On the in vivo systolic compressibility of left ventricular free wall myocardium in the normal and infarcted heart

In-silico heart model phantom to validate cardiac strain imaging

The quantification of cardiac strains as structural indices of cardiac function has a growing prevalence in clinical diagnosis. However, the highly heterogeneous four-dimensional (4D) cardiac motion challenges accurate "regional" strain quantification and leads to sizable differences in the estimated strains depending on the imaging modality and post-processing algorithm, limiting the translational potential of strains as incremental biomarkers of cardiac dysfunction. There remains a crucial need for a feasible benchmark that successfully replicates complex 4D cardiac kinematics to determine the reliability of strain calculation algorithms. In this study, we propose an in-silico heart phantom derived from finite element (FE) simulations to validate the quantification of 4D regional strains. First, as a proof-of-concept exercise, we created synthetic magnetic resonance (MR) images for a hollow thick-walled cylinder under pure torsion with an exact solution and demonstrated that "ground-truth" values can be recovered for the twist angle, which is also a key kinematic index in the heart. Next, we used mouse-specific FE simulations of cardiac kinematics to synthesize dynamic MR images by sampling various sectional planes of the left ventricle (LV). Strains were calculated using our recently developed non-rigid image registration (NRIR) framework in both problems. Moreover, we studied the effects of image quality on distorting regional strain calculations by conducting in-silico experiments for various LV configurations. Our studies offer a rigorous and feasible tool to standardize regional strain calculations to improve their clinical impact as incremental biomarkers.

A comprehensive experimental analysis of the local passive response across the healthy porcine left ventricle

This work provides a comprehensive characterization of porcine myocardial tissue, combining true biaxial (TBx), simple triaxial shear (STS) and confined compression (CC) tests to analyze its elastic behavior under cyclic loads. We expanded this study to different zones of the ventricular free wall, providing insights into the local behavior along the longitudinal and radial coordinates. The aging impact was also assessed by comparing two age groups (4 and 8 months). Resulting data showed that the myocardium exhibits a highly nonlinear hyperelastic and incompressible behavior. We observed an anisotropy ratio of 2-2.4 between averaged peak stresses in TBx tests and 1-0.59-0.40 orthotropy ratios for normalised fiber-sheet-normal peak stresses in STS tests. We obtained a highly incompressible response, reaching volumetric pressures of 2-7 MPa for perfused tissue in CC tests, with notable differences when fluid drainage was allowed, suggesting a high permeability. Regional analysis showed reduced stiffness and anisotropy (20-25%) at the apical region compared to the medial, which we attributed to differences in the fiber field dispersion. Compressibility also increased towards the epicardium and apical regions. Regarding age-related variations, 8-month animals showed stiffer response (at least 25% increase), particularly in directions where the mechanical stress is absorbed by collagenous fibers (more than 90%), as supported by a histological analysis. Although compressibility of perfused tissue remained unchanged, permeability significantly reduced in 8-month-old animals. Our findings offer new insights into myocardial properties, emphasizing on local variations, which can help to get a more realistic understanding of cardiac mechanics in this common animal model. STATEMENT OF SIGNIFICANCE: In this work, we conducted a comprehensive analysis of the passive mechanical behavior of porcine myocardial tissue through biaxial, triaxial shear, and confined compression tests. Unlike previous research, we investigated the variation in mechanical response across the left ventricular free wall, conventionally assumed homogeneous, revealing differences in terms of stiffness and compressibility. Additionally, we evaluated age-related effects on mechanical properties by comparing two age groups, observing significant variations in stiffness and permeability. To date, there has been no such in-depth exploration of myocardial elastic response and compressibility considering regional variations along the wall and may contribute to a better understanding of the cardiac tissue's passive mechanical response.

In-silico heart model phantom to validate cardiac strain imaging

The quantification of cardiac strains as structural indices of cardiac function has a growing prevalence in clinical diagnosis. However, the highly heterogeneous four-dimensional (4D) cardiac motion challenges accurate "regional" strain quantification and leads to sizable differences in the estimated strains depending on the imaging modality and post-processing algorithm, limiting the translational potential of strains as incremental biomarkers of cardiac dysfunction. There remains a crucial need for a feasible benchmark that successfully replicates complex 4D cardiac kinematics to determine the reliability of strain calculation algorithms. In this study, we propose an in-silico heart phantom derived from finite element (FE) simulations to validate the quantification of 4D regional strains. First, as a proof-of-concept exercise, we created synthetic magnetic resonance (MR) images for a hollow thick-walled cylinder under pure torsion with an exact solution and demonstrated that "ground-truth" values can be recovered for the twist angle, which is also a key kinematic index in the heart. Next, we used mouse-specific FE simulations of cardiac kinematics to synthesize dynamic MR images by sampling various sectional planes of the left ventricle (LV). Strains were calculated using our recently developed non-rigid image registration (NRIR) framework in both problems. Moreover, we studied the effects of image quality on distorting regional strain calculations by conducting in-silico experiments for various LV configurations. Our studies offer a rigorous and feasible tool to standardize regional strain calculations to improve their clinical impact as incremental biomarkers.

Multi-material Cardiac Sleeves with Variable Stiffness Enhance Regional Strain Markers

The regional kinematics of the myocardium are substantially altered post-myocardial infarction (MI). Physical support of the myocardium in the form of a cardiac sleeve has been introduced as a means to improve cardiac function and prevent adverse remodeling in the left ventricle (LV). This study focuses on the impact of multi-material cardiac sleeves with variable stiffness on regional myocardial mechanics following MI. Through in-silico modeling, this work evaluates the ability of tailored cardiac sleeves to modulate global volumetric makers, such as stroke volume and ejection fraction, as well as their influence on regional strain and stress distributions. The analysis highlights the role of material property gradients within the sleeve structure. While changes in global functional markers were modest, the sleeves showed sizable changes in regional myofiber strains, underscoring the potential for regionally targeted mechanical support to improve the remodeling processes in infarcted LV. The findings suggest that while passive sleeves may have a modest impact on overall cardiac function immediately post-implantation, their design can be crucial for optimizing regional biomechanical behavior and preventing a cascade of maladaptive chronic remodeling events. Our findings warrant further studies to explore the potential mitigation of adverse remodeling in MI through the use of spatially tailored passive support sleeves.

WarpPINN: Cine-MR image registration with physics-informed neural networks

The diagnosis of heart failure usually includes a global functional assessment, such as ejection fraction measured by magnetic resonance imaging. However, these metrics have low discriminate power to distinguish different cardiomyopathies, which may not affect the global function of the heart. Quantifying local deformations in the form of cardiac strain can provide helpful information, but it remains a challenge. In this work, we introduce WarpPINN, a physics-informed neural network to perform image registration to obtain local metrics of heart deformation. We apply this method to cine magnetic resonance images to estimate the motion during the cardiac cycle. We inform our neural network of the near-incompressibility of cardiac tissue by penalizing the Jacobian of the deformation field. The loss function has two components: an intensity-based similarity term between the reference and the warped template images, and a regularizer that represents the hyperelastic behavior of the tissue. The architecture of the neural network allows us to easily compute the strain via automatic differentiation to assess cardiac activity. We use Fourier feature mappings to overcome the spectral bias of neural networks, allowing us to capture discontinuities in the strain field. The algorithm is tested on synthetic examples and on a cine SSFP MRI benchmark of 15 healthy volunteers, where it is trained to learn the deformation mapping of each case. We outperform current methodologies in landmark tracking and provide physiological strain estimations in the radial and circumferential directions. WarpPINN provides precise measurements of local cardiac deformations that can be used for a better diagnosis of heart failure and can be used for general image registration tasks. Source code is available at https://github.com/fsahli/WarpPINN.

A multi-scale computational model for the passive mechanical behavior of right ventricular myocardium

We have previously demonstrated the importance of myofiber-collagen mechanical interactions in modeling the passive mechanical behavior of right ventricle free wall (RVFW) myocardium. To gain deeper insights into these coupling mechanisms, we developed a high-fidelity, micro-anatomically realistic 3D finite element model of right ventricle free wall (RVFW) myocardium by combining high-resolution imaging and supercomputer-based simulations. We first developed a representative tissue element (RTE) model at the sub-tissue scale by specializing the hyperelastic anisotropic structurally-based constitutive relations for myofibers and ECM collagen, and equi-biaxial and non-equibiaxial loading conditions were simulated using the open-source software FEniCS to compute the effective stress-strain response of the RTE. To estimate the model parameters of the RTE model, we first fitted a 'top-down' biaxial stress-strain behavior with our previous structurally based (tissue-scale) model, informed by the measured myofiber and collagen fiber composition and orientation distributions. Next, we employed a multi-scale approach to determine the tissue-level (5 x 5 x 0.7 mm specimen size) RVFW biaxial behavior via 'bottom-up' homogenization of the fitted RTE model, recapitulating the histologically measured myofiber and collagen orientation to the biaxial mechanical data. Our homogenization approach successfully reproduced the tissue-level mechanical behavior of our previous studies in all biaxial deformation modes, suggesting that the 3D micro-anatomical arrangement of myofibers and ECM collagen is indeed a primary mechanism driving myofiber-collagen interactions.

Backscatter tensor imaging and 3D speckle tracking for simultaneous ex vivo structure and deformation measurement of myocardium

OBJECTIVE

Biaxial mechanical testing is a common method for elucidation of mechanical properties of excised ventricular myocardium, especially in the context of structural remodeling that accompanies heart disease. Current imaging strategies in biaxial testing are based on optical camera imaging of the tissue surface, thus providing no information about the tissue microstructure and limiting strain measurements to two dimensions. Here, these limitations are overcome by replacing the camera with ultrasound imaging in order to measure both transmural fiber orientation and 3D tissue deformation during biaxial testing.

METHODS

Quasi-static biaxial mechanical testing is applied to four samples of excised porcine ventricular myocardium (two left- and two right-ventricular tissues). During testing, a rotational scan of an ultrasound linear array provides data for both backscatter tensor imaging and 3D speckle tracking, from which transmural fiber orientation and tissue deformation are computed, respectively. Ultrasound-derived fiber orientation and tissue strain are validated against histology and camera surface imaging, respectively.

DISCUSSION

Ultrasound-derived fiber angle and tissue strain exhibit good accuracy, with root-mean-square errors of 9.9° and 1.2% strain, respectively. Further investigation into the optimization of backscatter tensor imaging is warranted. Replacing the rotational scan of a linear array with volume imaging with a matrix array will improve the technique.

CONCLUSION

Ultrasound imaging can replace the optical camera measurement during biaxial mechanical testing of ventricular myocardium in order to accurately provide measurements of transmural fiber orientation and tissue strain. In situ knowledge of transmural fiber structure and tissue deformation can enhance the inverse problem used to determine tissue mechanical properties from biaxial testing.

Contractile Adaptation of the Left Ventricle Post-myocardial Infarction: Predictions by Rodent-Specific Computational Modeling

Myocardial infarction (MI) results in cardiac myocyte death and the formation of a fibrotic scar in the left ventricular free wall (LVFW). Following an acute MI, LVFW remodeling takes place consisting of several alterations in the structure and properties of cellular and extracellular components with a heterogeneous pattern across the LVFW. The normal function of the heart is strongly influenced by the passive and active biomechanical behavior of the LVFW, and progressive myocardial structural remodeling can have a detrimental effect on both diastolic and systolic functions of the LV leading to heart failure. Despite important advances in understanding LVFW passive remodeling in the setting of MI, heterogeneous remodeling in the LVFW active properties and its relationship to organ-level LV function remain understudied. To address these gaps, we developed high-fidelity finite-element (FE) rodent computational cardiac models (RCCMs) of MI using extensive datasets from MI rat hearts representing the heart remodeling from one-week (1-wk) to four-week (4-wk) post-MI timepoints. The rat-specific models (n = 2 for each timepoint) integrate detailed imaging data of the heart geometry, myocardial fiber architecture, and infarct zone determined using late gadolinium enhancement prior to terminal measurements. The computational models predicted a significantly higher level of active tension in remote myocardium in early post-MI hearts (1-wk post-MI) followed by a return to near the control level in late-stage MI (3- and 4-wk post-MI). The late-stage MI rats showed smaller myofiber ranges in the remote region and in-silico experiments using RCCMs suggested that the smaller fiber helicity is consistent with lower contractile forces needed to meet the measured ejection fractions in late-stage MI. In contrast, in-silico experiments predicted that collagen fiber transmural orientation in the infarct region has little influence on organ-level function. In addition, our MI RCCMs indicated that reduced and potentially positive circumferential strains in the infarct region at end-systole can be used to infer information about the time-varying properties of the infarct region. The detailed description of regional passive and active remodeling patterns can complement and enhance the traditional measures of LV anatomy and function that often lead to a gross and limited assessment of cardiac performance. The translation and implementation of our model in patient-specific organ-level simulations offer to advance the investigation of individualized prognosis and intervention for MI.

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 viscoelastic model for human myocardium

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena. STATEMENT OF SIGNIFICANCE: The viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.

DeepStrain: A Deep Learning Workflow for the Automated Characterization of Cardiac Mechanics

Myocardial strain analysis from cinematic magnetic resonance imaging (cine-MRI) data provides a more thorough characterization of cardiac mechanics than volumetric parameters such as left-ventricular ejection fraction, but sources of variation including segmentation and motion estimation have limited its wider clinical use. We designed and validated a fast, fully-automatic deep learning (DL) workflow to generate both volumetric parameters and strain measures from cine-MRI data consisting of segmentation and motion estimation convolutional neural networks. The final motion network design, loss function, and associated hyperparameters are the result of a thorough ad hoc implementation that we carefully planned specific for strain quantification, tested, and compared to other potential alternatives. The optimal configuration was trained using healthy and cardiovascular disease (CVD) subjects (n = 150). DL-based volumetric parameters were correlated (>0.98) and without significant bias relative to parameters derived from manual segmentations in 50 healthy and CVD test subjects. Compared to landmarks manually-tracked on tagging-MRI images from 15 healthy subjects, landmark deformation using DL-based motion estimates from paired cine-MRI data resulted in an end-point-error of 2.9 ± 1.5 mm. Measures of end-systolic global strain from these cine-MRI data showed no significant biases relative to a tagging-MRI reference method. On 10 healthy subjects, intraclass correlation coefficient for intra-scanner repeatability was good to excellent (>0.75) for all global measures and most polar map segments. In conclusion, we developed and evaluated the first end-to-end learning-based workflow for automated strain analysis from cine-MRI data to quantitatively characterize cardiac mechanics of healthy and CVD subjects.

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

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