Quantification of Shear Deformations and Corresponding Stresses in the Biaxially Tested Human Myocardium

Effect of mechanical fatigue on commercial bioprosthetic TAVR valve mechanical and microstructural properties

Valvular structural deterioration is of particular concern for transcatheter aortic valve replacements due to their suspected shorter longevity and increasing use in younger patient populations. In this work we investigated the mechanical and microstructural changes in commercial TAVR valves composed of both glutaraldehyde fixed bovine and porcine pericardium (GLBP and GLPP) following accelerated wear testing (AWT) as outlined in ISO 5840 standards. This provided greater physiological relevance to the loading compared to previous studies and by utilizing digital image correlation we were able to obtain strain contours for each leaflet pre and post fatigue and identify sites of fatigue damage. The areas of greatest change in mechanical strain for each leaflet were then further probed using biaxial tensile testing, confocal microscopy, and electron microscopy. It was observed that overall strain decreased in the GLPP valves following AWT of 200 million cycles while the GLBP valve showed an increase in overall strain. Biaxial tensile testing showed a statistically significant reduction in stress for GLPP while no significant changes were seen for GLBP. Both confocal and electron microscopy showed a disruption to the gross collagen organization and fibrillar structure, including fragmentation, for GLPP but only the former for GLBP. However, further test data is required to confirm these findings and to provide a better understanding of this fatigue pathway is required such that it can be incorporated into both valve design and selection processes to improve overall longevity for both GLPP and GLBP devices.

Multimodal experimental studies of the passive mechanical behavior of human aortas: Current approaches and future directions

Cardiovascular diseases are the leading cause of death worldwide and include, among others, critical conditions of the aortic wall. Importantly, such critical conditions require effective diagnosis and treatment, which are not yet accurate enough. However, they could be significantly strengthened with predictive material models of the aortic wall. In particular, such predictive models could support surgical decisions, preoperative planning, and estimation of postoperative tissue remodeling. However, developing a predictive model requires experimental data showing both structural parameters and mechanical behavior. Such experimental data can be obtained using multimodal experiments. This review therefore discusses the current approaches to multimodal experiments. Importantly, the strength of the aortic wall is determined primarily by its passive components, i.e., mainly collagen, elastin, and proteoglycans. Therefore, this review focuses on multimodal experiments that relate the passive mechanical behavior of the human aortic wall to the structure and organization of its passive components. In particular, the multimodal experiments are classified according to the expected results. Multiple examples are provided for each experimental class and summarized with highlighted advantages and disadvantages of the method. Finally, future directions of multimodal experiments are envisioned and evaluated. STATEMENT OF SIGNIFICANCE: Multimodal experiments are innovative approaches that have gained interest very quickly, but also recently. This review presents therefore a first clear summary of groundbreaking research in the field of multimodal experiments. The benefits and limitations of various types of multimodal experiments are thoroughly discussed, and a comprehensive overview of possible results is provided. Although this review focuses on multimodal experiments performed on human aortic tissues, the methods used and described are not limited to human aortic tissues but can be extended to other soft materials.

Biomechanical characterization of the passive porcine stomach

The complex mechanics of the gastric wall facilitates the main digestive tasks of the stomach. However, the interplay between the mechanical properties of the stomach, its microstructure, and its vital functions is not yet fully understood. Importantly, the pig animal model is widely used in biomedical research for preliminary or ethically prohibited studies of the human digestion system. Therefore, this study aims to thoroughly characterize the mechanical behavior and microstructure of the porcine stomach. For this purpose, multiple quasi-static mechanical tests were carried out with three different loading modes, i.e., planar biaxial extension, radial compression, and simple shear. Stress-relaxation tests complemented the quasi-static experiments to evaluate the deformation and strain-dependent viscoelastic properties. Each experiment was conducted on specimens of the complete stomach wall and two separate layers, mucosa and muscularis, from each of the three gastric regions, i.e., fundus, body, and antrum. The significant preconditioning effects and the considerable regional and layer-specific differences in the tissue response were analyzed. Furthermore, the mechanical experiments were complemented with histology to examine the influence of the microstructural composition on the macrostructural mechanical response and vice versa. Importantly, the shear tests showed lower stresses in the complete wall compared to the single layers which the loose network of submucosal collagen might explain. Also, the stratum arrangement of the muscularis might explain mechanical anisotropy during tensile tests. This study shows that gastric tissue is characterized by a highly heterogeneous microstructure with regional variations in layer composition reflecting not only functional differences but also diverse mechanical behavior. STATEMENT OF SIGNIFICANCE: Unfortunately, only few experimental data on gastric tissue are available for an adequate material parameter and model estimation. The present study therefore combines layer- and region-specific stomach wall mechanics obtained under multiple loading conditions with histological insights into the heterogeneous microstructure. On the one hand, the extensive data sets of this study expand our understanding of the interplay between gastric mechanics, motility and functionality, which could help to identify and treat associated pathologies. On the other hand, such data sets are of high relevance for the constitutive modeling of stomach tissue, and its application in the field of medical engineering, e.g., in the development of surgical staplers and the improvement of bariatric surgical interventions.

Quantifying the microstructural and biomechanical changes in the porcine ventricles during growth and remodelling

Cardiac tissue growth and remodelling (G & R) occur in response to the changing physiological demands of the heart after birth. The early shift to pulmonary circulation produces an immediate increase in ventricular workload, causing microstructural and biomechanical changes that serve to maintain overall physiological homoeostasis. Such cardiac G & R continues throughout life. Quantifying the tissue's mechanical and microstructural changes because of G & R is of increasing interest, dovetailing with the emerging fields of personalised and precision solutions. This study aimed to determine equibiaxial, and non-equibiaxial extension, stress-relaxation, and the underlying microstructure of the passive porcine ventricles tissue at four time points spanning from neonatal to adulthood. The three-dimensional microstructure was investigated via two-photon excited fluorescence and second-harmonic generation microscopy on optically cleared tissues, describing the 3D orientation, rotation and dispersion of the cardiomyocytes and collagen fibrils. The results revealed that during biomechanical testing, myocardial ventricular tissue possessed non-linear, anisotropic, and viscoelastic behaviour. An increase in stiffness and viscoelasticity was noted for the left and right ventricular free walls from neonatal to adulthood. Microstructural analyses revealed concomitant increases in cardiomyocyte rotation and dispersion. This study provides baseline data, describing the biomechanical and microstructural changes in the left and right ventricular myocardial tissue during G & R, which should prove valuable to researchers in developing age-specific, constitutive models for more accurate computational simulations. STATEMENT OF SIGNIFICANCE: There is a dearth of experimental data describing the growth and remodelling of left and right ventricular tissue. The published literature is fragmented, with data reported via different experimental techniques using tissues harvested from a variety of animals, with different gender and ages. This prevents developing a continuum of data spanning birth to death, so limiting the potential that can be leveraged to aid computational modelling and simulations. In this study, equibiaxial, non-equibiaxial, and stress-relaxation data are presented, describing directional-dependent material responses. The biomechanical data is consolidated with equivalent microstructural data, an important element for the development of future material models. Combined, these data describe microstructural and biomechanical changes in the ventricles, spanning G &R from neonatal to adulthood.

Regional biomechanical characterization of human ascending aortic aneurysms: Microstructure and biaxial mechanical response

The ascending thoracic aortic aneurysm (ATAA) is a permanent dilatation of the vessel with a high risk of adverse events, and shows heterogeneous properties. To investigate regional differences in the biomechanical properties of ATAAs, tissue samples were collected from 10 patients with tricuspid aortic valve phenotype and specimens from minor, anterior, major, and posterior regions were subjected to multi-ratio planar biaxial extension tests and second-harmonic generation (SHG) imaging. Using the data, parameters of a microstructure-motivated constitutive model were obtained considering fiber dispersion. SHG imaging showed disruptions in the organization of the layers. Structural and material parameters did not differ significantly between regions. The non-symmetric fiber dispersion model proposed by Holzapfel et al. [25] was used to fit the data. The mean angle of collagen fibers was negatively correlated between minor and anterior regions, and the parameter associated with collagen fiber stiffness was positively correlated between minor and major regions. Furthermore, correlations were found between the stiffness of the ground matrix and the mean fiber angle, and between the parameter associated with the collagen fiber stiffness and the out-of-plane dispersion parameter in the posterior and minor regions, respectively. The experimental data collected in this study contribute to the biomechanical data available in the literature on human ATAAs. Region-specific parameters for the constitutive models are fundamental to improve the current risk stratification strategies, which are mainly based on aortic size. Such investigations can facilitate the development of more advanced finite element models capable of capturing the regional heterogeneity of pathological tissues. STATEMENT OF SIGNIFICANCE: Tissue samples of human ascending thoracic aortic aneurysms (ATAA) were collected. Samples from four regions underwent multi-ratio planar biaxial extension tests and second-harmonic generation imaging. Region-specific parameters of a microstructure-motivated model considering fiber dispersion were obtained. Structural and material parameters did not differ significantly between regions, however, the mean fiber angle was negatively correlated between minor and anterior regions, and the parameter associated with collagen fiber stiffness was positively correlated between minor and major regions. Furthermore, correlations were found between the stiffness of the ground matrix and the mean fiber angle, and between the parameter associated with the collagen fiber stiffness and the out-of-plane dispersion parameter in the posterior and minor regions, respectively. This study provides a unique set of mechanical and structural data, supporting the microstructural influence on the tissue response. It may facilitate the development of better finite element models capable of capturing the regional tissue heterogeneity.

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

OBJECTIVE

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

METHODS

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

DISCUSSION

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

CONCLUSION

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

Changes in the microstructure of the human aortic adventitia under biaxial loading investigated by multi-photon microscopy

Among the three layers of the aortic wall, the media is primarily responsible for its mechanical properties, but the adventitia prevents the aorta from overstretching and rupturing. The role of the adventitia is therefore crucial with regard to aortic wall failure, and understanding the load-induced changes in tissue microstructure is of high importance. Specifically, the focus of this study is on the changes in collagen and elastin microstructure in response to macroscopic equibiaxial loading applied to the aortic adventitia. To observe these changes, multi-photon microscopy imaging and biaxial extension tests were performed simultaneously. In particular, microscopy images were recorded at 0.02 stretch intervals. The microstructural changes of collagen fiber bundles and elastin fibers were quantified with the parameters of orientation, dispersion, diameter, and waviness. The results showed that the adventitial collagen was divided from one into two fiber families under equibiaxial loading conditions. The almost diagonal orientation of the adventitial collagen fiber bundles remained unchanged, but the dispersion was substantially reduced. No clear orientation of the adventitial elastin fibers was observed at any stretch level. The waviness of the adventitial collagen fiber bundles decreased under stretch, but the adventitial elastin fibers showed no change. These original findings highlight differences between the medial and adventitial layers and provide insight into the stretching process of the aortic wall. STATEMENT OF SIGNIFICANCE: To provide accurate and reliable material models, it is essential to understand the mechanical behavior of the material and its microstructure. Such understanding can be enhanced with tracking of the microstructural changes caused by mechanical loading of the tissue. This study provides therefore a unique dataset of structural parameters of the human aortic adventitia obtained under equibiaxial loading. The structural parameters describe orientation, dispersion, diameter, and waviness of collagen fiber bundles and elastin fibers. Eventually, the microstructural changes in the human aortic adventitia are compared with the microstructural changes in the human aortic media from a previous study. This comparison reveals the cutting-edge findings on the differences in the response to the loading between these two human aortic layers.

Global and local stiffening of ex vivo-perfused stented human thoracic aortas: A mock circulation study

The effects of thoracic endovascular repair (TEVAR) on the biomechanical properties of aortic tissue have not been adequately studied. Understanding these features is important for the management of endograft-triggered complications of a biomechanical nature. This study aims to examine how stent-graft implantation affects the elastomechanical behavior of the aorta. Non-pathological human thoracic aortas (n=10) were subjected to long-standing perfusion (8h) within a mock circulation loop under physiological conditions. To quantify compliance and its mismatch in the test periods without and with a stent, the aortic pressure and the proximal cyclic circumferential displacement were measured. After perfusion, biaxial tension tests (stress-stretch) were carried out to examine the stiffness profiles between non-stented and stented tissue, followed by a histological assessment. Experimental evidence shows: (i) a significant reduction in aortic distensibility after TEVAR, indicating aortic stiffening and compliance mismatch, (ii) a stiffer behavior of the stented samples compared to the non-stented samples with an earlier entry into the nonlinear part of the stress-stretch curve and (iii) strut-induced histological remodeling of the aortic wall. The biomechanical and histological comparison of the non-stented and stented aortas provides new insights into the interaction between the stent-graft and the aortic wall. The knowledge gained could refine the stent-graft design to minimize the stent-induced impacts on the aortic wall and the resulting complications. STATEMENT OF SIGNIFICANCE: Stent-related cardiovascular complications occur the moment the stent-graft expands on the human aortic wall. Clinicians base their diagnosis on the anatomical morphology of CT scans while neglecting the endograft-triggered biomechanical events that compromise aortic compliance and wall mechanotransduction. Experimental replication of endovascular repair in cadaver aortas within a mock circulation loop may have a catalytic effect on biomechanical and histological findings without an ethical barrier. Demonstrating interactions between the stent and the wall can help clinicians make a broader diagnosis such as ECG-triggered oversizing and stent-graft characteristics based on patient-specific anatomical location and age. In addition, the results can be used to optimize towards more aortophilic stent grafts.

Region- and layer-specific investigations of the human menisci using SHG imaging and biaxial testing

In this paper, we examine the region- and layer-specific collagen fiber morphology via second harmonic generation (SHG) in combination with planar biaxial tension testing to suggest a structure-based constitutive model for the human meniscal tissue. Five lateral and four medial menisci were utilized, with samples excised across the thickness from the anterior, mid-body, and posterior regions of each meniscus. An optical clearing protocol enhanced the scan depth. SHG imaging revealed that the top samples consisted of randomly oriented fibers with a mean fiber orientation of 43.3 ^o . The bottom samples were dominated by circumferentially organized fibers, with a mean orientation of 9.5 ^o . Biaxial testing revealed a clear anisotropic response, with the circumferential direction being stiffer than the radial direction. The bottom samples from the anterior region of the medial menisci exhibited higher circumferential elastic modulus with a mean value of 21 MPa. The data from the two testing protocols were combined to characterize the tissue with an anisotropic hyperelastic material model based on the generalized structure tensor approach. The model showed good agreement in representing the material anisotropy with a mean r ² = 0.92.

Changes in the microstructure of the human aortic medial layer under biaxial loading investigated by multi-photon microscopy

Understanding the correlation between tissue architecture, health status, and mechanical properties is essential for improving material models and developing tissue engineering scaffolds. Since structural-based material models are state of the art, there is an urgent need for experimentally obtained structural parameters. For this purpose, the medial layer of nine human abdominal aortas was simultaneously subjected to equibiaxial loading and multi-photon microscopy. At each loading interval of 0.02, collagen and elastin fibers were imaged based on their second-harmonic generation signal and two-photon excited autofluorescence, respectively. The structural alterations in the fibers were quantified using the parameters of orientation, diameter, and waviness. The results of the mechanical tests divided the sample cohort into the ruptured and non-ruptured, and stiff and non-stiff groups, which were covered by the findings from histological investigations. The alterations in structural parameters provided an explanation for the observed mechanical behavior. In addition, the waviness parameters of both collagen and elastin fibers showed the potential to serve as indicators of tissue strength. The data provided address deficiencies in current material models and bridge multiscale mechanisms in the aortic media. STATEMENT OF SIGNIFICANCE: Available material models can reproduce, but cannot predict, the mechanical behavior of human aortas. This deficiency could be overcome with the help of experimentally validated structural parameters as provided in this study. Simultaneous multi-photon microscopy and biaxial extension testing revealed the microstructure of human aortic media at different stretch levels. Changes in the arrangement of collagen and elastin fibers were quantified using structural parameters such as orientation, diameter and waviness. For the first time, structural parameters of human aortic tissue under continuous loading conditions have been obtained. In particular, the waviness parameters at the reference configuration have been associated with tissue stiffness, brittleness, and the onset of atherosclerosis.

How viscous is the beating heart?: Insights from a computational study

Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress-relaxation curves, pressure-volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic.

Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle

We consider parameter inference in cardio-mechanic models of the left ventricle, in particular the one based on the Holtzapfel-Ogden (HO) constitutive law, using clinical in vivo data. The equations underlying these models do not admit closed form solutions and hence need to be solved numerically. These numerical procedures are computationally expensive making computational run times associated with numerical optimisation or sampling excessive for the uptake of the models in the clinical practice. To address this issue, we adopt the framework of Bayesian optimisation (BO), which is an efficient statistical technique of global optimisation. BO seeks the optimum of an unknown black-box function by sequentially training a statistical surrogate-model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off. To guarantee that the estimates based on the in vivo data are realistic also for high-pressures, unobservable in vivo, we include a penalty term based on a previously published empirical law developed using ex vivo data. Two case studies based on real data demonstrate that the proposed BO procedure outperforms the state-of-the-art inference algorithm for the HO constitutive law.

A machine learning model to estimate myocardial stiffness from EDPVR

In-vivo estimation of mechanical properties of the myocardium is essential for patient-specific diagnosis and prognosis of cardiac disease involving myocardial remodeling, including myocardial infarction and heart failure with preserved ejection fraction. Current approaches use time-consuming finite-element (FE) inverse methods that involve reconstructing and meshing the heart geometry, imposing measured loading, and conducting computationally expensive iterative FE simulations. In this paper, we propose a machine learning (ML) model that feasibly and accurately predicts passive myocardial properties directly from select geometric, architectural, and hemodynamic measures, thus bypassing exhaustive steps commonly required in cardiac FE inverse problems. Geometric and fiber-orientation features were chosen to be readily obtainable from standard cardiac imaging protocols. The end-diastolic pressure-volume relationship (EDPVR), which can be obtained using a single-point pressure-volume measurement, was used as a hemodynamic (loading) feature. A comprehensive ML training dataset in the geometry-architecture-loading space was generated, including a wide variety of partially synthesized rodent heart geometry and myofiber helicity possibilities, and a broad range of EDPVRs obtained using forward FE simulations. Latin hypercube sampling was used to create 2500 examples for training, validation, and testing. A multi-layer feed-forward neural network (MFNN) was used as a deep learning agent to train the ML model. The model showed excellent performance in predicting stiffness parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_f$$\end{document}af and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f$$\end{document}bf associated with fiber direction (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2_{a_f}=99.471\%$$\end{document}Raf2=99.471% and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2_{b_f}=92.837\%$$\end{document}Rbf2=92.837%). After conducting permutation feature importance analysis, the ML performance further improved for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f$$\end{document}bf (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2_{b_f}=96.240\%$$\end{document}Rbf2=96.240%), and the left ventricular volume and endocardial area were found to be the most critical geometric features for accurate predictions. The ML model predictions were evaluated further in two cases: (i) rat-specific stiffness data measured using ex-vivo mechanical testing, and (ii) patient-specific estimation using FE inverse modeling. Excellent agreements with ML predictions were found for both cases. The trained ML model offers a feasible technology to estimate patient-specific myocardial properties, thus, bridging the gap between EDPVR, as a confounded organ-level metric for tissue stiffness, and intrinsic tissue-level properties. These properties provide incremental information relative to traditional organ-level indices for cardiac function, improving the clinical assessment and prognosis of cardiac diseases.

An ultrastructural 3D reconstruction method for observing the arrangement of collagen fibrils and proteoglycans in the human aortic wall under mechanical load

An insight into changes of soft biological tissue ultrastructures under loading conditions is essential to understand their response to mechanical stimuli. Therefore, this study offers an approach to investigate the arrangement of collagen fibrils and proteoglycans (PGs), which are located within the mechanically loaded aortic wall. The human aortic samples were either fixed directly with glutaraldehyde in the load-free state or subjected to a planar biaxial extension test prior to fixation. The aortic ultrastructure was recorded using electron tomography. Collagen fibrils and PGs were segmented using convolutional neural networks, particularly the ESPNet model. The 3D ultrastructural reconstructions revealed a complex organization of collagen fibrils and PGs. In particular, we observed that not all PGs are attached to the collagen fibrils, but some fill the spaces between the fibrils with a clear distance to the collagen. The complex organization cannot be fully captured or can be severely misinterpreted in 2D. The approach developed opens up practical possibilities, including the quantification of the spatial relationship between collagen fibrils and PGs as a function of the mechanical load. Such quantification can also be used to compare tissues under different conditions, e.g., healthy and diseased, to improve or develop new material models. STATEMENT OF SIGNIFICANCE: The developed approach enables the 3D reconstruction of collagen fibrils and proteoglycans as they are embedded in the loaded human aortic wall. This methodological pipeline comprises the knowledge of arterial mechanics, imaging with transmission electron microscopy and electron tomography, segmentation of 3D image data sets with convolutional neural networks and finally offers a unique insight into the ultrastructural changes in the aortic tissue caused by mechanical stimuli.

Paired Pressure-Volume Loop Analysis and Biaxial Mechanical Testing Characterize Differences in Left Ventricular Tissue Stiffness of Volume Overload and Angiotensin-Induced Pressure Overload Hearts

Pressure overload (PO) and volume overload (VO) of the heart result in distinctive changes to geometry, due to compensatory structural remodeling. This remodeling potentially leads to changes in tissue mechanical properties. Understanding such changes is important, as tissue modulus has an impact on cardiac performance, disease progression, and influences on cell phenotype. Pressure-volume (PV) loop analysis, a clinically relevant method for measuring left ventricular (LV) chamber stiffness, was performed in vivo on control rat hearts and rats subjected to either chronic PO through Angiotensin-II infusion (4-weeks) or VO (8-weeks). Immediately following PV loops, biaxial testing was performed on LV free wall tissue to directly measure tissue mechanical properties. The β coefficient, an index of chamber stiffness calculated from the PV loop analysis, increased 98% in PO (n = 4) and decreased 38% in VO (n = 5) compared to control (n = 6). Material constants of LV walls obtained from ex vivo biaxial testing (n = 9-10) were not changed in Angiotensin-II induced PO and decreased by about half in VO compared to control (47% in the circumferential and 57% the longitudinal direction). PV loop analysis showed the expected increase in chamber stiffness of PO and expected decrease in chamber stiffness of VO. Biaxial testing showed a decreased modulus of the myocardium of the VO model, but no changes in the PO model, this suggests the increased chamber stiffness in PO, as shown in the PV loop analysis, may be secondary to changes in tissue mass and/or geometry but not an increase in passive tissue mechanical properties.

Passive mechanical properties in healthy and infarcted rat left ventricle characterised via a mixture model

During the cardiac cycle, electrical excitation is coupled with mechanical response of the myocardium. Besides the active contraction, passive mechanics plays an important role, and its behaviour differs in healthy and diseased hearts as well as among different animal species. The aim of this study is the characterisation of passive mechanical properties in healthy and infarcted rat myocardium by means of mechanical testing and subsequent parameter fitting. Elasticity assessments via uniaxial extension tests are performed on healthy and infarcted tissue samples from left ventricular rat myocardium. In order to fully characterise the orthotropic cardiac tissue, our experimental data are combined with other previously published tests in rats - shear tests on healthy myocardium and equibiaxial tests on infarcted tissue. In a first step, we calibrate the Holzapfel-Ogden strain energy function in the healthy case. Sa far, this orthotropic constitutive law for the passive myocardium has been fitted to experimental data in several species, however there is a lack of an appropriate parameter set for the rat. With our determined parameters, a finite element simulation of the end-diastolic filling is performed. In a second step, we propose a model for the infarcted tissue. It is represented as a mixture of intact myocardium and a transversely isotropic scar structure. In our mechanical experiments, the tissue after myocardial infarction shows significantly stiffer behaviour than in the healthy case, and the stiffness correlates with the amount of fibrosis. A similar relationship is observed in the computational simulation of the end-diastolic filling. We conclude that our new proposed material model can capture the behaviour of two kinds of tissues - healthy and infarcted rat myocardium, and its calibration with the fitted parameters represents the experimental data well.

Location- and layer-dependent biomechanical and microstructural characterisation of the porcine urinary bladder wall

The knowledge of the mechanical properties of the urinary bladder wall helps to explain its storage and micturition functions in health and disease studies; however, these properties largely remain unknown, especially with regard to its layer-specific characteristics and microstructure. Consequently, this study entails the assessment of the layer-specific differences in the mechanical properties and microstructure of the bladder wall, especially during loading. Accordingly, ninety-two (n=92) samples of porcine urinary bladder walls were mechanically and histologically analysed. Generally, the bladder wall and different tissue layers exhibit a non-linear stress-stretch relationship. In this study, the load transfer mechanisms were not only associated with the wavy structure of muscular and mucosal layers, but also with the entire bladder wall microstructure. Contextually, an interplay between the mucosal and muscular layers could be identified. Therefore, depending on the region and direction, the mucosal layer exhibited a stiffer mechanical response to equi-biaxial loading than that offered by the muscular layer when deformed to stretch levels higher than λ=1.6 to λ=2.2. For smaller stretches, the mucosal layer evinces no significant mechanical reaction, while the muscular layer bears the load. Owing to the orientation of its muscle fibres, the muscular layer shows an increased degree of anisotropy compared to the mucosal layer. Furthermore, the general incompressibility assumption is analysed for different layers by measuring the change in thickness during loading, which indicated a small volume loss.

Quantifying stent-induced damage in coronary arteries by investigating mechanical and structural alterations

Vascular damage develops with diverging severity during and after percutaneous coronary intervention with stent placement and is the prevailing stimulus for in-stent restenosis. Previous work has failed to link mechanical data obtained in a realistic in vivo or in vitro environment with data collected during imaging processes. We investigated whether specimens of porcine right coronary arteries soften when indented with a stent strut shaped structure, and if the softening results from damage mechanisms inside the fibrillar collagen structure. To simulate the multiaxial loading scenario of a stented coronary artery, we developed the testing device 'LAESIO' that can measure differences in the stress-stretch behavior of the arterial wall before and after the indentation of a strut-like stamp. The testing protocol was optimized according to preliminary experiments, more specifically equilibrium and relaxation tests. After chemical fixation of the specimens and subsequent tissue clearing, we performed three-dimensional surface and second-harmonic generation scans on the deformed specimens. We analyzed and correlated the mechanical response with structural parameters of high-affected tissue located next to the stamp indentation and low-affected tissue beyond the injured area. The results reveal that damage mechanisms, like tissue compression as well as softening, fiber dispersion, and the lesion extent, are direction-dependent, and the severity of them is linked to the strut orientation, indentation pressure, and position. The findings highlight the need for further investigations by applying the proposed methods to human coronary arteries. Additional data and insights might help to incorporate the observed damage mechanisms into material models for finite element analyses to perform more accurate simulations of stent-implantations.

Cells, Materials, and Fabrication Processes for Cardiac Tissue Engineering

Cardiovascular disease is the number one killer worldwide, with myocardial infarction (MI) responsible for approximately 1 in 6 deaths. The lack of endogenous regenerative capacity, added to the deleterious remodelling programme set into motion by myocardial necrosis, turns MI into a progressively debilitating disease, which current pharmacological therapy cannot halt. The advent of Regenerative Therapies over 2 decades ago kick-started a whole new scientific field whose aim was to prevent or even reverse the pathological processes of MI. As a highly dynamic organ, the heart displays a tight association between 3D structure and function, with the non-cellular components, mainly the cardiac extracellular matrix (ECM), playing both fundamental active and passive roles. Tissue engineering aims to reproduce this tissue architecture and function in order to fabricate replicas able to mimic or even substitute damaged organs. Recent advances in cell reprogramming and refinement of methods for additive manufacturing have played a critical role in the development of clinically relevant engineered cardiovascular tissues. This review focuses on the generation of human cardiac tissues for therapy, paying special attention to human pluripotent stem cells and their derivatives. We provide a perspective on progress in regenerative medicine from the early stages of cell therapy to the present day, as well as an overview of cellular processes, materials and fabrication strategies currently under investigation. Finally, we summarise current clinical applications and reflect on the most urgent needs and gaps to be filled for efficient translation to the clinical arena.

MECHANICAL CHARACTERIZATION OF SPINAL DURA USING A PD-CONTROLLED BIAXIAL TENSILE TESTER

In this study, we developed an equi-load biaxial tensile tester and applied it to a series of mechanical tests using specimens obtained from the porcine spinal dura mater. The dural sample exhibited a nonlinear and anisotropic behavior as it was more deformable in the longitudinal direction rather than in the circumferential direction at lower strains; i.e., mechanical response of the longitudinal direction was significantly compliant in the Toe region compared to that of the circumferential direction under 1:1 biaxial stretching. However, we have not observed a significant difference with respect to the resultant strain and Young’s modulus between the longitudinal and circumferential directions at higher strains or in the Linear region. Our results also indicated that the upper thoracic region (T1) was relatively compliant compared to the lumbar region (L), where the failure load was almost equal between them because the dural thickness of T1 was five-fold greater than that of L; i.e., spinal dura mater became stiffer and stronger at further distances from the brain. This shows structural effectiveness and may be preferable to mechanically protect the vulnerable spinal cord from externally applied impact loads.

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelastic, current biomechanical models in the computational community often assume hyperelastic material models. Fractional viscoelastic constitutive models have been successfully used in literature to capture viscoelastic material response; however, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is 𝒪 ( N T 2 ) and a storage cost that is 𝒪(N_T ) (N_T denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is 𝒪(N_T ) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and an error estimate is presented to demonstrate the efficacy of the method. The method, integrated into a finite element solid mechanics framework, is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying the accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem.

Insights into the passive mechanical behavior of left ventricular myocardium using a robust constitutive model based on full 3D kinematics

Myocardium possesses a hierarchical structure that results in complex three-dimensional (3D) mechanical behavior, forming a critical component of ventricular function in health and disease. A wide range of constitutive model forms have been proposed for myocardium since the first planar biaxial studies were performed by Demer and Yin (J. Physiol. 339 (1), 1983). While there have been extensive studies since, none have been based on full 3D kinematic data, nor have they utilized optimal experimental design to estimate constitutive parameters, which may limit their predictive capability. Herein we have applied our novel 3D numerical-experimental methodology (Avazmohammadi et al., Biomechanics Model. Mechanobiol. 2018) to explore the applicability of an orthotropic constitutive model for passive ventricular myocardium (Holzapfel and Ogden, Philos. Trans. R. Soc. Lond.: Math. Phys. Eng. Sci. 367, 2009) by integrating 3D optimal loading paths, spatially varying material structure, and inverse modeling techniques. Our findings indicated that the initial model form was not successful in reproducing all optimal loading paths, due to previously unreported coupling behaviors via shearing of myofibers and extracellular collagen fibers in the myocardium. This observation necessitated extension of the constitutive model by adding two additional terms based on the I8(C) pseudo-invariant in the fiber-normal and sheet-normal directions. The modified model accurately reproduced all optimal loading paths and exhibited improved predictive capabilities. These unique results suggest that more complete constitutive models are required to fully capture the full 3D biomechanical response of left ventricular myocardium. The present approach is thus crucial for improved understanding and performance in cardiac modeling in healthy, diseased, and treatment scenarios.

Biomechanical and microstructural characterisation of the porcine stomach wall: Location- and layer-dependent investigations

The mechanical properties of the stomach wall help to explain its function of storing, mixing, and emptying in health and disease. However, much remains unknown about its mechanical properties, especially regarding regional heterogeneities and wall microstructure. Consequently, the present study aimed to assess regional differences in the mechanical properties and microstructure of the stomach wall. In general, the stomach wall and the different tissue layers exhibited a nonlinear stress-stretch relationship. Regional differences were found in the mechanical response and the microstructure. The highest stresses of the entire stomach wall in longitudinal direction were found in the corpus (201.5 kPa), where food is ground followed by the antrum (73.1 kPa) and the fundus (26.6 kPa). In contrast, the maximum stresses in circumferential direction were 39.7 kPa, 26.2 kPa, and 15.7 kPa for the antrum, fundus, and corpus, respectively. Independent of the fibre orientation and with respect to the biaxial loading direction, partially clear anisotropic responses were detected in the intact wall and the muscular layer. In contrast, the innermost mucosal layer featured isotropic mechanical characteristics. Pronounced layers of circumferential and longitudinal muscle fibres were found in the fundus only, whereas corpus and antrum contained almost exclusively circumferential orientated muscle fibres. This specific stomach structure mirrors functional differences in the fundus as well as corpus and antrum. Within this study, the load transfer mechanisms, connected with these wavy layers but also in total with the stomach wall's microstructure, are discussed. STATEMENT OF SIGNIFICANCE: This article examines for the first time the layer-specific mechanical and histological properties of the stomach wall attending to the location of the sample. Moreover, both mechanical behaviour and microstructure were explicitly match identifying the heterogeneous characteristics of the stomach. On the one hand, the results of this study contribute to the understanding of stomach mechanics and thus to their functional understanding of stomach motility. On the other hand, they are relevant to the fields of constitutive formulation of stomach tissue, whole stomach mechanics, and stomach-derived scaffolds i.e., tissue-engineering grafts.

Mechanical and finite element evaluation of a bioprinted scaffold following recellularization in a rat subcutaneous model

Tissue engineered heart valves (TEHV) provide several advantages over currently available aortic heart valve replacements. Bioprinting provides a patient-specific means of developing a TEHV scaffold from imaging data, and the capability to embed the patient's own cells within the scaffold. In this work we investigated the remodeling capacity of a collagen-based bio-ink by implanting bioprinted disks in a rat subcutaneous model for 2, 4 and 12 weeks and evaluating the mechanical response using biaxial testing and subsequent finite element (FE) modeling. Samples explanted after 2 and 4 weeks showed inferior mechanical properties compared to native tissues while 12 week explants showed a mechanical response of similar magnitude but did not demonstrate the anisotropy present in native tissues. In the FE analysis, the model utilizing mechanical properties from samples explanted after 12 weeks showed the closest mechanical behavior to the native tissues. However, in diastole native tissues showed higher stress in the leaflet belly and lower strain at the commissures compared to 12 week explants, likely due to the anisotropy present in the native tissues. Thus, either further remodeling is required in situ in the aortic valve position or by in vitro preconditioning in an environment such as a bioreactor. Regardless, these results demonstrate the utility of FE analysis to optimize bioprinting process parameters for the most favorable in vivo mechanical performance.

Direct and inverse identification of constitutive parameters from the structure of soft tissues. Part 2: dispersed arrangement of collagen fibers

This paper investigates on the relationship between the arrangement of collagen fibers within soft tissues and parameters of constitutive models. Starting from numerical experiments based on biaxial loading conditions, the study addresses both the direct (from structure to mechanics) and the inverse (from mechanics to structure) problems, solved introducing optimization problems for model calibration and regression analysis. A campaign of parametric analyses is conducted in order to consider fibers distributions with different main orientation and angular dispersion. Different anisotropic constitutive models are employed, accounting for fibers dispersion either with a generalized structural approach or with an increasing number of strain energy terms. Benchmark data sets, toward which constitutive models are fitted, are built by employing a multiscale description of fiber nonlinearities and accounting for fibers dispersion with an angular integration method. Results show how the optimal values of constitutive parameters obtained from model calibration vary as a function of fibers arrangement and testing protocol. Moreover, the fitting capabilities of constitutive models are discussed. A novel strategy for model calibration is also proposed, in order to obtain a robust accuracy with respect to different loading conditions starting from a low number of mechanical tests. Furthermore, novel results useful for the inverse determination of the mean angle and the variance of fibers distribution are obtained. Therefore, the study contributes: to better design procedures for model calibration; to account for mechanical alterations due to remodeling mechanisms; and to gain structural information in a nondestructive way.

Biomechanical Restoration Potential of Pentagalloyl Glucose after Arterial Extracellular Matrix Degeneration

The objective of this study was to quantify pentagalloyl glucose (PGG) mediated biomechanical restoration of degenerated extracellular matrix (ECM). Planar biaxial tensile testing was performed for native (N), enzyme-treated (collagenase and elastase) (E), and PGG (P) treated porcine abdominal aorta specimens (n = 6 per group). An Ogden material model was fitted to the stress-strain data and finite element computational analyses of simulated native aorta and aneurysmal abdominal aorta were performed. The maximum tensile stress of the N group was higher than that in both E and P groups for both circumferential (43.78 ± 14.18 kPa vs. 10.03 ± 2.68 kPa vs. 13.85 ± 3.02 kPa; p = 0.0226) and longitudinal directions (33.89 ± 8.98 kPa vs. 9.04 ± 2.68 kPa vs. 14.69 ± 5.88 kPa; p = 0.0441). Tensile moduli in the circumferential direction was found to be in descending order as N > P > E (195.6 ± 58.72 kPa > 81.8 ± 22.76 kPa > 46.51 ± 15.04 kPa; p = 0.0314), whereas no significant differences were found in the longitudinal direction (p = 0.1607). PGG binds to the hydrophobic core of arterial tissues and the crosslinking of ECM fibers is one of the possible explanations for the recovery of biomechanical properties observed in this study. PGG is a beneficial polyphenol that can be potentially translated to clinical practice for preventing rupture of the aneurysmal arterial wall.

On the AIC-based model reduction for the general Holzapfel-Ogden myocardial constitutive law

Constitutive laws that describe the mechanical responses of cardiac tissue under loading hold the key to accurately model the biomechanical behaviour of the heart. There have been ample choices of phenomenological constitutive laws derived from experiments, some of which are quite sophisticated and include effects of microscopic fibre structures of the myocardium. A typical example is the strain-invariant-based Holzapfel–Ogden 2009 model that is excellently fitted to simple shear tests. It has been widely used and regarded as the state-of-the-art constitutive law for myocardium. However, there has been no analysis to show if it has both adequate descriptive and predictive capabilities for other tissue tests of myocardium. Indeed, such an analysis is important for any constitutive laws for clinically useful computational simulations. In this work, we perform such an analysis using combinations of tissue tests, uniaxial tension, biaxial tension and simple shear from three different sets of myocardial tissue studies. Starting from the general 14-parameter myocardial constitutive law developed by Holzapfel and Ogden, denoted as the general HO model, we show that this model has good descriptive and predictive capabilities for all the experimental tests. However, to reliably determine all 14 parameters of the model from experiments remains a great challenge. Our aim is to reduce the constitutive law using Akaike information criterion, to maintain its mechanical integrity whilst achieving minimal computational cost. A competent constitutive law should have descriptive and predictive capabilities for different tissue tests. By competent, we mean the model has least terms but is still able to describe and predict experimental data. We also investigate the optimal combinations of tissue tests for a given constitutive model. For example, our results show that using one of the reduced HO models, one may need just one shear response (along normal-fibre direction) and one biaxial stretch (ratio of 1 mean fibre : 1 cross-fibre) to satisfactorily describe Sommer et al. human myocardial mechanical properties. Our study suggests that single-state tests (i.e. simple shear or stretching only) are insufficient to determine the myocardium responses. We also found it is important to consider transmural fibre rotations within each myocardial sample of tests during the fitting process. This is done by excluding un-stretched fibres using an “effective fibre ratio”, which depends on the sample size, shape, local myofibre architecture and loading conditions. We conclude that a competent myocardium material model can be obtained from the general HO model using AIC analysis and a suitable combination of tissue tests.

Differential biomechanical properties of mouse distal colon and rectum innervated by the splanchnic and pelvic afferents

Visceral pain is one of the principal complaints of patients with irritable bowel syndrome, and this pain is reliably evoked by mechanical distension and stretch of distal colon and rectum (colorectum). This study focuses on the biomechanics of the colorectum that could play critical roles in mechanical neural encoding. We harvested the distal 30 mm of the colorectum from mice, divided evenly into three 10-mm-long segments (colonic, intermediate and rectal), and conducted biaxial mechanical stretch tests and opening-angle measurements for each tissue segment. In addition, we determined the collagen fiber orientations and contents across the thickness of the colorectal wall by nonlinear imaging via second harmonic generation (SHG). Our results reveal a progressive increase in tissue compliance and prestress from colonic to rectal segments, which supports prior electrophysiological findings of distinct mechanical neural encodings by afferents in the lumbar splanchnic nerves (LSN) and pelvic nerves (PN) that dominate colonic and rectal innervations, respectively. The colorectum is significantly more viscoelastic in the circumferential direction than in the axial direction. In addition, our SHG results reveal a rich collagen network in the submucosa and orients approximately ±30° to the axial direction, consistent with the biaxial test results presenting almost twice the stiffness in axial direction versus the circumferential direction. Results from current biomechanical study strongly indicate the prominent roles of local tissue biomechanics in determining the differential mechanical neural encoding functions in different regions of the colorectum. NEW & NOTEWORTHY Mechanical distension and stretch-not heat, cutting, or pinching-reliably evoke pain from distal colon and rectum. We report different local mechanics along the longitudinal length of the colorectum, which is consistent with the existing literature on distinct mechanotransduction of afferents innervating proximal and distal regions of the colorectum. This study draws attention to local mechanics as a potential determinant factor for mechanical neural encoding of the colorectum, which is crucial in visceral nociception.

The role of tissue remodeling in mechanics and pathogenesis of abdominal aortic aneurysms

Arterial walls can be regarded as composite materials consisting of collagen fibers embedded in an elastic matrix and smooth muscle cells. Remodeling of the structural proteins has been shown to play a significant role in the mechanical behavior of walls during pathogenesis of abdominal aortic aneurysms (AAA). In this study, we systematically studied the change in the microstructure, histology and mechanics to link them to AAA disease progression. We performed biaxial extension tests, second-harmonic generation imaging and histology on 15 samples from the anterior part of AAA walls harvested during open aneurysm surgery. Structural data were gained by fitting to a bivariate von Mises distribution and yielded the mean fiber direction and in- and out-of-plane fiber dispersions of collagen. Mechanical and structural data were fitted to a recently proposed material model. Additionally, the mechanical data were used to derive collagen recruitment points in the obtained stress-stretch curves. We derived 14 parameters from histology such as smooth muscle cell-, elastin-, and abluminal adipocyte content. In total, 22 parameters were obtained and statistically evaluated. Based on the collagen recruitment points we were able to define three different stages of disease progression. Significant differences in elastin content, collagen orientation and adipocyte contents were discovered. Nerves entrapped inside AAA walls pointed towards a significant deposition of newly formed collagen abluminally, which we propose as neo-adventitia formation. We were able to discriminate two types of remodeled walls with a high collagen content - potentially safe and possibly vulnerable walls with a high adipocyte content inside the wall and significant amounts of inflammation. The study yielded a hypothesis for disease progression, derived from the systematic comparison of mechanical, microstructural and histological changes in AAAs. STATEMENT OF SIGNIFICANCE: Remodeling of the structural proteins plays an important role in the mechanical behavior of walls during pathogenesis of abdominal aortic aneurysms (AAA). We analyzed changes in the microstructure, histology and biomechanics of 15 samples from the anterior part of AAA walls and, for the first time, linked the results to three different stages of disease progression. We identified significant differences in elastin content, collagen orientation, adipocyte contents, and also a deposition of newly formed collagen forming a neoadventitia. We could discriminate two types of remodeled walls: (i) potentially safe and (ii) possibly vulnerable associated with inflammation and a high amount of adipocytes.

In Silico Performance of a Recellularized Tissue Engineered Transcatheter Aortic Valve

Commercially available heart valves have many limitations, such as a lack of re-modeling, risk of calcification and thromboembolic problems. Many state-of-the-art tissue engineered heart valves rely on recellularization. Current in vitro testing is insufficient in characterizing a soon to be living valve. It is imperative to understand the performance of an in situ valve, but due to the complex in vivo environment this is difficult to accomplish. Finite element analysis has become a standard tool for modeling mechanical behavior of heart valves; yet, research to date has mostly focused on commercial valves. The purpose of this study has been to develop finite element models of a decellularized and recellularized tissue engineered heart valve. Mechanical properties from porcine aortic valves were utilized to develop finite element models, which were run through a full physiological cardiac cycle. Maximum principal stresses and strains from the leaflets and commissures were analyzed. The results of this study demonstrate that the explanted tissues had reduced mechanical strength compared to the implants but were similar to the native tissues. For the finite element models the explanted recellularized leaflets showed lower stress but increased compliance in the leaflet belly compared to native tissues and higher compliance than implant tissues. Histology demonstrated recellularization and remodeling although remodeled collagen had no clear directionality. In conclusion, we observed successful recellularization and remodeling of the tissue, however, the mechanical response indicates the further remodeling is required following implantation in the aortic/pulmonary position.

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

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

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

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

Location-dependent correlation between tissue structure and the mechanical behaviour of the urinary bladder

The mechanical properties of the urinary bladder wall are important to understand its filling-voiding cycle in health and disease. However, much remains unknown about its mechanical properties, especially regarding regional heterogeneities and wall microstructure. The present study aimed to assess the regional differences in the mechanical properties and microstructure of the urinary bladder wall. Ninety (n=90) samples of porcine urinary bladder wall (ten samples from nine different locations) were mechanically and histologically analysed. Half of the samples (n=45) were equibiaxially tested within physiological conditions, and the other half, matching the sample location of the mechanical tests, was frozen, cryosectioned, and stained with Picro-Sirius red to differentiate smooth muscle cells, extracellular matrix, and fat. The bladder wall shows a non-linear stress-stretch relationship with hysteresis and softening effects. Regional differences were found in the mechanical response and in the microstructure. The trigone region presents higher peak stresses and thinner muscularis layer compared to the rest of the bladder. Furthermore, the ventral side of the bladder presents anisotropic characteristics, whereas the dorsal side features perfect isotropic behaviour. This response matches the smooth muscle fibre bundle orientation within the tunica muscularis. This layer, comprising approximately 78% of the wall thickness, is composed of two fibre bundle arrangements that are cross-oriented, one with respect to the other, varying the angle between them across the organ. That is, the ventral side presents a 60°/120° cross-orientation structure, while the muscle bundles were oriented perpendicular in the dorsal side.

STATEMENT OF SIGNIFICANCE

In the present study, we demonstrate that the mechanical properties and the microstructure of the urinary bladder wall are heterogeneous across the organ. The mechanical properties and the microstructure of the urinary bladder wall within nine specific locations matching explicitly the mechanical and structural variations have been examined. On the one hand, the results of this study contribute to the understanding of bladder mechanics and thus to their functional understanding of bladder filling and voiding. On the other hand, they are relevant to the fields of constitutive formulation of bladder tissue, whole bladder mechanics, and bladder-derived scaffolds i.e., tissue-engineering grafts.

An in silico framework to analyze the anisotropic shear wave mechanics in cardiac shear wave elastography

Shear wave elastography (SWE) is a potential tool to non-invasively assess cardiac muscle stiffness. This study focused on the effect of the orthotropic material properties and mechanical loading on the performance of cardiac SWE, as it is known that these factors contribute to complex 3D anisotropic shear wave propagation. To investigate the specific impact of these complexities, we constructed a finite element model with an orthotropic material law subjected to different uniaxial stretches to simulate SWE in the stressed cardiac wall. Group and phase speed were analyzed in function of tissue thickness and virtual probe rotation angle. Tissue stretching increased the group and phase speed of the simulated shear wave, especially in the direction of the muscle fiber. As the model provided access to the true fiber orientation and material properties, we assessed the accuracy of two fiber orientation extraction methods based on SWE. We found a higher accuracy (but lower robustness) when extracting fiber orientations based on the location of maximal shear wave speed instead of the angle of the major axis of the ellipsoidal group speed surface. Both methods had a comparable performance for the center region of the cardiac wall, and performed less well towards the edges. Lastly, we also assessed the (theoretical) impact of pathology on shear wave physics and characterization in the model. It was found that SWE was able to detect changes in fiber orientation and material characteristics, potentially associated with cardiac pathologies such as myocardial fibrosis. Furthermore, the model showed clearly altered shear wave patterns for the fibrotic myocardium compared to the healthy myocardium, which forms an initial but promising outcome of this modeling study.

In vivo estimation of passive biomechanical properties of human myocardium

Identification of in vivo passive biomechanical properties of healthy human myocardium from regular clinical data is essential for subject-specific modelling of left ventricle (LV). In this work, myocardium was defined by Holzapfel-Ogden constitutive law. Therefore, the objectives of the study were (a) to estimate the ranges of the constitutive parameters for healthy human myocardium using non-invasive routine clinical data, and (b) to investigate the effect of geometry, LV end-diastolic pressure (EDP) and fibre orientations on estimated values. In order to avoid invasive measurements and additional scans, LV cavity volume, measured from routine MRI, and empirical pressure-normalised-volume relation (Klotz-curve) were used as clinical data. Finite element modelling, response surface method and genetic algorithm were used to inversely estimate the constitutive parameters. Due to the ill-posed nature of the inverse optimisation problem, the myocardial properties was extracted by identifying the ranges of the parameters, instead of finding unique values. Additional sensitivity studies were carried out to identify the effect of LV EDP, fibre orientation and geometry on estimated parameters. Although uniqueness of the solution cannot be achieved, the normal ranges of the parameters produced similar mechanical responses within the physiological ranges. These information could be used in future computational studies for designing heart failure treatments. Graphical abstract.

In vivo estimation of passive biomechanical properties of human myocardium

Identification of in vivo passive biomechanical properties of healthy human myocardium from regular clinical data is essential for subject-specific modelling of left ventricle (LV). In this work, myocardium was defined by Holzapfel-Ogden constitutive law. Therefore, the objectives of the study were (a) to estimate the ranges of the constitutive parameters for healthy human myocardium using non-invasive routine clinical data, and (b) to investigate the effect of geometry, LV end-diastolic pressure (EDP) and fibre orientations on estimated values. In order to avoid invasive measurements and additional scans, LV cavity volume, measured from routine MRI, and empirical pressure-normalised-volume relation (Klotz-curve) were used as clinical data. Finite element modelling, response surface method and genetic algorithm were used to inversely estimate the constitutive parameters. Due to the ill-posed nature of the inverse optimisation problem, the myocardial properties was extracted by identifying the ranges of the parameters, instead of finding unique values. Additional sensitivity studies were carried out to identify the effect of LV EDP, fibre orientation and geometry on estimated parameters. Although uniqueness of the solution cannot be achieved, the normal ranges of the parameters produced similar mechanical responses within the physiological ranges. These information could be used in future computational studies for designing heart failure treatments.

Microstructure and mechanics of healthy and aneurysmatic abdominal aortas: experimental analysis and modelling

Soft biological tissues such as aortic walls can be viewed as fibrous composites assembled by a ground matrix and embedded families of collagen fibres. Changes in the structural components of aortic walls such as the ground matrix and the embedded families of collagen fibres have been shown to play a significant role in the pathogenesis of aortic degeneration. Hence, there is a need to develop a deeper understanding of the microstructure and the related mechanics of aortic walls. In this study, tissue samples from 17 human abdominal aortas (AA) and from 11 abdominal aortic aneurysms (AAA) are systematically analysed and compared with respect to their structural and mechanical differences. The collagen microstructure is examined by analysing data from second-harmonic generation imaging after optical clearing. Samples from the intact AA wall, their individual layers and the AAA wall are mechanically investigated using biaxial stretching tests. A bivariate von Mises distribution was used to represent the continuous fibre dispersion throughout the entire thickness, and to provide two independent dispersion parameters to be used in a recently proposed material model. Remarkable differences were found between healthy and diseased tissues. The out-of-plane dispersion was significantly higher in AAA when compared with AA tissues, and with the exception of one AAA sample, the characteristic wall structure, as visible in healthy AAs with three distinct layers, could not be identified in AAA samples. The collagen fibres in the abluminal layer of AAAs lost their waviness and exhibited rather straight and thick struts of collagen. A novel set of three structural and three material parameters is provided. With the structural parameters fixed, the material model was fitted to the mechanical experimental data, giving a very satisfying fit although there are only three material parameters involved. The results highlight the need to incorporate the structural differences into finite-element simulations as otherwise simulations of AAA tissues might not be good predictors for the actual in vivo stress state.

Experimental characterization of the biaxial mechanical properties of porcine gastric tissue

Health problems related to the stomach are among the most important sources of morbidity in industrialized countries. There is evidence that mechanics may play an important role in various such pathologies. However, so far experimental data characterizing the mechanical properties of gastric tissue remain scarce, which significantly limits our understanding of the mechanics of the stomach. To help close this gap, we performed biaxial mechanical tests of porcine gastric tissue patches. Our experiments reveal a considerable anisotropy and different mechanical properties in the three major regions of the stomach (fundus, corpus, antrum). Moreover, they demonstrate that the mechanical properties of the gastric wall and the physiological function of the different regions of the stomach are closely related. This finding suggests that further examination of the mechanics of the gastric wall may indeed be a promising avenue of research towards a better understanding of the organic causes of frequent health problems related to the stomach.

Passive diastolic modelling of human ventricles: Effects of base movement and geometrical heterogeneity

Left-ventricular (LV) remodelling, associated with diastolic heart failure, is driven by an increase in myocardial stress. Therefore, normalisation of LV wall stress is the cornerstone of many therapeutic treatments. However, information regarding such regional stress-strain for human LV is still limited. Thus, the objectives of our study were to determine local diastolic stress-strain field in healthy LVs, and consequently, to identify the regional variations amongst them due to geometric heterogeneity. Effects of LV base movement on diastolic model predictions, which were ignored in the literature, were further explored. Personalised finite-element modelling of five normal human bi-ventricles was carried out using subject-specific myocardium properties. Model prediction was validated individually through comparison with end-diastolic volume and a new shape-volume based measurement of LV cavity, extracted from magnetic resonance imaging. Results indicated that incorporation of LV base movement improved the model predictions (shape-volume relevancy of LV cavity), and therefore, it should be considered in future studies. The LV endocardium always experienced higher fibre stress compared to the epicardium for all five subjects. The LV wall near base experienced higher stress compared to equatorial and apical locations. The lateral LV wall underwent greater stress distribution (fibre and sheet stress) compared to other three regions. In addition, normal ranges of different stress-strain components in different regions of LV wall were reported for five healthy ventricles. This information could be used as targets for future computational studies to optimise diastolic heart failure treatments or design new therapeutic interventions/devices.

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.

Non-invasive Model-Based Assessment of Passive Left-Ventricular Myocardial Stiffness in Healthy Subjects and in Patients with Non-ischemic Dilated Cardiomyopathy

Patient-specific modelling has emerged as a tool for studying heart function, demonstrating the potential to provide non-invasive estimates of tissue passive stiffness. However, reliable use of model-derived stiffness requires sufficient model accuracy and unique estimation of model parameters. In this paper we present personalised models of cardiac mechanics, focusing on improving model accuracy, while ensuring unique parametrisation. The influence of principal model uncertainties on accuracy and parameter identifiability was systematically assessed in a group of patients with dilated cardiomyopathy ([Formula: see text]) and healthy volunteers ([Formula: see text]). For all cases, we examined three circumferentially symmetric fibre distributions and two epicardial boundary conditions. Our results demonstrated the ability of data-derived boundary conditions to improve model accuracy and highlighted the influence of the assumed fibre distribution on both model fidelity and stiffness estimates. The model personalisation pipeline-based strictly on non-invasive data-produced unique parameter estimates and satisfactory model errors for all cases, supporting the selected model assumptions. The thorough analysis performed enabled the comparison of passive parameters between volunteers and dilated cardiomyopathy patients, illustrating elevated stiffness in diseased hearts.

Non-invasive Model-Based Assessment of Passive Left-Ventricular Myocardial Stiffness in Healthy Subjects and in Patients with Non-ischemic Dilated Cardiomyopathy

Patient-specific modelling has emerged as a tool for studying heart function, demonstrating the potential to provide non-invasive estimates of tissue passive stiffness. However, reliable use of model-derived stiffness requires sufficient model accuracy and unique estimation of model parameters. In this paper we present personalised models of cardiac mechanics, focusing on improving model accuracy, while ensuring unique parametrisation. The influence of principal model uncertainties on accuracy and parameter identifiability was systematically assessed in a group of patients with dilated cardiomyopathy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=3$$\end{document}n=3) and healthy volunteers (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=5$$\end{document}n=5). For all cases, we examined three circumferentially symmetric fibre distributions and two epicardial boundary conditions. Our results demonstrated the ability of data-derived boundary conditions to improve model accuracy and highlighted the influence of the assumed fibre distribution on both model fidelity and stiffness estimates. The model personalisation pipeline—based strictly on non-invasive data—produced unique parameter estimates and satisfactory model errors for all cases, supporting the selected model assumptions. The thorough analysis performed enabled the comparison of passive parameters between volunteers and dilated cardiomyopathy patients, illustrating elevated stiffness in diseased hearts.

Planar biaxial extension of the lumbar facet capsular ligament reveals significant in-plane shear forces

The lumbar facet capsular ligament (FCL) articulates with six degrees of freedom during spinal motions of flexion/extension, lateral bending, and axial rotation. The lumbar FCL is composed of highly aligned collagen fiber bundles on the posterior surface (oriented primarily laterally between the rigid articular facets) and irregularly oriented elastin on the anterior surface. Because the FCL is a capsule, it has multiple insertion sites across the lumbar facet joint, which, along with its material structure, give rise to complicated deformations in vivo. We performed planar equibiaxial mechanical tests on excised healthy cadaveric lumbar FCLs (n=6) to extract normal and shear reaction forces, and fit sample-specific two-fiber-family finite element models to the experimental force data. An eight-parameter anisotropic, hyperelastic model was used. Shear forces at maximum extension (mean values of 1.68N and 3.01N in the two directions) were of comparable magnitude to the normal forces perpendicular to the aligned collagen fiber bundles (4.67N) but smaller than normal forces in the fiber direction (16.11N). Inclusion of the experimental shear forces in the model optimization yielded fits with highly aligned fibers oriented at a specific angle across all samples, typically with one fiber population aligned nearly horizontally and the other at an oblique angle. Conversely, models fit to only the normal force data resulted in a broad range of fiber angles with low specificity. We found that shear forces generated through planar equibiaxial extension aided the model fit in describing the anisotropic nature of the FCL surface.

Coupled electro-mechanical models of fiber-distributed active tissues

We discuss a constitutive model for stochastically distributed fiber reinforced tissues, where the active behavior of the fibers depends on the relative orientation of the electric field. Unlike other popular approaches, based on numerical integration over the unit sphere, or on the use of second order structure tensors, for the passive behavior we adopt a second order approximation of the strain energy density of the distribution. The purely mechanical quantities result to be dependent on two (second and fourth order, respectively) averaged structure tensors. In line with the approximation used for the passive behavior, we model the active behavior accounting for the statistical fiber distribution. We extend the Helmholtz free energy density by introducing a directional active potential, dependent on a stochastic permittivity tensor associated to a particular direction, and approximate the total active potential through a second order Taylor expansion of the permittivity tensor. The approximation allows us to derive explicitly the active stress and the active constitutive tensors, which result to be dependent on the same two averaged structure tensors that characterize the passive response. Active anisotropy follows from the distribution of the fibers and inherits its stochastic parameters. Examples of passive and active behaviors predicted by the model in terms of response to biaxial testing are presented, and comparisons with passive experimental data are provided.

Designing Biopolymer Microthreads for Tissue Engineering and Regenerative Medicine

Native tissue structures possess elaborate extracellular matrix (ECM) architectures that inspire the design of fibrous structures in the field of regenerative medicine. We review the literature with respect to the successes and failures, as well as the future promise of biopolymer microthreads as scaffolds to promote endogenous and exogenous tissue regeneration. Biomimetic microthread tissue constructs have been proposed for the functional regeneration of tendon, ligament, skeletal muscle, and ventricular myocardial tissues. To date, biopolymer microthreads have demonstrated promising results as materials to recapitulate the hierarchical structure of simple and complex tissues and well as biochemical signaling cues to direct cell-mediated tissue regeneration. Biopolymer microthreads have also demonstrated exciting potential as a platform technology for the targeted delivery of stem cells and therapeutic molecules. Future studies will focus on the design of microthread-based tissue analogs that strategically integrate growth factors and progenitor cells to temporally direct cell-mediated processes that promote enhanced functional tissue regeneration.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

Biomechanical properties and microstructure of human ventricular myocardium

In the multidisciplinary field of heart research it is of utmost importance to identify accurate myocardium material properties for the description of phenomena such as mechano-electric feedback or heart wall thickening. A rationally-based material model is required to understand the highly nonlinear mechanics of complex structures such as the passive myocardium under different loading conditions. Unfortunately, to date there are no experimental data of human heart tissues available to estimate material parameters and to develop adequate material models. This study aimed to determine biaxial extension and triaxial shear properties and the underlying microstructure of the passive human ventricular myocardium. Using new state-of-the-art equipment, planar biaxial extension tests were performed to determine the biaxial extension properties of the passive ventricular human myocardium. Shear properties of the myocardium were examined by triaxial simple shear tests performed on small cubic specimens excised from an adjacent region of the biaxial extension specimens. The three-dimensional microstructure was investigated through second-harmonic generation (SHG) microscopy on optically cleared tissues, which emphasized the 3D orientation and dispersion of the myofibers and adjacent collagen fabrics. The results suggest that the passive human LV myocardium under quasi-static and dynamic multiaxial loadings is a nonlinear, anisotropic (orthotropic), viscoelastic and history-dependent soft biological material undergoing large deformations. Material properties of the tissue components along local microstructural axes drive the nonlinear and orthotropic features of the myocardium. SHG microscopy investigation revealed detailed information about the myocardial microstructure due to its high resolution. It enabled the identification of structural parameters such as the fiber and the sheet orientations and corresponding dispersions. With this complete set of material data, a sophisticated material model and associated material parameters can be defined for a better description of the biomechanical response of the ventricular myocardium in humans. Such a model will lead to more accurate computational simulations to better understand the fundamental underlying ventricular mechanics, a step needed in the improvement of medical treatment of heart diseases.

STATEMENT OF SIGNIFICANCE

Unfortunately, to date there are no experimental data of human heart tissues available for material parameter estimation and the development of adequate material models. In this manuscript novel biaxial tensile and shear test data at different specimen orientations are presented, which allowed to adequately capture the direction-dependent material response. With these complete sets of mechanical data, combined with their underlying microstructural data (also presented herein), sophisticated material models and associated material parameters can be defined for the description of the mechanical behavior of the ventricular myocardium in humans. Such models will lead to accurate computational simulations to better understand the fundamental underlying ventricular mechanics, a step needed in the improvement of medical treatment of heart diseases.