Multiscale Finite Element Modeling of Left Ventricular Growth in Simulations of Valve Disease

Multiscale models of the cardiovascular system are emerging as effective tools for investigating the mechanisms that drive ventricular growth and remodeling. These models can predict how molecular-level mechanisms impact organ-level structure and function and could provide new insights that help improve patient care. MyoFE is a multiscale computer framework that bridges molecular and organ-level mechanisms in a finite element model of the left ventricle that is coupled with the systemic circulation. In this study, we extend MyoFE to include a growth algorithm, based on volumetric growth theory, to simulate concentric growth (wall thickening/thinning) and eccentric growth (chamber dilation/constriction) in response to valvular diseases. Specifically in our model, concentric growth is controlled by time-averaged total stress along the fiber direction over a cardiac cycle while eccentric growth responds to time-averaged intracellular myofiber passive stress over a cardiac cycle. The new framework correctly predicted different forms of growth in response to two types of valvular diseases, namely aortic stenosis and mitral regurgitation. Furthermore, the model predicted that LV size and function are nearly restored (reversal of growth) when the disease-mimicking perturbation was removed in the simulations for each valvular disorder. In conclusion, the simulations suggest that time-averaged total stress along the fiber direction and time-averaged intracellular myofiber passive stress can be used to drive concentric and eccentric growth in simulations of valve disease.

A multiscale finite element model of left ventricular mechanics incorporating baroreflex regulation

Cardiovascular function is regulated by a short-term hemodynamic baroreflex loop, which tries to maintain arterial pressure at a normal level. In this study, we present a new multiscale model of the cardiovascular system named MyoFE. This framework integrates a mechanistic model of contraction at the myosin level into a finite-element-based model of the left ventricle pumping blood through the systemic circulation. The model is coupled with a closed-loop feedback control of arterial pressure inspired by a baroreflex algorithm previously published by our team. The reflex loop mimics the afferent neuron pathway via a normalized signal derived from arterial pressure. The efferent pathway is represented by a kinetic model that simulates the net result of neural processing in the medulla and cell-level responses to autonomic drive. The baroreflex control algorithm modulates parameters such as heart rate and vascular tone of vessels in the lumped-parameter model of systemic circulation. In addition, it spatially modulates intracellular Ca2+ dynamics and molecular-level function of both the thick and the thin myofilaments in the left ventricle. Our study demonstrates that the baroreflex algorithm can maintain arterial pressure in the presence of perturbations such as acute cases of altered aortic resistance, mitral regurgitation, and myocardial infarction. The capabilities of this new multiscale model will be utilized in future research related to computational investigations of growth and remodeling.

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.

Computational Modeling of the Subject-Specific Effects of Annuloplasty Ring Sizing on the Mitral Valve to Repair Functional Mitral Regurgitation

Surgical repair of functional mitral regurgitation (FMR) that occurs in nearly 60% of heart failure (HF) patients is currently performed with undersizing mitral annuloplasty (UMA), which lacks short- and long-term durability. Heterogeneity in valve geometry makes tailoring this repair to each patient challenging, and predictive models that can help with planning this surgery are lacking. In this study, we present a 3D echo-derived computational model, to enable subject-specific, pre-surgical planning of the repair. Three computational models of the mitral valve were created from 3D echo data obtained in three pigs with HF and FMR. An annuloplasty ring model in seven sizes was created, each ring was deployed, and post-repair valve closure was simulated. The results indicate that large annuloplasty rings (> 32 mm) were not effective in eliminating regurgitant gaps nor in restoring leaflet coaptation or reducing leaflet stresses and chordal tension. Smaller rings (≤ 32 mm) restored better systolic valve closure in all investigated cases,but excessive valve tethering and restricted motion of the leaflets were still present. This computational study demonstrates that for effective correction of FMR, the extent of annular reduction differs between subjects, and overly reducing the annulus has deleterious effects on the valve.

Smoothed finite element methods in simulation of active contraction of myocardial tissue samples

In modelling and simulation of cardiac mechanics, tetrahedral meshes are often used due to the easy availability of efficient meshing algorithms. This is beneficial in particular when complex geometries such as cardiac structures are considered. The gold standard in simulating the cardiac cycle is to solve the mechanical balance equations with the finite element method (FEM). However, using linear shape functions in the FEM in combination with nearly-incompressible material models is known to produce overly stiff approximations, whereas higher order elements are computationally more expensive. To overcome these problems, smoothed finite element methods (S-FEMs) have been proposed by Liu and co-workers. So far, S-FEMs in 3D have been utilised only in simulations of passive mechanics. In the present work, different S-FEMs are for the first time used for simulation of an active cardiac contraction on three-dimensional myocardial tissue samples. Further, node-based S-FEM (NS-FEM), face-based S-FEM (FS-FEM) and selective FS/NS-FEM are for the first time implemented as user subroutine in the commercial software Abaqus. Our results confirm that all S-FEMs perform softer than linear FEM and volumetric locking is reduced. The FS/NS-FEM produces solutions with the relative error in maximum displacement and rotation being less than 5% with respect to the reference solution obtained by the quadratic FEM for all considered mesh sizes, although linear shape functions are used. We therefore conclude that in particular FS/NS-FEM is an efficient and accurate numerical method in the simulation of an active cardiac muscle contraction.

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.

The Impact of Standard Ablation Strategies for Atrial Fibrillation on Cardiovascular Performance in a Four-Chamber Heart Model

PURPOSE

Atrial fibrillation is one of the most frequent cardiac arrhythmias in the industrialized world and ablation therapy is the method of choice for many patients. However, ablation scars alter the electrophysiological activation and the mechanical behavior of the affected atria. Different ablation strategies with the aim to terminate atrial fibrillation and prevent its recurrence exist but their impact on the performance of the heart is often neglected.

METHODS

In this work, we present a simulation study analyzing five commonly used ablation scar patterns and their combinations in the left atrium regarding their impact on the pumping function of the heart using an electromechanical whole-heart model. We analyzed how the altered atrial activation and increased stiffness due to the ablation scars affect atrial as well as ventricular contraction and relaxation.

RESULTS

We found that systolic and diastolic function of the left atrium is impaired by ablation scars and that the reduction of atrial stroke volume of up to 11.43% depends linearly on the amount of inactivated tissue. Consequently, the end-diastolic volume of the left ventricle, and thus stroke volume, was reduced by up to 1.4 and 1.8%, respectively. During ventricular systole, left atrial pressure was increased by up to 20% due to changes in the atrial activation sequence and the stiffening of scar tissue.

CONCLUSION

This study provides biomechanical evidence that atrial ablation has acute effects not only on atrial contraction but also on ventricular performance. Therefore, the position and extent of ablation scars is not only important for the termination of arrhythmias but is also determining long-term pumping efficiency. If confirmed in larger cohorts, these results have the potential to help tailoring ablation strategies towards minimal global cardiovascular impairment.

A fast computational model for circulatory dynamics: effects of left ventricle-aorta coupling

The course of diseases such as hypertension, systolic heart failure and heart failure with a preserved ejection fraction is affected by interactions between the left ventricle (LV) and the vasculature. To study these interactions, a computationally efficient, biophysically based mathematical model for the circulatory system is presented. In a four-chamber model of the heart, the LV is represented by a previously described low-order, wall volume-preserving model that includes torsion and base-to-apex and circumferential wall shortening and lengthening, and the other chambers are represented using spherical geometries. Active and passive myocardial mechanics of all four chambers are included. The cardiac model is coupled with a wave propagation model for the aorta and a closed lumped-parameter circulation model. Parameters for the normal heart and aorta are determined by fitting to experimental data. Changes in the timing and magnitude of pulse wave reflections by the aorta are demonstrated with changes in compliance and taper of the aorta as seen in aging (decreased compliance, increased diameter and length), and resulting effects on LV pressure-volume loops and LV fiber stress and sarcomere shortening are predicted. Effects of aging of the aorta combined with reduced LV contractile force (failing heart) are examined. In the failing heart, changes in aortic properties with aging affect stroke volume and sarcomere shortening without appreciable augmentation of aortic pressure, and the reflected pressure wave contributes an increased proportion of aortic pressure.

A cell-based framework for modeling cardiac mechanics

Cardiomyocytes are the functional building blocks of the heart-yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell-cell and cell-matrix interactions.

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.

Native cardiac magnetic resonance T1 mapping and cardiac mechanics as assessed by speckle tracking echocardiography in patients with beta-thalassaemia major

BACKGROUND

We hypothesize that cardiac magnetic resonance (CMR) native T1 is associated with myocardial deformation in thalassaemia patients. The present study aimed to compare CMR native T1 values to conventional T2* values in patients with beta-thalassaemia and to explore relationships between these CMR parameters of myocardial iron overload and left ventricular (LV) and left atrial (LA) myocardial deformation.

METHODS

Thirty-four (16 males) patients aged 35.5 ± 9.2 years were studied. Myocardial T2* and T1 mapping were performed to assess the cardiac iron overload, while two-dimensional speckle-tracking echocardiography was performed in determine LV and LA myocardial deformation.

RESULTS

T2* was 36.4 ± 8.7 ms with 3 patients having myocardial iron load (T2*<20 ms). The native T1 was 947.1 ± 84.8 ms, which was significantly lower than the reported normal values in the literature. There was a significant correlation between T1 and T2* values (r = 0.68, p < 0.001). There were no significant correlations between T1 and T2* values and conventional and tissue Doppler parameters of left ventricular systolic and diastolic function. On the other hand, T1, but not T2*, values were found to correlate negatively with maximum LA area indexed by body surface area (r = -0.34, p = 0.047) and positively with LA strain rate at atrial contraction (r = 0.36, p = 0.04). There were no associations between either of these CMR parameters with indices of ventricular deformation.

CONCLUSIONS

In patients with beta-thalassaemia major, native T1 values are decreased, associated with T2* values, and correlated with maximum LA area and LA strain rate at atrial contraction.

Cardiac geometry, function and mechanics in left ventricular non-compaction cardiomyopathy with preserved ejection fraction

BACKGROUND

Left ventricular non-compaction (LVNC) cardiomyopathy in adults has primarily been studied with a phenotypic expression of low ejection fraction (EF) and dilated cardiomyopathy; however, data on LVNC with preserved EF is scarce. The present study aimed to evaluate cardiac geometry and mechanics in LVNC patients with preserved EF.

METHODS

A retrospective cohort study of patients diagnosed with LVNC and a preserved EF between 2008 and 2019 was performed. LVNC was defined according to the presence of established transthoracic 2D echocardiographic (TTE) criteria as follows: (1) prominent LV trabeculations with deep recesses; (2) bi-layered myocardial appearance; and, (3) systolic non-compacted:compacted ratio≥ 2. Subjects were matched 1:1 to controls without LVNC referred for routine TTE. Geometric, functional and mechanics parameters were analyzed in the two cohorts using 2D and speckle-tracking TTE.

RESULTS

Seventeen patients with LVNC and preserved EF were identified. Compared with controls, patients with LVNC had similar LV systolic function and chamber dimensions, but a larger mass and relative wall thickness, and more abnormal LV geometry (76% vs. 18%, p = 0.002), LA remodeling, and pulmonary hypertension. Global longitudinal strain was significantly decreased (-15.4 ± 3.2 vs. -18.9 ± 2.8%, p =  < 0.01) and the prevalence of rigid body rotation was significantly increased (57% vs. 14%, p = 0.05) in the LVNC population. The peak twist values were comparable in both cohorts.

CONCLUSIONS

Impaired LV geometry and longitudinal mechanics, as well as increased myocardial stiffness as expressed by rigid body rotation, characterize LVNC with preserved EF when compared with controls.

Left ventricular mechanical, cardiac autonomic and metabolic responses to a single session of high intensity interval training

PURPOSE

High-intensity interval training (HIIT) produces significant health benefits. However, the acute physiological responses to HIIT are poorly understood. Therefore, we aimed to measure the acute cardiac autonomic, haemodynamic, metabolic and left ventricular mechanical responses to a single HIIT session.

METHODS

Fifty young, healthy participants completed a single HIIT session, comprising of three 30-s maximal exercise intervals on a cycle ergometer, interspersed with 2-min active recovery. Cardiac autonomics, haemodynamics and metabolic variables were measured pre-, during and post-HIIT. Conventional and speckle tracking echocardiography was used to record standard and tissue Doppler measures of left ventricular (LV) structure, function and mechanics pre- and post-HIIT.

RESULTS

Following a single HIIT session, there was significant post-exercise systolic hypotension (126 ± 13 to 111 ± 10 mmHg, p < 0.05), parallel to a significant reduction in total peripheral resistance (1640 ± 365 to 639 ± 177 dyne⋅s⋅cm⁵, p < 0.001) and significant increases in baroreceptor reflex sensitivity and baroreceptor effectiveness index (9.2 ± 11 to 24.8 ± 16.7 ms⋅mmHg^-1 and 41.8 ± 28 to 68.8 ± 16.2, respectively) during recovery compared to baseline. There was also a significant increase in the low- to high-frequency heart rate variability ratio in recovery (0.7 ± 0.48 to 1.7 ± 1, p < 0.001) and significant improvements in left ventricular global longitudinal strain (- 18.3 ± 1.2% to - 29.2 ± 2.3%, p < 0.001), and myocardial twist mechanics (1.27 ± 0.72 to 1.98 ± 0.72°·cm^-1, p = 0.028) post-HIIT compared to baseline.

CONCLUSION

A single HIIT session is associated with acute improvements in autonomic modulation, haemodynamic cardiovascular control and left ventricular function, structure and mechanics. The acute responses to HIIT provide crucial mechanistic information, which may have significant acute and chronic clinical implications.

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.

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.

The hemodynamic power of the heart differentiates normal from diseased right ventricles

Cardiac mechanics is primarily described by the pressure-volume relationship. The ventricular pressure-volume loop displays the instantaneous relationship between intraventricular pressure and volume throughout the cardiac cycle; however, it does not consider the shape of the ventricles, their spatiotemporal deformation patterns, and how these balance with the flowing blood. Our study demonstrates that the pressure-volume relationship represents a first level of approximation for the mechanical power of the ventricles, while, at a further level of approximation, the importance of hemodynamic power emerges through the balance between deformation patterns and fluid dynamics. The analysis is preliminarily tested in a healthy subject's right ventricle and two patients. Moreover, patients' geometry was then rescaled to present a normal volumetric profile to verify whether results were affected by volume size or by the spatiotemporal pattern of how that volume profile was achieved. Results show that alterations of hemodynamic power were found in the abnormal ventricles and that they were not directly caused by the ventricular size but by changes in the ability of intraventricular pressure gradient to generate blood flow. Therefore, hemodynamic power represents a physics-based measure that takes into account the dynamics of the space-time shape changes in combination with blood flow. Hemodynamic power is assessed non-invasively using cardiac imaging techniques and can be an early indicator of cardiac dysfunction before changes occur in volumetric measurements. These preliminary results provide a physical ground to evaluate its diagnostic or prognostic significance in future clinical studies.

Towards the simulation of active cardiac mechanics using a smoothed finite element method

In the last decades, various computational models have been developed to simulate cardiac electromechanics. The most common numerical tool is the finite element method (FEM). However, this method crucially depends on the mesh quality. For complex geometries such as cardiac structures, it is convenient to use tetrahedral discretisations which can be generated automatically. On the other hand, such automatic meshing with tetrahedrons together with large deformations often lead to elements distortion and volumetric locking. To overcome these difficulties, different smoothed finite element methods (S-FEMs) have been proposed in the recent years. They are known to be volumetric locking free, less sensitive to mesh distortion and so far have been used e.g. in simulation of passive cardiac mechanics. In this work, we extend for the first time node-based S-FEM (NS-FEM) towards active cardiac mechanics. Firstly, the sensitivity to mesh distortion is tested and compared to that of FEM. Secondly, an active contraction in circumferentially aligned fibre direction is modelled in the healthy and the infarcted case. We show, that the proposed method is more robust with respect to mesh distortion and computationally more efficient than standard FEM. Being furthermore free of volumetric locking problems makes S-FEM a promising alternative in modelling of active cardiac mechanics, respectively electromechanics.

Estimation of left ventricular stroke work based on a large cohort of healthy children

Left ventricular stroke work is an important prognostic marker to analyze cardiac function. Standard values for children are, however, missing. For clinicians, standards can help to improve the treatment decision of heart failures. For engineers, they can help to optimize medical devices. In this study, we estimated the left ventricular stroke work for children based on modeled pressure-volume loops. A lumped parameter model was fitted to clinical data of 340 healthy children. Reference curves for standard values were created over age, weight, and height. Left ventricular volume was measured with 3D echocardiography, while maximal ventricular pressure was approximated with a regression model from the literature. For validation of this method, we used 18 measurements acquired by a conductance catheter in 11 patients. The method demonstrated a low absolute mean difference of 0.033 J (SD: 0.031 J) for stroke work between measurement and estimation, while the percentage error was 21.66 %. According to the resulting reference curves, left ventricular stroke work of newborns has a median of 0.06 J and increases to 1.15 J at the age of 18 years. Stroke work increases over weight and height in a similar trend. The percentile curves depict the distribution. We demonstrate how reference curves can be used for quantification of differences and comparison in patients.

A new integrated approach to cardiac mechanics: reference values for normal left ventricle

The association between left ventricular (LV) myocardial deformation and hemodynamic forces is still mostly unexplored. The normative values and the effects of demographic and technical factors on hemodynamic forces are not known. The authors studied the association between LV myocardial deformation and hemodynamic forces in a large cohort of healthy volunteers. One-hundred seventy-six consecutive subjects (age range, 16-82; 51% women), with no cardiovascular risk factors or any relevant diseases, were enrolled. All subjects underwent an echo-Doppler examination. Both 2D global myocardial and endocardial longitudinal strain (GLS), circumferential strain (GCS), and the hemodynamic forces were measured with new software that enabled to calculate all these values and parameters from the three apical views. Higher LV mass index and larger LV volumes were found in males compared to females (85 ± 17 vs 74 ± 15 g/m² and 127 ± 28 vs 85 ± 18 ml, p < 0.0001 respectively) while no differences of the mean values of endocardial and myocardial GLS and of myocardial GCS were found (p = ns) and higher endocardial GCS in women (- 30.6 ± 4.2 vs - 31.8 ± 3.7; p = 0.05). LV longitudinal force, LV systolic longitudinal force and LV impulse were higher in men (16.2 ± 5.3 vs 13.2 ± 3.6; 25.1 ± 7.9 vs 19.4 ± 5.6 and 20.4 ± 7 vs 16.6 ± 5.2, p < 0.0001, respectively). A weak but statistically significant decline with age (p < 0.0001) was also found for these force parameters. This new integrated approach could differentiate normality from pathology by providing average deformation values and hemodynamic forces parameters, differentiated by age and gender.

The impact of wall thickness and curvature on wall stress in patient-specific electromechanical models of the left atrium

The left atrium (LA) has a complex anatomy with heterogeneous wall thickness and curvature. The anatomy plays an important role in determining local wall stress; however, the relative contribution of wall thickness and curvature in determining wall stress in the LA is unknown. We have developed electromechanical finite element (FE) models of the LA using patient-specific anatomical FE meshes with rule-based myofiber directions. The models of the LA were passively inflated to 10mmHg followed by simulation of the contraction phase of the atrial cardiac cycle. The FE models predicted maximum LA volumes of 156.5 mL, 99.3 mL and 83.4 mL and ejection fractions of 36.9%, 32.0% and 25.2%. The median wall thickness in the 3 cases was calculated as [Formula: see text] mm, [Formula: see text] mm, and [Formula: see text] mm. The median curvature was determined as [Formula: see text] [Formula: see text], [Formula: see text], and [Formula: see text]. Following passive inflation, the correlation of wall stress with the inverse of wall thickness and curvature was 0.55-0.62 and 0.20-0.25, respectively. At peak contraction, the correlation of wall stress with the inverse of wall thickness and curvature was 0.38-0.44 and 0.16-0.34, respectively. In the LA, the 1st principal Cauchy stress is more dependent on wall thickness than curvature during passive inflation and both correlations decrease during active contraction. This emphasizes the importance of including the heterogeneous wall thickness in electromechanical FE simulations of the LA. Overall, simulation results and sensitivity analyses show that in complex atrial anatomy it is unlikely that a simple anatomical-based law can be used to estimate local wall stress, demonstrating the importance of FE analyses.

MitraClip and left ventricular reverse remodelling: a strain imaging study

AIMS

The purpose of this study is to identify echocardiography predictors of clinical response and reverse left ventricular (LV) remodelling in patients with functional mitral regurgitation (FMR) treated with MitraClip.

METHOD AND RESULTS

We retrospectively analysed 86 high surgical risk patients with severe FMR; of those, 58 were implanted a MitraClip, and 28 received medical treatment and served as controls. At baseline and at 1-year follow-up, we performed clinical and echocardiography evaluation to assess global longitudinal strain (GLS) and myocardial work [global work index (GWI), global constructive work (GCW), global wasted work (GWW), global work efficiency (GWE)]. Mitral regurgitation was significantly reduced after MitraClip implantation (3.7 ± 0.4 vs. 1.7 ± 0.8, P < 0.001), and the procedure was associated with improvement in brain natriuretic peptide levels (980 ± 1027 vs. 420 ± 338 pg/mL, P < 0.001), New York Heart Association class status (3.2 ± 0.55 vs. 2.0 ± 0.6, P < 0.001), 6-min walking test (233 ± 154 vs. 286 ± 114 m, P = 0.01) at follow-up and reduction of left ventricle end-systolic (LVESV) and left ventricle end-diastolic volumes (LVEDV) (152 ± 68 vs. 136 ± 43 mL, P = 0.004 & 219 ± 74 vs. 193 ± 66 mL, P = 0.001, respectively). MitraClip procedure was associated with improvement of LV performance and significant increase of GWI (607 ± 282 vs. 650 ± 260 mmHg%, P = 0.045) and GCW (854 ± 288 vs. 949 ± 325 mmHg%, P < 0.001). Baseline ejection fraction (EF), GLS, GWI, GCW, and effective regurgitant orifice area were the variables that were associated with reduction of LVEDV 1 year after intervention (P < 0.05 for all) and baseline GCW of the LV was the only variable associated with reduction of LVESV (P = 0.002). Receiver operating characteristic curve analysis identified that a GLS cut-off value of -8.65% (AUC 0.815, P = 0.007) was associated with a 20% reduction of the LVEDV with a sensitivity and specificity of 72% and 70%, respectively, and that a GCW cut-off value of 846 mmHg% (AUC 0.759, P = 0.007) was associated with a 10% reduction of LVESV with sensitivity and specificity 79% and 74%, respectively.

CONCLUSIONS

Mitral valve repair with MitraClip has positive clinical and echocardiographic impact in patients with FMR 1 year after implantation. Preserved GLS and GCW values appear to be associated with LV reverse remodelling post intervention.

Intact myocardial preparations reveal intrinsic transmural heterogeneity in cardiac mechanics

Determining transmural mechanical properties in the heart provides a foundation to understand physiological and pathophysiological cardiac mechanics. Although work on mechanical characterisation has begun in isolated cells and permeabilised samples, the mechanical profile of living individual cardiac layers has not been examined. Myocardial slices are 300 μm-thin sections of heart tissue with preserved cellular stoichiometry, extracellular matrix, and structural architecture. This allows for cardiac mechanics assays in the context of an intact in vitro organotypic preparation. In slices obtained from the subendocardium, midmyocardium and subepicardium of rats, a distinct pattern in transmural contractility is found that is different from that observed in other models. Slices from the epicardium and midmyocardium had a higher active tension and passive tension than the endocardium upon stretch. Differences in total myocyte area coverage, and aspect ratio between layers underlined the functional readouts, while no differences were found in total sarcomeric protein and phosphoprotein between layers. Such intrinsic heterogeneity may orchestrate the normal pumping of the heart in the presence of transmural strain and sarcomere length gradients in the in vivo heart.

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The myocardial slice preparation is an intact cardiac model allowing the study of transmural properties.

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Mechanical behaviour is cardiac layer dependent.

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Structural differences in cardiomyocyte density, orientation, and aspect ratio may contribute to these findings.

Sensitivity Analysis of a Left Ventricle Model in the Context of Intraventricular Dyssynchrony

The objective of the current study was to propose a sensitivity analysis of a 3D left ventricle model in order to assess the influence of parameters on myocardial mechanical dispersion. A finite element model of LV electro-mechanical activity was proposed and a screening method was used to evaluate the sensitivity of model parameters on the standard deviation of time to peak strain. Results highlight the importance of propagation parameters associated with septal and lateral segments activation. Simulated curves were compared to myocardial strains, obtained from echocardiography of one healthy subject and one patient diagnosed with intraventricular dyssynchrony and coronary artery disease. Results show a close match between simulation and clinical strains and illustrate the model ability to reproduce myocardial strains in the context of intraventricular dyssynchrony.

20th Annual Feigenbaum Lecture: Echocardiography for Precision Medicine-Digital Biopsy to Deconstruct Biology

Heart failure with preserved ejection fraction (HFpEF) is a complex, heterogeneous syndrome in need of improved classification given its high morbidity and mortality and few effective treatment options. HFpEF represents an ideal setting to examine the utility and feasibility of a precision medicine approach. This article (based on the 20th annual Feigenbaum Lecture, presented at the 2019 American Society of Echocardiography Scientific Sessions) describes the utility of echocardiography as a "digital biopsy" and how deep quantitative echocardiographic phenotyping, coupled with machine learning, can be used to identify novel HFpEF phenotypes. The cellular and ultrastructural basis of abnormal speckle-tracking echocardiography- (STE-) based measurements of cardiac mechanics can provide a window into cardiomyocyte calcium homeostasis. STE-based measurements of longitudinal strain can thus inform the extent of myocardial involvement in patients with HFpEF, which may help to determine responsiveness to cardiac-specific HF medications. However, classifying the complex, systemic, multiorgan nature of HFpEF appropriately likely requires more advanced methods. Using unsupervised machine learning, HFpEF can be classified into three distinct phenogroups with differing clinical and echocardiographic characteristics and outcomes: (1) natriuretic peptide deficiency syndrome; (2) extreme cardiometabolic syndrome; and (3) right ventricle-cardio-abdomino-renal syndrome. Each can be probed to determine their biological basis. The goal of improved classification of HFpEF is to match the right patient with the right treatment, with the hope of improving the track record of HFpEF clinical trials. This article emphasizes the central role of echocardiography in advancing precision medicine and illustrates the integration of basic, translational, clinical, and population research in echocardiography with the goal of better understanding the pathobiology of a complex cardiovascular syndrome.

In-situ optical assessment of rat epicardial kinematic parameters reveals frequency-dependent mechanic heterogeneity related to gender

BACKGROUND

Gender-related cardiac mechanics following the electrical activity has been investigated from basic to clinical research, but results are still controversial. The aim of this work is to study the gender related cardiac mechanics and to focus on its heart rate dependency.

METHODS

We employed 12 Sprague Dawley rats (5 males and 7 females) of the same age and, through a novel high resolution artificial vision contactless approach, we evaluated in-situ cardiac kinematic. The hearts were paced on the right atria appendage via cathodal stimuli at rising frequency.

RESULTS

Kinematic data obtained at rising pacing rates are different between male and female rat hearts: male tended to maintain the same level of cardiac force, energy and contractility, while female responded with an increment of such parameters at increasing heart rate. Female hearts preserved their pattern of contraction and epicardial torsion (vorticity) at rising pacing rates compared to male. Furthermore, we observed a difference in the mechanical restitution: systolic time vs. diastolic time, as an index of cardiac performance, reached higher value in male compared to female hearts.

CONCLUSION

Our innovative technology was capable to evaluate in-situ rat epicardial kinematic at high stimulation frequency, revealing that male preserved kinematic parameters but varying the pattern of contraction/relaxation. On the contrary, female preserved the pattern of contraction/relaxation increasing kinematic parameters.

Modeling left ventricular dynamics with characteristic deformation modes

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

Microstructure-based finite element model of left ventricle passive inflation

Isolating the role(s) of microstructural pathological features in affecting diastolic filling is important in developing targeted treatments for heart diseases. We developed a microstructure-based constitutive model of the myocardium and implemented it in an efficient open-source finite element modeling framework to simulate passive inflation of the left ventricle (LV) in a representative 3D geometry based on experimentally measured muscle fiber architecture. The constitutive model was calibrated using previous tissue-level biaxial mechanical test data derived from the canine heart and validated with independent sets of measurements made at both the isolated constituent and organ level. Using the validated model, we investigated the load taken up by each tissue constituent and their effects on LV passive inflation. The model predicts that the LV compliance is sensitive to the collagen ultrastructure, specifically, the collagen fiber azimuthal angle with respect to the local muscle fiber direction and its waviness. The model also predicts that most of the load in the sub-epicardial and sub-endocardial regions is taken up, respectively, by the muscle fibers and collagen fiber network. This result suggests that normalizing LV passive stiffness by altering the collagen fiber network and myocyte stiffness is most effective when applied to the sub-endocardial and sub-epicardial regions, respectively. This finding may have implication for the development of new pharmaceutical treatments targeting individual cardiac tissue constituents to normalize LV filling function in heart diseases. STATEMENT OF SIGNIFICANCE: Current constitutive models describing the tissue mechanical behavior of the myocardium are largely phenomenological. While able to represent the bulk tissue mechanical behavior, these models cannot distinguish the contribution of the tissue constituents and their ultrastructure to heart function. Although microstructure-based constitutive models can be used to isolate the role of tissue ultrastructure, they have not been implemented in a computational framework that can accommodate realistic 3D organ geometry. The present study addresses these issues by developing and validating a microstructure-based computational modeling framework, which is used to investigate the role of tissue constituents and their ultrastructure in affecting heart function.

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.

In-silico assessment of the effects of right ventricular assist device on pulmonary arterial hypertension using an image based biventricular modeling framework

Pulmonary arterial hypertension (PAH) is a heart disease that is characterized by an abnormally high pressure in the pulmonary artery (PA). While right ventricular assist device (RVAD) has been considered recently as a treatment option for the end-stage PAH patients, its effects on biventricular mechanics are, however, largely unknown. To address this issue, we developed an image-based modeling framework consisting of a biventricular finite element (FE) model that is coupled to a lumped model describing the pulmonary and systemic circulations in a closed-loop system. The biventricular geometry was reconstructed from the magnetic resonance images of two PAH patients showing different degree of RV remodeling and a normal subject. The framework was calibrated to match patient-specific measurements of the left ventricular (LV) and RV volume and pressure waveforms. An RVAD model was incorporated into the calibrated framework and simulations were performed with different pump speeds. Results showed that RVAD unloads the RV, improves cardiac output and increases septum curvature, which are more pronounced in the PAH patient with severe RV remodeling. These improvements, however, are also accompanied by an adverse increase in the PA pressure. These results suggest that the RVAD implantation may need to be optimized depending on disease progression.

Clinical correlates and heritability of cardiac mechanics: The HyperGEN study

BACKGROUND

Indices of cardiac mechanics are sensitive markers of subclinical myocardial dysfunction. Improved understanding of the clinical correlates and heritability of cardiac mechanics could result in novel insight into the acquired and genetic risk factors for myocardial dysfunction. Therefore, we sought to determine the clinical correlates and heritability of indices of cardiac mechanics in whites and African Americans (AAs).

METHODS

We examined 2058 participants stratified by race (1104 whites, 954 AA) in the Hypertension Genetic Epidemiology Network (HyperGEN), a population- and family-based study, and performed digitization of analog echocardiograms with subsequent speckle-tracking analysis. We used linear mixed effects models to determine the clinical correlates of indices of cardiac mechanics (longitudinal, circumferential, radial strain; early diastolic strain rate; and early diastolic tissue velocities). Heritability estimates for cardiac mechanics were calculated using maximum-likelihood variance component analyses in Sequential Oligogenic Linkage Analysis Routine (SOLAR), with adjustment for clinical and echocardiographic covariates.

RESULTS

Several clinical characteristics and conventional echocardiographic parameters were found to be associated with speckle-tracking traits of cardiac mechanics. Male sex, blood pressure, and fasting glucose were associated with worse longitudinal strain (LS) (P < 0.05 for all) after multivariable adjustment. After adjustment for covariates, LS, e' velocity, and early diastolic strain rate were found to be heritable; LS and e' velocity had higher heritability estimates in AAs compared to whites.

CONCLUSIONS

Indices of cardiac mechanics are heritable traits even after adjustment for clinical and conventional echocardiographic correlates. These findings provide the basis for future studies of genetic determinants of these traits that may elucidate race-based differences in heart failure development.

Biomechanical properties and microstructure of neonatal porcine ventricles

Neonatal heart disorders represent a major clinical challenge, with congenital heart disease alone affecting 36,000 new-borns annually within the European Union. Surgical intervention to restore normal function includes the implantation of synthetic and biological materials; however, a lack of experimental data describing the mechanical behaviour of neonatal cardiac tissue is likely to contribute to the relatively poor short- and long-term outcome of these implants. This study focused on characterising the mechanical behaviour of neonatal cardiac tissue using a porcine model, to enhance the understanding of how this differs to the equivalent mature tissue. The biomechanical properties of neonatal porcine cardiac tissue were characterised by uniaxial tensile, biaxial tensile, and simple shear loading modes, using samples collected from the anterior and posterior walls of the right and left ventricles. Histological images were prepared using Masson's trichrome staining, to enable assessment of the microstructure and correlation with tissue behaviour. The mechanical tests demonstrated that the neonatal cardiac tissue is non-linear, anisotropic, viscoelastic and heterogeneous. Our data provide a baseline describing the biomechanical behaviour of immature porcine cardiac tissue. Comparison with published data also indicated that the neonatal porcine cardiac tissue exhibits one-half the stiffness of mature porcine tissue in uniaxial extension testing, one-third in biaxial extension testing, and one-fourth stiffness in simple shear testing; hence, it provides an indication as to the relative change in characteristics associated with tissue maturation. These data may prove valuable to researchers investigating neonatal cardiac mechanics.

In vivo estimation of elastic heterogeneity in an infarcted human heart

In myocardial infarction, muscle tissue of the heart is damaged as a result of ceased or severely impaired blood flow. Survivors have an increased risk of further complications, possibly leading to heart failure. Material properties play an important role in determining post-infarction outcome. Due to spatial variation in scarring, material properties can be expected to vary throughout the tissue of a heart after an infarction. In this study we propose a data assimilation technique that can efficiently estimate heterogeneous elastic material properties in a personalized model of cardiac mechanics. The proposed data assimilation is tested on a clinical dataset consisting of regional left ventricular strains and in vivo pressures during atrial systole from a human with a myocardial infarction. Good matches to regional strains are obtained, and simulated equi-biaxial tests are carried out to demonstrate regional heterogeneities in stress–strain relationships. A synthetic data test shows a good match of estimated versus ground truth material parameter fields in the presence of no to low levels of noise. This study is the first to apply adjoint-based data assimilation to the important problem of estimating cardiac elastic heterogeneities in 3-D from medical images.

Clinical Applications of Patient-Specific Models: The Case for a Simple Approach

Over the past several decades, increasingly sophisticated models of the heart have provided important insights into cardiac physiology and are increasingly used to predict the impact of diseases and therapies on the heart. In an era of personalized medicine, many envision patient-specific computational models as a powerful tool for personalizing therapy. Yet the complexity of current models poses important challenges, including identifying model parameters and completing calculations quickly enough for routine clinical use. We propose that early clinical successes are likely to arise from an alternative approach: relatively simple, fast, phenomenologic models with a small number of parameters that can be easily (and automatically) customized. We discuss examples of simple yet foundational models that have already made a tremendous impact on clinical education and practice, and make the case that reducing rather than increasing model complexity may be the key to realizing the promise of patient-specific modeling for clinical applications.

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.

Simulation of Left Ventricular Dynamics Using a Low-Order Mathematical Model

The eventual goal of this study is to develop methods for estimating dynamic stresses in the left ventricle (LV) that could be used on-line in clinical settings, based on routinely available measurements. Toward this goal, a low-order theoretical model is presented, in which LV shape is represented using a small number of parameters, allowing rapid computational simulations of LV dynamics. The LV is represented as a thick-walled prolate spheroid containing helical muscle fibers with nonlinear passive and time-dependent active contractile properties. The displacement field during the cardiac cycle is described by three time-dependent parameters, using a family of volume-preserving mappings based on prolate spheroidal coordinates. Stress equilibrium is imposed in weak form and the resulting force balance equations are coupled to a lumped-parameter model of the circulation, leading to a system of differential-algebraic equations, whose numerical solution yields predictions of LV pressure and volume, together with spatial distributions of stresses and strains throughout the cardiac cycle. When static loading of the passive LV is assumed, this approach yields displacement and stress fields that closely match results from a standard finite-element approach. When dynamic motion with active contraction is simulated, substantial variations of fiber stress and strain through the myocardium are predicted. This approach allows simulations of LV dynamics that run faster than real time, and could be used to determine patient-specific parameters of LV performance on-line from clinically available measurements, with the eventual goal of real-time, patient-specific analysis of cardiac parameters.

Comparison of Echocardiography, Cardiac Magnetic Resonance, and Computed Tomographic Imaging for the Evaluation of Left Ventricular Myocardial Function: Part 2 (Diastolic and Regional Assessment)

Assessing left ventricular diastolic and regional function is a crucial part of the cardiovascular evaluation. Diastolic function is as important as systolic function for left ventricular performance because it is the determinant of the ability of the left atrium and ventricle to fill at relatively low pressures. Additionally, diastolic function plays an important role in the management and prognosis of patients with symptoms and signs of heart failure. Technical advances in the imaging modalities have allowed a comprehensive noninvasive assessment of global and regional cardiac mechanics and precise estimation of cardiovascular hemodynamics. In this review, we will discuss and compare clinically available techniques and novel approaches using echocardiography, cardiac magnetic resonance, and computed tomography for the assessment of diastolic and regional left ventricular function.

Longitudinal strain assessed by cardiac magnetic resonance correlates to hemodynamic findings in patients with severe aortic stenosis and predicts positive remodeling after transcatheter aortic valve replacement

AIMS

To assess left-ventricular strain parameters before and after transcatheter aortic valve replacement (TAVR) by feature tracking cardiac magnetic resonance imaging (FT CMR) and to correlate the findings to hemodynamic state and left-ventricular remodeling.

METHODS AND RESULTS

Patients with symptomatic AS underwent FT CMR before and after TAVR. Patients were carefully evaluated by a comprehensive work-up including CMR, echocardiography and left and right heart catheterization. Thirty patients formed the study population. High-flow/high-gradient (HF/HG) aortic stenosis was diagnosed in 11 patients (36.7%), 6 patients (20.0%) exhibited low-flow/low-gradient AS (LF/LG) and 13 patients (43.3%) were classified to have so-called paradoxical low-flow/low-gradient (PLF/LG) AS. The HF/HG patients had a significantly reduced longitudinal strain which recovered after TAVR (-12.67 ± 4.60 to -15.46 ± 5.61%, p = 0.048). In the LF/LG group, an even more pronounced reduction of longitudinal strain and also an impairment of longitudinal velocity could be observed. Both parameters improved after therapy (strain: -5.06 ± 4.25 to -8.02 ± 3.28%, p = 0.045; velocity: 25.33 ± 9.63 to 37.13 ± 11.64 mm/s, p = 0.042). Patients with PLF/LG showed preserved longitudinal strain but a reduction of longitudinal velocity similar to the LF/LG group. These patients did not show a significant improvement of strain parameters after TAVR. Longitudinal velocity exhibited the highest predictive power for the identification of a low-flow state (sensitivity 75%, specificity 80%).

CONCLUSION

Improvement of longitudinal strain parameters after TAVR is dependent on the initial hemodynamically defined AS subgroup.

Effects of Cinching Force on the Tricuspid Annulus: A Species Comparison

PURPOSE

Tricuspid annuloplasty rings are commonly used to cinch an enlarged tricuspid annulus back to its original shape and size in patients with severe functional tricuspid regurgitation. However, the invasive operation is contraindicated for patients at risk for reoperation. Fortunately, transcatheter repair procedures, currently in the development process, are minimally invasive alternatives to current repair techniques. This study aims to determine the species-dependence of cinching force with the potential of informing transcatheter repair design by quantifying the minimum required cinching force necessary to reduce tricuspid regurgitation.

METHODS

The cinching force necessary to reduce the septal-lateral diameter of a dilated annuls was quantified and compared in ten ovine hearts and nine porcine hearts. Additionally, a deparaffinization protocol and Verhoeff-Van Gieson stain were used to compare the microscopic structure of tissue samples at different stages of the experimental procedure in the two species.

RESULTS

The maximum annulus dilation observed for the porcine was 11.2%, and the maximum cinching force was 0.40 ± 0.12 N. As previously demonstrated, ovine hearts yielded a maximum annulus dilation and cinching force of 8.82% and 0.38 ± 0.09 N respectively. Histological stains revealed no gross tissue differences between ovine and porcine septal or free wall tissues.

CONCLUSION

The cinching force was not species dependent between ovine and porcine models. This study is an essential first step for determining which animal model should be utilized for the development of transcatheter devices.

The importance of mechano-electrical feedback and inertia in cardiac electromechanics

In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.

Effects of cellular electromechanical coupling on functional heterogeneity in a one-dimensional tissue model of the myocardium

Based on the experimental evidence, we developed a one-dimensional (1D) model of heterogeneous myocardial tissue consisting of in-series connected cardiomyocytes from distant transmural regions using mathematical models of subendocardial and subepicardial cells. The regional deformation patterns produced by our 1D model are consistent with the transmural regional strain patterns obtained experimentally in the normal heart in vivo. The modelling results suggest that the mechanical load may essentially affect the transmural gradients in the electrical and mechanical properties of interacting myocytes within a tissue, thereby regulating global myocardial output.

Phenomapping for the Identification of Hypertensive Patients with the Myocardial Substrate for Heart Failure with Preserved Ejection Fraction

We sought to evaluate whether unbiased machine learning of dense phenotypic data ("phenomapping") could identify distinct hypertension subgroups that are associated with the myocardial substrate (i.e., abnormal cardiac mechanics) for heart failure with preserved ejection fraction (HFpEF). In the HyperGEN study, a population- and family-based study of hypertension, we studied 1273 hypertensive patients utilizing clinical, laboratory, and conventional echocardiographic phenotyping of the study participants. We used machine learning analysis of 47 continuous phenotypic variables to identify mutually exclusive groups constituting a novel classification of hypertension. The phenomapping analysis classified study participants into 2 distinct groups that differed markedly in clinical characteristics, cardiac structure/function, and indices of cardiac mechanics (e.g., phenogroup #2 had a decreased absolute longitudinal strain [12.8 ± 4.1 vs. 14.6 ± 3.5%] even after adjustment for traditional comorbidities [p < 0.001]). The 2 hypertension phenogroups may represent distinct subtypes that may benefit from targeted therapies for the prevention of HFpEF.

Transmural gradients of myocardial structure and mechanics: Implications for fiber stress and strain in pressure overload

Although a truly complete understanding of whole heart activation, contraction, and deformation is well beyond our current reach, a significant amount of effort has been devoted to discovering and understanding the mechanisms by which myocardial structure determines cardiac function to better treat patients with cardiac disease. Several experimental studies have shown that transmural fiber strain is relatively uniform in both diastole and systole, in contrast to predictions from traditional mechanical theory. Similarly, mathematical models have largely predicted uniform fiber stress across the wall. The development of this uniform pattern of fiber stress and strain during filling and ejection is due to heterogeneous transmural distributions of several myocardial structures. This review summarizes these transmural gradients, their contributions to fiber mechanics, and the potential functional effects of their remodeling during pressure overload hypertrophy.

Estimation of passive and active properties in the human heart using 3D tagged MRI

Advances in medical imaging and image processing are paving the way for personalised cardiac biomechanical modelling. Models provide the capacity to relate kinematics to dynamics and-through patient-specific modelling-derived material parameters to underlying cardiac muscle pathologies. However, for clinical utility to be achieved, model-based analyses mandate robust model selection and parameterisation. In this paper, we introduce a patient-specific biomechanical model for the left ventricle aiming to balance model fidelity with parameter identifiability. Using non-invasive data and common clinical surrogates, we illustrate unique identifiability of passive and active parameters over the full cardiac cycle. Identifiability and accuracy of the estimates in the presence of controlled noise are verified with a number of in silico datasets. Unique parametrisation is then obtained for three datasets acquired in vivo. The model predictions show good agreement with the data extracted from the images providing a pipeline for personalised biomechanical analysis.

Acute Haemodynamic and Echocardiographic Effects of Multiple Configurations of Left Ventricular Pacing Sites in Acute Myocardial Infarction: Experimental Study

BACKGROUND

Left ventricular (LV) pacing is unsuccessful in a significant number of patients, mainly due to sub-optimal LV pacing location. Nevertheless, data about the impact of different pacing sites on LV function in ischaemic myocardium are scarce. The purpose of this study was to investigate the effect of combinations of alternative LV pacing sites on LV mechanics after experimental acute anterior myocardial infarction (AMI), in order to define the optimal configuration.

METHODS

Atrioventricular epicardial pacing at alternative pacing sites was performed in 16 healthy pigs simultaneously, after experimental AMI. Standard right ventricular (RV) apical pacing was combined with: i) LV apex lateral wall; ii) LV basal posterior wall; iii) LV basal anterior wall, and; iv) LV basal anterior wall + LV basal posterior wall. Moreover the pacing configurations of, v) LV basal posterior wall + LV apex lateral wall; vi) LV basal posterior wall + LV basal anterior wall, and; vii) LV basal anterior wall + LV apex lateral wall were also investigated. Haemodynamic parameters, together with classic and novel echocardiographic indices were used, to evaluate the effect of each pacing combination. A speckle tracking technique using EchoPAC software was used.

RESULTS

After AMI, the pacing combination of LV apex lateral wall and LV basal posterior wall had the most favourable effect on LV function, leading to similar haemodynamic and torsional effects with sinus rhythm (all variables p>0.05).

CONCLUSIONS

In pig hearts after AMI, the combination of pacing LV apex lateral wall and LV basal posterior wall managed to maintain the LV function at a level comparable to the sinus rhythm.

Principles of cardiovascular magnetic resonance feature tracking and echocardiographic speckle tracking for informed clinical use

Tissue tracking technology of routinely acquired cardiovascular magnetic resonance (CMR) cine acquisitions has increased the apparent ease and availability of non-invasive assessments of myocardial deformation in clinical research and practice. Its widespread availability thanks to the fact that this technology can in principle be applied on images that are part of every CMR or echocardiographic protocol. However, the two modalities are based on very different methods of image acquisition and reconstruction, each with their respective strengths and limitations. The image tracking methods applied are not necessarily directly comparable between the modalities, or with those based on dedicated CMR acquisitions for strain measurement such as tagging or displacement encoding. Here we describe the principles underlying the image tracking methods for CMR and echocardiography, and the translation of the resulting tracking estimates into parameters suited to describe myocardial mechanics. Technical limitations are presented with the objective of suggesting potential solutions that may allow informed and appropriate use in clinical applications.

Neochord placement versus triangular resection in mitral valve repair: A finite element model

BACKGROUND

Recurrent mitral regurgitation after mitral valve repair is common, occurring in nearly 50% of patients within 10 years of surgery. Durability of repair is partly related to stress distribution over the mitral leaflets. We hypothesized that repair with neochords (NCs) results in lower stress than leaflet resection (LR).

MATERIALS AND METHODS

Magnetic resonance imaging and 3D echocardiography were performed before surgical repair of P2 prolapse in a single patient. A finite element model of the left ventricle and mitral valve was created previously, and the modeling program LS-DYNA was used to calculate leaflet stress for the following repairs: Triangular LR; LR with ring annuloplasty (LR + RA); One NC; Two NCs; and 2NC + RA.

RESULTS

(1) NC placement resulted in stable posterior leaflet stress: Baseline versus 2 NC at end diastole (ED), 12.1 versus 12.0 kPa, at end systole (ES) 20.3 versus 21.7 kPa. (2) In contrast, LR increased posterior leaflet stress: Baseline versus LR at ED 12.1 versus 40.8 kPa, at ES 20.3 versus 46.1 kPa. (3) All repair types reduced anterior leaflet stress: Baseline versus 2 NC versus LR 34.2 versus 25.8 versus 20.6 kPa at ED and 80.8 versus 76.8 versus 67.8 kPa at ES. (4) The addition of RA reduced leaflet stress relative to repair without RA.

CONCLUSIONS

Neochord repair restored normal leaflet coaptation without creating excessive leaflet stress, whereas leaflet resection more than doubled stress across the posterior leaflet. The excess stress created by leaflet resection was partially, but not completely, mitigated by ring annuloplasty.

Comprehensive left ventricular mechanics analysis by speckle tracking echocardiography in Chagas disease

Background

Chagas disease (CD) is a frequent cause of dilated cardiomyopathy (CMP) in developing countries, leading to clinical heart failure and worse prognosis. Therefore, the development and evolution of this CMP has always been a major topic in numbers of previous studies. A comprehensive echocardiographic study of left ventricular (LV) mechanics, fully assessing myocardial contraction, has never been done before. This could help characterize and improve the understanding of the evolution of this prevalent CMP.

Methods

A total of 47 chagasic and 84 control patients were included in this study and allocated in groups according to LV ejection fraction. 2D-Echocardiogram was acquired for LV mechanics analysis by speckle tracking echocardiography.

Results

Mean age of chagasic individuals was 55y and 16 (34 %) were men. Significant difference was found in global longitudinal velocity analysis, with lower values in indeterminate form. In the group with severe systolic dysfunction, a paradoxical increase in longitudinal and apical radial displacements were demonstrated. In parallel, segmental analyzes highlighted lower values of radial displacement, strain and strain rate into inferior and inferolateral walls, with increase of these values in septal and anterior walls.

Conclusion

Chagasic CMP has a vicarious pattern of contraction in the course of its evolution, defined by reduced displacement and strain into inferior and posterior walls with paradoxical increase in septal and anterior segments. Also, lower longitudinal velocities were demonstrated in CD indeterminate form, which may indicate an incipient myocardial injury.

Cardiac remodeling and dysfunction in childhood obesity: a cardiovascular magnetic resonance study

BACKGROUND

Obesity affects nearly one in five children and is associated with increased risk of premature death. Obesity-related heart disease contributes to premature death. We aimed to use cardiovascular magnetic resonance (CMR) to comprehensively characterize the changes in cardiac geometry and function in obese children.

METHODS AND RESULTS

Forty-one obese/overweight (age 12 ± 3 years, 56 % female) and 29 healthy weight children (age 14 ± 3 years, 41 % female) underwent CMR, including both standard cine imaging and displacement encoded imaging, for a complete assessment of left ventricular (LV) structure and function. After adjusting for age, LV mass index was 23 % greater (27 ± 4 g/m(2.7) vs 22 ± 3 g/m(2.7), p <0.001) and the LV myocardium was 10 % thicker (5.6 ± 0.8 mm vs 5.1 ± 0.8 mm, p <0.001) in the obese/overweight children. This evidence of cardiac remodeling was present in obese children as young as age 8. Twenty four percent of obese/overweight children had concentric hypertrophy, 59 % had normal geometry and 17 % had either eccentric hypertrophy or concentric remodeling. LV mass index, thickness, ejection fraction and peak longitudinal and circumferential strains all correlated with epicardial adipose tissue after adjusting for height and gender (all p <0.05). Peak longitudinal and circumferential strains showed a significant relationship with the type of LV remodeling, and were most impaired in children with concentric hypertrophy (p <0.001 and p = 0.003, respectively).

CONCLUSIONS

Obese children show evidence of significant cardiac remodeling and dysfunction, which begins as young as age 8. Obese children with concentric hypertrophy and impaired strain may represent a particularly high risk subgroup that demands further investigation.

An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment

This study deals with the viscoelastic constitutive modeling and the respective computational analysis of the human passive myocardium. We start by recapitulating the locally orthotropic inner structure of the human myocardial tissue and model the mechanical response through invariants and structure tensors associated with three orthonormal basis vectors. In accordance with recent experimental findings the ventricular myocardial tissue is assumed to be incompressible, thick-walled, orthotropic and viscoelastic. In particular, one spring element coupled with Maxwell elements in parallel endows the model with viscoelastic features such that four dashpots describe the viscous response due to matrix, fiber, sheet and fiber-sheet fragments. In order to alleviate the numerical obstacles, the strictly incompressible model is altered by decomposing the free-energy function into volumetric-isochoric elastic and isochoric-viscoelastic parts along with the multiplicative split of the deformation gradient which enables the three-field mixed finite element method. The crucial aspect of the viscoelastic formulation is linked to the rate equations of the viscous overstresses resulting from a 3-D analogy of a generalized 1-D Maxwell model. We provide algorithmic updates for second Piola-Kirchhoff stress and elasticity tensors. In the sequel, we address some numerical aspects of the constitutive model by applying it to elastic, cyclic and relaxation test data obtained from biaxial extension and triaxial shear tests whereby we assess the fitting capacity of the model. With the tissue parameters identified, we conduct (elastic and viscoelastic) finite element simulations for an ellipsoidal geometry retrieved from a human specimen.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.