Using a micro-device with a deformable ceiling to probe stiffness heterogeneities within 3D cell aggregates.

Recent advances in the field of mechanobiology have led to the development of methods to characterise single-cell or monolayer mechanical properties and link them to their functional behaviour. However, there remains a strong need to establish this link for three-dimensional (3D) multicellular aggregates, which better mimic tissue function. Here we present a platform to actuate and observe many such aggregates within one deformable micro-device. The platform consists of a single polydimethylsiloxane piece cast on a 3D-printed mould and bonded to a glass slide or coverslip. It consists of a chamber containing cell spheroids, which is adjacent to air cavities that are fluidically independent. Controlling the air pressure in these air cavities leads to a vertical displacement of the chamber's ceiling. The device can be used in static or dynamic modes over time scales of seconds to hours, with displacement amplitudes from a fewµm to several tens of microns. Further, we show how the compression protocols can be used to obtain measurements of stiffness heterogeneities within individual co-culture spheroids, by comparing image correlations of spheroids at different levels of compression with finite element simulations. The labelling of the cells and their cytoskeleton is combined with image correlation methods to relate the structure of the co-culture spheroid with its mechanical properties at different locations. The device is compatible with various microscopy techniques, including confocal microscopy, which can be used to observe the displacements and rearrangements of single cells and neighbourhoods within the aggregate. The complete experimental and imaging platform can now be used to provide multi-scale measurements that link single-cell behaviour with the global mechanical response of the aggregates.

Reduced left ventricular dynamics modeling based on a cylindrical assumption.

Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-order finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, for example, for pre-calibration of full-order models, fast predictions, real-time applications, and so forth. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of Guccione, McCulloch, & Waldman (1991); Guccione, Waldman, & McCulloch (1993), albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel aswell, with consistent spatial (finite element) and time discretizations. Finally, we analyze the sensitivity of the model response to various numerical and physical parameters, and study its physiological response.

Comparison of optimization parametrizations for regional lung compliance estimation using personalized pulmonary poromechanical modeling.

Interstitial lung diseases, such as idiopathic pulmonary fibrosis (IPF) or post-COVID-19 pulmonary fibrosis, are progressive and severe diseases characterized by an irreversible scarring of interstitial tissues that affects lung function. Despite many efforts, these diseases remain poorly understood and poorly treated. In this paper, we propose an automated method for the estimation of personalized regional lung compliances based on a poromechanical model of the lung. The model is personalized by integrating routine clinical imaging data - namely computed tomography images taken at two breathing levels in order to reproduce the breathing kinematic-notably through an inverse problem with fully personalized boundary conditions that is solved to estimate patient-specific regional lung compliances. A new parametrization of the inverse problem is introduced in this paper, based on the combined estimation of a personalized breathing pressure in addition to material parameters, improving the robustness and consistency of estimation results. The method is applied to three IPF patients and one post-COVID-19 patient. This personalized model could help better understand the role of mechanics in pulmonary remodeling due to fibrosis; moreover, patient-specific regional lung compliances could be used as an objective and quantitative biomarker for improved diagnosis and treatment follow up for various interstitial lung diseases.

On the structural origin of the anisotropy in the myocardium: Multiscale modeling and analysis.

Due to structural heterogeneities within the tissue, the myocardium displays an orthotropic material behavior. However, the link between the microstructure and the macroscopic mechanical properties is still not fully established. In particular, if it is admitted that the cardiomyocyte organization induces a transversely isotropic symmetry, the relative role in the observed orthotropic symmetry of cardiomyocyte orientation variation and perimysium collagen "sheetlet" structure, two mechanisms occurring at different scales, is still a matter of debate. In order to shed light on this question, we designed a multiscale model of the myocardium, bridging the cell, sheetlet and tissue scales. More precisely, we compared the macroscopic anisotropy obtained by homogenization of different mesostructures consisting in cardiomyocytes and extracellular collageneous layers, also taking into account the variation of cardiomyocyte and sheetlet orientations on the macroscale, to available experimental data. This study confirms the importance of sheetlets layers in assuring the tissue's anisotropic response, as cardiomyocytes-only mesostructures cannot reproduce the observed anisotropy. Moreover, our model shows the existence of a size effect in the myocardial tissue shear properties, which will require further experimental analysis.

Quantification of left ventricular strain and torsion by joint analysis of 3D tagging and cine MR images.

Cardiovascular magnetic resonance (CMR) imaging is the gold standard for the non-invasive assessment of left-ventricular (LV) function. Prognostic value of deformation metrics extracted directly from regular SSFP CMR images has been shown by numerous studies in the clinical setting, but with some limitations to detect torsion of the myocardium. Tagged CMR introduces trackable features in the myocardium that allow for the assessment of local myocardial deformation, including torsion; it is, however, limited in the quantification of radial strain, which is a decisive metric for assessing the contractility of the heart. In order to improve SSFP-only and tagged-only approaches, we propose to combine the advantages of both image types by fusing global shape motion obtained from SSFP images with the local deformation obtained from tagged images. To this end, tracking is first performed on SSFP images, and subsequently, the resulting motion is utilized to mask and track tagged data. Our implementation is based on a recent finite element-based motion tracking tool with mechanical regularization. Joint SSFP and tagged images registration performance is assessed based on deformation metrics including LV strain and twist using human and in-house porcine datasets. Results show that joint analysis of SSFP and 3DTAG images provides better quantification of LV strain and twist as either data source alone.

Estimation of Regional Pulmonary Compliance in Idiopathic Pulmonary Fibrosis Based on Personalized Lung Poromechanical Modeling.

Pulmonary function is tightly linked to the lung mechanical behavior, especially large deformation during breathing. Interstitial lung diseases, such as idiopathic pulmonary fibrosis (IPF), have an impact on the pulmonary mechanics and consequently alter lung function. However, IPF remains poorly understood, poorly diagnosed, and poorly treated. Currently, the mechanical impact of such diseases is assessed by pressure-volume curves, giving only global information. We developed a poromechanical model of the lung that can be personalized to a patient based on routine clinical data. The personalization pipeline uses clinical data, mainly computed tomography (CT) images at two time steps and involves the formulation of an inverse problem to estimate regional compliances. The estimation problem can be formulated both in terms of "effective", i.e., without considering the mixture porosity, or "rescaled," i.e., where the first-order effect of the porosity has been taken into account, compliances. Regional compliances are estimated for one control subject and three IPF patients, allowing to quantify the IPF-induced tissue stiffening. This personalized model could be used in the clinic as an objective and quantitative tool for IPF diagnosis.

A quasi-static poromechanical model of the lungs.

The lung vital function of providing oxygen to the body heavily relies on its mechanical behavior and the interaction with its complex environment. In particular, the large compliance and the porosity of the pulmonary tissue are critical for lung inflation and air inhalation, and the diaphragm, the pleura, the rib cage and intercostal muscles all play a role in delivering and controlling the breathing driving forces. In this paper, we introduce a novel poromechanical model of the lungs. The constitutive law is derived within a general poromechanics theory via the formulation of lung-specific assumptions, leading to a hyperelastic potential reproducing the volume response of the pulmonary mixture to a change of pressure. Moreover, physiological boundary conditions are formulated to account for the interaction of the lungs with their surroundings, including a following pressure and bilateral frictionless contact. A strategy is established to estimate the unloaded configuration from a given loaded state, with a particular focus on ensuring a positive porosity. Finally, we illustrate through several realistic examples the relevance of our model and its potential clinical applications.

In-silico study of accuracy and precision of left-ventricular strain quantification from 3D tagged MRI.

Cardiac Magnetic Resonance Imaging (MRI) allows quantifying myocardial tissue deformation and strain based on the tagging principle. In this work, we investigate accuracy and precision of strain quantification from synthetic 3D tagged MRI using equilibrated warping. To this end, synthetic biomechanical left-ventricular tagged MRI data with varying tag distance, spatial resolution and signal-to-noise ratio (SNR) were generated and processed to quantify errors in radial, circumferential and longitudinal strains relative to ground truth. Results reveal that radial strain is more sensitive to image resolution and noise than the other strain components. The study also shows robustness of quantifying circumferential and longitudinal strain in the presence of geometrical inconsistencies of 3D tagged data. In conclusion, our study points to the need for higher-resolution 3D tagged MRI than currently available in practice in order to achieve sufficient accuracy of radial strain quantification.

Biomechanical Modeling to Inform Pulmonary Valve Replacement in Tetralogy of Fallot Patients After Complete Repair.

BACKGROUND: A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health. METHODS: Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Qeff) was also compared with expected values. RESULTS: RV contractility before PVR (mean 66 ± 16 kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38-48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Qeff-both in line with published data. CONCLUSIONS: This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation.

A 3D personalized cardiac myocyte aggregate orientation model using MRI data-driven low-rank basis functions.

Cardiac myocyte aggregate orientation has a strong impact on cardiac electrophysiology and mechanics. Studying the link between structural characteristics, strain, and stresses over the cardiac cycle and cardiac function requires a full volumetric representation of the microstructure. In this work, we exploit the structural similarity across hearts to extract a low-rank representation of predominant myocyte orientation in the left ventricle from high-resolution magnetic resonance ex-vivo cardiac diffusion tensor imaging (cDTI) in porcine hearts. We compared two reduction methods, Proper Generalized Decomposition combined with Singular Value Decomposition and Proper Orthogonal Decomposition. We demonstrate the existence of a general set of basis functions of aggregated myocyte orientation which defines a data-driven, personalizable, parametric model featuring higher flexibility than existing atlas and rule-based approaches. A more detailed representation of microstructure matching the available patient data can improve the accuracy of personalized computational models. Additionally, we approximate the myocyte orientation of one ex-vivo human heart and demonstrate the feasibility of transferring the basis functions to humans.

Left Ventricular Torsion Obtained Using Equilibrated Warping in Patients with Repaired Tetralogy of Fallot.

Patients after surgical repair of Tetralogy of Fallot (rTOF) may suffer a decrease in left ventricular (LV) function. The aim of our study is to evaluate a novel method of assessing LV torsion in patients with rTOF, as an early indicator of systolic LV dysfunction. Motion tracking based on image registration regularized by the equilibrium gap principle, known as equilibrated warping, was employed to assess LV torsion. Seventy-six cases of rTOF and ten normal controls were included. The group of controls was assessed for reproducibility using both equilibrated warping and standard clinical tissue tracking software (CVI42, version 5.10.1, Calgary, Canada). Patients were dichotomized into two groups: normal vs. loss of torsion. Torsion by equilibrated warping was successfully obtained in 68 of 76 (89%) patients and 9 of 10 (90%) controls. For equilibrated warping, the intra- and interobserver coefficients of variation were 0.095 and 0.117, respectively, compared to 0.260 and 0.831 for tissue tracking by standard clinical software. The intra- and inter-observer intraclass correlation coefficients for equilibrated warping were 0.862 and 0.831, respectively, compared to 0.992 and 0.648 for tissue tracking. Loss of torsion was noted in 32 of the 68 (47%) patients with rTOF. There was no difference in LV or RV volumes or ejection fraction between these groups. The assessment of LV torsion by equilibrated warping is feasible and shows good reliability. Loss of torsion is common in patients with rTOF and its robust assessment might contribute into uncovering heart failure in an earlier stage.

Microstructural deformation observed by Mueller polarimetry during traction assay on myocardium samples.

Despite recent advances, the myocardial microstructure remains imperfectly understood. In particular, bundles of cardiomyocytes have been observed but their three-dimensional organisation remains debated and the associated mechanical consequences unknown. One of the major challenges remains to perform multiscale observations of the mechanical response of the heart wall. For this purpose, in this study, a full-field Mueller polarimetric imager (MPI) was combined, for the first time, with an in-situ traction device. The full-field MPI enables to obtain a macroscopic image of the explored tissue, while providing detailed information about its structure on a microscopic scale. Specifically it exploits the polarization of the light to determine various biophysical quantities related to the tissue scattering or anisotropy properties. Combined with a mechanical traction device, the full-field MPI allows to measure the evolution of such biophysical quantities during tissue stretch. We observe separation lines on the tissue, which are associated with a fast variation of the fiber orientation, and have the size of cardiomyocyte bundles. Thus, we hypothesize that these lines are the perimysium, the collagen layer surrounding these bundles. During the mechanical traction, we observe two mechanisms simultaneously. On one hand, the azimuth shows an affine behavior, meaning the orientation changes according to the tissue deformation, and showing coherence in the tissue. On the other hand, the separation lines appear to be resistant in shear and compression but weak against traction, with a forming of gaps in the tissue.

Three-dimensional biventricular strains in pulmonary arterial hypertension patients using hyperelastic warping.

BACKGROUND AND OBJECTIVE: Evaluation of biventricular function is an essential component of clinical management in pulmonary arterial hypertension (PAH). This study aims to examine the utility of biventricular strains derived from a model-to-image registration technique in PAH patients in comparison to age- and gender-matched normal controls. METHODS: A three-dimensional (3D) model was reconstructed from cine short- and long-axis cardiac magnetic resonance (CMR) images and subsequently partitioned into right ventricle (RV), left ventricle (LV) and septum. The hyperelastic warping method was used to register the meshed biventricular finite element model throughout the cardiac cycle and obtain the corresponding biventricular circumferential, longitudinal and radial strains. RESULTS: Intra- and inter-observer reproducibility of biventricular strains was excellent with all intra-class correlation coefficients > 0.84. 3D biventricular longitudinal, circumferential and radial strains for RV, LV and septum were significantly decreased in PAH patients compared with controls. Receiver operating characteristic (ROC) analysis showed that the 3D biventricular strains were better early markers (Area under the ROC curve = 0.96 for RV longitudinal strain) of ventricular dysfunction than conventional parameters such as two-dimensional strains and ejection fraction. CONCLUSIONS: Our highly reproducible methodology holds potential for extending CMR imaging to characterize 3D biventricular strains, eventually leading to deeper understanding of biventricular mechanics in PAH.

Computational quantification of patient-specific changes in ventricular dynamics associated with pulmonary hypertension.

Pulmonary arterial hypertension (PAH) causes an increase in the mechanical loading imposed on the right ventricle (RV) that results in progressive changes to its mechanics and function. Here, we quantify the mechanical changes associated with PAH by assimilating clinical data consisting of reconstructed three-dimensional geometry, pressure, and volume waveforms, as well as regional strains measured in patients with PAH (n = 12) and controls (n = 6) within a computational modeling framework of the ventricles. Modeling parameters reflecting regional passive stiffness and load-independent contractility as indexed by the tissue active tension were optimized so that simulation results matched the measurements. The optimized parameters were compared with clinical metrics to find usable indicators associated with the underlying mechanical changes. Peak contractility of the RV free wall (RVFW) γRVFW,max was found to be strongly correlated and had an inverse relationship with the RV and left ventricle (LV) end-diastolic volume ratio (i.e., RVEDV/LVEDV) (RVEDV/LVEDV)+ 0.44, R2 = 0.77). Correlation with RV ejection fraction (R2 = 0.50) and end-diastolic volume index (R2 = 0.40) were comparatively weaker. Patients with with RVEDV/LVEDV > 1.5 had 25% lower γRVFW,max (P < 0.05) than that of the control. On average, RVFW passive stiffness progressively increased with the degree of remodeling as indexed by RVEDV/LVEDV. These results suggest a mechanical basis of using RVEDV/LVEDV as a clinical index for delineating disease severity and estimating RVFW contractility in patients with PAH.NEW & NOTEWORTHY This article presents patient-specific data assimilation of a patient cohort and physical description of clinical observations.

Quantification of Biventricular Strains in Heart Failure With Preserved Ejection Fraction Patient Using Hyperelastic Warping Method.

Heart failure (HF) imposes a major global health care burden on society and suffering on the individual. About 50% of HF patients have preserved ejection fraction (HFpEF). More intricate and comprehensive measurement-focused imaging of multiple strain components may aid in the diagnosis and elucidation of this disease. Here, we describe the development of a semi-automated hyperelastic warping method for rapid comprehensive assessment of biventricular circumferential, longitudinal, and radial strains that is physiological meaningful and reproducible. We recruited and performed cardiac magnetic resonance (CMR) imaging on 30 subjects [10 HFpEF, 10 HF with reduced ejection fraction patients (HFrEF) and 10 healthy controls]. In each subject, a three-dimensional heart model including left ventricle (LV), right ventricle (RV), and septum was reconstructed from CMR images. The hyperelastic warping method was used to reference the segmented model with the target images and biventricular circumferential, longitudinal, and radial strain-time curves were obtained. The peak systolic strains are then measured and analyzed in this study. Intra- and inter-observer reproducibility of the biventricular peak systolic strains was excellent with all ICCs > 0.92. LV peak systolic circumferential, longitudinal, and radial strain, respectively, exhibited a progressive decrease in magnitude from healthy control→HFpEF→HFrEF: control (-15.5 ± 1.90, -15.6 ± 2.06, 41.4 ± 12.2%); HFpEF (-9.37 ± 3.23, -11.3 ± 1.76, 22.8 ± 13.1%); HFrEF (-4.75 ± 2.74, -7.55 ± 1.75, 10.8 ± 4.61%). A similar progressive decrease in magnitude was observed for RV peak systolic circumferential, longitudinal and radial strain: control (-9.91 ± 2.25, -14.5 ± 2.63, 26.8 ± 7.16%); HFpEF (-7.38 ± 3.17, -12.0 ± 2.45, 21.5 ± 10.0%); HFrEF (-5.92 ± 3.13, -8.63 ± 2.79, 15.2 ± 6.33%). Furthermore, septum peak systolic circumferential, longitudinal, and radial strain magnitude decreased gradually from healthy control to HFrEF: control (-7.11 ± 1.81, 16.3 ± 3.23, 18.5 ± 8.64%); HFpEF (-6.11 ± 3.98, -13.4 ± 3.02, 12.5 ± 6.38%); HFrEF (-1.42 ± 1.36, -8.99 ± 2.96, 3.35 ± 2.95%). The ROC analysis indicated LV peak systolic circumferential strain to be the most sensitive marker for differentiating HFpEF from healthy controls. Our results suggest that the hyperelastic warping method with the CMR-derived strains may reveal subtle impairment in HF biventricular mechanics, in particular despite a "normal" ventricular ejection fraction in HFpEF.

Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization.

Individually personalized computational models of heart mechanics can be used to estimate important physiological and clinically-relevant quantities that are difficult, if not impossible, to directly measure in the beating heart. Here, we present a novel and efficient framework for creating patient-specific biventricular models using a gradient-based data assimilation method for evaluating regional myocardial contractility and estimating myofiber stress. These simulations can be performed on a regular laptop in less than 2 h and produce excellent fit between measured and simulated volume and strain data through the entire cardiac cycle. By applying the framework using data obtained from 3 healthy human biventricles, we extracted clinically important quantities as well as explored the role of fiber angles on heart function. Our results show that steep fiber angles at the endocardium and epicardium are required to produce simulated motion compatible with measured strain and volume data. We also find that the contraction and subsequent systolic stresses in the right ventricle are significantly lower than that in the left ventricle. Variability of the estimated quantities with respect to both patient data and modeling choices are also found to be low. Because of its high efficiency, this framework may be applicable to modeling of patient specific cardiac mechanics for diagnostic purposes.

An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling.

Continued advances in computational power and methods have enabled image-based biomechanical modeling to become an important tool in basic science, diagnostic and therapeutic medicine, and medical device design. One of the many challenges of this approach, however, is identification of a stress-free reference configuration based on in vivo images of loaded and often prestrained or residually stressed soft tissues and organs. Fortunately, iterative methods have been proposed to solve this inverse problem, among them Sellier's method. This method is particularly appealing because it is easy to implement, convergences reasonably fast, and can be coupled to nearly any finite element package. By means of several practical examples, however, we demonstrate that in its original formulation Sellier's method is not optimally fast and may not converge for problems with large deformations. Fortunately, we can also show that a simple, inexpensive augmentation of Sellier's method based on Aitken's delta-squared process can not only ensure convergence but also significantly accelerate the method.

A virtual sizing tool for mitral valve annuloplasty.

Functional mitral regurgitation, a backward leakage of the mitral valve, is a result of left ventricular growth and mitral annular dilatation. Its gold standard treatment is mitral annuloplasty, the surgical reduction in mitral annular area through the implantation of annuloplasty rings. Recurrent regurgitation rates may, however, be as high as 30% and more. While the degree of annular downsizing has been linked to improved long-term outcomes, too aggressive downsizing increases the risk of ring dehiscences and significantly impairs repair durability. Here, we prototype a virtual sizing tool to quantify changes in annular dimensions, surgically induced tissue strains, mitral annular stretches, and suture forces in response to mitral annuloplasty. We create a computational model of dilated cardiomyopathy onto which we virtually implant annuloplasty rings of different sizes. Our simulations confirm the common intuition that smaller rings are more invasive to the surrounding tissue, induce higher strains, and require larger suture forces than larger rings: The total suture force was 2.2 N for a 24-mm ring, 1.9 N for a 28-mm ring, and 0.8 N for a 32-mm ring. Our model predicts the highest risk of dehiscence in the septal and postero-lateral annulus where suture forces are maximal. These regions co-localize with regional peaks in myocardial strain and annular stretch. Our study illustrates the potential of realistic predictive simulations in cardiac surgery to identify areas at risk for dehiscence, guide the selection of ring size and shape, rationalize the design of smart annuloplasty rings and, ultimately, improve long-term outcomes after surgical mitral annuloplasty. Copyright © 2016 John Wiley & Sons, Ltd.