Patient-Specific Models of Cardiac Biomechanics

Building Digital Twins for Cardiovascular Health: From Principles to Clinical Impact

The past several decades have seen rapid advances in diagnosis and treatment of cardiovascular diseases and stroke, enabled by technological breakthroughs in imaging, genomics, and physiological monitoring, coupled with therapeutic interventions. We now face the challenge of how to (1) rapidly process large, complex multimodal and multiscale medical measurements; (2) map all available data streams to the trajectories of disease states over the patient's lifetime; and (3) apply this information for optimal clinical interventions and outcomes. Here we review new advances that may address these challenges using digital twin technology to fulfill the promise of personalized cardiovascular medical practice. Rooted in engineering mechanics and manufacturing, the digital twin is a virtual representation engineered to model and simulate its physical counterpart. Recent breakthroughs in scientific computation, artificial intelligence, and sensor technology have enabled rapid bidirectional interactions between the virtual-physical counterparts with measurements of the physical twin that inform and improve its virtual twin, which in turn provide updated virtual projections of disease trajectories and anticipated clinical outcomes. Verification, validation, and uncertainty quantification builds confidence and trust by clinicians and patients in the digital twin and establishes boundaries for the use of simulations in cardiovascular medicine. Mechanistic physiological models form the fundamental building blocks of the personalized digital twin that continuously forecast optimal management of cardiovascular health using individualized data streams. We present exemplars from the existing body of literature pertaining to mechanistic model development for cardiovascular dynamics and summarize existing technical challenges and opportunities pertaining to the foundation of a digital twin.

Multiscale fiber remodeling in the infarcted left ventricle using a stress-based reorientation law

The organization of myofibers and extra cellular matrix within the myocardium plays a significant role in defining cardiac function. When pathological events occur, such as myocardial infarction (MI), this organization can become disrupted, leading to degraded pumping performance. The current study proposes a multiscale finite element (FE) framework to determine realistic fiber distributions in the left ventricle (LV). This is achieved by implementing a stress-based fiber reorientation law, which seeks to align the fibers with local traction vectors, such that contractile force and load bearing capabilities are maximized. By utilizing the total stress (passive and active), both myofibers and collagen fibers are reoriented. Simulations are conducted to predict the baseline fiber configuration in a normal LV as well as the adverse fiber reorientation that occurs due to different size MIs. The baseline model successfully captures the transmural variation of helical fiber angles within the LV wall, as well as the transverse fiber angle variation from base to apex. In the models of MI, the patterns of fiber reorientation in the infarct, border zone, and remote regions closely align with previous experimental findings, with a significant increase in fibers oriented in a left-handed helical configuration and increased dispersion in the infarct region. Furthermore, the severity of fiber reorientation and impairment of pumping performance both showed a correlation with the size of the infarct. The proposed multiscale modeling framework allows for the effective prediction of adverse remodeling and offers the potential for assessing the effectiveness of therapeutic interventions in the future. STATEMENT OF SIGNIFICANCE: The organization of muscle and collagen fibers within the heart plays a significant role in defining cardiac function. This organization can become disrupted after a heart attack, leading to degraded pumping performance. In the current study, we implemented a stress-based fiber reorientation law into a computer model of the heart, which seeks to realign the fibers such that contractile force and load bearing capabilities are maximized. The primary goal was to evaluate the effects of different sized heart attacks. We observed substantial fiber remodeling in the heart, which matched experimental observations. The proposed computational framework allows for the effective prediction of adverse remodeling and offers the potential for assessing the effectiveness of therapeutic interventions in the future.

Successful cardiac resynchronization therapy reduces negative septal work in patient-specific models of dyssynchronous heart failure

In patients with dyssynchronous heart failure (DHF), cardiac conduction abnormalities cause the regional distribution of myocardial work to be non-homogeneous. Cardiac resynchronization therapy (CRT) using an implantable, programmed biventricular pacemaker/defibrillator, can improve the synchrony of contraction between the right and left ventricles in DHF, resulting in reduced morbidity and mortality and increased quality of life. Since regional work depends on wall stress, which cannot be measured in patients, we used computational methods to investigate regional work distributions and their changes after CRT. We used three-dimensional multi-scale patient-specific computational models parameterized by anatomic, functional, hemodynamic, and electrophysiological measurements in eight patients with heart failure and left bundle branch block (LBBB) who received CRT. To increase clinical translatability, we also explored whether streamlined computational methods provide accurate estimates of regional myocardial work. We found that CRT increased global myocardial work efficiency with significant improvements in non-responders. Reverse ventricular remodeling after CRT was greatest in patients with the highest heterogeneity of regional work at baseline, however the efficacy of CRT was not related to the decrease in overall work heterogeneity or to the reduction in late-activated regions of high myocardial work. Rather, decreases in early-activated regions of myocardium performing negative myocardial work following CRT best explained patient variations in reverse remodeling. These findings were also observed when regional myocardial work was estimated using ventricular pressure as a surrogate for myocardial stress and changes in endocardial surface area as a surrogate for strain. These new findings suggest that CRT promotes reverse ventricular remodeling in human dyssynchronous heart failure by increasing regional myocardial work in early-activated regions of the ventricles, where dyssynchrony is specifically associated with hypoperfusion, late systolic stretch, and altered metabolic activity and that measurement of these changes can be performed using streamlined approaches.

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

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

Successful Cardiac Resynchronization Therapy Reduces Negative Septal Work in Patient-Specific Models of Dyssynchronous Heart Failure

In patients with dyssynchronous heart failure (DHF), cardiac conduction abnormalities cause the regional distribution of myocardial work to be non-homogeneous. Cardiac resynchronization therapy (CRT) using an implantable, programmed biventricular pacemaker/defibrillator, can improve the synchrony of contraction between the right and left ventricles in DHF, resulting in reduced morbidity and mortality and increased quality of life. Since regional work depends on wall stress, which cannot be measured in patients, we used computational methods to investigate regional work distributions and their changes after CRT. We used three-dimensional multi-scale patient-specific computational models parameterized by anatomic, functional, hemodynamic, and electrophysiological measurements in eight patients with heart failure and left bundle branch block (LBBB) who received CRT. To increase clinical translatability, we also explored whether streamlined computational methods provide accurate estimates of regional myocardial work. We found that CRT increased global myocardial work efficiency with significant improvements in non-responders. Reverse ventricular remodeling after CRT was greatest in patients with the highest heterogeneity of regional work at baseline, however the efficacy of CRT was not related to the decrease in overall work heterogeneity or to the reduction in late-activated regions of high myocardial work. Rather, decreases in early-activated regions of myocardium performing negative myocardial work following CRT best explained patient variations in reverse remodeling. These findings were also observed when regional myocardial work was estimated using ventricular pressure as a surrogate for myocardial stress and changes in endocardial surface area as a surrogate for strain. These new findings suggest that CRT promotes reverse ventricular remodeling in human dyssynchronous heart failure by increasing regional myocardial work in early-activated regions of the ventricles, where dyssynchrony is specifically associated with hypoperfusion, late systolic stretch, and altered metabolic activity and that measurement of these changes can be performed using streamlined approaches.

Current progress toward isogeometric modeling of the heart biophysics

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

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.

Computational modeling of ventricular-ventricular interactions suggest a role in clinical conditions involving heart failure

Introduction: The left (LV) and right (RV) ventricles are linked biologically, hemodynamically, and mechanically, a phenomenon known as ventricular interdependence. While LV function has long been known to impact RV function, the reverse is increasingly being realized to have clinical importance. Investigating ventricular interdependence clinically is challenging given the invasive measurements required, including biventricular catheterization, and confounding factors such as comorbidities, volume status, and other aspects of subject variability. Methods: Computational modeling allows investigation of mechanical and hemodynamic interactions in the absence of these confounding factors. Here, we use a threesegment biventricular heart model and simple circulatory system to investigate ventricular interdependence under conditions of systolic and diastolic dysfunction of the LV and RV in the presence of compensatory volume loading. We use the end-diastolic pressure-volume relationship, end-systolic pressure-volume relationship, Frank Starling curves, and cardiac power output as metrics. Results: The results demonstrate that LV systolic and diastolic dysfunction lead to RV compensation as indicated by increases in RV power. Additionally, RV systolic and diastolic dysfunction lead to impaired LV filling, interpretable as LV stiffening especially with volume loading to maintain systemic pressure. Discussion: These results suggest that a subset of patients with intact LV systolic function and diagnosed to have impaired LV diastolic function, categorized as heart failure with preserved ejection fraction (HFpEF), may in fact have primary RV failure. Application of this computational approach to clinical data sets, especially for HFpEF, may lead to improved diagnosis and treatment strategies and consequently improved outcomes.

Physical model of end-diastolic and end-systolic pressure-volume relationships of a heart

Left ventricular stiffness and contractility, characterized by the end-diastolic pressure-volume relationship (EDPVR) and the end-systolic pressure-volume relationship (ESPVR), are two important indicators of the performance of the human heart. Although much research has been conducted on EDPVR and ESPVR, no model with physically interpretable parameters combining both relationships has been presented, thereby impairing the understanding of cardiac physiology and pathology. Here, we present a model that evaluates both EDPVR and ESPVR with physical interpretations of the parameters in a unified framework. Our physics-based model fits the available experimental data and in silico results very well and outperforms existing models. With prescribed parameters, the new model is used to predict the pressure-volume relationships of the left ventricle. Our model provides a deeper understanding of cardiac mechanics and thus will have applications in cardiac research and clinical medicine.

A biomechanics-based parametrized cardiac end-diastolic pressure-volume relationship for accurate patient-specific calibration and estimation

A simple power law has been proposed in the pioneering work of Klotz et al. (Am J Physiol Heart Circ Physiol 291(1):H403-H412, 2006) to approximate the end-diastolic pressure-volume relationship of the left cardiac ventricle, with limited inter-individual variability provided the volume is adequately normalized. Nevertheless, we use here a biomechanical model to investigate the sources of the remaining data dispersion observed in the normalized space, and we show that variations of the parameters of the biomechanical model realistically account for a substantial part of this dispersion. We therefore propose an alternative law based on the biomechanical model that embeds some intrinsic physical parameters, which directly enables personalization capabilities, and paves the way for related estimation approaches.

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.

Correcting bias in cardiac geometries derived from multimodal images using spatiotemporal mapping

Cardiovascular imaging studies provide a multitude of structural and functional data to better understand disease mechanisms. While pooling data across studies enables more powerful and broader applications, performing quantitative comparisons across datasets with varying acquisition or analysis methods is problematic due to inherent measurement biases specific to each protocol. We show how dynamic time warping and partial least squares regression can be applied to effectively map between left ventricular geometries derived from different imaging modalities and analysis protocols to account for such differences. To demonstrate this method, paired real-time 3D echocardiography (3DE) and cardiac magnetic resonance (CMR) sequences from 138 subjects were used to construct a mapping function between the two modalities to correct for biases in left ventricular clinical cardiac indices, as well as regional shape. Leave-one-out cross-validation revealed a significant reduction in mean bias, narrower limits of agreement, and higher intraclass correlation coefficients for all functional indices between CMR and 3DE geometries after spatiotemporal mapping. Meanwhile, average root mean squared errors between surface coordinates of 3DE and CMR geometries across the cardiac cycle decreased from 7 ± 1 to 4 ± 1 mm for the total study population. Our generalised method for mapping between time-varying cardiac geometries obtained using different acquisition and analysis protocols enables the pooling of data between modalities and the potential for smaller studies to leverage large population databases for quantitative comparisons.

Validating MRI-Derived Myocardial Stiffness Estimates Using In Vitro Synthetic Heart Models

Impaired cardiac filling in response to increased passive myocardial stiffness contributes to the pathophysiology of heart failure. By leveraging cardiac MRI data and ventricular pressure measurements, we can estimate in vivo passive myocardial stiffness using personalized inverse finite element models. While it is well-known that this approach is subject to uncertainties, only few studies quantify the accuracy of these stiffness estimates. This lack of validation is, at least in part, due to the absence of ground truth in vivo passive myocardial stiffness values. Here, using 3D printing, we created soft, homogenous, isotropic, hyperelastic heart phantoms of varying geometry and stiffness and simulate diastolic filling by incorporating the phantoms into an MRI-compatible left ventricular inflation system. We estimate phantom stiffness from MRI and pressure data using inverse finite element analyses based on a Neo-Hookean model. We demonstrate that our identified softest and stiffest values of 215.7 and 512.3 kPa agree well with the ground truth of 226.2 and 526.4 kPa. Overall, our estimated stiffnesses revealed a good agreement with the ground truth ([Formula: see text] error) across all models. Our results suggest that MRI-driven computational constitutive modeling can accurately estimate synthetic heart material stiffnesses in the range of 200-500 kPa.

Optimization framework for patient-specific modeling under uncertainty

Estimating a patient-specific computational model's parameters relies on data that is often unreliable and ill-suited for a deterministic approach. We develop an optimization-based uncertainty quantification framework for probabilistic model tuning that discovers model inputs distributions that generate target output distributions. Probabilistic sampling is performed using a surrogate model for computational efficiency, and a general distribution parameterization is used to describe each input. The approach is tested on seven patient-specific modeling examples using CircAdapt, a cardiovascular circulatory model. Six examples are synthetic, aiming to match the output distributions generated using known reference input data distributions, while the seventh example uses real-world patient data for the output distributions. Our results demonstrate the accurate reproduction of the target output distributions, with a correct recreation of the reference inputs for the six synthetic examples. Our proposed approach is suitable for determining the parameter distributions of patient-specific models with uncertain data and can be used to gain insights into the sensitivity of the model parameters to the measured data.

Patient-specific stomach biomechanics before and after laparoscopic sleeve gastrectomy

BACKGROUND

Obesity has become a global epidemic. Bariatric surgery is considered the most effective therapeutic weapon in terms of weight loss and improvement of quality of life and comorbidities. Laparoscopic sleeve gastrectomy (LSG) is one of the most performed procedures worldwide, although patients carry a nonnegligible risk of developing post-operative GERD and BE.

OBJECTIVES

The aim of this work is the development of computational patient-specific models to analyze the changes induced by bariatric surgery, i.e., the volumetric gastric reduction, the mechanical response of the stomach during an inflation process, and the related elongation strain (ES) distribution at different intragastric pressures.

METHODS

Patient-specific pre- and post-surgical models were extracted from Magnetic Resonance Imaging (MRI) scans of patients with morbid obesity submitted to LSG. Twenty-three patients were analyzed, resulting in forty-six 3D-geometries and related computational analyses.

RESULTS

A significant difference between the mechanical behavior of pre- and post-surgical stomach subjected to the same internal gastric pressure was observed, that can be correlated to a change in the global stomach stiffness and a minor gastric wall tension, resulting in unusual activations of mechanoreceptors following food intake and satiety variation after LSG.

CONCLUSIONS

Computational patient-specific models may contribute to improve the current knowledge about anatomical and physiological changes induced by LSG, aiming at reducing post-operative complications and improving quality of life in the long run.

An Atlas-Based Analysis of Biventricular Mechanics in Tetralogy of Fallot

The current study proposes an efficient strategy for exploiting the statistical power of cardiac atlases to investigate whether clinically significant variations in ventricular shape are sufficient to explain corresponding differences in ventricular wall motion directly, or if they are indirect markers of altered myocardial mechanical properties. This study was conducted in a cohort of patients with repaired tetralogy of Fallot (rTOF) that face long-term right ventricular (RV) and/or left ventricular (LV) dysfunction as a consequence of adverse remodeling. Features of biventricular end-diastolic (ED) shape associated with RV apical dilation, LV dilation, RV basal bulging, and LV conicity correlated with components of systolic wall motion (SWM) that contribute most to differences in global systolic function. A finite element analysis of systolic biventricular mechanics was employed to assess the effect of perturbations in these ED shape modes on corresponding components of SWM. Perturbations to ED shape modes and myocardial contractility explained observed variation in SWM to varying degrees. In some cases, shape markers were partial determinants of systolic function and, in other cases, they were indirect markers for altered myocardial mechanical properties. Patients with rTOF may benefit from an atlas-based analysis of biventricular mechanics to improve prognosis and gain mechanistic insight into underlying myocardial pathophysiology.

Forward-Solution Noninvasive Computational Arrhythmia Mapping: The VMAP Study

BACKGROUND

The accuracy of noninvasive arrhythmia source localization using a forward-solution computational mapping system has not yet been evaluated in blinded, multicenter analysis. This study tested the hypothesis that a computational mapping system incorporating a comprehensive arrhythmia simulation library would provide accurate localization of the site-of-origin for atrial and ventricular arrhythmias and pacing using 12-lead ECG data when compared with the gold standard of invasive electrophysiology study and ablation.

METHODS

The VMAP study (Vectorcardiographic Mapping of Arrhythmogenic Probability) was a blinded, multicenter evaluation with final data analysis performed by an independent core laboratory. Eligible episodes included atrial and ventricular: tachycardia, fibrillation, pacing, premature atrial and ventricular complexes, and orthodromic atrioventricular reentrant tachycardia. Mapping system results were compared with the gold standard site of successful ablation or pacing during electrophysiology study and ablation. Mapping time was assessed from time-stamped logs. Prespecified performance goals were used for statistical comparisons.

RESULTS

A total of 255 episodes from 225 patients were enrolled from 4 centers. Regional accuracy for ventricular tachycardia and premature ventricular complexes in patients without significant structural heart disease (n=75, primary end point) was 98.7% (95% CI, 96.0%-100%; P<0.001 to reject predefined H0 <0.80). Regional accuracy for all episodes (secondary end point 1) was 96.9% (95% CI, 94.7%-99.0%; P<0.001 to reject predefined H0 <0.75). Accuracy for the exact or neighboring segment for all episodes (secondary end point 2) was 97.3% (95% CI, 95.2%-99.3%; P<0.001 to reject predefined H0 <0.70). Median spatial accuracy was 15 mm (n=255, interquartile range, 7-25 mm). The mapping process was completed in a median of 0.8 minutes (interquartile range, 0.4-1.4 minutes).

CONCLUSIONS

Computational ECG mapping using a forward-solution approach exceeded prespecified accuracy goals for arrhythmia and pacing localization. Spatial accuracy analysis demonstrated clinically actionable results. This rapid, noninvasive mapping technology may facilitate catheter-based and noninvasive targeted arrhythmia therapies.

REGISTRATION

URL: https://www.

CLINICALTRIALS

gov; Unique identifier: NCT04559061.

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.

Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics

Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

Simulation of the 3D Hyperelastic Behavior of Ventricular Myocardium using a Finite-Element Based Neural-Network Approach

High-fidelity cardiac models using attribute-rich finite element based models have been developed to a very mature stage. However, such finite-element based approaches remain time consuming, which have limited their clinical use. There remains a need for alternative methods for novel cardiac simulation methods of capable of high fidelity simulations in clinically relevant time frames. Surrogate models are one approach, which traditionally use a data-driven approach for training, requiring the generation of a sufficiently large number of simulation results as the training dataset. Alternatively, a physics-informed neural network can be trained by minimizing the PDE residuals or energy potentials. However, this approach does not provide for a general method to easily using existing finite element models. To address these challenges, we developed a hybrid approach that seamlessly bridged a neural network surrogate model with a differentiable finite element domain representation (NNFE). Given its importance in cardiac simulations, we applied this approach to simulations of the hyperelastic mechanical behavior of ventricular myocardium from recent 3D kinematic constitutive model (J Mech Behav Biomed Mater, 2020 doi: 10.1016/j.jmbbm.2019.103508). We utilized cuboidal domain and conducted numerical studies of individual myocardium specimens discretized by a finite element mesh and assigned with experimentally obtained myofiber architectures. Both parameterized Dirichlet and Neumann boundary conditions were studied. We developed a second-order Newton optimization method, instead of using stochastic gradient descent method, to train the neural network efficiently. The resulting trained neural network surrogate model demonstrated excellent agreement with the corresponding 'ground truth' finite element solutions over the entire physiological deformation range. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes for online predictions. For example, as the finite element mesh sized increased from 2744 to 175615 elements the NNFE computational time increased from 0.1108 s to 0.1393 s, while the 'ground truth' FE model increased from 4.541 s to 719.9 s. These results suggests that NNFE run times can be significantly reduced compared with the traditional large-deformation based finite element solution methods. The trade off is to train the NNFE off-line within a range of anticipated physiological responses. However, training time would only have to be performed once before any number of application uses. Moreover, since the NNFE is an analytical function its computational performance will be amplified when the corresponding problem becomes more complex.

Estimation of Regional Pulmonary Compliance in Idiopathic Pulmonary Fibrosis Based On Personalized Lung Poromechanical Modeling

Pulmonary function is tightly linked to the lung mechanical behavior, especially large deformation during breathing. Interstitial lung diseases, such as Idiopathic Pulmonary Fibrosis (IPF), have an impact on the pulmonary mechanics and consequently alter lung function. However, IPF remains poorly understood, poorly diagnosed and poorly treated. Currently, the mechanical impact of such diseases is assessed by pressure-volume curves, giving only global information. We developed a poromechanical model of the lung that can be personalized to a patient based on routine clinical data. The personalization pipeline uses clinical data, mainly CT-images at two time steps and involves the formulation of an inverse problem to estimate regional compliances. The estimation problem can be formulated both in terms of "effective", i.e., without considering the mixture porosity, or "rescaled", i.e., where the first-order effect of the porosity has been taken into account, compliances. Regional compliances are estimated for one control subject and three IPF patients, allowing to quantify the IPF-induced tissue stiffening. This personalized model could be used in the clinic as an objective and quantitative tool for IPF diagnosis.

The effects of viscoelasticity on residual strain in aortic soft tissues

Residual stress is thought to play a critical role in modulating stress distributions in soft biological tissues and in maintaining the mechanobiological stress environment of cells. Residual stresses in arteries and other tissues are classically assessed through opening angle experiments, which demonstrate the continuous release of residual stresses over hours. These results are then assessed through nonlinear biomechanical models to provide estimates of the residual stresses in the intact state. Although well studied, these analyses typically focus on hyperelastic material models despite significant evidence of viscoelastic phenomena over both short and long timescales. In this work, we extended the state-of-the-art structural tensor model for arterial tissues from Holzapfel and Ogden for fractional viscoelasticity. Models were tuned to capture consistent levels of hysteresis observed in biaxial experiments, while also minimizing the fractional viscoelastic weighting and opening angles to correctly capture opening angle dynamics. Results suggest that a substantial portion of the human abdominal aorta is viscoelastic, but exhibits a low fractional order (i.e. more elastically). Additionally, a significantly larger opening angle in the fully unloaded state is necessary to produce comparable hysteresis in biaxial testing. As a consequence, conventional estimates of residual stress using hyperelastic approaches over-estimate their viscoelastic counterparts by a factor of 2. Thus, a viscoelastic approach, such as the one illustrated in this study, in combination with an additional source of rate-controlled viscoelastic data is necessary to accurately analyze the residual stress distribution in soft biological tissues. STATEMENT OF SIGNIFICANCE: Residual stress plays a crucial role in achieving a homeostatic stress environment in soft biological tissues. However, the analysis of residual stress typically focuses on hyperelastic material models despite evidence of viscoelastic behavior. This work is the first attempt at analyzing the effects of viscoelasticity on residual stress. The application of viscoelasticity was crucial for producing realistic opening dynamics in arteries. The overall residual stresses were estimated to be 50% less than those from using hyperelastic material models, while the opening angles were projected to be 25% more than those measured after 16 hours, suggesting underestimated residual strain. This study highlights the importance viscoelasticity in the analysis of residual stress even in weakly dissipative materials like the human aorta.

Design and Evaluation of Personalized Percutaneous Coronary Intervention Surgery Simulation System

In recent years, medical simulators have been widely applied to a broad range of surgery training tasks. However, most of the existing surgery simulators can only provide limited immersive environments with a few pre-processed organ models, while ignoring the instant modeling of various personalized clinical cases, which brings substantive differences between training experiences and real surgery situations. To this end, we present a virtual reality (VR) based surgery simulation system for personalized percutaneous coronary intervention (PCI). The simulation system can directly take patient-specific clinical data as input and generate virtual 3D intervention scenarios. Specially, we introduce a fiber-based patient-specific cardiac dynamic model to simulate the nonlinear deformation among the multiple layers of the cardiac structure, which can well respect and correlate the atriums, ventricles and vessels, and thus gives rise to more effective visualization and interaction. Meanwhile, we design a tracking and haptic feedback hardware, which can enable users to manipulate physical intervention instruments and interact with virtual scenarios. We conduct quantitative analysis on deformation precision and modeling efficiency, and evaluate the simulation system based on the user studies from 16 cardiologists and 20 intervention trainees, comparing it to traditional desktop intervention simulators. The results confirm that our simulation system can provide a better user experience, and is a suitable platform for PCI surgery training and rehearsal.

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.

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.

Atlas-based methods for efficient characterization of patient-specific ventricular activation patterns

AIMS

Ventricular activation patterns can aid clinical decision-making directly by providing spatial information on cardiac electrical activation or indirectly through derived clinical indices. The aim of this work was to derive an atlas of the major modes of variation of ventricular activation from model-predicted 3D bi-ventricular activation time distributions and to relate these modes to corresponding vectorcardiograms (VCGs). We investigated how the resulting dimensionality reduction can improve and accelerate the estimation of activation patterns from surface electrogram measurements.

METHODS AND RESULTS

Atlases of activation time (AT) and VCGs were derived using principal component analysis on a dataset of simulated electrophysiology simulations computed on eight patient-specific bi-ventricular geometries. The atlases provided significant dimensionality reduction, and the modes of variation in the two atlases described similar features. Utility of the atlases was assessed by resolving clinical waveforms against them and the VCG atlas was able to accurately reconstruct the patient VCGs with fewer than 10 modes. A sensitivity analysis between the two atlases was performed by calculating a compact Jacobian. Finally, VCGs generated by varying AT atlas modes were compared with clinical VCGs to estimate patient-specific activation maps, and the resulting errors between the clinical and atlas-based VCGs were less than those from more computationally expensive method.

CONCLUSION

Atlases of activation and VCGs represent a new method of identifying and relating the features of these high-dimensional signals that capture the major sources of variation between patients and may aid in identifying novel clinical indices of arrhythmia risk or therapeutic outcome.

Deep reinforcement learning in medical imaging: A literature review

Deep reinforcement learning (DRL) augments the reinforcement learning framework, which learns a sequence of actions that maximizes the expected reward, with the representative power of deep neural networks. Recent works have demonstrated the great potential of DRL in medicine and healthcare. This paper presents a literature review of DRL in medical imaging. We start with a comprehensive tutorial of DRL, including the latest model-free and model-based algorithms. We then cover existing DRL applications for medical imaging, which are roughly divided into three main categories: (i) parametric medical image analysis tasks including landmark detection, object/lesion detection, registration, and view plane localization; (ii) solving optimization tasks including hyperparameter tuning, selecting augmentation strategies, and neural architecture search; and (iii) miscellaneous applications including surgical gesture segmentation, personalized mobile health intervention, and computational model personalization. The paper concludes with discussions of future perspectives.

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

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

Cardiorenal Systems Modeling: Left Ventricular Hypertrophy and Differential Effects of Antihypertensive Therapies on Hypertrophy Regression

Cardiac and renal function are inextricably connected through both hemodynamic and neurohormonal mechanisms, and the interaction between these organ systems plays an important role in adaptive and pathophysiologic remodeling of the heart, as well as in the response to renally acting therapies. Insufficient understanding of the integrative function or dysfunction of these physiological systems has led to many examples of unexpected or incompletely understood clinical trial results. Mathematical models of heart and kidney physiology have long been used to better understand the function of these organs, but an integrated model of renal function and cardiac function and cardiac remodeling has not yet been published. Here we describe an integrated cardiorenal model that couples existing cardiac and renal models, and expands them to simulate cardiac remodeling in response to pressure and volume overload, as well as hypertrophy regression in response to angiotensin receptor blockers and beta-blockers. The model is able to reproduce different patterns of hypertrophy in response to pressure and volume overload. We show that increases in myocyte diameter are adaptive in pressure overload not only because it normalizes wall shear stress, as others have shown before, but also because it limits excess volume accumulation and further elevation of cardiac stresses by maintaining cardiac output and renal sodium and water balance. The model also reproduces the clinically observed larger LV mass reduction with angiotensin receptor blockers than with beta blockers. We further provide a mechanistic explanation for this difference by showing that heart rate lowering with beta blockers limits the reduction in peak systolic wall stress (a key signal for myocyte hypertrophy) relative to ARBs.

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.

Etiology-Discriminative Multimodal Imaging of Left Ventricular Hypertrophy and Synchrotron-Based Assessment of Microstructural Tissue Remodeling

Background: Distinguishing the etiology of left ventricular hypertrophy (LVH) is clinically relevant due to patient outcomes and management. Easily obtained, echocardiography-based myocardial deformation patterns may improve standard non-invasive phenotyping, however, the relationship between deformation phenotypes and etiology-related, microstructural cardiac remodeling has not been reported. Synchrotron radiation-based X-ray phase-contrast imaging (X-PCI) can provide high resolution, three-dimensional (3D) information on myocardial microstructure. The aim of this pilot study is to apply a multiscale, multimodality protocol in LVH patients undergoing septal myectomy to visualize in vivo and ex vivo myocardial tissue and relate non-invasive LVH imaging phenotypes to the underlying synchrotron-assessed microstructure. Methods and findings: Three patients (P1-3) undergoing septal myectomy were comprehensively studied. Medical history was collected, and patients were imaged with echocardiography/cardiac magnetic resonance prior to the procedure. Myocardial tissue samples obtained during the myectomy were imaged with X-PCI generating high spatial resolution images (0.65 μm) to assess myocyte organization, 3D connective tissue distribution and vasculature remodeling. Etiology-centered non-invasive imaging phenotypes, based on findings of hypertrophy and late gadolinium enhancement (LGE) distribution, and enriched by speckle-tracking and tissue Doppler echocardiography deformation patterns, identified a clear phenotype of hypertensive heart disease (HTN) in P1, and hypertrophic cardiomyopathy (HCM) in P2/P3. X-PCI showed extensive interstitial fibrosis with normal 3D myocyte and collagen organization in P1. In comparison, in P2/P3, X-PCI showed 3D myocyte and collagen disarray, as well as arterial wall hypertrophy with increased perivascular collagen, compatible with sarcomere-mutation HCM in both patients. The results of this pilot study suggest the association of non-invasive deformation phenotypes with etiology-related myocyte and connective tissue matrix disorganization. A larger patient cohort could enable statistical analysis of group characteristics and the assessment of deformation pattern reproducibility. Conclusion: High-resolution, 3D X-PCI provides novel ways to visualize myocardial remodeling in LVH, and illustrates the correspondence of macrostructural and functional non-invasive phenotypes with invasive microstructural phenotypes, suggesting the potential clinical utility of non-invasive myocardial deformation patterns in phenotyping LVH in everyday clinical practice.

Computational methods for parametric evaluation of the biventricular mechanics of direct cardiac compression

Despite the increasing incidence of heart failure, advancements in mechanical circulatory support have become minimal. A new type of mechanical circulatory support, direct cardiac compression, is a novel support paradigm that involves a soft deformable cup around the ventricles, compressing it during systole. No group has yet investigated the biomechanical consequences of such an approach. This article uses a multiscale cardiac simulation software to create a patient-specific beating heart dilated cardiomyopathy model. Left and right ventricle (LV and RV) forces are applied parametrically, to a maximum of 2.9 and 0.46 kPa on each ventricle, respectively. Compression increased the ejection fraction in the left and right ventricles from 15.3% and 27.4% to 24.8% and 38.7%, respectively. During applied compression, the LV freewall thickening increased while the RV decreased; this was found to be due to a change in the balance of the preload and afterload in the freewalls. Principal strain renderings demonstrated strain concentrations on the anterior and posterior LV freewall. Strains in these regions were found to exponentially increase after 0.75 normalized LV force was applied. Component analysis of these strains illuminated a shift in the dominating strain from transmural to cross fiber once 0.75 normalized LV force is exceeded. An optimization plot was created by nondimensionalizing the stroke volume and maximum principal strain for each compression profile, selecting five potential compression schemes. This work demonstrates not only the importance of a computational approach to direct cardiac compression but a framework for tailoring compression profiles to patients.

Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement

The left ventricle of the heart is a fundamental structure in the human cardiac system that pumps oxygenated blood into the systemic circulation. Several valvular conditions can cause the aortic and mitral valves associated with the left ventricle to become severely diseased and require replacement. However, the clinical outcomes of such operations, specifically the postoperative ventricular hemodynamics of replacing both valves, are not well understood. This work uses computational fluid-structure interaction (FSI) to develop an improved understanding of this effect by modeling a left ventricle with the aortic and mitral valves replaced with bioprostheses. We use a hybrid Arbitrary Lagrangian-Eulerian/immersogeometric framework to accommodate the analysis of cardiac hemodynamics and heart valve structural mechanics in a moving fluid domain. The motion of the endocardium is obtained from a cardiac biomechanics simulation and provided as an input to the proposed numerical framework. The results from the simulations in this work indicate that the replacement of the native mitral valve with a tri-radially symmetric bioprosthesis dramatically changes the ventricular hemodynamics. Most significantly, the vortical motion in the left ventricle is found to reverse direction after mitral valve replacement. This study demonstrates that the proposed computational FSI framework is capable of simulating complex multiphysics problems and can provide an in-depth understanding of the cardiac mechanics.

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

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

Comparisons of simulation results between passive and active fluid structure interaction models for left ventricle in hypertrophic obstructive cardiomyopathy

BACKGROUND

Patient-specific active fluid-structure interactions (FSI) model is a useful approach to non-invasively investigate the hemodynamics in the heart. However, it takes a lot of effort to obtain the proper external force boundary conditions for active models, which heavily restrained the time-sensitive clinical applications of active computational models.

METHODS

The simulation results of 12 passive FSI models based on 6 patients' pre-operative and post-operative CT images were compared with corresponding active models to investigate the differences in hemodynamics and cardiac mechanics between these models.

RESULTS

In comparing the passive and active models, it was found that there was no significant difference in pressure difference and shear stress on mitral valve leaflet (MVL) at the pre-SAM time point, but a significant difference was found in wall stress on the inner boundary of left ventricle (endocardium). It was also found that pressure difference on the coapted MVL and the shear stress on MVL were significantly decreased after successful surgery in both active and passive models.

CONCLUSION

Our results suggested that the passive models may provide good approximated hemodynamic results at 5% RR interval, which is crucial for analyzing the initiation of systolic anterior motion (SAM). Comparing to active models, the passive models decrease the complexity of the modeling construction and the difficulty of convergence significantly. These findings suggest that, with proper boundary conditions and sufficient clinical data, the passive computational model may be a good substitution model for the active model to perform hemodynamic analysis of the initiation of SAM.

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

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

Mechanical difference of left ventricle between rabbits of myocardial infarction and hypertrophy

The analysis of cardiac wall stress is of importance to understand the development of heart failure (HF). The aim of the study is to carry out the cardiac mechanics analysis to show the changes of left ventricular (LV) wall stresses after LV hypertrophy (LVH) and myocardial infarction (MI). Here, LVH and MI were generated in rabbit hearts through the transverse aortic constriction (TAC) and the distal left circumflex (LCx) artery ligation operations, respectively. Physiological and CT measurements were carried out at postoperative 2 and 4 weeks, based on which a finite element (FE) model was developed to perform the mechanics computation. We found a gradual increase of end-diastolic myofiber stress in free wall and interventricular septum of LVH and MI (higher stress in the free wall than the septum). In the interventricular septum, the 4-weeks LVH group has the highest ED myofiber stresses (11.378 ± 3.022 kPa), while the 4-weeks MI group has the highest ED myofiber stresses (13.494 ± 2.835 kPa) in the free wall. LVH increased myocardial volume (3.49 ± 0.07 and 4.52 ± 0.26 ml at postoperative 2 and 4 weeks) while MI increased LV volume (from 2.75 ± 0.29 to 4.19 ± 0.27 ml). LVH and MI had different distributions of local myofiber stress.

Efficient estimation of load-free left ventricular geometry and passive myocardial properties using principal component analysis

Models of cardiac mechanics require a well-defined reference geometry from which deformations and hence myocardial strain and stress can be calculated. In the in vivo beating heart, the load-free (LF) geometry generally cannot be measured directly, since, in many cases, there is no stage at which the lumen pressures and contractile state are all zero. Therefore, there is a need for an efficient method to estimate the LF geometry, which is essential for an accurate mechanical simulation of left ventricular (LV) mechanics, and for estimations of passive and contractile constitutive parameters of the heart muscle. In this paper, we present a novel method for estimating both the LF geometry and the passive stiffness of the myocardium. A linear combination of principal components from a population of diastolic displacements is used to construct the LF geometry. For each estimate of the LF geometry and tissue stiffness, LV inflation is simulated, and the model predictions are compared with surface data at multiple stages during passive diastolic filling. The feasibility of this method was demonstrated using synthetically deformation data that were generated using LV models derived from clinical magnetic resonance image data, and the identifiability of the LF geometry and passive stiffness parameters were analysed using Hessian metrics. Applications of this method to clinical data would improve the accuracy of constitutive parameter estimation and allow a better simulation of LV wall strains and stresses.

Insights into the passive mechanical behavior of left ventricular myocardium using a robust constitutive model based on full 3D kinematics

Myocardium possesses a hierarchical structure that results in complex three-dimensional (3D) mechanical behavior, forming a critical component of ventricular function in health and disease. A wide range of constitutive model forms have been proposed for myocardium since the first planar biaxial studies were performed by Demer and Yin (J. Physiol. 339 (1), 1983). While there have been extensive studies since, none have been based on full 3D kinematic data, nor have they utilized optimal experimental design to estimate constitutive parameters, which may limit their predictive capability. Herein we have applied our novel 3D numerical-experimental methodology (Avazmohammadi et al., Biomechanics Model. Mechanobiol. 2018) to explore the applicability of an orthotropic constitutive model for passive ventricular myocardium (Holzapfel and Ogden, Philos. Trans. R. Soc. Lond.: Math. Phys. Eng. Sci. 367, 2009) by integrating 3D optimal loading paths, spatially varying material structure, and inverse modeling techniques. Our findings indicated that the initial model form was not successful in reproducing all optimal loading paths, due to previously unreported coupling behaviors via shearing of myofibers and extracellular collagen fibers in the myocardium. This observation necessitated extension of the constitutive model by adding two additional terms based on the I8(C) pseudo-invariant in the fiber-normal and sheet-normal directions. The modified model accurately reproduced all optimal loading paths and exhibited improved predictive capabilities. These unique results suggest that more complete constitutive models are required to fully capture the full 3D biomechanical response of left ventricular myocardium. The present approach is thus crucial for improved understanding and performance in cardiac modeling in healthy, diseased, and treatment scenarios.

Speckle tracking echocardiography could detect the difference of pressure overload-induced myocardial remodelling between young and adult rats

The assessment by speckle tracking echocardiography (STE) provides useful information on regional and global left ventricular (LV) functions. The aim of the study is to investigate if STE-based strain analysis could detect the difference of pressure overload-induced myocardial remodelling between young and adult rats. Physiological, haemodynamic, histological measurements were performed post-operatively in young and adult rats with transverse aortic constriction (TAC) as well as the age-matched shams. Two-way ANOVA was used to detect the statistical difference of various measured parameters. Pressure overload decreased the ejection fraction, fractional shortening, dp/dt_max and |dp/dtmin|, but increased the LV end-diastolic (ED) pressure in adult rat hearts for nine weeks after TAC operation than those in young rat hearts. Pressure overload also resulted in different changes of peak strain and strain rate in the free wall, but similar changes in the interventricular septum of young and adult rat hearts. The changes in myocardial remodelling were confirmed by the histological analysis including the increased apoptosis rate of myocytes and collagen area ratio in the free wall of adult rat hearts of LV hypertrophy when compared with the young. Pressure overload alters myocardial components in different degrees between young and adult animals. STE-based strain analysis could detect the subtle difference of pressure overload-induced myocardial remodelling between young and adult rats.

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.

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.

Optimization Framework for Patient-Specific Cardiac Modeling

PURPOSE

Patient-specific models of the heart can be used to improve the diagnosis of cardiac diseases, but practical application of these models can be impeded by the computational costs and numerical uncertainties of fitting mechanistic models to clinical measurements from individual patients. Reliable and efficient tuning of these models within clinically appropriate error bounds is a requirement for practical deployment in the time-constrained environment of the clinic.

METHODS

We developed an optimization framework to tune parameters of patient-specific mechanistic models using routinely-acquired non-invasive patient data more efficiently than manual methods. We employ a hybrid particle swarm and pattern search optimization algorithm, but the framework can be readily adapted to use other optimization algorithms.

RESULTS

We apply the proposed framework to tune full-cycle lumped parameter circulatory models using clinical data. We show that our framework can be easily adapted to optimize cross-species models by tuning the parameters of the same circulation model to four canine subjects.

CONCLUSIONS

This work will facilitate the use of biomechanics and circulatory cardiac models in both clinical and research environments by ameliorating the tedious process of manually fitting the parameters.

Cardiac wall mechanics analysis in hypertension-induced heart failure rats with preserved ejection fraction

Although cardiac wall mechanics is of importance for understanding heart failure with preserved ejection fraction (HFpEF), there is a lack of relevant mechanics studies. The aim of this study was to analyze the changes in stress and strain in the left ventricle (LV) in hypertension-induced HFpEF rats. Based on experimental measurements in DSS rats fed with high-salt (HS) and low-salt (LS) diets, LV stress and strain were computed throughout the cardiac cycle using Continuity software. HS-feeding increased myofiber stress and strain along both the transmural and longitudinal directions at the end-diastolic state but resulted in a lower absolute value of strain and relatively unchanged stress at the end-systolic state. Moreover, the end-diastolic stress and strain decreased with increasing radial position from the endocardial towards the epicardial walls despite negligible changes along the longitudinal direction. The changes in LV wall mechanics characterized the elevated diastolic LV stiffness and slow LV relaxation in HS-fed rats of HFpEF. These findings denote that a vicious cycle of increased stress and strain and diastolic dysfunction can prompt the development of HFpEF.

Multiscale Models of Cardiac Muscle Biophysics and Tissue Remodeling in Hypertrophic Cardiomyopathies

Myocardial hypertrophy is the result of sustained perturbations to the mechanical and/or neurohormonal homeostasis of cardiac cells and is driven by integrated, multiscale biophysical and biochemical processes that are currently not well defined. In this brief review, we highlight recent computational and experimental models of cardiac hypertrophy that span mechanisms from the molecular level to the tissue level. Specifically, we focus on: (i) molecular-level models of the structural dynamics of sarcomere proteins in hypertrophic hearts, (ii) cellular-level models of excitation-contraction coupling and mechanosensitive signaling in disease-state myocytes, and (iii) organ-level models of myocardial growth kinematics and predictors thereof. Finally, we discuss how spanning these scales and combining multiple experimental/computational models will provide new information about the processes governing hypertrophy and potential methods to prevent or reverse them.

Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

A new mathematical model of the cardiovascular system is proposed. The left ventricle is described by an axisymmetric multiscale model where myocardium is treated as an incompressible transversely isotropic medium with a realistic distribution of fibre orientation. Active tension and its regulation by Ca²⁺ ions are described by our recent kinetic model. A lumped parameter model is used for the simulation of blood circulation, in which the left and right atria and the right ventricle are described by a system of ordinary differential equations for active pressure-volume relationships. The stress and strain of the left ventricle myocardium were calculated by the finite element method implemented by the authors. The changes in the haemodynamics upon changes in preload of a healthy heart, upon physical exercise, and in case of atrioventricular block with different types of arrhythmias were simulated. To simulate the effect of stenosis or regurgitation of the aortic or mitral valves, the hydraulic and inertial flow resistances of the heart valves were set as functions of their orifice areas. The model reproduced a number of phenomena observed in clinical practice, including the classification of the severity of valve disease.

Modeling left ventricular dynamics with characteristic deformation modes

A computationally efficient method is described for simulating the dynamics of the left ventricle (LV) in three dimensions. LV motion is represented as a combination of a limited number of deformation modes, chosen to represent observed cardiac motions while conserving volume in the LV wall. The contribution of each mode to wall motion is determined by a corresponding time-dependent deformation variable. The principle of virtual work is applied to these deformation variables, yielding a system of ordinary differential equations for LV dynamics, including effects of muscle fiber orientations, active and passive stresses, and surface tractions. Passive stress is governed by a transversely isotropic elastic model. Active stress acts in the fiber direction and incorporates length-tension and force-velocity properties of cardiac muscle. Preload and afterload are represented by lumped vascular models. The variational equations and their numerical solutions are verified by comparison to analytic solutions of the strong form equations. Deformation modes are constructed using Fourier series with an arbitrary number of terms. Greater numbers of deformation modes increase deformable model resolution but at increased computational cost. Simulations of normal LV motion throughout the cardiac cycle are presented using models with 8, 23, or 46 deformation modes. Aggregate quantities that describe LV function vary little as the number of deformation modes is increased. Spatial distributions of stress and strain change as more deformation modes are included, but overall patterns are conserved. This approach yields three-dimensional simulations of the cardiac cycle on a clinically relevant time-scale.

Visualization of Myocardial Strain Pattern Uniqueness with Respect to Activation Time and Contractility: A Computational Study

Speckle tracking echography is used to measure myocardial strain patterns in order to assess the state of myocardial tissue. Because electro-mechanical coupling in myocardial tissue is complex and nonlinear, and because of the measurement errors the uniqueness of strain patterns is questionable. In this study, the uniqueness of strain patterns was visualized in order to revel characteristics that may improve their interpretation. A computational model of sarcomere mechanics was used to generate a database of 1681 strain patterns, each simulated with a different set of sarcomere parameters: time of activation (TA) and contractility (Con). TA and Con ranged from −100 ms to 100 ms and 2% to 202% in 41 steps respectively, thus forming a two-dimensional 41 × 41 parameter space. Uniqueness of the strain pattern was assessed by using a cohort of similar strain patterns defined by a measurement error. The cohort members were then visualized in the parameter space. Each cohort formed one connected component (or blob) in the parameter space; however, large differences in the shape, size, and eccentricity of the blobs were found for different regions in the parameter space. The blobs were elongated along the TA direction (±50 ms) when contractility was low, and along the Con direction (±50%) when contractility was high. The uniqueness of the strain patterns can be assessed and visualized in the parameter space. The strain patterns in the studied database are not degenerated because a cohort of similar strain patterns forms only one connected blob in the parameter space. However, the elongation of the blobs means that estimations of TA when contractility is low and of Con when contractility is high have high uncertainty.