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1.
An asymptotic analysis of a lubrication problem is presented for a model of articular cartilage and synovial fluid under the squeeze-film condition. This model is based upon the following constitutive assumptions: (1) articular cartilage is a linear porous-permeable biphasic material filled with a linearly viscous fluid (i.e. Newtonian fluid); (2) synovial fluid is also a linearly viscous fluid. The geometry of the problem is defined by assuming that (1) cartilage is a uniform layer of thickness H; (2) synovial fluid is a very thin layer compared to H; (3) the radius R of the load-supporting area (or the effective radius of curvature of joint surface, Ri) is large compared to H. Squeeze-film action is generated in the lubricant by a step loading function applied onto the two bearing surfaces. The model assumptions and the material properties yield two small parameters in the mathematical formulation. Based on these two small parameters, two coupled nonlinear partial differential equations were derived from an asymptotic analysis of the problem: one for the lubricant (analogous to the Reynolds equation) and one for the cartilage. For known properties of normal cartilage, our calculations show: (1) the cartilage layer deforms to enlarge the load-supporting area; (2) cartilage deformation acts to reduce the lateral fluid speed in the lubricant, thus prolonging the squeeze-film time which ranges from 1 to 10 s; (3) lubricant fluid in the gap is forced from the central high-pressure region into cartilage, and expelled from the tissue at the low-pressure periphery of the load-bearing region; and (4) tensile hoop stress exists at the cartilage surface despite the compressive squeeze-film loading condition. This hoop stress results directly from the radial flow of the interstitial fluid in the cartilage layer.  相似文献   

2.
Hemiarthroplasty is a potentially attractive alternative to knee replacement for young, active patients, as it allows preservation of more bone stock for potential revisions. However, there has been limited success with hemiarthroplasty or spacers to date. The wear and degradation of the biomaterial–cartilage interface is of paramount importance in the design and success of hemiarthroplasties. A comprehensive understanding of the tribological performance of hemiarthroplasty implants in the natural joint is required. The objective of this study was to investigate the tribological response of bovine medial compartmental knees, both natural and hemiarthroplasty replaced, under physiological loads and motion. The conformity of these metallic hemiarthroplasties was varied (conforming plates with radius of 50 mm and radius of 100 mm and a flat plate design), in order to examine the effects of conformity and contact stress, on the friction, friction shear stress and cartilage degeneration. With decreasing conformity of hemiarthroplasty bearings, an increase in contact stress was found, which resulted in elevated friction, elevated friction shear stress and increased cartilage degeneration. A strong correlation was found between contact stress and wear and between friction shear stress and wear. This new and unique in vitro tribological simulation has shown the direct elevation of friction, surface fibrillation and biomechanical wear of cartilage, upon replacing the tibia with a hemiarthroplasty, particularly when using low conformity hemiarthroplasty designs.  相似文献   

3.
Interstitial fluid pressurization, a consequence of a biphasic tissue structure, is essential to the load bearing and lubrication properties of articular cartilage. Focal tissue degradation may interfere with this protective mechanism, eventually leading to gross degeneration and osteoarthritis. Our long-term goal is to determine whether local contacts can be used as a means to probe local tissue integrity and functionality. In the present work, Hertzian rate-controlled microindentation was used as a model of the more complicated sliding system to directly determine the effects of contact radius and deformation rate on interstitial load support. During localized contact between a steel spherical probe and bovine articular cartilage, the equilibrium and non-equilibrium responses were well-fit by the Hertz model (R(2)>0.998) with a mean equilibrium contact modulus of 0.93 MPa. The effective contact modulus and fluid load fraction were independent of indentation depth, contact radius, and normal force; both increased monotonically with indentation rate. At 21 μm/s indentation rate, the cartilage was effectively stiffened by 6-fold with the fluid pressure supporting 85% of the contact force. The results motivated a simple analytical model that directly links the tribomechanical response (including fluid load support) and the Peclet number to measurable material properties and controllable experimental variables. This paper demonstrates that tribological contacts can be used to probe local functional properties. Such measurements can add important insights into the roles of focal tissue damage and impaired local functionality in the pathogenesis of osteoarthritis.  相似文献   

4.
Boundary lubrication of articular cartilage by conformal, molecularly thin films reduces friction and adhesion between asperities at the cartilage-cartilage contact interface when the contact conditions are not conducive to fluid film lubrication. In this study, the nanoscale friction and adhesion properties of articular cartilage from typical load-bearing and non-load-bearing joint regions were studied in the boundary lubrication regime under a range of physiological contact pressures using an atomic force microscope (AFM). Adhesion of load-bearing cartilage was found to be much lower than that of non-load-bearing cartilage. In addition, load-bearing cartilage demonstrated steady and low friction coefficient through the entire load range examined, whereas non-load-bearing cartilage showed higher friction coefficient that decreased nonlinearly with increasing normal load. AFM imaging and roughness calculations indicated that the above trends in the nanotribological properties of cartilage are not due to topographical (roughness) differences. However, immunohistochemistry revealed consistently higher surface concentration of boundary lubricant at load-bearing joint regions. The results of this study suggest that under contact conditions leading to joint starvation from fluid lubrication, the higher content of boundary lubricant at load-bearing cartilage sites preserves synovial joint function by minimizing adhesion and wear at asperity microcontacts, which are precursors for tissue degeneration.  相似文献   

5.
Boundary lubrication is characterized by sliding surfaces separated by a molecularly thin film that reduces friction and wear of the underlying substrate when fluid lubrication cannot be established. In this study, the wear and replenishment rates of articular cartilage were examined in the context of friction coefficient changes, protein loss, and direct imaging of the surface ultrastructure, to determine the efficiency of the boundary lubricant (BL) layer. Depletion of cartilage lubricity occurred with the concomitant loss of surface proteoglycans. Restoration of lubrication by incubation with synovial fluid was much faster than incubation with culture media and isolated superficial zone protein. The replenishment action of the BL layer in articular cartilage was rapid, with the rate of formation exceeding the rate of depletion of the BL layer to effectively protect the tissue from mechanical wear. The obtained results indicate that boundary lubrication in articular cartilage depends in part on a sacrificial layer mechanism. The present study provides insight into the natural mechanisms that minimize wear and resist tissue degeneration over the lifetime of an organism.  相似文献   

6.
Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.  相似文献   

7.
A mixture model of synovial fluid filtration by cartilage in the human ankle joint during walking is presented for steady sliding motion of the articular surfaces. In the paper the cartilage surface zone is assumed worn out. The same model has been recently applied to the squeeze-film problem for the human hip joint loaded by the body weight during standing (Hlavácek, Journal of Biomechanics 26, 1145-1150, 1151-1160, 1993; Hlavácek and Novák, Journal of Biomechanics 28, 1193-1198, 1199-1205, 1995). The linear biphasic model for cartilage (elastic porous matrix + ideal fluid) due to Prof. V. C. Mow and his co-workers and the biphasic model for synovial fluid (viscous fluid + ideal fluid), as used in the above-mentioned squeeze-film problem, are applied. For the physiologic parameters of the ankle joint during walking, a continuous synovial fluid film about 1 microm thick is maintained under steady entraining motion according to the classical model without the fluid transport across the articular surface. This is not the case in the filtration model with the cartilage surface zones worn out. On the contrary, this filtration model indicates that synovial fluid is intensively filtrated by such cartilage, so that no continuous fluid film is maintained and a synovial gel layer, about 10(-8) m thick, develops over the majority of the contact. Thus, if the cartilage surface zones are worn out, boundary lubrication should prevail in the ankle joint under steady sliding motion for the mean values of loading and the sliding velocity encountered in walking cycle.  相似文献   

8.
A finite element analysis is used to study a previously unresolved issue of the effects of platen-specimen friction on the response of the unconfined compression test; effects of platen permeability are also determined. The finite element formulation is based on the linear KLM biphasic model for articular cartilage and other hydrated soft tissues. A Galerkin weighted residual method is applied to both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via a penalty method. The solid phase displacements and fluid phase velocities are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problem of a cylindrical specimen of soft tissue in unconfined compression. These studies show that interfacial friction plays a major role in the unconfined compression response of articular cartilage specimens with small thickness to diameter ratios.  相似文献   

9.
Total disc arthroplasty (TDA) can be used to replace a degenerated intervertebral disc in the spine. There are different designs of prosthetic discs, but one of the most common is a ball-and-socket combination. Contact between the bearing surfaces can result in high frictional torque, which can then result in wear and implant loosening. This study was designed to determine the effects of ball radius on friction. Generic models of metal-on-metal TDA were manufactured with ball radii of 10, 12, 14 and 16 mm, with a radial clearance of 0.015 mm. A simulator was used to test each sample in flexion-extension, lateral bending and axial rotation at frequencies of 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 Hz under loads of 50, 600, 1200 and 2000 N, in new born calf serum. Frictional torque was measured and Stribeck curves were plotted to illustrate the lubrication regime in each case. It was observed that implants with a smaller ball radius showed lower friction and showed boundary and mixed lubrication regimes, whereas implants with larger ball radius showed boundary lubrication only. This study suggests designing metal-on-metal TDAs with ball radius of 10 or 12 mm, in order to reduce wear and implant loosening.  相似文献   

10.
This study presents an analysis of the contact of a rippled rigid impermeable indenter against a cartilage layer, which represents a first simulation of the contact of rough cartilage surfaces with lubricant entrapment. Cartilage was modeled with the biphasic theory for hydrated soft tissues, to account for fluid flow into or out of the lubricant pool. The findings of this study demonstrate that under contact creep, the trapped lubricant pool gets depleted within a time period on the order of seconds or minutes as a result of lubricant flow into the articular cartilage. Prior to depletion, hydrostatic fluid load support across the contact interface may be enhanced by the presence of the trapped lubricant pool, depending on the initial geometry of the lubricant pool. According to friction models based on the biphasic nature of the tissue, this enhancement in fluid load support produces a smaller minimum friction coefficient than would otherwise be predicted without a lubricant pool. The results of this study support the hypothesis that trapped lubricant decreases the initial friction coefficient following load application, independently of squeeze-film lubrication effects.  相似文献   

11.
This paper presents a computational simulator for the hip to compute the wear and heat generation on artificial joints. The friction produced on artificial hip joints originates wear rates that can lead to failure of the implant. Furthermore, the frictional heating can increase the wear. The developed computational model calculates the wear in the joint and the temperature in the surrounding zone, allowing the use of different combinations of joint materials, daily activities and different individuals. The pressure distribution on the joint bearing surfaces is obtained with the solution of a contact model. The heat generation by friction and the volumetric wear is computed from the pressure distribution and the sliding distance. The temperature is obtained from the solution of a transient heat conduction problem that includes the time-dependent heat generated by friction. The contact and heat conduction problems are solved numerically with the Finite Element Method. The developed computational model performs a full simulation of the acetabular bearing surface behaviour, which is useful for acetabular cup design and material selection. The results obtained by the present model agree with experimental and clinical data, as well as other numerical studies.  相似文献   

12.
The experimentally measured indentation displacement and friction of normal and degraded (treated with chondroitinase AC) bovine articular cartilage plugs against a smooth steel plate were compared with the predictions based on the biphasic theory using the finite element method. It was found that the measured indentation displacement of both cartilage specimens could be predicted from the biphasic theory and the permeability for the degraded cartilage specimen was increased approximately three times. However, the measured friction coefficient was much lower for short period of loading, and the difference in the finite element prediction of friction coefficient between the normal and degraded cartilage specimens was not observed in the experiment. Therefore, it was concluded that both biphasic and other mechanisms were important in controlling the frictional and lubricating characteristics of articular cartilage in mixed and boundary lubrication regimes.  相似文献   

13.
For nearly a century, articular cartilage has been known for its exceptional tribological properties. For nearly as long, there have been research efforts to elucidate the responsible mechanisms for application toward biomimetic bearing applications. It is now widely accepted that interstitial fluid pressurization is the primary mechanism responsible for the unusual lubrication and load bearing properties of cartilage. Although the biomechanics community has developed elegant mathematical theories describing the coupling of solid and fluid (biphasic) mechanics and its role in interstitial lubrication, quantitative gaps in our understanding of cartilage tribology have inhibited our ability to predict how tribological conditions and material properties impact tissue function. This paper presents an analytical model of the interstitial lubrication of biphasic materials under migrating contact conditions. Although finite element and other numerical models of cartilage mechanics exist, they typically neglect the important role of the collagen network and are limited to a specific set of input conditions, which limits general applicability. The simplified approach taken in this work aims to capture the broader underlying physics as a starting point for further model development. In agreement with existing literature, the model indicates that a large Peclet number, Pe, is necessary for effective interstitial lubrication. It also predicts that the tensile modulus must be large relative to the compressive modulus. This explains why hydrogels and other biphasic materials do not provide significant interstitial pressure under high Pe conditions. The model quantitatively agrees with in-situ measurements of interstitial load support and the results have interesting implications for tissue engineering and osteoarthritis problems. This paper suggests that a low tensile modulus (from chondromalacia or local collagen rupture after impact, for example) may disrupt interstitial pressurization, increase shear stresses, and activate a condition of progressive surface damage as a potential precursor of osteoarthritis.  相似文献   

14.
Modelling load bearing in diarthrodial joints is challenging, due to the complexity of the materials, the boundary and interface conditions and the geometry. The articulating surfaces are covered with cartilage layers that are filled with a fluid that plays a major role in load bearing [Mow, V.C., Holmes, M.H., Lai, W.M. (1984) "Survey article: fluid transport and mechanical properties of articular cartilage: a review", Journal of Biomechanics 17(5), 377-394]. Researchers have tended to approximate joint geometry using axisymmetry [Donzelli, P.S., Spilker, R.L., Ateshian, G.A., Mow, V.C. (1999) "Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure", Journal of Biomechanics 32, 1037-1047], often with a rounded upper articulating surface, creating a form of Hertz problem [Donzelli, P.S., Spilker, R.L., Ateshian, G.A., Mow, V.C. (1999) "Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure", Journal of Biomechanics 32, 1037-1047]. However, diarthrodial joints (shoulder, hip and knee) are equipped with peripheral structures (glenoid labrum, acetabular labrum and meniscus, respectively) that tend to deepen the joint contact and thus cause initial contact to be established at the periphery of the joint rather than "centrally". The surface geometries are purposefully incongruent, and the incongruency has a significant effect on the stresses, pressures and pressure gradients inside the tissue. The models show the importance of the peripheral structures and the incongruency from a load-bearing perspective. Joint shapes must provide a compromise between demands for load-bearing, lubrication and the supply of nutrients to the chondrocytes of the cartilage and cells of the peripheral structures. Retention and repair of the functionality of these peripheral structures should be a prime consideration in any surgical treatment of an injured joint.  相似文献   

15.
In situ friction measurement on murine cartilage by atomic force microscopy   总被引:2,自引:1,他引:1  
Articular cartilage provides a low-friction, wear-resistant surface for the motion of diarthrodial joints. The objective of this study was to develop a method for in situ friction measurement of murine cartilage using a colloidal probe attached to the cantilever of an atomic force microscope. Sliding friction was measured between a chemically functionalized microsphere and the cartilage of the murine femoral head. Friction was measured at normal loads ranging incrementally from 20 to 100 nN with a sliding speed of 40 microm/s and sliding distance of 64 microm. Under these test conditions, hydrostatic pressurization and biphasic load support in the cartilage were minimized, providing frictional measurements that predominantly reflect boundary lubrication properties. Friction coefficients measured on murine tissue (0.25+/-0.11) were similar to those measured on porcine tissue (0.23+/-0.09) and were in general agreement with measurements of boundary friction on cartilage by other researchers. Using the colloidal probe as an indenter, the elastic mechanical properties and surface roughness were measured in the same configuration. Interfacial shear was found to be the principal mechanism of friction generation, with little to no friction resulting from plowing forces, collision forces, or energy losses due to normal deformation. This measurement technique can be applied to future studies of cartilage friction and mechanical properties on genetically altered mice or other small animals.  相似文献   

16.
The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A "pseudo-no-slip" kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.  相似文献   

17.
It has been well established that articular cartilage is compositionally and mechanically inhomogenous through its depth. To what extent this structural inhomogeneity is a prerequisite for appropriate cartilage function and integrity is not well understood. The first hypothesis to be tested in this study was that the depth-dependent inhomogeneity of the cartilage acts to maximize the interstitial fluid load support at the articular surface, to provide efficient frictional and wear properties. The second hypothesis was that the inhomogeneity produces a more homogeneous state of elastic stress in the matrix than would be achieved with uniform properties. We have, for the first time, simultaneously determined depth-dependent tensile and compressive properties of human patellofemoral cartilage from unconfined compression stress relaxation tests. The results show that the tensile modulus increases significantly from 4.1 +/- 1.9 MPa in the deep zone to 8.3 +/- 3.7 MPa at the superficial zone, while the compressive modulus decreases from 0.73 +/- 0.26 MPa to 0.28 +/- 0.16 MPa. The experimental measurements were then implemented with the finite-element method to compute the response of an inhomogeneous and homogeneous cartilage layer to loading. The finite-element models demonstrate that structural inhomogeneity acts to increase the interstitial fluid load support at the articular surface. However, the state of stress, strain, or strain energy density in the solid matrix remained inhomogeneous through the depth of the articular layer, whether or not inhomogeneous material properties were employed. We suggest that increased fluid load support at the articular surface enhances the frictional and wear properties of articular cartilage, but that the tissue is not functionally adapted to produce homogeneous stress, strain, or strain energy density distributions. Interstitial fluid pressurization, but not a homogeneous elastic stress distribution, appears thus to be a prerequisite for the functional and morphological integrity of the cartilage.  相似文献   

18.
Modelling load bearing in diarthrodial joints is challenging, due to the complexity of the materials, the boundary and interface conditions and the geometry. The articulating surfaces are covered with cartilage layers that are filled with a fluid that plays a major role in load bearing [Mow, V.C., Holmes, M.H., Lai, W.M. (1984) “Survey article: fluid transport and mechanical properties of articular cartilage: a review”, Journal of Biomechanics 17(5), 377–394]. Researchers have tended to approximate joint geometry using axisymmetry [Donzelli, P.S., Spilker, R.L., Ateshian, G.A., Mow, V.C. (1999) “Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure”, Journal of Biomechanics 32, 1037–1047], often with a rounded upper articulating surface, creating a form of Hertz problem [Donzelli, P.S., Spilker, R.L., Ateshian, G.A., Mow, V.C. (1999) “Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure”, Journal of Biomechanics 32, 1037–1047]. However, diarthrodial joints (shoulder, hip and knee) are equipped with peripheral structures (glenoid labrum, acetabular labrum and meniscus, respectively) that tend to deepen the joint contact and thus cause initial contact to be established at the periphery of the joint rather than “centrally”. The surface geometries are purposefully incongruent, and the incongruency has a significant effect on the stresses, pressures and pressure gradients inside the tissue. The models show the importance of the peripheral structures and the incongruency from a load-bearing perspective. Joint shapes must provide a compromise between demands for load-bearing, lubrication and the supply of nutrients to the chondrocytes of the cartilage and cells of the peripheral structures. Retention and repair of the functionality of these peripheral structures should be a prime consideration in any surgical treatment of an injured joint.  相似文献   

19.
The tibial component of current knee prostheses made of ultra high molecular weight polyethylene (UHMWPE) has a high degree of wear that causes knee inflammation, prosthesis loosening and subsequent replacement in not more than 15 years. In order to know which UHMWPE material properties have more influence on wear, a steady state lubrication model with non-Newtonian synovial fluid has been studied through numerical solution. The results show that UHMWPE has a very high elastic modulus that makes difficult a well lubricated artificial joint and induces the formation of very thin lubricating films between the moving surfaces with the same magnitude of roughness components. This study shows that the use of deformable porous materials in the tibial component could cause the lubricating film thickness to be higher than the average roughness and the pressure levels to be lower than the one predicted for UHMWPE. These two facts imply friction and wear reduction.  相似文献   

20.
The growth, maintenance and ossification of cartilage are fundamental to skeletal development and are regulated throughout life by the mechanical cues that are imposed by physical activities. Finite element computer analyses have been used to study the role of local tissue mechanics on endochondral ossification patterns, skeletal morphology and articular cartilage thickness distributions. Using single-phase continuum material representations of cartilage, the results have indicated that local intermittent hydrostatic pressure promotes cartilage maintenance. Cyclic tensile strains (or shear), however, promote cartilage growth and ossification. Because single-phase material models cannot capture fluid exudation in articular cartilage, poroelastic (or biphasic) solid/fluid models are often implemented to study joint mechanics. In the middle and deep layers of articular cartilage where poroelastic analyses predict little fluid exudation, the cartilage phenotype is maintained by cyclic fluid pressure (consistent with the single-phase theory). In superficial articular layers the chondrocytes are exposed to tangential tensile strain in addition to the high fluid pressure. Furthermore, there is fluid exudation and matrix consolidation, leading to cell 'flattening'. As a result, the superficial layer assumes an altered, more fibrous phenotype. These computer model predictions of cartilage mechanobiology are consistent with results of in vitro cell and tissue and molecular biology experiments.  相似文献   

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