Three-dimensional cardiac computational modelling: methods, features and applications

Modeling 3D Cardiac Contraction and Relaxation With Point Cloud Deformation Networks

Global single-valued biomarkers, such as ejection fraction, are widely used in clinical practice to assess cardiac function. However, they only approximate the heart's true 3D deformation process, thus limiting diagnostic accuracy and the understanding of cardiac mechanics. Metrics based on 3D shape have been proposed to alleviate these shortcomings. In this work, we present the Point Cloud Deformation Network (PCD-Net) as a novel geometric deep learning approach for direct modeling of 3D cardiac mechanics of the biventricular anatomy between the extreme ends of the cardiac cycle. Its encoder-decoder architecture combines a low-dimensional latent space with recent advances in point cloud deep learning for effective multi-scale feature learning directly on flexible and memory-efficient point cloud representations of the cardiac anatomy. We first evaluate the PCD-Net's predictive capability for both cardiac contraction and relaxation on a large UK Biobank dataset of over 10,000 subjects and find average Chamfer distances between the predicted and ground truth anatomies below the pixel resolution of the underlying image acquisition. We then show the PCD-Net's ability to capture subpopulation-specific differences in 3D cardiac mechanics between normal and myocardial infarction (MI) subjects and visualize abnormal phenotypes between predicted normal 3D shapes and corresponding observed ones. Finally, we demonstrate that the PCD-Net's learned 3D deformation encodings outperform multiple clinical and machine learning benchmarks by 11% in terms of area under the receiver operating characteristic curve for the tasks of prevalent MI detection and incident MI prediction and by 7% in terms of Harrell's concordance index for MI survival analysis.

Advancements in Finite Element Modeling for Cardiac Device Leads and 3D Heart Models

The human heart's remarkable vitality necessitates a deep understanding of its mechanics, particularly concerning cardiac device leads. This paper presents advancements in finite element modeling for cardiac leads and 3D heart models, leveraging computational simulations to assess lead behavior over time. Through detailed modeling and meshing techniques, we accurately captured the complex interactions between leads and heart tissue. Material properties were assigned based on ASTM (American Society for Testing and Materials) standards and in vivo exposure data, ensuring realistic simulations. Our results demonstrate close agreement between experimental and simulated data for silicone insulation in pacemaker leads, with a mean force tolerance of 19.6 N ± 3.6 N, an ultimate tensile strength (UTS) of 6.3 MPa ± 1.15 MPa, and a percentage elongation of 125% ± 18.8%, highlighting the effectiveness of simulation in predicting lead performance. Similarly, for polyurethane insulation in ICD leads, we found a mean force of 65.87 N ± 7.1 N, a UTS of 10.7 MPa ± 1.15 MPa, and a percentage elongation of 259.3% ± 21.4%. Additionally, for polyurethane insulation in CRT leads, we observed a mean force of 53.3 N ± 2.06 N, a UTS of 22.11 MPa ± 0.85 MPa, and a percentage elongation of 251.6% ± 13.2%. Correlation analysis revealed strong relationships between mechanical properties, further validating the simulation models. Classification models constructed using both experimental and simulated data exhibited high discriminative ability, underscoring the reliability of simulation in analyzing lead behavior. These findings contribute to the ongoing efforts to improve cardiac device lead design and optimize patient outcomes.

Effects of cardiac growth on electrical dyssynchrony in the single ventricle patient

Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.

A Review of Personalised Cardiac Computational Modelling Using Electroanatomical Mapping Data

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

A Predictive Toxicokinetic Model for Nickel Leaching from Vascular Stents

In vitro testing methods offer valuable insights into the corrosion vulnerability of metal implants and enable prompt comparison between devices. However, they fall short in predicting the extent of leaching and the biodistribution of implant byproducts under in vivo conditions. Physiologically based toxicokinetic (PBTK) models are capable of quantitatively establishing such correlations and therefore provide a powerful tool in advancing nonclinical methods to test medical implants and assess patient exposure to implant debris. In this study, we present a multicompartment PBTK model and a simulation engine for toxicological risk assessment of vascular stents. The mathematical model consists of a detailed set of constitutive equations that describe the transfer of nickel ions from the device to peri-implant tissue and circulation and the nickel mass exchange between blood and the various tissues/organs and excreta. Model parameterization was performed using (1) in-house-produced data from immersion testing to compute the device-specific diffusion parameters and (2) full-scale animal in situ implantation studies to extract the mammalian-specific biokinetic functions that characterize the time-dependent biodistribution of the released ions. The PBTK model was put to the test using a simulation engine to estimate the concentration-time profiles, along with confidence intervals through probabilistic Monte Carlo, of nickel ions leaching from the implanted devices and determine if permissible exposure limits are exceeded. The model-derived output demonstrated prognostic conformity with reported experimental data, indicating that it may provide the basis for the broader use of modeling and simulation tools to guide the optimal design of implantable devices in compliance with exposure limits and other regulatory requirements.

Preclinical Models of Cardiac Disease: A Comprehensive Overview for Clinical Scientists

For recent decades, cardiac diseases have been the leading cause of death and morbidity worldwide. Despite significant achievements in their management, profound understanding of disease progression is limited. The lack of biologically relevant and robust preclinical disease models that truly grasp the molecular underpinnings of cardiac disease and its pathophysiology attributes to this stagnation, as well as the insufficiency of platforms that effectively explore novel therapeutic avenues. The area of fundamental and translational cardiac research has therefore gained wide interest of scientists in the clinical field, while the landscape has rapidly evolved towards an elaborate array of research modalities, characterized by diverse and distinctive traits. As a consequence, current literature lacks an intelligible and complete overview aimed at clinical scientists that focuses on selecting the optimal platform for translational research questions. In this review, we present an elaborate overview of current in vitro, ex vivo, in vivo and in silico platforms that model cardiac health and disease, delineating their main benefits and drawbacks, innovative prospects, and foremost fields of application in the scope of clinical research incentives.

Interactions between calcium-induced arrhythmia triggers and the electrophysiological-anatomical substrate underlying the induction of atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia and is sustained by spontaneous focal excitations and re-entry. Spontaneous electrical firing in the pulmonary vein (PV) sleeves is implicated in AF generation. The aim of this simulation study was to identify the mechanisms determining the localisation of AF triggers in the PVs and their contribution to the genesis of AF. A novel biophysical model of the canine atria was used that integrates stochastic, spontaneous subcellular Ca2+ release events (SCRE) with regional electrophysiological heterogeneity in ionic properties and a detailed three-dimensional model of atrial anatomy, microarchitecture and patchy fibrosis. Simulations highlighted the importance of the smaller inward rectifier potassium current (IK1 ) in PV cells compared to the surrounding atria, which enabled SCRE more readily to result in delayed-afterdepolarisations that induced triggered activity. There was a leftward shift in the dependence of the probability of triggered activity on sarcoplasmic reticulum Ca2+ load. This feature was accentuated in 3D tissue compared to single cells (Δ half-maximal [Ca2+ ]SR  = 58 μM vs. 22 μM). In 3D atria incorporating electrical heterogeneity, excitations preferentially emerged from the PV region. These triggered focal excitations resulted in transient re-entry in the left atrium. Addition of fibrotic patches promoted localised emergence of focal excitations and wavebreaks that had a more substantial impact on generating AF-like patterns than the PVs. Thus, a reduced IK1 , less negative resting membrane potential, and fibrosis-induced changes of the electrotonic load all contribute to the emergence of complex excitation patterns from spontaneous focal triggers. KEY POINTS: Focal excitations in the atria are most commonly associated with the pulmonary veins, but the mechanisms for this localisation are yet to be elucidated. We applied a multi-scale computational modelling approach to elucidate the mechanisms underlying such localisations. Myocytes in the pulmonary vein region of the atria have a less negative resting membrane potential and reduced time-independent potassium current; we demonstrate that both of these factors promote triggered activity in single cells and tissues. The less negative resting membrane potential also contributes to heterogeneous inactivation of the fast sodium current, which can enable re-entrant-like excitation patterns to emerge without traditional conduction block.

Simultaneous data assimilation and cardiac electrophysiology model correction using differentiable physics and deep learning

Modelling complex systems, like the human heart, has made great progress over the last decades. Patient-specific models, called 'digital twins', can aid in diagnosing arrhythmias and personalizing treatments. However, building highly accurate predictive heart models requires a delicate balance between mathematical complexity, parameterization from measurements and validation of predictions. Cardiac electrophysiology (EP) models range from complex biophysical models to simplified phenomenological models. Complex models are accurate but computationally intensive and challenging to parameterize, while simplified models are computationally efficient but less realistic. In this paper, we propose a hybrid approach by leveraging deep learning to complete a simplified cardiac model from data. Our novel framework has two components, decomposing the dynamics into a physics based and a data-driven term. This construction allows our framework to learn from data of different complexity, while simultaneously estimating model parameters. First, using in silico data, we demonstrate that this framework can reproduce the complex dynamics of cardiac transmembrane potential even in the presence of noise in the data. Second, using ex vivo optical data of action potentials (APs), we demonstrate that our framework can identify key physical parameters for anatomical zones with different electrical properties, as well as to reproduce the AP wave characteristics obtained from various pacing locations. Our physics-based data-driven approach may improve cardiac EP modelling by providing a robust biophysical tool for predictions.

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.

Improving Automatic Smartwatch Electrocardiogram Diagnosis of Atrial Fibrillation by Identifying Regularity within Irregularity

Smartwatches equipped with automatic atrial fibrillation (AF) detection through electrocardiogram (ECG) recording are increasingly prevalent. We have recently reported the limitations of the Apple Watch (AW) in correctly diagnosing AF. In this study, we aim to apply a data science approach to a large dataset of smartwatch ECGs in order to deliver an improved algorithm. We included 723 patients (579 patients for algorithm development and 144 patients for validation) who underwent ECG recording with an AW and a 12-lead ECG (21% had AF and 24% had no ECG abnormalities). Similar to the existing algorithm, we first screened for AF by detecting irregularities in ventricular intervals. However, as opposed to the existing algorithm, we included all ECGs (not applying quality or heart rate exclusion criteria) but we excluded ECGs in which we identified regular patterns within the irregular rhythms by screening for interval clusters. This "irregularly irregular" approach resulted in a significant improvement in accuracy compared to the existing AW algorithm (sensitivity of 90% versus 83%, specificity of 92% versus 79%, p < 0.01). Identifying regularity within irregular rhythms is an accurate yet inclusive method to detect AF using a smartwatch ECG.

A Systematic Review of Individualized Heart Surgery with a Personalized Prosthesis

Personalized surgery is not just a new trend but rather a patient-specific approach to therapy that makes it possible to adopt a targeted approach for a specific patient and closely mirrors the approach of personalized medicine. However, the application of tailored surgery in the context of cardiovascular replacement surgery has not been systematically reviewed. The ability to customize a device is highly dependent on the collection of radiological image data for precise prosthesis modeling. These facts are essential to "tailor-made" device design for precise prosthesis implantation. According to this study, computed tomography (CT) was the most prominent imaging modality; however, transesophageal echocardiography and echocardiography were also found to be helpful. Additionally, a dynamic finite element simulation was also found to be an attractive alternative to the finite element analysis for an in-silico experiment. Nonetheless, there is a paucity of relevant publications and only sporadic evidence. More clinical studies have been warranted, notwithstanding that the derived data and results from this insight into the use of therapeutic interventions may be evidence of multiple directives in clinical practices and beyond. This study may help the integration of personalized devices for better comprehension of predicted clinical outcomes, thus leading towards enhanced performance gains.

Smoothed finite element methods in simulation of active contraction of myocardial tissue samples

In modelling and simulation of cardiac mechanics, tetrahedral meshes are often used due to the easy availability of efficient meshing algorithms. This is beneficial in particular when complex geometries such as cardiac structures are considered. The gold standard in simulating the cardiac cycle is to solve the mechanical balance equations with the finite element method (FEM). However, using linear shape functions in the FEM in combination with nearly-incompressible material models is known to produce overly stiff approximations, whereas higher order elements are computationally more expensive. To overcome these problems, smoothed finite element methods (S-FEMs) have been proposed by Liu and co-workers. So far, S-FEMs in 3D have been utilised only in simulations of passive mechanics. In the present work, different S-FEMs are for the first time used for simulation of an active cardiac contraction on three-dimensional myocardial tissue samples. Further, node-based S-FEM (NS-FEM), face-based S-FEM (FS-FEM) and selective FS/NS-FEM are for the first time implemented as user subroutine in the commercial software Abaqus. Our results confirm that all S-FEMs perform softer than linear FEM and volumetric locking is reduced. The FS/NS-FEM produces solutions with the relative error in maximum displacement and rotation being less than 5% with respect to the reference solution obtained by the quadratic FEM for all considered mesh sizes, although linear shape functions are used. We therefore conclude that in particular FS/NS-FEM is an efficient and accurate numerical method in the simulation of an active cardiac muscle contraction.

Sex matters: the frequently overlooked importance of considering sex in computational models

Personalised medicine and the development of a virtual human or a digital twin comprises visions of the future of medicine. To realise these innovations, an understanding of the biology and physiology of all people are required if we wish to apply these technologies at a population level. Sex differences in health and biology is one aspect that has frequently been overlooked, with young white males being seen as the "average" human being. This has not been helped by the lack of inclusion of female cells and animals in biomedical research and preclinical studies or the historic exclusion, and still low in proportion, of women in clinical trials. However, there are many known differences in health between the sexes across all scales of biology which can manifest in differences in susceptibility to diseases, symptoms in a given disease, and outcomes to a given treatment. Neglecting these important differences in the development of any health technologies could lead to adverse outcomes for both males and females. Here we highlight just some of the sex differences in the cardio-respiratory systems with the goal of raising awareness that these differences exist. We discuss modelling studies that have considered sex differences and touch on how and when to create sex-specific models. Scientific studies should ensure sex differences are included right from the study planning phase and results reported using sex as a biological variable. Computational models must have sex-specific versions to ensure a movement towards personalised medicine is realised.

Characterization of the Electrophysiological Characteristics of Chronic Atrial Fibrillation for Efficient Simulations

Atrial biophysical simulations have the potential to enhance outcomes by enabling the simulation of pharmacological and ablative strategies. However, the high computational times associated with such simulations render them unsuitable for diagnostic purposes. To address this challenge, discrete models such as cellular automata (CA) have been developed, which consider a finite number of states, thus significantly reducing computational times. Yet, there is a pressing need to determine whether CA can replicate pathological simulations with accuracy. The analysis of simulations under different degrees of electrical remodeling shows an expected increase of Action Potential Duration (APD) with the previous Diastolic Interval (DI) interval, indicating short-term memory of atrial cardiomyocytes: shorter APD0 provoked shorter APD+1, and previous DI has a similar effect on APD+1. Independent prediction using both APD0 and DI was found to provide a far better estimation of APD+1 values, compared to relying on DI alone (p<<0.01). Finally, the CA models were able to replicate reentrant patterns and cycle lengths of different states of atrial remodeling with a high degree of accuracy when compared to biophysical simulations. Overall, the use of atrial CA with short-term memory allows accurate reproduction of arrhythmic behavior in pathological tissue within a clinically relevant timeframe.Clinical Relevance- Discrete electrophysiological models simulate pathological self-sustained arrhythmias in diagnostic times.

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

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

A Persistent Homology-Based Topological Loss for CNN-Based Multiclass Segmentation of CMR

Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a separation of data into anatomical components with known structure and configuration. The most popular CNN-based methods are optimised using pixel wise loss functions, ignorant of the spatially extended features that characterise anatomy. Therefore, whilst sharing a high spatial overlap with the ground truth, inferred CNN-based segmentations can lack coherence, including spurious connected components, holes and voids. Such results are implausible, violating anticipated anatomical topology. In response, (single-class) persistent homology-based loss functions have been proposed to capture global anatomical features. Our work extends these approaches to the task of multi-class segmentation. Building an enriched topological description of all class labels and class label pairs, our loss functions make predictable and statistically significant improvements in segmentation topology using a CNN-based post-processing framework. We also present (and make available) a highly efficient implementation based on cubical complexes and parallel execution, enabling practical application within high resolution 3D data for the first time. We demonstrate our approach on 2D short axis and 3D whole heart CMR segmentation, advancing a detailed and faithful analysis of performance on two publicly available datasets.

Cardiac Resynchronization Therapy for Adult Patients With a Failing Systemic Right Ventricle: A Multicenter Study

Background

The objective of this international multicenter study was to investigate both early and late outcomes of cardiac resynchronization therapy (CRT) in patients with a systemic right ventricle (SRV) and to identify predictors for congestive heart failure readmissions and mortality.

Methods and Results

This retrospective international multicenter study included 13 centers. The study population comprised 80 adult patients with SRV (48.9% women) with a mean age of 45±14 (range, 18–77) years at initiation of CRT. Median follow‐up time was 4.1 (25th–75th percentile, 1.3–8.3) years. Underlying congenital heart disease consisted of congenitally corrected transposition of the great arteries and dextro‐transposition of the great arteries in 63 (78.8%) and 17 (21.3%) patients, respectively. CRT resulted in significant improvement in functional class (before CRT: III, 25th–75th percentile, II–III; after CRT: II, 25th–75th percentile, II–III; P =0.005) and QRS duration (before CRT: 176±27; after CRT: 150±24 milliseconds; P =0.003) in patients with pre‐CRT ventricular pacing who underwent an upgrade to a CRT device (n=49). These improvements persisted during long‐term follow‐up with a marginal but significant increase in SRV function (before CRT; 30%, 25th–75th percentile, 25–35; after CRT: 31%, 25th–75th percentile, 21–38; P =0.049). In contrast, no beneficial change in the above‐mentioned variables was observed in patients who underwent de novo CRT (n=31). A quarter of all patients were readmitted for heart failure during follow‐up, and mortality at latest follow‐up was 21.3%.

Conclusions

This international experience with CRT in patients with an SRV demonstrated that CRT in selected patients with SRV dysfunction and pacing‐induced dyssynchrony yielded consistent improvement in QRS duration and New York Heart Association functional status, with a marginal increase in SRV function.

Fluid-Structure Interaction Model for Predicting Surgical Result of Total Anomalous Pulmonary Venous Connection and Estimating Pulmonary Venous Properties

OBJECTIVES

To build a fluid-structure interaction model of pulmonary veins with total anomalous pulmonary venous connection, which can be used to predict the result of surgical treatment and at the same time to estimate the elastic properties of pulmonary veins based on patient-specific data and clinic postoperative results.

METHODS

The fluid-structure interaction (FSI) model was used to simulate the anastomosis on pulmonary veins based on computed tomography angiography data collected from three children with total anomalous pulmonary venous connection (TAPVC), supra-cardiac type. The deformation and the stress of anastomosis, and also the velocity of blood flow were calculated in fluid-structure coupling algorithm. During the simulation the variable boundary conditions were applied, including the thickness of vessel wall and the vessel elasticity for which was selected a range of values. The calculation results were finally compared to postoperative results of same patients and discussed. The corresponding outcomes are given in the conclusions section.

RESULTS

The blood flow velocity through the outlet will vary depending on the properties of vessels, including physical properties and thickness of vessel wall. The stress on vessel is lower for smaller values of Young's modulus. The calculated blood flow velocity correlates well with the postoperative results for the Young's modulus of vessels ranging from 0.5 to 1.0 MPa.

CONCLUSIONS

The FSI model has high potential to predict the result of surgery for TAPVC and to estimate the physical properties of pulmonary vein. This model also has potential to guide the strategy for surgical treatment.

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.

Training machine learning models with synthetic data improves the prediction of ventricular origin in outflow tract ventricular arrhythmias

In order to determine the site of origin (SOO) in outflow tract ventricular arrhythmias (OTVAs) before an ablation procedure, several algorithms based on manual identification of electrocardiogram (ECG) features, have been developed. However, the reported accuracy decreases when tested with different datasets. Machine learning algorithms can automatize the process and improve generalization, but their performance is hampered by the lack of large enough OTVA databases. We propose the use of detailed electrophysiological simulations of OTVAs to train a machine learning classification model to predict the ventricular origin of the SOO of ectopic beats. We generated a synthetic database of 12-lead ECGs (2,496 signals) by running multiple simulations from the most typical OTVA SOO in 16 patient-specific geometries. Two types of input data were considered in the classification, raw and feature ECG signals. From the simulated raw 12-lead ECG, we analyzed the contribution of each lead in the predictions, keeping the best ones for the training process. For feature-based analysis, we used entropy-based methods to rank the obtained features. A cross-validation process was included to evaluate the machine learning model. Following, two clinical OTVA databases from different hospitals, including ECGs from 365 patients, were used as test-sets to assess the generalization of the proposed approach. The results show that V2 was the best lead for classification. Prediction of the SOO in OTVA, using both raw signals or features for classification, presented high accuracy values (>0.96). Generalization of the network trained on simulated data was good for both patient datasets (accuracy of 0.86 and 0.84, respectively) and presented better values than using exclusively real ECGs for classification (accuracy of 0.84 and 0.76 for each dataset). The use of simulated ECG data for training machine learning-based classification algorithms is critical to obtain good SOO predictions in OTVA compared to real data alone. The fast implementation and generalization of the proposed methodology may contribute towards its application to a clinical routine.

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

Integrative Computational Modeling of Cardiomyocyte Calcium Handling and Cardiac Arrhythmias: Current Status and Future Challenges

Cardiomyocyte calcium-handling is the key mediator of cardiac excitation-contraction coupling. In the healthy heart, calcium controls both electrical impulse propagation and myofilament cross-bridge cycling, providing synchronous and adequate contraction of cardiac muscles. However, calcium-handling abnormalities are increasingly implicated as a cause of cardiac arrhythmias. Due to the complex, dynamic and localized interactions between calcium and other molecules within a cardiomyocyte, it remains experimentally challenging to study the exact contributions of calcium-handling abnormalities to arrhythmogenesis. Therefore, multiscale computational modeling is increasingly being used together with laboratory experiments to unravel the exact mechanisms of calcium-mediated arrhythmogenesis. This article describes various examples of how integrative computational modeling makes it possible to unravel the arrhythmogenic consequences of alterations to cardiac calcium handling at subcellular, cellular and tissue levels, and discusses the future challenges on the integration and interpretation of such computational data.

Sex Matters: A Comprehensive Comparison of Female and Male Hearts

Cardiovascular disease in women remains under-diagnosed and under-treated. Recent studies suggest that this is caused, at least in part, by the lack of sex-specific diagnostic criteria. While it is widely recognized that the female heart is smaller than the male heart, it has long been ignored that it also has a different microstructural architecture. This has severe implications on a multitude of cardiac parameters. Here, we systematically review and compare geometric, functional, and structural parameters of female and male hearts, both in the healthy population and in athletes. Our study finds that, compared to the male heart, the female heart has a larger ejection fraction and beats at a faster rate but generates a smaller cardiac output. It has a lower blood pressure but produces universally larger contractile strains. Critically, allometric scaling, e.g., by lean body mass, reduces but does not completely eliminate the sex differences between female and male hearts. Our results suggest that the sex differences in cardiac form and function are too complex to be ignored: the female heart is not just a small version of the male heart. When using similar diagnostic criteria for female and male hearts, cardiac disease in women is frequently overlooked by routine exams, and it is diagnosed later and with more severe symptoms than in men. Clearly, there is an urgent need to better understand the female heart and design sex-specific diagnostic criteria that will allow us to diagnose cardiac disease in women equally as early, robustly, and reliably as in men.

Systematic Review Registration

https://livingmatter.stanford.edu/.

Restitution Slope Affects the Outcome of Dominant Frequency Ablation in Persistent Atrial Fibrillation: CUVIA-AF2 Post-Hoc Analysis Based on Computational Modeling Study

Introduction

Although the dominant frequency (DF) localizes the reentrant drivers and the maximal slope of the action potential duration (APD) restitution curve (Smax) reflects the tendency of the wave-break, their interaction has never been studied. We hypothesized that DF ablation has different effects on atrial fibrillation (AF) depending on Smax.

Methods

We studied the DF and Smax in 25 realistic human persistent AF model samples (68% male, 60 ± 10 years old). Virtual AF was induced by ramp pacing measuring Smax, followed by spatiotemporal DF evaluation for 34 s. We assessed the DF ablation effect depending on Smax in both computational modeling and a previous clinical trial, CUVIA-AF (170 patients with persistent AF, 70.6% male, 60 ± 11 years old).

Results

Mean DF had an inverse relationship with Smax regardless of AF acquisition timing (p &lt; 0.001). Virtual DF ablations increased the defragmentation rate compared to pulmonary vein isolation (PVI) alone (p = 0.015), especially at Smax &lt;1 (61.5 vs. 7.7%, p = 0.011). In post-DF ablation defragmentation episodes, DF was significantly higher (p = 0.002), and Smax was lower (p = 0.003) than in episodes without defragmentation. In the post-hoc analysis of CUVIA-AF2, we replicated the inverse relationship between Smax and DF (r = −0.47, p &lt; 0.001), and we observed better rhythm outcomes of clinical DF ablations in addition to a PVI than of empirical PVI at Smax &lt;1 [hazard ratio 0.45, 95% CI (0.22–0.89), p = 0.022; log-rank p = 0.021] but not at ≥ 1 (log-rank p = 0.177).

Conclusion

We found an inverse relationship between DF and Smax and the outcome of DF ablation after PVI was superior at the condition with Smax &lt;1 in both in-silico and clinical trials.

Taking It Personally: 3D Bioprinting a Patient-Specific Cardiac Patch for the Treatment of Heart Failure

Despite a massive global preventative effort, heart failure remains the major cause of death globally. The number of patients requiring a heart transplant, the eventual last treatment option, far outnumbers the available donor hearts, leaving many to deteriorate or die on the transplant waiting list. Treating heart failure by transplanting a 3D bioprinted patient-specific cardiac patch to the infarcted region on the myocardium has been investigated as a potential future treatment. To date, several studies have created cardiac patches using 3D bioprinting; however, testing the concept is still at a pre-clinical stage. A handful of clinical studies have been conducted. However, moving from animal studies to human trials will require an increase in research in this area. This review covers key elements to the design of a patient-specific cardiac patch, divided into general areas of biological design and 3D modelling. It will make recommendations on incorporating anatomical considerations and high-definition motion data into the process of 3D-bioprinting a patient-specific cardiac patch.

Thoroughly Calibrated Modular Agent-Based Model of the Human Cardiovascular and Renal Systems for Blood Pressure Regulation in Health and Disease

Here we present a modular agent-based mathematical model of the human cardiovascular and renal systems. It integrates the previous models primarily developed by A. C. Guyton, F. Karaaslan, K. M. Hallow, and Y. V. Solodyannikov. We performed the model calibration to find an equilibrium state within the normal vital sign ranges for a healthy adult. We verified the model's abilities to reproduce equilibrium states with abnormal physiological values related to different combinations of cardiovascular diseases (such as systemic hypertension, chronic heart failure, pulmonary hypertension, etc.). For the model creation and validation, we involved over 200 scientific studies covering known models of the human cardiovascular and renal functions, biosimulation platforms, and clinical measurements of physiological quantities in normal and pathological conditions. We compiled detailed documentation describing all equations, parameters and variables of the model with justification of all formulas and values. The model is implemented in BioUML and available in the web-version of the software.

3D Cardiac Computational Model for Evaluating the Progression of Myocardial Ischemia in a Supply-Demand Paradigm

In this paper, we present a cardiac computational framework aimed at simulating the effects of ischemia on cardiac potentials and hemodynamics. Proposed cardiac model uses an image based pipeline for modeling and analysis of the ischemic condition in-silico. We compute epicardial potential as well as body surface potential (BSP) for acute ischemic conditions based on data from animal model while varying both local coronary supply and global metabolic demand. Single lead ECG equivalent signal processed from computed BSP is used to drive a lumped hemodynamic model and derive left ventricular dynamics. Computational framework combining 3d structural information from image data and integrating electrophysiology and hemodynamics functionality is aimed to evaluate additional cardiac markers along with conventional electrical markers visible during acute ischemia and give a broader understanding of ischemic manifestation leading to pathophysiological changes. Simulation of epicardial to bodysurface potential followed by estimation of hemodynamic parameters like ejection fraction, contractility, blood pressure, etc, would help to infer subtle changes detectable beyond conventional ST segment changes.

Spatial Changes in the Atrial Fibrillation Wave-Dynamics After Using Antiarrhythmic Drugs: A Computational Modeling Study

Background: We previously reported that a computational modeling-guided antiarrhythmic drug (AAD) test was feasible for evaluating multiple AADs in patients with atrial fibrillation (AF). We explored the anti-AF mechanisms of AADs and spatial change in the AF wave-dynamics by a realistic computational model. Methods: We used realistic computational modeling of 25 AF patients (68% male, 59.8 ± 9.8 years old, 32.0% paroxysmal AF) reflecting the anatomy, histology, and electrophysiology of the left atrium (LA) to characterize the effects of five AADs (amiodarone, sotalol, dronedarone, flecainide, and propafenone). We evaluated the spatial change in the AF wave-dynamics by measuring the mean dominant frequency (DF) and its coefficient of variation [dominant frequency-coefficient of variation (DF-COV)] in 10 segments of the LA. The mean DF and DF-COV were compared according to the pulmonary vein (PV) vs. extra-PV, maximal slope of the restitution curves (Smax), and defragmentation of AF. Results: The mean DF decreased after the administration of AADs in the dose dependent manner (p < 0.001). Under AADs, the DF was significantly lower (p < 0.001) and COV-DF higher (p = 0.003) in the PV than extra-PV region. The mean DF was significantly lower at a high Smax (≥1.4) than a lower Smax condition under AADs. During the episodes of AF defragmentation, the mean DF was lower (p < 0.001), but the COV-DF was higher (p < 0.001) than that in those without defragmentation. Conclusions: The DF reduction with AADs is predominant in the PVs and during a high Smax condition and causes AF termination or defragmentation during a lower DF and spatially unstable (higher DF-COV) condition.

Clinically-Driven Virtual Patient Cohorts Generation: An Application to Aorta

The combination of machine learning methods together with computational modeling and simulation of the cardiovascular system brings the possibility of obtaining very valuable information about new therapies or clinical devices through in-silico experiments. However, the application of machine learning methods demands access to large cohorts of patients. As an alternative to medical data acquisition and processing, which often requires some degree of manual intervention, the generation of virtual cohorts made of synthetic patients can be automated. However, the generation of a synthetic sample can still be computationally demanding to guarantee that it is clinically meaningful and that it reflects enough inter-patient variability. This paper addresses the problem of generating virtual patient cohorts of thoracic aorta geometries that can be used for in-silico trials. In particular, we focus on the problem of generating a cohort of patients that meet a particular clinical criterion, regardless the access to a reference sample of that phenotype. We formalize the problem of clinically-driven sampling and assess several sampling strategies with two goals, sampling efficiency, i.e., that the generated individuals actually belong to the target population, and that the statistical properties of the cohort can be controlled. Our results show that generative adversarial networks can produce reliable, clinically-driven cohorts of thoracic aortas with good efficiency. Moreover, non-linear predictors can serve as an efficient alternative to the sometimes expensive evaluation of anatomical or functional parameters of the organ of interest.

Modelling sudden cardiac death risks factors in patients with coronavirus disease of 2019: the hydroxychloroquine and azithromycin case

AIMS

Coronavirus disease of 2019 (COVID-19) has rapidly become a worldwide pandemic. Many clinical trials have been initiated to fight the disease. Among those, hydroxychloroquine and azithromycin had initially been suggested to improve clinical outcomes. Despite any demonstrated beneficial effects, they are still in use in some countries but have been reported to prolong the QT interval and induce life-threatening arrhythmia. Since a significant proportion of the world population may be treated with such COVID-19 therapies, evaluation of the arrhythmogenic risk of any candidate drug is needed.

METHODS AND RESULTS

Using the O'Hara-Rudy computer model of human ventricular wedge, we evaluate the arrhythmogenic potential of clinical factors that can further alter repolarization in COVID-19 patients in addition to hydroxychloroquine (HCQ) and azithromycin (AZM) such as tachycardia, hypokalaemia, and subclinical to mild long QT syndrome. Hydroxychloroquine and AZM drugs have little impact on QT duration and do not induce any substrate prone to arrhythmia in COVID-19 patients with normal cardiac repolarization reserve. Nevertheless, in every tested condition in which this reserve is reduced, the model predicts larger electrocardiogram impairments, as with dofetilide. In subclinical conditions, the model suggests that mexiletine limits the deleterious effects of AZM and HCQ.

CONCLUSION

By studying the HCQ and AZM co-administration case, we show that the easy-to-use O'Hara-Rudy model can be applied to assess the QT-prolongation potential of off-label drugs, beyond HCQ and AZM, in different conditions representative of COVID-19 patients and to evaluate the potential impact of additional drug used to limit the arrhythmogenic risk.

Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning

We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.

Computational Modeling for Antiarrhythmic Drugs for Atrial Fibrillation According to Genotype

Background: The efficacy of antiarrhythmic drugs (AAD) can vary in patients with atrial fibrillation (AF), and the PITX2 gene affects the responsiveness of AADs. We explored the virtual AAD (V-AAD) responses between wild-type and PITX2 ^+/--deficient AF conditions by realistic in silico AF modeling. Methods: We tested the V-AADs in AF modeling integrated with patients' 3D-computed tomography and 3D-electroanatomical mapping, acquired in 25 patients (68% male, 59.8 ± 9.8 years old, 32.0% paroxysmal type). The ion currents for the PITX2 ^+/- deficiency and each AAD (amiodarone, sotalol, dronedarone, flecainide, and propafenone) were defined based on previous publications. Results: We compared the wild-type and PITX2 ^+/- deficiency in terms of the action potential duration (APD₉₀), conduction velocity (CV), maximal slope of restitution (Smax), and wave-dynamic parameters, such as the dominant frequency (DF), phase singularities (PS), and AF termination rates according to the V-AADs. The PITX2 ^+/--deficient model exhibited a shorter APD₉₀ (p < 0.001), a lower Smax (p < 0.001), mean DF (p = 0.012), PS number (p < 0.001), and a longer AF cycle length (AFCL, p = 0.011). Five V-AADs changed the electrophysiology in a dose-dependent manner. AAD-induced AFCL lengthening (p < 0.001) and reductions in the CV (p = 0.033), peak DF (p < 0.001), and PS number (p < 0.001) were more significant in PITX2 ^+/--deficient than wild-type AF. PITX2 ^+/--deficient AF was easier to terminate with class IC AADs than the wild-type AF (p = 0.018). Conclusions: The computational modeling-guided AAD test was feasible for evaluating the efficacy of multiple AADs in patients with AF. AF wave-dynamic and electrophysiological characteristics are different among the PITX2-deficient and the wild-type genotype models.

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.

Multimodal cardiovascular model for hemodynamic analysis: Simulation study on mitral valve disorders

Valvular heart diseases are a prevalent cause of cardiovascular morbidity and mortality worldwide, affecting a wide spectrum of the population. In-silico modeling of the cardiovascular system has recently gained recognition as a useful tool in cardiovascular research and clinical applications. Here, we present an in-silico cardiac computational model to analyze the effect and severity of valvular disease on general hemodynamic parameters. We propose a multimodal and multiscale cardiovascular model to simulate and understand the progression of valvular disease associated with the mitral valve. The developed model integrates cardiac electrophysiology with hemodynamic modeling, thus giving a broader and holistic understanding of the effect of disease progression on various parameters like ejection fraction, cardiac output, blood pressure, etc., to assess the severity of mitral valve disorders, naming Mitral Stenosis and Mitral Regurgitation. The model mimics an adult cardiovascular system, comprising a four-chambered heart with systemic, pulmonic circulation. The simulation of the model output comprises regulated pressure, volume, and flow for each heart chamber, valve dynamics, and Photoplethysmogram signal for normal physiological as well as pathological conditions due to mitral valve disorders. The generated physiological parameters are in agreement with published data. Additionally, we have related the simulated left atrium and ventricle dimensions, with the enlargement and hypertrophy in the cardiac chambers of patients with mitral valve disorders, using their Electrocardiogram available in Physionet PTBI dataset. The model also helps to create 'what if' scenarios and relevant analysis to study the effect in different hemodynamic parameters for stress or exercise like conditions.

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.

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.

Using cardiac ionic cell models to interpret clinical data

For over 100 years cardiac electrophysiology has been measured in the clinic. The electrical signals that can be measured span from noninvasive ECG and body surface potentials measurements through to detailed invasive measurements of local tissue electrophysiology. These electrophysiological measurements form a crucial component of patient diagnosis and monitoring; however, it remains challenging to quantitatively link changes in clinical electrophysiology measurements to biophysical cellular function. Multi-scale biophysical computational models represent one solution to this problem. These models provide a formal framework for linking cellular function through to emergent whole organ function and routine clinical diagnostic signals. In this review, we describe recent work on the use of computational models to interpret clinical electrophysiology signals. We review the simulation of human cardiac myocyte electrophysiology in the atria and the ventricles and how these models are being used to link organ scale function to patient disease mechanisms and therapy response in patients receiving implanted defibrillators, \cardiac resynchronisation therapy or suffering from atrial fibrillation and ventricular tachycardia. There is a growing use of multi-scale biophysical models to interpret clinical data. This allows cardiologists to link clinical observations with cellular mechanisms to better understand cardiopathophysiology and identify novel treatment strategies. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Cardiac multi-scale investigation of the right and left ventricle ex vivo: a review

The heart is a complex multi-scale system composed of components integrated at the subcellular, cellular, tissue and organ levels. The myocytes, the contractile elements of the heart, form a complex three-dimensional (3D) network which enables propagation of the electrical signal that triggers the contraction to efficiently pump blood towards the whole body. Cardiovascular diseases (CVDs), a major cause of mortality in developed countries, often lead to cardiovascular remodeling affecting cardiac structure and function at all scales, from myocytes and their surrounding collagen matrix to the 3D organization of the whole heart. As yet, there is no consensus as to how the myocytes are arranged and packed within their connective tissue matrix, nor how best to image them at multiple scales. Cardiovascular imaging is routinely used to investigate cardiac structure and function as well as for the evaluation of cardiac remodeling in CVDs. For a complete understanding of the relationship between structural remodeling and cardiac dysfunction in CVDs, multi-scale imaging approaches are necessary to achieve a detailed description of ventricular architecture along with cardiac function. In this context, ventricular architecture has been extensively studied using a wide variety of imaging techniques: ultrasound (US), optical coherence tomography (OCT), microscopy (confocal, episcopic, light sheet, polarized light), magnetic resonance imaging (MRI), micro-computed tomography (micro-CT) and, more recently, synchrotron X-ray phase contrast imaging (SR X-PCI). Each of these techniques have their own set of strengths and weaknesses, relating to sample size, preparation, resolution, 2D/3D capabilities, use of contrast agents and possibility of performing together with in vivo studies. Therefore, the combination of different imaging techniques to investigate the same sample, thus taking advantage of the strengths of each method, could help us to extract the maximum information about ventricular architecture and function. In this review, we provide an overview of available and emerging cardiovascular imaging techniques for assessing myocardial architecture ex vivo and discuss their utility in being able to quantify cardiac remodeling, in CVDs, from myocyte to whole organ.

Biomechanics of infarcted left ventricle: a review of modelling

Mathematical modelling in biomechanics of infarcted left ventricle (LV) serves as an indispensable tool for remodelling mechanism exploration, LV biomechanical property estimation and therapy assessment after myocardial infarction (MI). However, a review of mathematical modelling after MI has not been seen in the literature so far. In the paper, a systematic review of mathematical models in biomechanics of infarcted LV was established. The models include comprehensive cardiovascular system model, essential LV pressure-volume and stress-stretch models, constitutive laws for passive myocardium and scars, tension models for active myocardium, collagen fibre orientation optimization models, fibroblast and collagen fibre growth/degradation models and integrated growth-electro-mechanical model after MI. The primary idea, unique characteristics and key equations of each model were identified and extracted. Discussions on the models were provided and followed research issues on them were addressed. Considerable improvements in the cardiovascular system model, LV aneurysm model, coupled agent-based models and integrated electro-mechanical-growth LV model are encouraged. Substantial attention should be paid to new constitutive laws with respect to stress-stretch curve and strain energy function for infarcted passive myocardium, collagen fibre orientation optimization in scar, cardiac rupture and tissue damage and viscoelastic effect post-MI in the future.

Cardiac computational modelling

Cardiovascular diseases currently have a major social and economic impact, constituting one of the leading causes of mortality and morbidity. Personalized computational models of the heart are demonstrating their usefulness both to help understand the mechanisms underlying cardiac disease, and to optimize their treatment and predict the patient's response. Within this framework, the Spanish Research Network for Cardiac Computational Modelling (VHeart-SN) has been launched. The general objective of the VHeart-SN network is the development of an integrated, modular and multiscale multiphysical computational model of the heart. This general objective is addressed through the following specific objectives: a) to integrate the different numerical methods and models taking into account the specificity of patients; b) to assist in advancing knowledge of the mechanisms associated with cardiac and vascular diseases; and c) to support the application of different personalized therapies. This article presents the current state of cardiac computational modelling and different scientific works conducted by the members of the network to gain greater understanding of the characteristics and usefulness of these models.

Combination of "generalized Trotter operator splitting" and "quadratic adaptive algorithm" method for tradeoff among speedup, stability, and accuracy in the Markov chain model of sodium ion channels in the ventricular cell model

The fast hybrid operator splitting (HOS) and stable uniformization (UNI) methods have been proposed to save computation cost and enhance stability for Markov chain model in cardiac cell simulations. Moreover, Chen-Chen-Luo's quadratic adaptive algorithm (CCL) combined with HOS or UNI was used to improve the tradeoff between speedup and stability, but without considering accuracy. To compromise among stability, acceleration, and accuracy, we propose a generalized Trotter operator splitting (GTOS) method combined with CCL independent of the asymptotic property of a particular ion-channel model. Due to the accuracy underestimation of the mixed root mean square error (MRMSE) method, threshold root mean square error (TRMSE) is proposed to evaluate computation accuracy. With the fixed time-step RK4 as a reference, the second-order GTOS combined with CCL (30.8-fold speedup) for the wild-type Markov chain model with nine states (WT-9 model) or (7.4-fold) for the wild-type Markov chain model with eight states (WT-8 model) is faster than UNI combined with CCL (15.6-fold) for WT-9 model or (1.2-fold) for WT-8 model, separately. Besides, the second-order GTOS combined with CCL has 3.81% TRMSE for WT-9 model or 4.32% TRMSE for WT-8 model more accurate than 72.43% TRMSE for WT-9 model or 136.17% TRMSE for WT-8 model of HOS combined with CCL. To compromise speedup and accuracy, low-order GTOS combined with CCL is suggested to have the advantages of high precision and low computation cost. For high-accuracy requirements, high-order GTOS combined with CCL is recommended. Graphical abstract.

Myocardial Fluid Balance and Pathophysiology of Myocardial Edema in Coronary Artery Bypass Grafting

Myocardial edema is one of the most common complications of coronary artery bypass grafting (CABG) that is linearly related to many coronary artery diseases. Myocardial edema can cause several consequences including systolic dysfunction, diastolic dysfunction, arrhythmia, and cardiac tissue fibrosis that can increase mortality in CABG. Understanding myocardial fluid balance and tissue and systemic fluid regulation is crucial in order to ultimately link how coronary artery bypass grafting can cause myocardial edema in such a setting. The identification of susceptible patients by using imaging modalities is still challenging. Future studies about the technique of imaging modalities, examination protocols, prevention, and treatment of myocardial edema should be carried out, in order to limit myocardial edema occurrence and prevent complications.

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.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

How personalized heart modeling can help treatment of lethal arrhythmias: A focus on ventricular tachycardia ablation strategies in post-infarction patients

Precision Cardiology is a targeted strategy for cardiovascular disease prevention and treatment that accounts for individual variability. Computational heart modeling is one of the novel approaches that have been developed under the umbrella of Precision Cardiology. Personalized computational modeling of patient hearts has made strides in the development of models that incorporate the individual geometry and structure of the heart as well as other patient-specific information. Of these developments, one of the potentially most impactful is the research aimed at noninvasively predicting the targets of ablation of lethal arrhythmia, ventricular tachycardia (VT), using patient-specific models. The approach has been successfully applied to patients with ischemic cardiomyopathy in proof-of-concept studies. The goal of this paper is to review the strategies for computational VT ablation guidance in ischemic cardiomyopathy patients, from model developments to the intricacies of the actual clinical application. To provide context in describing the road these computational modeling applications have undertaken, we first review the state of the art in VT ablation in the clinic, emphasizing the benefits that personalized computational prediction of ablation targets could bring to the clinical electrophysiology practice. This article is characterized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine.