Improved identifiability of myocardial material parameters by an energy-based cost function

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.

Left Atrial Roof Enlargement Is a Distinct Feature of Heart Failure With Preserved Ejection Fraction

BACKGROUND

It remains unknown to what extent intrinsic atrial cardiomyopathy or left ventricular diastolic dysfunction drive atrial remodeling and functional failure in heart failure with preserved ejection fraction (HFpEF). Computational 3-dimensional (3D) models fitted to cardiovascular magnetic resonance allow state-of-the-art anatomic and functional assessment, and we hypothesized to identify a phenotype linked to HFpEF.

METHODS

Patients with exertional dyspnea and diastolic dysfunction on echocardiography (E/e', >8) were prospectively recruited and classified as HFpEF or noncardiac dyspnea based on right heart catheterization. All patients underwent rest and exercise-stress right heart catheterization and cardiovascular magnetic resonance. Computational 3D anatomic left atrial (LA) models were generated based on short-axis cine sequences. A fully automated pipeline was developed to segment cardiovascular magnetic resonance images and build 3D statistical models of LA shape and find the 3D patterns discriminant between HFpEF and noncardiac dyspnea. In addition, atrial morphology and function were quantified by conventional volumetric analyses and deformation imaging. A clinical follow-up was conducted after 24 months for the evaluation of cardiovascular hospitalization.

RESULTS

Beyond atrial size, the 3D LA models revealed roof dilation as the main feature found in masked HFpEF (diagnosed during exercise-stress only) preceding a pattern shift to overall atrial size in overt HFpEF (diagnosed at rest). Characteristics of the 3D model were integrated into the LA HFpEF shape score, a biomarker to characterize the gradual remodeling between noncardiac dyspnea and HFpEF. The LA HFpEF shape score was able to discriminate HFpEF (n=34) to noncardiac dyspnea (n=34; area under the curve, 0.81) and was associated with a risk for atrial fibrillation occurrence (hazard ratio, 1.02 [95% CI, 1.01-1.04]; P=0.003), as well as cardiovascular hospitalization (hazard ratio, 1.02 [95% CI, 1.00-1.04]; P=0.043).

CONCLUSIONS

LA roof dilation is an early remodeling pattern in masked HFpEF advancing to overall LA enlargement in overt HFpEF. These distinct features predict the occurrence of atrial fibrillation and cardiovascular hospitalization.

REGISTRATION

URL: https://www.clinicaltrials.gov; Unique identifier: NCT03260621.

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.

Phenotyping heart failure by echocardiography: imaging of ventricular function and haemodynamics at rest and exercise

Traditionally, congestive heart failure (HF) was phenotyped by echocardiography or other imaging techniques according to left ventricular (LV) ejection fraction (LVEF). The more recent echocardiographic modality speckle tracking strain is complementary to LVEF, as it is more sensitive to diagnose mild systolic dysfunction. Furthermore, when LV systolic dysfunction is associated with a small, hypertrophic ventricle, EF is often normal or supernormal, whereas LV global longitudinal strain can reveal reduced contractility. In addition, segmental strain patterns may be used to identify specific cardiomyopathies, which in some cases can be treated with patient-specific medicine. In HF with preserved EF (HFpEF), a diagnostic hallmark is elevated LV filling pressure, which can be diagnosed with good accuracy by applying a set of echocardiographic parameters. Patients with HFpEF often have normal filling pressure at rest, and a non-invasive or invasive diastolic stress test may be used to identify abnormal elevation of filling pressure during exercise. The novel parameter LV work index, which incorporates afterload, is a promising tool for quantification of LV contractile function and efficiency. Another novel modality is shear wave imaging for diagnosing stiff ventricles, but clinical utility remains to be determined. In conclusion, echocardiographic imaging of cardiac function should include LV strain as a supplementary method to LVEF. Echocardiographic parameters can identify elevated LV filling pressure with good accuracy and may be applied in the diagnostic workup of patients suspected of HFpEF.

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

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

Estimation of anisotropic properties of CMR patient-specific left ventricle using the virtual field method

Left ventricle (LV) myocardial dysfunction has been recently investigated using the estimation of isotropic myocardial stiffness from magnetic resonance imaging (MRI). However, Myocardium is known to have a 3D complex geometry with anisotropic stiffness. The assessment of the anisotropy properties characterizes structural changes in myocardium as a consequence of heart failure (HF). From image data, the virtual field method (VFM) can determine material stiffness in a non-invasive manner. In the present work, the objective is to compare two inverse identification methods, given the isotropic and anisotropic models in the characterization of properties of myocardium in acute lymphoblastic leukemia (ALL) survivors using VFM and MRI. Two types of VFM approach are presented. Using the first, the virtual displacements (VFs) allow whole-field LV to be imposed into VFM formulation and caused to directly estimate two independent parameters from isotropic constitutive relation. With the second, anisotropic parameters are estimated using piece-wise (Finite element-based) VFM. The resulting values showed significant differences between the subjects in comparative study of leukemia survivors, and variance in estimated parameters by two different VFM approach. This approach would be an efficient tool to characterize early cardiac dysfunction. This work elucidates the benefits and shortcomings of using VFM to determine anisotropic parameters of LV myocardium in linear elastic and of using the FEM application to generate meshes of patient-specific LVs from MRI images.

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

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

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.

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.

A clinically applicable strategy to estimate the in vivo distribution of mechanical material properties of the right ventricular wall

A clinically applicable approach to estimate the in vivo mechanical material properties of the heart wall is presented. This optimization-based inverse estimation approach applies a shape-based objective functional combined with rigid body registration and incremental parameterization of heterogeneity to use standard clinical imaging data along with simplified representations of cardiac function to provide consistent and physically meaningful solution estimates. The capability of the inverse estimation algorithm is evaluated through application to two clinically obtained human datasets to estimate the passive elastic mechanical properties of the heart wall, with an emphasis on the right ventricle. One dataset corresponded to a subject with normal heart function, while the other corresponded to a subject with severe pulmonary hypertension, and therefore expected to have a substantially stiffer right ventricle. Patient-specific pressure-driven bi-ventricle finite element analysis was used as the forward model and the endocardial surface of the right ventricle was used as the target data for the inverse problem. By using the right ventricle alone as the target of the inverse problem the relative sensitivity of the objective function to the right ventricle properties is increased. The method was able to identify material properties to accurately match the corresponding shape of the simplified forward model to the clinically obtained target data, and the properties obtained for the example cases are consistent with the clinical expectation for the right ventricle. Additionally, the material property estimates indicate significant heterogeneity in the heart wall for both subjects, and more so for the subject with pulmonary hypertension.

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.

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.

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

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

Finite-element based optimization of left ventricular passive stiffness in normal volunteers and patients after myocardial infarction: Utility of an inverse deformation gradient calculation of regional diastolic strain

INTRODUCTION

Left ventricular (LV) diastolic dysfunction (DD) is common after myocardial infarction (MI). Whereas current clinical assessment of DD relies on indirect markers including LV filling, finite element (FE) -based computational modeling directly measures regional diastolic stiffness. We hypothesized that an inverse deformation gradient (DG) method calculation of diastolic strain (IDGDS) allows the FE model-based calculation of regional diastolic stiffness (material parameters; MP) in post-MI patients with DD.

METHODS

Cardiac magnetic resonance (CMR) with tags (CSPAMM) and late gadolinium enhancement (LGE) was performed in 10 patients with post-MI DD and 10 healthy volunteers. The 3-dimensional (3D) LV DG from end-diastole (ED) to early diastolic filling (EDF; DG_ED→EDF) was calculated from CSPAMM. Diastolic strain was calculated from DG_EDF→ED by inverting the DG_ED→EDF. FE models were created with MI and non-MI (remote; RM) regions determined by LGE. Guccione MPs C, and exponential fiber, b_f, and transverse, b_t , terms were optimized with IDGDS strain.

RESULTS

3D circumferential and longitudinal diastolic strain (E_cc;E_ll) calculated using IDGDS in CSPAMM obtained in volunteers and MI patients were [Formula: see text]  = 0.27 ± 0.01, [Formula: see text]  = 0.24 ± 0.03 and [Formula: see text]  = 0.21 ± 0.02, and [Formula: see text]  = 0.15 ± 0.02, respectively. MPs in the volunteer group were C_H = 0.013 [0.001, 0.235] kPa, [Formula: see text]  = 20.280 ± 4.994, and [Formula: see text]  = 7.460 ± 2.171 and C_RM = 0.0105 [0.010, 0.011] kPa, [Formula: see text]  = 50.786 ± 13.511 (p = 0.0846), and [Formula: see text]  = 17.355 ± 2.743 (p = 0.0208) in the remote myocardium of post-MI patients.

CONCLUSION

Diastolic strain, calculated from CSPAMM with IDGDS, enables calculation of FE model-based regional diastolic material parameters. Transverse stiffness of the remote myocardium, , may be a valuable new metric for determination of DD in patients after MI.

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

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

Model order reduction for left ventricular mechanics via congruency training

Computational models of the cardiovascular system and specifically heart function are currently being investigated as analytic tools to assist medical practice and clinical trials. To achieve clinical utility, models should be able to assimilate the diagnostic multi-modality data available for each patient and generate consistent representations of the underlying cardiovascular physiology. While finite element models of the heart can naturally account for patient-specific anatomies reconstructed from medical images, optimizing the many other parameters driving simulated cardiac functions is challenging due to computational complexity. With the goal of streamlining parameter adaptation, in this paper we present a novel, multifidelity strategy for model order reduction of 3-D finite element models of ventricular mechanics. Our approach is centered around well established findings on the similarity between contraction of an isolated muscle and the whole ventricle. Specifically, we demonstrate that simple linear transformations between sarcomere strain (tension) and ventricular volume (pressure) are sufficient to reproduce global pressure-volume outputs of 3-D finite element models even by a reduced model with just a single myocyte unit. We further develop a procedure for congruency training of a surrogate low-order model from multi-scale finite elements, and we construct an example of parameter optimization based on medical images. We discuss how the presented approach might be employed to process large datasets of medical images as well as databases of echocardiographic reports, paving the way towards application of heart mechanics models in the clinical practice.

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.

A Contemporary Look at Biomechanical Models of Myocardium

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.

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

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

Gaussian Process Regressions for Inverse Problems and Parameter Searches in Models of Ventricular Mechanics

Patient specific models of ventricular mechanics require the optimization of their many parameters under the uncertainties associated with imaging of cardiac function. We present a strategy to reduce the complexity of parametric searches for 3-D FE models of left ventricular contraction. The study employs automatic image segmentation and analysis of an image database to gain geometric features for several classes of patients. Statistical distributions of geometric parameters are then used to design parametric studies investigating the effects of: (1) passive material properties during ventricular filling, and (2) infarct geometry on ventricular contraction in patients after a heart attack. Gaussian Process regression is used in both cases to build statistical models trained on the results of biophysical FEM simulations. The first statistical model estimates unloaded configurations based on either the intraventricular pressure or the end-diastolic fiber strain. The technique provides an alternative to the standard fixed-point iteration algorithm, which is more computationally expensive when used to unload more than 10 ventricles. The second statistical model captures the effects of varying infarct geometries on cardiac output. For training, we designed high resolution models of non-transmural infarcts including refinements of the border zone around the lesion. This study is a first effort in developing a platform combining HPC models and machine learning to investigate cardiac function in heart failure patients with the goal of assisting clinical diagnostics.

Quantitative characterization of viscoelastic behavior in tissue-mimicking phantoms and ex vivo animal tissues

Viscoelasticity of soft tissue is often related to pathology, and therefore, has become an important diagnostic indicator in the clinical assessment of suspect tissue. Surgeons, particularly within head and neck subsites, typically use palpation techniques for intra-operative tumor detection. This detection method, however, is highly subjective and often fails to detect small or deep abnormalities. Vibroacoustography (VA) and similar methods have previously been used to distinguish tissue with high-contrast, but a firm understanding of the main contrast mechanism has yet to be verified. The contributions of tissue mechanical properties in VA images have been difficult to verify given the limited literature on viscoelastic properties of various normal and diseased tissue. This paper aims to investigate viscoelasticity theory and present a detailed description of viscoelastic experimental results obtained in tissue-mimicking phantoms (TMPs) and ex vivo tissues to verify the main contrast mechanism in VA and similar imaging modalities. A spherical-tip micro-indentation technique was employed with the Hertzian model to acquire absolute, quantitative, point measurements of the elastic modulus (E), long term shear modulus (η), and time constant (τ) in homogeneous TMPs and ex vivo tissue in rat liver and porcine liver and gallbladder. Viscoelastic differences observed between porcine liver and gallbladder tissue suggest that imaging modalities which utilize the mechanical properties of tissue as a primary contrast mechanism can potentially be used to quantitatively differentiate between proximate organs in a clinical setting. These results may facilitate more accurate tissue modeling and add information not currently available to the field of systems characterization and biomedical research.