Molecular orientation of collagen in intact planar connective tissues under biaxial stretch

Understanding of the mechanical behavior of collagenous tissues at different size scales is necessary to understand their physiological function as well as to guide their use as heterograft biomaterials. We conducted a first investigation of the kinematics of collagen at the molecular and fiber levels under biaxial stretch in an intact planar collagenous tissue. A synchrotron small angle X-ray scattering (SAXS) technique combined with a custom biaxial stretching apparatus was used. Collagen fiber behavior under biaxial stretch was then studied with the same specimens using small angle light scattering (SALS) under identical biaxial stretch states. Both native and glutaraldehyde modified bovine pericardium were investigated to explore the effects of chemical modification to collagen. Results indicated that collagen fiber and molecular orientation did not change under equibiaxial strain, but were observed to profoundly change under uniaxial stretch. Interestingly, collagen molecular strain initiated only after approximately 15% global tissue strain, potentially due to fiber-level reorganization occurring prior to collagen molecule loading. Glutaraldehyde treatment also did not affect collagen molecular strain behavior, indicating that chemical fixation does not alter intrinsic collagen molecular stiffness. No detectable changes in the angular distribution and D-period strain were found after 80 min of stress relaxation. It can be speculated that other mechanisms may be responsible for the reduction in stress with time under biaxial stretch. The results of this first study suggest that collagen fiber/molecular kinematics under biaxial stretch are more complex than under uniaxial deformation, and warrant future studies.     

Biaxial mechanical/structural effects of equibiaxial strain during crosslinking of bovine pericardial xenograft materials

We have investigated the effect of biaxial constraint during glutaraldehyde crosslinking on the equibiaxial mechanical properties of bovine pericardium. Crosslinking of cruciate samples was carried out with: (i) no applied load, (ii) an initial 25 g ( approximately 30 kPa) equibiaxial load, or (iii) an initial 200 g (approximately 250 kPa) equibiaxial load. All loading during crosslinking was done under a defined initial equibiaxial load and subsequently fixed biaxial strain. Load changes during crosslinking were monitored. Mechanical testing and constraint during crosslinking were carried out in a custom-built biaxial servo-hydraulic testing system incorporating four actuators with phase-controlled waveform synthesis, high frame-rate video dimension analysis, and computer-interfaced data acquisition. The paired biaxial stress strain responses under equibiaxial loading at 1 Hz (before and after treatment) were evaluated for changes in anisotropic extensibility by calculation of an anisotropy index. Scanning electron microscopy (SEM) was performed on freeze-fractured samples to relate collagen crimp morphology to constraint during crosslinking. Fresh tissue was markedly anisotropic with the base-to-apex direction of the pericardium being less extensible and stiffer than the circumferential direction. After unconstrained crosslinking, the extensibility in the circumferential direction, the stiffness in the base-to-apex direction, and the tissue's anisotropy were all reduced. Anisotropy was preserved in the tissue treated with an applied 25 g load; however, tissue treated with an applied 200 g load became extremely stiff and nearly isotropic. SEM micrographs correlated well with observed extensibility in that the collagen fibre morphology changed from very crimped (unconstrained crosslinking), to straight (200 g applied load). Biaxial stress-fixation may allow engineering of bioprosthetic materials for specific medical applications.     

In vitro technique in estimation of passive mechanical properties of bovine heart part I. Experimental techniques and data

Myocardium generally demonstrates viscoelastic behavior. Since the stress-stain relationships of tissues are pseudo-elastic, their mechanical behavior can be defined as hyperelastic. In this work, mechanical properties of bovine heart were studied. In this study, the experimental technique for testing myocardium is explained and the experimental data are presented. First, the heart was perfused and the specimens were cut from different regions of the heart. Second, the materials preferred direction was identified. Then, a series of uniaxial, biaxial and equibiaxial test were performed on specimens taken from: left ventricle free wall (LVFW), right ventricle free wall (RVFW), left ventricle mid-wall (LVMW) and apex. Test specimens were preconditioned by applying cyclic load to reduce the viscoelastic effect. After preconditioning, the samples were tested at various stretch rates and loading conditions. Finally, a conclusion is made on the experimental data.     

Biaxial Response of Passive Human Cerebral Arteries

The cerebral circulation is fundamental to the health and maintenance of brain tissue, but injury and disease may result in dysfunction of the vessels. Characterization of cerebral vessel mechanical response is an important step toward a more complete understanding of injury mechanisms and disease development in these vessels, paving the way for improved prevention and treatment. We recently reported a large series of uniaxial tests on fresh human cerebral vessels, but the multi-axial behavior of these vessels has not been previously described. Twelve arteries were obtained from the surface of the temporal lobe of patients undergoing surgery and were subjected to various combinations of axial stretch and pressure around typical physiological conditions before being stretched to failure. Axial and circumferential responses were compared, and measured data were fit to a four-parameter, Fung-type hyperelastic constitutive model. Artery behavior was nonlinear and anisotropic, with considerably greater resistance to deformation in the axial direction than around the circumference. Results from axial failure tests of pressurized vessels resulted in a small shift in stress–stretch response compared to previously reported data from unpressurized specimens. These results further define the biaxial response of the cerebral arteries and provide data required for more rigorous study of head injury mechanisms and development of cerebrovascular disease.     

Hydrogel-electrospun mesh composites for coronary artery bypass grafts

The aim of the present study was to investigate the potential of hydrogel-electrospun mesh hybrid scaffolds as coronary artery bypass grafts. The circumferential mechanical properties of blood vessels modulate a broad range of phenomena, including vessel stress and mass transport, which, in turn, have a critical impact on cardiovascular function. Thus, coronary artery bypass grafts should mimic key features of the nonlinear stress-strain behavior characteristic of coronary arteries. In native arteries, this J-shaped circumferential stress-strain curve arises primarily from initial load transfer to low stiffness elastic fibers followed by progressive recruitment and tensing of higher stiffness arterial collagen fibers. This nonlinear mechanical response is difficult to achieve with a single-component scaffold while simultaneously meeting the suture retention strength and tensile strength requirements of an implantable graft. For instance, although electrospun scaffolds have a number of advantages for arterial tissue engineering, including relatively high tensile strengths, tubular mesh constructs formed by conventional electrospinning methods do not generally display biphasic stress-strain curves. In the present work, we demonstrate that a multicomponent scaffold comprised of polyurethane electrospun mesh layers (intended to mimic the role of arterial collagen fibers) bonded together by a fibrin hydrogel matrix (designed to mimic the role of arterial elastic fibers) results in a composite construct which retains the high tensile strength and suture retention strength of electrospun mesh but which displays a J-shaped mechanical response similar to that of native coronary artery. Moreover, we show that these hybrid constructs support cell infiltration and extracellular matrix accumulation following 12-day exposure to continuous cyclic distension.     

Prediction of equibiaxial loading stress in collagen-based extracellular matrix using a three-dimensional unit cell model

Mechanical signals are important factors in determining cell fate. Therefore, insights as to how mechanical signals are transferred between the cell and its surrounding three-dimensional collagen fibril network will provide a basis for designing the optimum extracellular matrix (ECM) microenvironment for tissue regeneration. Previously we described a cellular solid model to predict fibril microstructure–mechanical relationships of reconstituted collagen matrices due to unidirectional loads (Acta Biomater 2010;6:1471–86). The model consisted of representative volume elements made up of an interconnected network of flexible struts. The present study extends this work by adapting the model to account for microstructural anisotropy of the collagen fibrils and a biaxial loading environment. The model was calibrated based on uniaxial tensile data and used to predict the equibiaxial tensile stress–stretch relationship. Modifications to the model significantly improved its predictive capacity for equibiaxial loading data. With a comparable fibril length (model 5.9–8 μm, measured 7.5 μm) and appropriate fibril anisotropy the anisotropic model provides a better representation of the collagen fibril microstructure. Such models are important tools for tissue engineering because they facilitate prediction of microstructure–mechanical relationships for collagen matrices over a wide range of microstructures and provide a framework for predicting cell–ECM interactions.     

Cyclic strain anisotropy regulates valvular interstitial cell phenotype and tissue remodeling in three-dimensional culture

Many planar connective tissues exhibit complex anisotropic matrix fiber arrangements that are critical to their biomechanical function. This organized structure is created and modified by resident fibroblasts in response to mechanical forces in their environment. The directionality of applied strain fields changes dramatically during development, aging, and disease, but the specific effect of strain direction on matrix remodeling is less clear. Current mechanobiological inquiry of planar tissues is limited to equibiaxial or uniaxial stretch, which inadequately simulates many in vivo environments. In this study, we implement a novel bioreactor system to demonstrate the unique effect of controlled anisotropic strain on fibroblast behavior in three-dimensional (3-D) engineered tissue environments, using aortic valve interstitial fibroblast cells as a model system. Cell seeded 3-D collagen hydrogels were subjected to cyclic anisotropic strain profiles maintained at constant areal strain magnitude for up to 96 h at 1 Hz. Increasing anisotropy of biaxial strain resulted in increased cellular orientation and collagen fiber alignment along the principal directions of strain and cell orientation was found to precede fiber reorganization. Cellular proliferation and apoptosis were both significantly enhanced under increasing biaxial strain anisotropy (P<0.05). While cyclic strain reduced both vimentin and alpha-smooth muscle actin compared to unstrained controls, vimentin and alpha-smooth muscle actin expression increased with strain anisotropy and correlated with direction (P<0.05). Collectively, these results suggest that strain field anisotropy is an independent regulator of fibroblast cell phenotype, turnover, and matrix reorganization, which may inform normal and pathological remodeling in soft tissues.     

Biaxial mechanical modeling of the small intestine

Capsule endoscopes are pill-size devices provided with a camera that capture images of the small intestine from inside the body after being ingested by a patient. The interaction between intestinal tissue and capsule endoscopes needs to be investigated to optimize capsule design while preventing tissue damage. To that purpose, a constitutive model that can reliably predict the mechanical response of the intestinal tissue under complex mechanical loading is required. This paper describes the development and numerical validation of a phenomenological constitutive model for the porcine duodenum, jejunum and ileum. Parameters characterizing the mechanical behavior of the material were estimated from planar biaxial test data, where intestinal tissue specimens were simultaneously loaded along the circumferential and longitudinal directions. Specimen-specific Fung constitutive models were able to accurately predict the planar stress-strain behavior of the tested samples under a wide range of loading conditions. To increase model generality, average anisotropic constitutive relationships were also generated for each tissue region by fitting average stress-strain curves to the Fung potential. Due to the observed variability in the direction of maximum stiffness, the average Fung models were less anisotropic than the specimen-specific models. Hence, average isotropic models in the Neo-Hookean and Mooney-Rivlin forms were attempted, but they could not adequately describe the degree of nonlinearity in the tissue. Values of the R2 for the nonlinear regressions were 0.17, 0.44 and 0.93 for the average Neo-Hookean, Mooney-Rivlin and Fung models, respectively. Average models were successfully implemented into FORTRAN routines and used to simulate capsule deployment with a finite element method analysis.     

Characterization of Biaxial Mechanical Behavior of Porcine Aorta under Gradual Elastin Degradation

Arteries are composed of multiple constituents that endow the wall with proper structure and function. Many vascular diseases are associated with prominent mechanical and biological alterations in the wall constituents. In this study, planar biaxial tensile test data of elastase-treated porcine aortic tissue (Chow et al. in Biomech Model Mechanobiol 2013) is re-examined to characterize the altered mechanical behavior at multiple stages of digestion through constitutive modeling. Exponential-based as well as recruitment-based strain energy functions are employed and the associated constitutive parameters for individual digestion stages are identified using nonlinear parameter estimation. It is shown that when the major portion of elastin is degraded from a cut-open artery in the load-free state, the embedded collagen fibers are recruited at lower stretch levels under biaxial loads, leading to a rapid stiffening behavior of the tissue. Multiphoton microscopy illustrates that the collagen waviness decreases significantly with the degradation time, resulting in a rapid recruitment when the tissue is loaded. It is concluded that even when residual stresses are released, there exists an intrinsic mechanical interaction between arterial elastin and collagen that determines the mechanics of arteries and carries important implications to vascular mechanobiology.     

A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment

In breast elastography, breast tissue usually undergoes large compression resulting in significant geometric and structural changes. This implies that breast elastography is associated with tissue nonlinear behavior. In this study, an elastography technique is presented and an inverse problem formulation is proposed to reconstruct parameters characterizing tissue hyperelasticity. Such parameters can potentially be used for tumor classification. This technique can also have other important clinical applications such as measuring normal tissue hyperelastic parameters in vivo. Such parameters are essential in planning and conducting computer-aided interventional procedures. The proposed parameter reconstruction technique uses a constrained iterative inversion; it can be viewed as an inverse problem. To solve this problem, we used a nonlinear finite element model corresponding to its forward problem. In this research, we applied Veronda-Westmann, Yeoh and polynomial models to model tissue hyperelasticity. To validate the proposed technique, we conducted studies involving numerical and tissue-mimicking phantoms. The numerical phantom consisted of a hemisphere connected to a cylinder, while we constructed the tissue-mimicking phantom from polyvinyl alcohol with freeze-thaw cycles that exhibits nonlinear mechanical behavior. Both phantoms consisted of three types of soft tissues which mimic adipose, fibroglandular tissue and a tumor. The results of the simulations and experiments show feasibility of accurate reconstruction of tumor tissue hyperelastic parameters using the proposed method. In the numerical phantom, all hyperelastic parameters corresponding to the three models were reconstructed with less than 2% error. With the tissue-mimicking phantom, we were able to reconstruct the ratio of the hyperelastic parameters reasonably accurately. Compared to the uniaxial test results, the average error of the ratios of the parameters reconstructed for inclusion to the middle and external layers were 13% and 9.6%, respectively. Given that the parameter ratios of the abnormal tissues to the normal ones range from three times to more than ten times, this accuracy is sufficient for tumor classification.     

Nonhomogeneous Deformation in the Anterior Leaflet of the Mitral Valve

In the mitral valve, regional variations in structure and material properties combine to affect the biomechanics of the entire valve. Previous biaxial testing has shown that mitral valve leaflet tissue is highly extensible, and exhibits nonlinear, anisotropic material properties. In this study, experimental measurements of mitral valve leaflet deformation under quasi-static pressure loading were performed on isolated porcine hearts. Biplane video images of markers placed on the anterior leaflet surface were used to reconstruct the 3D position of the markers at several pressure levels over the physiological range. A least-squares finite-element method was used to fit parametric models to the markers and to calculate the deformation over the surface. The results showed that the leaflet deformations were anisotropic, exhibiting a large nonhomogeneous radial stretch and a small circumferential stretch. This information can be used to better understand how the valve deforms under physiological loading, and to help design treatments for valve problems, such as mitral regurgitation.     

Polyvinyl alcohol cryogel: Optimizing the parameters of cryogenic treatment using hyperelastic models

The PVA gels obtained by freezing/thawing cycles of PVA solutions, also called cryogels, exhibit non-linear elastic behavior and can mimic, within certain limits, the behavior of biological soft tissues such as arterial tissue. Several authors have investigated the effects of cryogenic processing parameters on the Young’s modulus. However, an elastic modulus does not describe the non-linearity of the cryogel’s stress–strain response. This study examines the non-linear elastic response of PVA cryogel under uniaxial tension and investigates how processing parameters such as the concentration, the number of thermal cycles, and the thawing rate affect this response. The relationship between the coefficients of the material model and the processing parameters was interpolated to find the set of parameters that would best approximate the elastic response of healthy porcine coronary arteries under uniaxial tension.     

Biaxial Testing of Human Annulus Fibrosus and Its Implications for a Constitutive Formulation

Internal pressure in the healthy human annulus fibrosus leads to multiaxial stress in vivo, yet uniaxial tests have been used exclusively to characterize its in vitro mechanical response and to determine its elastic strain energy function (W). We expected that biaxial tension tests would provide unique and necessary data for characterizing the annular material response, and thereby, for determining W. We performed uniaxial and biaxial tests on specimens of annulus, then developed an objective methodology for defining an appropriate form for W that considers data from multiple experiments simultaneously and allows the data to dictate more directly the form and the number of parameters needed. We found that the stresses attained in the biaxial tests were higher, while the strains were considerably lower, than those observed in the uniaxial tests. A comparison of strain energy functions determined from the different data sets demonstrated that constitutive models derived from uniaxial data could not predict annulus behavior in biaxial tension and vice versa. Since the annulus is in a state of multaxial stress in vivo, we conclude that uniaxial tests alone are insufficient to prescribe a physiologically relevant W for this tissue.     

Mechanical properties of dilated human ascending aorta

Dilation of the ascending aorta, associated with Marfan Syndrome, bicuspid aortic valve, or advanced age, may lead to aortic dissection and rupture. Mathematical models can be used to assess the relative importance of increased wall stresses and decreased strength in these mechanical failures. To obtain needed inputs for such models, mechanical properties of dilated human ascending aorta were measured in vitro. Specimens for opening angle, biaxial elastic, and uniaxial circumferential strength tests were cut from excised tissue obtained from 54 patients (age 18–81 years) undergoing elective aortic graft replacement surgery. Opening angle was significantly greater in patients older than 50 years (262°±76°, n=21) compared to younger patients (202°±70°, n=13 All biaxial elastic specimens n=40 exhibited nonlinear stress-strain behavior. Rapid increases in circumferential and axial stresses occurred at lower strains in the older patient group than in the younger. Mean strength was significantly lower in older patients (1.35±0.37 MPa, n=14) than younger (2.04 ± 0.46 MPa, n=11, age <50 years). These changes in mechanical properties suggest that age may influence the risk of aortic dissection or rupture of dilated ascending aorta. © 2002 Biomedical Engineering Society. PAC2002: 8719Rr, 8719Hh     

Age related constitutive laws and stress distribution in human main coronary arteries with reference to residual strain

An analytical model has been used to simulate the effects of tissue aging on residual strain, constitutive relations and stiffness parameter in the main right and left (ramus circumflexus) human coronary arteries, based on experimental data. The experimental opening angle theta scatters considerably with age. The optimum angle theta(op) approximately equals 70 degrees, which makes the circumferential stress uniform in the arterial wall at a normal blood pressure, is approximately constant throughout aging. Above age of the 15 years the estimated and experimental values of theta are greater than theta(op) and therefore the mechanical load of the inner layers of the media and the intima decreases and the adventitia is overloaded. On the basis of nonlinear regression analysis, age-related constitutive laws of arterial wall circumferential stiffness have been determined. Above the age of 30, arterial wall hardening increases rapidly. The left coronary artery is stiffer than the right artery for groups from 35 to 45 years of age. Hyperelasticity theory has been used to identify age-related multiaxial stress through wall thickness. A theoretical model based on the reduced Green strain provides a very good representation of the coronary artery circumferential mechanical response and predicts its nearly isotropic behavior. Bio-composite material forms non-homogeneous stresses and, in the course of aging, it increases the adventitia loading. In groups aged from 10 to 15 years, whose coronary artery residual strains are low, the circumferential stress distribution has a classic form. Stiffness parameter beta gradually increases with age and this increase is significant above the age of 60. Parameter beta tends to decrease when the opening angle theta increases.     

Full-field bulge test for planar anisotropic tissues: Part I – Experimental methods applied to human skin tissue

The nonlinear anisotropic properties of human skin tissue were investigated using bulge testing. Full-field displacement data were obtained during testing of human skin tissues procured from the lower back of post-mortem human subjects using 3-D digital image correlation. To measure anisotropy, the dominant fiber direction of the tissue was determined from the deformed geometry of the specimen. Local strains and stress resultants were calculated along both the dominant fiber direction and the perpendicular direction. Variation in anisotropy and stiffness was observed between specimens. The use of stress resultants rather than the membrane stress approximation accounted for bending effects, which are significant for a thick nonlinear tissue. Of the six specimens tested, it was observed that specimens from older donors exhibited a stiffer and more isotropic response than those from younger donors. It was seen that the mechanical response of the tissue was negligibly impacted by preconditioning or the ambient humidity. The methods presented in this work for skin tissue are sufficiently general to be applied to other planar tissues, such as pericardium, gastrointestinal tissue, and fetal membranes. The stress resultant–stretch relations will be used in a companion paper to obtain material parameters for a nonlinear anisotropic hyperelastic model.     

The nonlinear elastic and viscoelastic passive properties of left ventricular papillary muscle of a guinea pig heart

The mechanical behavior of the heart muscle tissues is the central problem in finite element simulation of the heart contraction, excitation propagation and development of an artificial heart. Nonlinear elastic and viscoelastic passive material properties of the left ventricular papillary muscle of a guinea pig heart were determined based on in-vitro precise uniaxial and relaxation tests. The nonlinear elastic behavior was modeled by a hypoelastic model and different hyperelastic strain energy functions such as Ogden and Mooney-Rivlin. Nonlinear least square fitting and constrained optimization were conducted under MATLAB and MSC.MARC in order to obtain the model material parameters. The experimental tensile data was used to get the nonlinear elastic mechanical behavior of the heart muscle. However, stress relaxation data was used to determine the relaxation behavior as well as viscosity of the tissues. Viscohyperelastic behavior was constructed by a multiplicative decomposition of a standard Ogden strain energy function, W, for instantaneous deformation and a relaxation function, R(t), in a Prony series form. The study reveals that hypoelastic and hyperelastic (Ogden) models fit the tissue mechanical behaviors well and can be safely used for heart mechanics simulation. Since the characteristic relaxation time (900 s) of heart muscle tissues is very large compared with the actual time of heart beating cycle (800 ms), the effect of viscosity can be reasonably ignored. The amount and type of experimental data has a strong effect on the Ogden parameters. The in vitro passive mechanical properties are good initial values to start running the biosimulation codes for heart mechanics. However, an optimization algorithm is developed, based on clinical intact heart measurements, to estimate and re-correct the material parameters in order to get the in vivo mechanical properties, needed for very accurate bio-simulation and for the development of new materials for the artificial heart.     

Characterization of the Highly Nonlinear and Anisotropic Vascular Tissues from Experimental Inflation Data: A Validation Study Toward the Use of Clinical Data for <Emphasis Type="Italic">In-Vivo</Emphasis> Modeling and Analysis

We study whether an inverse modeling approach is applicable for characterizing vascular tissue subjected to various levels of internal pressure and axial stretch that approximate in-vivo conditions. To compensate for the limitation of axial-displacement/pressure/diameter data typical of clinical data, which does not provide information about axial force, we propose to constrain the ratio of axial to circumferential elastic moduli to a typical range. Vessel wall constitutive behavior is modeled with a transversely isotropic hyperelastic equation that accounts for dispersed collagen fibers. A single-layer and a bi-layer approximation to vessel ultrastructure are examined, as is the possibility of obtaining the fiber orientation as part of the optimization. Characterization is validated against independent pipette-aspiration biaxial data on the same samples. It was found that the single-layer model based on homogeneous wall assumption could not reproduce the validation data. In contrast, the constrained bi-layer model was in excellent agreement with both types of experimental data. Due to covariance, estimations of fiber angle were slightly outside of the normal range, which can be resolved by predefining the angles to normal values. Our approach is relatively invariant to a constant or a variable axial response. We believe that it is suitable for in-vivo characterization.     

猪降主动脉环向力学性质的实验研究

目的研究猪降主动脉的力学特性。方法猪降主动脉按照距心脏距离分成5组,各组由左右两侧组织、腹侧面组织构成。使用单轴拉伸方法拉伸组织,获得应力与伸张比曲线。采用经典数学模型分析5个部位(位置1～5)弹性、胶原纤维模量以及胶原纤维激活参数等特征,并对比腹侧面与两侧组织之间的力学差异。结果在环向上,胶原纤维模量随着远离心脏的方向逐渐增长,而弹性纤维模量位置1～4随着距心脏的距离增加而逐渐增大,位置5的弹性纤维模量减小,且位置5两侧的环向弹性纤维模量小于腹侧面约19%;在轴向上,弹性纤维模量小于腹侧面约37%,位置5腹侧面的弹性纤维模量相比于位置4差异不大(均值差异约5%)。在整个降主动脉中,侧面环向胶原纤维模量大于腹侧面约26%,环向弹性纤维模量在靠近心脏的四部分侧面高于腹侧面约16%。结论猪胸主动脉的环向力学特性和位置有关,最远端的部分在低应力下表现出较软特点。研究结果有助于科研人员更好理解主动脉的力学特征以及开展更细致的计算机建模。