Collagen fibril morphology and organization: implications for force transmission in ligament and tendon.

Connective tissue mechanical behavior is primarily determined by the composition and organization of collagen. In ligaments and tendons, type I collagen is the principal structural element of the extracellular matrix, which acts to transmit force between bones or bone and muscle, respectively. Therefore, characterization of collagen fibril morphology and organization in fetal and skeletally mature animals is essential to understanding how tissues develop and obtain their mechanical attributes. In this study, tendons and ligaments from fetal rat, bovine, and feline, and mature rat were examined with scanning electron microscopy. At early fetal developmental stages, collagen fibrils show fibril overlap and interweaving, apparent fibril ends, and numerous bifurcating/fusing fibrils. Late in fetal development, collagen fibril ends are still present and fibril bundles (fibers) are clearly visible. Examination of collagen fibrils from skeletally mature tissues, reveals highly organized regions but still include fibril interweaving, and regions that are more randomly organized. Fibril bifurcations/fusions are still present in mature tissues but are less numerous than in fetal tissue. To address the continuity of fibrils in mature tissues, fibrils were examined in individual micrographs and consecutive overlaid micrographs. Extensive microscopic analysis of mature tendons and ligaments detected no fibril ends. These data strongly suggest that fibrils in mature ligament and tendon are either continuous or functionally continuous. Based upon this information and published data, we conclude that force within these tissues is directly transferred through collagen fibrils and not through an interfibrillar coupling, such as a proteoglycan bridge.     

Radial organization of interstitial exchange pathway and influence of collagen in synovium.

The synovial intercellular space is the path by which water, nutrients, cytokines, and macromolecules enter and leave the joint cavity. In this study two structural factors influencing synovial permeability were quantified by morphometry (Delesse's principle) of synovial electronmicrographs (rabbit knee), namely interstitial volume fraction Vv.1 and the fraction of the interstitium obstructed by collagen fibrils. Mean Vv.1 across the full thickness was 0.66 +/- 0.03 SEM (n = 11); but Vv.1 actually varied systematically with depth normal to the surface, increasing nonlinearly from 0.40 +/- 0.04 (n = 5 joints) near the free surface to 0.92 +/- 0.02 near the subsynovial interface. Tending to offset this increase in transport space, however, the space "blocked" by collagen fibrils also increased nonlinearly with depth. Bundles of collagen fibrils occupied 13.6 +/- 2.4% of interstitial volume close to the free surface but 49 +/- 4.8% near the subsynovial surface (full-thickness average, 40.5 +/- 3.5%), with fibrils accounting for 48.6-57.1% of the bundle space. Because of the two counteracting compositional gradients, the space available for fibril-excluded transport (hydraulic flow and macromolecular diffusion) was relatively constant > 4 microns below the surface but constricted at the synovium-cavity interface. The space available to extracellular polymers was only 51-53% of tissue volume, raising their effective concentration and hence the lining's resistance to flow and ability to confine the synovial fluid.     

Structure and mechanical properties of the longitudinal ligaments and ligamentum flavum of the spine

Stress-strain curves were recorded from anterior and posterior longitudinal ligaments and ligamenta flava dissected from pig lumbar spines. Ligaments were examined during extension by light microscopy, to observe crimp structure, and by X-ray diffraction, to determine collagen fibril orientations. Scanning electron microscopy (SEM) was used to examine ligaments fixed at high and low strains. Initial stages of ligament extension involvd alignment of collagen fibrils. Collagen fibrils in unstrained ligamentum flavum were much more disoriented than in the longitudinal ligaments. Thus, fibril alignment, and consequent stiffening, occurred at much higher strains than for longitudinal ligaments, allowing ligamentum flavum to exploit the extensibility of its elastin.     

The dynamics of collagen uncrimping and lateral contraction in tendon and the effect of ionic concentration

Under tensile loading, tendon undergoes a number of unique structural changes that govern its mechanical response. For example, stretching a tendon is known to induce both the progressive “uncrimping” of wavy collagen fibrils and extensive lateral contraction mediated by fluid flow out of the tissue. However, it is not known whether these processes are interdependent. Moreover, the rate-dependence of collagen uncrimping and its contribution to tendon's viscoelastic mechanical properties are unknown. Therefore, the objective of this study was to (a) develop a methodology allowing for simultaneous measurement of crimp, stress, axial strain and lateral contraction in tendon under dynamic loading; (b) determine the interdependence of collagen uncrimping and lateral contraction by testing tendons in different swelling conditions; and (c) assess how the process of collagen uncrimping depends on loading rate. Murine flexor carpi ulnaris (FCU) tendons in varying ionic environments were dynamically stretched to a set strain level and imaged through a plane polariscope with the polarizer and analyzer at a fixed angle. Analysis of the resulting images allowed for direct measurement of the crimp frequency and indirect measurement of the tendon thickness. Our findings demonstrate that collagen uncrimping and lateral contraction can occur independently and interstitial fluid impacts tendon mechanics directly. Furthermore, tensile stress, transverse contraction and degree of collagen uncrimping were all rate-dependent, suggesting that collagen uncrimping plays a role in tendon's dynamic mechanical response. This study is the first to characterize the time-dependence of collagen uncrimping in tendon, and establishes structure–function relationships for healthy tendons that can be used to better understand and assess changes in tendon mechanics after disease or injury.     

Effect of the glycocalyx layer on transmission of interstitial flow shear stress to embedded cells

In this paper, a simple theoretical model is developed to describe the transmission of force from interstitial fluid flow to the surface of a cell covered by a proteoglycan / glycoprotein layer (glycocalyx) and embedded in an extracellular matrix. Brinkman equations are used to describe flow through the extracellular matrix and glycocalyx layers and the solid mechanical stress developed in the glycocalyx by the fluid flow loading is determined. Using reasonable values for the Darcy permeability of extracellular matrix and glycocalyx layers and interstitial flow velocity, we are able to estimate the fluid and solid shear stresses imposed on the surface of embedded vascular, cartilage and tumor cells in vivo and in vitro. The principal finding is that the surface solid stress is typically one to two orders of magnitude larger than the surface fluid stress. This indicates that interstitial flow shear stress can be sensed by the cell surface glycocalyx, supporting numerous recent observations that interstitial flow can induce mechanotransduction in embedded cells. This study may contribute to understanding of interstitial flow-related mechanobiology in embryogenesis, tumorigenesis, tissue physiology and diseases and has implications in tissue engineering.     

Ultrastructural morphometry of membrane-bound intracytoplasmic collagen fibrils in tendon fibroblasts exposed to He:Ne laser beam.

Collagen fibrils are not found in fibroblast cytoplasm except in certain pathological conditions or in the presence of drugs and other agents that accelerate collagen turnover. Because low energy laser photostimulation is both a non-pathogenic and non-chemical accelerator of collagen synthesis, its effects were studied on four groups of calcaneal tendons from 18 rabbits (1) to test the hypothesis that vacuolar fibrils are not produced exclusively by diseases and chemical agents, and (2) to compare the morphometry of matrical and vacuolar fibrils. The right calcaneal tendons of nine rabbits were surgically tenotomized and repaired; six of these were transcutaneously irradiated with He:Ne laser everyday. The right calcaneal tendon of six of the remaining nine rabbits were similarly irradiated with laser, but without prior tenotomy and repair. 21 days later, all tendons were fixed in situ and processed for electron microscopy. Fibril-bearing vacuoles were found only in fibroblasts of tenotomized laser-irradiated tendons. Similar vacuoles were not seen in non-tenotomized laser-irradiated tendons nor in non-irradiated tendons whether tenotomized or not. Mann-Whitney U tests revealed no statistically significant differences in the cross-sectional areas or diameters of matrical and vacuolar fibrils. These findings suggest (a) that matrical and vacuolar fibrils have a common origin, and (b) that vacuolar fibrils can be induced by a non-pathologic, non-chemical accelerator of collagen synthesis.     

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.     

The role of fibril reinforcement in the mechanical behavior of cartilage

Collagen fibril reinforcement was incorporated into a nonlinear poroelastic model for articular cartilage in unconfined compression. It was found that the radial fibrils play a predominant role in the transient mechanical behavior but a less important role in the equilibrium response of cartilage. The radial fibrils are in tension and can be highly stressed during compression, in contrast to low compressive stresses in all directions for the proteoglycan matrix after a small initial compression. The strain dependent fibril stiffening produces strong nonlinear transient response; the fibrils provide extra stiffness to balance a rising fluid pressure and to restrain stress increase in the proteoglycans. The fibril reinforcement, induced by the fluid pressure and flow, also accounts for a complex pattern of strain-magnitude and strain-rate dependence of cartilage stiffness.     

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman–Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.     

Agarose-dextran gels as synthetic analogs of glomerular basement membrane: water permeability

Novel agarose-dextran hydrogels were synthesized and their suitability as experimental models of glomerular basement membrane was examined by measuring their Darcy (hydraulic) permeabilities (kappa). Immobilization of large dextran molecules in agarose was achieved by electron beam irradiation. Composite gels were made with agarose volume fractions (phi(a)) of 0.04 or 0.08 and dextran volume fractions (phi(d)) ranging from 0 to 0.02 (fiber volume/gel volume), using either of two dextran molecular weights (500 or 2000). At either agarose concentration and for either size of dextran, kappa decreased markedly as the amount of dextran was increased. Statistically significant deviations from the value of kappa for pure agarose were obtained for remarkably small volume fractions of dextran: phi(d) > or = 0.0003 for phi(a) = 0.04 and phi(d) > or = 0.001 for phi(a) = 0.08. The Darcy permeabilities were much more sensitive to phi(d) than to phi(a), and were as much as 26 times smaller than those of pure agarose. Although phi(d) was an important variable, dextran molecular weight was not. The effects of dextran addition on kappa were described fairly well using simple structural idealizations. At high agarose concentrations, the dextran chains behaved as fine fibers interspersed among coarse agarose fibrils, whereas, at low concentrations, the dextran molecules began to resemble spherical obstacles embedded in agarose gels. The ability to achieve physiologically relevant Darcy permeabilities with these materials (as low as 1.6 nm2) makes them an attractive experimental model for glomerular basement membrane and possibly other extracellular matrices.     

Towards patient-specific medializing calcaneal osteotomy for adult flatfoot: a finite element study

Clinically in medializing calcaneal osteotomy (MCO), foot and ankle surgeons are facing difficulties in choosing appropriate surgical parameters due to the individual differences in deformities among flatfoot patients. Traditional cadaveric studies have provided important information regarding the biomechanical effects of tendons, ligaments, and plantar fascia, but limitations have been reached when dealing with individual differences and tailoring patient-specific surgeries. Therefore, this study aimed at implementing the finite element (FE) method to investigate the effect of different MCO parameters to help foot and ankle surgeons performing patient-specific surgeries. This study constructed FE models of a flatfoot and a healthy foot based on computed tomography (CT) images. After validating the FE models with experimental measurements, differences in plantar stress were compared between two models and a criterion was established for evaluating the performance of surgical simulations. Four MCO parameters were then studied through FE simulations. Results suggested that the transverse angle, β, and translation distance, d, affected surgical performance. Therefore, special attentions may be recommended when choosing these two parameters clinically. However, the sagittal angle, α, and osteotomy position, p, were found to have less effect on the MCO performance.     

Dermatan sulphate-rich proteoglycan associates with rat tail-tendon collagen at the d band in the gap region.

Rat tail tendon was stained with a cationic phthalocyanin dye, Cupromeronic Blue, in a 'critical-electrolyte-concentration' method [Scott (1980) Biochem. J. 187, 887-891] specifically to demonstrate proteoglycan by electron microscopy. Hyaluronidase digestion in the presence of proteinase inhibitors corroborated the results. Collagen was stained with uranyl acetate and/or phosphotungstic acid to demonstrate the banding pattern a-e in the D period. Proteoglycan was distributed about the collagen fibrils in an orthogonal array, the transverse elements of which were located almost exclusively at the d band, in the gap zone. The proteoglycan may inhibit (1) fibril radial growth by accretion of collagen molecules or fibril fusion, through interference with cross-linking, and (2) calcification by occupying the holes in the gap region later to be filled with hydroxyapatite.     

Nanoliter scale microbioreactor array for quantitative cell biology

A nanoliter scale microbioreactor array was designed for multiplexed quantitative cell biology. An addressable 8 x 8 array of three nanoliter chambers was demonstrated for observing the serum response of HeLa human cancer cells in 64 parallel cultures. The individual culture unit was designed with a "C" shaped ring that effectively decoupled the central cell growth regions from the outer fluid transport channels. The chamber layout mimics physiological tissue conditions by implementing an outer channel for convective "blood" flow that feeds cells through diffusion into the low shear "interstitial" space. The 2 microm opening at the base of the "C" ring established a differential fluidic resistance up to 3 orders of magnitude greater than the fluid transport channel within a single mold microfluidic device. Three-dimensional (3D) finite element simulation were used to predict fluid transport properties based on chamber dimensions and verified experimentally. The microbioreactor array provided a continuous flow culture environment with a Peclet number (0.02) and shear stress (0.01 Pa) that approximated in vivo tissue conditions without limiting mass transport (10 s nutrient turnover). This microfluidic design overcomes the major problems encountered in multiplexing nanoliter culture environments by enabling uniform cell loading, eliminating shear, and pressure stresses on cultured cells, providing stable control of fluidic addressing, and permitting continuous on-chip optical monitoring.     

Insights into interstitial flow,shear stress,and mass transport effects on ECM heterogeneity in bioreactor-cultivated engineered cartilage hydrogels

Interstitial flow in articular cartilage is secondary to compressive and shear deformations during joint motion and has been linked with the well-characterized heterogeneity in structure and composition of its extracellular matrix. In this study, we investigated the effects of introducing gradients of interstitial flow on the evolution of compositional heterogeneity in engineered cartilage. Using a parallel-plate bioreactor, we observed that Poiseuille flow stimulation of chondrocyte-seeded agarose hydrogels led to an increase in glycosaminoglycan and type II collagen deposition in the surface region of the hydrogel exposed to flow. Experimental measurements of the interstitial flow fields based on the fluorescence recovery after photobleaching technique suggested that the observed heterogeneity in composition is associated with gradients in interstitial flow in a boundary layer at the hydrogel surface. Interestingly, the interstitial flow velocity profiles were nonlinearly influenced by flow rate, which upon closer examination led us to the original observation that the apparent hydrogel permeability decreased exponentially with increased interfacial shear stress. We also observed that interstitial flow enhances convective mass transport irrespective of molecular size within the boundary layer near the hydrogel surface and that the convective contribution to transport diminishes with depth in association with interstitial flow gradients. The implications of the nonlinearly inverse relationship between the interfacial shear stress and the interstitial flux and permeability and its consequences for convective transport are important for tissue engineering, since porous scaffolds comprise networks of Poiseuille channels (pores) through which interstitial flow must navigate under mechanical stimulation or direct perfusion.     

Col V siRNA engineered tenocytes for tendon tissue engineering

The presence of uniformly small collagen fibrils in tendon repair is believed to play a major role in suboptimal tendon healing. Collagen V is significantly elevated in healing tendons and plays an important role in fibrillogenesis. The objective of this study was to investigate the effect of a particular chain of collagen V on the fibrillogenesis of Sprague-Dawley rat tenocytes, as well as the efficacy of Col V siRNA engineered tenocytes for tendon tissue engineering. RNA interference gene therapy and a scaffold free tissue engineered tendon model were employed. The results showed that scaffold free tissue engineered tendon had tissue-specific tendon structure. Down regulation of collagen V α1 or α2 chains by siRNAs (Col5α1 siRNA, Col5α2 siRNA) had different effects on collagen I and decorin gene expressions. Col5α1 siRNA treated tenocytes had smaller collagen fibrils with abnormal morphology; while those Col5α2 siRNA treated tenocytes had the same morphology as normal tenocytes. Furthermore, it was found that tendons formed by coculture of Col5α1 siRNA treated tenocytes with normal tenocytes at a proper ratio had larger collagen fibrils and relative normal contour. Conclusively, it was demonstrated that Col V siRNA engineered tenocytes improved tendon tissue regeneration. And an optimal level of collagen V is vital in regulating collagen fibrillogenesis. This may provide a basis for future development of novel cellular- and molecular biology-based therapeutics for tendon diseases.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Finite element implementation of a new model of slight compressibility for transversely isotropic materials

Modelling transversely isotropic materials in finite strain problems is a complex task in biomechanics, and is usually addressed by using finite element (FE) simulations. The standard method developed to account for the quasi-incompressible nature of soft tissues is to decompose the strain energy function (SEF) into volumetric and deviatoric parts. However, this decomposition is only valid for fully incompressible materials, and its use for slightly compressible materials yields an unphysical response during the simulation of hydrostatic tension/compression of a transversely isotropic material. This paper presents the FE implementation as subroutines of a new volumetric model solving this deficiency in two FE codes: Abaqus and FEBio. This model also has the specificity of restoring the compatibility with small strain theory. The stress and elasticity tensors are first derived for a general SEF. This is followed by a successful convergence check using a particular SEF and a suite of single-element tests showing that this new model does not only correct the hydrostatic deficiency but may also affect stresses during shear tests (Poynting effect) and lateral stretches during uniaxial tests (Poisson's effect). These FE subroutines have numerous applications including the modelling of tendons, ligaments, heart tissue, etc. The biomechanics community should be aware of specificities of the standard model, and the new model should be used when accurate FE results are desired in the case of compressible materials.     

The molecular and fibrillar structure of collagen and its relationship to the mechanical properties of connective tissue

The conformation of type I collagen molecules has been refined using a linked-atom least-squares procedure in conjunction with high-quality X-ray diffraction data. In many tendons these molecules pack in crystalline arrays and a careful measurement of the positions of the Bragg reflections allows the unit cell to be determined with high precision. From a further analysis of the X-ray data it can be shown that the highly ordered overlap region of the collagen fibrils consists of a crystalline array of molecular segments inclined by a small angle with respect to the fibril axis. In contrast, the gap region is less well ordered and contains molecular segments that are likely to be inclined by a similar angle but in a different vertical plane to that found in the overlap region. The collagen molecule thus has a D-periodic crimp in addition to the macroscopic crimp observed visually in the collagen fibres of many connective tissues. The growth and development of collagen fibrils have been studied by electron microscopy for a diverse range of connective tissues and the general pattern of fibril growth has been established as a function of age. In particular, relationships between fibril size distribution, the content and composition of the glycosaminoglycans in the matrix and the mechanical role played by the fibrils in the tissue have been formulated and these now seem capable of explaining many new facets of connective tissue structure and function.     

Matrix protein microarrays for spatially and compositionally controlled microspot thrombosis under laminar flow

Microarraying allows the spatial and compositional control of surfaces, typically for the purpose of binding reactions. Collagen and/or von Willebrand Factor (vWF) in 5% glycerol was contact printed onto glass slides to create defined microspots (176-microm diameter) of adsorbed protein without sample dehydration. The arrays were mounted on flow chambers allowing video microscopy during perfusion (wall shear rate of 100-500 s(-1)) of recalcified corn trypsin inhibitor-treated whole blood or platelet rich plasma and subsequent array scanning via anti-GPIbalpha and anti-fibrin(ogen) immunofluorescence. To mimic the subendothelial matrix, vWF was microarrayed over sonicated type I collagen microspots. For whole blood perfusion (500 s(-1), 10 min) over collagen, vWF, and collagen/vWF microspots, the amount of platelet deposition on the collagen/vWF spots was approximately 2 times greater in comparison to the collagen spots and approximately 18 times greater in comparison to the vWF spots. The amount of fibrin(ogen) deposition on the collagen/vWF spots was approximately 2 times greater in comparison to the collagen spots and approximately 4 times greater in comparison to the vWF spots. This protocol allowed for highly uniform (CV = 18%) and precisely located thrombus formation at a density of >or=400 spots/cm(2). Microarrays are ideal for the combinatorial assembly of adhesive and procoagulant proteins to study thrombosis as well as to study axial and lateral transport effects between discrete microspots of distinct composition.     

On bone adaptation due to venous stasis

This paper addresses the question of whether or not interstitial fluid flow due to the blood circulation accounts for the observed periosteal bone formation associated with comprised venous return (venous stasis). Increased interstitial fluid flow induced by increased intramedullary pressure has been proposed to account for the periosteal response in venous stasis. To investigate the shear stresses acting on bone cell processes due to the blood circulation-driven interstitial fluid flow, a poroelastic model is extended to the situation in which the interstitial fluid flow in an osteon is driven by the pulsatile extravascular pressure in the osteonal canal as well as by the applied cyclic mechanical loading. Our results show that under normal conditions, the pulsatile extravascular pressure in the osteonal canal due to cardiac contraction (10mm Hg at 2Hz) and skeletal muscle contraction (30mm Hg at 1Hz) induce peak shear stresses on the osteocyte cell processes that are two orders of magnitude lower than those induced by physiological mechanical loading (100 microstrain at 1Hz). In venous stasis the induced peak shear stress is reduced further compared to the normal conditions because, although the mean intramedullary pressure is increased, the amplitude of its pulsatile component is decreased. These results suggest that the interstitial fluid flow is unlikely to cause the periosteal bone formation in venous stasis. However, the mean interstitial fluid pressure is found to increase in venous stasis, which may pressurize the periosteum and thus play a role in periosteal bone formation.