Finite element stress analysis of left ventricular mechanics in the beating dog heart

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

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

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

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.

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.

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

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

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

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

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

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

Cardiac electro-mechanical activity in a deforming human cardiac tissue: modeling, existence-uniqueness, finite element computation and application to multiple ischemic disease

In this study, the cardiac electro-mechanical model in a deforming domain is taken with the addition of mechanical feedback and stretch-activated channel current coupled with the ten Tusscher human ventricular cell level model that results in a coupled PDE-ODE system. The existence and uniqueness of such a coupled system in a deforming domain is proved. At first, the existence of a solution is proved in the deformed domain. The local existence of the solution is proved using the regularization and the Faedo-Galerkin technique. Then, the global existence is proved using the energy estimates in appropriate Banach spaces, Gronwall lemma, and the compactness procedure. The existence of the solution in an undeformed domain is proved using the lower semi-continuity of the norms. Uniqueness is proved using Young's inequality, Gronwall lemma, and the Cauchy-Schwartz inequality. For the application purpose, this model is applied to understand the electro-mechanical activity in ischemic cardiac tissue. It also takes care of the development of active tension, conductive, convective, and ionic feedback. The Second Piola-Kirchoff stress tensor arising in Lagrangian mapping between reference and moving frames is taken as a combination of active, passive, and volumetric components. We investigated the effect of varying strength of hyperkalemia and hypoxia, in the ischemic subregions of human cardiac tissue with local multiple ischemic subregions, on the electro-mechanical activity of healthy and ischemic zones. This system is solved numerically using the [Formula: see text] finite element method in space and the implicit-explicit Euler method in time. Discontinuities arising with the modeled multiple ischemic regions are treated to the desired order of accuracy by a simple regularization technique using the interpolating polynomials. We examined the cardiac electro-mechanical activity for several cases in multiple hyperkalemic and hypoxic human cardiac tissue. We concluded that local multiple ischemic subregions severely affect the cardiac electro-mechanical activity more, in terms of action potential (v) and mechanical parameters, intracellular calcium ion concentration [Formula: see text], active tension ([Formula: see text]), stretch ([Formula: see text]) and stretch rate ([Formula: see text]), of a healthy cell in its vicinity, compared to a single Hyperkalemic or Hypoxic subregion. The four moderate hypoxically generated ischemic subregions affect the waveform of the stretch along the fiber and the stretch rate more than a single severe ischemic subregion.

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

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

Personalization of biomechanical simulations of the left ventricle by in-vivo cardiac DTI data: Impact of fiber interpolation methods

Simulations of cardiac electrophysiology and mechanics have been reported to be sensitive to the microstructural anisotropy of the myocardium. Consequently, a personalized representation of cardiac microstructure is a crucial component of accurate, personalized cardiac biomechanical models. In-vivo cardiac Diffusion Tensor Imaging (cDTI) is a non-invasive magnetic resonance imaging technique capable of probing the heart's microstructure. Being a rather novel technique, issues such as low resolution, signal-to noise ratio, and spatial coverage are currently limiting factors. We outline four interpolation techniques with varying degrees of data fidelity, different amounts of smoothing strength, and varying representation error to bridge the gap between the sparse in-vivo data and the model, requiring a 3D representation of microstructure across the myocardium. We provide a workflow to incorporate in-vivo myofiber orientation into a left ventricular model and demonstrate that personalized modelling based on fiber orientations from in-vivo cDTI data is feasible. The interpolation error is correlated with a trend in personalized parameters and simulated physiological parameters, strains, and ventricular twist. This trend in simulation results is consistent across material parameter settings and therefore corresponds to a bias introduced by the interpolation method. This study suggests that using a tensor interpolation approach to personalize microstructure with in-vivo cDTI data, reduces the fiber uncertainty and thereby the bias in the simulation results.

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.

Developing a biomechanical model-based elasticity imaging method for assessing hormone receptor positive breast cancer treatment-related myocardial stiffness changes

Purpose: Assessing cardiotoxicity as a result of breast cancer therapeutics is increasingly important as breast cancer diagnoses are trending younger and overall survival is increasing. With evidence showing that prevention of cardiotoxicity plays a significant role in increasing overall survival, there is an unmet need for accurate non-invasive methods to assess cardiac injury due to cancer therapies. Current clinical methods are too coarse and emerging research methods have not yet achieved clinical implementation. Approach: As a proof of concept, we examine myocardial elasticity imaging in the setting of premenopausal women diagnosed with hormone receptor positive (HR-positive) breast cancer undergoing severe estrogen depletion, as cardiovascular injury from early estrogen depletion is well-established. We evaluate the ability of our model-based cardiac elasticity imaging analysis method to indicate subclinical cancer therapy-related cardiac decline by examining differences in the change in cardiac elasticity over time in two cohorts of premenopausal women either undergoing severe estrogen depletion for HR-positive breast cancer or triple negative breast cancer patients as comparators. Results: Our method was capable of producing functional mechanical elasticity maps of the left ventricle (LV). Using these elasticity maps, we show significant differences in cardiac mechanical elasticity in the HR-positive breast cancer cohort compared to the comparator cohort. Conclusions: We present our methodology to assess the mechanical stiffness of the LV by interrogating cardiac magnetic resonance images within a computational biomechanical model. Our preliminary study suggests the potential of this method for examining cardiac tissue mechanical stiffness properties as an early indicator of cardiac decline.

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.

Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator

The results of numerical simulations of cardiac electromechanics are typically characterized by a long transient before reaching a periodic solution known as limit cycle. This yields a serious computational overhead, as the only clinically relevant output is associated with such limit cycle. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator, built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated with the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, can provide the 3D model with an initial guess, such that in just two heartbeats a solution is reached that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the 3D model. The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. Indeed, the construction of the emulator does not have to be repeated when the parameters of the circulation model it is coupled with vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. This paper is accompanied by a Python library implementing the proposed algorithm, open to integration with existing cardiac solvers.

Influence of Fibrosis Amount and Patterns on Ventricular Arrhythmogenesis and Pumping Efficacy: Computational Study

Myocardial fibrosis is an integral component of most forms of heart failure. Clinical and computational studies have reported that spatial fibrosis pattern and fibrosis amount play a significant role in ventricular arrhythmogenicity. This study investigated the effect of the spatial distribution of fibrosis and fibrosis amount on the electrophysiology and mechanical performance of the human ventricles. Seventy-five fibrosis distributions comprising diffuse, patchy, and compact fibrosis types that contain 10-50% fibrosis amount were generated. The spatial fibrosis distribution was quantified using the fibrosis entropy (FE) metric. Electrical simulations under reentry conditions induced using the S1-S2 protocol were conducted to investigate the fibrosis arrhythmogenicity. We also performed mechanical simulations to examine the influence of the fibrosis amount and the spatial distribution of fibrosis on the pumping efficacy of the LV. We observed that the mean FE of the compact type is the largest among the three types. The electrical simulation results revealed that the ventricular arrhythmogenicity of diffuse fibrosis depends on the fibrosis amount and marginally on the spatial distribution of fibrosis. Meanwhile, the ventricular arrhythmogenicity of the compact and patchy fibrosis pattern is more reliant on the spatial distribution of fibrosis than on the fibrosis amount. The average number of phase singularities (PSs) in the compact fibrosis pattern was the highest among the three patterns of fibrosis. The diffuse type of fibrosis has the lowest average number of PSs than that in the patchy and compact fibrosis. The reduction in the stroke volume (SV) showed high influence from the electrical instabilities induced by the fibrosis amount and pattern. The compact fibrosis exhibited the lowest SV among the three patterns except in the 40% fibrosis amount. In conclusion, the fibrosis pattern is as crucial as the fibrosis amount for sustaining and aggravating ventricular arrhythmogenesis.

Transverse isotropic modelling of left-ventricle passive filling: Mechanical characterization for epicardial biomaterial manufacturing

Biomaterials applied to the epicardium have been studied intensively in recent years for different therapeutic purposes. Their mechanical influence on the heart, however, has not been clearly identified. Most biomaterials for epicardial applications are manufactured as membranes or cardiac patches that have isotropic geometry, which is not well suited to myocardial wall motion. Myocardial wall motion during systole and diastole produces a complex force in different directions. Membrane or cardiac patches that cannot adapt to these specific directions will exert an inappropriate force on the heart, at the risk of overly restricting or dilating it. Accurately characterizing the mechanical properties of the myocardial wall is thus essential, through analysis of muscle orientation and elasticity. In this study, we investigated the Hertz contact theory for characterizing cardiac tissue, using nanoindentation measurements to distinguish different patterns in the local myocardium. We then evaluated the predictive accuracy of this model using Finite Element Analysis (FEA) to mimic the diastolic phase of the heart. Our results, extracted from instrumented nanoindentation experiments in a liquid environment using five pig hearts, revealed variations in elasticity according to the local orientation of the myocardial tissue. In addition, applying the Finite Element Method (FEM) in our model based on transverse isotropy and local tissue orientation proved able to accurately simulate the passive filling of a left ventricle (LV) in a representative 3D geometry. Our model enables improved understanding of the underlying mechanical properties of the LV wall and can serve as a guide for designing and manufacturing biomedical material better adapted to the local epicardial tissue.

Computational analysis of the effect of KCNH2 L532P mutation on ventricular electromechanical behaviors

The KCNH2 L532P mutation is an alteration in the I_Kr channel that is associated with short QT syndrome and atrial fibrillation in zebrafish. In preliminary studies, the electrophysiological effects of the hERG L532P mutation were investigated using a mathematical model in a single-cell and 2D sheet medium. The objective of this study was to quantify the effects of the KCNH2 L532P mutation on the 3D ventricular electrophysiological behavior and the mechanical pumping responses. We used a realistic three-dimensional ventricular electrophysiological-mechanical model, which was adjusted into two conditions: the wild-type (WT) condition, i.e., the original case of the Tusscher et al. model, and the L532P mutation condition, with modification of the original I_Kr equation. The action potential duration (APD) in the mutant ventricle was reduced by 73% owing to the significant increase of the I_Kr current density. In the 3D simulation, the L532P mutation maintained the sustainability of reentrant waves; however, the reentry was terminated in the WT condition. The contractility of the ventricle with L532P mutation was significantly reduced compared with that in WT which results in sustain shivering heart during reentry condition. The reduction of the contractility was associated with the shortening APD which simultaneously shortened the duration of the Ca²⁺ channel opening. In conclusion, the ventricle with KCNH2 L532P mutation is prone to reentry generation with a sustained chaotic condition, and the mutation significantly reduced the pumping performance of the ventricles.

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.

Multiscale Modeling of Cardiovascular Function Predicts That the End-Systolic Pressure Volume Relationship Can Be Targeted via Multiple Therapeutic Strategies

Most patients who develop heart failure are unable to elevate their cardiac output on demand due to impaired contractility and/or reduced ventricular filling. Despite decades of research, few effective therapies for heart failure have been developed. In part, this may reflect the difficulty of predicting how perturbations to molecular-level mechanisms that are induced by drugs will scale up to modulate system-level properties such as blood pressure. Computer modeling might help with this process and thereby accelerate the development of better therapies for heart failure. This manuscript presents a new multiscale model that uses a single contractile element to drive an idealized ventricle that pumps blood around a closed circulation. The contractile element was formed by linking an existing model of dynamically coupled myofilaments with a well-established model of myocyte electrophysiology. The resulting framework spans from molecular-level events (including opening of ion channels and transitions between different myosin states) to properties such as ejection fraction that can be measured in patients. Initial calculations showed that the model reproduces many aspects of normal cardiovascular physiology including, for example, pressure-volume loops. Subsequent sensitivity tests then quantified how each model parameter influenced a range of system level properties. The first key finding was that the End Systolic Pressure Volume Relationship, a classic index of cardiac contractility, was ∼50% more sensitive to parameter changes than any other system-level property. The second important result was that parameters that primarily affect ventricular filling, such as passive stiffness and Ca²⁺ reuptake via sarco/endoplasmic reticulum Ca²⁺-ATPase (SERCA), also have a major impact on systolic properties including stroke work, myosin ATPase, and maximum ventricular pressure. These results reinforce the impact of diastolic function on ventricular performance and identify the End Systolic Pressure Volume Relationship as a particularly sensitive system-level property that can be targeted using multiple therapeutic strategies.

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

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

Reference Ranges for Left Ventricular Curvedness and Curvedness-Based Functional Indices Using Cardiovascular Magnetic Resonance in Healthy Asian Subjects

Curvature-based three-dimensional cardiovascular magnetic resonance (CMR) allows regional function characterization without an external spatial frame of reference. However, introduction of this modality into clinical practice is hampered by lack of reference values. We aim to establish normal ranges for 3D left ventricular (LV) regional parameters in relation to age and gender for 171 healthy subjects. LV geometrical reconstruction and automatic calculation of regional parameters were implemented by in-house software (CardioWerkz) using stacks of short-axis cine slices. Parameter normal ranges were stratified by gender and age categories (≤44, 45-64, 65-74 and 75-84 years). Our software had excellent intra- and inter-observer agreement. Ageing was significantly associated with increases in end-systolic (ES) curvedness (C_ES) and area strain (AS) with higher rates of increase in males, end-diastolic (ED) and ES wall thickness (WT_ED, WT_ES) with higher rates of increase in females, and reductions in ED and ES wall stress indices (σ_i,ED) with higher rates of increase in females. Females exhibited greater ED curvedness, C_ES, σ_i,ED and AS than males, but smaller WT_ED and WT_ES. Age × gender interaction was not observed for any parameter. This study establishes age and gender specific reference values for 3D LV regional parameters using CMR without additional image acquisition.

Regional variations in ex-vivo diffusion tensor anisotropy are associated with cardiomyocyte remodeling in rats after left ventricular pressure overload

BACKGROUND

Pressure overload left ventricular (LV) hypertrophy is characterized by increased cardiomyocyte width and ventricle wall thickness, however the regional variation of this remodeling is unclear. Cardiovascular magnetic resonance (CMR) diffusion tensor imaging (DTI) may provide a non-invasive, comprehensive, and geometrically accurate method to detect regional differences in structural remodeling in hypertrophy. We hypothesized that DTI parameters, such as fractional and planar anisotropy, would reflect myocyte remodeling due to pressure overload in a regionally-dependent manner.

METHODS

We investigated the regional distributions of myocyte remodeling in rats with or without transverse aortic constriction (TAC) via direct measurement of myocyte dimensions with confocal imaging of thick tissue sections, and correlated myocyte cross-sectional area and other geometric features with parameters of diffusivity from ex-vivo DTI in the same regions of the same hearts.

RESULTS

We observed regional differences in several parameters from DTI between TAC hearts and SHAM controls. Consistent with previous studies, helix angles from DTI correlated strongly with those measured directly from histological sections (p < 0.001, R2 = 0.71). There was a transmural gradient in myocyte cross-sectional area in SHAM hearts that was diminished in the TAC group. We also found several regions of significantly altered DTI parameters in TAC LV compared to SHAM, especially in myocyte sheet angle dispersion and planar anisotropy. Among others, these parameters correlated significantly with directly measured myocyte aspect ratios.

CONCLUSIONS

These results show that structural remodeling in pressure overload LV hypertrophy is regionally heterogeneous, especially transmurally, with a greater degree of remodeling in the sub-endocardium compared to the sub-epicardium. Additionally, several parameters derived from DTI correlated significantly with measurements of myocyte geometry from direct measurement in histological sections. We suggest that DTI may provide a non-invasive, comprehensive method to detect regional structural myocyte LV remodeling during disease.

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

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

Relationship Between Electrical Instability and Pumping Performance During Ventricular Tachyarrhythmia: Computational Study

There are representative electrical parameters for understanding the mechanism of reentrant waves in studies on tachyarrhythmia, namely the action potential duration (APD), dominant frequency, phase singularity, and filament. However, there are no studies that have directly identified the correlation between these electrophysiological parameters and cardiac contractility. Therefore, we have identified individual and integrative correlations between these electrical phenomena and contractility during tachyarrhythmia by deriving regression equations and also investigated the electrophysiological parameters affecting cardiac contractility during tachyarrhythmia. We simulated ventricular tachyarrhythmia with 48 types of electrical patterns by applying four reentry generation methods and changing the electrical conductivity of the potassium channel, which has the greatest effect on ventricular tissue. The mechanical responses reflecting electrical complexity were obtained through deterministic simulations of excitation–contraction coupling. We used the stroke volume and amplitude of myocardial tension (ampTens) as the variables representing contractility. We derived stochastic models through single- and multivariable regression analyses to identify the electrical parameters affecting contractility during tachyarrhythmia. In single-variable regression analysis, the APD, dominant frequency, and filament, excluding phase singularity, have statistically significant correlations with the stroke volume and ampTens. Among them, the APD has the maximum influence on these two mechanical parameters (standard beta coefficient: 0.859 for stroke volume, 0.930 for ampTens). The stochastic model using all four electrical parameters fails to accurately predict contractility owing to the multicollinearity between the APD and dominant frequency. We have rederived the multi-variable stochastic model using three electrical parameters without the APD. The filament has the greatest effect on the stroke volume stochastically (standard beta coefficient: 0.853 and 0.752). The dominant frequency has the greatest effect on ampTens statistically (standard beta coefficient: −0.813). We conclude that among the electrical parameters, the APD has the highest individual influence on mechanical contraction, and the filament has the highest integrative influence in both statistical terms.

Effects of myocardial function and systemic circulation on regional coronary perfusion

Cardiac-coronary interaction and the effects of its pathophysiological variations on spatial heterogeneity of coronary perfusion and myocardial work are still poorly understood. This hypothesis-generating study predicts spatial heterogeneities in both regional cardiac work and perfusion that offer a new paradigm on the vulnerability of the subendocardium to ischemia, particularly at the apex. We propose a mathematical and computational modeling framework to simulate the interaction of left ventricular mechanics, systemic circulation, and coronary microcirculation. The computational simulations revealed that the relaxation rate of the myocardium has a significant effect whereas the contractility has a marginal effect on both the magnitude and transmural distribution of coronary perfusion. The ratio of subendocardial to subepicardial perfusion density (Q_endo/Q_epi) changed by -12 to +6% from a baseline value of 1.16 when myocardial contractility was varied by +25 and -10%, respectively; Q_endo/Q_epi changed by 37% when sarcomere relaxation rate, b, was faster and increased by 10% from the baseline value. The model predicts axial differences in regional myocardial work and perfusion density across the wall thickness. Regional myofiber work done at the apex is 30-50% lower than at the center region, whereas perfusion density in the apex is lower by only 18% compared with the center. There are large axial differences in coronary flow and myocardial work at the subendocardial locations, with the highest differences located at the apex region. A mismatch exists between perfusion density and regional work done at the subendocardium. This mismatch is speculated to be compensated by coronary autoregulation.NEW & NOTEWORTHY We present a model of left ventricle perfusion based on an anatomically realistic coronary tree structure that includes its interaction with the systemic circulation. Left ventricular relaxation rate has a significant effect on the regional distribution of coronary flow and myocardial work.

Multisite pacing and myocardial scars: a computational study

Cardiac resynchronization therapy (CRT) is a frequently effective treatment modality for dyssynchronous heart failure, however, 30% of patients do not respond, usually due to suboptimal activation of the left ventricle (LV). Multisite pacing (MSP) may increase the response rate, but its effect in the presence of myocardial scars is not fully understood. We use a computational model to study the outcome of MSP in an LV with scars in two different locations and of two different sizes. The LV was stimulated from anterior, posterior and lateral locations individually and in pairs, while a septal stimulation site represented right ventricular (RV) pacing. Intraventricular pressures were measured, and outcomes evaluated in terms of maximum LV pressure gradient (dP/dt_max)- change compared to isolated RV pacing. The best result obtained using various LV pacing locations included a combination of sites remote from scars and the septum. The highest dP/dt_max increase was achieved, regardless of scar size, using MSP with one pacing site located on the LV free wall opposite to the scar and one site opposite to the septum. These in silico modelling results suggest that making placement of pacing electrodes dependent on location of scarring, may alter acute haemodynamics and that such modelling may contribute to future CRT optimization.

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.

Detailed structural assessment of healthy interventricular septum in the presence of remodeling infarct in the free wall - A finite element model

Purpose

Computational modelling may improve the fundamental understanding of various mechanisms of diseases more particularly related to clinical challenges. In this study the effect of remodeling infarct presence in the left ventricle on the interventricular septal wall is studied using the finite element methods.

Methods

In this study, two rat heart (one model with healthy myocardium and one model with remodeling free wall and healthy septal wall) with magnetic resonance imaging data was gathered to reconstruct three-dimensional (3D) rat heart models. 3D data points from Segment® were imported into SolidEdge® for creation of 3D rat heart models. Abaqus® was used for finite element modeling.

Results

The strain in the healthy interventricular septum of the infarcted left ventricle wall increased when compared to the healthy interventricular septum in the healthy left ventricle. Similarly, the average stress in the healthy left ventricle was observed to have increased on the healthy the interventricular septum where the free wall is subjected to remodeling infarct. When comparing the infarcted models to the healthy model, it was found that the average strain had greatly increased by up to 50.0 %.

Conclusions

The remodeling infarct in the left ventricle has an impact on the healthy interventricular septal wall. Even though the interventricular septal wall was modelled as healthy, it was observed that it has undergone considerable changes in stresses and strains in circumferential and longitudinal direction. The observed changes in myocardial stresses and strains may result in poor global functioning of the heart.

Computational modeling of human left ventricle to assess the role of trabeculae carneae on the diastolic and systolic functions

Trabeculae carneae are irregular structures that cover the endocardial surfaces of both ventricles and account for a significant portion of human ventricular mass. The role of trabeculae carneae in diastolic and systolic functions of the left ventricle (LV) is not well understood. Thus, the objective of this study was to investigate the functional role of trabeculae carneae in the LV. Finite element analyses of ventricular functions were conducted for three different models of human LV derived from high-resolution magnetic resonance imaging (MRI). The first model comprised trabeculae carneae and papillary muscles, while the second model had papillary muscles and partial trabeculae carneae, and the third model had a smooth endocardial surface. We customized these patient-specific models with myofiber architecture generated with a rule-based algorithm, diastolic material parameters using Fung strain energy function derived from bi-axial tests and adjusted with the empirical Klotz relationship, and myocardial contractility constants optimized for average normal ejection fraction of the human LV. Results showed that the partial trabeculae cutting model had enlarged end-diastolic volume, reduced wall stiffness and even increased end-systolic function, indicating that the absence of trabeculae carneae increased the compliance of the LV during diastole, while maintaining systolic function.

Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response

Computational cardiac modelling is a mature area of biomedical computing and is currently evolving from a pure research tool to aiding in clinical decision making. Assessing the reliability of computational model predictions is a key factor for clinical use, and uncertainty quantification (UQ) and sensitivity analysis are important parts of such an assessment. In this study, we apply UQ in computational heart mechanics to study uncertainty both in material parameters characterizing global myocardial stiffness and in the local muscle fiber orientation that governs tissue anisotropy. The uncertainty analysis is performed using the polynomial chaos expansion (PCE) method, which is a nonintrusive meta-modeling technique that surrogates the original computational model with a series of orthonormal polynomials over the random input parameter space. In addition, in order to study variability in the muscle fiber architecture, we model the uncertainty in orientation of the fiber field as an approximated random field using a truncated Karhunen-Loéve expansion. The results from the UQ and sensitivity analysis identify clear differences in the impact of various material parameters on global output quantities. Furthermore, our analysis of random field variations in the fiber architecture demonstrate a substantial impact of fiber angle variations on the selected outputs, highlighting the need for accurate assignment of fiber orientation in computational heart mechanics models.

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.

Effect of myocardial heterogeneity on ventricular electro-mechanical responses: a computational study

BACKGROUND

The heart wall exhibits three layers of different thicknesses: the outer epicardium, mid-myocardium, and inner endocardium. Among these layers, the mid-myocardium is typically the thickest. As indicated by preliminary studies, heart-wall layers exhibit various characteristics with regard to electrophysiology, pharmacology, and pathology. Construction of an accurate three-dimensional (3D) model of the heart is important for predicting physiological behaviors. However, the wide variability of myocardial shapes and the unclear edges between the epicardium and soft tissues are major challenges in the 3D model segmentation approach for identifying the boundaries of the epicardium, mid-myocardium, and endocardium. Therefore, this results in possible variations in the heterogeneity ratios between the epicardium, mid-myocardium, and endocardium. The objective of this study was to observe the effects of different thickness ratios of the epicardium, mid-myocardium, and endocardium on cardiac arrhythmogenesis, reentry instability, and mechanical responses during arrhythmia.

METHODS

We used a computational method and simulated three heterogeneous ventricular models: Model 1 had the thickest M cell layer and thinnest epicardium and endocardium. Model 2 had intermediate layer thicknesses. Model 3 exhibited the thinnest mid-myocardium and thickest epicardium and endocardium. Electrical and mechanical simulations of the three heterogeneous models were performed under normal sinus rhythm and reentry conditions.

RESULTS

Model 1 exhibited the highest probability of terminating reentrant waves, and Model 3 exhibited to experience greater cardiac arrhythmia. In the reentry simulation, at 8 s, Model 3 generated the largest number of rotors (eight), while Models 1 and 2 produced five and seven rotors, respectively. There was no significant difference in the cardiac output obtained during the sinus rhythm. Under the reentry condition, the highest cardiac output was generated by Model 1 (19 mL/s), followed by Model 2 (9 mL/s) and Model 3 (7 mL/s).

CONCLUSIONS

A thicker mid-myocardium led to improvements in the pumping efficacy and contractility and reduced the probability of cardiac arrhythmia. Conversely, thinner M cell layers generated more unstable reentrant spiral waves and hindered the ventricular pumping.

Comparison of Biomechanical Properties and Microstructure of Trabeculae Carneae, Papillary Muscles, and Myocardium in the Human Heart

Trabeculae carneae account for a significant portion of human ventricular mass, despite being considered embryologic remnants. Recent studies have found trabeculae hypertrophy and fibrosis in hypertrophied left ventricles with various pathological conditions. The objective of this study was to investigate the passive mechanical properties and microstructural characteristics of trabeculae carneae and papillary muscles compared to the myocardium in human hearts. Uniaxial tensile tests were performed on samples of trabeculae carneae and myocardium strips, while biaxial tensile tests were performed on samples of papillary muscles and myocardium sheets. The experimental data were fitted with a Fung-type strain energy function and material coefficients were determined. The secant moduli at given diastolic stress and strain levels were determined and compared among the tissues. Following the mechanical testing, histology examinations were performed to investigate the microstructural characteristics of the tissues. Our results demonstrated that the trabeculae carneae were significantly stiffer (Secant modulus SM2 = 80.06 ± 10.04 KPa) and had higher collagen content (16.10 ± 3.80%) than the myocardium (SM2 = 55.14 ± 20.49 KPa, collagen content = 10.06 ± 4.15%) in the left ventricle. The results of this study improve our understanding of the contribution of trabeculae carneae to left ventricular compliance and will be useful for building accurate computational models of the human heart.

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.

A transmurally heterogeneous orthotropic activation model for ventricular contraction and its numerical validation

Models for cardiac mechanics require an activation mechanism properly representing the stress-strain relations in the contracting myocardium. In this paper, we propose a new activation model that accounts for the transmural heterogeneities observed in myocardial strain measurements. In order to take the anisotropy of the active mechanics into account, our model is based on an active strain formulation. Thanks to multiplicative decomposition of the deformation gradient tensor, in this formulation, the active strains orthogonal to the fibers can be naturally described. We compare the results of our novel formulation against different anisotropic models of the active contraction of the cardiac muscle, as well as against experimental data available in the literature. We show that with the currently available models, the strain distributions are not in agreement with the reported experimental measurements. Conversely, we show that our new transmurally heterogeneous orthotropic activation model improves the accuracy of shear strains related to in-plane rotations and torsion.

Assessment of wall stresses and mechanical heart power in the left ventricle: Finite element modeling versus Laplace analysis

INTRODUCTION

Stenotic aortic valve disease (AS) causes pressure overload of the left ventricle (LV) that may trigger adverse remodeling and precipitate progression towards heart failure (HF). As myocardial energetics can be impaired during AS, LV wall stresses and biomechanical power provide a complementary view of LV performance that may aide in better assessing the state of disease.

OBJECTIVES

Using a high-resolution electro-mechanical (EM) in silico model of the LV as a reference, we evaluated clinically feasible Laplace-based methods for assessing global LV wall stresses and biomechanical power.

METHODS

We used N = 4 in silico finite element (FE) EM models of LV and aorta of patients suffering from AS. All models were personalized with clinical data under pretreatment conditions. Left ventricle wall stresses and biomechanical power were computed accurately from FE kinematic data and compared with Laplace-based estimation methods, which were applied to the same FE model data.

RESULTS AND CONCLUSION

Laplace estimates of LV wall stress are able to provide a rough approximation of global mean stress in the circumferential-longitudinal plane of the LV. However, according to FE results, spatial heterogeneity of stresses in the LV wall is significant, leading to major discrepancies between local stresses and global mean stress. Assessment of mechanical power with Laplace methods is feasible, but these are inferior in accuracy compared with FE models. The accurate assessment of stress and power density distribution in the LV wall is only feasible based on patient-specific FE modeling.

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

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

Electromechanical Model to Predict Cardiac Resynchronization Therapy

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

GEMS: A Fully Integrated PETSc-Based Solver for Coupled Cardiac Electromechanics and Bidomain Simulations

Cardiac contraction is coordinated by a wave of electrical excitation which propagates through the heart. Combined modeling of electrical and mechanical function of the heart provides the most comprehensive description of cardiac function and is one of the latest trends in cardiac research. The effective numerical modeling of cardiac electromechanics remains a challenge, due to the stiffness of the electrical equations and the global coupling in the mechanical problem. Here we present a short review of the inherent assumptions made when deriving the electromechanical equations, including a general representation for deformation-dependent conduction tensors obeying orthotropic symmetry, and then present an implicit-explicit time-stepping approach that is tailored to solving the cardiac mono- or bidomain equations coupled to electromechanics of the cardiac wall. Our approach allows to find numerical solutions of the electromechanics equations using stable and higher order time integration. Our methods are implemented in a monolithic finite element code GEMS (Ghent Electromechanics Solver) using the PETSc library that is inherently parallelized for use on high-performance computing infrastructure. We tested GEMS on standard benchmark computations and discuss further development of our software.

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.

Influence of the KCNQ1 S140G Mutation on Human Ventricular Arrhythmogenesis and Pumping Performance: Simulation Study

The KCNQ1 S140G mutation, which is involved in I_Ks current, affects atrial fibrillation. However, little is known about its effect on the mechanical behavior of the heart. Therefore, we assessed the influence of the KCNQ1 S140G mutation on ventricular electrophysiological stability and mechanical pumping performance using a multi-scale model of cardiac electromechanics. An image-based electromechanical model was used to assess the effect on electrical propagation and arrhythmogenesis of the KCNQ1 S140G mutation. In addition, it was used to compare the mechanical response under the wild-type (WT) and S140G mutation conditions. The intracellular calcium transient obtained from the electrophysiological model was applied as an input parameter to a mechanical model to implement excitation–contraction coupling. The I_Ks current equation was modified to account for expression of the KCNQ1 S140G mutation, and it included a scaling factor (ϕ) for mutant expressivity. The WT and S140G mutation conditions were compared at the single-cell and three-dimensional (3D) tissue levels. The action potential duration (APD) was reduced by 60% by the augmented I_Ks current under the S140G mutation condition, which resulted in shorter QT interval. This reduced the 3D sinus rhythm wavelength by 60% and the sustained re-entry by 56%. However, pumping efficiency of mutant ventricles was superior in sinus rhythm condition. In addition, the shortened wavelength in cardiac tissue allowed a re-entrant circuit to form and increased the probability of sustaining ventricular tachycardia and ventricular fibrillation. In contrast, under the WT condition, a normal wavelength (20.8 cm) was unlikely to initiate and sustain re-entry in the cardiac tissue. Subsequently, the S140G mutant ventricles developed a higher dominant frequency distribution range (2.0–5.3 Hz) than the WT condition (2.8–3.7 Hz). In addition, stroke volume of mutant ventricles was reduced by 65% in sustained re-entry compared to the WT condition. In conclusion, signs of the S140G mutation might be difficult to identify in sinus rhythm even though the mutant ventricles show shortened QT interval. This suggests that the KCNQ1 S140G mutation increases the risk of death by sudden cardiac arrest. In addition, the KCNQ1 S140G mutation can induce ventricular arrhythmia and lessen ventricular contractility under re-entrant conditions.

Left Ventricular Diastolic Myocardial Stiffness and End-Diastolic Myofibre Stress in Human Heart Failure Using Personalised Biomechanical Analysis

Understanding the aetiology of heart failure with preserved (HFpEF) and reduced (HFrEF) ejection fraction requires knowledge of biomechanical factors such as diastolic myocardial stiffness and stress. Cine CMR images and intra-ventricular pressure recordings were acquired in 8 HFrEF, 11 HFpEF and 5 control subjects. Diastolic myocardial stiffness was estimated using biomechanical models and found to be greater in HFrEF (6.4 ± 1.2 kPa) than HFpEF (2.7 ± 0.6 kPa, p < 0.05) and also greater than control (1.2 ± 0.4 kPa, p < 0.005). End-diastolic mid-ventricular myofibre stress derived from the personalised biomechanics model was higher in HFrEF (2.9 ± 0.3 kPa) than control (0.9 ± 0.3 kPa, p < 0.01). Chamber stiffness, measured from the slope of the diastolic pressure-volume relationship, is determined by the intrinsic tissue properties as well as the size and shape of the heart, and was unable to distinguish between any of the three groups (p > 0.05). Personalised biomechanical analysis may provide more specific information about myocardial mechanical behaviour than global chamber indices, which are confounded by variations in ventricular geometry.

Towards a Computational Framework for Modeling the Impact of Aortic Coarctations Upon Left Ventricular Load

Computational fluid dynamics (CFD) models of blood flow in the left ventricle (LV) and aorta are important tools for analyzing the mechanistic links between myocardial deformation and flow patterns. Typically, the use of image-based kinematic CFD models prevails in applications such as predicting the acute response to interventions which alter LV afterload conditions. However, such models are limited in their ability to analyze any impacts upon LV load or key biomarkers known to be implicated in driving remodeling processes as LV function is not accounted for in a mechanistic sense. This study addresses these limitations by reporting on progress made toward a novel electro-mechano-fluidic (EMF) model that represents the entire physics of LV electromechanics (EM) based on first principles. A biophysically detailed finite element (FE) model of LV EM was coupled with a FE-based CFD solver for moving domains using an arbitrary Eulerian-Lagrangian (ALE) formulation. Two clinical cases of patients suffering from aortic coarctations (CoA) were built and parameterized based on clinical data under pre-treatment conditions. For one patient case simulations under post-treatment conditions after geometric repair of CoA by a virtual stenting procedure were compared against pre-treatment results. Numerical stability of the approach was demonstrated by analyzing mesh quality and solver performance under the significantly large deformations of the LV blood pool. Further, computational tractability and compatibility with clinical time scales were investigated by performing strong scaling benchmarks up to 1536 compute cores. The overall cost of the entire workflow for building, fitting and executing EMF simulations was comparable to those reported for image-based kinematic models, suggesting that EMF models show potential of evolving into a viable clinical research tool.

The effect of heart failure and left ventricular assist device treatment on right ventricular mechanics: a computational study

Background and aims

Although it is important to analyze the hemodynamic factors related to the right ventricle (RV) after left ventricular assist device (LVAD) implantation, previous studies have focused only on the alteration of the ventricular shape and lack quantitative analysis of the various hemodynamic parameters. Therefore, we quantitatively analyzed various hemodynamic parameters related to the RV under normal, heart failure (HF), and HF incorporated with continuous flow LVAD therapy by using a computational model.

Methods

In this study, we combined a three-dimensional finite element electromechanical model of ventricles, which is based on human ventricular morphology captured by magnetic resonance imaging (MRI) with a lumped model of the circulatory system and continuous flow LVAD function in order to construct an integrated model of an LVAD implanted-cardiovascular system. To induce systolic dysfunction, the magnitude of the calcium transient function under HF condition was reduced to 70% of the normal value, and the time constant was reduced by 30% of the normal value.

Results

Under the HF condition, the left ventricular end systolic pressure decreased, the left ventricular end diastolic pressure increased, and the pressure in the right atrium (RA), RV, and pulmonary artery (PA) increased compared with the normal condition. The LVAD therapy decreased the end-systolic pressure of the LV by 41%, RA by 29%, RV by 53%, and PA by 71%, but increased the right ventricular ejection fraction by 52% and cardiac output by 40%, while the stroke work was reduced by 67% compared with the HF condition without LVAD. The end-systolic ventricular tension and strain decreased with the LVAD treatment.

Conclusion

LVAD enhances CO and mechanical unloading of the LV as well as those of the RV and prevents pulmonary hypertension which can be induced by HF.

Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics

Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance.

Left Ventricular Wall Stress Is Sensitive Marker of Hypertrophic Cardiomyopathy With Preserved Ejection Fraction

Hypertrophic cardiomyopathy (HCM) patients present altered myocardial mechanics due to the hypertrophied ventricular wall and are typically diagnosed by the increase in myocardium wall thickness. This study aimed to quantify regional left ventricular (LV) shape, wall stress and deformation from cardiac magnetic resonance (MR) images in HCM patients and controls, in order to establish superior measures to differentiate HCM from controls. A total of 19 HCM patients and 19 controls underwent cardiac MR scans. The acquired MR images were used to reconstruct 3D LV geometrical models and compute the regional parameters (i.e., wall thickness, curvedness, wall stress, area strain and ejection fraction) based on the standard 16 segment model using our in-house software. HCM patients were further classified into four quartiles based on wall thickness at end diastole (ED) to assess the impact of wall thickness on these regional parameters. There was a significant difference between the HCM patients and controls for all regional parameters (P < 0.001). Wall thickness was greater in HCM patients at the end-diastolic and end-systolic phases, and thickness was most pronounced in segments at the septal regions. A multivariate stepwise selection algorithm identified wall stress index at ED (σ_i,ED) as the single best independent predictor of HCM (AUC = 0.947). At the cutoff value σ_i,ED < 1.64, both sensitivity and specificity were 94.7%. This suggests that the end-diastolic wall stress index incorporating regional wall curvature—an index based on mechanical principle—is a sensitive biomarker for HCM diagnosis with potential utility in diagnostic and therapeutic assessment.

Changes and classification in myocardial contractile function in the left ventricle following acute myocardial infarction

In this research, we hypothesized that novel biomechanical parameters are discriminative in patients following acute ST-segment elevation myocardial infarction (STEMI). To identify these biomechanical biomarkers and bring computational biomechanics ‘closer to the clinic’, we applied state-of-the-art multiphysics cardiac modelling combined with advanced machine learning and multivariate statistical inference to a clinical database of myocardial infarction. We obtained data from 11 STEMI patients (ClinicalTrials.gov NCT01717573) and 27 healthy volunteers, and developed personalized mathematical models for the left ventricle (LV) using an immersed boundary method. Subject-specific constitutive parameters were achieved by matching to clinical measurements. We have shown, for the first time, that compared with healthy controls, patients with STEMI exhibited increased LV wall active tension when normalized by systolic blood pressure, which suggests an increased demand on the contractile reserve of remote functional myocardium. The statistical analysis reveals that the required patient-specific contractility, normalized active tension and the systolic myofilament kinematics have the strongest explanatory power for identifying the myocardial function changes post-MI. We further observed a strong correlation between two biomarkers and the changes in LV ejection fraction at six months from baseline (the required contractility (r = − 0.79, p < 0.01) and the systolic myofilament kinematics (r = 0.70, p = 0.02)). The clinical and prognostic significance of these biomechanical parameters merits further scrutinization.