In vivo estimation of elastic heterogeneity in an infarcted human heart

Personalized evaluation of the passive myocardium in ischemic cardiomyopathy via computational modeling using Bayesian optimization

Biomechanics-based patient-specific modeling is a promising approach that has proved invaluable for its clinical potential to assess the adversities caused by ischemic heart disease (IHD). In the present study, we propose a framework to find the passive material properties of the myocardium and the unloaded shape of cardiac ventricles simultaneously in patients diagnosed with ischemic cardiomyopathy (ICM). This was achieved by minimizing the difference between the simulated and the target end-diastolic pressure-volume relationships (EDPVRs) using black-box Bayesian optimization, based on the finite element analysis (FEA). End-diastolic (ED) biventricular geometry and the location of the ischemia were determined from cardiac magnetic resonance (CMR) imaging. We employed our pipeline to model the cardiac ventricles of three patients aged between 57 and 66 years, with and without the inclusion of valves. An excellent agreement between the simulated and the target EDPVRs has been reached. Our results revealed that the incorporation of valvular springs typically leads to lower hyperelastic parameters for both healthy and ischemic myocardium, as well as a higher fiber Green strain in the viable regions compared to models without valvular stiffness. Furthermore, the addition of valve-related effects did not result in significant changes in myofiber stress after optimization. We concluded that more accurate results could be obtained when cardiac valves were considered in modeling ventricles. The present novel and practical methodology paves the way for developing digital twins of ischemic cardiac ventricles, providing a non-invasive assessment for designing optimal personalized therapies in precision medicine.

A data-driven computational model for engineered cardiac microtissues

Engineered heart tissues (EHTs) present a potential solution to some of the current challenges in the treatment of heart disease; however, the development of mature, adult-like cardiac tissues remains elusive. Mechanical stimuli have been observed to improve whole-tissue function and cardiomyocyte (CM) maturation, although our ability to fully utilize these mechanisms is hampered, in part, by our incomplete understanding of the mechanobiology of EHTs. In this work, we leverage experimental data, produced by a mechanically tunable experimental setup, to introduce a tissue-specific computational modeling pipeline of EHTs. Our new modeling pipeline generates simulated, image-based EHTs, capturing ECM and myofibrillar structure as well as functional parameters estimated directly from experimental data. This approach enables the unique estimation of EHT function by data-based estimation of CM active stresses. We use this experimental and modeling pipeline to study different mechanical environments, where we contrast the force output of the tissue with the computed active stress of CMs. We show that the significant differences in measured experimental forces can largely be explained by the levels of myofibril formation achieved by the CMs in the distinct mechanical environments, with active stress showing more muted variations across conditions. The presented model also enables us to dissect the relative contributions of myofibrils and extracellular matrix to tissue force output, a task difficult to address experimentally. These results highlight the importance of tissue-specific modeling to augment EHT experiments, providing deeper insights into the mechanobiology driving EHT function. STATEMENT OF SIGNIFICANCE: Engineered heart tissues (EHTs) have the potential to revolutionize the way heart disease is treated. However, developing mature cardiomyocytes (CM) in these tissues remains a challenge due, in part, to our incomplete understanding of the fundamental biomechanical mechanisms that drive EHT development. This work integrates the experimental data of an EHT platform developed to study the influence of mechanics in CM maturation with computational biomechanical models. This approach is used to augment conclusions obtained in-vitro - by measuring quantities such as cell stress and strain - and to dissect the relevance of each component in the whole tissue performance. Our results show how a combination of specialized in-silico and in-vitro approaches can help us better understand the mechanobiology of EHTs.

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.

Regional Left Ventricular Fiber Stress Analysis for Cardiac Resynchronization Therapy Response

Cardiac resynchronization therapy (CRT) is an effective treatment for a subgroup of heart failure (HF) patients, but more than 30% of those selected do not improve after CRT implantation. Imperfect pre-procedural criteria for patient selection and optimization are the main causes of the high non-response rate. In this study, we evaluated a novel measure for assessing CRT response. We used a computational modeling framework to calculate the regional stress of the left ventricular wall of seven CRT patients and seven healthy controls. The standard deviation of regional wall stress at the time of mitral valve closure (SD_MVC) was used to quantify dyssynchrony and compared between patients and controls and among the patients. The results show that SD_MVC is significantly lower in controls than patients and correlates with long-term response in patients, based on end-diastolic volume reduction. In contrast to our initial hypothesis, patients with lower SD_MVC respond better to therapy. The patient with the highest SD_MVC was the only non-responder in the patient cohort. The distribution of fiber stress at the beginning of the isovolumetric phase seems to correlate with the degree of response and the use of this measurement could potentially improve selection criteria for CRT implantation. Further studies with a larger cohort of patients are needed to validate these results.

Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle

We consider parameter inference in cardio-mechanic models of the left ventricle, in particular the one based on the Holtzapfel-Ogden (HO) constitutive law, using clinical in vivo data. The equations underlying these models do not admit closed form solutions and hence need to be solved numerically. These numerical procedures are computationally expensive making computational run times associated with numerical optimisation or sampling excessive for the uptake of the models in the clinical practice. To address this issue, we adopt the framework of Bayesian optimisation (BO), which is an efficient statistical technique of global optimisation. BO seeks the optimum of an unknown black-box function by sequentially training a statistical surrogate-model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off. To guarantee that the estimates based on the in vivo data are realistic also for high-pressures, unobservable in vivo, we include a penalty term based on a previously published empirical law developed using ex vivo data. Two case studies based on real data demonstrate that the proposed BO procedure outperforms the state-of-the-art inference algorithm for the HO constitutive law.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Estimating cardiac active tension from wall motion-An inverse problem of cardiac biomechanics

The contraction of the human heart is a complex process as a consequence of the interaction of internal and external forces. In current clinical routine, the resulting deformation can be imaged during an entire heart beat. However, the active tension development cannot be measured in vivo but may provide valuable diagnostic information. In this work, we present a novel numerical method for solving an inverse problem of cardiac biomechanics-estimating the dynamic active tension field, provided the motion of the myocardial wall is known. This ill-posed non-linear problem is solved using second order Tikhonov regularization in space and time. We conducted a sensitivity analysis by varying the fiber orientation in the range of measurement accuracy. To achieve RMSE <20% of the maximal tension, the fiber orientation needs to be provided with an accuracy of 10°. Also, variation was added to the deformation data in the range of segmentation accuracy. Here, imposing temporal regularization led to an eightfold decrease in the error down to 12%. Furthermore, non-contracting regions representing myocardial infarct scars were introduced in the left ventricle and could be identified accurately in the inverse solution (sensitivity >0.95). The results obtained with non-matching input data are promising and indicate directions for further improvement of the method. In future, this method will be extended to estimate the active tension field based on motion data from clinical images, which could provide important insights in terms of a new diagnostic tool for the identification and treatment of diseased heart tissue.

Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

Myocardial supply changes to accommodate the variation of myocardial demand across the heart wall to maintain normal cardiac function. A computational framework that couples the systemic circulation of a left ventricular (LV) finite element model and coronary perfusion in a closed loop is developed to investigate the transmural distribution of the myocardial demand (work density) and supply (perfusion) ratio. Calibrated and validated against measurements of LV mechanics and coronary perfusion, the model is applied to investigate changes in the transmural distribution of passive coronary perfusion, myocardial work density, and their ratio in response to changes in LV contractility, preload, afterload, wall thickness, and cavity volume. The model predicts the following: (1) Total passive coronary flow varies from a minimum value at the endocardium to a maximum value at the epicardium transmurally that is consistent with the transmural distribution of IMP; (2) Total passive coronary flow at different transmural locations is increased with an increase in either contractility, afterload, or preload of the LV, whereas is reduced with an increase in wall thickness or cavity volume; (3) Myocardial work density at different transmural locations is increased transmurally with an increase in either contractility, afterload, preload or cavity volume of the LV, but is reduced with an increase in wall thickness; (4) Myocardial work density-perfusion mismatch ratio at different transmural locations is increased with an increase in contractility, preload, wall thickness or cavity volume of the LV, and the ratio is higher at the endocardium than the epicardium. These results suggest that an increase in either contractility, preload, wall thickness, or cavity volume of the LV can increase the vulnerability of the subendocardial region to ischemia.

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.

Multiphysics computational modelling of the cardiac ventricles

Development of cardiac multiphysics models has progressed significantly over the decades and simulations combining multiple physics interactions have become increasingly common. In this review, we summarise the progress in this field focusing on various approaches of integrating ventricular structures. electrophysiological properties, myocardial mechanics, as well as incorporating blood hemodynamics and the circulatory system. Common coupling approaches are discussed and compared, including the advantages and shortcomings of each. Currently used strategies for patient-specific implementations are highlighted and potential future improvements considered.

Characterizing regional myofiber damage post acute myocardial infarction using global optimization

Medical imaging derived cardiac biomechanical models offer a wealth of new information to be used in diagnosis and prognosis of cardiovascular disease. A noteworthy feature of such models is the ability to predict myofiber contraction stresses during acute or chronic ischemic events. Current techniques for heterogeneous contraction models require tissue motion tracking capabilities which are neither available on all imaging modalities, nor currently used in the clinic. Proposed in this article is a proof of concept of a tissue tracking independent technique focused on shape optimization to predict the contraction stresses of in-silico left ventricle models simulating various acute myocardial infarction events. The technique involves three variables defined in the left ventricle muscle. Two of the variables represent the contraction stresses in the healthy and infarct regions while the third is a novel periinfarct variable defining a non-contracting myofiber state allowing finer classification of local myofiber damage. Results indicate that the contraction stress reconstruction errors are overall smaller than 12% when considering standard errors associated with population modelling for the new variable of interest.

In vivo estimation of normal left ventricular stiffness and contractility based on routine cine MR acquisition

Post-myocardial infarction remodeling process is known to alter the mechanical properties of the heart. Biomechanical parameters, such as tissue stiffness and contractility, would be useful for clinicians to better assess the severity of the diseased heart. However, these parameters are difficult to obtain in the current clinical practice. In this paper, we estimated subject-specific in vivo myocardial stiffness and contractility from 21 healthy volunteers, based on left ventricle models constructed from data acquired from routine cardiac MR acquisition only. The subject-specific biomechanical parameters were quantified using an inverse finite-element modelling approach. The personalized models were evaluated against relevant clinical metrics extracted from the MR data, such as circumferential strain, wall thickness and fractional thickening. We obtained the ranges of healthy biomechanical indices of 1.60 ± 0.22 kPa for left ventricular stiffness and 95.13 ± 14.56 kPa for left ventricular contractility. These reference normal values can be used for future model-based investigation on the stiffness and contractility of ischemic myocardium.

A Composite Material Based Neural Network for Tissue Mechanical Properties Estimation Toward Stage Assessment of Infarction

Cardiac biomechanical modelling is a promising new tool to be used in prognostic medicine and therapy planning for patients suffering from a variety of cardiovascular diseases and injuries. In order to have an accurate biomechanical model, personalized parameters to define loading, boundary conditions and mechanical properties are required. Achieving personalized modelling parameters often requires inverse optimization which is computationally expensive; hence techniques to reduce the multivariable complexity are in need. Presented in this paper is the fundamental blueprint to create a library of scar tissue mechanical properties to be used in modelling the healing mechanics of hearts that have suffered acute myocardial infarction. This library can be used to reduce the number of variables necessary to capture the scar tissue mechanical properties down to 1. This single parameter also carries information pertaining to staging of the scar tissue healing, predict its rate, and predict its collagen density. This information can be potentially used as valuable biomarkers to adjust existing or develop new treatment plans for patients.

Maladaptive Contractility of 3D Human Cardiac Microtissues to Mechanical Nonuniformity

Cardiac tissues are able to adjust their contractile behavior to adapt to the local mechanical environment. Nonuniformity of the native tissue mechanical properties contributes to the development of heart dysfunctions, yet the current in vitro cardiac tissue models often fail to recapitulate the mechanical nonuniformity. To address this issue, a 3D cardiac microtissue model is developed with engineered mechanical nonuniformity, enabled by 3D-printed hybrid matrices composed of fibers with different diameters. When escalating the complexity of tissue mechanical environments, cardiac microtissues start to develop maladaptive hypercontractile phenotypes, demonstrated in both contractile motion analysis and force-power analysis. This novel hybrid system could potentially facilitate the establishment of "pathologically-inspired" cardiac microtissue models for deeper understanding of heart pathology due to nonuniformity of the tissue mechanical environment.

Effects of left ventricle wall thickness uncertainties on cardiac mechanics

Computational models of the heart have reached a level of maturity that enables sophisticated patient-specific simulations and hold potential for important applications in diagnosis and therapy planning. However, such clinical use puts strict demands on the reliability and accuracy of the models and requires the sensitivity of the model predictions due to errors and uncertainty in the model inputs to be quantified. The models typically contain a large number of parameters, which are difficult to measure and therefore associated with considerable uncertainty. Additionally, patient-specific geometries are usually constructed by semi-manual processing of medical images and must be assumed to be a potential source of model uncertainty. In this paper, we assess the model accuracy by considering the impact of geometrical uncertainties, which typically occur in image-based computational geometries. An approach based on 17 AHA segments diagram is used to consider uncertainties in wall thickness and also in the material properties and fiber orientation, and we perform a comprehensive uncertainty quantification and sensitivity analysis based on polynomial chaos expansions. The quantities considered include stress, strain and global deformation parameters of the left ventricle. The results indicate that important quantities of interest may be more affected by wall thickness, and highlight the need for accurate geometry reconstructions in patient-specific cardiac mechanics models.