Patient-specific electromechanical models of the heart for the prediction of pacing acute effects in CRT: a preliminary clinical validation

Parameter subset reduction for imaging-based digital twin generation of patients with left ventricular mechanical discoordination

BACKGROUND

Integration of a patient's non-invasive imaging data in a digital twin (DT) of the heart can provide valuable insight into the myocardial disease substrates underlying left ventricular (LV) mechanical discoordination. However, when generating a DT, model parameters should be identifiable to obtain robust parameter estimations. In this study, we used the CircAdapt model of the human heart and circulation to find a subset of parameters which were identifiable from LV cavity volume and regional strain measurements of patients with different substrates of left bundle branch block (LBBB) and myocardial infarction (MI). To this end, we included seven patients with heart failure with reduced ejection fraction (HFrEF) and LBBB (study ID: 2018-0863, registration date: 2019-10-07), of which four were non-ischemic (LBBB-only) and three had previous MI (LBBB-MI), and six narrow QRS patients with MI (MI-only) (study ID: NL45241.041.13, registration date: 2013-11-12). Morris screening method (MSM) was applied first to find parameters which were important for LV volume, regional strain, and strain rate indices. Second, this parameter subset was iteratively reduced based on parameter identifiability and reproducibility. Parameter identifiability was based on the diaphony calculated from quasi-Monte Carlo simulations and reproducibility was based on the intraclass correlation coefficient ( ICC ) obtained from repeated parameter estimation using dynamic multi-swarm particle swarm optimization. Goodness-of-fit was defined as the mean squared error (χ 2 ) of LV myocardial strain, strain rate, and cavity volume.

RESULTS

A subset of 270 parameters remained after MSM which produced high-quality DTs of all patients (χ 2  < 1.6), but minimum parameter reproducibility was poor (ICC min  = 0.01). Iterative reduction yielded a reproducible (ICC min  = 0.83) subset of 75 parameters, including cardiac output, global LV activation duration, regional mechanical activation delay, and regional LV myocardial constitutive properties. This reduced subset produced patient-resembling DTs (χ 2  < 2.2), while septal-to-lateral wall workload imbalance was higher for the LBBB-only DTs than for the MI-only DTs (p < 0.05).

CONCLUSIONS

By applying sensitivity and identifiability analysis, we successfully determined a parameter subset of the CircAdapt model which can be used to generate imaging-based DTs of patients with LV mechanical discoordination. Parameters were reproducibly estimated using particle swarm optimization, and derived LV myocardial work distribution was representative for the patient's underlying disease substrate. This DT technology enables patient-specific substrate characterization and can potentially be used to support clinical decision making.

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.

Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

Haemodynamic effects of hypertension and type 2 diabetes: Insights from a 4D flow MRI-based personalized cardiovascular mathematical model

Type 2 diabetes (T2D) and hypertension increase the risk of cardiovascular diseases mediated by whole-body changes to metabolism, cardiovascular structure and haemodynamics. The haemodynamic changes related to hypertension and T2D are complex and subject-specific, however, and not fully understood. We aimed to investigate the haemodynamic mechanisms in T2D and hypertension by comparing the haemodynamics between healthy controls and subjects with T2D, hypertension, or both. For all subjects, we combined 4D flow magnetic resonance imaging data, brachial blood pressure and a cardiovascular mathematical model to create a comprehensive subject-specific analysis of central haemodynamics. When comparing the subject-specific haemodynamic parameters between the four groups, the predominant haemodynamic difference is impaired left ventricular relaxation in subjects with both T2D and hypertension compared to subjects with only T2D, only hypertension and controls. The impaired relaxation indicates that, in this cohort, the long-term changes in haemodynamic load of co-existing T2D and hypertension cause diastolic dysfunction demonstrable at rest, whereas either disease on its own does not. However, through subject-specific predictions of impaired relaxation, we show that altered relaxation alone is not enough to explain the subject-specific and group-related differences; instead, a combination of parameters is affected in T2D and hypertension. These results confirm previous studies that reported more adverse effects from the combination of T2D and hypertension compared to either disease on its own. Furthermore, this shows the potential of personalized cardiovascular models in providing haemodynamic mechanistic insights and subject-specific predictions that could aid in the understanding and treatment planning of patients with T2D and hypertension. KEY POINTS: The combination of 4D flow magnetic resonance imaging data and a cardiovascular mathematical model allows for a comprehensive analysis of subject-specific haemodynamic parameters that otherwise cannot be derived non-invasively. Using this combination, we show that diastolic dysfunction in subjects with both type 2 diabetes (T2D) and hypertension is the main group-level difference between controls, subjects with T2D, subjects with hypertension, and subjects with both T2D and hypertension. These results suggest that, in this relatively healthy population, the additional load of both hypertension and T2D affects the haemodynamic function of the left ventricle, whereas each disease on its own is not enough to cause significant effects under resting conditions. Finally, using the subject-specific model, we show that the haemodynamic effects of diastolic dysfunction alone are not sufficient to explain all the observed haemodynamic differences. Instead, additional subject-specific variations in cardiac and vascular function combine to explain the complex haemodynamics of subjects affected by hypertension and/or T2D.

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

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

Combination of personalized computational modeling and machine learning for optimization of left ventricular pacing site in cardiac resynchronization therapy

Introduction: The 30-50% non-response rate to cardiac resynchronization therapy (CRT) calls for improved patient selection and optimized pacing lead placement. The study aimed to develop a novel technique using patient-specific cardiac models and machine learning (ML) to predict an optimal left ventricular (LV) pacing site (ML-PS) that maximizes the likelihood of LV ejection fraction (LVEF) improvement in a given CRT candidate. To validate the approach, we evaluated whether the distance D_PS between the clinical LV pacing site (ref-PS) and ML-PS is associated with improved response rate and magnitude. Materials and methods: We reviewed retrospective data for 57 CRT recipients. A positive response was defined as a more than 10% LVEF improvement. Personalized models of ventricular activation and ECG were created from MRI and CT images. The characteristics of ventricular activation during intrinsic rhythm and biventricular (BiV) pacing with ref-PS were derived from the models and used in combination with clinical data to train supervised ML classifiers. The best logistic regression model classified CRT responders with a high accuracy of 0.77 (ROC AUC = 0.84). The LR classifier, model simulations and Bayesian optimization with Gaussian process regression were combined to identify an optimal ML-PS that maximizes the ML-score of CRT response over the LV surface in each patient. Results: The optimal ML-PS improved the ML-score by 17 ± 14% over the ref-PS. Twenty percent of the non-responders were reclassified as positive at ML-PS. Selection of positive patients with a max ML-score >0.5 demonstrated an improved clinical response rate. The distance D_PS was shorter in the responders. The max ML-score and D_PS were found to be strong predictors of CRT response (ROC AUC = 0.85). In the group with max ML-score > 0.5 and D_PS< 30 mm, the response rate was 83% compared to 14% in the rest of the cohort. LVEF improvement in this group was higher than in the other patients (16 ± 8% vs. 7 ± 8%). Conclusion: A new technique combining clinical data, personalized heart modelling and supervised ML demonstrates the potential for use in clinical practice to assist in optimizing patient selection and predicting optimal LV pacing lead position in HF candidates for CRT.

Comparison of novel ventricular pacing strategies using an electro-mechanical simulation platform

AIMS

Focus of pacemaker therapy is shifting from right ventricular (RV) apex pacing (RVAP) and biventricular pacing (BiVP) to conduction system pacing. Direct comparison between the different pacing modalities and their consequences to cardiac pump function is difficult, due to the practical implications and confounding variables. Computational modelling and simulation provide the opportunity to compare electrical, mechanical, and haemodynamic consequences in the same virtual heart.

METHODS AND RESULTS

Using the same single cardiac geometry, electrical activation maps following the different pacing strategies were calculated using an Eikonal model on a three-dimensional geometry, which were then used as input for a lumped mechanical and haemodynamic model (CircAdapt). We then compared simulated strain, regional myocardial work, and haemodynamic function for each pacing strategy. Selective His-bundle pacing (HBP) best replicated physiological electrical activation and led to the most homogeneous mechanical behaviour. Selective left bundle branch (LBB) pacing led to good left ventricular (LV) function but significantly increased RV load. RV activation times were reduced in non-selective LBB pacing (nsLBBP), reducing RV load but increasing heterogeneity in LV contraction. LV septal pacing led to a slower LV and more heterogeneous LV activation than nsLBBP, while RV activation was similar. BiVP led to a synchronous LV-RV, but resulted in a heterogeneous contraction. RVAP led to the slowest and most heterogeneous contraction. Haemodynamic differences were small compared to differences in local wall behaviour.

CONCLUSION

Using a computational modelling framework, we investigated the mechanical and haemodynamic outcome of the prevailing pacing strategies in hearts with normal electrical and mechanical function. For this class of patients, nsLBBP was the best compromise between LV and RV function if HBP is not possible.

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.

Fast and robust parameter estimation with uncertainty quantification for the cardiac function

BACKGROUND AND OBJECTIVES

Parameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Many model parameters regarding cardiac electromechanics and cardiovascular hemodynamics need to be robustly fitted by starting from a few, possibly non-invasive, noisy observations. Moreover, short execution times and a small amount of computational resources are required for the effective clinical translation.

METHODS

In the framework of Bayesian statistics, we combine Maximum a Posteriori estimation and Hamiltonian Monte Carlo to find an approximation of model parameters and their posterior distributions. Fast simulations and minimal memory requirements are achieved by using an accurate and geometry-specific Artificial Neural Network surrogate model for the cardiac function, matrix-free methods, automatic differentiation and automatic vectorization. Furthermore, we account for the surrogate modeling error and measurement error.

RESULTS

We perform three different in silico test cases, ranging from the ventricular function to the entire cardiocirculatory system, involving whole-heart mechanics, arterial and venous hemodynamics. By employing a single central processing unit on a standard laptop, we attain highly accurate estimations for all model parameters in short computational times. Furthermore, we obtain posterior distributions that contain the true values inside the 90% credibility regions.

CONCLUSIONS

Many model parameters regarding the entire cardiovascular system can be fastly and robustly identified with minimal hardware requirements. This can be achieved when a small amount of non-invasive data is available and when high levels of signal-to-noise ratio are present in the quantities of interest. With these features, our approach meets the requirements for clinical exploitation, while being compliant with Green Computing practices.

The saga of dyssynchrony imaging: Are we getting to the point

Cardiac resynchronisation therapy (CRT) has an established role in the management of patients with heart failure, reduced left ventricular ejection fraction (LVEF &lt; 35%) and widened QRS (&gt;130 msec). Despite the complex pathophysiology of left ventricular (LV) dyssynchrony and the increasing evidence supporting the identification of specific electromechanical substrates that are associated with a higher probability of CRT response, the assessment of LVEF is the only imaging-derived parameter used for the selection of CRT candidates.

This review aims to (1) provide an overview of the evolution of cardiac imaging for the assessment of LV dyssynchrony and its role in the selection of patients undergoing CRT; (2) highlight the main pitfalls and advantages of the application of cardiac imaging for the assessment of LV dyssynchrony; (3) provide some perspectives for clinical application and future research in this field.

Conclusion

the road for a more individualized approach to resynchronization therapy delivery is open and imaging might provide important input beyond the assessment of LVEF.

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

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

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

Altered Aortic Hemodynamics and Relative Pressure in Patients with Dilated Cardiomyopathy

Ventricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol.

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.

Determining anatomical and electrophysiological detail requirements for computational ventricular models of porcine myocardial infarction

BACKGROUND

Computational models of the heart built from cardiac MRI and electrophysiology (EP) data have shown promise for predicting the risk of and ablation targets for myocardial infarction (MI) related ventricular tachycardia (VT), as well as to predict paced activation sequences in heart failure patients. However, most recent studies have relied on low resolution imaging data and little or no EP personalisation, which may affect the accuracy of model-based predictions.

OBJECTIVE

To investigate the impact of model anatomy, MI scar morphology, and EP personalisation strategies on paced activation sequences and VT inducibility to determine the level of detail required to make accurate model-based predictions.

METHODS

Imaging and EP data were acquired from a cohort of six pigs with experimentally induced MI. Computational models of ventricular anatomy, incorporating MI scar, were constructed including bi-ventricular or left ventricular (LV) only anatomy, and MI scar morphology with varying detail. Tissue conductivities and action potential duration (APD) were fitted to 12-lead ECG data using the QRS duration and the QT interval, respectively, in addition to corresponding literature parameters. Paced activation sequences and VT induction were simulated. Simulated paced activation and VT inducibility were compared between models and against experimental data.

RESULTS

Simulations predict that the level of model anatomical detail has little effect on simulated paced activation, with all model predictions comparing closely with invasive EP measurements. However, detailed scar morphology from high-resolution images, bi-ventricular anatomy, and personalized tissue conductivities are required to predict experimental VT outcome.

CONCLUSION

This study provides clear guidance for model generation based on clinical data. While a representing high level of anatomical and scar detail will require high-resolution image acquisition, EP personalisation based on 12-lead ECG can be readily incorporated into modelling pipelines, as such data is widely available.

Optimization of cardiac resynchronization therapy based on a cardiac electromechanics-perfusion computational model

Cardiac resynchronization therapy (CRT) is an established treatment for left bundle branch block (LBBB) resulting in mechanical dyssynchrony. Approximately 1/3 of patients with CRT, however, are non-responders. To understand factors affecting CRT response, an electromechanics-perfusion computational model based on animal-specific left ventricular (LV) geometry and coronary vascular networks located in the septum and LV free wall is developed. The model considers contractility-flow and preload-activation time relationships, and is calibrated to simultaneously match the experimental measurements in terms of the LV pressure, volume waveforms and total coronary flow in the left anterior descending and left circumflex territories from 2 swine models under right atrium and right ventricular pacing. The model is then applied to investigate the responses of CRT indexed by peak LV pressure and (dP/dt)max at multiple pacing sites with different degrees of perfusion in the LV free wall. Without the presence of ischemia, the model predicts that basal-lateral endocardial region is the optimal pacing site that can best improve (dP/dt)max by 20%, and is associated with the shortest activation time. In the presence of ischemia, a non-ischemic region becomes the optimal pacing site when coronary flow in the ischemic region fell below 30% of its original value. Pacing at the ischemic region produces little response at that perfusion level. The optimal pacing site is associated with one that optimizes the LV activation time. These findings suggest that CRT response is affected by both pacing site and coronary perfusion, which may have clinical implication in improving CRT responder rates.

Machine Learning Prediction of Cardiac Resynchronisation Therapy Response From Combination of Clinical and Model-Driven Data

Background: Up to 30–50% of chronic heart failure patients who underwent cardiac resynchronization therapy (CRT) do not respond to the treatment. Therefore, patient stratification for CRT and optimization of CRT device settings remain a challenge.

Objective: The main goal of our study is to develop a predictive model of CRT outcome using a combination of clinical data recorded in patients before CRT and simulations of the response to biventricular (BiV) pacing in personalized computational models of the cardiac electrophysiology.

Materials and Methods: Retrospective data from 57 patients who underwent CRT device implantation was utilized. Positive response to CRT was defined by a 10% increase in the left ventricular ejection fraction in a year after implantation. For each patient, an anatomical model of the heart and torso was reconstructed from MRI and CT images and tailored to ECG recorded in the participant. The models were used to compute ventricular activation time, ECG duration and electrical dyssynchrony indices during intrinsic rhythm and BiV pacing from the sites of implanted leads. For building a predictive model of CRT response, we used clinical data recorded before CRT device implantation together with model-derived biomarkers of ventricular excitation in the left bundle branch block mode of activation and under BiV stimulation. Several Machine Learning (ML) classifiers and feature selection algorithms were tested on the hybrid dataset, and the quality of predictors was assessed using the area under receiver operating curve (ROC AUC). The classifiers on the hybrid data were compared with ML models built on clinical data only.

Results: The best ML classifier utilizing a hybrid set of clinical and model-driven data demonstrated ROC AUC of 0.82, an accuracy of 0.82, sensitivity of 0.85, and specificity of 0.78, improving quality over that of ML predictors built on clinical data from much larger datasets by more than 0.1. Distance from the LV pacing site to the post-infarction zone and ventricular activation characteristics under BiV pacing were shown as the most relevant model-driven features for CRT response classification.

Conclusion: Our results suggest that combination of clinical and model-driven data increases the accuracy of classification models for CRT outcomes.

Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare

Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient's pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSM_pre, and patient-specific models of the same patients created post-PVR (PSM_post)-both created in our previous published work. Using the PSM_pre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSM_post, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSM_post model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.

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.

Fast Posterior Estimation of Cardiac Electrophysiological Model Parameters via Bayesian Active Learning

Probabilistic estimation of cardiac electrophysiological model parameters serves an important step toward model personalization and uncertain quantification. The expensive computation associated with these model simulations, however, makes direct Markov Chain Monte Carlo (MCMC) sampling of the posterior probability density function (pdf) of model parameters computationally intensive. Approximated posterior pdfs resulting from replacing the simulation model with a computationally efficient surrogate, on the other hand, have seen limited accuracy. In this study, we present a Bayesian active learning method to directly approximate the posterior pdf function of cardiac model parameters, in which we intelligently select training points to query the simulation model in order to learn the posterior pdf using a small number of samples. We integrate a generative model into Bayesian active learning to allow approximating posterior pdf of high-dimensional model parameters at the resolution of the cardiac mesh. We further introduce new acquisition functions to focus the selection of training points on better approximating the shape rather than the modes of the posterior pdf of interest. We evaluated the presented method in estimating tissue excitability in a 3D cardiac electrophysiological model in a range of synthetic and real-data experiments. We demonstrated its improved accuracy in approximating the posterior pdf compared to Bayesian active learning using regular acquisition functions, and substantially reduced computational cost in comparison to existing standard or accelerated MCMC sampling.

An Implementation of Patient-Specific Biventricular Mechanics Simulations With a Deep Learning and Computational Pipeline

Parameterised patient-specific models of the heart enable quantitative analysis of cardiac function as well as estimation of regional stress and intrinsic tissue stiffness. However, the development of personalised models and subsequent simulations have often required lengthy manual setup, from image labelling through to generating the finite element model and assigning boundary conditions. Recently, rapid patient-specific finite element modelling has been made possible through the use of machine learning techniques. In this paper, utilising multiple neural networks for image labelling and detection of valve landmarks, together with streamlined data integration, a pipeline for generating patient-specific biventricular models is applied to clinically-acquired data from a diverse cohort of individuals, including hypertrophic and dilated cardiomyopathy patients and healthy volunteers. Valve motion from tracked landmarks as well as cavity volumes measured from labelled images are used to drive realistic motion and estimate passive tissue stiffness values. The neural networks are shown to accurately label cardiac regions and features for these diverse morphologies. Furthermore, differences in global intrinsic parameters, such as tissue anisotropy and normalised active tension, between groups illustrate respective underlying changes in tissue composition and/or structure as a result of pathology. This study shows the successful application of a generic pipeline for biventricular modelling, incorporating artificial intelligence solutions, within a diverse cohort.

Applications of artificial intelligence in cardiovascular imaging

Research into artificial intelligence (AI) has made tremendous progress over the past decade. In particular, the AI-powered analysis of images and signals has reached human-level performance in many applications owing to the efficiency of modern machine learning methods, in particular deep learning using convolutional neural networks. Research into the application of AI to medical imaging is now very active, especially in the field of cardiovascular imaging because of the challenges associated with acquiring and analysing images of this dynamic organ. In this Review, we discuss the clinical questions in cardiovascular imaging that AI can be used to address and the principal methodological AI approaches that have been developed to solve the related image analysis problems. Some approaches are purely data-driven and rely mainly on statistical associations, whereas others integrate anatomical and physiological information through additional statistical, geometric and biophysical models of the human heart. In a structured manner, we provide representative examples of each of these approaches, with particular attention to the underlying computational imaging challenges. Finally, we discuss the remaining limitations of AI approaches in cardiovascular imaging (such as generalizability and explainability) and how they can be overcome.

A clinical-in silico study on the effectiveness of multipoint bicathodic and cathodic-anodal pacing in cardiac resynchronization therapy

Up to one-third of patients undergoing cardiac resynchronization therapy (CRT) are nonresponders. Multipoint bicathodic and cathodic-anodal left ventricle (LV) stimulations could overcome this clinical challenge, but their effectiveness remains controversial. Here we evaluate the performance of such stimulations through both in vivo and in silico experiments, the latter based on computer electromechanical modeling. Seven patients, all candidates for CRT, received a quadripolar LV lead. Four stimulations were tested: right ventricular (RVS); conventional single point biventricular (S-BS); multipoint biventricular bicathodic (CC-BS) and multipoint biventricular cathodic-anodal (CA-BS). The following parameters were processed: QRS duration; maximal time derivative of arterial pressure (dPdt_max); systolic arterial pressure (P_sys); and stroke volume (SV). Echocardiographic data of each patient were then obtained to create an LV geometric model. Numerical simulations were based on a strongly coupled Bidomain electromechanical coupling model. Considering the in vivo parameters, when comparing S-BS to RVS, there was no significant decrease in SV (from 45 ± 11 to 44 ± 20 ml) and 6% and 4% increases of dPdt_max and P_sys, respectively. Focusing on in silico parameters, with respect to RVS, S-BS exhibited a significant increase of SV, dPdt_max and P_sys. Neither the in vivo nor in silico results showed any significant hemodynamic and electrical difference among S-BS, CC-BS and CA-BS configurations. These results show that CC-BS and CA-BS yield a comparable CRT performance, but they do not always yield improvement in terms of hemodynamic parameters with respect to S-BS. The computational results confirmed the in vivo observations, thus providing theoretical support to the clinical experiments.

Bayesian Calibration of Electrophysiology Models Using Restitution Curve Emulators

Calibration of cardiac electrophysiology models is a fundamental aspect of model personalization for predicting the outcomes of cardiac therapies, simulation testing of device performance for a range of phenotypes, and for fundamental research into cardiac function. Restitution curves provide information on tissue function and can be measured using clinically feasible measurement protocols. We introduce novel "restitution curve emulators" as probabilistic models for performing model exploration, sensitivity analysis, and Bayesian calibration to noisy data. These emulators are built by decomposing restitution curves using principal component analysis and modeling the resulting coordinates with respect to model parameters using Gaussian processes. Restitution curve emulators can be used to study parameter identifiability via sensitivity analysis of restitution curve components and rapid inference of the posterior distribution of model parameters given noisy measurements. Posterior uncertainty about parameters is critical for making predictions from calibrated models, since many parameter settings can be consistent with measured data and yet produce very different model behaviors under conditions not effectively probed by the measurement protocols. Restitution curve emulators are therefore promising probabilistic tools for calibrating electrophysiology models.

Investigating the reference domain influence in personalised models of cardiac mechanics : Effect of unloaded geometry on cardiac biomechanics

A major concern in personalised models of heart mechanics is the unknown zero-pressure domain, a prerequisite for accurately predicting cardiac biomechanics. As the reference configuration cannot be captured by clinical data, studies often employ in-vivo frames which are unlikely to correspond to unloaded geometries. Alternatively, zero-pressure domain is approximated through inverse methodologies, which, however, entail assumptions pertaining to boundary conditions and material parameters. Both approaches are likely to introduce biases in estimated biomechanical properties; nevertheless, quantification of these effects is unattainable without ground-truth data. In this work, we assess the unloaded state influence on model-derived biomechanics, by employing an in-silico modelling framework relying on experimental data on porcine hearts. In-vivo images are used for model personalisation, while in-situ experiments provide a reliable approximation of the reference domain, creating a unique opportunity for a validation study. Personalised whole-cycle cardiac models are developed which employ different reference domains (image-derived, inversely estimated) and are compared against ground-truth model outcomes. Simulations are conducted with varying boundary conditions, to investigate the effect of data-derived constraints on model accuracy. Attention is given to modelling the influence of the ribcage on the epicardium, due to its close proximity to the heart in the porcine anatomy. Our results find merit in both approaches for dealing with the unknown reference domain, but also demonstrate differences in estimated biomechanical quantities such as material parameters, strains and stresses. Notably, they highlight the importance of a boundary condition accounting for the constraining influence of the ribcage, in forward and inverse biomechanical models.

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

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

Sensitivity analysis of an electrophysiology model for the left ventricle

Modelling the cardiac electrophysiology entails dealing with the uncertainties related to the input parameters such as the heart geometry and the electrical conductivities of the tissues, thus calling for an uncertainty quantification (UQ) of the results. Since the chambers of the heart have different shapes and tissues, in order to make the problem affordable, here we focus on the left ventricle with the aim of identifying which of the uncertain inputs mostly affect its electrophysiology. In a first phase, the uncertainty of the input parameters is evaluated using data available from the literature and the output quantities of interest (QoIs) of the problem are defined. According to the polynomial chaos expansion, a training dataset is then created by sampling the parameter space using a quasi-Monte Carlo method whereas a smaller independent dataset is used for the validation of the resulting metamodel. The latter is exploited to run a global sensitivity analysis with nonlinear variance-based indices and thus reduce the input parameter space accordingly. Thereafter, the uncertainty probability distribution of the QoIs are evaluated using a direct UQ strategy on a larger dataset and the results discussed in the light of the medical knowledge.

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.

Effects of Mechanical Dyssynchrony on Coronary Flow: Insights From a Computational Model of Coupled Coronary Perfusion With Systemic Circulation

Mechanical dyssynchrony affects left ventricular (LV) mechanics and coronary perfusion. Due to the confounding effects of their bi-directional interactions, the mechanisms behind these changes are difficult to isolate from experimental and clinical studies alone. Here, we develop and calibrate a closed-loop computational model that couples the systemic circulation, LV mechanics, and coronary perfusion. The model is applied to simulate the impact of mechanical dyssynchrony on coronary flow in the left anterior descending artery (LAD) and left circumflex artery (LCX) territories caused by regional alterations in perfusion pressure and intramyocardial pressure (IMP). We also investigate the effects of regional coronary flow alterations on regional LV contractility in mechanical dyssynchrony based on prescribed contractility-flow relationships without considering autoregulation. The model predicts that LCX and LAD flows are reduced by 7.2%, and increased by 17.1%, respectively, in mechanical dyssynchrony with a systolic dyssynchrony index of 10% when the LAD's IMP is synchronous with the arterial pressure. The LAD flow is reduced by 11.6% only when its IMP is delayed with respect to the arterial pressure by 0.07 s. When contractility is sensitive to coronary flow, mechanical dyssynchrony can affect global LV mechanics, IMPs and contractility that in turn, further affect the coronary flow in a feedback loop that results in a substantial reduction of dP_LV/dt, indicative of ischemia. Taken together, these findings imply that regional IMPs play a significant role in affecting regional coronary flows in mechanical dyssynchrony and the changes in regional coronary flow may produce ischemia when contractility is sensitive to the changes in coronary flow.

Patient-specific heart simulation can identify non-responders to cardiac resynchronization therapy

To identify non-responders to cardiac resynchronization therapy (CRT), various biomarkers have been proposed, but these attempts have not been successful to date. We tested the clinical applicability of computer simulation of CRT for the identification of non-responders. We used the multi-scale heart simulator “UT-Heart,” which can reproduce the electrophysiology and mechanics of the heart based on a molecular model of the excitation–contraction mechanism. Patient-specific heart models were created for eight heart failure patients who were treated with CRT, based on the clinical data recorded before treatment. Using these heart models, bi-ventricular pacing simulations were performed at multiple pacing sites adopted in clinical practice. Improvement in pumping function measured by the relative change of maximum positive derivative of left ventricular pressure (%ΔdP/dt_max) was compared with the clinical outcome. The operators of the simulation were blinded to the clinical outcome. In six patients, the relative reduction in end-systolic volume exceeded 15% in the follow-up echocardiogram at 3 months (responders) and the remaining two patients were judged as non-responders. The simulated %ΔdP/dt_max at the best lead position could identify responders and non-responders successfully. With further refinement of the model, patient-specific simulation could be a useful tool for identifying non-responders to CRT.

Hierarchical modeling of force generation in cardiac muscle

Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models, however, may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models-from the more refined to the more simplified-that are rigorously and systematically related to each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three model families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation.

Considering discrepancy when calibrating a mechanistic electrophysiology model

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

An audit of uncertainty in multi-scale cardiac electrophysiology models

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Monitoring of cardiovascular physiology augmented by a patient-specific biomechanical model during general anesthesia. A proof of concept study

During general anesthesia (GA), direct analysis of arterial pressure or aortic flow waveforms may be inconclusive in complex situations. Patient-specific biomechanical models, based on data obtained during GA and capable to perform fast simulations of cardiac cycles, have the potential to augment hemodynamic monitoring. Such models allow to simulate Pressure-Volume (PV) loops and estimate functional indicators of cardiovascular (CV) system, e.g. ventricular-arterial coupling (Vva), cardiac efficiency (CE) or myocardial contractility, evolving throughout GA. In this prospective observational study, we created patient-specific biomechanical models of heart and vasculature of a reduced geometric complexity for n = 45 patients undergoing GA, while using transthoracic echocardiography and aortic pressure and flow signals acquired in the beginning of GA (baseline condition). If intraoperative hypotension (IOH) appeared, diluted norepinephrine (NOR) was administered and the model readjusted according to the measured aortic pressure and flow signals. Such patients were a posteriori assigned into a so-called hypotensive group. The accuracy of simulated mean aortic pressure (MAP) and stroke volume (SV) at baseline were in accordance with the guidelines for the validation of new devices or reference measurement methods in all patients. After NOR administration in the hypotensive group, the percentage of concordance with 10% exclusion zone between measurement and simulation was >95% for both MAP and SV. The modeling results showed a decreased Vva (0.64±0.37 vs 0.88±0.43; p = 0.039) and an increased CE (0.8±0.1 vs 0.73±0.11; p = 0.042) in hypotensive vs normotensive patients. Furthermore, Vva increased by 92±101%, CE decreased by 13±11% (p < 0.001 for both) and contractility increased by 14±11% (p = 0.002) in the hypotensive group post-NOR administration. In this work we demonstrated the application of fast-running patient-specific biophysical models to estimate PV loops and functional indicators of CV system using clinical data available during GA. The work paves the way for model-augmented hemodynamic monitoring at operating theatres or intensive care units to enhance the information on patient-specific physiology.

Transmural Remodeling of Cardiac Microstructure in Aged Spontaneously Hypertensive Rats by Diffusion Tensor MRI

The long-standing high blood pressure (also known as hypertension) overworks the heart. Microstructural remodeling is a key factor of hypertensive heart disease progression. Diffusion tensor magnetic resonance imaging (DT-MRI) is a powerful tool for the rapid noninvasive nondestructive delineation of the cardiomyocyte organization. The spontaneously hypertensive rat (SHR) is a well-established model of genetic hypertension. The goal of this study was to employ high-resolution DT-MRI and the SHR animal model to assess the transmural layer-specific remodeling of myocardial microstructure associated with hypertension. Ex vivo experiments were performed on excised formalin-fixed hearts of aged SHRs (n = 4) and age-matched controls (n = 4). The DT-MRI-derived fractional anisotropy (FA), longitudinal diffusivity (λ_L), transversal diffusivity (λ_T), and mean diffusivity (MD) served as the readout parameters investigated at three transmural zones (i.e., endocardium, mesocardium, and epicardium). The helix angles (HAs) of the aggregated cardiomyocytes and the orientation of laminar sheetlets were also studied. Compared with controls, the SHRs exhibited decreased epicardial FA, while FA changes in the other two transmural regions were insignificant. No substantial differences were observed in the diffusivity parameters and the transmural course of HAs between the two groups. A consistent distribution pattern of laminar sheetlet orientation was not identified for either group. Our findings are in line with the known cellular microstructure from early painstaking histological studies. Biophysical explanations of the study outcomes are provided. In conclusion, our experimental findings indicate that the epicardial microstructure is more vulnerable to high blood pressure leading to more pronounced changes in this region during remodeling. DT-MRI is well-suited for elucidating these alterations. The revealed transmural nonuniformity of myocardial reorganization may shed light on the mechanisms of the microstructure-function relationship in hypertension progression. Our results provide insights into the management of patients with systemic arterial hypertension, thus prevent the progression toward heart failure. The findings of this study should be acknowledged by electromechanical models of the heart that simulate the specific cardiac pathology.

Embedding high-dimensional Bayesian optimization via generative modeling: Parameter personalization of cardiac electrophysiological models

The estimation of patient-specific tissue properties in the form of model parameters is important for personalized physiological models. Because tissue properties are spatially varying across the underlying geometrical model, it presents a significant challenge of high-dimensional (HD) optimization at the presence of limited measurement data. A common solution to reduce the dimension of the parameter space is to explicitly partition the geometrical mesh. In this paper, we present a novel concept that uses a generative variational auto-encoder (VAE) to embed HD Bayesian optimization into a low-dimensional (LD) latent space that represents the generative code of HD parameters. We further utilize VAE-encoded knowledge about the generative code to guide the exploration of the search space. The presented method is applied to estimating tissue excitability in a cardiac electrophysiological model in a range of synthetic and real-data experiments, through which we demonstrate its improved accuracy and substantially reduced computational cost in comparison to existing methods that rely on geometry-based reduction of the HD parameter space.

Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling

Understanding (patho)physiological phenomena and mechanisms of failure in patients with Fontan circulation-a surgically established circulation for patients born with a functionally single ventricle-remains challenging due to the complex hemodynamics and high inter-patient variations in anatomy and function. In this work, we present a biomechanical model of the heart and circulation to augment the diagnostic evaluation of Fontan patients with early-stage heart failure. The proposed framework employs a reduced-order model of heart coupled with a simplified circulation including venous return, creating a closed-loop system. We deploy this framework to augment the information from data obtained during combined cardiac catheterization and magnetic resonance exams (XMR), performed at rest and during dobutamine stress in 9 children with Fontan circulation and 2 biventricular controls. We demonstrate that our modeling framework enables patient-specific investigation of myocardial stiffness, contractility at rest, contractile reserve during stress and changes in vascular resistance. Hereby, the model allows to identify key factors underlying the pathophysiological response to stress in these patients. In addition, the rapid personalization of the model to patient data and fast simulation of cardiac cycles make our framework directly applicable in a clinical workflow. We conclude that the proposed modeling framework is a valuable addition to the current clinical diagnostic XMR exam that helps to explain patient-specific stress hemodynamics and can identify potential mechanisms of failure in patients with Fontan circulation.

Open-Source Routines for Building Personalized Left Ventricular Models From Cardiac Magnetic Resonance Imaging Data

Creating patient-specific models of the heart is a promising approach for predicting outcomes in response to congenital malformations, injury, or disease, as well as an important tool for developing and customizing therapies. However, integrating multimodal imaging data to construct patient-specific models is a nontrivial task. Here, we propose an approach that employs a prolate spheroidal coordinate system to interpolate information from multiple imaging datasets and map those data onto a single geometric model of the left ventricle (LV). We demonstrate the mapping of the location and transmural extent of postinfarction scar segmented from late gadolinium enhancement (LGE) magnetic resonance imaging (MRI), as well as mechanical activation calculated from displacement encoding with stimulated echoes (DENSE) MRI. As a supplement to this paper, we provide MATLAB and Python versions of the routines employed here for download from SimTK.

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.

A relaxed growth modeling framework for controlling growth-induced residual stresses

BACKGROUND

Constitutive models of the mechanical response of soft tissues have been established and are widely accepted, but models of soft tissues remodeling are more controversial. Specifically for growth, one important question arises pertaining to residual stresses: existing growth models inevitably introduce residual stresses, but it is not entirely clear if this is physiological or merely an artifact of the modeling framework. As a consequence, in simulating growth, some authors have chosen to keep growth-induced residual stresses, and others have chosen to remove them.

METHODS

In this paper, we introduce a novel "relaxed growth" framework allowing for a fine control of the amount of residual stresses generated during tissue growth. It is a direct extension of the classical framework of the multiplicative decomposition of the transformation gradient, to which an additional sub-transformation is introduced in order to let the original unloaded configuration evolve, hence relieving some residual stresses. We provide multiple illustrations of the framework mechanical response, on time-driven constrained growth as well as the strain-driven growth problem of the artery under internal pressure, including the opening angle experiment.

FINDINGS

The novel relaxed growth modeling framework introduced in this paper allows for a better control of growth-induced residual stresses compared to standard growth models based on the multiplicative decomposition of the transformation gradient.

INTERPRETATION

Growth-induced residual stresses should be better handled in soft tissues biomechanical models, especially in patient-specific models of diseased organs that are aimed at augmented diagnosis and treatment optimization.

A rule-based method for predicting the electrical activation of the heart with cardiac resynchronization therapy from non-invasive clinical data

Background

Cardiac Resynchronization Therapy (CRT) is one of the few effective treatments for heart failure patients with ventricular dyssynchrony. The pacing location of the left ventricle is indicated as a determinant of CRT outcome.

Objective

Patient specific computational models allow the activation pattern following CRT implant to be predicted and this may be used to optimize CRT lead placement.

Methods

In this study, the effects of heterogeneous cardiac substrate (scar, fast endocardial conduction, slow septal conduction, functional block) on accurately predicting the electrical activation of the LV epicardium were tested to determine the minimal detail required to create a rule based model of cardiac electrophysiology. Non-invasive clinical data (CT or CMR images and 12 lead ECG) from eighteen patients from two centers were used to investigate the models.

Results

Validation with invasive electro-anatomical mapping data identified that computer models with fast endocardial conduction were able to predict the electrical activation with a mean distance errors of 9.2 ± 0.5 mm (CMR data) or (CT data) 7.5 ± 0.7 mm.

Conclusion

This study identified a simple rule-based fast endocardial conduction model, built using non-invasive clinical data that can be used to rapidly and robustly predict the electrical activation of the heart. Pre-procedural prediction of the latest electrically activating region to identify the optimal LV pacing site could potentially be a useful clinical planning tool for CRT procedures.

Cardiac Resynchronization Therapy Optimization: A Comprehensive Approach

Since the first report on biventricular pacing in 1994, cardiac resynchronization therapy (CRT) has become standard for patients with advanced heart failure (HF) and ventricular conduction delay. CRT improves myocardial function by resynchronizing myocardial contraction, which results in reverse left ventricular remodeling and improves symptoms and clinical outcomes. Despite the accelerated development of CRT device technology and its increased application in treating HF patients, almost one-third of these patients do not respond to the therapy or gain any clinical benefit from device implantation. Over the last decade, multiple cardiac imaging modalities have provided a deeper understanding of myocardial pathophysiology, thereby improving HF treatment management. However, the optimal strategy for improving the CRT response remains debatable. This article provides an updated overview of the electropathophysiology of myocardial dysfunction in ventricular conduction delay and the diagnostic approaches involving the use of multiple modalities.

Population-based priors in cardiac model personalisation for consistent parameter estimation in heterogeneous databases

Personalised cardiac models are a virtual representation of the patient heart, with parameter values for which the simulation fits the available clinical measurements. Models usually have a large number of parameters while the available data for a given patient are typically limited to a small set of measurements; thus, the parameters cannot be estimated uniquely. This is a practical obstacle for clinical applications, where accurate parameter values can be important. Here, we explore an original approach based on an algorithm called Iteratively Updated Priors (IUP), in which we perform successive personalisations of a full database through maximum a posteriori (MAP) estimation, where the prior probability at an iteration is set from the distribution of personalised parameters in the database at the previous iteration. At the convergence of the algorithm, estimated parameters of the population lie on a linear subspace of reduced (and possibly sufficient) dimension in which for each case of the database, there is a (possibly unique) parameter value for which the simulation fits the measurements. We first show how this property can help the modeller select a relevant parameter subspace for personalisation. In addition, since the resulting priors in this subspace represent the population statistics in this subspace, they can be used to perform consistent parameter estimation for cases where measurements are possibly different or missing in the database, which we illustrate with the personalisation of a heterogeneous database of 811 cases.

A short history of the development of mathematical models of cardiac mechanics

Cardiac mechanics plays a crucial role in atrial and ventricular function, in the regulation of growth and remodelling, in the progression of disease, and the response to treatment. The spatial scale of the critical mechanisms ranges from nm (molecules) to cm (hearts) with the fastest events occurring in milliseconds (molecular events) and the slowest requiring months (growth and remodelling). Due to its complexity and importance, cardiac mechanics has been studied extensively both experimentally and through mathematical models and simulation. Models of cardiac mechanics evolved from seminal studies in skeletal muscle, and developed into cardiac specific, species specific, human specific and finally patient specific calculations. These models provide a formal framework to link multiple experimental assays recorded over nearly 100 years into a single unified representation of cardiac function. This review first provides a summary of the proteins, physiology and anatomy involved in the generation of cardiac pump function. We then describe the evolution of models of cardiac mechanics starting with the early theoretical frameworks describing the link between sarcomeres and muscle contraction, transitioning through myosin-level models to calcium-driven systems, and ending with whole heart patient-specific models.

Uniqueness of local myocardial strain patterns with respect to activation time and contractility of the failing heart: a computational study

Background

Myocardial deformation measured by strain is used to detect electro-mechanical abnormalities in cardiac tissue. Estimation of myocardial properties from regional strain patterns when multiple pathologies are present is therefore a promising application of computer modelling. However, if different tissue properties lead to indistinguishable strain patterns (‘degeneracy’), the applicability of any such method will be limited. We investigated whether estimation of local activation time (AT) and contractility from myocardial strain patterns is theoretically possible.

Methods

For four different global cardiac pathologies local myocardial strain patterns for 1025 combinations of AT and contractility were simulated with a computational model (CircAdapt). For each strain pattern, a cohort of similar patterns was found within estimated measurement error using the sum of least-squared differences. Cohort members came from (1) the same pathology only, and (2) all four pathologies. Uncertainty was calculated as accuracy and precision of cohort members in parameter space. Connectedness within the cohorts was also studied.

Results

We found that cohorts drawn from one pathology had parameters with adjacent values although their distribution was neither constant nor symmetrical. In comparison cohorts drawn from four pathologies had disconnected components with drastically different parameter values and accuracy and precision values up to three times higher.

Conclusions

Global pathology must be known when extracting AT and contractility from strain patterns, otherwise degeneracy occurs causing unacceptable uncertainty in derived parameters.

Electronic supplementary material

The online version of this article (10.1186/s12938-018-0614-1) contains supplementary material, which is available to authorized users.

Fully coupled fluid-electro-mechanical model of the human heart for supercomputers

In this work, we present a fully coupled fluid-electro-mechanical model of a 50th percentile human heart. The model is implemented on Alya, the BSC multi-physics parallel code, capable of running efficiently in supercomputers. Blood in the cardiac cavities is modeled by the incompressible Navier-Stokes equations and an arbitrary Lagrangian-Eulerian (ALE) scheme. Electrophysiology is modeled with a monodomain scheme and the O'Hara-Rudy cell model. Solid mechanics is modeled with a total Lagrangian formulation for discrete strains using the Holzapfel-Ogden cardiac tissue material model. The three problems are simultaneously and bidirectionally coupled through an electromechanical feedback and a fluid-structure interaction scheme. In this paper, we present the scheme in detail and propose it as a computational cardiac workbench.

Electromechanical Model to Predict Cardiac Resynchronization Therapy

Cardiac resynchronization therapy (CRT) can substantially improve dyssynchronous heart failure and reduce mortality. However, one-third of the CRT patients derive no measurable benefit from CRT, due to suboptimal placement of the left ventricular (LV) lead. We introduce a pipeline for improved CRT-therapy by creating an electromechanical model using patient-specific geometric parameters allowing individualization of therapy. The model successfully mimics expected changes when variables for tension, stiffness, and conduction are entered. Changing LV pacing site had a notable effect on maximum pressure gradient (dP/dt_max) in the presence of cardiac scarring, causing non-uniform excitation propagation through the LV. Tailoring CRT to the individual requires simulations with patient-specific biventricular meshes including cardiac geometry and conductivity properties.