Anisotropic hydraulic permeability in compressed articular cartilage

The extent to which articular cartilage hydraulic permeability is anisotropic is largely unknown, despite its importance for understanding mechanisms of joint lubrication, load bearing, transport phenomena, and mechanotransduction. We developed and applied new techniques for the direct measurement of hydraulic permeability within statically compressed adult bovine cartilage explant disks, dissected such that disk axes were perpendicular to the articular surface. Applied pressure gradients were kept small to minimize flow-induced matrix compaction, and fluid outflows were measured by observation of a meniscus in a glass capillary under a microscope. Explant disk geometry under radially unconfined axial compression was measured by direct microscopic observation. Pressure, flow, and geometry data were input to a finite element model where hydraulic permeabilities in the disk axial and radial directions were determined. At less than 10% static compression, near free-swelling conditions, hydraulic permeability was nearly isotropic, with values corresponding to those of previous studies. With increasing static compression, hydraulic permeability decreased, but the radially directed permeability decreased more dramatically than the axially directed permeability such that strong anisotropy (a 10-fold difference between axial and radial directions) in the hydraulic permeability tensor was evident for static compression of 20-40%. Results correspond well with predictions of a previous microstructurally-based model for effects of tissue mechanical deformations on glycosaminoglycan architecture and cartilage hydraulic permeability. Findings inform understanding of structure-function relationships in cartilage matrix, and suggest several biomechanical roles for compression-induced anisotropic hydraulic permeability in articular cartilage.     

Tissue softening of guinea pig oesophagus tested by the tri-axial test machine

Tissue softening is commonly reported during mechanical testing of biological tissues in vitro. The loss of stiffness may be due to viscoelasticity-induced softening (the time-history of load-caused softening) and strain-induced stress softening (the maximum previous load-caused softening). However, the knowledge about tissue softening behaviour is presently poor. The aims of this study were to distinguish whether the loss of the stiffness during preconditioning was due to strain softening or viscoelasticity and to test the tissue softening in circumferential and longitudinal direction in the guinea pig oesophagus. Eight repeated pressure controlled ramp distensions and eight uniaxial tensile-release ramp stretches in three series were done on eight guinea pig oesophagi. The stress–strain curves were used to display the time-dependency (viscoelasticity) and the maximum previous load-caused softening (strain softening) in circumferential and longitudinal directions. For both the longitudinal and the circumferential softening, the peak stress and stiffness produced during the first loading were bigger than those produced in the remaining loadings. The stress loss due to strain softening was about three times more than that due to viscoelasticity in the longitudinal direction. The strain increased more than two times between the strain softening and viscoelastic softening in the circumferential direction. With a stress level of 20 kPa, the stiffness in the circumferential direction lost more than that in the longitudinal direction (P<0.05), indicating the anisotropic softening properties in the oesophagus. In conclusion, the stiffness loss during preconditioning is mainly attributed to strain softening, appears irreversible and is anisotropic.     

Mechanical anisotropy of inflated elastic tissue from the pig aorta

Uniaxial and biaxial mechanical properties of purified elastic tissue from the proximal thoracic aorta were studied to understand physiological load distributions within the arterial wall. Stress–strain behaviour was non-linear in uniaxial and inflation tests. Elastic tissue was 40% stiffer in the circumferential direction compared to axial in uniaxial tests and～100% stiffer in vessels at an axial stretch ratio of 1.2 or 1.3 and inflated to physiological pressure. Poisson’s ratio v_θz averaged 0.2 and v_zθ increased with circumferential stretch from ～0.2 to ～0.4. Axial stretch had little impact on circumferential behaviour. In intact (unpurified) vessels at constant length, axial forces decreased with pressure at low axial stretches but remained constant at higher stretches. Such a constant axial force is characteristic of incrementally isotropic arteries at their in vivo dimensions. In purified elastic tissue, force decreased with pressure at all axial strains, showing no trend towards isotropy. Analysis of the force–length–pressure data indicated a vessel with v_θz≈0.2 would stretch axially 2–4% with the cardiac pulse yet maintain constant axial force. We compared the ability of 4 mathematical models to predict the pressure-circumferential stretch behaviour of tethered, purified elastic tissue. Models that assumed isotropy could not predict the stretch at zero pressure. The neo-Hookean model overestimated the non-linearity of the response and two non-linear models underestimated it. A model incorporating contributions from orthogonal fibres captured the non-linearity but not the zero-pressure response. Models incorporating anisotropy and non-linearity should better predict the mechanical behaviour of elastic tissue of the proximal thoracic aorta.     

Regional variation in the mechanical role of knee meniscus glycosaminoglycans

High compressive properties of cartilaginous tissues are commonly attributed to the sulfated glycosaminoglycan (GAG) fraction of the extracellular matrix (ECM), but this relationship has not been directly measured in the knee meniscus, which shows regional variation in GAG content. In this study, biopsies from each meniscus region (outer, middle, and inner) were either subjected to chondroitinase ABC (CABC) to remove all sulfated GAGs or not. Compressive testing revealed that GAG depletion in the inner and middle meniscus regions caused a significant decrease in modulus of relaxation (58% and 41% decreases, respectively, at 20% strain), and all regions exhibited a significant decrease in viscosity (outer: 29%; middle: 58%; inner: 62% decrease). Tensile properties following CABC treatment were unaffected for outer and middle meniscus specimens, but the inner meniscus displayed significant increases in Young's modulus (41% increase) and ultimate tensile stress (40% increase) following GAG depletion. These findings suggest that, in the outer meniscus, GAGs contribute to increasing tissue viscosity, whereas in the middle and inner meniscus, where GAGs are most abundant, these molecules also enhance the tissue's ability to withstand compressive loads. GAGs in the inner meniscus also contribute to reducing the circumferential tensile properties of the tissue, perhaps due to the pre-stress on the collagen network from increased hydration of the ECM. Understanding the mechanical role of GAGs in each region of the knee meniscus is important for understanding meniscus structure-function relationships and creating design criteria for functional meniscus tissue engineering efforts.     

Stress fibers of the aortic smooth muscle cells in tissues do not align with the principal strain direction during intraluminal pressurization

Stress fibers (SFs) in cells transmit external forces to cell nuclei, altering the DNA structure, gene expression, and cell activity. To determine whether SFs are involved in mechanosignal transduction upon intraluminal pressure, this study investigated the SF direction in smooth muscle cells (SMCs) in aortic tissue and strain in the SF direction. Aortic tissues were fixed under physiological pressure of 120 mmHg. First, we observed fluorescently labeled SFs using two-photon microscopy. It was revealed that SFs in the same smooth muscle layers were aligned in almost the same direction, and the absolute value of the alignment angle from the circumferential direction was 16.8° ± 5.2° (n = 96, mean ± SD). Second, we quantified the strain field in the aortic tissue in reference to photo-bleached markers. It was found in the radial-circumferential plane that the largest strain direction was − 21.3° ± 11.1°, and the zero normal strain direction was 28.1° ± 10.2°. Thus, the SFs in aortic SMCs were not in line with neither the largest strain direction nor the zero strain direction, although their orientation was relatively close to the zero strain direction. These results suggest that SFs in aortic SMCs undergo stretch, but not maximal and transmit the force to nuclei under intraluminal pressure.

     

Characterization of the mechanical behavior of the optic nerve sheath and its role in spaceflight-induced ophthalmic changes

Visual impairment and intracranial pressure (VIIP) syndrome is characterized by a number of permanent ophthalmic changes, including loss of visual function. It occurs in some astronauts during long-duration spaceflight missions. Thus, understanding the pathophysiology of VIIP is currently a major priority in space medicine research. It is hypothesized that maladaptive remodeling of the optic nerve sheath (ONS), in response to microgravity-induced elevations in intracranial pressure (ICP), contributes to VIIP. However, little is known about ONS biomechanics. In this study, we developed a custom mechanical testing system that allowed for unconfined lengthening, twisting, and circumferential distension of the porcine ONS during inflation and axial loading. Data were fit to a four-fiber family constitutive equation to extract material and structural parameters. Inflation testing showed a characteristic “cross-over point” in the pressure–diameter curves under different axial loads in all samples that were tested; the cross-over pressure was \(10.3 \pm 0.95\) mmHg (\(\hbox {mean} \pm \hbox {SEM}\)). Large sample-to-sample variations were observed in the circumferential strain, while only modest variations were observed in the circumferential stress. Multiphoton microscopy revealed that the collagen fibers of the ONS were primarily oriented axially when the tissue was loaded. The existence of this cross-over behavior is expected to be neuroprotective, as it would avoid optic nerve compression during routine changes in gaze angle, so long as ICP was within the normal range. Including these observations into computational models of VIIP will help provide insight into the pathophysiology of VIIP and could help identify risk factors and potential interventions.     

Improved characterization of cartilage mechanical properties using a combination of stress relaxation and creep

Mechanical characterization of cartilage, other soft tissues and gels has become a ubiquitous and essential aspect of biomechanics and biomaterials research. Current progress in theoretical modeling and tools for data analysis often exceed what is required for routine mechanical characterization assays in experimental studies, making selection of methodologies difficult for the nonspecialist. We have therefore developed an approach for measurement of confined compression modulus and hydraulic permeability based on simple poroelasticity theory and requiring only linear regression tools for data analysis. This technique involves a new application of an early-time solution for creep combined with stress relaxation measurements to characterize soft tissue mechanical parameters as a function of compressive strain or water content. This combined methodology allows measurement of hydraulic permeability by two different techniques with only a modest increase in experimental duration, providing a more precise assessment of permeability and associated measurement error.     

Biaxial mechanical properties of bovine jugular venous valve leaflet tissues

Venous valve incompetence has been implicated in diseases ranging from chronic venous insufficiency (CVI) to intracranial venous hypertension. However, while the mechanical properties of venous valve leaflet tissues are central to CVI biomechanics and mechanobiology, neither stress–strain curves nor tangent moduli have been reported. Here, equibiaxial tensile mechanical tests were conducted to assess the tangent modulus, strength and anisotropy of venous valve leaflet tissues from bovine jugular veins. Valvular tissues were stretched to 60% strain in both the circumferential and radial directions, and leaflet tissue stress–strain curves were generated for proximal and distal valves (i.e., valves closest and furthest from the right heart, respectively). Toward linking mechanical properties to leaflet microstructure and composition, Masson’s trichrome and Verhoeff–Van Gieson staining and collagen assays were conducted. Results showed: (1) Proximal bovine jugular vein venous valves tended to be bicuspid (i.e., have two leaflets), while distal valves tended to be tricuspid; (2) leaflet tissues from proximal valves exhibited approximately threefold higher peak tangent moduli in the circumferential direction than in the orthogonal radial direction (i.e., proximal valve leaflet tissues were anisotropic; \(p<0.01\)); (3) individual leaflets excised from the same valve apparatus appeared to exhibit different mechanical properties (i.e., intra-valve variability); and (4) leaflets from distal valves exhibited a trend of higher soluble collagen concentrations than proximal ones (i.e., inter-valve variability). To the best of the authors’ knowledge, this is the first study reporting biaxial mechanical properties of venous valve leaflet tissues. These results provide a baseline for studying venous valve incompetence at the tissue level and a quantitative basis for prosthetic venous valve design.     

Three-dimensional stress and strain distribution in a two-layer model of a coronary artery

For a right coronary artery, three-dimensional stress and strain distributions at a physiological intraluminal pressure and an axial extension ratio were computed on the basis of a two-layer elastic model. To validate the model, curves of external radius versus pressure and of axial force versus pressure were computed for three axial extension ratios. To analyze mechanical properties, stress-free configurations of media and adventitia, and the constitutive law of each layer in literature, were used. The present study showed that the peak circumferential stress and the peak axial stress appear in the media at the boundary between the media and adventitia. This result is due to the opening angle of the media being larger than π (rad) and the larger value of a material constant of the strain energy function for the media than for the adventitia. The circumferential stress and strain were discontinuous at the boundary. On the other hand, the radial stress was continuous at the boundary because of the boundary condition for stress. The circumferential stress and axial stress in the adventitia were almost uniformly distributed, and smaller than in the media. The residual stress and strain were also computed. The circumferential residual stress and strain were almost linearly distributed in each layer, although discontinuity appeared at the boundary between the two layers.     

Transmural flow bioreactor for vascular tissue engineering

Nutrient transport limitation remains a fundamental issue for in vitro culture of engineered tissues. In this study, perfusion bioreactor configurations were investigated to provide uniform delivery of oxygen to media equivalents (MEs) being developed as the basis for tissue‐engineered arteries. Bioreactor configurations were developed to evaluate oxygen delivery associated with complete transmural flow (through the wall of the ME), complete axial flow (through the lumen), and a combination of these flows. In addition, transport models of the different flow configurations were analyzed to determine the most uniform oxygen profile throughout the tissue, incorporating direct measurements of tissue hydraulic conductivity, cellular O₂ consumption kinetics, and cell density along with ME physical dimensions. Model results indicate that dissolved oxygen (DO) uniformity is improved when a combination of transmural and axial flow is implemented; however, detrimental effects could occur due to lumenal pressure exceeding the burst pressure or damaging interstitial shear stress imparted by excessive transmural flow rates or decreasing hydraulic conductivity due to ME compaction. The model was verified by comparing predicted with measured outlet DO concentrations. Based on these results, the combination of a controlled transmural flow coupled with axial flow presents an attractive means to increase the transport of nutrients to cells within the cultured tissue to improve growth (increased cell and extracellular matrix concentrations) as well as uniformity. Biotechnol. Bioeng. 2009; 104: 1197–1206. © 2009 Wiley Periodicals, Inc.     

Glycosaminoglycan network geometry may contribute to anisotropic hydraulic permeability in cartilage under compression.

Resistance to fluid flow within cartilage extracellular matrix is provided primarily by a dense network of rod-like glycosaminoglycans (GAGs). If the geometrical organization of this network is random, the hydraulic permeability tensor of cartilage is expected to be isotropic. However, experimental data have suggested that hydraulic permeability may become anisotropic when the matrix is mechanically compressed, contributing to cartilage biomechanical functions such as lubrication. We hypothesized that this may be due to preferred GAG rod orientations and directionally-dependent reduction of inter-GAG spacings which reflect molecular responses to tissue deformations. To examine this hypothesis, we developed a model for effects of compression which allows the GAG rod network to deform consistently with tissue-scale deformations but while still respecting limitations imposed by molecular structure. This network deformation model was combined with a perturbation analysis of a classical analytical model for hydraulic permeability based on molecular structure. Finite element analyses were undertaken to ensure that this approach exhibited results similar to those emerging from more exact calculations. Model predictions for effects of uniaxial confined compression on the hydraulic permeability tensor were consistent with previous experimental results. Permeability decreased more rapidly in the direction perpendicular to compression than in the parallel direction, for matrix solid volume fractions associated with fluid transport in articular cartilage. GAG network deformations may therefore introduce anisotropy to the permeability (and other GAG-associated matrix properties) as physiological compression is applied, and play an important role in cartilage lubrication and other biomechanical functions.     

Permeability evaluation of 45S5 Bioglass®-based scaffolds for bone tissue engineering

Permeability is a key parameter for microstructural design of scaffolds, since it is related to their capability for waste removal and nutrients/oxygen supply. In this framework, Darcy's experiments were carried out in order to determine the relationship between the pressure drop gradient and the fluid flow velocity in Bioglass^®-based scaffolds to obtain the scaffold's permeability. Using deionised water as working fluid, the measured average permeability value on scaffolds of 90–95% porosity was 1.96×10^?9 m². This value lies in the published range of permeability values for trabecular bone.     

Determination of the strain-dependent hydraulic permeability of the compressed bovine nucleus pulposus

The hydraulic permeability, k, of the nucleus pulposus (NP) is crucial, both in withstanding compressive stress and for convective transport of nutrients within the disc. Permeability has previously been determined using biphasic mathematical models, but has not been found by direct permeation experiments, which is the objective of this study. Bovine coccygeal nucleus samples (n=64), phi10mm and thickness 683+/-49microm (mean+/-S.D.) were compressed axially to one of lambda=1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4 or 0.3, where lambda is the stretch ratio. Ringer's solution was permeated through the sample, with an o-ring ensuring axial flow. During stress equilibrium, k was determined and fitted to four permeability-strain equations. Permeability decreased exponentially with compression, and was best described by Values of k were comparable to those arising from mathematical models, lending confidence to permeability being determined from such models.     

Patient-Specific Artery Shrinkage and 3D Zero-Stress State in Multi-Component 3D FSI Models for Carotid Atherosclerotic Plaques Based on <i>In Vivo</i> MRI Data

Image-based computational models for atherosclerotic plaques have been developed to perform mechanical analysis to quantify critical flow and stress/strain conditions related to plaque rupture which often leads directly to heart attack or stroke. An important modeling issue is how to determine zero stress state from in vivo plaque geometries. This paper presents a method to quantify human carotid artery axial and inner circumferential shrinkages by using patient-specific ex vivo and in vivo MRI images. A shrink-stretch process based on patient-specific in vivo plaque morphology and shrinkage data was introduced to shrink the in vivo geometry first to find the zero-stress state (opening angle was ignored to reduce the complexity), and then stretch and pressurize to recover the in vivo plaque geometry with computed initial stress, strain, flow pressure and velocity conditions. Effects of the shrink-stretch process on plaque stress/strain distributions were demonstrated based on patient-specific data using 3D models with fluid-structure interactions (FSI). The average artery axial and inner circumferential shrinkages were 25% and 7.9%, respectively, based on a data set obtained from 10 patients. Maximum values of maximum principal stress and strain increased 349.8% and 249% respectively with 33% axial stretch. Influence of inner circumferential shrinkage (7.9%) was not very noticeable under 33% axial stretch, but became more noticeable under smaller axial stretch. Our results indicated that accurate knowledge of artery shrinkages and the shrink-stretch process will considerably improve the accuracy of computational predictions made based on results from those in vivo MRI-based FSI models.     

Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus

Nonlinear, linear and failure properties of articular cartilage and meniscus in opposing contact surfaces are poorly known in tension. Relationships between the tensile properties of articular cartilage and meniscus in contact with each other within knee joints are also not known. In the present study, rectangular samples were prepared from the superficial lateral femoral condyle cartilage and lateral meniscus of bovine knee joints. Tensile tests were carried out with a loading rate of 5 mm/min until the tissue rupture. Nonlinear properties of the toe region, linear properties in larger strains, and failure properties of both tissues were analysed. The strain-dependent tensile modulus of the toe region, Young's modulus of the linear region, ultimate tensile stress and toughness were on average 98.2, 8.3, 4.0 and 1.9 times greater (p<0.05) for meniscus than for articular cartilage. In contrast, the toe region strain, yield strain and failure strain were on average 9.4, 3.1 and 2.3 times greater (p<0.05) for cartilage than for meniscus. There was a significant negative correlation between the strain-dependent tensile moduli of meniscus and articular cartilage samples within the same joints (r=−0.690, p=0.014). In conclusion, the meniscus possesses higher nonlinear and linear elastic stiffness and energy absorption capability before rupture than contacting articular cartilage, while cartilage has longer nonlinear region and can withstand greater strains before failure. These findings point out different load carrying demands that both articular cartilage and meniscus have to fulfil during normal physiological loading activities of knee joints.     

On the anisotropy and inhomogeneity of permeability in articular cartilage

Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is "directed" by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.     

Subject-specific multiscale modeling of aortic valve biomechanics

A Finite Element workflow for the multiscale analysis of the aortic valve biomechanics was developed and applied to three physiological anatomies with the aim of describing the aortic valve interstitial cells biomechanical milieu in physiological conditions, capturing the effect of subject-specific and leaflet-specific anatomical features from the organ down to the cell scale. A mixed approach was used to transfer organ-scale information down to the cell-scale. Displacement data from the organ model were used to impose kinematic boundary conditions to the tissue model, while stress data from the latter were used to impose loading boundary conditions to the cell level. Peak of radial leaflet strains was correlated with leaflet extent variability at the organ scale, while circumferential leaflet strains varied over a narrow range of values regardless of leaflet extent. The dependency of leaflet biomechanics on the leaflet-specific anatomy observed at the organ length-scale is reflected, and to some extent emphasized, into the results obtained at the lower length-scales. At the tissue length-scale, the peak diastolic circumferential and radial stresses computed in the fibrosa correlated with the leaflet surface area. At the cell length-scale, the difference between the strains in two main directions, and between the respective relationships with the specific leaflet anatomy, was even more evident; cell strains in the radial direction varied over a relatively wide range (\(0.36-0.87\)) with a strong correlation with the organ length-scale radial strain (\(R^{2}= 0.95\)); conversely, circumferential cell strains spanned a very narrow range (\(0.75-0.88\)) showing no correlation with the circumferential strain at the organ level (\(R^{2}= 0.02\)). Within the proposed simulation framework, being able to account for the actual anatomical features of the aortic valve leaflets allowed to gain insight into their effect on the structural mechanics of the leaflets at all length-scales, down to the cell scale.

     

Anisotropic hydraulic permeability under finite deformation

The structural organization of biological tissues and cells often produces anisotropic transport properties. These tissues may also undergo large deformations under normal function, potentially inducing further anisotropy. A general framework for formulating constitutive relations for anisotropic transport properties under finite deformation is lacking in the literature. This study presents an approach based on representation theorems for symmetric tensor-valued functions and provides conditions to enforce positive semidefiniteness of the permeability or diffusivity tensor. Formulations are presented, which describe materials that are orthotropic, transversely isotropic, or isotropic in the reference state, and where large strains induce greater anisotropy. Strain-induced anisotropy of the permeability of a solid-fluid mixture is illustrated for finite torsion of a cylinder subjected to axial permeation. It is shown that, in general, torsion can produce a helical flow pattern, rather than the rectilinear pattern observed when adopting a more specialized, unconditionally isotropic spatial permeability tensor commonly used in biomechanics. The general formulation presented in this study can produce both affine and nonaffine reorientations of the preferred directions of material symmetry with strain, depending on the choice of material functions. This study addresses a need in the biomechanics literature by providing guidelines and formulations for anisotropic strain-dependent transport properties in porous-deformable media undergoing large deformations.     

Ex vivo deformations of the urinary bladder wall during whole bladder filling: Contributions of extracellular matrix and smooth muscle

As the complete understanding of urinary bladder function requires knowledge of organ level deformations, we conducted ex vivo studies of surface strains of whole bladders during controlled filling. The surface strains derived from displacements of surface markers applied to the posterior surface of excised rat bladders were tracked under slow filling with pressure and volume simultaneously recorded in the passive and completely inactivated states (i.e. with and without smooth muscle tone, respectively). Bladders evaluated in the passive state exhibited spontaneous contractions and larger average peak pressures (16.7 mmHg compared to 6.4 mmHg in the inactive state). Overall, the bladders exhibited anisotropic deformations and were stiffer in the circumferential direction, with average peak stretch values of ～2.3 and ～1.9 in the longitudinal and circumferential directions, respectively, for both states. Although bladders in the passive state were stiffer, they had similar average peak areal stretches of 4.3 in both states. However, differences early in the filling process as a result of a loss in smooth muscle tone in the inactive state resulted in longitudinal lengthening of 36%. Idealizing the bladder as a prolate spheroid, we estimated the wall stress–strain relation during filling and demonstrated that the intact bladder exhibited the classic stress–stretch relation, with a significantly protracted low stress region and peak stresses of 36 and 51 kPa in the longitudinal and circumferential directions, respectively. The present study fills a major gap in the urinary bladder biomechanics literature, wherein knowledge of the pressure–volume–wall stress–wall strain relation was explored for the first time in a functioning organ ex vivo.