery, metabolic inhibition, the rate of adenine nucleotide exchange, and Ca(2+). The model is able to reproduce, qualitatively and semiquantitatively, experimental data concerning mitochondrial bioenergetics, Ca(2+) dynamics, and respiratory control. Significant increases in oxygen consumption (V(O(2))), proton efflux, NADH, and ATP synthesis, in response to an increase in cytoplasmic Ca(2+), are obtained when the Ca(2+)-sensitive dehydrogenases are the main rate-controlling steps of respiratory flux. These responses diminished when control is shifted downstream (e.g., the respiratory chain or adenine nucleotide translocator). The time-dependent behavior of the model, under conditions simulating an increase in workload, closely reproduces experimentally observed mitochondrial NADH dynamics in heart trabeculae subjected to changes in pacing frequency. The steady-state and time-dependent behavior of the model support the hypothesis that mitochondrial matrix Ca(2+) plays an important role in matching energy supply with demand in cardiac myocytes.     

The effects of right ventricular apical pacing on left ventricular function. Stimulation of the right ventricular apex: should it still be the gold standard?

Current pacing practice is undergoing continuous and substantial changes. Initially pacing had an exclusively palliative role, since it was reserved for patients developing complete heart block or severe symptomatic bradycardia. With the appearance of novel pacing indications such as pacing for heart failure and atrial fibrillation, the effect of pacing site on cardiac function has become a critically important issue and a subject for consideration. It seems that the classical pacing site in the right ventricular apex is no longer the gold standard because of possible disadvantageous effects on cardiac function. The aim of this review article is to discuss the effect of right ventricular apical pacing on cardiac function including cellular and hemodynamic changes. We also aim to discuss the role of alternative pacing sites in the light of cardiac function.     

Low Energy Defibrillation in Human Cardiac Tissue: A Simulation Study

We aim to assess the effectiveness of feedback-controlled resonant drift pacing as a method for low energy defibrillation. Antitachycardia pacing is the only low energy defibrillation approach to have gained clinical significance, but it is still suboptimal. Low energy defibrillation would avoid adverse side effects associated with high voltage shocks and allow the application of implantable cardioverter defibrillator (ICD) therapy, in cases where such therapy is not tolerated today. We present results of computer simulations of a bidomain model of cardiac tissue with human atrial ionic kinetics. Reentry was initiated and low energy shocks were applied with the same period as the reentry, using feedback to maintain resonance. We demonstrate that such stimulation can move the core of reentrant patterns, in the direction that depends on the location of the electrodes and the time delay in the feedback. Termination of reentry is achieved with shock strength one-order-of-magnitude weaker than in conventional single-shock defibrillation. We conclude that resonant drift pacing can terminate reentry at a fraction of the shock strength currently used for defibrillation and can potentially work where antitachycardia pacing fails, due to the feedback mechanisms. Success depends on a number of details that these numerical simulations have uncovered.     

Linear algebraic transformations of the bidomain equations: Implications for numerical methods

A mathematical framework is presented for the treatment of the bidomain equations used to model propagation in cardiac tissue. This framework is independent of the model used to represent membrane ionic currents and incorporates boundary conditions and other constraints. By representing the bidomain equations in the operator notation , various algebraic transformations can be expressed as , where P and Q are linear operators. The authors show how previous work fits into this framework and discuss the implications of various transformation for numerical methods of solution. Although such transformations allow many choices of independent variable, these results emphasize the fundamental importance of the transmembrane potential.     

Is Cardiac Resynchronisation Therapy Proarrhythmic?

It is well established that cardiac resynchronisation therapy (CRT) using biventricular pacing prolongs survival by its effects on pump failure. The rate of sudden cardiac death in patients undergoing CRT, however, remains high. Animal and human studies have shown that reversal of normal sequence of myocardial activation during epicardial pacing, as applied during CRT, increases the transmural dispersion of repolarisation (TDR), a substrate for ventricular arrhythmias. Cohort studies in humans suggest that CRT has a differential effect on the arrhythmogenic substrate, antiarrhythmic in some and proarrhythmic in others. This review the focuses on the possibility that CRT may, under certain circumstances, promote arrhythmogenesis.     

A mathematical model of action potentials of mouse sinoatrial node cells with molecular bases

Genetically modified mice are popular experimental models for studying the molecular bases and mechanisms of cardiac arrhythmia. A postgenome challenge is to classify the functional roles of genes in cardiac function. To unveil the functional role of various genetic isoforms of ion channels in generating cardiac pacemaking action potentials (APs), a mathematical model for spontaneous APs of mouse sinoatrial node (SAN) cells was developed. The model takes into account the biophysical properties of membrane ionic currents and intracellular mechanisms contributing to spontaneous mouse SAN APs. The model was validated by its ability to reproduce the physiological exceptionally short APs and high pacing rates of mouse SAN cells. The functional roles of individual membrane currents were evaluated by blocking their coding channels. The roles of intracellular Ca(2+)-handling mechanisms on cardiac pacemaking were also investigated in the model. The robustness of model pacemaking behavior was evaluated by means of one- and two-parameter analyses in wide parameter value ranges. This model provides a predictive tool for cellular level outcomes of electrophysiological experiments. It forms the basis for future model development and further studies into complex pacemaking mechanisms as more quantitative experimental data become available.     

Interaction between spiral and paced waves in cardiac tissue

For prevention of lethal arrhythmias, patients at risk receive implantable cardioverter-defibrillators, which use high-frequency antitachycardia pacing (ATP) to convert tachycardias to a normal rhythm. One of the suggested ATP mechanisms involves paced-induced drift of rotating waves followed by their collision with the boundary of excitable tissue. This study provides direct experimental evidence of this mechanism. In monolayers of neonatal rat cardiomyocytes in which rotating waves of activity were initiated by premature stimuli, we used the Ca(2+)-sensitive indicator fluo 4 to observe propagating wave patterns. The interaction of the spiral tip with a paced wave was then monitored at a high spatial resolution. In the course of the experiments, we observed spiral wave pinning to local heterogeneities within the myocyte layer. High-frequency pacing led, in a majority of cases, to successful termination of spiral activity. Our data show that 1) stable spiral waves in cardiac monolayers tend to be pinned to local heterogeneities or areas of altered conduction, 2) overdrive pacing can shift a rotating wave from its original site, and 3) the wave break, formed as a result of interaction between the spiral tip and a paced wave front, moves by a paced-induced drift mechanism to an area where it may become unstable or collide with a boundary. The data were complemented by numerical simulations, which was used to further analyze experimentally observed behavior.     

Visitor reaction to pacing behavior: influence on the perception of animal care and interest in supporting zoological institutions

Many publications within the field of zoo animal welfare have stated the importance of decreasing stereotypic behavior (e.g., pacing) to help ensure a positive visitor experience. The idea behind these statements is that visitors want to see animals engaged in natural behavior. Additionally, it is thought that watching an animal exhibit species-appropriate behavior could help increase a visitor's connection to wildlife and ultimately their interest in conservation. However, until recently, no information was available to validate such statements. The purpose of this research was to examine people's reaction to viewing an animal engaged in pacing behavior. Participants were randomly selected to fill out a survey after watching a short video of either a tiger pacing or resting (control). Results indicate that having viewed a tiger pacing significantly decreases people's perception of the level of care animals receive at that facility. In addition, people's interest in supporting zoos decreased as a result of viewing this behavior. Results are discussed from an animal welfare, business, and conservation perspective.     

Effect of beta-adrenergic blockade on dynamic electrical restitution in vivo

The slope of the action potential duration (APD) restitution curve may be a significant determinant of the propensity to develop ventricular fibrillation, with steeper slopes associated with a more arrhythmogenic substrate. We hypothesized that one mechanism by which beta-blockers reduce sudden cardiac death is by flattening the APD restitution curve. Therefore, we investigated whether infusion of esmolol modulates the APD restitution curve in vivo. In 10 Yorkshire pigs, dynamic APD restitution curves were determined from measurements of APD at 90% repolarization with a monophasic action potential catheter positioned against the right ventricular septum during right ventricular apical pacing in the basal state and during infusion of esmolol. APD restitution curves were fitted to the three-parameter (a, b, c) exponential equation, APD = a.[1 - e((-b.DI))] + c, where DI is the diastolic interval. Esmolol decreased the maximal APD slope, 0.68 +/- 0.14 vs. 0.94 +/- 0.24 (baseline), P = 0.002, and flattened the APD restitution curve at shorter DIs, 75 and 100 ms (P < 0.05). To compare the slopes of the APD restitution curves at similar steady states, slopes were also computed at points of intersection between the restitution curve and the lines representing pacing at a fixed cycle length (CL) of 200, 225, 250, 275, and 300 ms using the relationship CL = APD + DI. Esmolol decreased APD restitution slopes at CLs 200-275 ms (P < 0.05). Esmolol flattens the cardiac APD restitution curve in vivo, particularly at shorter CLs and DIs. This may represent a novel mechanism by which beta-blockers prevent sudden cardiac death.