Whole-heart modeling: applications to cardiac electrophysiology and electromechanics

Simulating left atrial arrhythmias with an interactive N-body model

BACKGROUND

Heart disease and strokes are leading global killers. While atrial arrhythmias are not deadly by themselves, they can disrupt blood flow in the heart, causing blood clots. These clots can travel to the brain, causing strokes, or to the coronary arteries, causing heart attacks. Additionally, prolonged periods of elevated heart rates can lead to structural and functional changes in the heart, ultimately leading to heart failure if untreated. The left atrium, with its more complex topology, is the primary site for complex arrhythmias. Much remains unknown about the causes of these arrhythmias, and computer modeling is employed to study them.

METHODS

We use N-body modeling techniques and parallel computing to build an interactive model of the left atrium. Through user input, individual muscle attributes can be adjusted, and ectopic events can be placed to induce arrhythmias in the model. Users can test ablation scenarios to determine the most effective way to eliminate these arrhythmias.

RESULTS

We set up muscle conditions that either spontaneously generate common arrhythmias or, with a properly timed and located ectopic event, induce an arrhythmia. These arrhythmias were successfully eliminated with simulated ablation.

CONCLUSIONS

We believe the model could be useful to doctors, researchers, and medical students studying left atrial arrhythmias.

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.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

A transferable in-silico augmented ischemic model for virtual myocardial perfusion imaging and myocardial infarction detection

This paper proposes an innovative approach to generate a generalized myocardial ischemia database by modeling the virtual electrophysiology of the heart and the 12-lead electrocardiography projected by the in-silico model can serve as a ready-to-use database for automatic myocardial infarction/ischemia (MI) localization and classification. Although the virtual heart can be created by an established technique combining the cell model with personalized heart geometry to observe the spatial propagation of depolarization and repolarization waves, we developed a strategy based on the clinical pathophysiology of MI to generate a heterogeneous database with a generic heart while maintaining clinical relevance and reduced computational complexity. First, the virtual heart is simplified into 11 regions that match the types and locations, which can be diagnosed by 12-lead ECG; the major arteries were divided into 3-5 segments from the upstream to the downstream based on the general anatomy. Second, the stenosis or infarction of the major or minor coronary artery branches can cause different perfusion drops and infarct sizes. We simulated the ischemic sites in different branches of the arteries by meandering the infarction location to elaborate on possible ECG representations, which alters the infraction's size and changes the transmembrane potential (TMP) of the myocytes associated with different levels of perfusion drop. A total of 8190 different case combinations of cardiac potentials with ischemia and MI were simulated, and the corresponding ECGs were generated by forward calculations. Finally, we trained and validated our in-silico database with a sparse representation classification (SRC) and tested the transferability of the model on the real-world Physikalisch Technische Bundesanstalt (PTB) database. The overall accuracies for localizing the MI region on the PTB data achieved 0.86, which is only 2% drop compared to that derived from the simulated database (0.88). In summary, we have shown a proof-of-concept for transferring an in-silico model to real-world database to compensate for insufficient data.

The role of computational methods in cardiovascular medicine: a narrative review

Background and Objective

Computational models of the cardiovascular system allow for a detailed and quantitative investigation of both physiological and pathological conditions, thanks to their ability to combine clinical-possibly patient-specific-data with physical knowledge of the processes underlying the heart function. These models have been increasingly employed in clinical practice to understand pathological mechanisms and their progression, design medical devices, support clinicians in improving therapies. Hinging upon a long-year experience in cardiovascular modeling, we have recently constructed a computational multi-physics and multi-scale integrated model of the heart for the investigation of its physiological function, the analysis of pathological conditions, and to support clinicians in both diagnosis and treatment planning. This narrative review aims to systematically discuss the role that such model had in addressing specific clinical questions, and how further impact of computational models on clinical practice are envisaged.

Methods

We developed computational models of the physical processes encompassed by the heart function (electrophysiology, electrical activation, force generation, mechanics, blood flow dynamics, valve dynamics, myocardial perfusion) and of their inherently strong coupling. To solve the equations of such models, we devised advanced numerical methods, implemented in a flexible and highly efficient software library. We also developed computational procedures for clinical data post-processing-like the reconstruction of the heart geometry and motion from diagnostic images-and for their integration into computational models.

Key Content and Findings

Our integrated computational model of the heart function provides non-invasive measures of indicators characterizing the heart function and dysfunctions, and sheds light on its underlying processes and their coupling. Moreover, thanks to the close collaboration with several clinical partners, we addressed specific clinical questions on pathological conditions, such as arrhythmias, ventricular dyssynchrony, hypertrophic cardiomyopathy, degeneration of prosthetic valves, and the way coronavirus disease 2019 (COVID-19) infection may affect the cardiac function. In multiple cases, we were also able to provide quantitative indications for treatment.

Conclusions

Computational models provide a quantitative and detailed tool to support clinicians in patient care, which can enhance the assessment of cardiac diseases, the prediction of the development of pathological conditions, and the planning of treatments and follow-up tests.

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

Creating Computational Models of Ion Channel Dynamics

Markov models are widely used to represent ion channel protein configurations as different states in the model's topology. Such models allow for dynamic simulation of ion channel kinetics through the simulated application of voltage potentials across a cell membrane. In this chapter, we present a general method for creating Markov models of ion channel kinetics using computational optimization alongside a fully featured example model of a cardiac potassium channel. Our methods cover designing training protocols, iteratively testing potential model topologies for structure identification, creation of algorithms for model simulation, as well as methods for assessing the quality of fit for a finalized model.

Current progress toward isogeometric modeling of the heart biophysics

In this paper, we review a powerful methodology to solve complex numerical simulations, known as isogeometric analysis, with a focus on applications to the biophysical modeling of the heart. We focus on the hemodynamics, modeling of the valves, cardiac tissue mechanics, and on the simulation of medical devices and treatments. For every topic, we provide an overview of the methods employed to solve the specific numerical issue entailed by the simulation. We try to cover the complete process, starting from the creation of the geometrical model up to the analysis and post-processing, highlighting the advantages and disadvantages of the methodology.

Reconstruction and completion of high-resolution 3D cardiac shapes using anisotropic CMRI segmentations and continuous implicit neural representations

Since the onset of computer-aided diagnosis in medical imaging, voxel-based segmentation has emerged as the primary methodology for automatic analysis of left ventricle (LV) function and morphology in cardiac magnetic resonance images (CMRI). In standard clinical practice, simultaneous multi-slice 2D cine short-axis MR imaging is performed under multiple breath-holds resulting in highly anisotropic 3D images. Furthermore, sparse-view CMRI often lacks whole heart coverage caused by large slice thickness and often suffers from inter-slice misalignment induced by respiratory motion. Therefore, these volumes only provide limited information about the true 3D cardiac anatomy which may hamper highly accurate assessment of functional and anatomical abnormalities. To address this, we propose a method that learns a continuous implicit function representing 3D LV shapes by training an auto-decoder. For training, high-resolution segmentations from cardiac CT angiography are used. The ability of our approach to reconstruct and complete high-resolution shapes from manually or automatically obtained sparse-view cardiac shape information is evaluated by using paired high- and low-resolution CMRI LV segmentations. The results show that the reconstructed LV shapes have an unconstrained subvoxel resolution and appear smooth and plausible in through-plane direction. Furthermore, Bland-Altman analysis reveals that reconstructed high-resolution ventricle volumes are closer to the corresponding reference volumes than reference low-resolution volumes with bias of [limits of agreement] -3.51 [-18.87, 11.85] mL, and 12.96 [-10.01, 35.92] mL respectively. Finally, the results demonstrate that the proposed approach allows recovering missing shape information and can indirectly correct for limited motion-induced artifacts.

GPU accelerated digital twins of the human heart open new routes for cardiovascular research

The recruitment of patients for rare or complex cardiovascular diseases is a bottleneck for clinical trials and digital twins of the human heart have recently been proposed as a viable alternative. In this paper we present an unprecedented cardiovascular computer model which, relying on the latest GPU-acceleration technologies, replicates the full multi-physics dynamics of the human heart within a few hours per heartbeat. This opens the way to extensive simulation campaigns to study the response of synthetic cohorts of patients to cardiovascular disorders, novel prosthetic devices or surgical procedures. As a proof-of-concept we show the results obtained for left bundle branch block disorder and the subsequent cardiac resynchronization obtained by pacemaker implantation. The in-silico results closely match those obtained in clinical practice, confirming the reliability of the method. This innovative approach makes possible a systematic use of digital twins in cardiovascular research, thus reducing the need of real patients with their economical and ethical implications. This study is a major step towards in-silico clinical trials in the era of digital medicine.

A compact multi-functional model of the rabbit atrioventricular node with dual pathways

The atrioventricular node (AVN) is considered a “black box”, and the functioning of its dual pathways remains controversial and not fully understood. In contrast to numerous clinical studies, there are only a few mathematical models of the node. In this paper, we present a compact, computationally lightweight multi-functional rabbit AVN model based on the Aliev-Panfilov two-variable cardiac cell model. The one-dimensional AVN model includes fast (FP) and slow (SP) pathways, primary pacemaking in the sinoatrial node, and subsidiary pacemaking in the SP. To obtain the direction-dependent conduction properties of the AVN, together with gradients of intercellular coupling and cell refractoriness, we implemented the asymmetry of coupling between model cells. We hypothesized that the asymmetry can reflect some effects related to the complexity of the real 3D structure of AVN. In addition, the model is accompanied by a visualization of electrical conduction in the AVN, revealing the interaction between SP and FP in the form of ladder diagrams. The AVN model demonstrates broad functionality, including normal sinus rhythm, AVN automaticity, filtering of high-rate atrial rhythms during atrial fibrillation and atrial flutter with Wenckebach periodicity, direction-dependent properties, and realistic anterograde and retrograde conduction curves in the control case and the cases of FP and SP ablation. To show the validity of the proposed model, we compare the simulation results with the available experimental data. Despite its simplicity, the proposed model can be used both as a stand-alone module and as a part of complex three-dimensional atrial or whole heart simulation systems, and can help to understand some puzzling functions of AVN.

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges

Intracellular calcium (Ca) cycling in the heart plays key roles in excitation-contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.

Interpretable machine learning of action potential duration restitution kinetics in single-cell models of atrial cardiomyocytes

Action potential duration (APD) restitution curve and its maximal slope (Smax) reflect single cell-level dynamic instability for inducing chaotic heart rhythms. However, conventional parameter sensitivity analysis often fails to describe nonlinear relationships between ion channel parameters and electrophysiological phenotypes, such as Smax. We explored the parameter-phenotype mapping in a population of 5000 single-cell atrial cell models through interpretable machine learning (ML) approaches. Parameter sensitivity analyses could explain the linear relationships between parameters and electrophysiological phenotypes, including APD₉₀, resting membrane potential, Vmax, refractory period, and APD/calcium alternans threshold, but not for Smax. However, neural network models had better prediction performance for Smax. To interpret the ML model, we evaluated the parameter importance at the global and local levels by computing the permutation feature importance and the local interpretable model-agnostic explanations (LIME) values, respectively. Increases in I_CaL, I_NCX, and I_Kr, and decreases in I_K1, I_b,Cl, I_Kur, I_SERCA, and I_to are correlated with higher Smax values. The LIME algorithm determined that I_NaK plays a significant role in determining Smax as well as I_to and I_Kur. The atrial cardiomyocyte population was hierarchically clustered into three distinct groups based on the LIME values and the single-cell simulation confirmed that perturbations in I_NaK resulted in different behaviors of APD restitution curves in three clusters. Our combined top-down interpretable ML and bottom-up mechanistic simulation approaches uncovered the role of I_NaK in heterogeneous behaviors of Smax in the atrial cardiomyocyte population.

From evidence-based medicine to digital twin technology for predicting ventricular tachycardia in ischaemic cardiomyopathy

Survivors of myocardial infarction are at risk of life-threatening ventricular tachycardias (VTs) later in their lives. Current guidelines for implantable cardioverter defibrillators (ICDs) implantation to prevent VT-related sudden cardiac death is solely based on symptoms and left ventricular ejection fraction. Catheter ablation of scar-related VTs is performed following ICD therapy, reducing VTs, painful shocks, anxiety, depression and worsening heart failure. We postulate that better prediction of the occurrence and circuit of VT, will improve identification of patients at risk for VT and boost preventive ablation, reducing mortality and morbidity. For this purpose, multiple time-evolving aspects of the underlying pathophysiology, including the anatomical substrate, triggers and modulators, should be part of VT prediction models. We envision digital twins as a solution combining clinical expertise with three prediction approaches: evidence-based medicine (clinical practice), data-driven models (data science) and mechanistic models (biomedical engineering). This paper aims to create a mutual understanding between experts in the different fields by providing a comprehensive description of the clinical problem and the three approaches in an understandable manner, leveraging future collaborations and technological innovations for clinical decision support. Moreover, it defines open challenges and gains for digital twin solutions and discusses the potential of hybrid modelling.

Thermal ablation effects on rotors that characterize functional re-entry cardiac arrhythmia

Thermal ablation is a well-established successful treatment for cardiac arrhythmia, but it still presents limitations that require further studies and developments. In the rotor-driven functional re-entry arrhythmia, tissue heterogeneity results on the generation of spiral/scroll waves and wave break dynamics that may cause dangerous sustainable fibrillation. The selection of the target region to perform thermal ablation to mitigate this type of arrhythmia is challenging, since it considerably affects the local electrophysiology dynamics. This work deals with the numerical simulation of the thermal ablation of a cardiac muscle tissue and its effects on the dynamics of rotor-driven functional re-entry arrhythmia. A non-homogeneous two-dimensional rectangular region is used in the present numerical analysis, where radiofrequency ablation is performed. The electrophysiology problem for the propagation of the action potential in the cardiac tissue is simulated with the Fenton-Karma model. Thermal damage caused to the tissue by the radiofrequency heating is modeled by the Arrhenius equation. The effects of size and position of a heterogeneous region in the original muscle tissue were first analyzed, in order to verify the possible existence of the functional re-entry arrhythmia during the time period considered in the simulations. For each case that exhibited re-entry arrhythmia, six different ablation procedures were analyzed, depending on the position of the radiofrequency electrode and heating time. The obtained results revealed the effects of different model parameters on the existence and possible mitigation of the functional re-entry arrhythmia.

Resource-Efficient Use of Modern Processor Architectures For Numerically Solving Cardiac Ionic Cell Models

A central component in simulating cardiac electrophysiology is the numerical solution of nonlinear ordinary differential equations, also called cardiac ionic cell models, that describe cross-cell-membrane ion transport. Biophysically detailed cell models often require a considerable amount of computation, including calls to special mathematical functions. This paper systematically studies how to efficiently use modern multicore CPUs for this costly computational task. We start by investigating the code restructurings needed to effectively enable compiler-supported SIMD vectorisation, which is the most important performance booster in this context. It is found that suitable OpenMP directives are sufficient for achieving both vectorisation and parallelisation. We then continue with an evaluation of the performance optimisation technique of using lookup tables. Due to increased challenges for automated vectorisation, the obtainable benefits of lookup tables are dependent on the hardware platforms chosen. Throughout the study, we report detailed time measurements obtained on Intel Xeon, Xeon Phi, AMD Epyc and two ARM processors including Fujitsu A64FX, while attention is also paid to the impact of SIMD vectorisation and lookup tables on the computational accuracy. As a realistic example, the benefits of performance enhancement are demonstrated by a 109-run ensemble on the Oakforest-PACS system, where code restructurings and SIMD vectorisation yield an 84% reduction in computing time, corresponding to 63,270 node hours.

Comparison of interpolation methods of predominant cardiomyocyte orientation from in vivo and ex vivo cardiac diffusion tensor imaging data

Cardiac electrophysiology and cardiac mechanics both depend on the average cardiomyocyte long-axis orientation. In the realm of personalized medicine, knowledge of the patient-specific changes in cardiac microstructure plays a crucial role. Patient-specific computational modelling has emerged as a tool to better understand disease progression. In vivo cardiac diffusion tensor imaging (cDTI) is a vital tool to non-destructively measure the average cardiomyocyte long-axis orientation in the heart. However, cDTI suffers from long scan times, rendering volumetric, high-resolution acquisitions challenging. Consequently, interpolation techniques are needed to populate bio-mechanical models with patient-specific average cardiomyocyte long-axis orientations. In this work, we compare five interpolation techniques applied to in vivo and ex vivo porcine input data. We compare two tensor interpolation approaches, one rule-based approximation, and two data-driven, low-rank models. We demonstrate the advantage of tensor interpolation techniques, resulting in lower interpolation errors than do low-rank models and rule-based methods adapted to cDTI data. In an ex vivo comparison, we study the influence of three imaging parameters that can be traded off against acquisition time: in-plane resolution, signal to noise ratio, and number of acquired short-axis imaging slices.

Pro-Arrhythmic Effects of Discontinuous Conduction at the Purkinje Fiber-Ventricle Junction Arising From Heart Failure-Induced Ionic Remodeling - Insights From Computational Modelling

Heart failure is associated with electrical remodeling of the electrical properties and kinetics of the ion channels and transporters that are responsible for cardiac action potentials. However, it is still unclear whether heart failure-induced ionic remodeling can affect the conduction of excitation waves at the Purkinje fiber-ventricle junction contributing to pro-arrhythmic effects of heart failure, as the complexity of the heart impedes a detailed experimental analysis. The aim of this study was to employ computational models to investigate the pro-arrhythmic effects of heart failure-induced ionic remodeling on the cardiac action potentials and excitation wave conduction at the Purkinje fiber-ventricle junction. Single cell models of canine Purkinje fiber and ventricular myocytes were developed for control and heart failure. These single cell models were then incorporated into one-dimensional strand and three-dimensional wedge models to investigate the effects of heart failure-induced remodeling on propagation of action potentials in Purkinje fiber and ventricular tissue and at the Purkinje fiber-ventricle junction. This revealed that heart failure-induced ionic remodeling of Purkinje fiber and ventricular tissue reduced conduction safety and increased tissue vulnerability to the genesis of the unidirectional conduction block. This was marked at the Purkinje fiber-ventricle junction, forming a potential substrate for the genesis of conduction failure that led to re-entry. This study provides new insights into proarrhythmic consequences of heart failure-induced ionic remodeling.

A Transmural Path Model Improves the Definition of the Orthotropic Tissue Structure in Heart Simulations

In the past decades, the structure of the heart, human as well as other species, has been explored in a detailed way, e.g., via histological studies or diffusion tensor magnetic resonance imaging. Nevertheless, the assignment of the characteristic orthotropic structure in a patient-specific finite element model remains a challenging task. Various types of rule-based models, which define the local fiber and sheet orientation depending on the transmural depth, have been developed. However, the correct assessment of the transmural depth is not trivial. Its accuracy has a substantial influence on the overall mechanical and electrical properties in rule-based models. The main purpose of this study is the development of a finite element-based approach to accurately determine the transmural depth on a general unstructured grid. Instead of directly using the solution of the Laplace problem as the transmural depth, we make use of a well-established model for the assessment of the transmural thickness. It is based on two hyperbolic first-order partial differential equations for the definition of a transmural path, whereby the transmural thickness is defined as the arc length of this path. Subsequently, the transmural depth is determined based on the position on the transmural path. Originally, the partial differential equations were solved via finite differences on structured grids. In order to circumvent the need of two grids and mapping between the structured (to determine the transmural depth) and unstructured (electromechanical heart simulation) grids, we solve the equations directly on the same unstructured tetrahedral mesh. We propose a finite-element-based discontinuous Galerkin approach. Based on the accurate transmural depth, we assign the local material orientation of the orthotropic tissue structure in a usual fashion. We show that this approach leads to a more accurate definition of the transmural depth. Furthermore, for the left ventricle, we propose functions for the transmural fiber and sheet orientation by fitting them to literature-based diffusion tensor magnetic resonance imaging data. The proposed functions provide a distinct improvement compared to existing rules from the literature.

Heart-on-Chip for Combined Cellular Dynamics Measurements and Computational Modeling Towards Clinical Applications

Organ-on-chip or micro-engineered three-dimensional cellular or tissue models are increasingly implemented in the study of cardiovascular pathophysiology as alternatives to traditional in vitro cell culture. Drug induced cardiotoxicity is a key issue in drug development pipelines, but the current in vitro and in vivo studies suffer from inter-species differences, high costs, and lack of reliability and accuracy in predicting cardiotoxicity. Microfluidic heart-on-chip devices can impose a paradigm shift to the current tools. They can not only recapitulate cardiac tissue level functionality and the communication between cells and extracellular matrices but also allow higher throughput studies conducive to drug screening especially with their added functionalities or sensors that extract disease-specific phenotypic, genotypic, and electrophysiological information in real-time. Such electrical and mechanical components can tailor the electrophysiology and mechanobiology of the experiment to better mimic the in vivo condition as well. Recent advancements and challenges are reviewed in the fabrication, functionalization and sensor assisted mechanical and electrophysiological measurements, numerical and computational modeling of cardiomyocytes' behavior, and the clinical applications in drug screening and disease modeling. This review concludes with the current challenges and perspectives on the future of such organ-on-chip platforms.

UT-Heart: A Finite Element Model Designed for the Multiscale and Multiphysics Integration of our Knowledge on the Human Heart

To fully understand the health and pathology of the heart, it is necessary to integrate knowledge accumulated at molecular, cellular, tissue, and organ levels. However, it is difficult to comprehend the complex interactions occurring among the building blocks of biological systems across these scales. Recent advances in computational science supported by innovative high-performance computer hardware make it possible to develop a multiscale multiphysics model simulating the heart, in which the behavior of each cell model is controlled by molecular mechanisms and the cell models themselves are arranged to reproduce elaborate tissue structures. Such a simulator could be used as a tool not only in basic science but also in clinical settings. Here, we describe a multiscale multiphysics heart simulator, UT-Heart, which uses unique technologies to realize the abovementioned features. As examples of its applications, models for cardiac resynchronization therapy and surgery for congenital heart disease will be also shown.

What keeps us ticking? Sinoatrial node mechano-sensitivity: the grandfather clock of cardiac rhythm

The rhythmic and spontaneously generated electrical excitation that triggers the heartbeat originates in the sinoatrial node (SAN). SAN automaticity has been thoroughly investigated, which has uncovered fundamental mechanisms involved in cardiac pacemaking that are generally categorised into two interacting and overlapping systems: the 'membrane' and 'Ca²⁺ clock'. The principal focus of research has been on these two systems of oscillators, which have been studied primarily in single cells and isolated tissue, experimental preparations that do not consider mechanical factors present in the whole heart. SAN mechano-sensitivity has long been known to be a contributor to SAN pacemaking-both as a driver and regulator of automaticity-but its essential nature has been underappreciated. In this review, following a description of the traditional 'clocks' of SAN automaticity, we describe mechanisms of SAN mechano-sensitivity and its vital role for SAN function, making the argument that the 'mechanics oscillator' is, in fact, the 'grandfather clock' of cardiac rhythm.

Analyzing the Role of Repolarization Gradients in Post-infarct Ventricular Tachycardia Dynamics Using Patient-Specific Computational Heart Models

Aims: Disease-induced repolarization heterogeneity in infarcted myocardium contributes to VT arrhythmogenesis but how apicobasal and transmural (AB-TM) repolarization gradients additionally affect post-infarct VT dynamics is unknown. The goal of this study is to assess how AB-TM repolarization gradients impact post-infarct VT dynamics using patient-specific heart models.

Method: 3D late gadolinium-enhanced cardiac magnetic resonance images were acquired from seven post-infarct patients. Models representing the patient-specific scar and infarct border zone distributions were reconstructed without (baseline) and with repolarization gradients along both the AB-TM axes. AB only and TM only models were created to assess the effects of each ventricular gradient on VT dynamics. VTs were induced in all models via rapid pacing.

Results: Ten baseline VTs were induced. VT inducibility in AB-TM models was not significantly different from baseline (p>0.05). Reentry pathways in AB-TM models were different than baseline pathways due to alterations in the location of conduction block (p<0.05). VT exit sites in AB-TM models were different than baseline VT exit sites (p<0.05). VT inducibility of AB only and TM only models were not significantly different than that of baseline (p>0.05) or AB-TM models (p>0.05). Reentry pathways and VT exit sites in AB only and TM only models were different than in baseline (p<0.05). Lastly, repolarization gradients uncovered multiple VT morphologies with different reentrant pathways and exit sites within the same structural, conducting channels.

Conclusion: VT inducibility was not impacted by the addition of AB-TM repolarization gradients, but the VT reentrant pathway and exit sites were greatly affected due to modulation of conduction block. Thus, during ablation procedures, physiological and pharmacological factors that impact the ventricular repolarization gradient might need to be considered when targeting the VTs.

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.

Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia

We developed a novel patient-specific computational model for the numerical simulation of ventricular electromechanics in patients with ischemic cardiomyopathy (ICM). This model reproduces the activity both in sinus rhythm (SR) and in ventricular tachycardia (VT). The presence of scars, grey zones and non-remodeled regions of the myocardium is accounted for by the introduction of a spatially heterogeneous coefficient in the 3D electromechanics model. This 3D electromechanics model is firstly coupled with a 2-element Windkessel afterload model to fit the pressure-volume (PV) loop of a patient-specific left ventricle (LV) with ICM in SR. Then, we employ the coupling with a 0D closed-loop circulation model to analyze a VT circuit over multiple heartbeats on the same LV. We highlight similarities and differences on the solutions obtained by the electrophysiology model and those of the electromechanics model, while considering different scenarios for the circulatory system. We observe that very different parametrizations of the circulation model induce the same hemodynamical considerations for the patient at hand. Specifically, we classify this VT as unstable. We conclude by stressing the importance of combining electrophysiological, mechanical and hemodynamical models to provide relevant clinical indicators in how arrhythmias evolve and can potentially lead to sudden cardiac death.

Computationally efficient model of myocardial electromechanics for multiscale simulations

A model of myocardial electromechanics is suggested. It combines modified and simplified versions of previously published models of cardiac electrophysiology, excitation-contraction coupling, and mechanics. The mechano-calcium and mechano-electrical feedbacks, including the strain-dependence of the propagation velocity of the action potential, are also accounted for. The model reproduces changes in the twitch amplitude and Ca2+-transients upon changes in muscle strain including the slow response. The model also reproduces the Bowditch effect and changes in the twitch amplitude and duration upon changes in the interstimulus interval, including accelerated relaxation at high stimulation frequency. Special efforts were taken to reduce the stiffness of the differential equations of the model. As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator

The results of numerical simulations of cardiac electromechanics are typically characterized by a long transient before reaching a periodic solution known as limit cycle. This yields a serious computational overhead, as the only clinically relevant output is associated with such limit cycle. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator, built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated with the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, can provide the 3D model with an initial guess, such that in just two heartbeats a solution is reached that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the 3D model. The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. Indeed, the construction of the emulator does not have to be repeated when the parameters of the circulation model it is coupled with vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. This paper is accompanied by a Python library implementing the proposed algorithm, open to integration with existing cardiac solvers.

Automated Localization of Focal Ventricular Tachycardia From Simulated Implanted Device Electrograms: A Combined Physics-AI Approach

Background: Focal ventricular tachycardia (VT) is a life-threating arrhythmia, responsible for high morbidity rates and sudden cardiac death (SCD). Radiofrequency ablation is the only curative therapy against incessant VT; however, its success is dependent on accurate localization of its source, which is highly invasive and time-consuming. Objective: The goal of our study is, as a proof of concept, to demonstrate the possibility of utilizing electrogram (EGM) recordings from cardiac implantable electronic devices (CIEDs). To achieve this, we utilize fast and accurate whole torso electrophysiological (EP) simulations in conjunction with convolutional neural networks (CNNs) to automate the localization of focal VTs using simulated EGMs. Materials and Methods: A highly detailed 3D torso model was used to simulate ∼4000 focal VTs, evenly distributed across the left ventricle (LV), utilizing a rapid reaction-eikonal environment. Solutions were subsequently combined with lead field computations on the torso to derive accurate electrocardiograms (ECGs) and EGM traces, which were used as inputs to CNNs to localize focal sources. We compared the localization performance of a previously developed CNN architecture (Cartesian probability-based) with our novel CNN algorithm utilizing universal ventricular coordinates (UVCs). Results: Implanted device EGMs successfully localized VT sources with localization error (8.74 mm) comparable to ECG-based localization (6.69 mm). Our novel UVC CNN architecture outperformed the existing Cartesian probability-based algorithm (errors = 4.06 mm and 8.07 mm for ECGs and EGMs, respectively). Overall, localization was relatively insensitive to noise and changes in body compositions; however, displacements in ECG electrodes and CIED leads caused performance to decrease (errors 16-25 mm). Conclusion: EGM recordings from implanted devices may be used to successfully, and robustly, localize focal VT sources, and aid ablation planning.

The impact of myocardial compressibility on organ-level simulations of the normal and infarcted heart

Myocardial infarction (MI) rapidly impairs cardiac contractile function and instigates maladaptive remodeling leading to heart failure. Patient-specific models are a maturing technology for developing and determining therapeutic modalities for MI that require accurate descriptions of myocardial mechanics. While substantial tissue volume reductions of 15-20% during systole have been reported, myocardium is commonly modeled as incompressible. We developed a myocardial model to simulate experimentally-observed systolic volume reductions in an ovine model of MI. Sheep-specific simulations of the cardiac cycle were performed using both incompressible and compressible tissue material models, and with synchronous or measurement-guided contraction. The compressible tissue model with measurement-guided contraction gave best agreement with experimentally measured reductions in tissue volume at peak systole, ventricular kinematics, and wall thickness changes. The incompressible model predicted myofiber peak contractile stresses approximately double the compressible model (182.8 kPa, 107.4 kPa respectively). Compensatory changes in remaining normal myocardium with MI present required less increase of contractile stress in the compressible model than the incompressible model (32.1%, 53.5%, respectively). The compressible model therefore provided more accurate representation of ventricular kinematics and potentially more realistic computed active contraction levels in the simulated infarcted heart. Our findings suggest that myocardial compressibility should be incorporated into future cardiac models for improved accuracy.

A modified approach to determine the six cardiac bidomain conductivities

Accurate values for the six cardiac bidomain conductivities are crucial for meaningful computational studies of conduction in cardiac tissue, and are yet to be determined by experimental means. Although previous studies have proposed an approach using a multi-electrode array to measure potentials, from which the conductivities can be determined, it has been found that the conductivities cannot be retrieved consistently when the noise in the potentials varies. This paper presents a protocol, which not only has been shown to retrieve the conductivities to a reasonable accuracy, but does so under the presence of a more appropriate additive Gaussian noise model, while using fewer computational resources. Through repetitions of the protocol, a comparison of two pre-fabricated 128 electrode arrays, one array with a square arrangement of electrodes and the other with a rectangular arrangement, was made against a 75-electrode array proposed in previous studies. Results indicated that the two pre-fabricated arrays were generally more capable of obtaining the cardiac conductivities to a higher degree of accuracy than the 75-electrode array. The 128-electrode rectangular array was orientated such that the length of the array first ran along the direction of the fibres, then was reorientated such that the length of the array ran perpendicular to the direction of the fibres. The 128-electrode rectangular array, when orientated in this manner, was more capable of retrieving the conductivities than the remainder of the arrays tested, and thus we suggest this arrangement be used during experimental trials.

Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function

In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh-size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms-implemented in the open-source software vmtk-can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.

Recapitulating Cardiac Structure and Function In Vitro from Simple to Complex Engineering

Cardiac tissue engineering aims to generate in vivo-like functional tissue for the study of cardiac development, homeostasis, and regeneration. Since the heart is composed of various types of cells and extracellular matrix with a specific microenvironment, the fabrication of cardiac tissue in vitro requires integrating technologies of cardiac cells, biomaterials, fabrication, and computational modeling to model the complexity of heart tissue. Here, we review the recent progress of engineering techniques from simple to complex for fabricating matured cardiac tissue in vitro. Advancements in cardiomyocytes, extracellular matrix, geometry, and computational modeling will be discussed based on a technology perspective and their use for preparation of functional cardiac tissue. Since the heart is a very complex system at multiscale levels, an understanding of each technique and their interactions would be highly beneficial to the development of a fully functional heart in cardiac tissue engineering.

A Review of Ex Vivo X-ray Microfocus Computed Tomography-Based Characterization of the Cardiovascular System

Cardiovascular malformations and diseases are common but complex and often not yet fully understood. To better understand the effects of structural and microstructural changes of the heart and the vasculature on their proper functioning, a detailed characterization of the microstructure is crucial. In vivo imaging approaches are noninvasive and allow visualizing the heart and the vasculature in 3D. However, their spatial image resolution is often too limited for microstructural analyses, and hence, ex vivo imaging is preferred for this purpose. Ex vivo X-ray microfocus computed tomography (microCT) is a rapidly emerging high-resolution 3D structural imaging technique often used for the assessment of calcified tissues. Contrast-enhanced microCT (CE-CT) or phase-contrast microCT (PC-CT) improve this technique by additionally allowing the distinction of different low X-ray-absorbing soft tissues. In this review, we present the strengths of ex vivo microCT, CE-CT and PC-CT for quantitative 3D imaging of the structure and/or microstructure of the heart, the vasculature and their substructures in healthy and diseased state. We also discuss their current limitations, mainly with regard to the contrasting methods and the tissue preparation.

Application of physics-based flow models in cardiovascular medicine: Current practices and challenges

Personalized physics-based flow models are becoming increasingly important in cardiovascular medicine. They are a powerful complement to traditional methods of clinical decision-making and offer a wealth of physiological information beyond conventional anatomic viewing using medical imaging data. These models have been used to identify key hemodynamic biomarkers, such as pressure gradient and wall shear stress, which are associated with determining the functional severity of cardiovascular diseases. Importantly, simulation-driven diagnostics can help researchers understand the complex interplay between geometric and fluid dynamic parameters, which can ultimately improve patient outcomes and treatment planning. The possibility to compute and predict diagnostic variables and hemodynamics biomarkers can therefore play a pivotal role in reducing adverse treatment outcomes and accelerate development of novel strategies for cardiovascular disease management.

Area Available for Atrial Fibrillation to Propagate Is an Important Determinant of Recurrence After Ablation

OBJECTIVES

This study sought to evaluate atrial fibrillation (AF) ablation outcomes based on scar patterns and contiguous area available for AF wavefronts to propagate.

BACKGROUND

The relevance of ablation scar pattern acting as a barrier for electrical propagation in recurrence after catheter ablation for persistent AF is unknown.

METHODS

Three-month post-ablation atrial cardiac magnetic resonance was used to determine post-ablation scar. The left atrium (LA) was divided into 5 areas based on anatomical landmarks and scar patterns. The length of gaps in scar on the area boundaries was used to calculate fibrillatory areas (FAs) by adding the weighted contribution of adjacent areas. Cylindrical as well as patient-specific computational models were used to further confirm findings.

RESULTS

A total of 75 patients that underwent an initial ablation for AF with 2 years of follow-up were included. The average maximum FA was 7,896 ± 1,988 mm² in patients with recurrence (n = 40) and 6,559 ± 1,784 mm² in patients without recurrence (n = 35) (p < 0.008). After redo ablation in 19 patients with recurrence, average maximum FA was 7,807 ± 1,392 mm² in 9 patients with recurrence and 5,030 ± 1,765 mm² in 10 without recurrence (p < 0.007). LA volume and total scar were not significant predictors of recurrence after the first ablation. In the cylindrical model, AF self-terminated after reducing the FAs. In the patient-specific models, simulation matched the clinical outcomes with larger FAs associated with post-ablation arrhythmia recurrences.

CONCLUSIONS

This data provides mechanistic insights into AF recurrence, suggesting that post-ablation scar pattern dividing the atria into smaller regions is an important and better predictor than LA volume and total scar, with improved long-term outcomes in persistent AF.

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.

Precision medicine in human heart modeling : Perspectives, challenges, and opportunities

Precision medicine is a new frontier in healthcare that uses scientific methods to customize medical treatment to the individual genes, anatomy, physiology, and lifestyle of each person. In cardiovascular health, precision medicine has emerged as a promising paradigm to enable cost-effective solutions that improve quality of life and reduce mortality rates. However, the exact role in precision medicine for human heart modeling has not yet been fully explored. Here, we discuss the challenges and opportunities for personalized human heart simulations, from diagnosis to device design, treatment planning, and prognosis. With a view toward personalization, we map out the history of anatomic, physical, and constitutive human heart models throughout the past three decades. We illustrate recent human heart modeling in electrophysiology, cardiac mechanics, and fluid dynamics and highlight clinically relevant applications of these models for drug development, pacing lead failure, heart failure, ventricular assist devices, edge-to-edge repair, and annuloplasty. With a view toward translational medicine, we provide a clinical perspective on virtual imaging trials and a regulatory perspective on medical device innovation. We show that precision medicine in human heart modeling does not necessarily require a fully personalized, high-resolution whole heart model with an entire personalized medical history. Instead, we advocate for creating personalized models out of population-based libraries with geometric, biological, physical, and clinical information by morphing between clinical data and medical histories from cohorts of patients using machine learning. We anticipate that this perspective will shape the path toward introducing human heart simulations into precision medicine with the ultimate goals to facilitate clinical decision making, guide treatment planning, and accelerate device design.

On the Role of Ionic Modeling on the Signature of Cardiac Arrhythmias for Healthy and Diseased Hearts

Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies.

Towards the simulation of active cardiac mechanics using a smoothed finite element method

In the last decades, various computational models have been developed to simulate cardiac electromechanics. The most common numerical tool is the finite element method (FEM). However, this method crucially depends on the mesh quality. For complex geometries such as cardiac structures, it is convenient to use tetrahedral discretisations which can be generated automatically. On the other hand, such automatic meshing with tetrahedrons together with large deformations often lead to elements distortion and volumetric locking. To overcome these difficulties, different smoothed finite element methods (S-FEMs) have been proposed in the recent years. They are known to be volumetric locking free, less sensitive to mesh distortion and so far have been used e.g. in simulation of passive cardiac mechanics. In this work, we extend for the first time node-based S-FEM (NS-FEM) towards active cardiac mechanics. Firstly, the sensitivity to mesh distortion is tested and compared to that of FEM. Secondly, an active contraction in circumferentially aligned fibre direction is modelled in the healthy and the infarcted case. We show, that the proposed method is more robust with respect to mesh distortion and computationally more efficient than standard FEM. Being furthermore free of volumetric locking problems makes S-FEM a promising alternative in modelling of active cardiac mechanics, respectively electromechanics.

Prediction of Cardiac Mechanical Performance From Electrical Features During Ventricular Tachyarrhythmia Simulation Using Machine Learning Algorithms

In ventricular tachyarrhythmia, electrical instability features including action potential duration, dominant frequency, phase singularity, and filaments are associated with mechanical contractility. However, there are insufficient studies on estimated mechanical contractility based on electrical features during ventricular tachyarrhythmia using a stochastic model. In this study, we predicted cardiac mechanical performance from features of electrical instability during ventricular tachyarrhythmia simulation using machine learning algorithms, including support vector regression (SVR) and artificial neural network (ANN) models. We performed an electromechanical tachyarrhythmia simulation and extracted 12 electrical instability features and two mechanical properties, including stroke volume and the amplitude of myocardial tension (ampTens). We compared predictive performance according to kernel types of the SVR model and the number of hidden layers of the ANN model. In the SVR model, the prediction accuracies of stroke volume and ampTens were the highest when using the polynomial kernel and linear kernel, respectively. The predictive performance of the ANN model was better than that of the SVR model. The prediction accuracies were the highest when the ANN model consisted of three hidden layers. Accordingly, we propose the ANN model with three hidden layers as an optimal model for predicting cardiac mechanical contractility in ventricular tachyarrhythmia. The results of this study are expected to be used to indirectly estimate the hemodynamic response from the electrical cardiac map measured by the optical mapping system during cardiac surgery, as well as cardiac contractility under normal sinus rhythm conditions.

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.

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

Genetic Algorithm For Fitting Cardiac Cell Biophysical Model Formulations

Modeling cardiac cell electrophysiology relies on fitting model equations to experimental data obtained under voltage/current clamping conditions. The fitting procedure for these often-nonlinear ionic current equations are mostly executed by trial-and-error by hand or by gradient-based optimization approaches. These methods, though sometimes sufficient at converging at optimal solutions is based on the premise that the characteristic objective function is convex, which often does not apply to cardiac model equations. Meta-heuristic methods, such as evolutionary algorithms and particle swarm algorithms, have proven resilient against early convergence to local optima and saddle-point parameter solutions. This work presents a genetic algorithm-based approach for fitting the adult cardiomyocyte biophysical model formulations to the experimental data obtained in human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM). Specifically, whole-cell patch clamp ionic current data of rapid delayed rectifier potassium current, I_Kr, transient outward potassium current, I_to and hyperpolarization-activated current, I_f, was used for fitting. Using a two-point crossover scheme along with initial population and mutation constraints randomly selected from a uniformly distributed constrained parameter space, near-optimal fitting was achieved with R² values (n = 5) of 0.9960±0.0007, 0.9995±0.0002, and 0.9974±0.0014 for I_Kr, I_to and I_f respectively.

Deep learning-based reduced order models in cardiac electrophysiology

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters), as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms—such as deep feedforward neural networks and convolutional autoencoders—to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstrating that DL-ROM outperforms classical projection-based ROMs.