Predictive capabilities of various constitutive models for arterial tissue

AT1b receptors contribute to regional disparities in angiotensin II mediated aortic remodelling in mice

The renin-angiotensin system plays a key role in regulating blood pressure, which has motivated many investigations of associated mouse models of hypertensive arterial remodelling. Such studies typically focus on histological and cell biological changes, not wall mechanics. This study explores tissue-level ramifications of chronic angiotensin II infusion in wild-type (WT) and type 1b angiotensin II (AngII) receptor null (Agtr1b -/-) mice. Biaxial biomechanical and immunohistological changes were quantified and compared in the thoracic and abdominal aorta in these mice following 14 and 28 days of angiotensin II infusion. Preliminary results showed that changes were largely independent of sex. Associated thickening and stiffening of the aortic wall in male mice differed significantly between thoracic and abdominal regions and between genotypes. Notwithstanding multiple biomechanical changes in both WT and Agtr1b -/- mice, AngII infusion caused distinctive wall thickening and inflammation in the descending thoracic aorta of WT, but not Agtr1b -/-, mice. Our study underscores the importance of exploring differential roles of receptor-dependent angiotensin II signalling along the aorta and its influence on distinct cell types involved in regional histomechanical remodelling. Disrupting the AT1b receptor primarily affected inflammatory cell responses and smooth muscle contractility, suggesting potential therapeutic targets.

Experimental Protocols to Test Aortic Soft Tissues: A Systematic Review

Experimental protocols are fundamental for quantifying the mechanical behaviour of soft tissue. These data are crucial for advancing the understanding of soft tissue mechanics, developing and calibrating constitutive models, and informing the development of more accurate and predictive computational simulations and artificial intelligence tools. This paper offers a comprehensive review of experimental tests conducted on soft aortic tissues, employing the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology, based on the Scopus, Web of Science, IEEE, Google Scholar and PubMed databases. This study includes a detailed overview of the test method protocols, providing insights into practical methodologies, specimen preparation and full-field measurements. The review also briefly discusses the post-processing methods applied to extract material parameters from experimental data. In particular, the results are analysed and discussed providing representative domains of stress-strain curves for both uniaxial and biaxial tests on human aortic tissue.

Multiscale insights into postnatal aortic development

Despite its vital importance for establishing proper cardiovascular function, the process through which the vasculature develops and matures postnatally remains poorly understood. From a clinical perspective, an ability to mechanistically model the developmental time course in arteries and veins, as well as to predict how various pathologies and therapeutic interventions alter the affected vessels, promises to improve treatment strategies and long-term clinical outcomes, particularly in pediatric patients suffering from congenital heart defects. In the present study, we conducted a multiscale investigation into the postnatal development of the murine thoracic aorta, examining key allometric relations as well as relationships between in vivo mechanical stresses, collagen and elastin expression, and the gradual accumulation of load-bearing constituents within the aortic wall. Our findings suggest that the production of fibrillar collagens in the developing aorta associates strongly with the ratio of circumferential stresses between systole and diastole, hence emphasizing the importance of a pulsatile mechanobiological stimulus. Moreover, rates of collagen turnover and elastic fiber compaction can be inferred directly by synthesizing transcriptional data and quantitative histological measurements of evolving collagen and elastin content. Consistent with previous studies, we also observed that wall shear stresses acting on the aorta are similar at birth and in maturity, supporting the hypothesis that at least some stress targets are established early in development and maintained thereafter, thus providing a possible homeostatic basis to guide future experiments and inform future predictive modeling.

Need for transverse strain data for fitting constitutive models of arterial tissue to uniaxial tests

The study deals with the process of estimation of material parameters from uniaxial test data of arterial tissue and focuses on the role of transverse strains. Two fitting strategies are analyzed and their impact on the predictive and descriptive capabilities of the resulting model is evaluated. The standard fitting procedure (strategy A) based on longitudinal stress-strain curves is compared with the enhanced approach (strategy B) taking also the transverse strain test data into account. The study is performed on a large set of material data adopted from literature and for a variety of constitutive models developed for fibrous soft tissues. The standard procedure (A) ignoring the transverse strain test data is found rather hazardous, leading often to unrealistic predictions of the model exhibiting auxetic behaviour. In contrast, the alternative fitting method (B) ensures a realistic strain response of the model and is proved to be superior since it does not require any significant demands of computational effort or additional testing. The results presented in this paper show that even the artificial transverse strain data (i.e., not measured during testing but generated ex post based on assumed Poisson's ratio) are much less hazardous than total disregard of the transverse strain response.

MATLAB-Based Algorithm and Software for Analysis of Wavy Collagen Fibers

Knowledge of soft tissue fiber structure is necessary for accurate characterization and modeling of their mechanical response. Fiber configuration and structure informs both our understanding of healthy tissue physiology and of pathological processes resulting from diseased states. This study develops an automatic algorithm to simultaneously estimate fiber global orientation, abundance, and waviness in an investigated image. To our best knowledge, this is the first validated algorithm which can reliably separate fiber waviness from its global orientation for considerably wavy fibers. This is much needed feature for biological tissue characterization. The algorithm is based on incremental movement of local regions of interest (ROI) and analyzes two-dimensional images. Pixels belonging to the fiber are identified in the ROI, and ROI movement is determined according to local orientation of fiber within the ROI. The algorithm is validated with artificial images and ten images of porcine trachea containing wavy fibers. In each image, 80-120 fibers were tracked manually to serve as verification. The coefficient of determination R2 between curve lengths and histograms documenting the fiber waviness and global orientation were used as metrics for analysis. Verification-confirmed results were independent of image rotation and degree of fiber waviness, with curve length accuracy demonstrated to be below 1% of fiber curved length. Validation-confirmed median and interquartile range of R2, respectively, were 0.90 and 0.05 for curved length, 0.92 and 0.07 for waviness, and 0.96 and 0.04 for global orientation histograms. Software constructed from the proposed algorithm was able to track one fiber in about 1.1 s using a typical office computer. The proposed algorithm can reliably and accurately estimate fiber waviness, curve length, and global orientation simultaneously, moving beyond the limitations of prior methods.

Remodeling of the uterine artery during and early after pregnancy in the mouse

Pregnancy associates with dramatic changes in maternal cardiovascular physiology that ensure that the utero-placental circulation can support the developing fetus. Particularly striking is the marked flow-induced remodeling of uterine arteries during pregnancy and their recovery following birth. Whereas details are available in the literature on alterations in hemodynamics within and changes in the dimensions of uterine arteries during and following pregnancy in mice, we report here the first biaxial biomechanical phenotyping of these arteries during this dynamic period of growth and remodeling (G&R). To gain additional insight into the measured G&R, we also use a computational constrained mixture model to describe and predict findings, including simulations related to complications that may arise during pregnancy. It is found that dramatic pregnancy-induced remodeling of the uterine artery is largely, but not completely, reversed in the postpartum period, which appears to be driven by increases in collagen turnover among other intramural changes. By contrast, data on the remodeling of the ascending aorta, an elastic artery, reveal modest changes that are fully recovered postpartum. There is strong motivation to continue biomechanical studies on this critical aspect of women's health, which has heretofore not received appropriate consideration from the biomechanics community.

Effects of Age, Sex, and Extracellular Matrix Integrity on Aortic Dilatation and Rupture in a Mouse Model of Marfan Syndrome

BACKGROUND

Transmural failure of the aorta is responsible for substantial morbidity and mortality; it occurs when mechanical stress exceeds strength. The aortic root and ascending aorta are susceptible to dissection and rupture in Marfan syndrome, a connective tissue disorder characterized by a progressive reduction in elastic fiber integrity. Whereas competent elastic fibers endow the aorta with compliance and resilience, cross-linked collagen fibers confer stiffness and strength. We hypothesized that postnatal reductions in matrix cross-linking increase aortopathy when turnover rates are high.

METHODS

We combined ex vivo biaxial mechanical testing with multimodality histological examinations to quantify expected age- and sex-dependent structural vulnerability of the ascending aorta in Fbn1C1041G/+ Marfan versus wild-type mice without and with 4-week exposures to β-aminopropionitrile, an inhibitor of lysyl oxidase-mediated cross-linking of newly synthesized elastic and collagen fibers.

RESULTS

We found a strong β-aminopropionitrile-associated sexual dimorphism in aortic dilatation in Marfan mice and aortic rupture in wild-type mice, with dilatation correlating with compromised elastic fiber integrity and rupture correlating with compromised collagen fibril organization. A lower incidence of rupture of β-aminopropionitrile-exposed Marfan aortas associated with increased lysyl oxidase, suggesting a compensatory remodeling of collagen that slows disease progression in the otherwise compromised Fbn1C1041G/+ aorta.

CONCLUSIONS

Collagen fiber structure and function in the Marfan aorta are augmented, in part, by increased lysyl oxidase in female and especially male mice, which improves structural integrity, particularly via fibrils in the adventitia. Preserving or promoting collagen cross-linking may represent a therapeutic target for an otherwise vulnerable aorta.

Biomechanical and transcriptional evidence that smooth muscle cell death drives an osteochondrogenic phenotype and severe proximal vascular disease in progeria

Hutchinson-Gilford Progeria Syndrome results in rapid aging and severe cardiovascular sequelae that accelerate near end-of-life. We found a progressive disease process in proximal elastic arteries that was less evident in distal muscular arteries. Changes in aortic structure and function were then associated with changes in transcriptomics assessed via both bulk and single cell RNA sequencing, which suggested a novel sequence of progressive aortic disease: adverse extracellular matrix remodeling followed by mechanical stress-induced smooth muscle cell death, leading a subset of remnant smooth muscle cells to an osteochondrogenic phenotype that results in an accumulation of proteoglycans that thickens the aortic wall and increases pulse wave velocity, with late calcification exacerbating these effects. Increased central artery pulse wave velocity is known to drive left ventricular diastolic dysfunction, the primary diagnosis in progeria children. It appears that mechanical stresses above ~ 80 kPa initiate this progressive aortic disease process, explaining why elastic lamellar structures that are organized early in development under low wall stresses appear to be nearly normal whereas other medial constituents worsen progressively in adulthood. Mitigating early mechanical stress-driven smooth muscle cell loss/phenotypic modulation promises to have important cardiovascular implications in progeria patients.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

Low cycle fatigue properties of porcine aorta - Pilot study

INTRODUCTION

Biomechanical rupture risk assessment of aortic tissues is commonly based on computed stress to measured uniaxial static strength comparison. Loading of the arterial wall, however, is cyclic; thus, the static strength may not be a proper limit value. This study investigates the low cycle fatigue of porcine aortic samples tested in a circumferential direction.

METHODS

7 porcine descending aorta (both thoracic and abdominal) were harvested and 56 dogbone-shaped samples were prepared. Static strength was measured, the limit of engineering stress was chosen and then force controlled cyclic loading was performed up to 100,000 cycles. Efforts were made to obtain a sufficient number of points across the entire range of 0-100,000 cycles. Data were fitted by both linear and logarithmic law and extrapolated towards 1 cycle for validation against static strength/ultimate tension. Data dispersion was evaluated via normalised root mean square error.

RESULTS

Out of 56 samples from 7pigs, 28 samples from 4 pigs were successfully tested. There was a strong negative correlation between applied stress/tension and number of cycles to failure. The fitting of both linear and logarithmic values resulted in a similar accuracy (R²=0.72 and 0.71 for stress and R²=0.62 and 0.7 for tension, respectively), while predicting static failure properties was more accurate by logarithmic law. NRMSE was lower for absolute values (20-21%) than for relative values (27-30%).

CONCLUSIONS

Absolute values of cyclic strength and tension are less dispersed than relative ones. Logarithmic fits are more robust in predicting static strength from cyclic data, while linear fits serve as a lower limit estimation.

New Computational Approach to Shunt Design in Congenital Heart Palliation

Shunts are commonly used to redirect blood to pulmonary arteries in procedures that palliate congenital cardiovascular defects. Previous clinical studies and hemodynamic simulations reveal a critical role of shunt diameter in balancing flow to pulmonary versus systemic vessels, but the biomechanical process of creating the requisite anastomosis between the shunt and host vessel has received little attention. Here, we report a new Lagrange multiplier-based finite element approach that represents the shunt and host vessels as individual structures and predicts the anastomosis geometry and attachment force that result when the shunt is sutured at an incision in the host, followed by pressurization. Simulations suggest that anastomosis orifice opening increases markedly with increasing length of the host incision and moderately with increasing blood pressure. The host artery is further predicted to conform to common stiff synthetic shunts, whereas more compliant umbilical vessel shunts should conform to the host, with orifice area transitioning between these two extremes via a Hill-type function of shunt stiffness. Moreover, a direct relationship is expected between attachment forces and shunt stiffness. This new computational approach promises to aid in surgical planning for diverse vascular shunts by predicting in vivo pressurized geometries.

The multiscale characterization and constitutive modeling of healthy and type 2 diabetes mellitus Sprague Dawley rat skin

In type 2 diabetes mellitus (T2DM), elevated glucose level impairs the biochemistry of the skin which may result in alteration of its mechanical and structural properties. The several aspects of structural and mechanical changes in skin due to T2DM remain poorly understood. To fill these research gaps, we developed a non-obese T2DM rat (Sprague Dawley (SD)) model for investigating the effect of T2DM on the in vivo strain stress state, mechanical and structural properties of skin. In vivo strain and mechanical anisotropy of healthy and T2DM skin were measured using the digital imaging correlation (DIC) technique and DIC coupled bulge experiment, respectively. Fluorescence microscopy and histology were used to assess the collagen and elastin fibers microstructure whereas nanoscale structure was captured through atomic force microscopy (AFM). Based on the microstructural observations, skin was modeled as a multilayer membrane where in and out of plane distribution of collagen fibers and planar distribution of elastin fibers were cast in constitutive model. Further, the state of in vivo stresses of healthy and T2DM were measured using model parameters and in vivo strain in the constitutive model. The results showed that T2DM causes significant loss in in vivo stresses (p < 0.01) and increase in anisotropy (p < 0.001) of skin. These changes were found in good correlation with T2DM associated alteration in skin microstructure. Statistical analysis emphasized that increase in blood glucose concentration (HbA1c) was the main cause of impaired biomechanical properties of skin. The presented data in this study can help to understand the skin pathology and to simulate the skin related clinical procedures. STATEMENT OF SIGNIFICANCE: Our study is significant as it presents findings related to the effect of T2DM on the physiologic stress strain, structural and mechanical response of SD rat skin. In this study, we developed a non-obese T2DM SD rat model which mimics the phenotype of Asian type 2 diabetics (non-obese). Several structural and mechanical characterization techniques were explored for multiscale characterization of healthy and T2DM skin. Further, based on microstructural information, we presented the constitutive models that incorporate the real microstructure of skin. The presented results can be helpful to simulate the realistic mechanical response of skin during various clinical trials.

Importance of experimental evaluation of structural parameters for constitutive modelling of aorta

The study compares stresses and strains in the aortic wall derived using different constitutive models for various stress-strain conditions. Structure-based constitutive models with two fibre families with (GOH) and without (HGO) dispersion of collagen fibres are compared. The constitutive models were fitted to data from equibiaxial tension tests of two separated layers of the porcine aortic wall. The initial fit was evaluated with unrestricted parameters and subsequently, the mean angles of the fibre families and the angular dispersion were fixed to the values obtained from histology. Surprisingly, none of the tested models was capable to provide a good quality fit with histologically obtained structural parameters. Fitting the HGO model to experimental data resulted in two fibre families under angles close to ±45°, while the GOH model resulted in a nearly isotropic fibre distribution. These results indicate that both of these models suffer from the absence of isotropic strain stiffening. After having modified both models with corresponding additional members based on the Yeoh model of matrix, we obtained a perfect fit to the measured data while keeping the structural histology-based parameters. Finally, significant differences in compliance and resulting stresses and strains between different models are shown by means of simulations of uniaxial tension test, equibiaxial tension tests and inflation of the aorta.

Smooth Muscle Cell Death Drives an Osteochondrogenic Phenotype and Severe Proximal Vascular Disease in Progeria

Hutchinson-Gilford Progeria Syndrome results in rapid aging and severe cardiovascular sequelae that accelerate near end of life. We associate progressive deterioration of arterial structure and function with single cell transcriptional changes, which reveals a rapid disease process in proximal elastic arteries that largely spares distal muscular arteries. These data suggest a novel sequence of progressive vascular disease in progeria: initial extracellular matrix remodeling followed by mechanical stress-induced smooth muscle cell death in proximal arteries, leading a subset of remnant smooth muscle cells to an osteochondrogenic phenotypic modulation that results in an accumulation of proteoglycans that thickens the wall and increases pulse wave velocity, with late calcification exacerbating these effects. Increased pulse wave velocity drives left ventricular diastolic dysfunction, the primary diagnosis in progeria children. Mitigating smooth muscle cell loss / phenotypic modulation promises to have important cardiovascular implications in progeria patients.

Region-dependent mechanical characterization of porcine thoracic aorta with a one-to-many correspondence method to create virtual datasets using uniaxial tensile tests

The simulation of the cardiovascular system and in silico clinical trials have garnered attention in the biomedical engineering field. Physics-based modeling is essential to associate with physical and clinical features. In physics-based constitutive modeling, the identification of the parameters and estimation of their ranges based on appropriate experiments are required. Uniaxial tests are commonly used in the field of vascular mechanics, but they have limitations in fully characterizing the regional mechanical behavior of the aorta. Therefore, this study is aimed at identifying a method to integrate constitutive models with experimental data to elucidate regional aortic behavior. To create a virtual two-dimensional dataset, a pair of uniaxial experimental datasets in the longitudinal and circumferential directions was combined using a one-to-many correspondence method such as bootstrap aggregation. The proposed approach is subsequently applied to three constitutive models, i.e., the Fung model, Holzapfel model, and constrained mixture model, to estimate the material parameters based on the four test regions of the porcine thoracic aorta. Finally, the regional difference in the mechanical behavior of the aorta, the correlation between the experimental characteristics and model parameters, and the inter-correlation of the material parameters are confirmed. This integrative approach will enhance the prediction capability of the model with respect to the regions of the aorta.

G2Φnet: Relating genotype and biomechanical phenotype of tissues with deep learning

Many genetic mutations adversely affect the structure and function of load-bearing soft tissues, with clinical sequelae often responsible for disability or death. Parallel advances in genetics and histomechanical characterization provide significant insight into these conditions, but there remains a pressing need to integrate such information. We present a novel genotype-to-biomechanical phenotype neural network (G2Φnet) for characterizing and classifying biomechanical properties of soft tissues, which serve as important functional readouts of tissue health or disease. We illustrate the utility of our approach by inferring the nonlinear, genotype-dependent constitutive behavior of the aorta for four mouse models involving defects or deficiencies in extracellular constituents. We show that G2Φnet can infer the biomechanical response while simultaneously ascribing the associated genotype by utilizing limited, noisy, and unstructured experimental data. More broadly, G2Φnet provides a powerful method and a paradigm shift for correlating genotype and biomechanical phenotype quantitatively, promising a better understanding of their interplay in biological tissues.

Predicting and understanding arterial elasticity from key microstructural features by bidirectional deep learning

Microstructural features and mechanical properties are closely related in all soft biological tissues. Both yet exhibit considerable inter-individual differences and are affected by factors such as aging and disease and its progression. Histological analysis, modern in situ imaging, and biomechanical testing have deepened our understanding of these complex interrelations, yet two key questions remain: (1) Given the specific microstructure, can one predict the macroscopic mechanical properties without mechanical testing? (2) Can one quantify individual contributions of the different microstructural features to the macroscopic mechanical properties in an automated, systematic and largely unbiased way? Here we propose a bidirectional deep learning architecture to address these two questions. Our architecture uses data from standard histological analyses, two-photon microscopy and biaxial biomechanical testing. Its capabilities are demonstrated by predicting with high accuracy (R²=0.92) the evolving mechanical properties of the murine aorta during maturation and aging. Moreover, our architecture reveals that the extracellular matrix composition and organization are the most prominent factors governing the macroscopic mechanical properties of the tissues studied herein. STATEMENT OF SIGNIFICANCE:  .

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Experimental Investigation of the Anisotropic Mechanical Response of the Porcine Thoracic Aorta

Knowledge of the mechanical properties of blood vessels and determining appropriate constitutive relations are essential in developing methodologies for accurate prognosis of vascular diseases. We examine the directional variation of the mechanical properties of the porcine thoracic aorta by performing uniaxial extension tests on dumbbell-shaped specimens cut at five different orientations with respect to the circumferential direction of the aorta. Specimens in all the orientations considered exhibit a nonlinear constitutive response that is typical of collagenous soft tissues. Shear strain under uniaxial extension demonstrates clearly discernible anisotropy of the mechanical response of the porcine aorta, and samples oriented at 45[Formula: see text] and 60[Formula: see text] with respect to the circumferential direction show a peculiar crescent-shaped shear strain-nominal stretch response not displayed by axial and circumferential specimens. Failure stress indicates decreasing tensile strength of the porcine aortic wall from the circumferential direction to the longitudinal direction. Furthermore, we determine the material parameters for the four-fiber-family and Gasser-Holzapfel-Ogden models from the mechanical response data of the circumferential and longitudinal specimens. It is shown how the material parameters derived from the uniaxial tests on circumferential and longitudinal specimens are insufficient to characterize the response of off-axis specimens.

On the Role and Effects of Uncertainties in Cardiovascular in silico Analyses

The assessment of cardiovascular hemodynamics with computational techniques is establishing its fundamental contribution within the world of modern clinics. Great research interest was focused on the aortic vessel. The study of aortic flow, pressure, and stresses is at the basis of the understanding of complex pathologies such as aneurysms. Nevertheless, the computational approaches are still affected by sources of errors and uncertainties. These phenomena occur at different levels of the computational analysis, and they also strongly depend on the type of approach adopted. With the current study, the effect of error sources was characterized for an aortic case. In particular, the geometry of a patient-specific aorta structure was segmented at different phases of a cardiac cycle to be adopted in a computational analysis. Different levels of surface smoothing were imposed to define their influence on the numerical results. After this, three different simulation methods were imposed on the same geometry: a rigid wall computational fluid dynamics (CFD), a moving-wall CFD based on radial basis functions (RBF) CFD, and a fluid-structure interaction (FSI) simulation. The differences of the implemented methods were defined in terms of wall shear stress (WSS) analysis. In particular, for all the cases reported, the systolic WSS and the time-averaged WSS (TAWSS) were defined.

Mechanical properties of whole-body soft human tissues: a review

The mechanical properties of soft tissues play a key role in studying human injuries and their mitigation strategies. While such properties are indispensable for computational modelling of biological systems, they serve as important references in loading and failure experiments, and also for the development of tissue simulants. To date, experimental studies have measured the mechanical properties of peripheral tissues (e.g. skin)in-vivoand limited internal tissuesex-vivoin cadavers (e.g. brain and the heart). The lack of knowledge on a majority of human tissues inhibit their study for applications ranging from surgical planning, ballistic testing, implantable medical device development, and the assessment of traumatic injuries. The purpose of this work is to overcome such challenges through an extensive review of the literature reporting the mechanical properties of whole-body soft tissues from head to toe. Specifically, the available linear mechanical properties of all human tissues were compiled. Non-linear biomechanical models were also introduced, and the soft human tissues characterized using such models were summarized. The literature gaps identified from this work will help future biomechanical studies on soft human tissue characterization and the development of accurate medical models for the study and mitigation of injuries.

Evolving structure-function relations during aortic maturation and aging revealed by multiphoton microscopy

The evolving microstructure and mechanical properties that promote homeostasis in the aorta are fundamental to age-specific adaptations and disease progression. We combine ex vivo multiphoton microscopy and biaxial biomechanical phenotyping to quantify and correlate layer-specific microstructural parameters, for the primary extracellular matrix components (fibrillar collagen and elastic lamellae) and cells (endothelial, smooth muscle, and adventitial), with mechanical properties of the mouse aorta from weaning through natural aging up to one year. The aging endothelium was characterized by progressive reductions in cell density and altered cellular orientation. The media similarly showed a progressive decrease in smooth muscle cell density and alignment though with inter-lamellar widening from intermediate to older ages, suggesting cell hypertrophy, matrix accumulation, or both. Despite not changing in tissue thickness, the aging adventitia exhibited a marked thickening and straightening of collagen fiber bundles and reduction in cell density, suggestive of age-related remodeling not growth. Multiple microstructural changes correlated with age-related increases in circumferential and axial material stiffness, among other mechanical metrics. Because of the importance of aging as a risk factor for cardiovascular diseases, understanding the normal progression of structural and functional changes is essential when evaluating superimposed disease-related changes as a function of the age of onset.

Potential damage in pulmonary arterial hypertension: An experimental study of pressure-induced damage of pulmonary artery

Pulmonary arterial hypertension (PAH) is associated with elevated pulmonary arterial pressure. PAH prognosis remains poor with a 15% mortality rate within 1 year, even with modern clinical management. Previous clinical studies proposed wall shear stress (WSS) to be an important hemodynamic factor affecting cell mechanotransduction, growth and remodeling, and disease progress in PAH. However, WSS in vivo is typically at most 2.5 Pa and a doubt has been cast whether WSS alone can drive disease progress. Furthermore, our current understanding of PAH pathology largely comes from small animals' studies in which caliber enlargement, a hallmark of PAH in humans, is rarely reported. Therefore, a large-animal experiment on pulmonary arteries (PAs) is needed to validate whether increased pressure can induce enlargement of PAs caliber. In this study, we use an inflation testing device to characterize the mechanical behavior, both nonlinear elastic behavior and irreversible damage of porcine arteries. The parameters of elastic behavior are estimated from the inflation test at a low-pressure range before and after over-pressurization. Then, histological images are qualitatively examined for medial and adventitial layers. This study sheds light on the relevance of pressure-induced damage mechanism in human PAH.

Sources of inconsistency in mean mechanical response of abdominal aortic aneurysm tissue

INTRODUCTION

There is a striking difference in the reported mean response of abdominal aortic aneurysm tissue in academic literature depending on the type of tests (uniaxial vs biaxial) performed. In this paper, the hypothesis variability caused by differences in experimental protocols is explored using porcine aortic tissue as a substitute for aneurysmal tissue.

METHODS

Nine samples of porcine aorta were created and both uniaxial and biaxial tests were performed. Three effects were investigated. (i) Effect of sample (non) preconditioning, (ii) effect of objective function used (normalised vs non-normalised), and (iii) effect of chosen procedure used for mean response calculation: constant averaging (CA) vs fit to averaged response (FAR) vs fit to all data (FAD). Both the overall shape of mean curve and mean initial stiffness were compared.

RESULTS

(i) Non-preconditioning led to a much stiffer response, and initial stiffness was about three times higher for a non-preconditioned response based on uniaxial data compared to a preconditioned biaxial response. (ii) CA led to a much stiffer response compared to FAR and FAD procedures which gave similar results. (iii) Normalised objective function produced a mean response with six times lower initial stiffness and more pronounced nonlinearity compared to non-normalised objective function.

DISCUSSION

It is possible to reproduce a mechanically inconsistent response purely by using the chosen experimental protocol. Non-preconditioned data from failure tests should be used for FE simulation of the elastic response of aneurysms. CA should not be used to obtain a mean response.

A generic physics-informed neural network-based constitutive model for soft biological tissues

Constitutive modeling is a cornerstone for stress analysis of mechanical behaviors of biological soft tissues. Recently, it has been shown that machine learning (ML) techniques, trained by supervised learning, are powerful in building a direct linkage between input and output, which can be the strain and stress relation in constitutive modeling. In this study, we developed a novel generic physics-informed neural network material (NNMat) model which employs a hierarchical learning strategy by following the steps: (1) establishing constitutive laws to describe general characteristic behaviors of a class of materials; (2) determining constitutive parameters for an individual subject. A novel neural network structure was proposed which has two sets of parameters: (1) a class parameter set for characterizing the general elastic properties; and (2) a subject parameter set (three parameters) for describing individual material response. The trained NNMat model may be directly adopted for a different subject without re-training the class parameters, and only the subject parameters are considered as constitutive parameters. Skip connections are utilized in the neural network to facilitate hierarchical learning. A convexity constraint was imposed to the NNMat model to ensure that the constitutive model is physically relevant. The NNMat model was trained, cross-validated and tested using biaxial testing data of 63 ascending thoracic aortic aneurysm tissue samples, which was compared to expert-constructed models (Holzapfel-Gasser-Ogden, Gasser-Ogden-Holzapfel, and four-fiber families) using the same fitting and testing procedure. Our results demonstrated that the NNMat model has a significantly better performance in both fitting (R² value of 0.9632 vs 0.9019, p=0.0053) and testing (R² value of 0.9471 vs 0.8556, p=0.0203) than the Holzapfel-Gasser-Ogden model. The proposed NNMat model provides a convenient and general methodology for constitutive modeling.

Failure properties of abdominal aortic aneurysm tissue are orientation dependent

INTRODUCTION

Biomechanical rupture risk assessment of abdominal aortic aneurysm (AAA) requires information about failure properties of aneurysmal tissue. There are large differences between reported values. Among others, studies vary in using either axially or circumferentially oriented samples. This study investigates the effect of sample orientation on failure properties.

METHODS

Aneurysmal tissues from 45 patients (11 females) were harvested during open AAA repair, cut into uniaxial samples (90) and tested mechanically within 3 h. If possible, the samples were cut in both axial (49 samples) and circumferential (41 samples) directions. Wall thickness, First Piola-Kirchhoff strength P_ult and ultimate tension T_ult were recorded. Influence of sample orientation and other clinical parameters were investigated using non parametric tests.

RESULTS

Medians of P_ult (values 1100 kPa for circumferential vs. 715 kPa for axial direction, p < 10^-4) and T_ult (17.4 N/cm in circumferential vs. 11.2 N/cm in axial direction, p < 10^-4) were significantly higher in circumferential direction. For paired data, the median of difference was 411 kPa (p < 10^-3) in P_ult and 7.4 N/cm (p < 10^-4) in T_ult in favor of circumferential direction.

CONCLUSIONS

In this first study of anisotropy in AAA wall failure properties using paired comparisons, the strength in circumferential orientation was found to be higher than in axial orientation.

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Characterization of chemoelastic effects in arteries using digital volume correlation and optical coherence tomography

Understanding stress-strain relationships in arteries is important for fundamental investigations in mechanobiology. Here we demonstrate the essential role of chemoelasticity in determining the mechanical properties of arterial tissues. Stepwise stress-relaxation uniaxial tensile tests were carried out on samples of porcine thoracic aortas immersed in a hyperosmotic solution. The tissue deformations were tracked using optical coherence tomography (OCT) during the tensile tests and digital volume correlation (DVC) was used to obtain measurements of depth-resolved strains across the whole thickness of the tested aortas. The hyperosmotic solution exacerbated chemoelastic effects, and we were able to measure different manifestations of these chemoelastic effects: swelling of the media inducing a modification of its optical properties, and existence of a transverse tensile strain. For the first time ever to our best knowledge, 3D strains induced by chemoelastic effects in soft tissues were quantified thanks to the OCT-DVC method. Without doubt, chemoelasticity plays an essential role in arterial mechanobiology in vivo and future work should focus on characterizing chemoelastic effects in arterial walls under physiological and disease conditions. STATEMENT OF SIGNIFICANCE: Chemoelasticity, coupling osmotic phenomena and mechanical stresses, is essential in soft tissue mechanobiology. For the first time ever, we measure and analyze 3D strain fields induced by these chemoelastic effects thanks to the unique combination of OCT imaging and digital volume correlation.

On the optimal choice of a hyperelastic model of ruptured and unruptured cerebral aneurysm

In the last decade, preoperative modelling of the treatment of cerebral aneurysms is being actively developed. Fluid-structure interaction problem is a key point of a such modelling. Hence arises the question about the reasonable choice of the model of the vessel and aneurysm wall material to build the adequate model from the physical point of view. This study covers experimental investigation of 8 tissue samples of cerebral aneurysms and 1 tissue sample of a healthy cerebral artery. Results on statistical significance in ultimate stress for the classification of 2 cohorts of aneurysms: ruptured and unruptured described earlier in the literature were confirmed (p ≤ 0.01). We used the four most common models of hyperelastic material: Yeoh, Neo-Hookean and Mooney-Rivlin (3 and 5 parameter) models to describe the experimental data. In this study for the first time, we obtained a classification of hyperelastic models of cerebral aneurysm tissue, which allows to choose the most appropriate model for the simulation problems requirements depending on the physical interpretation of the considered problem: aneurysm status and range of deformation.

Arterial Stiffness: Different Metrics, Different Meanings

Findings from basic science and clinical studies agree that arterial stiffness is fundamental to both the mechanobiology and the biomechanics that dictate vascular health and disease. There is, therefore, an appropriately growing literature on arterial stiffness. Perusal of the literature reveals, however, that many different methods and metrics are used to quantify arterial stiffness, and reported values often differ by orders of magnitude and have different meanings. Without clear definitions and an understanding of possible inter-relations therein, it is increasingly difficult to integrate results from the literature to glean true understanding. In this paper, we briefly review methods that are used to infer values of arterial stiffness that span studies on isolated cells, excised intact vessels, and clinical assessments. We highlight similarities and differences and identify a single theoretical approach that can be used across scales and applications and thus could help to unify future results. We conclude by emphasizing the need to move toward a synthesis of many disparate reports, for only in this way will we be able to move from our current fragmented understanding to a true appreciation of how vascular cells maintain, remodel, or repair the arteries that are fundamental to cardiovascular properties and function.

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.

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Clinical assessment of arterial stiffness relies on noninvasive measurements of regional pulse wave velocity or local distensibility. However, arterial stiffness measures do not discriminate underlying changes in arterial wall constituent properties (e.g., in collagen, elastin, or smooth muscle), which is highly relevant for development and monitoring of treatment. In arterial stiffness in recent clinical-epidemiological studies, we systematically review clinical-epidemiological studies (2012–) that interpreted arterial stiffness changes in terms of changes in arterial wall constituent properties (63 studies included of 514 studies found). Most studies that did so were association studies (52 of 63 studies) providing limited causal evidence. Intervention studies (11 of 63 studies) addressed changes in arterial stiffness through the modulation of extracellular matrix integrity (5 of 11 studies) or smooth muscle tone (6 of 11 studies). A handful of studies (3 of 63 studies) used mathematical modeling to discriminate between extracellular matrix components. Overall, there exists a notable gap in the mechanistic interpretation of stiffness findings. In constitutive model-based interpretation, we first introduce constitutive-based modeling and use it to illustrate the relationship between constituent properties and stiffness measurements (“forward” approach). We then review all literature on modeling approaches for the constitutive interpretation of clinical arterial stiffness data (“inverse” approach), which are aimed at estimation of constitutive properties from arterial stiffness measurements to benefit treatment development and monitoring. Importantly, any modeling approach requires a tradeoff between model complexity and measurable data. Therefore, the feasibility of changing in vivo the biaxial mechanics and/or vascular smooth muscle tone should be explored. The effectiveness of modeling approaches should be confirmed using uncertainty quantification and sensitivity analysis. Taken together, constitutive modeling can significantly improve clinical interpretation of arterial stiffness findings.

Biomechanical characterization of murine pulmonary arteries

The biomechanical properties of the major pulmonary arteries play critical roles in normal physiology as well as in diverse pathophysiologies and clinical interventions. Importantly, advances in medical imaging enable simulations of pulmonary hemodynamics, but such models cannot reach their full potential until they are informed with region-specific material properties. In this paper, we present passive and active biaxial biomechanical data for the right and left main pulmonary arteries from wild-type mice. We also evaluate the suitability of a four-fiber family constitutive model as a descriptor of the passive behavior. Despite regional differences in size, the biaxial mechanical properties, including passive stiffness and elastic energy storage, the biaxial wall stresses at in vivo pressures, and the overall contractile capacity in response to smooth muscle cell stimulation under in vivo conditions are remarkably similar between the right and left branches. The proposed methods and results can serve as baseline protocols and measurements for future biaxial experiments on murine models of pulmonary pathologies, and the constitutive model can inform computational models of normal pulmonary growth and remodeling. Our use of consistent experimental protocols and data analyses can also facilitate comparative studies in health and disease across the systemic and pulmonary circulations as well as studies seeking to understand remodeling in surgeries such as the Fontan procedure, which involves different types of vessels.

Magic angles and fibre stretch in arterial tissue: Insights from the linear theory

This work is motivated by the current widespread interest in modelling the mechanical response of arterial tissue. A widely used approach within the context of anisotropic nonlinear elasticity is to use an orthotropic incompressible hyperelasticity model which, in general, involves a strain-energy density that depends on seven independent invariants. The complexity of such an approach in its full generality is daunting and so a number of simplifications have been introduced in the literature to facilitate analytical tractability. An extremely popular model of this type is where the strain energy involves only three invariants. While such models and their generalisations have been remarkably successful in capturing the main features of the mechanical response of arterial tissue, it is generally acknowledged that such simplified models must also have some drawbacks. In particular, it is intuitively clear that the correlation of such models with experiment will suffer limitations due to the restricted number of invariants considered. Our purpose here is to use the linearised theory for infinitesimal deformations to provide some guidelines for the development of a more robust nonlinear theory. The linearised theory for incompressible orthotropic materials is developed and involves six independent elastic constants. The general stress-strain law is inverted to provide an expression for the fibre stretch in terms of the stress. We examine the linearised response for simple tension in two mutually perpendicular directions corresponding to the axial and circumferential directions in the artery, obtaining an explicit expression for the fibre stretch in terms of the applied tension, fibre angle and linear elastic constants. The focus is then on determining the range of fibre orientation angles that ensure that the fibres are in tension in these simple tension tests. It is shown that the fibre stretch is positive for both simple tension tests if and only if the fibre angle is restricted to lie between two special angles called generalised magic angles. For the special case where the strain-energy function for the nonlinear model depends only on the three invariants I₁,I₄,I₆, it is shown that the corresponding linearised model, called the standard linear model (SLM), depends on three elastic constants and the fibre stretch is positive only in the small range of fibre angles between the classic magic angles 35.26° and 54.74°. However, when the two additional invariants I₅,I₇ are included in the nonlinear strain energy so that the corresponding linear model involves four elastic constants, it is shown that the domain of fibre angle for which the stretch is positive is much larger and that the fibre stretch is monotonic with respect to the fibre angle in this range.