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.     

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.     

Effect of elastin degradation on carotid wall mechanics as assessed by a constituent-based biomechanical model

Arteries display a nonlinear anisotropic behavior dictated by the elastic properties and structural arrangement of its main constituents, elastin, collagen, and vascular smooth muscle. Elastin provides for structural integrity and for the compliance of the vessel at low pressure, whereas collagen gives the tensile resistance required at high pressures. Based on the model of Zulliger et al. (Zulliger MA, Rachev A, Stergiopulos N. Am J Physiol Heart Circ Physiol 287: H1335-H1343, 2004), which considers the contributions of elastin, collagen, and vascular smooth muscle cells (VSM) in an explicit form, we assessed the effects of enzymatic degradation of elastin on biomechanical properties of rabbit carotids. Pressure-diameter curves were obtained for controls and after elastin degradation, from which elastic and structural properties were derived. Data were fitted into the model of Zulliger et al. to assess elastic constants of elastin and collagen as well as the characteristics of the collagen engagement profile. The arterial segments were also prepared for histology to visualize and quantify elastin and collagen. Elastase treatment leads to a diameter enlargement, suggesting the existence of significant compressive prestresses within the wall. The elastic modulus was more ductile in treated arteries at low circumferential stretches and significantly greater at elevated circumferential stretches. Abrupt collagen fiber recruitment in elastase-treated arteries leads to a much stiffer vessel at high extensions. This change in collagen engagement properties results from structural alterations provoked by the degradation of elastin, suggesting a clear interaction between elastin and collagen, often neglected in previous constituent-based models of the arterial wall.     

Biomechanical and morphological properties of the multiparous ovine vagina and effect of subsequent pregnancy

Pelvic floor soft tissues undergo changes during the pregnancy. However, the degree and nature of this process is not completely characterized. This study investigates the effect of subsequent pregnancy on biomechanical and structural properties of ovine vagina. Vaginal wall from virgin, pregnant (in their third pregnancy) and parous (one year after third vaginal delivery) Swifter sheep (n = 5 each) was harvested. Samples for biomechanics and histology, were cut in longitudinal axis (proximal and distal regions). Outcome measurements describing Young’s modulus, ultimate stress and elongation were obtained from stress-strain curves. For histology samples were stained with Miller's Elastica staining. Collagen, elastin and muscle cells and myofibroblasts contents were estimated, using image processing techniques. Statistical analyses were performed in order to determine significant differences among experimental groups. Significant regional differences were identified. The proximal vagina was stiffer than distal, irrespective the reproductive status. During the pregnancy proximal vagina become more compliant than in parous (+47.45%) or virgin sheep (+64.35%). This coincided with lower collagen (−15 to −21%), higher elastin (+30 to +60%), and more smooth muscle cells (+17 to +37%). Vaginal tissue from parous ewes was weaker than of virgins, coinciding with lower collagen (−10%), higher elastin (+50%), more smooth muscle cells (+20%). It could be proposed that after pregnancy biomechanical properties of vagina do not recover to those of virgins. Since elastin has a significant influence on the compliance of soft tissues and collagen is the main “actor” regarding strength, histological analysis performed in this study justifies the mechanical behavior observed.     

Structural strain energy function applied to the ageing of the human aorta

Stiffening of the aorta with progressing age leads to decrease of aortic compliance and thus to an increase of pulse pressure amplitude. Using a strain energy function (SEF) which takes into account the composition of the arterial wall, we have studied the evolution of key structural components of the human thoracic aorta using data obtained from the literature. The SEF takes into account the wavy nature of collagen, which upon gradual inflation of the blood vessel is assumed to straighten out and become engaged in bearing load. The engagement of the individual fibers is assumed to be distributed log-logistically. The use of a SEF enables the consideration of axial stretch (lambda(z)) and residual strain (opening angle) in the biomechanical analysis. Both lambda(z) and opening angle are known to change with age. Results obtained from applying the SEF to the measurements of aortic pressure-diameter curves indicate that the changes in aortic biomechanics with progressing age are not to be sought in the elastic constants of elastin and collagen or their volume fractions of the aortic wall but moreover in alterations of the collagen mesh arrangement and the waviness of the collagen fibers. In old subjects, the collagen fiber ensemble engages in load bearing much more abruptly than in young subjects. Reasons for this change in collagen fiber dynamics may include fiber waviness remodeling or cross-linkage by advanced glycation end-products (AGE). The abruptness of collagen fiber engagement is also the model parameter that is most responsible for the decreased compliance at progressed ages.     

3D Mechanical properties of the layered esophagus: experiment and constitutive model

The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases.     

Stomach stress and strain depend on location, direction and the layered structure

The stomach is as other parts of the gastrointestinal tract functionally subjected to dimensional change. Hence, the biomechanical properties are of functional importance. Our group has previously demonstrated that the stress–strain properties of the rat and rabbit stomach wall were species-, location- and direction-dependent. We further wanted to study the anisotropic biomechanical properties of the stomach wall in pigs. Furthermore, we made an in-depth biomechanical test on the layered wall of the stomach in different regions. Two stomach strips were cut both in longitudinal direction (parallel with the greater curvature) and circumferential direction (perpendicular to the greater curvature) from the gastric fundus, corpus and antrum. One strip was used for the non-separated (intact) wall test and the other one was separated for the test on the mucosa–submucosa and muscle layers individually. The length, thickness and width of each strip were measured from digital images. The uni-axial stress and strain were computed from the force generation and the tissue strip deformation during stretching. The muscle layer was the thickest in the antrum whereas the mucosal–submucosal layer was the thickest in the corpus of the stomach (P<0.01). The strips from the corpus were stiffest among the three regions in both longitudinal and circumferential directions (P<0.001). The longitudinal strips was stiffer than the circumferential strips in all three regions (P<0.001) and the mucosa–submucosa strips was stiffer than the intact wall and the muscle layer in both directions for the fundus and the corpus (P<0.001). The constant a of the intact wall and mucosa–submucosa layer was in both directions linearly associated with the mucosa–submucosa thickness. In conclusion, the uni-axial stress–strain curves of pig stomach were location-, direction- and layer-dependent. The stiffer wall in the corpus is likely due to its thicker mucosa, i.e., the stiffness of the mucosa–submucosa layer seems can explain the intact wall stiffness. Since the structure and function of the pig stomach are similar to the human stomach, we believe that the data obtained from this study can be extended to humans. Detailed biomechanical mapping of the stomach will likely help us to understand physiological functions of the different parts of the human stomach, such as gastric accommodation and mechanosensation.     

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.     

Multiphoton microscopy observations of 3D elastin and collagen fiber microstructure changes during pressurization in aortic media

Elastin and collagen fibers play important roles in the mechanical properties of aortic media. Because knowledge of local fiber structures is required for detailed analysis of blood vessel wall mechanics, we investigated 3D microstructures of elastin and collagen fibers in thoracic aortas and monitored changes during pressurization. Using multiphoton microscopy, autofluorescence images from elastin and second harmonic generation signals from collagen were acquired in media from rabbit thoracic aortas that were stretched biaxially to restore physiological dimensions. Both elastin and collagen fibers were observed in all longitudinal–circumferential plane images, whereas alternate bright and dark layers were observed along the radial direction and were recognized as elastic laminas (ELs) and smooth muscle-rich layers (SMLs), respectively. Elastin and collagen fibers are mainly oriented in the circumferential direction, and waviness of collagen fibers was significantly higher than that of elastin fibers. Collagen fibers were more undulated in longitudinal than in radial direction, whereas undulation of elastin fibers was equibiaxial. Changes in waviness of collagen fibers during pressurization were then evaluated using 2-dimensional fast Fourier transform in mouse aortas, and indices of waviness of collagen fibers decreased with increases in intraluminal pressure. These indices also showed that collagen fibers in SMLs became straight at lower intraluminal pressures than those in EL, indicating that SMLs stretched more than ELs. These results indicate that deformation of the aorta due to pressurization is complicated because of the heterogeneity of tissue layers and differences in elastic properties of ELs, SMLs, and surrounding collagen and elastin.     

The visceral pericardium: macromolecular structure and contribution to passive mechanical properties of the left ventricle

Much attention has been focused on the passive mechanical properties of the myocardium, which determines left ventricular (LV) diastolic mechanics, but the significance of the visceral pericardium (VP) has not been extensively studied. A unique en face three-dimensional volumetric view of the porcine VP was obtained using two-photon excitation fluorescence to detect elastin and backscattered second harmonic generation to detect collagen, in addition to standard light microscopy with histological staining. Below a layer of mesothelial cells, collagen and elastin fibers, extending several millimeters, form several distinct layers. The configuration of the collagen and elastin layers as well as the location of the VP at the epicardium providing a geometric advantage led to the hypothesis that VP mechanical properties play a role in the residual stress and passive stiffness of the heart. The removal of the VP by blunt dissection from porcine LV slices changed the opening angle from 53.3 +/- 10.3 to 27.3 +/- 5.7 degrees (means +/- SD, P < 0.05, n = 4). In four porcine hearts where the VP was surgically disrupted, a significant decrease in opening angle was found (35.5 +/- 4.0 degrees ) as well as a rightward shift in the ex vivo pressure-volume relationship before and after disruption and a decrease in LV passive stiffness at lower LV volumes (P < 0.05). These data demonstrate the significant and previously unreported role that the VP plays in the residual stress and passive stiffness of the heart. Alterations in this layer may occur in various disease states that effect diastolic function.     

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.     

美洲黑石斑鱼消化道的形态结构

采用解剖和光镜技术观察了美洲黑石斑鱼消化道的形态及组织学结构。消化道由口咽腔、食道、胃、肠构成。口咽腔较大,具颌齿、腭齿及犁齿;舌由基舌骨突出部分覆盖粘膜构成。食道、胃及肠均由粘膜层、粘膜下层、肌层及外膜构成。食道粘膜层绒毛分柱状上皮区及扁平上皮区,扁平上皮区表面为杯状细胞层;食道粘膜下层中有食道腺。胃呈V形,由贲门部、胃体部及幽门部组成,胃壁粘膜层上皮为单层柱状上皮,胃腺位于贲门部与胃体部的固有层中。肠细长,呈S型,由前、中、后肠构成,粘膜层向肠腔突起形成肠绒毛,粘膜上皮为单层柱状上皮,上皮游离面有微绒毛密集排列而成的纹状缘,上皮中含有杯状细胞,且杯状细胞的数量从前向后呈递减趋势;肠长/体长约为1.6。胃与小肠相接处有3对指状幽门盲囊,幽门盲囊的组织学结构与肠相同。     

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.     

Characterization of evolving biomechanical properties of tissue engineered vascular grafts in the arterial circulation

We used a murine model to assess the evolving biomechanical properties of tissue engineered vascular grafts (TEVGs) implanted in the arterial circulation. The initial polymeric tubular scaffold was fabricated from poly(lactic acid)(PLA) and coated with a 50:50 copolymer of poly(caprolactone) and poly(lactic acid)(P[PC/LA]). Following seeding with syngeneic bone marrow derived mononuclear cells, TEVGs (n=50) were implanted as aortic interposition grafts in wild-type mice and monitored serially using ultrasound. A custom biaxial mechanical testing device was used to quantify the in vitro circumferential and axial mechanical properties of grafts explanted at 3 or 7 months. At both times, TEVGs were much stiffer than native tissue in both directions. Repeated mechanical testing of some TEVGs treated with elastase or collagenase suggested that elastin did not contribute significantly to the overall stiffness whereas collagen did contribute. Traditional histology and immunostaining revealed smooth muscle cell layers, significant collagen deposition, and increasing elastin production in addition to considerable scaffold at both 3 and 7 months, which likely dominated the high stiffness seen in mechanical testing. These results suggest that PLA has inadequate in vivo degradation, which impairs cell-mediated development of vascular neotissue having properties closer to native arteries. Assessing contributions of individual components, such as elastin and collagen, to the developing neovessel is needed to guide computational modeling that may help to optimize the design of the TEVG.     

可口革囊星虫消化道的形态及组织学结构

对可口革囊星虫(Phascolosoma esculenta)消化道各部分结构进行了形态学和组织学观察,表明可口革囊星虫消化道由翻吻、咽、食道、肠、直肠和肛门组成。翻吻收缩性很强;肠道极长,沿纺锤肌螺旋缠绕成肠索。消化道管壁由内向外分为粘膜层、粘膜下层、肌层和外膜。粘膜上皮主要由柱状细胞组成。除肠外,消化道上皮细胞均有发达的纤毛,肠上皮细胞主要具发达的微绒毛;粘膜下层及肌层的发达程度因消化道的部位不同而异。