Biomechanical and histological characteristics of passive esophagus: Experimental investigation and comparative constitutive modeling

Information on the passive biomechanical properties of two-layered esophagus is still limited, although this would enhance our understanding of its physiology/pathophysiology and help to address problems in surgery, medical-device applications, and for the optimal design of prostheses. In this study, rabbit esophagi were excised and dissected into mucosa–submucosa and muscle layers that were submitted to histological quantification of elastin and collagen content and orientation, as well as to inflation-extension testing and geometrical analysis, i.e. delineation of the zero-stress state serving as a reference configuration for biomechanical analysis. The pressure–radius data of both layers displayed a monotonically rising slope with inflating pressure, unlike the sigma shape characterizing elastin-rich tissues, for which biphasic constitutive models were initially postulated. Three phenomenological expressions of strain-energy function (SEF), commonly appearing in soft-tissue biomechanics literature, were used in an attempt to model the pseudoelastic response of esophageal tissue, namely the exponential Fung-type SEF, and the combined neo-Hookean (isotropic) or quadratic (anisotropic) and exponential Fung-type SEF. Accurate fits were attained for the pressure–radius–force data, spanning a wide range of longitudinal stretch ratios, when using the exponential form; the biphasic SEFs failed to generate improved fits, being also over-parameterized. According to the calculated material parameters, mucosa–submucosa was stiffer than muscle in both directions, justified by our histological observation of increased collagen content in that layer, and tissue was stiffer longitudinally, substantiated by the increased elastin and collagen contents and their preferential alignment towards that direction. Our results demonstrate that the passive response of esophagus is best modeled with an exponential Fung-type SEF.     

Strain-energy function and three-dimensional stress distribution in esophageal biomechanics

Knowledge of the transmural stress and stretch fields in esophageal wall is necessary to quantify growth and remodeling, and the response to mechanically based clinical interventions or traumatic injury, but there are currently conflicting reports on this issue and the mechanical properties of intact esophagus have not been rigorously addressed. This paper offers multiaxial data on rabbit esophagus, warranted for proper identification of the 3D mechanical properties. The Fung-type strain-energy function was adopted to model our data for esophagus, taken as a thick-walled (1 or 2-layer) tubular structure subjected to inflation and longitudinal extension. Accurate predictions of the pressure–radius–force data were obtained using the 1-layer model, covering a broad range of extensions; the calculated material parameters indicated that intact wall was equally stiff as mucosa–submucosa, but stiffer than muscle in both principal axes, and tissue was stiffer longitudinally, concurring our histological findings (Stavropoulou et al., Journal of Biomechanics. 42 (2009) 2654–2663). Employing the material parameters of individual layers, with reference to their zero-stress state, a reasonable fit was obtained to the data for intact wall, modeled as a 2-layer tissue. Different from the stress distributions presented hitherto in the esophagus literature, consideration of residual stresses led to less dramatic homogenization of stresses under loading. Comparison of the 1- and 2-layer models of esophagus demonstrated that heterogeneity induced a more uniform distribution of residual stresses in each layer, a discontinuity in circumferential and longitudinal stresses at the interface among layers, and a considerable rise of stresses in mucosa, with a reduction in muscle.     

A strain energy function for arteries accounting for wall composition and structure

Identification of a Strain Energy Function (SEF) is used when describing the complex mechanical properties of soft biological tissues such as the arterial wall. Classic SEFs, such as the one proposed by Chuong and Fung (J. Biomech. Eng. 105(3) (1983) 268), have been mostly phenomenological and neglect the particularities of the wall structure. A more structural model was proposed by Holzapfel et al. (J. Elasticity 61 (2000) 1-48.) when they included the characteristic angle at which the collagen fibers are helically wrapped, resulting in an excellent SEF for applications such as finite element modeling. We have expanded upon the idea of structural SEFs by including not only the wavy nature of the collagen but also the fraction of both elastin and collagen contained in the media, which can be determined by histology. The waviness of the collagen is assumed to be distributed log-logistically. In order to evaluate this novel SEF, we have used it to fit experimental data from inflation-extension tests performed on rat carotids. We have compared the results of the fit to the SEFs of Choung and Fung and Holzapfel et al. The novel SEF is found to behave similarly to that of Holzapfel et al., both succeed in describing the typical S-shaped pressure-radius curves with comparable quality of fit. The parameters of the novel SEF obtained from the fitting, bearing the physical meaning of the elastic modulus of collagen, the elastic modulus of elastin, the collagen waviness, and the collagen fiber angle, were compared to experimental data and discussed.     

Role of elastin anisotropy in structural strain energy functions of arterial tissue

The vascular wall exhibits nonlinear anisotropic mechanical properties. The identification of a strain energy function (SEF) is the preferred method to describe its complex nonlinear elastic properties. Earlier constituent-based SEF models, where elastin is modeled as an isotropic material, failed in describing accurately the tissue response to inflation–extension loading. We hypothesized that these shortcomings are partly due to unaccounted anisotropic properties of elastin. We performed inflation–extension tests on common carotid of rabbits before and after enzymatic degradation of elastin and applied constituent-based SEFs, with both an isotropic and an anisotropic elastin part, on the experimental data. We used transmission electron microscopy (TEM) and serial block-face scanning electron microscopy (SBFSEM) to provide direct structural evidence of the assumed anisotropy. In intact arteries, the SEF including anisotropic elastin with one family of fibers in the circumferential direction fitted better the inflation–extension data than the isotropic SEF. This was supported by TEM and SBFSEM imaging, which showed interlamellar elastin fibers in the circumferential direction. In elastin-degraded arteries, both SEFs succeeded equally well in predicting anisotropic wall behavior. In elastase-treated arteries fitted with the anisotropic SEF for elastin, collagen engaged later than in intact arteries. We conclude that constituent-based models with an anisotropic elastin part characterize more accurately the mechanical properties of the arterial wall when compared to models with simply an isotropic elastin. Microstructural imaging based on electron microscopy techniques provided evidence for elastin anisotropy. Finally, the model suggests a later and less abrupt collagen engagement after elastase treatment.     

The effects of aneurysm on the biaxial mechanical behavior of human abdominal aorta

The biomechanical response of normal and pathologic human abdominal aortic tissue to uniaxial loading conditions is insufficient for the characterization of its three-dimensional (3D) mechanical behavior. Planar biaxial mechanical evaluation allows for 3D constitutive modeling of nearly incompressible tissues, as well as the investigation of the nature of mechanical anisotropy. In the current study, 26 abdominal aortic aneurysm (AAA) tissue samples and 8 age-matched (> 60 years of age) nonaneurysmal abdominal aortic (AA) tissue samples were obtained and tested using a tension-controlled biaxial testing protocol. Graphical response functions (Sun et al., 2003. J. Biomech. Eng. 125, 372-380) were used as a guide to describe the pseudo-elastic response of AA and AAA. Based on the observed pseudo-elastic response, a four-parameter exponential strain energy function developed by Vito (1990. J. Biomech. Eng. 112, 153-159) was used from which both an individual specimen and group material parameter sets were determined for both AA and AAA. Peak Green strain values in the circumferential (Ethetatheta,max) and longitudinal (ELL,max) directions under an equibiaxial tension of 120 N/m were also compared. The strain energy function fit all of the individual specimens well with an average R2 of 0.95 +/- 0.02 and 0.90 +/- 0.02 (mean +/- SEM) for the AA and AAA groups, respectively. The average Ethetatheta,max at 200 N/m equibiaxial tension was found to be significantly smaller for AAAs as compared to AAs (0.07 +/- 0.01 versus 0.13 +/- 0.03, respectively; p < 0.01). There was also a pronounced increase in the circumferential stiffness for AAA tissue as compared to AA tissue, indicating a larger degree of anisotropy for this tissue as compared to age-matched AA tissue. We also observed that the four-parameter Fung-elastic model was not able to fit the AAA tissue mechanical response using physically realistic material parameter values. It was concluded that aneurysmal degeneration of the abdominal aorta is associated with an increase in mechanical anisotropy, with preferential stiffening in the circumferential direction.     

A finite element study of invariant-based orthotropic constitutive equations in the context of myocardial material parameter estimation

A previous study investigated a number of invariant-based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. The study was based on the assumption of a homogeneous deformation. Here, we extend the previous study by performing an inverse finite element material parameter estimation. This ensures a more realistic deformation state and material parameter estimates. The constitutive relations were compared on the basis of (i) ‘goodness of fit’: how well they fit a set of six shear deformation tests and (ii) ‘variability’: how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive relations. It was found that a specific form of the polyconvex type as well as the exponential Fung-type equations were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.     

A mechanical characterization of the porcine atria at the healthy stage and after ventricular tachypacing

Atrial fibrillation (AF) is a cardiac arrhythmia that highly increases the risk of stroke and is associated with significant but still unexplored changes in the mechanical behavior of the tissue. Planar biaxial tests were performed on tissue specimens from pigs at the healthy stage and after ventricular tachypacing (VTP), a procedure applied to reproduce the relevant features of AF. The local arrangement of the fiber bundles in the tissue was investigated on specimens from rabbit atria by means of circularly polarized light. Based on this, mechanical data were fitted to two anisotropic constitutive relationships, including a four-parameter Fung-type model and a microstructurally-motivated model. Accounting for the fiber-induced anisotropy brought average R(2) = 0.807 for the microstructurally-motivated model and average R(2) = 0.949 for the Fung model. Validation of the fitted constitutive relationships was performed by means of FEM simulations coupled to FORTRAN routines. The performances of the two material models in predicting the second Piola-Kirchhoff stress were comparable, with average errors <3.1%. However, the Fung model outperformed the other in the prediction of the Green-Lagrange strain, with 9.2% maximum average error. To increase model generality, a proper averaging procedure accounting for nonlinearities was used to obtain average material parameters. In general, a stiffer behavior after VTP was noted.     

Myocardial material parameter estimation

The passive material properties of myocardium play a major role in diastolic performance of the heart. In particular, the shear behaviour is thought to play an important mechanical role due to the laminar architecture of myocardium. We have previously compared a number of myocardial constitutive relations with the aim to extract their suitability for inverse material parameter estimation. The previous study assumed a homogeneous deformation. In the present study we relaxed the homogeneous assumption by implementing these laws into a finite element environment in order to obtain more realistic measures for the suitability of these laws in both their ability to fit a given set of experimental data, as well as their stability in the finite element environment. In particular, we examined five constitutive laws and compare them on the basis of (i) "goodness of fit": how well they fit a set of six shear deformation tests, (ii) "determinability": how well determined the objective function is at the optimal parameter fit, and (iii) "variability": how well determined the material parameters are over the range of experiments. Furthermore, we compared the FE results with those from the previous study.It was found that the same material law as in the previous study, the orthotropic Fung-type "Costa-Law", was the most suitable for inverse material parameter estimation for myocardium in simple shear.     

Prediction of nonlinear elastic behaviour of vaginal tissue: experimental results and model formulation

The mechanical properties of the vaginal tissue need to be characterised to perform accurate simulations of prolapse and other pelvic disorders that commonly affect women. This is also a fundamental step towards the improvement of therapeutic techniques such as surgery. Issues like the efficiency of using autologous tissue in pelvic reconstruction may be addressed. The goal of this study was to characterise the elastic behaviour of vaginal tissue. For this purpose, prolapsed vaginal tissue from eight different post-menopausal patients, excised during prolapse corrective surgery, was mechanically tested. The mechanical testing of vaginal tissue, consisting of uniaxial tension tests performed along the longitudinal axis of the vagina, revealed the nonlinear mechanical behaviour of the tissue. The material model parameters were fit to the experimental data using the Levenberg–Marquardt optimisation algorithm. All the curve fittings showed a good agreement between experimental and theoretical results, evidenced by R ² values close to 1 and by very low ? values.     

Myocardial material parameter estimation: a comparison of invariant based orthotropic constitutive equations

This study investigated a number of invariant based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue.

A number of orthotropic laws based on Green strain components and one microstructurally based law have previously been investigated to fit experimental measurements of stress-strain behaviour. Here we extend this investigation to include several recently proposed functional forms, i.e. invariant based orthotropic and transversely isotropic constitutive relations.

These laws were compared on the basis of (i) ‘goodness of fit’: how well they fit a set of six shear deformation tests, (ii) ‘variability’: how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive laws.

It was found that a specific form of the polyconvex type as well as the exponential Fung-type law from the previous study were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.     

Biomechanical response of ascending thoracic aortic aneurysms: association with structural remodelling

Ascending thoracic aortic aneurysms (ATAA) were resected from patients during graft replacement and non-aneurysmal vessels during autopsy. Tissues were histomechanically tested according to region and orientation, and the experimental recordings reduced with a Fung-type strain--energy function, affording faithful biomechanical characterisation of the vessel response. The material and rupture properties disclosed that ATAA and non-aneurysmal aorta were stiffer and stronger circumferentially, accounted by preferential collagen reinforcement. The deviation of microstructure in the right lateral region, with a longitudinal extracellular matrix and smooth muscle element sub-intimally, reflects the regional differences in material properties identified. ATAA had no effect on strength, but caused stiffening and extensibility reduction, corroborating our histological observation of deficient elastin but not collagen content. Our findings may serve as input data for the implementation of finite element models, to be used as improved surgical intervention criteria, and may further our understanding of the pathophysiology of ATAA and aortic dissection.     

Identification and characterisation of regional variations in the material properties of ureter according to microstructure

There are few previous studies on the elastic properties of ureter and most have been limited to essentially one-dimensional deformation measurements. The object of this study was, therefore, to identify regional variations in the multiaxial behaviour of rabbit ureter, subjected to in vitro inflation/extension testing under a physiological range of intraluminal pressures and longitudinal forces. A microstructure-motivated material model (via two- and four-fibre families in turn for elastin and collagen) was implemented and its capacity to mathematically characterise the experimental data contrasted favourably with that of the well-established phenomenological models, but it was compromised by parameter covariance. Extensive optimisation studies confirmed that the reduced model without contribution to the elastin and circumferential-fibre (collagen) families characterised the data equally well without over-parameterisation. In view of the fitted parameters, the ureteral tissue was stiffer longitudinally, justified by the preferential alignment of collagen along that axis and the lower ureter was stiffer than the upper ureter, justified by the histological observation of a thickest lamina propria, i.e. of highest collagen content, there. The lower ureter was less anisotropic than the upper ureter, possessing a comparatively larger amount of diagonally arranged collagen fibres in tunica mucosa, while having the usual amounts of longitudinally arranged fibres in tunica adventitia and of circumferentially arranged fibres in tunica muscularis. The present data may be used as inputs to mathematical models of the ureter, assessing regional and intramural stress distributions, through which it is hoped that an improved appreciation of ureteral function may be attained in both health and disease.     

Determination of material models for arterial walls from uniaxial extension tests and histological structure

An approach is proposed that allows the determination of material models from uniaxial tests and histostructural data including fiber orientation of the tissue. A combination of neo-Hookean and Fung-type strain-energy functions is utilized, and inequality constraints imposed on the constitutive parameters are derived providing strict local convexity and preferred fiber orientations. It is shown how the Fung-type model gets a pseudo-structural aspect inherent in the phenomenological model; a correlation between the fiber structure and the parameters of the Fung-type model is explicitly provided. In order to apply the proposed approach, quasi-static uniaxial extension tests of preconditioned prepared strips from the intima, media and adventitia of a human aorta with non-atherosclerotic intimal thickening are acquired in axial and circumferential directions; structural information from histological analyses for each aortic tissue are documented. Data reveal a remarkable thickness, load-bearing capacity and stiffness of the intimal samples in comparison with the media and adventitia. Constitutive parameters for each aortic tissue layer are determined by solving the constrained problem using a penalty function method; a new approach for the estimation of appropriate start values is proposed. Finally, the predictivity and efficacy of the material models is shown by comparing model data with data from the uniaxial extension tests and histological image analyses.     

Linking hyperelastic theoretical models and experimental data of vaginal tissue through histological data

Mechanical characterization of living tissues and computer-based simulations related to medical issues, has become increasingly important to improve diagnostic processes and treatments evaluation. This work proposes a link between the mechanical testing and the material model predictions through histological data of vaginal tissue. Histological data was used to link tensile testing experiments with material-dependent parameters; the approach was adequate to capture the nonlinear response of ovine vaginal tissue over a large strain range.The experimental data obtained on a previous study, has two main components: tensile testing and histological analysis of the ovine vaginal tissue. Uniaxial tensile test data and histological data were collected from three sheep groups: virgins, pregnant and parous. The distal part of vaginal wall was selected since it is prone to tears induced by vaginal delivery.The HGO (Holzapfel-Gasser-Ogden) model parameters were fitted using a stochastic approach, namely the Simple Genetic Algorithm (SGA). The SGA was able to fit the experimental data successfully (R² > 0.986). The dimensionless coefficient ξ, was highly correlated with histological data. The ratio was seen to increase linearly with increasing collagen content.Coefficient ξ brings a new way of interpreting and understanding experimental data; it connects the nonlinear mechanical behaviour (tensile test) with tissue’s morphology (histology). It can be used as an ‘inverse’ (approximate) method to estimate the mechanical properties without direct experimental measurements, through basic histology.In this context, the proposed methodology appears very promising in estimating the response of the tissue via histological information.     

Anisotropic AAA: Computational comparison between four and two fiber family material models

Abdominal aortic aneurysm (AAA) is a cardiovascular disease with high incidence among elderly population. Biomechanical computational analyses can provide fundamental insights into AAA pathogenesis and clinical management, but modeling should be sufficiently accurate. Several constitutive models of the AAA wall are present in the literature, and some of them seem to well describe the experimental behavior of the aneurysmatic human aorta. In this work we compare a two (2FF) and a four (4FF) fiber families constitutive models of the AAA wall. Both these models satisfactorily fit literature data from biaxial tests on the aneurysmatic tissue. To investigate the peculiar characteristics of these models, we considered the problem of AAA inflation, and solved it by implementing the constitutive equations in a finite element code. A 20% axial stretch was imposed to the aneurysm ends, to simulate the physiological condition. Although fitted on the same dataset, the two material models lead to considerably different outcomes. In particular, adopting a 4FF strain energy function (SEF), an increase of the circumferential stress values can be observed, while higher axial stresses are recorded for the 2FF model. These differences can be attributed to the intrinsic characteristics of the SEFs and to the effective stress field, with respect to the one experienced in biaxial experimental tests on which the fitting is based. In fact the two SEFs appear similar within the region of the stress-strain experimental data, but become different outside it, as in case of aneurysms, due to the effects of the data extrapolation process. It is suggested that experimental data should be obtained for conditions similar to those of the application for which they are intended.     

Method for characterizing viscoelasticity of human gluteal tissue

Characterizing compressive transient large deformation properties of biological tissue is becoming increasingly important in impact biomechanics and rehabilitation engineering, which includes devices interfacing with the human body and virtual surgical guidance simulation. Individual mechanical in vivo behaviour, specifically of human gluteal adipose and passive skeletal muscle tissue compressed with finite strain, has, however, been sparsely characterised. Employing a combined experimental and numerical approach, a method is presented to investigate the time-dependent properties of in vivo gluteal adipose and passive skeletal muscle tissue. Specifically, displacement-controlled ramp-and-hold indentation relaxation tests were performed and documented with magnetic resonance imaging. A time domain quasi-linear viscoelasticity (QLV) formulation with Prony series valid for finite strains was used in conjunction with a hyperelastic model formulation for soft tissue constitutive model parameter identification and calibration of the relaxation test data. A finite element model of the indentation region was employed. Strong non-linear elastic but linear viscoelastic tissue material behaviour at finite strains was apparent for both adipose and passive skeletal muscle mechanical properties with orthogonal skin and transversal muscle fibre loading. Using a force-equilibrium assumption, the employed material model was well suited to fit the experimental data and derive viscoelastic model parameters by inverse finite element parameter estimation. An individual characterisation of in vivo gluteal adipose and muscle tissue could thus be established. Initial shear moduli were calculated from the long-term parameters for human gluteal skin/fat: G(∞,S/F)=1850 Pa and for cross-fibre gluteal muscle tissue: G(∞,M)=881 Pa. Instantaneous shear moduli were found at the employed ramp speed: G(0,S/F)=1920 Pa and G(0,M)=1032 Pa.