A guide to modelling cardiac electrical activity in anatomically detailed ventricles

Implementation of a Cellular Automaton for efficient simulations of atrial arrhythmias

In silico models offer a promising advancement for studying cardiac arrhythmias and their clinical implications. However, existing detailed mathematical models often suffer from prolonged computational time compared to diagnostic needs. This study introduces a Cellular Automaton (CA) model tailored to replicate atrial electrophysiology in different stages of Atrial Fibrillation (AF), including persistent AF (PsAF). The CA, using a finite set of states, has been trained using biophysical simulations on a reduced domain for a large set of pacing conditions. Fine-tuning included tissue heterogeneity and anisotropic propagation through pacing simulations. Characterized by Action Potential Duration (APD), Diastolic Interval (DI) and Conduction Velocity (CV) for varying levels of electrical remodeling, the biophysical simulations introduced restitution curves or surfaces into the CA. Validation involved a comprehensive comparison with realistic 2D and 3D atrial models, evaluating healthy and pro-arrhythmic behaviors. Comparisons between CA and biophysical solver revealed striking proximity, with a Cycle Length difference of <10 ms in self-sustained re-entry and a 4.66±0.57 ms difference in depolarization times across the complete atrial geometry. Notably, the CA model exhibited a 80% accuracy, 96% specificity and 45% sensitivity in predicting AF inducibility under different pacing sites and substrate conditions. Additionally, the CA allowed for a 64-fold decrease in computing time compared to the biophysical solver. CA emerges as an efficient and valid model for simulation of atrial electrophysiology across different stages of AF, with potential as a general screening tool for rapid tests. While biophysical tests are recommended for investigating specific mechanisms, CA proves valuable in clinical applications for personalized therapy planning through digital twin simulations.

Chained occurrences of early afterdepolarizations may create a directional triggered activity to initiate reentrant ventricular tachyarrhythmias

BACKGROUND AND OBJECTIVE

It has been believed that polymorphic ventricular tachycardia (VT) such as torsades de pointes (TdP) seen in patients with long QT syndromes is triggered by creating early afterdepolarization (EAD)-mediated triggered activity (TA). Although the mechanisms creating the TA have been studied intensively, characteristics of the arrhythmogenic (torsadogenic) substrates that link EAD developments to TA formation are still not well understood.

METHODS

Computer simulations of excitation propagation in a homogenous two-dimensional ventricular tissue with an anisotropic conduction property were performed to characterize torsadogenic substrates that potentially form TA. We examined how the configuration of islands (clusters) of myocytes with synchronously chained occurrence of EADs within the tissue, each EAD cluster size and stimulation from different directions impact the TA creation.

RESULTS

The presence of EAD clusters within the tissue created local regions of cardiomyocytes maintained at a depolarized membrane potential above 0 mV due to the chained occurrence of EADs. When the local area contained a concave surface border, the TA was created depending on its curvature. We found that the distance of EAD clusters was a critical factor for the development of EAD-mediated TA and polymorphic VT in long QT syndromes, that there existed a region of the distance favorable for the development of TA and VT, and that the TA was always created along the myocardial fiber orientation regardless of stimulating directions.

CONCLUSION

The chained occurrences of EADs may create a directional TA. Our findings provide deeper understandings of the cardiac arrhythmogenic substrates for preventing and treating arrhythmias.

A Matlab Toolbox for cardiac electrophysiology simulations on patient-specific geometries

In this paper, we present CardioMat, a Matlab toolbox for cardiac electrophysiology simulation based on patient-specific anatomies. The strength of CardioMat is the easy and fast construction of electrophysiology cardiac digital twins from segmented anatomical images in a general-purpose software such as Matlab. CardioMat implements a quasi-automatic pipeline that guides the user toward the construction of anatomically detailed cardiac electrophysiology models. Importantly, the CardioMat framework includes the generation of physiologically plausible fiber orientation and Purkinje networks. The main novelty of our framework is its ability to handle voxel-based geometries as produced by segmentation procedures directly, without the need for an unstructured mesh. Indeed, the CardioMat monodomain solver uses a smoothed boundary approach and runs completely on GPU for fast simulations. We employed CardioMat in different application scenarios to show its potentialities and provide preliminary assessment of the feasibility, diagnostic performance, and accuracy of the toolbox. In particular, we showed that CardioMat simulations derived from post-infarction patients hold high sensitivity, specificity, predictive value, and accuracy for localization of deceleration zones in sinus rhythm.

Evaluating computational efforts and physiological resolution of mathematical models of cardiac tissue

Computational techniques have significantly advanced our understanding of cardiac electrophysiology, yet they have predominantly concentrated on averaged models that do not represent the intricate dynamics near individual cardiomyocytes. Recently, accurate models representing individual cells have gained popularity, enabling analysis of the electrophysiology at the micrometer level. Here, we evaluate five mathematical models to determine their computational efficiency and physiological fidelity. Our findings reveal that cell-based models introduced in recent literature offer both efficiency and precision for simulating small tissue samples (comprising thousands of cardiomyocytes). Conversely, the traditional bidomain model and its simplified counterpart, the monodomain model, are more appropriate for larger tissue masses (encompassing millions to billions of cardiomyocytes). For simulations requiring detailed parameter variations along individual cell membranes, the EMI model emerges as the only viable choice. This model distinctively accounts for the extracellular (E), membrane (M), and intracellular (I) spaces, providing a comprehensive framework for detailed studies. Nonetheless, the EMI model's applicability to large-scale tissues is limited by its substantial computational demands for subcellular resolution.

Theoretical prediction of early afterdepolarization-evoked triggered activity formation initiating ventricular reentrant arrhythmias

BACKGROUND AND OBJECTIVE

Excessive prolongation of QT interval on ECGs in patients with congenital/acquired long QT syndrome and heart failure is a sign suggesting the development of early afterdepolarization (EAD), an abnormal repolarization in the action potential of ventricular cardiomyocytes. The development of EAD has been believed to be a trigger for fatal tachyarrhythmia, which can be a risk for sudden cardiac death. The role of EAD in triggering ventricular tachycardia (VT) remains unclear. The aim of this study was to elucidate the mechanism of EAD-induced triggered activity formation that leads to the VT such as Torsades de Pointes.

METHODS

We investigated the relationship between EAD and tachyarrhythmia initiation by constructing homogeneous myocardial sheet models consisting of the mid-myocardial cell version of a human ventricular myocyte model and performing simulations of excitation propagation.

RESULTS

A solitary island-like (clustering) occurrence of EADs in the homogeneous myocardial sheet could induce a focal excitation wave. However, reentrant excitation, an entity of tachyarrhythmia, was not able to be triggered regardless of the EAD cluster size when the focal excitation wave formed a repolarization potential difference boundary consisting of only a convex surface. The discontinuous distribution of multiple EAD clusters in the ventricular tissue formed a specific repolarization heterogeneity due to the repolarization potential difference, the shape of which depended on EAD cluster size and placed intervals. We found that the triggered activity was formed in such a manner that the repolarization potential difference boundary included a concave surface.

CONCLUSIONS

The formation of triggered activity that led to tachyarrhythmia required not only the occurrence of EAD onset-mediated focal excitation wave but also a repolarization heterogeneity-based specific repolarization potential difference boundary shape formed within the tissue.

The simplified Kirchhoff network model (SKNM): a cell-based reaction-diffusion model of excitable tissue

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

Efficient, cell-based simulations of cardiac electrophysiology; The Kirchhoff Network Model (KNM)

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

A smoothed boundary bidomain model for cardiac simulations in anatomically detailed geometries

This manuscript presents a novel finite difference method to solve cardiac bidomain equations in anatomical models of the heart. The proposed method employs a smoothed boundary approach that represents the boundaries between the heart and the surrounding medium as a spatially diffuse interface of finite thickness. The bidomain boundary conditions are implicitly implemented in the smoothed boundary bidomain equations presented in the manuscript without the need of a structured mesh that explicitly tracks the heart-torso boundaries. We reported some significant examples assessing the method's accuracy using nontrivial test geometries and demonstrating the applicability of the method to complex anatomically detailed human cardiac geometries. In particular, we showed that our approach could be employed to simulate cardiac defibrillation in a human left ventricle comprising fiber architecture. The main advantage of the proposed method is the possibility of implementing bidomain boundary conditions directly on voxel structures, which makes it attractive for three dimensional, patient specific simulations based on medical images. Moreover, given the ease of implementation, we believe that the proposed method could provide an interesting and feasible alternative to finite element methods, and could find application in future cardiac research guiding electrotherapy with computational models.

Computational analysis of arrhythmogenesis in KCNH2 T618I mutation-associated short QT syndrome and the pharmacological effects of quinidine and sotalol

Short QT syndrome (SQTS) is a rare but dangerous genetic disease. In this research, we conducted a comprehensive in silico investigation into the arrhythmogenesis in KCNH2 T618I-associated SQTS using a multi-scale human ventricle model. A Markov chain model of IKr was developed firstly to reproduce the experimental observations. It was then incorporated into cell, tissue, and organ models to explore how the mutation provided substrates for ventricular arrhythmias. Using this T618I Markov model, we explicitly revealed the subcellular level functional alterations by T618I mutation, particularly the changes of ion channel states that are difficult to demonstrate in wet experiments. The following tissue and organ models also successfully reproduced the changed dynamics of reentrant spiral waves and impaired rate adaptions in hearts of T618I mutation. In terms of pharmacotherapy, we replicated the different effects of a drug under various conditions using identical mathematical descriptions for drugs. This study not only simulated the actions of an effective drug (quinidine) at various physiological levels, but also elucidated why the IKr inhibitor sotalol failed in SQT1 patients through profoundly analyzing its mutation-dependent actions.

Artificial intelligence analysis of the impact of fibrosis in arrhythmogenesis and drug response

Background: Cardiac fibrosis has been identified as a major factor in conduction alterations leading to atrial arrhythmias and modification of drug treatment response. Objective: To perform an in silico proof-of-concept study of Artificial Intelligence (AI) ability to identify susceptibility for conduction blocks in simulations on a population of models with diffused fibrotic atrial tissue and anti-arrhythmic drugs. Methods: Activity in 2D cardiac tissue planes were simulated on a population of variable electrophysiological and anatomical profiles using the Koivumaki model for the atrial cardiomyocytes and the Maleckar model for the diffused fibroblasts (0%, 5% and 10% fibrosis area). Tissue sheets were of 2 cm side and the effect of amiodarone, dofetilide and sotalol was simulated to assess the conduction of the electrical impulse across the planes. Four different AI algorithms (Quadratic Support Vector Machine, QSVM, Cubic Support Vector Machine, CSVM, decision trees, DT, and K-Nearest Neighbors, KNN) were evaluated in predicting conduction of a stimulated electrical impulse. Results: Overall, fibrosis implementation lowered conduction velocity (CV) for the conducting profiles (0% fibrosis: 67.52 ± 7.3 cm/s; 5%: 58.81 ± 14.04 cm/s; 10%: 57.56 ± 14.78 cm/s; p < 0.001) in combination with a reduced 90% action potential duration (0% fibrosis: 187.77 ± 37.62 ms; 5%: 93.29 ± 82.69 ms; 10%: 106.37 ± 85.15 ms; p < 0.001) and peak membrane potential (0% fibrosis: 89.16 ± 16.01 mV; 5%: 70.06 ± 17.08 mV; 10%: 82.21 ± 19.90 mV; p < 0.001). When the antiarrhythmic drugs were present, a total block was observed in most of the profiles. In those profiles in which electrical conduction was preserved, a decrease in CV was observed when simulations were performed in the 0% fibrosis tissue patch (Amiodarone ΔCV: -3.59 ± 1.52 cm/s; Dofetilide ΔCV: -13.43 ± 4.07 cm/s; Sotalol ΔCV: -0.023 ± 0.24 cm/s). This effect was preserved for amiodarone in the 5% fibrosis patch (Amiodarone ΔCV: -4.96 ± 2.15 cm/s; Dofetilide ΔCV: 0.14 ± 1.87 cm/s; Sotalol ΔCV: 0.30 ± 4.69 cm/s). 10% fibrosis simulations showed that part of the profiles increased CV while others showed a decrease in this variable (Amiodarone ΔCV: 0.62 ± 9.56 cm/s; Dofetilide ΔCV: 0.05 ± 1.16 cm/s; Sotalol ΔCV: 0.22 ± 1.39 cm/s). Finally, when the AI algorithms were tested for predicting conduction on input of variables from the population of modelled, Cubic SVM showed the best performance with AUC = 0.95. Conclusion: In silico proof-of-concept study demonstrates that fibrosis can alter the expected behavior of antiarrhythmic drugs in a minority of atrial population models and AI can assist in revealing the profiles that will respond differently.

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.

A transmurally heterogeneous model of the ventricular tissue and its application for simulation of Brugada Syndrome

We present a transmurally heterogeneous phe-nomenological model of ventricular tissue that is designed to reproduce the most important features of action potential prop-agation of endocardial, midmyocardial, and epicardial tissue. Our model consists of only 3 variables and 20 parameters. Therefore, it is highly computational efficient and easy to fit to experimental data. We exploited our myocyte model to simulate action potential propagation in a 3D slab of cardiac tissue both in healthy conditions and in presence of Brugada syndrome. The results show that our model can accurately reproduce the transmural heterogeneity of the ventricular wall and the main characteristics of electrocardiographic pattern both in healthy and pathological conditions.

Patient-specific finite element analysis of heart failure and the impact of surgical intervention in pulmonary hypertension secondary to mitral valve disease

Pulmonary hypertension (PH), a chronic and complex medical condition affecting 1% of the global population, requires clinical evaluation of right ventricular maladaptation patterns under various conditions. A particular challenge for clinicians is a proper quantitative assessment of the right ventricle (RV) owing to its intimate coupling to the left ventricle (LV). We, thus, proposed a patient-specific computational approach to simulate PH caused by left heart disease and its main adverse functional and structural effects on the whole heart. Information obtained from both prospective and retrospective studies of two patients with severe PH, a 72-year-old female and a 61-year-old male, is used to present patient-specific versions of the Living Heart Human Model (LHHM) for the pre-operative and post-operative cardiac surgery. Our findings suggest that before mitral and tricuspid valve repair, the patients were at risk of right ventricular dilatation which may progress to right ventricular failure secondary to their mitral valve disease and left ventricular dysfunction. Our analysis provides detailed evidence that mitral valve replacement and subsequent chamber pressure unloading are associated with a significant decrease in failure risk post-operatively in the context of pulmonary hypertension. In particular, right-sided strain markers, such as tricuspid annular plane systolic excursion (TAPSE) and circumferential and longitudinal strains, indicate a transition from a range representative of disease to within typical values after surgery. Furthermore, the wall stresses across the RV and the interventricular septum showed a notable decrease during the systolic phase after surgery, lessening the drive for further RV maladaptation and significantly reducing the risk of RV failure.

Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve

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

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

Mechanisms of ventricular arrhythmias elicited by coexistence of multiple electrophysiological remodeling in ischemia: A simulation study

Myocardial ischemia, injury and infarction (MI) are the three stages of acute coronary syndrome (ACS). In the past two decades, a great number of studies focused on myocardial ischemia and MI individually, and showed that the occurrence of reentrant arrhythmias is often associated with myocardial ischemia or MI. However, arrhythmogenic mechanisms in the tissue with various degrees of remodeling in the ischemic heart have not been fully understood. In this study, biophysical detailed single-cell models of ischemia 1a, 1b, and MI were developed to mimic the electrophysiological remodeling at different stages of ACS. 2D tissue models with different distributions of ischemia and MI areas were constructed to investigate the mechanisms of the initiation of reentrant waves during the progression of ischemia. Simulation results in 2D tissues showed that the vulnerable windows (VWs) in simultaneous presence of multiple ischemic conditions were associated with the dynamics of wave propagation in the tissues with each single pathological condition. In the tissue with multiple pathological conditions, reentrant waves were mainly induced by two different mechanisms: one is the heterogeneity along the excitation wavefront, especially the abrupt variation in conduction velocity (CV) across the border of ischemia 1b and MI, and the other is the decreased safe factor (SF) for conduction at the edge of the tissue in MI region which is attributed to the increased excitation threshold of MI region. Finally, the reentrant wave was observed in a 3D model with a scar reconstructed from MRI images of a MI patient. These comprehensive findings provide novel insights for understanding the arrhythmic risk during the progression of myocardial ischemia and highlight the importance of the multiple pathological stages in designing medical therapies for arrhythmias in ischemia.

Fractional Modeling Applied to the Dynamics of the Action Potential in Cardiac Tissue

We investigate a class of fractional time-partial differential equations describing the dynamics of the fast action potential process in contractile myocytes. The system is explored in both one and two dimensional cases. Homogeneous and nonhomogeneous solutions are derived. We also numerically simulate some of the proposed fractional solutions to provide a different modeling perspective on distinct phases of cardiac membrane potential. Results indicate that the fractional diffusion-wave equation may be employed to model membrane potential dynamics with the fractional order working as an extra asset to modulate electricity conduction, particularly for lower fractional order values.

Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons

The bidomain model is considered to be the gold standard for numerical simulation of the electrophysiology of cardiac tissue. The model provides important insights into the conduction properties of the electrochemical wave traversing the cardiac muscle in every heartbeat. However, in normal resolution, the model represents the average over a large number of cardiomyocytes, and more accurate models based on representations of all individual cells have therefore been introduced in order to gain insight into the conduction properties close to the myocytes. The more accurate model considered here is referred to as the EMI model since both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model. Here, we show that the bidomain model can be derived from the cell-based EMI model and we thus reveal the close relation between the two models, and obtain an indication of the error introduced in the approximation. Also, we present numerical simulations comparing the results of the two models and thereby highlight both similarities and differences between the models. We observe that the deviations between the solutions of the models become larger for larger cell sizes. Furthermore, we observe that the bidomain model provides solutions that are very similar to the EMI model when conductive properties of the tissue are in the normal range, but large deviations are present when the resistance between cardiomyocytes is increased.

A method of parameter estimation for cardiovascular hemodynamics based on deep learning and its application to personalize a reduced-order model

Precise model personalization is a key step towards the application of cardiovascular physical models. In this manuscript, we propose to use deep learning (DL) to solve the parameter estimation problem in cardiovascular hemodynamics. Based on the convolutional neural network (CNN) and fully connected neural network (FCNN), a multi-input deep neural network (DNN) model is developed to map the nonlinear relationship between measurements and the parameters to be estimated. In this model, two separate network structures are designed to extract the features of two types of measurement data, including pressure waveforms and a vector composed of heart rate (HR) and pulse transit time (PTT), and a shared structure is used to extract their combined dependencies on the parameters. Besides, we try to use the transfer learning (TL) technology to further strengthen the personalized characteristics of a trained-well network. For assessing the proposed method, we conducted the parameter estimation using synthetic data and in vitro data respectively, and in the test with synthetic data, we evaluated the performance of the TL algorithm through two individuals with different characteristics. A series of estimation results show that the estimated parameters are in good agreement with the true values. Furthermore, it is also found that the estimation accuracy can be significantly improved by a multicycle combination strategy. Therefore, we think that the proposed method has the potential to be used for parameter estimation in cardiovascular hemodynamics, which can provide an immediate, accurate, and sustainable personalization process, and deserves more attention in the future.

It's clearly the heart! Optical transparency, cardiac tissue imaging, and computer modelling

Recent developments in clearing and microscopy enable 3D imaging with cellular resolution up to the whole organ level. These methods have been used extensively in neurobiology, but their uptake in other fields has been much more limited. Application of this approach to the human heart and effective use of the data acquired present challenges of scale and complexity. Four interlinked issues need to be addressed: 1) efficient clearing and labelling of heart tissue, 2) fast microscopic imaging of human-scale samples, 3) handling and processing of multi-terabyte 3D images, and 4) extraction of structural information in computationally tractable structure-based models of cardiac function. Preliminary studies show that each of these requirements can be achieved with the appropriate application and development of existing technologies.

Artificial Intelligence-Driven Algorithm for Drug Effect Prediction on Atrial Fibrillation: An in silico Population of Models Approach

Background: Antiarrhythmic drugs are the first-line treatment for atrial fibrillation (AF), but their effect is highly dependent on the characteristics of the patient. Moreover, anatomical variability, and specifically atrial size, have also a strong influence on AF recurrence. Objective: We performed a proof-of-concept study using artificial intelligence (AI) that enabled us to identify proarrhythmic profiles based on pattern identification from in silico simulations. Methods: A population of models consisting of 127 electrophysiological profiles with a variation of nine electrophysiological variables (G _Na , I _NaK , G _K1, G _CaL , G _Kur , I _KCa , [Na] _ext , and [K] _ext and diffusion) was simulated using the Koivumaki atrial model on square planes corresponding to a normal (16 cm²) and dilated (22.5 cm²) atrium. The simple pore channel equation was used for drug implementation including three drugs (isoproterenol, flecainide, and verapamil). We analyzed the effect of every ionic channel combination to evaluate arrhythmia induction. A Random Forest algorithm was trained using the population of models and AF inducibility as input and output, respectively. The algorithm was trained with 80% of the data (N = 832) and 20% of the data was used for testing with a k-fold cross-validation (k = 5). Results: We found two electrophysiological patterns derived from the AI algorithm that was associated with proarrhythmic behavior in most of the profiles, where G _K1 was identified as the most important current for classifying the proarrhythmicity of a given profile. Additionally, we found different effects of the drugs depending on the electrophysiological profile and a higher tendency of the dilated tissue to fibrillate (Small tissue: 80 profiles vs Dilated tissue: 87 profiles). Conclusion: Artificial intelligence algorithms appear as a novel tool for electrophysiological pattern identification and analysis of the effect of antiarrhythmic drugs on a heterogeneous population of patients with AF.

Combined In-silico and Machine Learning Approaches Toward Predicting Arrhythmic Risk in Post-infarction Patients

Background: Remodeling due to myocardial infarction (MI) significantly increases patient arrhythmic risk. Simulations using patient-specific models have shown promise in predicting personalized risk for arrhythmia. However, these are computationally- and time- intensive, hindering translation to clinical practice. Classical machine learning (ML) algorithms (such as K-nearest neighbors, Gaussian support vector machines, and decision trees) as well as neural network techniques, shown to increase prediction accuracy, can be used to predict occurrence of arrhythmia as predicted by simulations based solely on infarct and ventricular geometry. We present an initial combined image-based patient-specific in silico and machine learning methodology to assess risk for dangerous arrhythmia in post-infarct patients. Furthermore, we aim to demonstrate that simulation-supported data augmentation improves prediction models, combining patient data, computational simulation, and advanced statistical modeling, improving overall accuracy for arrhythmia risk assessment.

Methods: MRI-based computational models were constructed from 30 patients 5 days post-MI (the “baseline” population). In order to assess the utility biophysical model-supported data augmentation for improving arrhythmia prediction, we augmented the virtual baseline patient population. Each patient ventricular and ischemic geometry in the baseline population was used to create a subfamily of geometric models, resulting in an expanded set of patient models (the “augmented” population). Arrhythmia induction was attempted via programmed stimulation at 17 sites for each virtual patient corresponding to AHA LV segments and simulation outcome, “arrhythmia,” or “no-arrhythmia,” were used as ground truth for subsequent statistical prediction (machine learning, ML) models. For each patient geometric model, we measured and used choice data features: the myocardial volume and ischemic volume, as well as the segment-specific myocardial volume and ischemia percentage, as input to ML algorithms. For classical ML techniques (ML), we trained k-nearest neighbors, support vector machine, logistic regression, xgboost, and decision tree models to predict the simulation outcome from these geometric features alone. To explore neural network ML techniques, we trained both a three - and a four-hidden layer multilayer perceptron feed forward neural networks (NN), again predicting simulation outcomes from these geometric features alone. ML and NN models were trained on 70% of randomly selected segments and the remaining 30% was used for validation for both baseline and augmented populations.

Results: Stimulation in the baseline population (30 patient models) resulted in reentry in 21.8% of sites tested; in the augmented population (129 total patient models) reentry occurred in 13.0% of sites tested. ML and NN models ranged in mean accuracy from 0.83 to 0.86 for the baseline population, improving to 0.88 to 0.89 in all cases.

Conclusion: Machine learning techniques, combined with patient-specific, image-based computational simulations, can provide key clinical insights with high accuracy rapidly and efficiently. In the case of sparse or missing patient data, simulation-supported data augmentation can be employed to further improve predictive results for patient benefit. This work paves the way for using data-driven simulations for prediction of dangerous arrhythmia in MI patients.

Effect of Shock Vector Orientation in Modulating and Terminating Rotors - a Simulation Study

The main treatment option for Ventricular Fibrillation (VF), especially in out-of-hospital cardiac arrests (OHCA) is defibrillation. Typically, the survival-to-discharge rates are very poor for OHCA. Existing studies have shown that rotors may be the sources of arrhythmia and ablating them could modulate or terminate VF. However, tracking rotors and ablating them is not a feasible solution in a OHCA scenario. Hence, if the sources (or rotors) can be regionally localized non-invasively and this information can be used to direct the orientation of the shock vectors, it may aid the termination of rotors and defibrillation success. In this work, using computational modeling, we present our initial results on testing the effect of shock vector orientation on modulating (or) terminating rotors. A combination of Sovilj's and Aliev Panfilov's monodomain cardiac models were used in inducing rotors and testing the effect of shock vector magnitude and direction. Based on our simulation results on an average with four experimental trials, a shock vector directed in the perpendicular direction along the axis of the rotor terminated the rotor with 16% lesser magnitude than parallel direction and 38% lesser magnitude than in oblique direction.Clinical Relevance- A rotor localization dependent defibrillation strategy may aid the defibrillation protocol procedures to improve the survival rates. Based on the four experimental trials, the results indicate shock vectors oriented perpendicular to the axis of the rotors were efficient in modulating or terminating rotors with lower magnitude than other directions.

From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

Electrophysiological Characterization of Human Atria: The Understated Role of Temperature

Ambient temperature has a profound influence on cellular electrophysiology through direct control over the gating mechanisms of different ion channels. In the heart, low temperature is known to favor prolongation of the action potential. However, not much is known about the influence of temperature on other important characterization parameters such as the resting membrane potential (RMP), excitability, morphology and characteristics of the action potential (AP), restitution properties, conduction velocity (CV) of signal propagation, etc. Here we present the first, detailed, systematic in silico study of the electrophysiological characterization of cardiomyocytes from different regions of the normal human atria, based on the effects of ambient temperature (5-50°C). We observe that RMP decreases with increasing temperature. At ~ 48°C, the cells lose their excitability. Our studies show that different parts of the atria react differently to the same changes in temperature. In tissue simulations a drop in temperature correlated positively with a decrease in CV, but the decrease was region-dependent, as expected. In this article we show how this heterogeneous response can provide an explanation for the development of a proarrhythmic substrate during mild hypothermia. We use the above concept to propose a treatment strategy for atrial fibrillation that involves severe hypothermia in specific regions of the heart for a duration of only ~ 200 ms.

KEY FACTORS TO THE RATE DEPENDENCE OF EARLY AFTERDEPOLARIZATIONS: A SIMULATION STUDY

Early afterdepolarizations (EADs) in cardiac myocytes have been reported to be associated with a series of cardiac arrhythmias. The generation of EADs has a high correlation with the excitation period, leading to repolarization dispersion over the cardiac tissue. However, the mechanism of EAD rate dependence has not been thoroughly revealed. In this study, the simulation approach was used to investigate the mechanism underlying EAD rate dependence. The results indicated that the gating variable of the delayed rectifier potassium current ([Formula: see text]-gate) and the intracellular sodium ion concentration ([Na[Formula: see text]][Formula: see text] were key factors contributing to EAD rate dependence. Also, different mathematical models showed different types of EAD rate dependence, which needs to be considered in the future simulation research related to EADs.

Optimal pacing sites in cardiac resynchronization by left ventricular activation front analysis

Cardiac resynchronization therapy (CRT) can substantially improve dyssynchronous heart failure and reduce mortality. However, about one-third of patients who are implanted, derive no measurable benefit from CRT. Non-response may partly be due to suboptimal activation of the left ventricle (LV) caused by electrophysiological heterogeneities. The goal of this study is to investigate the performance of a newly developed method used to analyze electrical wavefront propagation in a heart model including myocardial scar and compare this to clinical benchmark studies. We used computational models to measure the maximum activation front (MAF) in the LV during different pacing scenarios. Different heart geometries and scars were created based on cardiac MR images of three patients. The right ventricle (RV) was paced from the apex and the LV was paced from 12 different sites, single site, dual-site and triple site. Our results showed that for single LV site pacing, the pacing site with the largest MAF corresponded with the latest activated regions of the LV demonstrated during RV pacing, which also agrees with previous markers used for predicting optimal single-site pacing location. We then demonstrated the utility of MAF in predicting optimal electrode placements in more complex scenarios including scar and multi-site LV pacing. This study demonstrates the potential value of computational simulations in understanding and planning CRT.

Sensitivity analysis of a strongly-coupled human-based electromechanical cardiac model: Effect of mechanical parameters on physiologically relevant biomarkers

The human heart beats as a result of multiscale nonlinear dynamics coupling subcellular to whole organ processes, achieving electrophysiologically-driven mechanical contraction. Computational cardiac modelling and simulation have achieved a great degree of maturity, both in terms of mathematical models of underlying biophysical processes and the development of simulation software. In this study, we present the detailed description of a human-based physiologically-based, and fully-coupled ventricular electromechanical modelling and simulation framework, and a sensitivity analysis focused on its mechanical properties. The biophysical detail of the model, from ionic to whole-organ, is crucial to enable future simulations of disease and drug action. Key novelties include the coupling of state-of-the-art human-based electrophysiology membrane kinetics, excitation-contraction and active contraction models, and the incorporation of a pre-stress model to allow for pre-stressing and pre-loading the ventricles in a dynamical regime. Through high performance computing simulations, we demonstrate that 50% to 200% - 1000% variations in key parameters result in changes in clinically-relevant mechanical biomarkers ranging from diseased to healthy values in clinical studies. Furthermore mechanical biomarkers are primarily affected by only one or two parameters. Specifically, ejection fraction is dominated by the scaling parameter of the active tension model and its scaling parameter in the normal direction ( k ort 2 ); the end systolic pressure is dominated by the pressure at which the ejection phase is triggered ( P ej ) and the compliance of the Windkessel fluid model ( C ); and the longitudinal fractional shortening is dominated by the fibre angle ( ϕ ) and k ort 2 . The wall thickening does not seem to be clearly dominated by any of the considered input parameters. In summary, this study presents in detail the description and implementation of a human-based coupled electromechanical modelling and simulation framework, and a high performance computing study on the sensitivity of mechanical biomarkers to key model parameters. The tools and knowledge generated enable future investigations into disease and drug action on human ventricles.

Accurate Conduction Velocity Maps and Their Association With Scar Distribution on Magnetic Resonance Imaging in Patients With Postinfarction Ventricular Tachycardias

BACKGROUND

Characterizing myocardial conduction velocity (CV) in patients with ischemic cardiomyopathy (ICM) and ventricular tachycardia (VT) is important for understanding the patient-specific proarrhythmic substrate of VTs and therapeutic planning. The objective of this study is to accurately assess the relation between CV and myocardial fibrosis density on late gadolinium-enhanced cardiac magnetic resonance imaging (LGE-CMR) in patients with ICM.

METHODS

We enrolled 6 patients with ICM undergoing VT ablation and 5 with structurally normal left ventricles (controls) undergoing premature ventricular contraction or VT ablation. All patients underwent LGE-CMR and electroanatomic mapping (EAM) in sinus rhythm (2960 electroanatomic mapping points analyzed). We estimated CV from electroanatomic mapping local activation time using the triangulation method that provides an accurate estimate of CV as it accounts for the direction of wavefront propagation. We evaluated the association between LGE-CMR intensity and CV with multilevel linear mixed models.

RESULTS

Median CV in patients with ICM and controls was 0.41 m/s and 0.65 m/s, respectively. In patients with ICM, CV in areas with no visible fibrosis was 0.81 m/s (95% CI, 0.59-1.12 m/s). For each 25% increase in normalized LGE intensity, CV decreased by 1.34-fold (95% CI, 1.25-1.43). Dense scar areas have, on average, 1.97- to 2.66-fold slower CV compared with areas without dense scar. Ablation lesions that terminated VTs were localized in areas of slow conduction on CV maps.

CONCLUSIONS

CV is inversely associated with LGE-CMR fibrosis density in patients with ICM. Noninvasive derivation of CV maps from LGE-CMR is feasible. Integration of noninvasive CV maps with electroanatomic mapping during substrate mapping has the potential to improve procedural planning and outcomes. Visual Overview: A visual overview is available for this article.

Accelerating simulations of cardiac electrical dynamics through a multi-GPU platform and an optimized data structure

Simulations of cardiac electrophysiological models in tissue, particularly in 3D require the solutions of billions of differential equations even for just a couple of milliseconds, thus highly demanding in computational resources. In fact, even studies in small domains with very complex models may take several hours to reproduce seconds of electrical cardiac behavior. Today's Graphics Processor Units (GPUs) are becoming a way to accelerate such simulations, and give the added possibilities to run them locally without the need for supercomputers. Nevertheless, when using GPUs, bottlenecks related to global memory access caused by the spatial discretization of the large tissue domains being simulated, become a big challenge. For simulations in a single GPU, we propose a strategy to accelerate the computation of the diffusion term through a data-structure and memory access pattern designed to maximize coalescent memory transactions and minimize branch divergence, achieving results approximately 1.4 times faster than a standard GPU method. We also combine this data structure with a designed communication strategy to take advantage in the case of simulations in multi-GPU platforms. We demonstrate that, in the multi-GPU approach performs, simulations in 3D tissue can be just 4× slower than real time.

The role of the size of infarcted area on two kinds of vulnerable window in two dimension ventricular tissue

AIMS

Sudden cardiac death (SCD) is mainly induced by ventricular arrhythmia, especially among patients with myocardial infarction (MI). Previous studies have shown that ventricular tachycardia and fibrillation are thought to be caused by re-entrant waves of excitation. Although in heterogeneous tissue, the traditional vulnerable window of unidirectional block and the vulnerable window when bidirectional propagation was initiated could coexist, little studies are based on effects of infarcted areas on both vulnerable windows.

METHODS AND RESULTS

The electrophysiology remodeling was based on TP06 model in the present study. In simulation of two-dimension (2D) ideal models, excitation wave conduction in ventricular tissue was simulated under three different types of stimulus. 2D ideal models of ventricular tissue were constructed as loop areas in the center of a square tissue with the resolution of 600×600 grid points and cell size of 0.35mm. Simulation results showed that the traditional vulnerable window when unidirectional propagation was initiated was consistent no matter where the position of stimulus is and how long and how wide the size of the infarcted area is. However, the vulnerable window when bidirectional propagation was initiated varies in different conditions.

CONCLUSION

The traditional vulnerable window could not reflect the role of the infarcted area on arrhythmogenesis. The vulnerable window when bidirectional propagation was initiated increases with the increasement of the width and the length of the infarcted area with the appropriate position of the stimulus, which could help us to conclude the arrhythmogenesis according to the size of infarcted areas.

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics

Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.

Proarrhythmia in the p.Met207Val PITX2c-Linked Familial Atrial Fibrillation-Insights From Modeling

Functional analysis has shown that the p.Met207Val mutation was linked to atrial fibrillation and caused an increase in transactivation activity of PITX2c, which caused changes in mRNA synthesis related to ionic channels and intercellular electrical coupling. We assumed that these changes were quantitatively translated to the functional level. This study aimed to investigate the potential impact of the PITX2c p.Met207Val mutation on atrial electrical activity through multiscale computational models. The well-known Courtemanche-Ramirez-Nattel (CRN) model of human atrial cell action potentials (APs) was modified to incorporate experimental data on the expected p.Met207Val mutation-induced changes in ionic channel currents (I_NaL, I_Ks, and I_Kr) and intercellular electrical coupling. The cell models for wild-type (WT), heterozygous (Mutant/Wild type, MT/WT), and homozygous (Mutant, MT) PITX2c cases were incorporated into homogeneous multicellular 1D and 2D tissue models. Effects of this mutation-induced remodeling were quantified as changes in AP profile, AP duration (APD) restitution, conduction velocity (CV) restitution and wavelength (WL). Temporal and spatial vulnerabilities of atrial tissue to the genesis of reentry were computed. Dynamic behaviors of re-entrant excitation waves (Life span, tip trajectory and dominant frequency) in a homogeneous 2D tissue model were characterized. Our results suggest that the PITX2c p.Met207Val mutation abbreviated atrial APD and flattened APD restitution curves. It reduced atrial CV and WL that facilitated the conduction of high rate atrial excitation waves. It increased the tissue's temporal vulnerability by increasing the vulnerable window for initiating reentry and increased the tissue spatial vulnerability by reducing the substrate size necessary to sustain reentry. In the 2D models, the mutation also stabilized and accelerated re-entrant excitation waves, leading to rapid and sustained reentry. In conclusion, electrical and structural remodeling arising from the PITX2c p.Met207Val mutation may increase atrial susceptibility to arrhythmia due to shortened APD, reduced CV and increased tissue vulnerability, which, in combination, facilitate initiation and maintenance of re-entrant excitation waves.

Influence of the distribution of fibrosis within an area of myocardial infarction on wave propagation in ventricular tissue

The presence of fibrosis in heart tissue is strongly correlated with an incidence of arrhythmia, which is a leading cause of sudden cardiac death (SCD). However, it remains incompletely understood how different distributions, sizes and positions of fibrotic tissues contribute to arrhythmogenesis. In this study, we designed 4 different ventricular models mimicking wave propagation in cardiac tissues under normal, myocardial infarction (MI), MI with random fibrosis and MI with gradient fibrosis conditions. Simulation results of ideal square tissues indicate that vulnerable windows (VWs) of random and gradient fibrosis distributions are similar with low levels of fibrosis. However, with a high level of fibrosis, the VWs significantly increase in random fibrosis tissue but not in gradient fibrosis tissue. In addition, we systematically analyzed the effects of the size and position of fibrosis tissues on VWs. Simulation results show that it is more likely for a reentry wave to appear when the length of the infarcted area is greater than 25% of the perimeter of the ventricle, when the width is approximately half that of the ventricular wall, or when the infarcted area is attached to the inside or outside of the ventricular wall.

Simulation of action potential propagation based on the ghost structure method

In this paper, a ghost structure (GS) method is proposed to simulate the monodomain model in irregular computational domains using finite difference without regenerating body-fitted grids. In order to verify the validity of the GS method, it is first used to solve the Fitzhugh-Nagumo monodomain model in rectangular and circular regions at different states (the stationary and moving states). Then, the GS method is used to simulate the propagation of the action potential (AP) in transverse and longitudinal sections of a healthy human heart, and with left bundle branch block (LBBB). Finally, we analyze the AP and calcium concentration under healthy and LBBB conditions. Our numerical results show that the GS method can accurately simulate AP propagation with different computational domains either stationary or moving, and we also find that LBBB will cause the left ventricle to contract later than the right ventricle, which in turn affects synchronized contraction of the two ventricles.

Smeared multiscale finite element model for electrophysiology and ionic transport in biological tissue

Basic functions of living organisms are governed by the nervous system through bidirectional signals transmitted from the brain to neural networks. These signals are similar to electrical waves. In electrophysiology the goal is to study the electrical properties of biological cells and tissues, and the transmission of signals. From a physics perspective, there exists a field of electrical potential within the living body, the nervous system, extracellular space and cells. Electrophysiological problems can be investigated experimentally and also theoretically by developing appropriate mathematical or computational models. Due to the enormous complexity of biological systems, it would be almost impossible to establish a detailed computational model of the electrical field, even for only a single organ (e.g. heart), including the entirety of cells comprising the neural network. In order to make computational models feasible for practical applications, we here introduce the concept of smeared fields, which represents a generalization of the previously formulated multiscale smeared methodology for mass transport in blood vessels, lymph, and tissue. We demonstrate the accuracy of the smeared finite element computational models for the electric field in numerical examples. The electrical field is further coupled with ionic mass transport within tissue composed of interstitial spaces extracellularly and by cytoplasm and organelles intracellularly. The proposed methodology, which couples electrophysiology and molecular ionic transport, is applicable to a variety of biological systems.

Geometry-Dependent Arrhythmias in Electrically Excitable Tissues

Little is known about how individual cells sense the macroscopic geometry of their tissue environment. Here, we explore whether long-range electrical signaling can convey information on tissue geometry to individual cells. First, we studied an engineered electrically excitable cell line. Cells grown in patterned islands of different shapes showed remarkably diverse firing patterns under otherwise identical conditions, including regular spiking, period-doubling alternans, and arrhythmic firing. A Hodgkin-Huxley numerical model quantitatively reproduced these effects, showing how the macroscopic geometry affected the single-cell electrophysiology via the influence of gap junction-mediated electrical coupling. Qualitatively similar geometry-dependent dynamics were observed in human induced pluripotent stem cell (iPSC)-derived cardiomyocytes. The cardiac results urge caution in translating observations of arrhythmia in vitro to predictions in vivo, where the tissue geometry is very different. We study how to extrapolate electrophysiological measurements between tissues with different geometries and different gap junction couplings.

Effect of ventricular myocardium characteristics on the defibrillation threshold

Myocardium characteristics differ markedly among individuals and play an important role in defibrillation threshold. The accuracy of simulation models used in most published studies are still have room to be improved and most of them only discussed the effect of myocardial anisotropy on defibrillation threshold. In our manuscript, a rabbit ventricular finite-element (FE) volume conductor model with high precision was constructed. Ventricular myocardium characteristics include cardiomyocyte coupling and the degree of myocardial anisotropy, which are represented as the value and the ratio of anisotropic conductivity, respectively. Quantitative analysis was performed simultaneously in terms of cardiomyocyte coupling and the degree of myocardial anisotropy. Based on this, the combined effects of these two factors were further discussed. The electric field distributions of shocks and the defibrillation thresholds under different myocardial characteristics were simulated on this model. The simulation results revealed that as the degree of myocardial anisotropy increases, defibrillation threshold increases, and cardiomyocyte decoupling (decrease in electrical conductivity) can considerably increase the defibrillation threshold.

Patient-Specific Cardiovascular Computational Modeling: Diversity of Personalization and Challenges

Patient-specific computer models have been developed representing a variety of aspects of the cardiovascular system spanning the disciplines of electrophysiology, electromechanics, solid mechanics, and fluid dynamics. These physiological mechanistic models predict macroscopic phenomena such as electrical impulse propagation and contraction throughout the entire heart as well as flow and pressure dynamics occurring in the ventricular chambers, aorta, and coronary arteries during each heartbeat. Such models have been used to study a variety of clinical scenarios including aortic aneurysms, coronary stenosis, cardiac valvular disease, left ventricular assist devices, cardiac resynchronization therapy, ablation therapy, and risk stratification. After decades of research, these models are beginning to be incorporated into clinical practice directly via marketed devices and indirectly by improving our understanding of the underlying mechanisms of health and disease within a clinical context.

Computational Cardiac Modeling Reveals Mechanisms of Ventricular Arrhythmogenesis in Long QT Syndrome Type 8: CACNA1C R858H Mutation Linked to Ventricular Fibrillation

Functional analysis of the L-type calcium channel has shown that the CACNA1C R858H mutation associated with severe QT interval prolongation may lead to ventricular fibrillation (VF). This study investigated multiple potential mechanisms by which the CACNA1C R858H mutation facilitates and perpetuates VF. The Ten Tusscher-Panfilov (TP06) human ventricular cell models incorporating the experimental data on the kinetic properties of L-type calcium channels were integrated into one-dimensional (1D) fiber, 2D sheet, and 3D ventricular models to investigate the pro-arrhythmic effects of CACNA1C mutations by quantifying changes in intracellular calcium handling, action potential profiles, action potential duration restitution (APDR) curves, dispersion of repolarization (DOR), QT interval and spiral wave dynamics. R858H “mutant” L-type calcium current (I_CaL) augmented sarcoplasmic reticulum calcium content, leading to the development of afterdepolarizations at the single cell level and focal activities at the tissue level. It also produced inhomogeneous APD prolongation, causing QT prolongation and repolarization dispersion amplification, rendering R858H “mutant” tissue more vulnerable to the induction of reentry compared with other conditions. In conclusion, altered I_CaL due to the CACNA1C R858H mutation increases arrhythmia risk due to afterdepolarizations and increased tissue vulnerability to unidirectional conduction block. However, the observed reentry is not due to afterdepolarizations (not present in our model), but rather to a novel blocking mechanism.

Identification of Ion Currents Components Generating Field Potential Recorded in MEA From hiPSC-CM

OBJECTIVE

Multi electrodes arrays (MEAs) combined with cardiomyocytes derived from human-induced pluripotent stem cells (hiPSC-CMs) can enable high- or medium-throughput drug screening in safety pharmacology. This technology has recently attracted a lot of attention, in particular from an international initiative named CiPA. But it is currently limited by the difficulty to analyze the measured signals. We propose a strategy to analyze the signals acquired by the MEA and to automatically deduce the channels affected by the drug.

METHODS

Our method is based on the bidomain equations, a model for the MEA electrodes, and an inverse problem strategy.

RESULTS

in silico MEA signals are obtained for two commercial devices and an example of early after depolarization is presented. Then, by processing real signals obtained for four different compounds, our algorithm was able to provide dose-response curves for potassium, sodium, and calcium channels. For ivabradine and moxifloxacin, the IC50 and dose-response curves are in very good agreement with known values.

SIGNIFICANCE

The proposed strategy offers a possible answer to a major question raised by the community of safety pharmacology. By allowing a more automated analysis of the signals, our approach could contribute to promote the technology based on MEA and hiPSC-CMs and, therefore, improve reliability and efficiency of drug screening.

Spatially Adaptive Multi-Scale Optimization for Local Parameter Estimation in Cardiac Electrophysiology

To obtain a patient-specific cardiac electro-physiological (EP) model, it is important to estimate the 3-D distributed tissue properties of the myocardium. Ideally, the tissue property should be estimated at the resolution of the cardiac mesh. However, such high-dimensional estimation faces major challenges in identifiability and computation. Most existing works reduce this dimension by partitioning the cardiac mesh into a pre-defined set of segments. The resulting low-resolution solutions have a limited ability to represent the underlying heterogeneous tissue properties of varying sizes, locations, and distributions. In this paper, we present a novel framework that, going beyond a uniform low-resolution approach, is able to obtain a higher resolution estimation of tissue properties represented by spatially non-uniform resolution. This is achieved by two central elements: 1) a multi-scale coarse-to-fine optimization that facilitates higher resolution optimization using the lower resolution solution and 2) a spatially adaptive decision criterion that retains lower resolution in homogeneous tissue regions and allows higher resolution in heterogeneous tissue regions. The presented framework is evaluated in estimating the local tissue excitability properties of a cardiac EP model on both synthetic and real data experiments. Its performance is compared with optimization using pre-defined segments. Results demonstrate the feasibility of the presented framework to estimate local parameters and to reveal heterogeneous tissue properties at a higher resolution without using a high number of unknowns.

A composite visualization method for electrophysiology-morphous merging of human heart

BACKGROUND

Electrophysiological behavior is of great importance for analyzing the cardiac functional mechanism under cardiac physiological and pathological condition. Due to the complexity of cardiac structure and biophysiological function, visualization of a cardiac electrophysiological model compositively is still a challenge. The lack of either modality of the whole organ structure or cardiac electrophysiological behaviors makes analysis of the intricate mechanisms of cardiac dynamic function a difficult task. This study aims at exploring 3D conduction of stimulus and electrical excitation reactivity on the level of organ with the authentic fine cardiac anatomy structure.

METHODS

In this paper, a cardiac electrical excitation propagation model is established based on the human cardiac cross-sectional data to explore detailed cardiac electrical activities. A novel biophysical merging visualization method is then presented for biophysical integration of cardiac anatomy and electrophysiological properties in the form of the merging optical model, which provides the corresponding position, spatial relationship and the whole process in 3D space with the context of anatomical structure for representing the biophysical detailed electrophysiological activity.

RESULTS

The visualization result present the action potential propagation of the left ventricle within the excitation cycle with the authentic fine cardiac organ anatomy. In the visualized images, all vital organs are identified and distinguished without ambiguity. The three dimensional spatial position, relation and the process of cardiac excitation conduction and re-entry propagation in the anatomical structure during the phase of depolarization and repolarization is also shown in the result images, which exhibits the performance of a more detailed biophysical understanding of the electrophysiological kinetics of human heart in vivo.

CONCLUSIONS

Results suggest that the proposed merging optical model can merge cardiac electrophysiological activity with the anatomy structure. By specifying the respective opacity for the cardiac anatomy structure and the electrophysiological model in the merging attenuation function, the visualized images can provide an in-depth insight into the biophysical detailed cardiac functioning phenomena and the corresponding electrophysiological behavior mechanism, which is helpful for further speculating cardiac physiological and pathological responses and is fundamental to the cardiac research and clinical diagnoses.

BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.

A mathematical model for active contraction in healthy and failing myocytes and left ventricles

Cardiovascular disease is one of the leading causes of death worldwide, in particular myocardial dysfunction, which may lead to heart failure eventually. Understanding the electro-mechanics of the heart will help in developing more effective clinical treatments. In this paper, we present a multi-scale electro-mechanics model of the left ventricle (LV). The Holzapfel-Ogden constitutive law was used to describe the passive myocardial response in tissue level, a modified Grandi-Pasqualini-Bers model was adopted to model calcium dynamics in individual myocytes, and the active tension was described using the Niederer-Hunter-Smith myofilament model. We first studied the electro-mechanics coupling in a single myocyte in the healthy and diseased left ventricle, and then the single cell model was embedded in a dynamic LV model to investigate the compensation mechanism of LV pump function due to myocardial dysfunction caused by abnormality in cellular calcium dynamics. The multi-scale LV model was solved using an in-house developed hybrid immersed boundary method with finite element extension. The predictions of the healthy LV model agreed well with the clinical measurements and other studies, and likewise, the results in the failing states were also consistent with clinical observations. In particular, we found that a low level of intracellular Ca2+ transient in myocytes can result in LV pump function failure even with increased myocardial contractility, decreased systolic blood pressure, and increased diastolic filling pressure, even though they will increase LV stroke volume. Our work suggested that treatments targeted at increased contractility and lowering the systolic blood pressure alone are not sufficient in preventing LV pump dysfunction, restoring a balanced physiological Ca2+ handling mechanism is necessary.