Exploiting mathematical models to illuminate electrophysiological variability between individuals

Cell-to-cell heterogeneity in ion channel conductance impacts substrate vulnerability to arrhythmia

Determining whether an ectopic depolarization will lead to a self-perpetuating arrhythmia is of critical importance in determining arrhythmia risk, so it is necessary to understand what factors impact substrate vulnerability. This study sought to explore the impact of cell-to-cell heterogeneity in ion channel conductance on substrate vulnerability to arrhythmia by measuring the duration of the vulnerable window in computational models of one-dimensional cables of ventricular cardiomyocytes. We began by using a population of uniform cable models to determine the mechanisms underlying the vulnerable window phenomenon. We found that in addition to the known importance of GNa, the conductances GCa,L and GKr also play a minor role in determining the vulnerable window duration. We also found that a steeper slope of the repolarizing action potential during the vulnerable window correlated with a shorter vulnerable window duration in uniform cables. We applied our understanding from these initial simulations to an investigation of the vulnerable window in heterogeneous cable models. The heterogeneous cables displayed a great deal of intra-cable variation in vulnerable window duration, highly sensitive to the cardiomyocytes in the local environment of the ectopic stimulus. Coupling strength modulated not only the magnitude of the vulnerable window duration but also the extent of intra-tissue variability in vulnerable window duration.NEW & NOTEWORTHY We investigate the impact of cell-to-cell heterogeneity in ion channel conductance on substrate vulnerability to arrhythmia by measuring the vulnerable window duration in computational cardiomyocyte cable models. We demonstrate a wide range of intra-cable variability in vulnerable window duration (VWD) and show how this is changed by ion channel block and coupling strength perturbations.

Estimating the probability of early afterdepolarizations and predicting arrhythmic risk associated with long QT syndrome type 1 mutations

Early afterdepolarizations (EADs) are action potential (AP) repolarization abnormalities that can trigger lethal arrhythmias. Simulations using biophysically detailed cardiac myocyte models can reveal how model parameters influence the probability of these cellular arrhythmias; however, such analyses can pose a huge computational burden. We have previously developed a highly simplified approach in which logistic regression models (LRMs) map parameters of complex cell models to the probability of ectopic beats. Here, we extend this approach to predict the probability of EADs (P(EAD)) as a mechanistic metric of arrhythmic risk. We use the LRM to investigate how changes in parameters of the slow-activating delayed rectifier current (IKs) affect P(EAD) for 17 different long QT syndrome type 1 (LQTS1) mutations. In this LQTS1 clinical arrhythmic risk prediction task, we compared P(EAD) for these 17 mutations with two other recently published model-based arrhythmia risk metrics (AP morphology metric across populations of myocyte models and transmural repolarization prolongation based on a one-dimensional [1D] tissue-level model). These model-based risk metrics yield similar prediction performance; however, each fails to stratify clinical risk for a significant number of the 17 studied LQTS1 mutations. Nevertheless, an interpretable ensemble model using multivariate linear regression built by combining all of these model-based risk metrics successfully predicts the clinical risk of 17 mutations. These results illustrate the potential of computational approaches in arrhythmia risk prediction.

Rapid ionic current phenotyping (RICP) identifies mechanistic underpinnings of iPSC-CM AP heterogeneity

As a renewable, easily accessible, human-derived in vitro model, human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) are a promising tool for studying arrhythmia-related factors, including cardiotoxicity and congenital proarrhythmia risks. An oft-mentioned limitation of iPSC-CMs is the abundant cell-to-cell variability in recordings of their electrical activity. Here, we develop a new method, rapid ionic current phenotyping (RICP), that utilizes a short (10 s) voltage clamp protocol to quantify cell-to-cell heterogeneity in key ionic currents. We correlate these ionic current dynamics to action potential recordings from the same cells and produce mechanistic insights into cellular heterogeneity. We present evidence that the L-type calcium current is the main determinant of upstroke velocity, rapid delayed rectifier K+ current is the main determinant of the maximal diastolic potential, and an outward current in the excitable range of slow delayed rectifier K+ is the main determinant of action potential duration. We measure an unidentified outward current in several cells at 6 mV that is not recapitulated by iPSC-CM mathematical models but contributes to determining action potential duration. In this way, our study both quantifies cell-to-cell variability in membrane potential and ionic currents, and demonstrates how the ionic current variability gives rise to action potential heterogeneity. Based on these results, we argue that iPSC-CM heterogeneity should not be viewed simply as a problem to be solved but as a model system to understand the mechanistic underpinnings of cellular variability.

Lysosomal calcium loading promotes spontaneous calcium release by potentiating ryanodine receptors

Spontaneous calcium release by ryanodine receptors (RyRs) due to intracellular calcium overload results in delayed afterdepolarizations, closely associated with life-threatening arrhythmias. In this regard, inhibiting lysosomal calcium release by two-pore channel 2 (TPC2) knockout has been shown to reduce the incidence of ventricular arrhythmias under β-adrenergic stimulation. However, mechanistic investigations into the role of lysosomal function on RyR spontaneous release remain missing. We investigate the calcium handling mechanisms by which lysosome function modulates RyR spontaneous release, and determine how lysosomes are able to mediate arrhythmias by its influence on calcium loading. Mechanistic studies were conducted using a population of biophysically detailed mouse ventricular models including for the first time modeling of lysosomal function, and calibrated by experimental calcium transients modulated by TPC2. We demonstrate that lysosomal calcium uptake and release can synergistically provide a pathway for fast calcium transport, by which lysosomal calcium release primarily modulates sarcoplasmic reticulum calcium reuptake and RyR release. Enhancement of this lysosomal transport pathway promoted RyR spontaneous release by elevating RyR open probability. In contrast, blocking either lysosomal calcium uptake or release revealed an antiarrhythmic impact. Under conditions of calcium overload, our results indicate that these responses are strongly modulated by intercellular variability in L-type calcium current, RyR release, and sarcoplasmic reticulum calcium-ATPase reuptake. Altogether, our investigations identify that lysosomal calcium handling directly influences RyR spontaneous release by regulating RyR open probability, suggesting antiarrhythmic strategies and identifying key modulators of lysosomal proarrhythmic action.

Emergent activity, heterogeneity, and robustness in a calcium feedback model of the sinoatrial node

The sinoatrial node (SAN) is the primary pacemaker of the heart. SAN activity emerges at an early point in life and maintains a steady rhythm for the lifetime of the organism. The ion channel composition and currents of SAN cells can be influenced by a variety of factors. Therefore, the emergent activity and long-term stability imply some form of dynamical feedback control of SAN activity. We adapt a recent feedback model-previously utilized to describe control of ion conductances in neurons-to a model of SAN cells and tissue. The model describes a minimal regulatory mechanism of ion channel conductances via feedback between intracellular calcium and an intrinsic target calcium level. By coupling a SAN cell to the calcium feedback model, we show that spontaneous electrical activity emerges from quiescence and is maintained at steady state. In a 2D SAN tissue model, spatial variability in intracellular calcium targets lead to significant, self-organized heterogeneous ion channel expression and calcium transients throughout the tissue. Furthermore, multiple pacemaking regions appear, which interact and lead to time-varying cycle length, demonstrating that variability in heart rate is an emergent property of the feedback model. Finally, we demonstrate that the SAN tissue is robust to the silencing of leading cells or ion channel knockouts. Thus, the calcium feedback model can reproduce and explain many fundamental emergent properties of activity in the SAN that have been observed experimentally based on a minimal description of intracellular calcium and ion channel regulatory networks.

Electrophysiological heterogeneity in large populations of rabbit ventricular cardiomyocytes

AIMS

Cardiac electrophysiological heterogeneity includes: (i) regional differences in action potential (AP) waveform, (ii) AP waveform differences in cells isolated from a single region, (iii) variability of the contribution of individual ion currents in cells with similar AP durations (APDs). The aim of this study is to assess intra-regional AP waveform differences, to quantify the contribution of specific ion channels to the APD via drug responses and to generate a population of mathematical models to investigate the mechanisms underlying heterogeneity in rabbit ventricular cells.

METHODS AND RESULTS

APD in ∼50 isolated cells from subregions of the LV free wall of rabbit hearts were measured using a voltage-sensitive dye. When stimulated at 2 Hz, average APD90 value in cells from the basal epicardial region was 254 ± 25 ms (mean ± standard deviation) in 17 hearts with a mean interquartile range (IQR) of 53 ± 17 ms. Endo-epicardial and apical-basal APD90 differences accounted for ∼10% of the IQR value. Highly variable changes in APD occurred after IK(r) or ICa(L) block that included a sub-population of cells (HR) with an exaggerated (hyper) response to IK(r) inhibition. A set of 4471 AP models matching the experimental APD90 distribution was generated from a larger population of models created by random variation of the maximum conductances (Gmax) of 8 key ion channels/exchangers/pumps. This set reproduced the pattern of cell-specific responses to ICa(L) and IK(r) block, including the HR sub-population. The models exhibited a wide range of Gmax values with constrained relationships linking ICa(L) with IK(r), ICl, INCX, and INaK.

CONCLUSION

Modelling the measured range of inter-cell APDs required a larger range of key Gmax values indicating that ventricular tissue has considerable inter-cell variation in channel/pump/exchanger activity. AP morphology is retained by relationships linking specific ionic conductances. These interrelationships are necessary for stable repolarization despite large inter-cell variation of individual conductances and this explains the variable sensitivity to ion channel block.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K^＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca^2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Metabolically driven maturation of human-induced-pluripotent-stem-cell-derived cardiac microtissues on microfluidic chips

The immature physiology of cardiomyocytes derived from human induced pluripotent stem cells (hiPSCs) limits their utility for drug screening and disease modelling. Here we show that suitable combinations of mechanical stimuli and metabolic cues can enhance the maturation of hiPSC-derived cardiomyocytes, and that the maturation-inducing cues have phenotype-dependent effects on the cells' action-potential morphology and calcium handling. By using microfluidic chips that enhanced the alignment and extracellular-matrix production of cardiac microtissues derived from genetically distinct sources of hiPSC-derived cardiomyocytes, we identified fatty-acid-enriched maturation media that improved the cells' mitochondrial structure and calcium handling, and observed divergent cell-source-dependent effects on action-potential duration (APD). Specifically, in the presence of maturation media, tissues with abnormally prolonged APDs exhibited shorter APDs, and tissues with aberrantly short APDs displayed prolonged APDs. Regardless of cell source, tissue maturation reduced variabilities in spontaneous beat rate and in APD, and led to converging cell phenotypes (with APDs within the 300-450 ms range characteristic of human left ventricular cardiomyocytes) that improved the modelling of the effects of pro-arrhythmic drugs on cardiac tissue.

Comparison of fluid dynamics changes due to physical activity in 3D printed patient specific coronary phantoms with the Windkessel equivalent model of coronary flow

Background

3D printing (3DP) used to replicate the geometry of normal and abnormal vascular pathologies has been demonstrated in many publications; however, reproduction of hemodynamic changes due to physical activities, such as rest versus moderate exercise, need to be investigated. We developed a new design for patient specific coronary phantoms, which allow adjustable physiological variables such as coronary distal resistance and coronary compliance in patients with coronary artery disease. The new design was tested in precise benchtop experiments and compared with a theoretical Windkessel electrical circuit equivalent, that models coronary flow and pressure using arterial resistance and compliance.

Methods

Five phantoms from patients who underwent clinically indicated elective invasive coronary angiography were built from CCTA scans using multi-material 3D printing. Each phantom was used in a controlled flow system where patient specific flow conditions were simulated by a programmable cardiac pump. To simulate the arteriole and capillary beds flow resistance and the compliance for various physical activities, we designed a three-chamber outlet system which controls the outflow dynamics of each coronary tree. Benchtop pressure measurements were recorded using sensors embedded in each of the main coronary arteries. Using the Windkessel model, patient specific flow equivalent electrical circuit models were designed for each coronary tree branch, and flow in each artery was determined for known inflow conditions. Local flow resistances were calculated through Poiseuille’s Law derived from the radii and lengths of the coronary arteries using CT angiography based multi-planar reconstructions. The coronary stenosis flow rates from the benchtop and the electrical models were compared to the localized flow rates calculated from invasive pressure measurements recorded in the angio-suites.

Results

The average Pearson correlations of the localized flow rates at the location of the stenosis between each of the models (Benchtop/Electrical, Benchtop/Angio, Electrical/Angio) are 0.970, 0.981, and 0.958 respectively.

Conclusions

3D printed coronary phantoms can be used to replicate the human arterial anatomy as well as blood flow conditions. It displays high levels of correlation when compared to hemodynamics calculated in electrically-equivalent coronary Windkessel models as well as invasive angio-suite pressure measurements.

Neuronal population models reveal specific linear conductance controllers sufficient to rescue preclinical disease phenotypes

Preclinical drug candidates are screened for their ability to ameliorate in vitro neuronal electrophysiology, and go/no-go decisions progress drugs to clinical trials based on population means across cells and animals. However, these measures do not mitigate clinical endpoint risk. Population-based modeling captures variability across multiple electrophysiological measures from healthy, disease, and drug phenotypes. We pursued optimizing therapeutic targets by identifying coherent sets of ion channel target modulations for recovering heterogeneous wild-type (WT) population excitability profiles from a heterogeneous Huntington's disease (HD) population. Our approach combines mechanistic simulations with population modeling of striatal neurons using evolutionary optimization algorithms to design 'virtual drugs'. We introduce efficacy metrics to score populations and rank virtual drug candidates. We found virtual drugs using heuristic approaches that performed better than single target modulators and standard classification methods. We compare a real drug to virtual candidates and demonstrate a novel in silico triaging method.

Interactive 3D Human Heart Simulations on Segmented Human MRI Hearts

Understanding cardiac arrhythmic mechanisms and developing new strategies to control and terminate them using computer simulations requires realistic physiological cell models with anatomically accurate heart structures. Furthermore, numerical simulations must be fast enough to study and validate model and structure parameters. Here, we present an interactive parallel approach for solving detailed cell dynamics in high-resolution human heart structures with a local PC's GPU. In vitro human heart MRI scans were manually segmented to produce 3D structures with anatomically realistic electrophysiology. The Abubu.js library was used to create an interactive code to solve the OVVR human ventricular cell model and the FDA extension of the model in the human MRI heart structures, allowing the simulation of reentrant waves and investigation of their dynamics in real time. Interactive simulations of a physiological cell model in a detailed anatomical human heart reveals propagation of waves through the fine structures of the trabeculae and pectinate muscle that can perpetuate arrhythmias, thereby giving new insights into effects that may need to be considered when planning ablation and other defibrillation methods.

A computational method for identifying an optimal combination of existing drugs to repair the action potentials of SQT1 ventricular myocytes

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.

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.

Inflammation as a Risk Factor in Cardiotoxicity: An Important Consideration for Screening During Drug Development

Numerous commonly prescribed drugs, including antiarrhythmics, antihistamines, and antibiotics, carry a proarrhythmic risk and may induce dangerous arrhythmias, including the potentially fatal Torsades de Pointes. For this reason, cardiotoxicity testing has become essential in drug development and a required step in the approval of any medication for use in humans. Blockade of the hERG K⁺ channel and the consequent prolongation of the QT interval on the ECG have been considered the gold standard to predict the arrhythmogenic risk of drugs. In recent years, however, preclinical safety pharmacology has begun to adopt a more integrative approach that incorporates mathematical modeling and considers the effects of drugs on multiple ion channels. Despite these advances, early stage drug screening research only evaluates QT prolongation in experimental and computational models that represent healthy individuals. We suggest here that integrating disease modeling with cardiotoxicity testing can improve drug risk stratification by predicting how disease processes and additional comorbidities may influence the risks posed by specific drugs. In particular, chronic systemic inflammation, a condition associated with many diseases, affects heart function and can exacerbate medications’ cardiotoxic effects. We discuss emerging research implicating the role of inflammation in cardiac electrophysiology, and we offer a perspective on how in silico modeling of inflammation may lead to improved evaluation of the proarrhythmic risk of drugs at their early stage of development.

Mechanisms underlying age-associated manifestation of cardiac sodium channel gain-of-function

Cardiac action potentials are initiated by sodium ion (Na+) influx through voltage-gated Na+ channels. Na+ channel gain-of-function (GOF) can arise in inherited conditions due to mutations in the gene encoding the cardiac Na+ channel, such as Long QT syndrome type 3 (LQT3). LQT3 can be a "concealed" disease, as patients with LQT3-associated mutations can remain asymptomatic until later in life; however, arrhythmias can also arise early in life in LQT3 patients, demonstrating a complex age-associated manifestation. We and others recently demonstrated that cardiac Na+ channels preferentially localize at the intercalated disc (ID) in adult cardiac tissue, which facilitates ephaptic coupling and formation of intercellular Na+ nanodomains that regulate pro-arrhythmic early afterdepolarization (EAD) formation in tissue with Na+ channel GOF. Several properties related to ephaptic coupling vary with age, such as cell size and Na+ channel and gap junction (GJ) expression and distribution: neonatal cells have immature IDs, with Na+ channels and GJs primarily diffusively distributed, while adult myocytes have mature IDs with preferentially localized Na+ channels and GJs. Here, we perform an in silico study varying critical age-dependent parameters to investigate mechanisms underlying age-associated manifestation of Na+ channel GOF in a model of guinea pig cardiac tissue. Simulations predict that total Na+ current conductance is a critical factor in action potential duration (APD) prolongation. We find a complex cell size/ Na+ channel expression relationship: increases in cell size (without concurrent increases in Na+ channel expression) suppress EAD formation, while increases in Na+ channel expression (without concurrent increases in cell size) promotes EAD formation. Finally, simulations with neonatal and early age-associated parameters predict normal APD with minimal dependence on intercellular cleft width; however, variability in cellular properties can lead to EADs presenting in early developmental stages. In contrast, for adult-associated parameters, EAD formation is highly dependent on cleft width, consistent with a mechanism underlying the age-associated manifestation of the Na+ channel GOF.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

Computational prediction of drug response in short QT syndrome type 1 based on measurements of compound effect in stem cell-derived cardiomyocytes

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.

In Silico Assessment of Class I Antiarrhythmic Drug Effects on Pitx2-Induced Atrial Fibrillation: Insights from Populations of Electrophysiological Models of Human Atrial Cells and Tissues

Electrical remodelling as a result of homeodomain transcription factor 2 (Pitx2)-dependent gene regulation was linked to atrial fibrillation (AF) and AF patients with single nucleotide polymorphisms at chromosome 4q25 responded favorably to class I antiarrhythmic drugs (AADs). The possible reasons behind this remain elusive. The purpose of this study was to assess the efficacy of the AADs disopyramide, quinidine, and propafenone on human atrial arrhythmias mediated by Pitx2-induced remodelling, from a single cell to the tissue level, using drug binding models with multi-channel pharmacology. Experimentally calibrated populations of human atrial action po-tential (AP) models in both sinus rhythm (SR) and Pitx2-induced AF conditions were constructed by using two distinct models to represent morphological subtypes of AP. Multi-channel pharmaco-logical effects of disopyramide, quinidine, and propafenone on ionic currents were considered. Simulated results showed that Pitx2-induced remodelling increased maximum upstroke velocity (dVdtmax), and decreased AP duration (APD), conduction velocity (CV), and wavelength (WL). At the concentrations tested in this study, these AADs decreased dVdtmax and CV and prolonged APD in the setting of Pitx2-induced AF. Our findings of alterations in WL indicated that disopyramide may be more effective against Pitx2-induced AF than propafenone and quinidine by prolonging WL.

Cardiac transmembrane ion channels and action potentials: cellular physiology and arrhythmogenic behavior

Cardiac arrhythmias are among the leading causes of mortality. They often arise from alterations in the electrophysiological properties of cardiac cells and their underlying ionic mechanisms. It is therefore critical to further unravel the pathophysiology of the ionic basis of human cardiac electrophysiology in health and disease. In the first part of this review, current knowledge on the differences in ion channel expression and properties of the ionic processes that determine the morphology and properties of cardiac action potentials and calcium dynamics from cardiomyocytes in different regions of the heart are described. Then the cellular mechanisms promoting arrhythmias in congenital or acquired conditions of ion channel function (electrical remodeling) are discussed. The focus is on human-relevant findings obtained with clinical, experimental, and computational studies, given that interspecies differences make the extrapolation from animal experiments to human clinical settings difficult. Deepening the understanding of the diverse pathophysiology of human cellular electrophysiology will help in developing novel and effective antiarrhythmic strategies for specific subpopulations and disease conditions.

A Novel Computational Model of the Rabbit Atrial Cardiomyocyte With Spatial Calcium Dynamics

Models of cardiac electrophysiology are widely used to supplement experimental results and to provide insight into mechanisms of cardiac function and pathology. The rabbit has been a particularly important animal model for studying mechanisms of atrial pathophysiology and atrial fibrillation, which has motivated the development of models for the rabbit atrial cardiomyocyte electrophysiology. Previously developed models include detailed representations of membrane currents and intracellular ionic concentrations, but these so-called “common-pool” models lack a spatially distributed description of the calcium handling system, which reflects the detailed ultrastructure likely found in cells in vivo. Because of the less well-developed T-tubular system in atrial compared to ventricular cardiomyocytes, spatial gradients in intracellular calcium concentrations may play a more significant role in atrial cardiomyocyte pathophysiology, rendering common-pool models less suitable for investigating underlying electrophysiological mechanisms. In this study, we developed a novel computational model of the rabbit atrial cardiomyocyte incorporating detailed compartmentalization of intracellular calcium dynamics, in addition to a description of membrane currents and intracellular processes. The spatial representation of calcium was based on dividing the intracellular space into eighteen different compartments in the transversal direction, each with separate systems for internal calcium storage and release, and tracking ionic fluxes between compartments in addition to the dynamics driven by membrane currents and calcium release. The model was parameterized employing a population-of-models approach using experimental data from different sources. The parameterization of this novel model resulted in a reduced population of models with inherent variability in calcium dynamics and electrophysiological properties, all of which fall within the range of observed experimental values. As such, the population of models may represent natural variability in cardiomyocyte electrophysiology or inherent uncertainty in the underlying experimental data. The ionic model population was also able to reproduce the U-shaped waveform observed in line-scans of triggered calcium waves in atrial cardiomyocytes, characteristic of the absence of T-tubules, resulting in a centripetal calcium wave due to subcellular calcium diffusion. This novel spatial model of the rabbit atrial cardiomyocyte can be used to integrate experimental findings, offering the potential to enhance our understanding of the pathophysiological role of calcium-handling abnormalities under diseased conditions, such as atrial fibrillation.

Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics

Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm's sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Variability in electrophysiological properties and conducting obstacles controls re-entry risk in heterogeneous ischaemic tissue

Ischaemia, in which inadequate blood supply compromises and eventually kills regions of cardiac tissue, can cause many types of arrhythmia, some life-threatening. A significant component of this is the effects of the resulting hypoxia, and concomitant hyperklaemia and acidosis, on the electrophysiological properties of myocytes. Clinical and experimental data have also shown that regions of structural heterogeneity (fibrosis, necrosis, fibro-fatty infiltration) can act as triggers for arrhythmias under acute ischaemic conditions. Mechanistic models have successfully captured these effects in silico. However, the relative significance of these separate facets of the condition, and how sensitive arrhythmic risk is to the extents of each, is far less explored. In this work, we use partitioned Gaussian process emulation and new metrics for source-sink mismatch that rely on simulations of bifurcating cardiac fibres to interrogate a model of heterogeneous ischaemic tissue. Re-entries were most sensitive to the level of hypoxia and the fraction of non-excitable tissue. In addition, our results reveal both protective and pro-arrhythmic effects of hyperklaemia, and present the levels of hyperklaemia, hypoxia and percentage of non-excitable tissue that pose the highest arrhythmic risks. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Creation and application of virtual patient cohorts of heart models

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Administration of Defective Virus Inhibits Dengue Transmission into Mosquitoes

The host-vector shuttle and the bottleneck in dengue transmission is a significant aspect with regard to the study of dengue outbreaks. As mosquitoes require 100–1000 times more virus to become infected than human, the transmission of dengue virus from human to mosquito is a vulnerability that can be targeted to improve disease control. In order to capture the heterogeneity in the infectiousness of an infected patient population towards the mosquito population, we calibrate a population of host-to-vector virus transmission models based on an experimentally quantified infected fraction of a mosquito population. Once the population of models is well-calibrated, we deploy a population of controls that helps to inhibit the human-to-mosquito transmission of the dengue virus indirectly by reducing the viral load in the patient body fluid. We use an optimal bang-bang control on the administration of the defective virus (transmissible interfering particles (TIPs)) to symptomatic patients in the course of their febrile period and observe the dynamics in successful reduction of dengue spread into mosquitoes.

Genetic algorithm-based personalized models of human cardiac action potential

We present a novel modification of genetic algorithm (GA) which determines personalized parameters of cardiomyocyte electrophysiology model based on set of experimental human action potential (AP) recorded at different heart rates. In order to find the steady state solution, the optimized algorithm performs simultaneous search in the parametric and slow variables spaces. We demonstrate that several GA modifications are required for effective convergence. Firstly, we used Cauchy mutation along a random direction in the parametric space. Secondly, relatively large number of elite organisms (6-10% of the population passed on to new generation) was required for effective convergence. Test runs with synthetic AP as input data indicate that algorithm error is low for high amplitude ionic currents (1.6±1.6% for IKr, 3.2±3.5% for IK1, 3.9±3.5% for INa, 8.2±6.3% for ICaL). Experimental signal-to-noise ratio above 28 dB was required for high quality GA performance. GA was validated against optical mapping recordings of human ventricular AP and mRNA expression profile of donor hearts. In particular, GA output parameters were rescaled proportionally to mRNA levels ratio between patients. We have demonstrated that mRNA-based models predict the AP waveform dependence on heart rate with high precision. The latter also provides a novel technique of model personalization that makes it possible to map gene expression profile to cardiac function.

A distinct molecular mechanism by which phenytoin rescues a novel long QT 3 variant

BACKGROUND

Genetic variants in SCN5A can result in channelopathies such as the long QT syndrome type 3 (LQT3), but the therapeutic response to Na⁺ channel blockers can vary. We previously reported a case of an infant with malignant LQT3 and a missense Q1475P SCN5A variant, who was effectively treated with phenytoin, but only partially with mexiletine. Here, we functionally characterized this variant and investigated possible mechanisms for the differential drug actions.

METHODS

Wild-type or mutant Na_v1.5 cDNAs were examined in transfected HEK293 cells with patch clamping and biochemical assays. We used computational modeling to provide insights into altered channel kinetics and to predict effects on the action potential.

RESULTS

The Q1475P variant in Na_v1.5 reduced the current density and channel surface expression, characteristic of a trafficking defect. The variant also led to positive shifts in the voltage dependence of steady-state activation and inactivation, faster inactivation and recovery from inactivation, and increased the "late" Na⁺ current. Simulations of Na_v1.5 gating with a 9-state Markov model suggested that transitions from inactivated to closed states were accelerated in Q1475P channels, leading to accumulation of channels in non-inactivated closed states. Simulations with a human ventricular myocyte model predicted action potential prolongation with Q1475P, compared with wild type, channels. Patch clamp data showed that mexiletine and phenytoin similarly rescued some of the gating defects. Chronic incubation with mexiletine, but not phenytoin, rescued the Na_v1.5-Q1475P trafficking defect, thus increasing mutant channel expression.

CONCLUSIONS

The gain-of-function effects of Na_v1.5-Q1475P predominate to cause a malignant long QT phenotype. Phenytoin partially corrects the gating defect without restoring surface expression of the mutant channel, whereas mexiletine restores surface expression of the mutant channel, which may explain the lack of efficacy of mexiletine when compared to phenytoin. Our data makes a case for experimental studies before embarking on a one-for-all therapy of arrhythmias.

Sensitivity and Uncertainty Analysis of Two Human Atrial Cardiac Cell Models Using Gaussian Process Emulators

Biophysically detailed cardiac cell models reconstruct the action potential and calcium dynamics of cardiac myocytes. They aim to capture the biophysics of current flow through ion channels, pumps, and exchangers in the cell membrane, and are highly detailed. However, the relationship between model parameters and model outputs is difficult to establish because the models are both complex and non-linear. The consequences of uncertainty and variability in model parameters are therefore difficult to determine without undertaking large numbers of model evaluations. The aim of the present study was to demonstrate how sensitivity and uncertainty analysis using Gaussian process emulators can be used for a systematic and quantitive analysis of biophysically detailed cardiac cell models. We selected the Courtemanche and Maleckar models of the human atrial action potential for analysis because these models describe a similar set of currents, with different formulations. In our approach Gaussian processes emulate the main features of the action potential and calcium transient. The emulators were trained with a set of design data comprising samples from parameter space and corresponding model outputs, initially obtained from 300 model evaluations. Variance based sensitivity indices were calculated using the emulators, and first order and total effect indices were calculated for each combination of parameter and output. The differences between the first order and total effect indices indicated that the effect of interactions between parameters was small. A second set of emulators were then trained using a new set of design data with a subset of the model parameters with a sensitivity index of more than 0.1 (10%). This second stage analysis enabled comparison of mechanisms in the two models. The second stage sensitivity indices enabled the relationship between the L-type Ca 2+ current and the action potential plateau to be quantified in each model. Our quantitative analysis predicted that changes in maximum conductance of the ultra-rapid K + channel I Kur would have opposite effects on action potential duration in the two models, and this prediction was confirmed by additional simulations. This study has demonstrated that Gaussian process emulators are an effective tool for sensitivity and uncertainty analysis of biophysically detailed cardiac cell models.

Quantitative analysis of variability in an integrated model of human ventricular electrophysiology and β-adrenergic signaling

In ventricular myocytes, stimulation of β-adrenergic receptors activates critical cardiac signaling pathways, leading to shorter action potentials and increased contraction strength during the "fight-or-flight" response. These changes primarily result, at the cellular level, from the coordinated phosphorylation of multiple targets by protein kinase A. Although mathematical models of the intracellular signaling downstream of β-adrenergic receptor activation have previously been described, only a limited number of studies have explored quantitative interactions between intracellular signaling and electrophysiology in human ventricular myocytes. Accordingly, our objective was to develop an integrative mathematical model of β-adrenergic receptor signaling, electrophysiology, and intracellular calcium (Ca²⁺) handling in the healthy human ventricular myocyte. We combined published mathematical models of intracellular signaling and electrophysiology, then calibrated the model results against voltage clamp data and physiological changes occurring after stimulation of β-adrenergic receptors with isoproterenol. We subsequently: (1) explored how molecular variability in different categories of model parameters translated into phenotypic variability; (2) identified the most important parameters determining physiological cellular outputs in the model before and after β-adrenergic receptor stimulation; and (3) investigated which molecular level alterations can produce a phenotype indicative of heart failure with preserved ejection fraction (HFpEF). Major results included: (1) variability in parameters that controlled intracellular signaling caused qualitatively different behavior than variability in parameters controlling ion transport pathways; (2) the most important model parameters determining action potential duration and intracellular Ca²⁺ transient amplitude were generally consistent before and after β-adrenergic receptor stimulation, except for a shift in the importance of K⁺ currents in determining action potential duration; and (3) decreased Ca²⁺ uptake into the sarcoplasmic reticulum, increased Ca²⁺ extrusion through Na⁺/Ca²⁺ exchanger and decreased Ca²⁺ leak from the sarcoplasmic reticulum may contribute to HFpEF. Overall, this study provided novel insight into the phenotypic consequences of molecular variability, and our integrated model may be useful in the design and interpretation of future experimental studies of interactions between β-adrenergic signaling and cellular physiology in human ventricular myocytes.

Cell Fate Forecasting: A Data-Assimilation Approach to Predict Epithelial-Mesenchymal Transition

Epithelial-mesenchymal transition (EMT) is a fundamental biological process that plays a central role in embryonic development, tissue regeneration, and cancer metastasis. Transforming growth factor-β (TGFβ) is a potent inducer of this cellular transition, which is composed of transitions from an epithelial state to intermediate or partial EMT state(s) to a mesenchymal state. Using computational models to predict cell state transitions in a specific experiment is inherently difficult for reasons including model parameter uncertainty and error associated with experimental observations. In this study, we demonstrate that a data-assimilation approach using an ensemble Kalman filter, which combines limited noisy observations with predictions from a computational model of TGFβ-induced EMT, can reconstruct the cell state and predict the timing of state transitions. We used our approach in proof-of-concept “synthetic” in silico experiments, in which experimental observations were produced from a known computational model with the addition of noise. We mimic parameter uncertainty in in vitro experiments by incorporating model error that shifts the TGFβ doses associated with the state transitions and reproduces experimentally observed variability in cell state by either shifting a single parameter or generating “populations” of model parameters. We performed synthetic experiments for a wide range of TGFβ doses, investigating different cell steady-state conditions, and conducted parameter studies varying properties of the data-assimilation approach including the time interval between observations and incorporating multiplicative inflation, a technique to compensate for underestimation of the model uncertainty and mitigate the influence of model error. We find that cell state can be successfully reconstructed and the future cell state predicted in synthetic experiments, even in the setting of model error, when experimental observations are performed at a sufficiently short time interval and incorporate multiplicative inflation. Our study demonstrates the feasibility and utility of a data-assimilation approach to forecasting the fate of cells undergoing EMT.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

R-From-T as a Common Mechanism of Arrhythmia Initiation in Long QT Syndromes

BACKGROUND

Long QT syndromes (LQTS) arise from many genetic and nongenetic causes with certain characteristic ECG features preceding polymorphic ventricular tachyarrhythmias (PVTs). However, how the many molecular causes result in these characteristic ECG patterns and how these patterns are mechanistically linked to the spontaneous initiation of PVT remain poorly understood.

METHODS

Anatomic human ventricle and simplified tissue models were used to investigate the mechanisms of spontaneous initiation of PVT in LQTS.

RESULTS

Spontaneous initiation of PVT was elicited by gradually ramping up ICa,L to simulate the initial phase of a sympathetic surge or by changing the heart rate, reproducing the different genotype-dependent clinical ECG features. In LQTS type 2 (LQT2) and LQTS type 3 (LQT3), T-wave alternans was observed followed by premature ventricular complexes (PVCs). Compensatory pauses occurred resulting in short-long-short sequences. As ICa,L increased further, PVT episodes occurred, always preceded by a short-long-short sequence. However, in LQTS type 1 (LQT1), once a PVC occurred, it always immediately led to an episode of PVT. Arrhythmias in LQT2 and LQT3 were bradycardia dependent, whereas those in LQT1 were not. In all 3 genotypes, PVCs always originated spontaneously from the steep repolarization gradient region and manifested on ECG as R-on-T. We call this mechanism R-from-T, to distinguish it from the classic explanation of R-on-T arrhythmogenesis in which an exogenous PVC coincidentally encounters a repolarizing region. In R-from-T, the PVC and the T wave are causally related, where steep repolarization gradients combined with enhanced ICa,L lead to PVCs emerging from the T wave. Since enhanced ICa,L was required for R-from-T to occur, suppressing window ICa,L effectively prevented arrhythmias in all 3 genotypes.

CONCLUSIONS

Despite the complex molecular causes, these results suggest that R-from-T is likely a common mechanism for PVT initiation in LQTS. Targeting ICa,L properties, such as suppressing window ICa,L or preventing excessive ICa,L increase, could be an effective unified therapy for arrhythmia prevention in LQTS.

Heterogeneous alpha-cell population modeling of glucose-induced inhibition of electrical activity

Glucagon release from the pancreatic alpha-cells is regulated by glucose, but the underlying mechanisms are far from understood. It is known that the alpha-cell population is very heterogeneous, but - compared to the insulin-secreting beta-cells - the consequences of this cell-to-cell variation are much less studied. Since the alpha-cells are not electrically coupled, large differences in the single cell responses are to be expected, and this variation may contribute to the confusion regarding the mechanisms of glucose-induced suppression of glucagon release. Using mathematical modeling of alpha-cells with realistic cell-to-cell parameter variation based on recent experimental results, we show that the simulated alpha-cells exhibit great diversity in their electrophysiological behavior. To robustly reproduce experimental recordings from alpha-cell exposed to a rise in glucose levels, we must assume that both intrinsic mechanisms and paracrine signals contribute to glucose-induced changes in electrical activity. Our simulations suggest that the sum of different electrophysiological responses due to alpha-cell heterogeneity is involved in glucose-suppressed glucagon secretion, and that more than one mechanism contribute to control the alpha-cell populations' behavior. Finally, we apply regression analysis to our synthetic alpha-cell population to infer which membrane currents influence electrical activity in alpha-cells at different glucose levels. The results from such statistical modeling suggest possible disturbances underlying defect regulation of alpha-cell electrical behavior in diabetics. Thus, although alpha-cells appear to be inherently complex and heterogeneous as reflected in published data, realistic modeling of the alpha-cells at the population level provides insight into the mechanisms of glucagon release.

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron’s 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.

Electrophysiological activity of the neuronal membrane and concomitant ion channel properties are highly variable within groups of neurons of the same type from the same brain region. Reconciliation of the mechanisms generating neuronal activity is challenging due to the complexity of the interactions between the channel currents involved. Here we present a set of mathematical analyses that uncover the low-dimensional intracellular parameter combinations capable of regulating features of subthreshold oscillations and spontaneous firing in empirically constrained models of nigral dopaminergic neurons. This method generates, from a naive starting point, linear combinations of ion channel properties that are surprisingly capable of reliably controlling a wide variety of emergent electrophysiological activity, thereby predicting drug effects and shedding light on unsuspected compensatory mechanisms that contribute to neuronal function.

Detecting undetectables: Can conductances of action potential models be changed without appreciable change in the transmembrane potential?

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.

Comprehensive Uncertainty Quantification and Sensitivity Analysis for Cardiac Action Potential Models

Recent efforts to ensure the reliability of computational model-based predictions in healthcare, such as the ASME V&V40 Standard, emphasize the importance of uncertainty quantification (UQ) and sensitivity analysis (SA) when evaluating computational models. UQ involves empirically determining the uncertainty in model inputs-typically resulting from natural variability or measurement error-and then calculating the resultant uncertainty in model outputs. SA involves calculating how uncertainty in model outputs can be apportioned to input uncertainty. Rigorous comprehensive UQ/SA provides confidence that model-based decisions are robust to underlying uncertainties. However, comprehensive UQ/SA is not currently feasible for whole heart models, due to numerous factors including model complexity and difficulty in measuring variability in the many parameters. Here, we present a significant step to developing a framework to overcome these limitations. We: (i) developed a novel action potential (AP) model of moderate complexity (six currents, seven variables, 36 parameters); (ii) prescribed input variability for all parameters (not empirically derived); (iii) used a single "hyper-parameter" to study increasing levels of parameter uncertainty; (iv) performed UQ and SA for a range of model-derived quantities with physiological relevance; and (v) present quantitative and qualitative ways to analyze different behaviors that occur under parameter uncertainty, including "model failure". This is the first time uncertainty in every parameter (including conductances, steady-state parameters, and time constant parameters) of every ionic current in a cardiac model has been studied. This approach allowed us to demonstrate that, for this model, the simulated AP is fully robust to low levels of parameter uncertainty - to our knowledge the first time this has been shown of any cardiac model. A range of dynamics was observed at larger parameter uncertainty (e.g., oscillatory dynamics); analysis revealed that five parameters were highly influential in these dynamics. Overall, we demonstrate feasibility of performing comprehensive UQ/SA for cardiac cell models and demonstrate how to assess robustness and overcome model failure when performing cardiac UQ analyses. The approach presented here represents an important and significant step toward the development of model-based clinical tools which are demonstrably robust to all underlying uncertainties and therefore more reliable in safety-critical decision-making.

Data-Driven Identification of Stochastic Model Parameters and State Variables: Application to the Study of Cardiac Beat-to-Beat Variability

OBJECTIVE

Enhanced spatiotemporal ventricular repolarization variability has been associated with ventricular arrhythmias and sudden cardiac death, but the involved mechanisms remain elusive. In this paper, a methodology for estimation of parameters and state variables of stochastic human ventricular cell models from input voltage data is proposed for investigation of repolarization variability.

METHODS

The proposed methodology formulates state-space representations based on developed stochastic cell models and uses the unscented Kalman filter to perform joint parameter and state estimation. Evaluation over synthetic and experimental data is presented.

RESULTS

Results on synthetically generated data show the ability of the methodology to: first, filter out measurement noise from action potential (AP) traces; second, identify model parameters and state variables from each of those individual AP traces, thus allowing robust characterization of cell-to-cell variability; and, third, replicate statistical population's distributions of input AP-based markers, including dynamic markers quantifying beat-to-beat variability. Application onto experimental data demonstrates the ability of the methodology to match input AP traces while concomitantly inferring the characteristics of underlying stochastic cell models.

CONCLUSION

A novel methodology is presented for estimation of parameters and hidden variables of stochastic cardiac computational models, with the advantage of providing a one-to-one match between each individual AP trace and a corresponding set of model characteristics.

SIGNIFICANCE

The proposed methodology can greatly help in the characterization of temporal (beat-to-beat) and spatial (cell-to-cell) variability in human ventricular repolarization and in ascertaining the corresponding underlying mechanisms, particularly in scenarios with limited available experimental data.

Real-time interactive simulations of large-scale systems on personal computers and cell phones: Toward patient-specific heart modeling and other applications

Cardiac dynamics modeling has been useful for studying and treating arrhythmias. However, it is a multiscale problem requiring the solution of billions of differential equations describing the complex electrophysiology of interconnected cells. Therefore, large-scale cardiac modeling has been limited to groups with access to supercomputers and clusters. Many areas of computational science face similar problems where computational costs are too high for personal computers so that supercomputers or clusters currently are necessary. Here, we introduce a new approach that makes high-performance simulation of cardiac dynamics and other large-scale systems like fluid flow and crystal growth accessible to virtually anyone with a modest computer. For cardiac dynamics, this approach will allow not only scientists and students but also physicians to use physiologically accurate modeling and simulation tools that are interactive in real time, thereby making diagnostics, research, and education available to a broader audience and pushing the boundaries of cardiac science.

Transient outward K+ current can strongly modulate action potential duration and initiate alternans in the human atrium

Efforts to identify the mechanisms for the initiation and maintenance of human atrial fibrillation (AF) often focus on changes in specific elements of the atrial "substrate," i.e., its electrophysiological properties and/or structural components. We used experimentally validated mathematical models of the human atrial myocyte action potential (AP), both at baseline in sinus rhythm (SR) and in the setting of chronic AF, to identify significant contributions of the Ca2+-independent transient outward K+ current ( Ito) to electrophysiological instability and arrhythmia initiation. First, we explored whether changes in the recovery or restitution of the AP duration (APD) and/or its dynamic stability (alternans) can be modulated by Ito. Recent reports have identified disease-dependent spatial differences in expression levels of the specific K+ channel α-subunits that underlie Ito in the left atrium. Therefore, we studied the functional consequences of this by deletion of 50% of native Ito (Kv4.3) and its replacement with Kv1.4. Interestingly, significant changes in the short-term stability of the human atrial AP waveform were revealed. Specifically, this K+ channel isoform switch produced discontinuities in the initial slope of the APD restitution curve and appearance of APD alternans. This pattern of in silico results resembles some of the changes observed in high-resolution clinical electrophysiological recordings. Important insights into mechanisms for these changes emerged from known biophysical properties (reactivation kinetics) of Kv1.4 versus those of Kv4.3. These results suggest new approaches for pharmacological management of AF, based on molecular properties of specific K+ isoforms and their changed expression during progressive disease. NEW & NOTEWORTHY Clinical studies identify oscillations (alternans) in action potential (AP) duration as a predictor for atrial fibrillation (AF). The abbreviated AP in AF also involves changes in K+ currents and early repolarization of the AP. Our simulations illustrate how substitution of Kv1.4 for the native current, Kv4.3, alters the AP waveform and enhances alternans. Knowledge of this "isoform switch" and related dynamics in the AF substrate may guide new approaches for detection and management of AF.

Inversion and computational maturation of drug response using human stem cell derived cardiomyocytes in microphysiological systems

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.

The Ca2+ transient as a feedback sensor controlling cardiomyocyte ionic conductances in mouse populations

Conductances of ion channels and transporters controlling cardiac excitation may vary in a population of subjects with different cardiac gene expression patterns. However, the amount of variability and its origin are not quantitatively known. We propose a new conceptual approach to predict this variability that consists of finding combinations of conductances generating a normal intracellular Ca²⁺ transient without any constraint on the action potential. Furthermore, we validate experimentally its predictions using the Hybrid Mouse Diversity Panel, a model system of genetically diverse mouse strains that allows us to quantify inter-subject versus intra-subject variability. The method predicts that conductances of inward Ca²⁺ and outward K⁺ currents compensate each other to generate a normal Ca²⁺ transient in good quantitative agreement with current measurements in ventricular myocytes from hearts of different isogenic strains. Our results suggest that a feedback mechanism sensing the aggregate Ca²⁺ transient of the heart suffices to regulate ionic conductances.

Generalized polynomial chaos-based uncertainty quantification and propagation in multi-scale modeling of cardiac electrophysiology

Uncertainty and physiological variability are ubiquitous in cardiac electrical signaling. It is important to address the uncertainty and variability in cardiac modeling to provide reliable and realistic predictions of heart function, thus ensuring trustworthy computer-aided medical decision-making and treatment planning. Statistical techniques such as Monte Carlo (MC) simulations have been applied to uncertainty quantification and propagation in cardiac modeling. However, MC simulation-based methods are computationally prohibitive for complex cardiac models with a great number of parameters and governing equations. In this paper, we propose to use the Generalized Polynomial Chaos (gPC) expansion in combination with Galerkin projection to analytically quantify parametric uncertainty in ion channel models of mouse ventricular cell, and further propagate the uncertainty across different organizational levels of cell and tissue. To identify the most significant parametric uncertainty in cardiac ion channel and cell models, variance decomposition-based sensitivity analysis was first performed. Following this, gPC was integrated with deterministic cardiac models to propagate uncertainty through ion current, ventricular cell, 1D cable, and 2D tissue to account for the stochasticity and cell-to-cell variability. As compared to MC, the gPC in this work shows the superior performance in terms of computational efficiency. In addition, the gPC models can provide a measure of confidence in model predictions, which can improve the reliability of computer simulations of cardiac electrophysiology for clinical applications.

Bridging the Data Gap From in vitro Toxicity Testing to Chemical Safety Assessment Through Computational Modeling

Chemical toxicity testing is moving steadily toward a human cell and organoid-based in vitro approach for reasons including scientific relevancy, efficiency, cost, and ethical rightfulness. Inferring human health risk from chemical exposure based on in vitro testing data is a challenging task, facing various data gaps along the way. This review identifies these gaps and makes a case for the in silico approach of computational dose-response and extrapolation modeling to address many of the challenges. Mathematical models that can mechanistically describe chemical toxicokinetics (TK) and toxicodynamics (TD), for both in vitro and in vivo conditions, are the founding pieces in this regard. Identifying toxicity pathways and in vitro point of departure (PoD) associated with adverse health outcomes requires an understanding of the molecular key events in the interacting transcriptome, proteome, and metabolome. Such an understanding will in turn help determine the sets of sensitive biomarkers to be measured in vitro and the scope of toxicity pathways to be modeled in silico. In vitro data reporting both pathway perturbation and chemical biokinetics in the culture medium serve to calibrate the toxicity pathway and virtual tissue models, which can then help predict PoDs in response to chemical dosimetry experienced by cells in vivo. Two types of in vitro to in vivo extrapolation (IVIVE) are needed. (1) For toxic effects involving systemic regulations, such as endocrine disruption, organism-level adverse outcome pathway (AOP) models are needed to extrapolate in vitro toxicity pathway perturbation to in vivo PoD. (2) Physiologically-based toxicokinetic (PBTK) modeling is needed to extrapolate in vitro PoD dose metrics into external doses for expected exposure scenarios. Linked PBTK and TD models can explore the parameter space to recapitulate human population variability in response to chemical insults. While challenges remain for applying these modeling tools to support in vitro toxicity testing, they open the door toward population-stratified and personalized risk assessment.

Slow Recovery of Excitability Increases Ventricular Fibrillation Risk as Identified by Emulation

Purpose: Rotor stability and meandering are key mechanisms determining and sustaining cardiac fibrillation, with important implications for anti-arrhythmic drug development. However, little is yet known on how rotor dynamics are modulated by variability in cellular electrophysiology, particularly on kinetic properties of ion channel recovery.

Methods: We propose a novel emulation approach, based on Gaussian process regression augmented with machine learning, for data enrichment, automatic detection, classification, and analysis of re-entrant biomarkers in cardiac tissue. More than 5,000 monodomain simulations of long-lasting arrhythmic episodes with Fenton-Karma ionic dynamics, further enriched by emulation to 80 million electrophysiological scenarios, were conducted to investigate the role of variability in ion channel densities and kinetics in modulating rotor-driven arrhythmic behavior.

Results: Our methods predicted the class of excitation behavior with classification accuracy up to 96%, and emulation effectively predicted frequency, stability, and spatial biomarkers of functional re-entry. We demonstrate that the excitation wavelength interpretation of re-entrant behavior hides critical information about rotor persistence and devolution into fibrillation. In particular, whereas action potential duration directly modulates rotor frequency and meandering, critical windows of excitability are identified as the main determinants of breakup. Further novel electrophysiological insights of particular relevance for ventricular arrhythmias arise from our multivariate analysis, including the role of incomplete activation of slow inward currents in mediating tissue rate-dependence and dispersion of repolarization, and the emergence of slow recovery of excitability as a significant promoter of this mechanism of dispersion and increased arrhythmic risk.

Conclusions: Our results mechanistically explain pro-arrhythmic effects of class Ic anti-arrhythmics in the ventricles despite their established role in the pharmacological management of atrial fibrillation. This is mediated by their slow recovery of excitability mode of action, promoting incomplete activation of slow inward currents and therefore increased dispersion of repolarization, given the larger influence of these currents in modulating the action potential in the ventricles compared to the atria. These results exemplify the potential of emulation techniques in elucidating novel mechanisms of arrhythmia and further application to cardiac electrophysiology.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

Quantitative systems models illuminate arrhythmia mechanisms in heart failure: Role of the Na+ -Ca2+ -Ca2+ /calmodulin-dependent protein kinase II-reactive oxygen species feedback

Quantitative systems modeling aims to integrate knowledge in different research areas with models describing biological mechanisms and dynamics to gain a better understanding of complex clinical syndromes. Heart failure (HF) is a chronic complex cardiac disease that results from structural or functional disorders impairing the ability of the ventricle to fill with or eject blood. Highly interactive and dynamic changes in mechanical, structural, neurohumoral, metabolic, and electrophysiological properties collectively predispose the failing heart to cardiac arrhythmias, which are responsible for about a half of HF deaths. Multiscale cardiac modeling and simulation integrate structural and functional data from HF experimental models and patients to improve our mechanistic understanding of this complex arrhythmia syndrome. In particular, they allow investigating how disease-induced remodeling alters the coupling of electrophysiology, Ca²⁺ and Na⁺ handling, contraction, and energetics that lead to rhythm derangements. The Ca²⁺ /calmodulin-dependent protein kinase II, which expression and activity are enhanced in HF, emerges as a critical hub that modulates the feedbacks between these various subsystems and promotes arrhythmogenesis. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Introduction to biological complexity as a missing link in drug discovery

INTRODUCTION

Despite a burgeoning knowledge of the intricacies and mechanisms responsible for human disease, technological advances in medicinal chemistry, and more efficient assays used for drug screening, it remains difficult to discover novel and effective pharmacologic therapies. Areas covered: By reference to the primary literature and concepts emerging from academic and industrial drug screening landscapes, the authors propose that this disconnect arises from the inability to scale and integrate responses from simpler model systems to outcomes from more complex and human-based biological systems. Expert opinion: Further collaborative efforts combining target-based and phenotypic-based screening along with systems-based pharmacology and informatics will be necessary to harness the technological breakthroughs of today to derive the novel drug candidates of tomorrow. New questions must be asked of enabling technologies-while recognizing inherent limitations-in a way that moves drug development forward. Attempts to integrate mechanistic and observational information acquired across multiple scales frequently expose the gap between our knowledge and our understanding as the level of complexity increases. We hope that the thoughts and actionable items highlighted will help to inform the directed evolution of the drug discovery process.

Model-Based Feature Augmentation for Cardiac Ablation Target Learning From Images

GOAL

We present a model-based feature augmentation scheme to improve the performance of a learning algorithm for the detection of cardiac radio-frequency ablation (RFA) targets with respect to learning from images alone.

METHODS

Initially, we compute image features from delayed-enhanced magnetic resonance imaging (DE-MRI) to describe local tissue heterogeneities and feed them into a machine learning framework with uncertainty assessment for the identification of potential ablation targets. Next, we introduce the use of a patient-specific image-based model derived from DE-MRI coupled with the Mitchell-Schaeffer electrophysiology model and a dipole formulation for the simulation of intracardiac electrograms. Relevant features are extracted from these simulated signals which serve as a feature augmentation scheme for the learning algorithm. We assess the classifier's performance when using only image features and with model-based feature augmentation.

RESULTS

We obtained average classification scores of 97.2 % accuracy, 82.4 % sensitivity, and 95.0 % positive predictive value by using a model-based feature augmentation scheme. Preliminary results also show that training the algorithm on the closest patient from the database, instead of using all the patients, improves the classification results.

CONCLUSION

We presented a feature augmentation scheme based on biophysical cardiac electrophysiology modeling to increase the prediction scores of a machine learning framework for the RFA target prediction.

SIGNIFICANCE

The results derived from this study are a proof of concept that the use of model-based feature augmentation strengthens the performance of a purely image driven learning scheme for the prediction of cardiac ablation targets.

Population-based mechanistic modeling allows for quantitative predictions of drug responses across cell types

Quantitative mismatches between human physiology and experimental models can be problematic for the development of effective therapeutics. When the effects of drugs on human adult cardiac electrophysiology are of interest, phenotypic differences with animal cells, and more recently stem cell-derived models, can present serious limitations. We addressed this issue through a combination of mechanistic mathematical modeling and statistical analyses. Physiological metrics were simulated in heterogeneous populations of models describing cardiac myocytes from adult ventricles and those derived from induced pluripotent stem cells (iPSC-CMs). These simulated measures were used to construct a cross-cell type regression model that predicts adult myocyte drug responses from iPSC-CM behaviors. We found that (1) quantitatively accurate predictions of responses to selective or non-selective ion channel blocking drugs could be generated based on iPSC-CM responses under multiple experimental conditions; (2) altering extracellular ion concentrations is an effective experimental perturbation for improving the model’s predictive strength; (3) the method can be extended to predict and contrast drug responses in diseased as well as healthy cells, indicating a broader application of the concept. This cross-cell type model can be of great value in drug development, and the approach, which can be applied to other fields, represents an important strategy for overcoming experimental model limitations.

The quantitative limitations of experimental models, which can impair the development of effective therapeutics, can be overcome through a combination of mechanistic simulations and statistical analysis. A team from Icahn School of Medicine at Mount Sinai led by Eric Sobie devised a computational method to quantitatively translate drug responses across cell types. The method involves mechanism-based simulations of heterogeneous populations combined with a multivariable regression model that translates between cell types. Simulation results presented in the study show that the response to a drug in one cell type can be predicted with quantitative accuracy from physiological recordings made in another cell type, as can differential drug responses observed in diseased compared with healthy cells. This methodology can be used in drug development to better predict clinical responses based on experiments performed in preclinical models.

Inverse estimation of cardiac activation times via gradient-based optimization

Computational modeling may provide a quantitative framework for integrating multiscale data to gain insight into mechanisms of heart disease, identify and test pharmacological and electrical therapy and interventions, and support clinical decisions. Patient-specific computational cardiac models can help guide such procedures, and cardiac inverse modeling is a promising alternative to adequately personalize these models. Indeed, full cardiac inverse modeling is currently becoming computationally feasible; however, fundamental work to assess the feasibility of emerging techniques is still needed. In this study, we use a partial differential equation-constrained optimal control approach to numerically investigate the identifiability of an initial activation sequence from synthetic (partial) observations of the extracellular potential using the bidomain approximation and 2D representations of cardiac tissue. Our results demonstrate that activation times and duration of several stimuli can be recovered even with high levels of noise, that it is sufficient to sample the observations at the electrocardiogram-relevant sampling frequency of 1 kHz, and that spatial resolutions that are coarser than the standard in electrophysiological simulations can be used. The optimization of activation times is still effective when synthetic data are generated with a different cell membrane kinetics model than optimized for. The findings thus indicate that the presented approach has potential for finding activation sequences from clinical data modalities, as an extension to existing cardiac imaging approaches.