Data-Driven Uncertainty Quantification for Cardiac Electrophysiological Models: Impact of Physiological Variability on Action Potential and Spiral Wave Dynamics

A probabilistic modeling framework for the prediction of spontaneous premature beats and reentry initiation

BACKGROUND

Spontaneously occurring life-threatening reentrant arrhythmias result when a propagating premature beat encounters a region with significant dispersion of refractoriness. Although localized structural tissue heterogeneities and prescribed cell functional gradients have been incorporated into computational electrophysiologic models, a quantitative framework for the evolution from normal to abnormal behavior that occurs by disease is lacking.

OBJECTIVE

The purpose of this study was to develop a probabilistic modeling framework representing the complex interplay of cell function and tissue structure in health and disease that predicts the emergence of premature beats and the initiation of reentry.

METHODS

An action potential model of the rabbit was developed with data-driven uncertainty characterization as done previously. A novel tissue model using the discrete-cell monodomain equations was developed by implementing cellular uncertainty as a random spatial field.

RESULTS

Cellular action potentials exhibited a wide range of duration and even a variety of behaviors, with 67% exhibiting normal repolarization, 27% displaying early afterdepolarizations, and 6% showing repolarization failure. Nevertheless, simulations in tissue resulted in localized synchronized repolarization. Thus, cellular variability provided "tissue-level robustness," and premature beats and reentry induction were never observed even with abnormalities in cell function (IKr block) or tissue structure (increased tissue resistance). Alterations of both cell function and tissue structure were necessary for the generation of premature beats and arrhythmia initiation.

CONCLUSION

Once extended to whole hearts and validated for a specific context, this modeling framework provides a means to predict the probability of the initiation of life-threatening arrhythmias.

Fast interactive simulations of cardiac electrical activity in anatomically accurate heart structures by compressing sparse uniform cartesian grids

BACKGROUND AND OBJECTIVE

Numerical simulations are valuable tools for studying cardiac arrhythmias. Not only do they complement experimental studies, but there is also an increasing expectation for their use in clinical applications to guide patient-specific procedures. However, numerical studies that solve the reaction-diffusion equations describing cardiac electrical activity remain challenging to set up, are time-consuming, and in many cases, are prohibitively computationally expensive for long studies. The computational cost of cardiac simulations of complex models on anatomically accurate structures necessitates parallel computing. Graphics processing units (GPUs), which have thousands of cores, have been introduced as a viable technology for carrying out fast cardiac simulations, sometimes including real-time interactivity. Our main objective is to increase the performance and accuracy of such GPU implementations while conserving computational resources.

METHODS

In this work, we present a compression algorithm that can be used to conserve GPU memory and improve efficiency by managing the sparsity that is inherent in using Cartesian grids to represent cardiac structures directly obtained from high-resolution MRI and mCT scans. Furthermore, we present a discretization scheme that includes the cross-diagonal terms in the computational cell to increase numerical accuracy, which is especially important for simulating thin tissue sections without the need for costly mesh refinement.

RESULTS

Interactive WebGL simulations of atrial/ventricular structures (on PCs, laptops, tablets, and phones) demonstrate the algorithm's ability to reduce memory demand by an order of magnitude and achieve calculations up to 20x faster. We further showcase its superiority in slender tissues and validate results against experiments performed in live explanted human hearts.

CONCLUSIONS

In this work, we present a compression algorithm that accelerates electrical activity simulations on realistic anatomies by an order of magnitude (up to 20x), thereby allowing the use of finer grid resolutions while conserving GPU memory. Additionally, improved accuracy is achieved through cross-diagonal terms, which are essential for thin tissues, often found in heart structures such as pectinate muscles and trabeculae, as well as Purkinje fibers. Our method enables interactive simulations with even interactive domain boundary manipulation (unlike finite element/volume methods). Finally, agreement with experiments and ease of mesh import into WebGL paves the way for virtual cohorts and digital twins, aiding arrhythmia analysis and personalized therapies.

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

A cross species thermoelectric and spatiotemporal analysis of alternans in live explanted hearts using dual voltage-calcium fluorescence optical mapping

Objective.Temperature plays a crucial role in influencing the spatiotemporal dynamics of the heart. Electrical instabilities due to specific thermal conditions typically lead to early period-doubling bifurcations and beat-to-beat alternans. These pro-arrhythmic phenomena manifest in voltage and calcium traces, resulting in compromised contractile behaviors. In such intricate scenario, dual optical mapping technique was used to uncover unexplored multi-scale and nonlinear couplings, essential for early detection and understanding of cardiac arrhythmia.Approach.We propose a methodological analysis of synchronized voltage-calcium signals for detecting alternans, restitution curves, and spatiotemporal alternans patterns under different thermal conditions, based on integral features calculation. To validate our approach, we conducted a cross-species investigation involving rabbit and guinea pig epicardial ventricular surfaces and human endocardial tissue under pacing-down protocols.Main results.We show that the proposed integral feature, as the area under the curve, could be an easily applicable indicator that may enhance the predictability of the onset and progression of cardiac alternans. Insights into spatiotemporal correlation analysis of characteristic spatial lengths across different heart species were further provided.Significance.Exploring cross-species thermoelectric features contributes to understanding temperature-dependent proarrhythmic regimes and their implications on coupled spatiotemporal voltage-calcium dynamics. The findings provide preliminary insights and potential strategies for enhancing arrhythmia detection and treatment.

A Review of Personalised Cardiac Computational Modelling Using Electroanatomical Mapping Data

Computational models of cardiac electrophysiology have gradually matured during the past few decades and are now being personalised to provide patient-specific therapy guidance for improving suboptimal treatment outcomes. The predictive features of these personalised electrophysiology models hold the promise of providing optimal treatment planning, which is currently limited in the clinic owing to reliance on a population-based or average patient approach. The generation of a personalised electrophysiology model entails a sequence of steps for which a range of activation mapping, calibration methods and therapy simulation pipelines have been suggested. However, the optimal methods that can potentially constitute a clinically relevant in silico treatment are still being investigated and face limitations, such as uncertainty of electroanatomical data recordings, generation and calibration of models within clinical timelines and requirements to validate or benchmark the recovered tissue parameters. This paper is aimed at reporting techniques on the personalisation of cardiac computational models, with a focus on calibrating cardiac tissue conductivity based on electroanatomical mapping data.

Virtual clinical QT exposure-response studies - A translational computational approach

BACKGROUND AND PURPOSE

A recent paradigm shift in proarrhythmic risk assessment suggests that the integration of clinical, non-clinical, and computational evidence can be used to reach a comprehensive understanding of the proarrhythmic potential of drug candidates. While current computational methodologies focus on predicting the incidence of proarrhythmic events after drug administration, the objective of this study is to predict concentration-response relationships of QTc as a clinical endpoint.

EXPERIMENTAL APPROACH

Full heart computational models reproducing human cardiac populations were created to predict the concentration-response relationship of changes in the QT interval as recommended for clinical trials. The concentration-response relationship of the QT-interval prolongation obtained from the computational cardiac population was compared against the relationship from clinical trial data for a set of well-characterized compounds: moxifloxacin, dofetilide, verapamil, and ondansetron.

KEY RESULTS

Computationally derived concentration-response relationships of QT interval changes for three of the four drugs had slopes within the confidence interval of clinical trials (dofetilide, moxifloxacin and verapamil) when compared to placebo-corrected concentration-ΔQT and concentration-ΔQT regressions. Moxifloxacin showed a higher intercept, outside the confidence interval of the clinical data, demonstrating that in this example, the standard linear regression does not appropriately capture the concentration-response results at very low concentrations. The concentrations corresponding to a mean QTc prolongation of 10 ms were consistently lower in the computational model than in clinical data. The critical concentration varied within an approximate ratio of 0.5 (moxifloxacin and ondansetron) and 1 times (dofetilide, verapamil) the critical concentration observed in human clinical trials. Notably, no other in silico methodology can approximate the human critical concentration values for a QT interval prolongation of 10 ms.

CONCLUSION AND IMPLICATIONS

Computational concentration-response modelling of a virtual population of high-resolution, 3-dimensional cardiac models can provide comparable information to clinical data and could be used to complement pre-clinical and clinical safety packages. It provides access to an unlimited exposure range to support trial design and can improve the understanding of pre-clinical-clinical translation.

The importance of mechanical conditions in the testing of excitation abnormalities in a population of electro-mechanical models of human ventricular cardiomyocytes

Background: Populations of in silico electrophysiological models of human cardiomyocytes represent natural variability in cell activity and are thoroughly calibrated and validated using experimental data from the human heart. The models have been shown to predict the effects of drugs and their pro-arrhythmic risks. However, excitation and contraction are known to be tightly coupled in the myocardium, with mechanical loads and stretching affecting both mechanics and excitation through mechanisms of mechano-calcium-electrical feedback. However, these couplings are not currently a focus of populations of cell models. Aim: We investigated the role of cardiomyocyte mechanical activity under different mechanical conditions in the generation, calibration, and validation of a population of electro-mechanical models of human cardiomyocytes. Methods: To generate a population, we assumed 11 input parameters of ionic currents and calcium dynamics in our recently developed TP + M model as varying within a wide range. A History matching algorithm was used to generate a non-implausible parameter space by calibrating the action potential and calcium transient biomarkers against experimental data and rejecting models with excitation abnormalities. The population was further calibrated using experimental data on human myocardial force characteristics and mechanical tests involving variations in preload and afterload. Models that passed the mechanical tests were validated with additional experimental data, including the effects of drugs with high or low pro-arrhythmic risk. Results: More than 10% of the models calibrated on electrophysiological data failed mechanical tests and were rejected from the population due to excitation abnormalities at reduced preload or afterload for cell contraction. The final population of accepted models yielded action potential, calcium transient, and force/shortening outputs consistent with experimental data. In agreement with experimental and clinical data, the models demonstrated a high frequency of excitation abnormalities in simulations of Dofetilide action on the ionic currents, in contrast to Verapamil. However, Verapamil showed a high frequency of failed contractions at high concentrations. Conclusion: Our results highlight the importance of considering mechanoelectric coupling in silico cardiomyocyte models. Mechanical tests allow a more thorough assessment of the effects of interventions on cardiac function, including drug testing.

Fiber Organization Has Little Effect on Electrical Activation Patterns During Focal Arrhythmias in the Left Atrium

Over the past two decades there has been a steady trend towards the development of realistic models of cardiac conduction with increasing levels of detail. However, making models more realistic complicates their personalization and use in clinical practice due to limited availability of tissue and cellular scale data. One such limitation is obtaining information about myocardial fiber organization in the clinical setting. In this study, we investigated a chimeric model of the left atrium utilizing clinically derived patient-specific atrial geometry and a realistic, yet foreign for a given patient fiber organization. We discovered that even significant variability of fiber organization had a relatively small effect on the spatio-temporal activation pattern during regular pacing. For a given pacing site, the activation maps were very similar across all fiber organizations tested.

Fiber Organization has Little Effect on Electrical Activation Patterns during Focal Arrhythmias in the Left Atrium

Over the past two decades there has been a steady trend towards the development of realistic models of cardiac conduction with increasing levels of detail. However, making models more realistic complicates their personalization and use in clinical practice due to limited availability of tissue and cellular scale data. One such limitation is obtaining information about myocardial fiber organization in the clinical setting. In this study, we investigated a chimeric model of the left atrium utilizing clinically derived patient-specific atrial geometry and a realistic, yet foreign for a given patient fiber organization. We discovered that even significant variability of fiber organization had a relatively small effect on the spatio-temporal activation pattern during regular pacing. For a given pacing site, the activation maps were very similar across all fiber organizations tested.

Credibility assessment of patient-specific computational modeling using patient-specific cardiac modeling as an exemplar

Reliable and robust simulation of individual patients using patient-specific models (PSMs) is one of the next frontiers for modeling and simulation (M&S) in healthcare. PSMs, which form the basis of digital twins, can be employed as clinical tools to, for example, assess disease state, predict response to therapy, or optimize therapy. They may also be used to construct virtual cohorts of patients, for in silico evaluation of medical product safety and/or performance. Methods and frameworks have recently been proposed for evaluating the credibility of M&S in healthcare applications. However, such efforts have generally been motivated by models of medical devices or generic patient models; how best to evaluate the credibility of PSMs has largely been unexplored. The aim of this paper is to understand and demonstrate the credibility assessment process for PSMs using patient-specific cardiac electrophysiological (EP) modeling as an exemplar. We first review approaches used to generate cardiac PSMs and consider how verification, validation, and uncertainty quantification (VVUQ) apply to cardiac PSMs. Next, we execute two simulation studies using a publicly available virtual cohort of 24 patient-specific ventricular models, the first a multi-patient verification study, the second investigating the impact of uncertainty in personalized and non-personalized inputs in a virtual cohort. We then use the findings from our analyses to identify how important characteristics of PSMs can be considered when assessing credibility with the approach of the ASME V&V40 Standard, accounting for PSM concepts such as inter- and intra-user variability, multi-patient and “every-patient” error estimation, uncertainty quantification in personalized vs non-personalized inputs, clinical validation, and others. The results of this paper will be useful to developers of cardiac and other medical image based PSMs, when assessing PSM credibility.

Patient-specific models are computational models that have been personalized using data from a patient. After decades of research, recent computational, data science and healthcare advances have opened the door to the fulfilment of the enormous potential of such models, from truly personalized medicine to efficient and cost-effective testing of new medical products. However, reliability (credibility) of patient-specific models is key to their success, and there are currently no general guidelines for evaluating credibility of patient-specific models. Here, we consider how frameworks and model evaluation activities that have been developed for generic (not patient-specific) computational models, can be extended to patient specific models. We achieve this through a detailed analysis of the activities required to evaluate cardiac electrophysiological models, chosen as an exemplar field due to its maturity and the complexity of such models. This is the first paper on the topic of reliability of patient-specific models and will help pave the way to reliable and trusted patient-specific modeling across healthcare applications.

Simulation of atrial fibrillation in a non-ohmic propagation model with dynamic gap junctions

Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel-Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100  μm resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.

Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation

Understanding and predicting the mechanisms promoting the onset and sustainability of cardiac arrhythmias represent a primary concern in the scientific and medical communities still today. Despite the long-lasting effort in clinical and physico-mathematical research, a critical aspect to be fully characterized and unveiled is represented by spatiotemporal alternans patterns of cardiac excitation. The identification of discordant alternans and higher-order alternating rhythms by advanced data analyses as well as their prediction by reliable mathematical models represents a major avenue of research for a broad and multidisciplinary scientific community. Current limitations concern two primary aspects: 1) robust and general-purpose feature extraction techniques and 2) in silico data assimilation within reliable and predictive mathematical models. Here, we address both aspects. At first, we extend our previous works on Fourier transformation imaging (FFI), applying the technique to whole-ventricle fluorescence optical mapping. Overall, we identify complex spatial patterns of voltage alternans and characterize higher-order rhythms by a frequency-series analysis. Then, we integrate the optical ultrastructure obtained by FFI analysis within a fine-tuned electrophysiological mathematical model of the cardiac action potential. We build up a novel data assimilation procedure demonstrating its reliability in reproducing complex alternans patterns in two-dimensional computational domains. Finally, we prove that the FFI approach applied to both experimental and simulated signals recovers the same information, thus closing the loop between the experiment, data analysis, and numerical simulations.

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.

Neural Network Differential Equations For Ion Channel Modelling

Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. These models provide an abstract description of the underlying conformational changes of the ion channels. However, due to the abstracted conformation states and assumptions for the rates of transition between them, there are differences between the models and reality-termed model discrepancy or misspecification. In this paper, we demonstrate the feasibility of using a mechanistically-inspired neural network differential equation model, a hybrid non-parametric model, to model ion channel kinetics. We apply it to the hERG potassium ion channel as an example, with the aim of providing an alternative modelling approach that could alleviate certain limitations of the traditional approach. We compare and discuss multiple ways of using a neural network to approximate extra hidden states or alternative transition rates. In particular we assess their ability to learn the missing dynamics, and ask whether we can use these models to handle model discrepancy. Finally, we discuss the practicality and limitations of using neural networks and their potential applications.

A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction-diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters' space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.