Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

Patient-specific multi-physics simulations of fibrotic changes in left atrial tissue mechanics impact on hemodynamics

Stroke is a leading cause of death and disability worldwide. Atrial myopathy, including fibrosis, is associated with an increased risk of ischemic stroke, but the mechanisms underlying this association are poorly understood. Fibrosis modifies myocardial structure, impairing electrical propagation and tissue biomechanics, and creating stagnant flow regions where clots could form. Fibrosis can be mapped non-invasively using late gadolinium enhancement magnetic resonance imaging (LGE-MRI). However, fibrosis maps are not currently incorporated into stroke risk calculations or computational electro-mechano-fluidic models. We present multi-physics simulations of left atrial (LA) myocardial motion and hemodynamics using patient-specific anatomies and fibrotic maps from LGE-MRI. We modify tissue stiffness and active tension generation in fibrotic regions and investigate how these changes affect LA flow for different fibrotic burdens. We find that fibrotic regions and, to a lesser extent, non-fibrotic regions experience reduced myocardial strain, resulting in decreased LA emptying fraction consistent with clinical observations. Both fibrotic tissue stiffening and hypocontractility independently reduce LA function, but together, these two alterations cause more pronounced effects than either one alone. Fibrosis significantly alters flow patterns throughout the atrial chamber, and particularly, the filling and emptying jets of the left atrial appendage (LAA). The effects of fibrosis in LA flow are largely captured by the concomitant changes in LA emptying fraction except inside the LAA, where a multi-factorial behavior is observed. This work illustrates how high-fidelity, multi-physics models can be used to study thrombogenesis mechanisms in a patient-specific manner, shedding light onto the link between atrial fibrosis and ischemic stroke.

Key points

Left atrial (LA) fibrosis is associated with arrhythmogenesis and increased risk of ischemic stroke; its extent and pattern can be quantified on a patient-specific basis using late gadolinium enhancement magnetic resonance imaging.Current stroke risk prediction tools have limited personalization, and their accuracy could be improvedfib by incorporating patient-specific information like fibrotic maps and hemodynamic patterns.We present the first electro-mechano-fluidic multi-physics computational simulations of LA flow, including fibrosis and anatomies from medical imaging.Mechanical changes in fibrotic tissue impair global LA motion, decreasing LA and left atrial appendage (LAA) emptying fractions, especially in subjects with higher fibrosis burdens.Fibrotic-mediated LA motion impairment alters LA and LAA flow near the endocardium and the whole cavity, ultimately leading to more stagnant blood regions in the LAA.

Whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations

Cardiac digital twins provide a physics and physiology informed framework to deliver personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. We use Latent Neural Ordinary Differential Equations (LNODEs) to learn the pressure-volume dynamics of a heart failure patient. Our surrogate model is trained from 400 simulations while accounting for 43 parameters describing cell-to-organ cardiac electromechanics and cardiovascular hemodynamics. LNODEs provide a compact representation of the 3D-0D model in a latent space by means of an Artificial Neural Network that retains only 3 hidden layers with 13 neurons per layer and allows for numerical simulations of cardiac function on a single processor. We employ LNODEs to perform global sensitivity analysis and parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor.

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

Background and Objective

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

Methods

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

Key Content and Findings

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

Conclusions

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

Differential effects of mechano-electric feedback mechanisms on whole-heart activation, repolarization, and tension

The human heart is subject to highly variable amounts of strain during day-to-day activities and needs to adapt to a wide range of physiological demands. This adaptation is driven by an autoregulatory loop that includes both electrical and the mechanical components. In particular, mechanical forces are known to feed back into the cardiac electrophysiology system, which can result in pro- and anti-arrhythmic effects. Despite the widespread use of computational modelling and simulation for cardiac electrophysiology research, the majority of in silico experiments ignore this mechano-electric feedback entirely due to the high computational cost associated with solving cardiac mechanics. In this study, we therefore use an electromechanically coupled whole-heart model to investigate the differential and combined effects of electromechanical feedback mechanisms with a focus on their physiological relevance during sinus rhythm. In particular, we consider troponin-bound calcium, the effect of deformation on the tissue diffusion tensor, and stretch-activated channels. We found that activation of the myocardium was only significantly affected when including deformation into the diffusion term of the monodomain equation. Repolarization, on the other hand, was influenced by both troponin-bound calcium and stretch-activated channels and resulted in steeper repolarization gradients in the atria. The latter also caused afterdepolarizations in the atria. Due to its central role for tension development, calcium bound to troponin affected stroke volume and pressure. In conclusion, we found that mechano-electric feedback changes activation and repolarization patterns throughout the heart during sinus rhythm and lead to a markedly more heterogeneous electrophysiological substrate. KEY POINTS: The electrophysiological and mechanical function of the heart are tightly interrelated by excitation-contraction coupling (ECC) in the forward direction and mechano-electric feedback (MEF) in the reverse direction. While ECC is considered in many state-of-the-art computational models of cardiac electromechanics, less is known about the effect of different MEF mechanisms. Accounting for calcium bound to troponin increases stroke volume and delays repolarization. Geometry-mediated MEF leads to more heterogeneous activation and repolarization with steeper gradients. Both effects combine in an additive way. Non-selective stretch-activated channels as an additional MEF mechanism lead to heterogeneous diastolic transmembrane voltage, higher developed tension and delayed repolarization or afterdepolarizations in highly stretched parts of the atria. The differential and combined effects of these three MEF mechanisms during sinus rhythm activation in a human four-chamber heart model may have implications for arrhythmogenesis, both in terms of substrate (repolarization gradients) and triggers (ectopy).

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

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

Turbulent blood dynamics in the left heart in the presence of mitral regurgitation: a computational study based on multi-series cine-MRI

In this work, we performed a computational image-based study of blood dynamics in the whole left heart, both in a healthy subject and in a patient with mitral valve regurgitation. We elaborated multi-series cine-MRI with the aim of reconstructing the geometry and the corresponding motion of left ventricle, left atrium, mitral and aortic valves, and aortic root of the subjects. This allowed us to prescribe such motion to computational blood dynamics simulations where, for the first time, the whole left heart motion of the subject is considered, allowing us to obtain reliable subject-specific information. The final aim is to investigate and compare between the subjects the occurrence of turbulence and the risk of hemolysis and of thrombi formation. In particular, we modeled blood with the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian framework, with a large eddy simulation model to describe the transition to turbulence and a resistive method to manage the valve dynamics, and we used a finite element discretization implemented in an in-house code for the numerical solution.

A comprehensive mathematical model for cardiac perfusion

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes-Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.

Personalized biomechanical insights in atrial fibrillation: opportunities & challenges

INTRODUCTION

Atrial fibrillation (AF) is an increasingly prevalent and significant worldwide health problem. Manifested as an irregular atrial electrophysiological activation, it is associated with many serious health complications. AF affects the biomechanical function of the heart as contraction follows the electrical activation, subsequently leading to reduced blood flow. The underlying mechanisms behind AF are not fully understood, but it is known that AF is highly correlated with the presence of atrial fibrosis, and with a manifold increase in risk of stroke.

AREAS COVERED

In this review, we focus on biomechanical aspects in atrial fibrillation, current and emerging use of clinical images, and personalized computational models. We also discuss how these can be used to provide patient-specific care.

EXPERT OPINION

Understanding the connection betweenatrial fibrillation and atrial remodeling might lead to valuable understanding of stroke and heart failure pathophysiology. Established and emerging imaging modalities can bring us closer to this understanding, especially with continued advancements in processing accuracy, reproducibility, and clinical relevance of the associated technologies. Computational models of cardiac electromechanics can be used to glean additional insights on the roles of AF and remodeling in heart function.

Cell to whole organ global sensitivity analysis on a four-chamber heart electromechanics model using Gaussian processes emulators

Cardiac pump function arises from a series of highly orchestrated events across multiple scales. Computational electromechanics can encode these events in physics-constrained models. However, the large number of parameters in these models has made the systematic study of the link between cellular, tissue, and organ scale parameters to whole heart physiology challenging. A patient-specific anatomical heart model, or digital twin, was created. Cellular ionic dynamics and contraction were simulated with the Courtemanche-Land and the ToR-ORd-Land models for the atria and the ventricles, respectively. Whole heart contraction was coupled with the circulatory system, simulated with CircAdapt, while accounting for the effect of the pericardium on cardiac motion. The four-chamber electromechanics framework resulted in 117 parameters of interest. The model was broken into five hierarchical sub-models: tissue electrophysiology, ToR-ORd-Land model, Courtemanche-Land model, passive mechanics and CircAdapt. For each sub-model, we trained Gaussian processes emulators (GPEs) that were then used to perform a global sensitivity analysis (GSA) to retain parameters explaining 90% of the total sensitivity for subsequent analysis. We identified 45 out of 117 parameters that were important for whole heart function. We performed a GSA over these 45 parameters and identified the systemic and pulmonary peripheral resistance as being critical parameters for a wide range of volumetric and hemodynamic cardiac indexes across all four chambers. We have shown that GPEs provide a robust method for mapping between cellular properties and clinical measurements. This could be applied to identify parameters that can be calibrated in patient-specific models or digital twins, and to link cellular function to clinical indexes.

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

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

Mechanoelectric effects in healthy cardiac function and under Left Bundle Branch Block pathology

Mechanoelectric feedback (MEF) in the heart operates through several mechanisms which serve to regulate cardiac function. Stretch activated channels (SACs) in the myocyte membrane open in response to cell lengthening, while tension generation depends on stretch, shortening velocity, and calcium concentration. How all of these mechanisms interact and their effect on cardiac output is still not fully understood. We sought to gauge the acute importance of the different MEF mechanisms on heart function. An electromechanical computer model of a dog heart was constructed, using a biventricular geometry of 500K tetrahedral elements. To describe cellular behavior, we used a detailed ionic model to which a SAC model and an active tension model, dependent on stretch and shortening velocity and with calcium sensitivity, were added. Ventricular inflow and outflow were connected to the CircAdapt model of cardiovascular circulation. Pressure-volume loops and activation times were used for model validation. Simulations showed that SACs did not affect acute mechanical response, although if their trigger level was decreased sufficiently, they could cause premature excitations. The stretch dependence of tension had a modest effect in reducing the maximum stretch, and stroke volume, while shortening velocity had a much bigger effect on both. MEF served to reduce the heterogeneity in stretch while increasing tension heterogeneity. In the context of left bundle branch block, a decreased SAC trigger level could restore cardiac output by reducing the maximal stretch when compared to cardiac resynchronization therapy. MEF is an important aspect of cardiac function and could potentially mitigate activation problems.

Computational analysis of ventricular mechanics in hypertrophic cardiomyopathy patients

Hypertrophic cardiomyopathy (HCM) is a genetic heart disease that is associated with many pathological features, such as a reduction in global longitudinal strain (GLS), myofiber disarray and hypertrophy. The effects of these features on left ventricle (LV) function are, however, not clear in two phenotypes of HCM, namely, obstructive and non-obstructive. To address this issue, we developed patient-specific computational models of the LV using clinical measurements from 2 female HCM patients and a control subject. Left ventricular mechanics was described using an active stress formulation and myofiber disarray was described using a structural tensor in the constitutive models. Unloaded LV configuration for each subject was first determined from their respective end-diastole LV geometries segmented from the cardiac magnetic resonance images, and an empirical single-beat estimation of the end-diastolic pressure volume relationship. The LV was then connected to a closed-loop circulatory model and calibrated using the clinically measured LV pressure and volume waveforms, peak GLS and blood pressure. Without consideration of myofiber disarray, peak myofiber tension was found to be lowest in the obstructive HCM subject (60 kPa), followed by the non-obstructive subject (242 kPa) and the control subject (375 kPa). With increasing myofiber disarray, we found that peak tension has to increase in the HCM models to match the clinical measurements. In the obstructive HCM patient, however, peak tension was still depressed (cf. normal subject) at the largest degree of myofiber disarray found in the clinic. The computational modeling workflow proposed here can be used in future studies with more HCM patient data.

The Impact of Standard Ablation Strategies for Atrial Fibrillation on Cardiovascular Performance in a Four-Chamber Heart Model

PURPOSE

Atrial fibrillation is one of the most frequent cardiac arrhythmias in the industrialized world and ablation therapy is the method of choice for many patients. However, ablation scars alter the electrophysiological activation and the mechanical behavior of the affected atria. Different ablation strategies with the aim to terminate atrial fibrillation and prevent its recurrence exist but their impact on the performance of the heart is often neglected.

METHODS

In this work, we present a simulation study analyzing five commonly used ablation scar patterns and their combinations in the left atrium regarding their impact on the pumping function of the heart using an electromechanical whole-heart model. We analyzed how the altered atrial activation and increased stiffness due to the ablation scars affect atrial as well as ventricular contraction and relaxation.

RESULTS

We found that systolic and diastolic function of the left atrium is impaired by ablation scars and that the reduction of atrial stroke volume of up to 11.43% depends linearly on the amount of inactivated tissue. Consequently, the end-diastolic volume of the left ventricle, and thus stroke volume, was reduced by up to 1.4 and 1.8%, respectively. During ventricular systole, left atrial pressure was increased by up to 20% due to changes in the atrial activation sequence and the stiffening of scar tissue.

CONCLUSION

This study provides biomechanical evidence that atrial ablation has acute effects not only on atrial contraction but also on ventricular performance. Therefore, the position and extent of ablation scars is not only important for the termination of arrhythmias but is also determining long-term pumping efficiency. If confirmed in larger cohorts, these results have the potential to help tailoring ablation strategies towards minimal global cardiovascular impairment.

Calibration of Cohorts of Virtual Patient Heart Models Using Bayesian History Matching

Previous patient-specific model calibration techniques have treated each patient independently, making the methods expensive for large-scale clinical adoption. In this work, we show how we can reuse simulations to accelerate the patient-specific model calibration pipeline. To represent anatomy, we used a Statistical Shape Model and to represent function, we ran electrophysiological simulations. We study the use of 14 biomarkers to calibrate the model, training one Gaussian Process Emulator (GPE) per biomarker. To fit the models, we followed a Bayesian History Matching (BHM) strategy, wherein each iteration a region of the parameter space is ruled out if the emulation with that set of parameter values produces is "implausible". We found that without running any extra simulations we can find 87.41% of the non-implausible parameter combinations. Moreover, we showed how reducing the uncertainty of the measurements from 10 to 5% can reduce the final parameter space by 6 orders of magnitude. This innovation allows for a model fitting technique, therefore reducing the computational load of future biomedical studies.

Weakly supervised inference of personalized heart meshes based on echocardiography videos

Echocardiography provides recordings of the heart chamber size and function and is a central tool for non-invasive diagnosis of heart diseases. It produces high-dimensional video data with substantial stochasticity in the measurements, which frequently prove difficult to interpret. To address this challenge, we propose an automated framework to enable the inference of a high resolution personalized 4D (3D plus time) surface mesh of the cardiac structures from 2D echocardiography video data. Inferring such shape models arises as a key step towards accurate personalized simulation that enables an automated assessment of the cardiac chamber morphology and function. The proposed method is trained using only unpaired echocardiography and heart mesh videos to find a mapping between these distinct visual domains in a self-supervised manner. The resulting model produces personalized 4D heart meshes, which exhibit a high correspondence with the input echocardiography videos. Furthermore, the 4D heart meshes enable the automatic extraction of echocardiographic variables, such as ejection fraction, myocardial muscle mass, and volumetric changes of chamber volumes over time with high temporal resolution.

Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models

Computational Fluid Dynamics (CFD) is used to assist in designing artificial valves and planning procedures, focusing on local flow features. However, assessing the impact on overall cardiovascular function or predicting longer-term outcomes may requires more comprehensive whole heart CFD models. Fitting such models to patient data requires numerous computationally expensive simulations, and depends on specific clinical measurements to constrain model parameters, hampering clinical adoption. Surrogate models can help to accelerate the fitting process while accounting for the added uncertainty. We create a validated patient-specific four-chamber heart CFD model based on the Navier-Stokes-Brinkman (NSB) equations and test Gaussian Process Emulators (GPEs) as a surrogate model for performing a variance-based global sensitivity analysis (GSA). GSA identified preload as the dominant driver of flow in both the right and left side of the heart, respectively. Left-right differences were seen in terms of vascular outflow resistances, with pulmonary artery resistance having a much larger impact on flow than aortic resistance. Our results suggest that GPEs can be used to identify parameters in personalized whole heart CFD models, and highlight the importance of accurate preload measurements.

Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration

Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.

A coupling strategy for a first 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

A key factor governing the mechanical performance of the heart is the bidirectional coupling with the vascular system, where alterations in vascular properties modulate the pulsatile load imposed on the heart. Current models of cardiac electromechanics (EM) use simplified 0D representations of the vascular system when coupling to anatomically accurate 3D EM models is considered. However, these ignore important effects related to pulse wave transmission. Accounting for these effects requires 1D models, but a 3D-1D coupling remains challenging. In this work, we propose a novel, stable strategy to couple a 3D cardiac EM model to a 1D model of blood flow in the largest systemic arteries. For the first time, a personalised coupled 3D-1D model of left ventricle and arterial system is built and used in numerical benchmarks to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system's physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our first 3D-1D coupled model is shown to be efficient and robust, with negligible additional computational costs compared to 3D-0D models. We further demonstrate that the calibrated 3D-1D model produces simulated data that match with clinical data under baseline conditions, and that known physiological responses to alterations in vascular resistance and stiffness are correctly replicated. Thus, using our coupled 3D-1D model will be beneficial in modelling studies investigating wave propagation phenomena.

Dyssynchronous Left Ventricular Activation is Insufficient for the Breakdown of Wringing Rotation

Cardiac resynchronization therapy is a valuable tool to restore left ventricular function in patients experiencing dyssynchronous ventricular activation. However, the non-responder rate is still as high as 40%. Recent studies suggest that left ventricular torsion or specifically the lack thereof might be a good predictor for the response of cardiac resynchronization therapy. Since left ventricular torsion is governed by the muscle fiber orientation and the heterogeneous electromechanical activation of the myocardium, understanding the relation between these components and the ability to measure them is vital. To analyze if locally altered electromechanical activation in heart failure patients affects left ventricular torsion, we conducted a simulation study on 27 personalized left ventricular models. Electroanatomical maps and late gadolinium enhanced magnetic resonance imaging data informed our in-silico model cohort. The angle of rotation was evaluated in every material point of the model and averaged values were used to classify the rotation as clockwise or counterclockwise in each segment and sector of the left ventricle. 88% of the patient models (n = 24) were classified as a wringing rotation and 12% (n = 3) as a rigid-body-type rotation. Comparison to classification based on in vivo rotational NOGA XP maps showed no correlation. Thus, isolated changes of the electromechanical activation sequence in the left ventricle are not sufficient to reproduce the rotation pattern changes observed in vivo and suggest that further patho-mechanisms are involved.

An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an isochoric part is a very common approach. However, the finite element analysis of such problems often suffers from severe volumetric locking effects and numerical instabilities. In this paper, we present novel methods to overcome volumetric locking phenomena for using stabilized P1-P1 elements. We introduce different stabilization techniques and demonstrate the high robustness and computational efficiency of the chosen methods. In two benchmark problems from the literature as well as an advanced application to cardiac electromechanics, we compare the approach to standard linear elements and show the accuracy and versatility of the methods to simulate anisotropic, nearly and fully incompressible materials. We demonstrate the potential of this numerical framework to accelerate accurate simulations of biological tissues to the extent of enabling patient-specific parameterization studies, where numerous forward simulations are required.

Impact of Intraventricular Septal Fiber Orientation on Cardiac Electromechanical Function

Cardiac fiber direction is an important factor determining the propagation of electrical activity, as well as the development of mechanical force. In this article, we imaged the ventricles of several species with special attention to the intraventricular septum to determine the functional consequences of septal fiber organization. First, we identified a dual-layer organization of the fiber orientation in the intraventricular septum of ex vivo sheep hearts using diffusion tensor imaging at high field MRI. To expand the scope of the results, we investigated the presence of a similar fiber organization in five mammalian species (rat, canine, pig, sheep, and human) and highlighted the continuity of the layer with the moderator band in large mammalian species. We implemented the measured septal fiber fields in three-dimensional electromechanical computer models to assess the impact of the fiber orientation. The downward fibers produced a diamond activation pattern superficially in the right ventricle. Electromechanically, there was very little change in pressure volume loops although the stress distribution was altered. In conclusion, we clarified that the right ventricular septum has a downwardly directed superficial layer in larger mammalian species, which can have modest effects on stress distribution.

NEW & NOTEWORTHY A dual-layer organization of the fiber orientation in the intraventricular septum was identified in ex vivo hearts of large mammals. The RV septum has a downwardly directed superficial layer that is continuous with the moderator band. Electrically, it produced a diamond activation pattern. Electromechanically, little change in pressure volume loops were noticed but stress distribution was altered. Fiber distribution derived from diffusion tensor imaging should be considered for an accurate strain and stress analysis.

An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics—A Multi-Fidelity Approach for Personalising Active Mechanics

Personalised computer models of cardiac function, referred to as cardiac digital twins, are envisioned to play an important role in clinical precision therapies of cardiovascular diseases. A major obstacle hampering clinical translation involves the significant computational costs involved in the personalisation of biophysically detailed mechanistic models that require the identification of high-dimensional parameter vectors. An important aspect to identify in electromechanics (EM) models are active mechanics parameters that govern cardiac contraction and relaxation. In this study, we present a novel, fully automated, and efficient approach for personalising biophysically detailed active mechanics models using a two-step multi-fidelity solution. In the first step, active mechanical behaviour in a given 3D EM model is represented by a purely phenomenological, low-fidelity model, which is personalised at the organ scale by calibration to clinical cavity pressure data. Then, in the second step, median traces of nodal cellular active stress, intracellular calcium concentration, and fibre stretch are generated and utilised to personalise the desired high-fidelity model at the cellular scale using a 0D model of cardiac EM. Our novel approach was tested on a cohort of seven human left ventricular (LV) EM models, created from patients treated for aortic coarctation (CoA). Goodness of fit, computational cost, and robustness of the algorithm against uncertainty in the clinical data and variations of initial guesses were evaluated. We demonstrate that our multi-fidelity approach facilitates the personalisation of a biophysically detailed active stress model within only a few (2 to 4) expensive 3D organ-scale simulations—a computational effort compatible with clinical model applications.

A Fully-Coupled Electro-Mechanical Whole-Heart Computational Model: Influence of Cardiac Contraction on the ECG

The ECG is one of the most commonly used non-invasive tools to gain insights into the electrical functioning of the heart. It has been crucial as a foundation in the creation and validation of in silico models describing the underlying electrophysiological processes. However, so far, the contraction of the heart and its influences on the ECG have mainly been overlooked in in silico models. As the heart contracts and moves, so do the electrical sources within the heart responsible for the signal on the body surface, thus potentially altering the ECG. To illuminate these aspects, we developed a human 4-chamber electro-mechanically coupled whole heart in silico model and embedded it within a torso model. Our model faithfully reproduces measured 12-lead ECG traces, circulatory characteristics, as well as physiological ventricular rotation and atrioventricular valve plane displacement. We compare our dynamic model to three non-deforming ones in terms of standard clinically used ECG leads (Einthoven and Wilson) and body surface potential maps (BSPM). The non-deforming models consider the heart at its ventricular end-diastatic, end-diastolic and end-systolic states. The standard leads show negligible differences during P-Wave and QRS-Complex, yet during T-Wave the leads closest to the heart show prominent differences in amplitude. When looking at the BSPM, there are no notable differences during the P-Wave, but effects of cardiac motion can be observed already during the QRS-Complex, increasing further during the T-Wave. We conclude that for the modeling of activation (P-Wave/QRS-Complex), the associated effort of simulating a complete electro-mechanical approach is not worth the computational cost. But when looking at ventricular repolarization (T-Wave) in standard leads as well as BSPM, there are areas where the signal can be influenced by cardiac motion of the heart to an extent that should not be ignored.

A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D-0D model to a limit cycle under baseline conditions, the model's ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible.

A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D-0D model to a limit cycle under baseline conditions, the model's ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible.

A deep-learning approach for direct whole-heart mesh reconstruction

Automated construction of surface geometries of cardiac structures from volumetric medical images is important for a number of clinical applications. While deep-learning-based approaches have demonstrated promising reconstruction precision, these approaches have mostly focused on voxel-wise segmentation followed by surface reconstruction and post-processing techniques. However, such approaches suffer from a number of limitations including disconnected regions or incorrect surface topology due to erroneous segmentation and stair-case artifacts due to limited segmentation resolution. We propose a novel deep-learning-based approach that directly predicts whole heart surface meshes from volumetric CT and MR image data. Our approach leverages a graph convolutional neural network to predict deformation on mesh vertices from a pre-defined mesh template to reconstruct multiple anatomical structures in a 3D image volume. Our method demonstrated promising performance of generating whole heart reconstructions with as good or better accuracy than prior deep-learning-based methods on both CT and MR data. Furthermore, by deforming a template mesh, our method can generate whole heart geometries with better anatomical consistency and produce high-resolution geometries from lower resolution input image data. Our method was also able to produce temporally-consistent surface mesh predictions for heart motion from CT or MR cine sequences, and therefore can potentially be applied for efficiently constructing 4D whole heart dynamics. Our code and pre-trained networks are available at https://github.com/fkong7/MeshDeformNet.

A finite element model of the cardiac ventricles with coupled circulation: Biventricular mesh generation with hexahedral elements, airbags and a functional mockup interface to the circulation

INTRODUCTION

Finite element (FE) mechanics models of the heart are becoming more sophisticated. However, there is lack of consensus about optimal element type and coupling of FE models to the circulation. We describe biventricular (left (LV) and right (RV) ventricles) FE mechanics model creation using hexahedral elements, airbags and a functional mockup interface (FMI) to lumped-parameter models of the circulation.

METHODS

Cardiac MRI (CMR) was performed in two healthy volunteers and a single patient with ischemic heart disease (IHD). CMR images were segmented and surfaced, meshing with hexahedral elements was performed with a "thin butterfly with septum" topology. LV and RV inflow and outflow airbags were coupled to lumped-parameter circulation models with an FMI interface. Pulmonary constriction (PAC) and vena cava occlusion (VCO) were simulated and end-systolic pressure-volume relations (ESPVR) were calculated.

RESULTS

Mesh construction was prompt with representative contouring and mesh adjustment requiring 32 and 26 min Respectively. The numbers of elements ranged from 4104 to 5184 with a representative Jacobian of 1.0026 ± 0.4531. Agreement between CMR-based surfaces and mesh was excellent with root-mean-squared error of 0.589 ± 0.321 mm. The LV ESPVR slope was 3.37 ± 0.09 in volunteers but 2.74 in the IHD patient. The effect of PAC and VCO on LV ESPVR was consistent with ventricular interaction (p = 0.0286).

CONCLUSION

Successful co-simulation using a biventricular FE mechanics model with hexahedral elements, airbags and an FMI interface to lumped-parameter model of the circulation was demonstrated. Future studies will include comparison of element type and study of cardiovascular pathologies and device therapies.

The openCARP simulation environment for cardiac electrophysiology

BACKGROUND AND OBJECTIVE

Cardiac electrophysiology is a medical specialty with a long and rich tradition of computational modeling. Nevertheless, no community standard for cardiac electrophysiology simulation software has evolved yet. Here, we present the openCARP simulation environment as one solution that could foster the needs of large parts of this community.

METHODS AND RESULTS

openCARP and the Python-based carputils framework allow developing and sharing simulation pipelines which automate in silico experiments including all modeling and simulation steps to increase reproducibility and productivity. The continuously expanding openCARP user community is supported by tailored infrastructure. Documentation and training material facilitate access to this complementary research tool for new users. After a brief historic review, this paper summarizes requirements for a high-usability electrophysiology simulator and describes how openCARP fulfills them. We introduce the openCARP modeling workflow in a multi-scale example of atrial fibrillation simulations on single cell, tissue, organ and body level and finally outline future development potential.

CONCLUSION

As an open simulator, openCARP can advance the computational cardiac electrophysiology field by making state-of-the-art simulations accessible. In combination with the carputils framework, it offers a tailored software solution for the scientific community and contributes towards increasing use, transparency, standardization and reproducibility of in silico experiments.

GEASI: Geodesic-based earliest activation sites identification in cardiac models

The identification of the initial ventricular activation sequence is a critical step for the correct personalization of patient-specific cardiac models. In healthy conditions, the Purkinje network is the main source of the electrical activation, but under pathological conditions the so-called earliest activation sites (EASs) are possibly sparser and more localized. Yet, their number, location and timing may not be easily inferred from remote recordings, such as the epicardial activation or the 12-lead electrocardiogram (ECG), due to the underlying complexity of the model. In this work, we introduce GEASI (Geodesic-based Earliest Activation Sites Identification) as a novel approach to simultaneously identify all EASs. To this end, we start from the anisotropic eikonal equation modeling cardiac electrical activation and exploit its Hamilton-Jacobi formulation to minimize a given objective function, for example, the quadratic mismatch to given activation measurements. This versatile approach can be extended to estimate the number of activation sites by means of the topological gradient, or fitting a given ECG. We conducted various experiments in 2D and 3D for in-silico models and an in-vivo intracardiac recording collected from a patient undergoing cardiac resynchronization therapy. The results demonstrate the clinical applicability of GEASI for potential future personalized models and clinical intervention.

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

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

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling.

A numerical study on the effects of spatial and temporal discretization in cardiac electrophysiology

Millions of degrees of freedom are often required to accurately represent the electrophysiology of the myocardium due to the presence of discretization effects. This study seeks to explore the influence of temporal and spatial discretization on the simulation of cardiac electrophysiology in conjunction with changes in modeling choices. Several finite element analyses are performed to examine how discretization affects solution time, conduction velocity and electrical excitation. Discretization effects are considered along with changes in the electrophysiology model and solution approach. Two action potential models are considered: the Aliev-Panfilov model and the ten Tusscher-Noble-Noble-Panfilov model. The solution approaches consist of two time integration schemes and different treatments for solving the local system of ordinary differential equations. The efficiency and stability of the calculation approaches are demonstrated to be dependent on the action potential model. The dependency of the conduction velocity on the element size and time step is shown to be different for changes in material parameters. Finally, the discrepancies between the wave propagation in coarse and fine meshes are analyzed based on the temporal evolution of the transmembrane potential at a node and its neighboring Gauss points. Insight obtained from this study can be used to suggest new methods to improve the efficiency of simulations in cardiac electrophysiology.

A Framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs

Cardiac digital twins (Cardiac Digital Twin (CDT)s) of human electrophysiology (Electrophysiology (EP)) are digital replicas of patient hearts derived from clinical data that match like-for-like all available clinical observations. Due to their inherent predictive potential, CDTs show high promise as a complementary modality aiding in clinical decision making and also in the cost-effective, safe and ethical testing of novel EP device therapies. However, current workflows for both the anatomical and functional twinning phases within CDT generation, referring to the inference of model anatomy and parameters from clinical data, are not sufficiently efficient, robust and accurate for advanced clinical and industrial applications. Our study addresses three primary limitations impeding the routine generation of high-fidelity CDTs by introducing; a comprehensive parameter vector encapsulating all factors relating to the ventricular EP; an abstract reference frame within the model allowing the unattended manipulation of model parameter fields; a novel fast-forward electrocardiogram (Electrocardiogram (ECG)) model for efficient and bio-physically-detailed simulation required for parameter inference. A novel workflow for the generation of CDTs is then introduced as an initial proof of concept. Anatomical twinning was performed within a reasonable time compatible with clinical workflows (<4h) for 12 subjects from clinically-attained magnetic resonance images. After assessment of the underlying fast forward ECG model against a gold standard bidomain ECG model, functional twinning of optimal parameters according to a clinically-attained 12 lead ECG was then performed using a forward Saltelli sampling approach for a single subject. The achieved results in terms of efficiency and fidelity demonstrate that our workflow is well-suited and viable for generating biophysically-detailed CDTs at scale.

Linking statistical shape models and simulated function in the healthy adult human heart

Cardiac anatomy plays a crucial role in determining cardiac function. However, there is a poor understanding of how specific and localised anatomical changes affect different cardiac functional outputs. In this work, we test the hypothesis that in a statistical shape model (SSM), the modes that are most relevant for describing anatomy are also most important for determining the output of cardiac electromechanics simulations. We made patient-specific four-chamber heart meshes (n = 20) from cardiac CT images in asymptomatic subjects and created a SSM from 19 cases. Nine modes captured 90% of the anatomical variation in the SSM. Functional simulation outputs correlated best with modes 2, 3 and 9 on average (R = 0.49 ± 0.17, 0.37 ± 0.23 and 0.34 ± 0.17 respectively). We performed a global sensitivity analysis to identify the different modes responsible for different simulated electrical and mechanical measures of cardiac function. Modes 2 and 9 were the most important for determining simulated left ventricular mechanics and pressure-derived phenotypes. Mode 2 explained 28.56 ± 16.48% and 25.5 ± 20.85, and mode 9 explained 12.1 ± 8.74% and 13.54 ± 16.91% of the variances of mechanics and pressure-derived phenotypes, respectively. Electrophysiological biomarkers were explained by the interaction of 3 ± 1 modes. In the healthy adult human heart, shape modes that explain large portions of anatomical variance do not explain equivalent levels of electromechanical functional variation. As a result, in cardiac models, representing patient anatomy using a limited number of modes of anatomical variation can cause a loss in accuracy of simulated electromechanical function.

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

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

An Inverse Eikonal Method for Identifying Ventricular Activation Sequences from Epicardial Activation Maps

A key mechanism controlling cardiac function is the electrical activation sequence of the heart's main pumping chambers termed the ventricles. As such, personalization of the ventricular activation sequences is of pivotal importance for the clinical utility of computational models of cardiac electrophysiology. However, a direct observation of the activation sequence throughout the ventricular volume is virtually impossible. In this study, we report on a novel method for identification of activation sequences from activation maps measured at the outer surface of the heart termed the epicardium. Conceptually, the method attempts to identify the key factors governing the ventricular activation sequence - the timing of earliest activation sites (EAS) and the velocity tensor field within the ventricular walls - from sparse and noisy activation maps sampled from the epicardial surface and fits an Eikonal model to the observations. Regularization methods are first investigated to overcome the severe ill-posedness of the inverse problem in a simplified 2D example. These methods are then employed in an anatomically accurate biventricular model with two realistic activation models of varying complexity - a simplified trifascicular model (3F) and a topologically realistic model of the His-Purkinje system (HPS). Using epicardial activation maps at full resolution, we first demonstrate that reconstructing the volumetric activation sequence is, in principle, feasible under the assumption of known location of EAS and later evaluate robustness of the method against noise and reduced spatial resolution of observations. Our results suggest that the FIMIN algorithm is able to robustly recover the full 3D activation sequence using epicardial activation maps at a spatial resolution achievable with current mapping systems and in the presence of noise. Comparing the accuracy achieved in the reconstructed activation maps with clinical data uncertainties suggests that the FIMIN method may be suitable for the patient- specific parameterization of activation models.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology

In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.

Structural Responses of Integrated Parametric Aortic Valve in an Electro-Mechanical Full Heart Model

The aortic valve (AV) is located between the left ventricle and the aorta and responsible for maintaining an outward unidirectional flow. Many AV hemodynamic and structural aspects of have been extensively studied, however, more sophisticated models are needed to better understand the AV biomechanical behavior. This study deals with integrating a new parametric AV structural model with the electro-mechanical Living Heart Human Model® (LHHM). The LHHM is a finite element model simulating human heart capable of realistic electro-mechanical simulations. Different geometric metrics of AV have been examined. New integrated structural AV model within the LHHM better predict local stresses during the cardiac cycle due to the realistic boundary condition derived from the LHHM. It was found that ellipticity index (EI), calculated as the ratio between the maximal (Max) and minimal (Min) aortic annulus (AA) diameters, well correlates with measured clinical data obtained from patients undergoing computed tomography (CT) while the annular perimeter (Perim) matches the same trend. This increases the confidence in the predicted kinematic behavior, leaflets coaptation, and the overall stresses. From the clinical aspect, the new proposed coupled and integrated AV modeling can serve as a platform for design and implementation of pre-transcatheter aortic valve replacement (TAVR) procedures.

In-silico human electro-mechanical ventricular modelling and simulation for drug-induced pro-arrhythmia and inotropic risk assessment

Human-based computational modelling and simulation are powerful tools to accelerate the mechanistic understanding of cardiac patho-physiology, and to develop and evaluate therapeutic interventions. The aim of this study is to calibrate and evaluate human ventricular electro-mechanical models for investigations on the effect of the electro-mechanical coupling and pharmacological action on human ventricular electrophysiology, calcium dynamics, and active contraction. The most recent models of human ventricular electrophysiology, excitation-contraction coupling, and active contraction were integrated, and the coupled models were calibrated using human experimental data. Simulations were then conducted using the coupled models to quantify the effects of electro-mechanical coupling and drug exposure on electrophysiology and force generation in virtual human ventricular cardiomyocytes and tissue. The resulting calibrated human electro-mechanical models yielded active tension, action potential, and calcium transient metrics that are in agreement with experiments for endocardial, epicardial, and mid-myocardial human samples. Simulation results correctly predicted the inotropic response of different multichannel action reference compounds and demonstrated that the electro-mechanical coupling improves the robustness of repolarisation under drug exposure compared to electrophysiology-only models. They also generated additional evidence to explain the partial mismatch between in-silico and in-vitro experiments on drug-induced electrophysiology changes. The human calibrated and evaluated modelling and simulation framework constructed in this study opens new avenues for future investigations into the complex interplay between the electrical and mechanical cardiac substrates, its modulation by pharmacological action, and its translation to tissue and organ models of cardiac patho-physiology.

A publicly available virtual cohort of four-chamber heart meshes for cardiac electro-mechanics simulations

Computational models of the heart are increasingly being used in the development of devices, patient diagnosis and therapy guidance. While software techniques have been developed for simulating single hearts, there remain significant challenges in simulating cohorts of virtual hearts from multiple patients. To facilitate the development of new simulation and model analysis techniques by groups without direct access to medical data, image analysis techniques and meshing tools, we have created the first publicly available virtual cohort of twenty-four four-chamber hearts. Our cohort was built from heart failure patients, age 67±14 years. We segmented four-chamber heart geometries from end-diastolic (ED) CT images and generated linear tetrahedral meshes with an average edge length of 1.1±0.2mm. Ventricular fibres were added in the ventricles with a rule-based method with an orientation of -60° and 80° at the epicardium and endocardium, respectively. We additionally refined the meshes to an average edge length of 0.39±0.10mm to show that all given meshes can be resampled to achieve an arbitrary desired resolution. We ran simulations for ventricular electrical activation and free mechanical contraction on all 1.1mm-resolution meshes to ensure that our meshes are suitable for electro-mechanical simulations. Simulations for electrical activation resulted in a total activation time of 149±16ms. Free mechanical contractions gave an average left ventricular (LV) and right ventricular (RV) ejection fraction (EF) of 35±1% and 30±2%, respectively, and a LV and RV stroke volume (SV) of 95±28mL and 65±11mL, respectively. By making the cohort publicly available, we hope to facilitate large cohort computational studies and to promote the development of cardiac computational electro-mechanics for clinical applications.

Personalization of electro-mechanical models of the pressure-overloaded left ventricle: fitting of Windkessel-type afterload models

Computer models of left ventricular (LV) electro-mechanics (EM) show promise as a tool for assessing the impact of increased afterload upon LV performance. However, the identification of unique afterload model parameters and the personalization of EM LV models remains challenging due to significant clinical input uncertainties. Here, we personalized a virtual cohort of N = 17 EM LV models under pressure overload conditions. A global-local optimizer was developed to uniquely identify parameters of a three-element Windkessel (Wk3) afterload model. The sensitivity of Wk3 parameters to input uncertainty and of the EM LV model to Wk3 parameter uncertainty was analysed. The optimizer uniquely identified Wk3 parameters, and outputs of the personalized EM LV models showed close agreement with clinical data in all cases. Sensitivity analysis revealed a strong dependence of Wk3 parameters on input uncertainty. However, this had limited impact on outputs of EM LV models. A unique identification of Wk3 parameters from clinical data appears feasible, but it is sensitive to input uncertainty, thus depending on accurate invasive measurements. By contrast, the EM LV model outputs were less sensitive, with errors of less than 8.14% for input data errors of 10%, which is within the bounds of clinical data uncertainty. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Parameter subset reduction for patient-specific modelling of arrhythmogenic cardiomyopathy-related mutation carriers in the CircAdapt model

Arrhythmogenic cardiomyopathy (AC) is an inherited cardiac disease, clinically characterized by life-threatening ventricular arrhythmias and progressive cardiac dysfunction. Patient-specific computational models could help understand the disease progression and may help in clinical decision-making. We propose an inverse modelling approach using the CircAdapt model to estimate patient-specific regional abnormalities in tissue properties in AC subjects. However, the number of parameters (n = 110) and their complex interactions make personalized parameter estimation challenging. The goal of this study is to develop a framework for parameter reduction and estimation combining Morris screening, quasi-Monte Carlo (qMC) simulations and particle swarm optimization (PSO). This framework identifies the best subset of tissue properties based on clinical measurements allowing patient-specific identification of right ventricular tissue abnormalities. We applied this framework on 15 AC genotype-positive subjects with varying degrees of myocardial disease. Cohort studies have shown that atypical regional right ventricular (RV) deformation patterns reveal an early-stage AC disease. The CircAdapt model of cardiovascular mechanics and haemodynamics has already demonstrated its ability to capture typical deformation patterns of AC subjects. We, therefore, use clinically measured cardiac deformation patterns to estimate model parameters describing myocardial disease substrates underlying these AC-related RV deformation abnormalities. Morris screening reduced the subset to 48 parameters. qMC and PSO further reduced the subset to a final selection of 16 parameters, including regional tissue contractility, passive stiffness, activation delay and wall reference area. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Creation and application of virtual patient cohorts of heart models

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

The impact of wall thickness and curvature on wall stress in patient-specific electromechanical models of the left atrium

The left atrium (LA) has a complex anatomy with heterogeneous wall thickness and curvature. The anatomy plays an important role in determining local wall stress; however, the relative contribution of wall thickness and curvature in determining wall stress in the LA is unknown. We have developed electromechanical finite element (FE) models of the LA using patient-specific anatomical FE meshes with rule-based myofiber directions. The models of the LA were passively inflated to 10mmHg followed by simulation of the contraction phase of the atrial cardiac cycle. The FE models predicted maximum LA volumes of 156.5 mL, 99.3 mL and 83.4 mL and ejection fractions of 36.9%, 32.0% and 25.2%. The median wall thickness in the 3 cases was calculated as [Formula: see text] mm, [Formula: see text] mm, and [Formula: see text] mm. The median curvature was determined as [Formula: see text] [Formula: see text], [Formula: see text], and [Formula: see text]. Following passive inflation, the correlation of wall stress with the inverse of wall thickness and curvature was 0.55-0.62 and 0.20-0.25, respectively. At peak contraction, the correlation of wall stress with the inverse of wall thickness and curvature was 0.38-0.44 and 0.16-0.34, respectively. In the LA, the 1st principal Cauchy stress is more dependent on wall thickness than curvature during passive inflation and both correlations decrease during active contraction. This emphasizes the importance of including the heterogeneous wall thickness in electromechanical FE simulations of the LA. Overall, simulation results and sensitivity analyses show that in complex atrial anatomy it is unlikely that a simple anatomical-based law can be used to estimate local wall stress, demonstrating the importance of FE analyses.

An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law, for both active stress and active strain formulations of active mechanics, coupled with a four-variable phenomenological model for human cardiac cell electrophysiology, which produces an accurate description of the action potential. The conductivities in the model of electric propagation are modified according to stress, inducing an additional degree of nonlinearity and anisotropy in the coupling mechanisms, and the activation model assumes a simplified stretch-calcium interaction generating active tension or active strain. The influence of the new terms in the electromechanical model is evaluated through a sensitivity analysis, and we provide numerical validation through a set of computational tests using a novel mixed-primal finite element scheme.

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.

Simulating ventricular systolic motion in a four-chamber heart model with spatially varying robin boundary conditions to model the effect of the pericardium

The pericardium affects cardiac motion by limiting epicardial displacement normal to the surface. In computational studies, it is important for the model to replicate realistic motion, as this affects the physiological fidelity of the model. Previous computational studies showed that accounting for the effect of the pericardium allows for a more realistic motion simulation. In this study, we describe the mechanism through which the pericardium causes improved cardiac motion. We simulated electrical activation and contraction of the ventricles on a four-chamber heart in the presence and absence of the effect of the pericardium. We simulated the mechanical constraints imposed by the pericardium by applying normal Robin boundary conditions on the ventricular epicardium. We defined a regional scaling of normal springs stiffness based on image-derived motion from CT images. The presence of the pericardium reduced the error between simulated and image-derived end-systolic configurations from 12.8±4.1 mm to 5.7±2.5 mm. First, the pericardium prevents the ventricles from spherising during isovolumic contraction, reducing the outward motion of the free walls normal to the surface and the upwards motion of the apex. Second, by restricting the inward motion of the free and apical walls of the ventricles the pericardium increases atrioventricular plane displacement by four folds during ejection. Our results provide a mechanistic explanation of the importance of the pericardium in physiological simulations of electromechanical cardiac function.

Computational models in cardiology

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

Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics

Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational efficiency remains to be highly relevant. In this paper, we present two methods to overcome locking phenomena, one based on a displacement-pressure formulation using a stable finite element pairing with bubble functions, and another one using a simple pressure-projection stabilized ℙ₁ - ℙ₁ finite element pair. A key advantage is the versatility of the proposed methods: with minor adjustments they are applicable to all kinds of finite elements and generalize easily to transient dynamics. The proposed methods are compared to and verified with standard benchmarks previously reported in the literature. Benchmark results demonstrate that both approaches provide a robust and computationally efficient way of simulating nearly and fully incompressible materials.