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In the initial hours following the application of the calcium channel blocker (CCB) nifedipine to microtissues consisting of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), we observe notable variations in the drug's efficacy. Here, we investigate the possibility that these temporal changes in CCB effects are associated with adaptations in the expression of calcium ion channels in cardiomyocyte membranes. To explore this, we employ a recently developed mathematical model that delineates the regulation of calcium ion channel expression by intracellular calcium concentrations. According to the model, a decline in intracellular calcium levels below a certain target level triggers an upregulation of calcium ion channels. Such an upregulation, if instigated by a CCB, would then counteract the drug's inhibitory effect on calcium currents. We assess this hypothesis using time-dependent measurements of hiPSC-CMs dynamics and by refining an existing mathematical model of myocyte action potentials incorporating the dynamic nature of the number of calcium ion channels. The revised model forecasts that the CCB-induced reduction in intracellular calcium concentrations leads to a subsequent increase in calcium ion channel expression, thereby attenuating the drug's overall efficacy. The data and fit models suggest that dynamic changes in cardiac cells in the presence of CCBs may be explainable by induced changes in protein expression, and that this may lead to challenges in understanding calcium based drug effects on the heart unless timings of applications are carefully considered. [ABSTRACT FROM AUTHOR]

Cell-based models of excitable tissues offer the advantage of cell-level precision, which cannot be achieved using traditional homogenized electrophysiological models. However, this enhanced accuracy comes at the cost of increased computational demands, necessitating the development of efficient cell-based models. The widely-accepted bidomain model serves as the standard in computational cardiac electrophysiology, and under certain anisotropy ratio conditions, it is well known that it can be reduced to the simpler monodomain model. Recently, the Kirchhoff Network Model (KNM) was developed as a cell-based counterpart to the bidomain model. In this paper, we aim to demonstrate that KNM can be simplified using the same steps employed to derive the monodomain model from the bidomain model. We present the cell-based Simplified Kirchhoff Network Model (SKNM), which produces results closely aligned with those of KNM while requiring significantly less computational resources. [ABSTRACT FROM AUTHOR]

Mathematical models based on homogenized representation of cardiac tissue have greatly improved our understanding of cardiac electrophysiology. However, these models are too coarse to investigate the dynamics at the level of the myocytes since the cells are not present in homogenized models. Recently, fine scale models have been proposed to allow for cell-level resolution of the dynamics, but these models are too computationally expensive to be used in applications like whole heart simulations of large animals. To address this issue, we propose a model that balances computational demands and physiological accuracy. The model is founded on Kirchhoff's current law, and represents every myocyte in the tissue. This allows specific properties to be assigned to individual cardiomyocytes, and other cell types like fibroblasts can be added to the model in an accurate manner while keeping the computing efforts reasonable. [ABSTRACT FROM AUTHOR]

The basic building blocks of the electrophysiology of cardiomyocytes are ion channels integrated in the cell membranes. Close to the ion channels there are very strong electrical and chemical gradients. However, these gradients extend for only a few nano-meters and are therefore commonly ignored in mathematical models. The full complexity of the dynamics is modelled by the Poisson-Nernst-Planck (PNP) equations but these equations must be solved using temporal and spatial scales of nano-seconds and nano-meters. Here we report solutions of the PNP equations in a fraction of two abuttal cells separated by a tiny extracellular space. We show that when only the potassium channels of the two cells are open, a stationary solution is reached with the well-known Debye layer close to the membranes. When the sodium channels of one of the cells are opened, a very strong and brief electrochemical wave emanates from the channels. If the extracellular space is sufficiently small and the number of sodium channels is sufficiently high, the wave extends all the way over to the neighboring cell and may therefore explain cardiac conduction even at very low levels of gap junctional coupling. Author summary: Mathematical models are extensively used to understand how the electrochemical wave traversing the myocardium in every heartbeat work and fail, and how failures can be repaired. The models are based on averaging over small length-scales and traditionally represent cardiac tissue on the millimeter level. More recently, cell-based models have been developed representing the individual cardiomyocytes on the micro-meter scale. The cell-based models can accurately simulate electrochemical processes inside and around individual cells, but fail to accurately represent the strong gradients in the electrical potential and the ion concentrations very close to the cell membranes, referred to as the Debye layer. In order to resolve these gradients in a simulation, it is necessary to solve the Poisson-Nernst-Planck (PNP) equations and the solution of these equations requires a mesh resolution on the order of nano-meters, thus strongly limiting the spatial domain that can be simulated. Here, we solve the PNP equations in a small domain including parts of two neighboring cells and the extracellular space between the cells. Our main observation is that the action potential of one cell can induce electrochemical waves that are sufficiently strong to affect a sufficiently close neighboring cell. This confirms that ephaptic coupling between cardiomyocytes is theoretically possible. [ABSTRACT FROM AUTHOR]

In the heart, electrophysiological dysregulation arises from defects at many biological levels (from point mutations in ion channel proteins to gross structural abnormalities). These defects disrupt the normal pattern of electrical activation, producing ectopic activity and reentrant arrhythmia. To interrogate mechanisms that link these primary biological defects to macroscopic electrophysiologic dysregulation most prior computational studies have utilized either (i) detailed models of myocyte ion channel dynamics at limited spatial scales, or (ii) homogenized models of action potential conduction that reproduce arrhythmic activity at tissue and organ levels. Here we apply our recent model (EMI), which integrates electrical activation and propagation across these scales, to study human atrial arrhythmias originating in the pulmonary vein (PV) sleeves. These small structures initiate most supraventricular arrhythmias and include pronounced myocyte-to-myocyte heterogeneities in ion channel expression and intercellular coupling. To test EMI's cell-based architecture in this physiological context we asked whether ion channel mutations known to underlie atrial fibrillation are capable of initiating arrhythmogenic behavior via increased excitability or reentry in a schematic PV sleeve geometry. Our results illustrate that EMI's improved spatial resolution can directly interrogate how electrophysiological changes at the individual myocyte level manifest in tissue and as arrhythmia in the PV sleeve. [ABSTRACT FROM AUTHOR]

In the heart, electrophysiological dysregulation arises from defects at many biological levels (from point mutations in ion channel proteins to gross structural abnormalities). These defects disrupt the normal pattern of electrical activation, producing ectopic activity and reentrant arrhythmia. To interrogate mechanisms that link these primary biological defects to macroscopic electrophysiologic dysregulation most prior computational studies have utilized either (i) detailed models of myocyte ion channel dynamics at limited spatial scales, or (ii) homogenized models of action potential conduction that reproduce arrhythmic activity at tissue and organ levels. Here we apply our recent model (EMI), which integrates electrical activation and propagation across these scales, to study human atrial arrhythmias originating in the pulmonary vein (PV) sleeves. These small structures initiate most supraventricular arrhythmias and include pronounced myocyte-to-myocyte heterogeneities in ion channel expression and intercellular coupling. To test EMI's cell-based architecture in this physiological context we asked whether ion channel mutations known to underlie atrial fibrillation are capable of initiating arrhythmogenic behavior via increased excitability or reentry in a schematic PV sleeve geometry. Our results illustrate that EMI's improved spatial resolution can directly interrogate how electrophysiological changes at the individual myocyte level manifest in tissue and as arrhythmia in the PV sleeve. [ABSTRACT FROM AUTHOR]

Mutations are known to cause perturbations in essential functional features of integral membrane proteins, including ion channels. Even restricted or point mutations can result in substantially changed properties of ion currents. The additive effect of these alterations for a specific ion channel can result in significantly changed properties of the action potential (AP). Both AP shortening and AP prolongation can result from known mutations, and the consequences can be life-threatening. Here, we present a computational method for identifying new drugs utilizing combinations of existing drugs. Based on the knowledge of theoretical effects of existing drugs on individual ion currents, our aim is to compute optimal combinations that can 'repair' the mutant AP waveforms so that the baseline AP-properties are restored. More specifically, we compute optimal, combined, drug concentrations such that the waveforms of the transmembrane potential and the cytosolic calcium concentration of the mutant cardiomyocytes (CMs) becomes as similar as possible to their wild type counterparts after the drug has been applied. In order to demonstrate the utility of this method, we address the question of computing an optimal drug for the short QT syndrome type 1 (SQT1). For the SQT1 mutation N588K, there are available data sets that describe the effect of various drugs on the mutated K+ channel. These published findings are the basis for our computational analysis which can identify optimal compounds in the sense that the AP of the mutant CMs resembles essential biomarkers of the wild type CMs. Using recently developed insights regarding electrophysiological properties among myocytes from different species, we compute optimal drug combinations for hiPSC-CMs, rabbit ventricular CMs and adult human ventricular CMs with the SQT1 mutation. Since the 'composition' of ion channels that form the AP is different for the three types of myocytes under consideration, so is the composition of the optimal drug. Author summary: Poly-pharmacology (using multiple drugs to treat disease) has been proposed for improving cardiac anti-arrhythmic therapy for at least two decades. However, the specific arrhythmia contexts in which polytherapy is likely to be both safe and effective have remained elusive. Type 1 short QT syndrome (SQT1) is a rare form of cardiac arrhythmia that results from mutations to the human Ether-á-go-go Related Gene (hERG) potassium channel. Functionally, these mutations are remarkably consistent in that they permit the channel to open earlier during each heart beat. While hundreds of compounds are known to inhibit hERG channels, the specific effect of SQT1 mutations that allows for early channel opening also limits the ability of most of those compounds to correct SQT1 dysfunction. Here, we have applied a suite of ventricular cardiomyocyte computational models to ask whether polytherapy may offer a more effective therapeutic strategy in SQT1, and if so, what the likely characteristics of that strategy are. Our analyses suggest that simultaneous induction of late sodium current and partial hERG blockade offers a promising strategy. While no activators of late sodium current have been clinically approved, several experimental compounds are available and may provide a basis for interrogating this strategy. The method presented here can be used to compute optimal drug combinations provided that the effect of each drug on every relevant ion channel is known. [ABSTRACT FROM AUTHOR]

Short QT (SQT) syndrome is a genetic cardiac disorder characterized by an abbreviated QT interval of the patient's electrocardiogram. The syndrome is associated with increased risk of arrhythmia and sudden cardiac death and can arise from a number of ion channel mutations. Cardiomyocytes derived from induced pluripotent stem cells generated from SQT patients (SQT hiPSC-CMs) provide promising platforms for testing pharmacological treatments directly in human cardiac cells exhibiting mutations specific for the syndrome. However, a difficulty is posed by the relative immaturity of hiPSC-CMs, with the possibility that drug effects observed in SQT hiPSC-CMs could be very different from the corresponding drug effect in vivo. In this paper, we apply a multistep computational procedure for translating measured drug effects from these cells to human QT response. This process first detects drug effects on individual ion channels based on measurements of SQT hiPSC-CMs and then uses these results to estimate the drug effects on ventricular action potentials and QT intervals of adult SQT patients. We find that the procedure is able to identify IC50 values in line with measured values for the four drugs quinidine, ivabradine, ajmaline and mexiletine. In addition, the predicted effect of quinidine on the adult QT interval is in good agreement with measured effects of quinidine for adult patients. Consequently, the computational procedure appears to be a useful tool for helping predicting adult drug responses from pure in vitro measurements of patient derived cell lines. Author summary: A number of cardiac disorders originate from genetic mutations affecting the function of ion channels populating the membrane of cardiomyocytes. One example is short QT syndrome, associated with increased risk of arrhythmias and sudden cardiac death. Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) provide a promising platform for testing potential pharmacological treatments for such disorders, as human cardiomyocytes exhibiting specific mutations can be generated and exposed to drugs in vitro. However, the electrophysiological properties of hiPSC-CMs differ significantly from those of adult native cardiomyocytes. Therefore, drug effects observed for hiPSC-CMs could possibly be very different from corresponding drug effects for adult cells in vivo. In this study, we apply a computational framework for translating drug effects observed for hiPSC-CMs derived from a short QT patient to drug effects for adult short QT cardiomyocytes. For one of the considered drugs, the effect on adult QT intervals has been measured and these measurements turn out to be in good agreement with the response estimated by the computational procedure. Thus, the computational framework shows promise for being a useful tool for predicting adult drug responses from measurements of hiPSC-CMs, allowing earlier identification of compounds to accurately treat cardiac diseases. [ABSTRACT FROM AUTHOR]

Using animal cells and tissues as precise measuring devices for developing new drugs presents a long-standing challenge for the pharmaceutical industry. Despite the very significant resources that continue to be dedicated to animal testing of new compounds, only qualitative results can be obtained. This often results in both false positives and false negatives. Here, we show how the effect of drugs applied to animal ventricular myocytes can be translated, quantitatively, to estimate a number of different effects of the same drug on human cardiomyocytes. We illustrate and validate our methodology by translating, from animal to human, the effect of dofetilide applied to dog cardiomyocytes, the effect of E-4031 applied to zebrafish cardiomyocytes, and, finally, the effect of sotalol applied to rabbit cardiomyocytes. In all cases, the accuracy of our quantitative estimates are demonstrated. Our computations reveal that, in principle, electrophysiological data from testing using animal ventricular myocytes, can give precise, quantitative estimates of the effect of new compounds on human cardiomyocytes. [ABSTRACT FROM AUTHOR]

Mathematical models describing the dynamics of the cardiac action potential are of great value for understanding how changes to the system can disrupt the normal electrical activity of cells and tissue in the heart. However, to represent specific data, these models must be parameterized, and adjustment of the maximum conductances of the individual contributing ionic currents is a commonly used method. Here, we present a method for investigating the uniqueness of such resulting parameterizations. Our key question is: Can the maximum conductances of a model be changed without giving any appreciable changes in the action potential? If so, the model parameters are not unique and this poses a major problem in using the models to identify changes in parameters from data, for instance, to evaluate potential drug effects. We propose a method for evaluating this uniqueness, founded on the singular value decomposition of a matrix consisting of the individual ionic currents. Small singular values of this matrix signify lack of parameter uniqueness and we show that the conclusion from linear analysis of the matrix carries over to provide insight into the uniqueness of the parameters in the nonlinear case. Using numerical experiments, we quantify the identifiability of the maximum conductances of well-known models of the cardiac action potential. Furthermore, we show how the identifiability depends on the time step used in the observation of the currents, how the application of drugs may change identifiability, and, finally, how the stimulation protocol can be used to improve the identifiability of a model. [ABSTRACT FROM AUTHOR]

The conduction of electrical signals through cardiac tissue is essential for maintaining the function of the heart, and conduction abnormalities are known to potentially lead to life-threatening arrhythmias. The properties of cardiac conduction have therefore been the topic of intense study for decades, but a number of questions related to the mechanisms of conduction still remain unresolved. In this paper, we demonstrate how the so-called EMI model may be used to study some of these open questions. In the EMI model, the extracellular space, the cell membrane, the intracellular space and the cell connections are all represented as separate parts of the computational domain, and the model therefore allows for study of local properties that are hard to represent in the classical homogenized bidomain or monodomain models commonly used to study cardiac conduction. We conclude that a non-uniform sodium channel distribution increases the conduction velocity and decreases the time delays over gap junctions of reduced coupling in the EMI model simulations. We also present a theoretical optimal cell length with respect to conduction velocity and consider the possibility of ephaptic coupling (i.e. cell-to-cell coupling through the extracellular potential) acting as an alternative or supporting mechanism to gap junction coupling. We conclude that for a non-uniform distribution of sodium channels and a sufficiently small intercellular distance, ephaptic coupling can influence the dynamics of the sodium channels and potentially provide cell-to-cell coupling when the gap junction connection is absent. [ABSTRACT FROM AUTHOR]

While cardiomyocytes differentiated from human induced pluripotent stems cells (hiPSCs) hold great promise for drug screening, the electrophysiological properties of these cells can be variable and immature, producing results that are significantly different from their human adult counterparts. Here, we describe a computational framework to address this limitation, and show how in silico methods, applied to measurements on immature cardiomyocytes, can be used to both identify drug action and to predict its effect in mature cells. Our synthetic and experimental results indicate that optically obtained waveforms of voltage and calcium from microphysiological systems can be inverted into information on drug ion channel blockage, and then, through assuming functional invariance of proteins during maturation, this data can be used to predict drug induced changes in mature ventricular cells. Together, this pipeline of measurements and computational analysis could significantly improve the ability of hiPSC derived cardiomycocytes to predict dangerous drug side effects. [ABSTRACT FROM AUTHOR]