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Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration
Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration Andrew D. Speirs a,n, Paul E. Beaulé b, Stephen J. Ferguson c, Hanspeter Frei a a
Department of Mechanical and Aerospace Engineering, Carleton University, 3135 Mackenzie, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6 Division of Orthopaedic Surgery, Ottawa Hospital, Ottawa, Canada c Institute for Biomechanics, ETH Zurich, Zurich, Switzerland b
art ic l e i nf o
a b s t r a c t
Article history: Accepted 17 April 2014
The understanding of load support mechanisms in cartilage has evolved with computational models that better mimic the tissue ultrastructure. Fibril-reinforced poroelastic models can reproduce cartilage behaviour in a variety of test conditions and can be used to model tissue anisotropy as well as assess stress and pressure partitioning to the tissue constituents. The goal of this study was to examine the stress distribution in the fibrillar and non-fibrillar solid phase and pressure in the fluid phase of cartilage in axisymmetric models of a healthy and osteoarthritic hip joint. Material properties, based on values from the literature, were assigned to the fibrillar and poroelastic components of cartilage and cancellous and subchondral compact bone regions. A cyclic load representing walking was applied for 25 cycles. Contact stresses in the fibrillar and non-fibrillar solid phase supported less than 1% of the contact force and increased only minimally with load cycles. Simulated proteoglycan depletion increased stresses in the radial and tangential collagen fibrils, whereas fibrillation of the tangential fibrils resulted in increased compressive stress in the non-fibrillar component and tensile stress in the radial fibrils. However neither had an effect on fluid pressure. Subchondral sclerosis was found to have the largest effect, resulting in increased fluid pressure, non-fibrillar compressive stress, tangential fibril stress and greater cartilage consolidation. Subchondral bone stiffening may play an important role in the degenerative cascade and may adversely affect tissue repair and regeneration treatments. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Cartilage Bone Osteoarthritis Finite element analysis Hip joint
1. Introduction Articular cartilage can transmit large joint loads while allowing motion with very low friction. To accomplish this, the tissue has a complex multi-phase structure of water and macromolecules, primarily type II collagen and proteoglycan (Muir, 1978). Viscous and electrostatic forces between water and proteoglycan molecules impairs fluid exudation (Frank and Grodzinsky, 1987; Mow et al., 1980), resulting in elevated fluid pressures that support a substantial portion of the joint loads (Donzelli et al., 1999; Macirowski et al., 1994; Mak et al., 1987; Mow et al., 1980). This decreases the load supported by stresses in the solid component, reducing wear processes in the joint (Basalo et al., 2005). Collagen fibrils act primarily in tension, but interact with the proteoglycan network and influence the compressive properties of the tissue (Li et al., 1999; Williamson et al., 2003). Analysis of the interactions of these constituents and their role in supporting compressive
n
Corresponding author. Tel.: þ 1 613 520 5089; fax: þ 1 613 520 5715. E-mail address: [email protected] (A.D. Speirs).
loads will improve our understanding of the biomechanics of cartilage and degeneration. Stress analysis of cartilage has evolved from early linear elastic material models (Brown et al., 1984; Hayes et al., 1972; Wei et al., 2005) to viscoelastic (Zhu et al., 1993), poroelastic (Mow et al., 1980; Wu et al., 1998) and poro-viscoelastic (Suh and Bai, 1998) to better reproduce in vitro experimental data under various loading conditions. Coupled stress-fluid flow analysis in poroelastic models can provide proteoglycan stresses and fluid pressures to study load transmission through the tissue. A transversely isotropic poroelastic model predicted regions of high stress which correspond to sites of failure, and was more sensitive to surface curvature compared to isotropic models (Donzelli et al., 1999). Fibril reinforcement of poroelastic models can also provide depth- and orientation-dependent behaviour observed in cartilage (Chegini and Ferguson, 2010; Krishnan et al., 2003; Li et al., 2009; Pierce et al., 2013a, 2013b; Wilson et al., 2004). These models better reproduce in vitro experimental results under a variety of loading conditions compared to homogeneous or isotropic models. Furthermore, separation of material behaviour to mimic tissue ultrastructure in computational models allows analysis of stresses within the different cartilage constituents (Chegini and Ferguson,
http://dx.doi.org/10.1016/j.jbiomech.2014.04.031 0021-9290/& 2014 Elsevier Ltd. All rights reserved.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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2010; Li et al., 2009). However analyses using fibril-reinforcement have been mostly limited to models representing cartilage plugs or cartilage regions with low curvature (Chegini and Ferguson, 2010; Li et al., 2009; Mononen et al., 2011). Donzelli et al. (1999) showed that increased curvature shifts the location of peak stress from the cartilage surface to the cartilage-bone interface, as well as away from the centre of contact compared to planar surfaces. Thus the goal of this study was to analyse stress and pressure in a poroelastic, fibril-reinforced cartilage model in the highly curved hip joint. The role in load support of the fibrillar and poroelastic components was examined by comparing stress and pressure in a healthy joint, as well as changes in load sharing with cyclic loading. The influence of typical osteoarthritic degenerative changes in the periarticular tissues on load sharing between cartilage constituents and consolidation was examined by simulating proteoglycan depletion, collagen fibrillation and subchondral sclerosis.
2. Methods A generic axisymmetric hip joint model was created (Fig. 1). All analyses were performed in Abaqus (v6.10, Dassault Systèmes) using the non-linear solver to account for contact and finite strain formulations. The femoral head subchondral bone surface was arbitrarily based on a sphere of 26 mm and the acetabular subchondral surface had a radius 2.5 mm larger (Anderson et al., 2010). The femoral and acetabular cartilage layers were 1 mm thick, similar to cartilage on the superior femoral head (Athanasiou et al., 1994) resulting in a minor incongruity at the periphery (Menschik, 1997; Neusel et al., 1996). Cartilage regions were modelled with bi-linear poroelastic elements (CAX4P). Each cartilage region consisted of 25 elements in the depth direction and 800 elements in the tangential direction. The subchondral compact bone layer was 2 mm thick and consisted of bi-linear elements (CAX4). The cancellous regions consisted of both four and three node linear elements (CAX3 and CAX4).
2.1. Material models An elastic modulus of 1.37 GPa was assigned to compact bone regions (Brown and Vrahas, 1984) and 247 MPa to the cancellous regions (Brown et al., 2002). The cartilage layers were modelled as a fibril-reinforced poroelastic material (Chegini and Ferguson, 2010) with properties based on data reported from the human femoral head. In a poroelastic model, the solid and fluid phases are assumed to be incompressible. Thus any macroscopic compression of the tissue results in changes in the pore volume only and requires outflow of the fluid. The fluid flow is impeded by fluid-solid interactions such as viscous shear and hydrostatic forces, measured by the permeability. The poroelastic non-fibrillar component, simulating proteoglycan and water, was governed by the modulus (E), Poisson's ratio (v) and permeability (k), which were assumed to be uniform and
isotropic. For the initial “healthy” model, E¼ 1.64 MPa and v ¼0.3 (Démarteau et al., 2006). Poisson's ratio was calculated from the relationship between elastic and aggregate moduli since the observed Poisson's ratio is influenced by the collagen fibrils (Chegini and Ferguson, 2010). Permeability decreases exponentially with cartilage consolidation (Lai et al., 1981). A permeability–void ratio relationship was determined from data reported for femoral head cartilage (Démarteau et al., 2006; Li et al., 1999): k ¼ 1:0610 17 expf2:0eg where e is the void ratio. For an initial void ratio of 2.7, i.e. water content of 73% (Démarteau et al., 2006), the permeability in the unloaded state was 2.3 10 15 m4/N s. The fibrillar component was modelled with a strain- and depth-dependent, tensile-only modulus defined in a user subroutine (UMAT). Mesh regions were created for the fibrillar component with the same mesh density as the poroelastic component. The tensile-only strain-dependent modulus of the tangential fibrils was calculated at each material point (Korhonen et al., 2003): Et ¼ sð1:0εt þ 190Þ
for
εt 40
where εt is the strain in the tangential direction and s is a scale factor. The scale factor was 1.0 at the bearing surface to provide maximum tensile stiffness tangent to the surface. It decreased linearly to 0.38 at the tidemark to simulate the preferred fibril orienation such that fibril stiffness in the tangential direction at the tidemark was reduced by 62% (Chegini and Ferguson, 2010; Verteramo and Seedhom, 2004). For compressive strains, the modulus was arbitrarily set to 0.00001 MPa to improve solver convergence. Comparable data was not available for radial fibrils. However, since fibril density is approximately the same in deep and superficial zones, a similar continuum model was implemented for radial fibrils. The modulus was calculated from the radial strain and linearly scaled from 100% stiffness at the tidemark to 38% at the bearing surface. These were applied as tangent moduli to increment the fibril stress from the strain increment. It was assumed that all off-diagonal shear terms of the fibril stress tensor were zero. 2.2. Constraints Due to identical mesh geometry, the nodes of the fibril mesh regions were coincided with and displacements were constrained to the nodes of the underlying poroelastic regions. Adjacent mesh regions were fully constrained along the common boundary (TIE constraint) and the cartilage/bone boundary was impermeable. Contact at the bearing surfaces was modelled with a non-linear penalty formulation. Free draining of open cartilage surfaces was implemented with an adaptive seepage algorithm in a user subroutine (FLOW) to create a more physiological boundary condition (Federico et al., 2004; Ferguson et al., 2000; Pawaskar et al., 2010; Warner et al., 2001). A surface material point was closed if the contact stress at the closest surface node was greater than zero, or open otherwise. Seepage from an open surface maintained the surface pore pressure close to zero simulating a free-draining boundary condition. 2.3. Loading and boundary conditions All nodes at the outer edge of the acetabulum were constrained to have no displacement in the vertical or horizontal directions. The hip contact force was applied through a single node on the symmetry axis which was kinematically coupled to all nodes on the upper bone surface of the femur region. The hip contact force was applied to the femur to simulate normal walking. The time-varying force measured in a patient over a 1.04 s gait cycle was applied, which varied from 266 N to 2072 N (31–241% of body weight) (Bergmann et al., 2001). The load profile was repeated for 25 cycles. 2.4. Simulation of degeneration In order to investigate the role of degenerative changes in peri-articular tissues in the hip model, associated changes in properties were applied. Proteoglycan depletion and collagen fibrillation (Muir, 1978) and increased subchondral bone density i.e. sclerosis (Kellgren and Lawrence, 1957; Tö nnis, 1976) have been reported in osteoarthritic joints. Four different models were used to investigate the effects of changes in the biomechanical properties of periarticular tissues. Each model is described relative to the healthy reference model:
Fig. 1. The generic axisymmetric model of the hip was based on the cross section in the oblique sagittal slice of a computed tomography scan, outlined in blue (right). The compact bone layers are highlighted in red. The material properties were assigned for each region identified. A time-varying cyclic force, F, was applied to the femoral head. Fibril preferred stiffness directions are defined relative to the locally radial (R) and tangential (T) directions of the cartilage tissue shown by the black lines (left). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
1. Proteoglycan depletion: the poroelastic modulus (E) was decreased by 15% for moderate degeneration. Permeability (k) was correspondingly increased by 20% (Armstrong and Mow, 1982). 2. Fibrillation: due to a lack of reference data, the modulus (Et) of the tangential fibrils was arbitrarily decreased by 50% from the calculated value while the modulus of the radial fibrils was not modified. 3. Subchondral sclerosis: the modulus of all bone regions was increased by 50%, corresponding to differences predicted by bone mineral density changes in the hip (Speirs et al., 2013).
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
A.D. Speirs et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 4. Tidemark advancement: the two layers of cartilage adjacent to the bone, representing a thickness of 0.08 mm, were converted to bone material to simulate tidemark duplication (Brandt et al., 2008). In this model the bone was assigned the properties as in the healthy model. The influence of degenerative changes was assessed by comparing the maximum fluid pressure, proteoglycan (non-fibrillar) compressive stress, radial and tangential fibril stresses and cartilage consolidation, defined as the volumetric strain. Volumetric strains measure the local change in volume of the tissue as well as the loss in fluid, and are independent of orientation.
3. Results
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Within the fibrils, peak stresses occurred near the edge of the contact region where pore pressure decreased (Fig. 2) in both radial and tangential fibrils. The superficial tangential stresses were highest in the acetabular cartilage whereas the deep radial stresses were higher in the femoral cartilage. The actions of the fibril stresses were primarily to resist tension perpendicular to the minimum principal stresses in the proteoglycan at the corresponding locations. Changes in stresses in the three components, i.e. proteoglycan, water and collagen fibrils, near the edge of contact on the acetabular cartilage surface over the 25 cycles are shown in Fig. 3. As water was exuded the superficial proteoglycan component was gradually
A mesh sensitivity analysis showed a change in maximum pressure of 0.6% and in minimum principal stress of 0.4% when the mesh size was increased from 12,000 to 20,000 elements in each cartilage region, which we considered acceptable. 3.1. Healthy cartilage model The distribution of fluid pressure and minimum principal stress in the poroelastic component at the peak of the 25th load cycle is shown in Fig. 2. A pressure of 1.16 MPa was observed at the symmetry axis, however the highest pressures, of up to 1.5 MPa, were observed approximately one third of the circumference from the symmetry axis. Pore pressure was approximately constant through the tissue thickness, except near the free-draining boundaries. Peak compressive stresses in the proteoglycan reached 0.13 MPa on the femoral side and 0.11 MPa on the acetabular side, corresponding to the location of decreasing pore pressure (Fig. 2). This occurred at the bone/cartilage boundary in both the femoral and acetabular cartilage, whereas the stresses at the bearing surface were lower.
Fig. 3. Fluid pressure gradually decreased with cyclic loading as fibril tensile stress and proteoglycan (PG) compressive stress magnitude increased. Data is shown for a location on the acetabular surface near the peak tangential fibril stress.
Fig. 2. Top: Fluid pressure (left) and minimum principal stress (right) in the poroelastic component of the reference model at the instant of maximum hip force during the final load cycle. Bottom: Tensile stress in radial fibrils (left) and tangential fibrils (right). Note that fluid pressure was high near the central portion of the joint (symmetry axis) and tapered near the edge of contact where stresses in the solid components were higher.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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compressed, resulting in a slow increase in compressive stress from a peak of 0.018 MPa in the first cycle to 0.063 MPa in the last cycle. The peak tensile stress in the tangential fibrils increased from 0.029 MPa to 0.18 MPa over 25 cycles. This prevented tangential expansion, effectively decreasing the apparent Poisson's ratio in order to sustain fluid pressure. The fluid pressure gradually decreased with load cycles, from a peak of 1.1 MPa in the first cycle to 1.0 in the last cycle. Over the whole contact surface, the proportion of the external load supported by the proteoglycan increased slightly, from 0.76% to 0.79%, while fluid pressure accounted for the remainder. Peak radial fibril stresses were highest at the femoral cartilage/ bone interface. At a corresponding location in the femur, the peak increased from 0.011 MPa to 0.11 MPa. 3.2. Proteoglycan depletion Simulated proteoglycan depletion primarily resulted in increased fibril stresses (Fig. 4). The highest minimum principal stresses in the proteoglycan component at the peak of the 25th load cycle differed by less than 0.1% compared to the healthy model (Fig. 4). However higher compressive strains were observed in the PG-depleted model due to the lower modulus. At the cartilage/bone interface the highest minimum principal strains were 0.113 in the PG-depleted model compared to 0.099 in the healthy reference model, an increase in the magnitude of 14%. The highest pore pressure was unaffected by proteoglycan depletion, with a difference less than 1%. Volumetric strain exhibited the largest differences between the models (Fig. 4). The highest volumetric strains were observed at the edge of the contact region due to exudation of water from the nearby cartilage surface. Here the highest volumetric strain was 0.0415 in the PG-depleted model compared to 0.038 in the healthy reference model, an increase of 9%. Volumetric strains near the symmetry axis were 0.015 in the PG-depleted model compared to 0.0086 in the Reference model, and were lower in both cases due to high fluid pressure in the region. The peak radial and tangential fibril stresses increased by 8% and 10%, respectively, compared to the reference model. The proportion of the applied peak load borne by the proteoglycan in the final cycle decreased to 0.74%, compared to 0.79% for the base model as described above. 3.3. Fibrillation Simulated fibril weakness similarly had little effect on peak fluid pressure, with a difference of 0.8%. However the peak minimum principal stress of the poroelastic component was 6%
Fig. 4. Changes in maximum pressure, stresses and consolidation in the cartilage components due to simulated degenerative changes. Values are normalized to the corresponding maximum value in the healthy reference model.
higher than in the reference model. Furthermore, weakening of the tangential fibrils resulted in a 12% increase in the maximum stress in the radial fibrils. Volumetric strains were 9% higher than in the reference model at the symmetry axis and 12% higher at the edge of contact. 3.4. Subchondral sclerosis Stiffening of the subchondral bone resulted in a 10% increase in fluid pressure and a 11% increase in the minimum principal stress of the poroelastic component compared to the reference model. Peak stresses in the superficial tangential fibrils increased by 11%, however the radial fibril stresses were only 2% higher than in the reference model. Volumetric strain increased by 7% at the symmetry axis and up to 26% near the edge of contact. 3.5. Tidemark advancement Simulated tidemark advancement had almost no influence on peak fluid pressure, with a difference of only 1% from the reference model, and minimum principal stresses decreased by 4%. The largest effects were seen in the tangential fibril stress (þ7%) and the maximum volumetric strain (þ11%).
4. Discussion This study examined stresses, pore pressure and consolidation in a fibril-reinforced poroelastic model of cartilage in a simplified axisymmetric hip model with realistic material properties and under physiological loading. Cyclic loading resulted in localized consolidation of the cartilage and increased stresses in the fibrillar and poroelastic components, i.e. collagen and proteoglycan, respectively. At the cartilage surface, compressive stress in the poroelastic solid component supported less than 1% of the hip contact force, with the remainder supported by fluid pressure. Minor redistribution to the poroelastic solid component occurred due to fluid exudation and consolidation over the 25 load cycles, although the tangential fibrils bore higher stresses (Fig. 3). Consistent with other studies, fluid pressure was approximately constant through the depth of the cartilage within the area of joint contact, but varied near the edge of contact as the surface fluid was able to drain from the cartilage (Krishnan et al., 2003; Warner et al., 2004). The study also demonstrated the influence of bone and cartilage property changes on loading of the individual cartilage components. Simulated proteoglycan depletion resulted in increased stress in the fibrils, whereas fibrillation resulted in increased compressive stress in the proteoglycan matrix. Both models of degeneration resulted in large regions of high volumetric strains compared to the reference model, with increases of 7–12% in the maximum volumetric strain. Early cartilage degeneration was not found to substantially influence fluid pressure. Global changes in the subchondral bone regions resulted in increased fluid pressure (þ10%), proteoglycan compressive stress (þ11%), tangential fibril stress (þ11%), as well as up to 26% higher volumetric strains. The models exhibited differences in cartilage tissue stresses, however the simulation was a simplification of the natural hip joint. The fibril-reinforced poroelastic model of cartilage greatly simplifies the complex structure and interactions of the molecular network in cartilage such as cross-linking between collagen fibrils and proteoglycan (van der Rest and Mayne, 1988; Wu and Eyre, 1995). We assumed an arbitrary reduction in tangential fibril stiffness due to a lack of experimental data. However the influence on tissue component stresses was small, suggesting that substantial fibrillation is required to affect tissue stresses. We assumed an isotropic permeability for the model although anisotropy in the permeability is known to exist, particularly at the bearing and tidemark surfaces.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
A.D. Speirs et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
Within the area of joint contact, fluid was constrained to flow in the tangent direction due to the impermeable bone and opposing cartilage such that anisotropy is likely to have little effect. At the edge of contact where flow patterns are more complex the anisotropy may have a stronger but localized effect. Tissue consolidation and loading of chondrocytes in this region could be investigated in the future using anisotropic permeability and multi-scale models. However this material model has reproduced in vitro cartilage behaviour under a variety of conditions (Chegini and Ferguson, 2010; Korhonen et al., 2003; Li et al., 1999). Another limitation is the simplified joint geometry and lack of tangential motion due to joint rotation. The geometry of the pelvis approximated the crosssection of the acetabulum, however the model did not include the acetabular fossa, which is assumed to be non-load bearing. The bearing surfaces were assumed to be spherical with a small incongruity between the acetabulum and femur which may occur in the hip joint (Menschik, 1997; Neusel et al., 1996). Anderson et al. (2010) reported large changes in the maximum contact pressure due to the assumed shape of the joint. However the effect may be overestimated since that study assumed a modulus of 17 GPa in the subchondral bone compared to 1.37 GPa used in the current study and reported in human femoral subchondral bone (Brown and Vrahas, 1984). Patient-specific models derived from medical imaging scans may be used to estimate values of pressure and stress in the cartilage of those patients, however image partial-volume effects, practical limits of image resolution and inter-patient variability may obscure differences due to material properties. The model used in this study did not include the effects of the labrum, which can maintain high fluid pressure within the joint space thereby reducing cartilage consolidation (Ferguson et al., 2000). A damaged labrum in a degenerated joint would result in a lower pressure allowing greater fluid exudation and therefore larger differences between the degenerated and healthy model results could be expected. Difficulties were encountered with the finite element solver due to many non-linear effects in the model, especially due to the adaptive surface seepage used to allow free-draining of open cartilage surfaces (Pawaskar et al., 2010). Abaqus requires the highest volume flux in an increment to be less than 0.5% of the time- and spatially-averaged volume flux to accept an equilibrium solution. Since the volume flux near the contact region was several orders of magnitude higher than in the rest of the model, residuals were also large, and the default equilibrium tolerance was relaxed from the default 0.5% to 5% in order to obtain a solution. When this tolerance was changed from 2% to 10%, the maximum pressure difference on the bearing surface was 0.02 MPa, and the mean difference was 0.0001 MPa compared to a nominal pressure of 1.6 MPa. Differences in stresses were similarly small. Previous studies have examined cartilage stresses with varying degrees of geometric and material complexity. Preferred stiffness directions of collagen fibres through the tissue depth result in a nonuniform stress and pressure distribution (Krishnan et al., 2003; Li et al., 2009; Mononen et al., 2012; Pierce et al., 2013a, 2013b) as seen in this study. Donzelli et al. (1999) showed that a transversely isotropic model of cartilage resulted in high stresses in joint regions where cartilage failure is seen. In the current study, simulation of the constituents of cartilage in a fibril-reinforced poroelastic model achieved a similar effect, but also provided stresses and pressure in the individual components. Similar to Donzelli et al. (1999), the highest proteoglycan stresses were seen in the convex femoral cartilage near the cartilage–bone interface. The influence of subchondral bone changes has been reported with conflicting results, although previous studies have implemented a linear elastic cartilage region. Brown et al. (1984) showed that increased subchondral bone stiffness had only a minor influence on cartilage stresses, although increased compressive stress of up to 50% was seen adjacent to localized stiffening of the subchondral bone. Wei et al. (2005)
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showed that doubling subchondral bone stiffness resulted in a 7.5% increase in the cartilage compressive stress. Dar and Aspden (2003) similarly showed that subchondral bone stiffness has a minor influence on cartilage stress in compression. However in the current study the boundary conditions of the pelvis result in a bending mode. This can be seen in the high fluid pressures and stresses offset from the symmetry axis where the structural stiffness of the acetabulum is higher. The current study found bone stiffness had a larger influence on fluid pressure, proteoglycan compressive stress, and cartilage consolidation compared to cartilage degeneration, as well as a large influence on the tangential fibril stress. These phenomena cannot be examined with the elastic models of previous studies of the hip. In a canine experimental model, Ewald et al. (1982) found that replacement of femoral head cancellous bone with stiffer polymethylmethacrylate cement induced cartilage degeneration, in agreement with the current findings, although nutritional, toxicity or thermal factors may have been involved in that study. Although this study demonstrated differences in cartilage behaviour due to cartilage degeneration and increased bone stiffness, the specific conditions at the molecular or cellular level that induce degeneration are not known. The loading conditions in the hip are below the typical gel diffusion rate of cartilage, in which case chondrocyte death may occur due to extensive tissue consolidation i.e. high volume strain, possibly as a result of dehydration (Morel and Quinn, 2004). Alternatively, increased strains may directly alter chondrocyte activity through mitochondria (Wolff et al., 2013). Non-mechanical factors may also influence chondrocyte survival such as impaired nutrient supply (Arkill and Winlove, 2008) or disruption of cellular signalling as a result of thickening of the compact subchondral bone layer (Amin et al., 2009). It is not clear whether the differences in tissue stresses observed in this study are sufficient to induce or sustain degeneration, and in fact are smaller than might be expected. The confining, concave shape of the acetabulum helps reduce fluid loss from the joint space compared to a more open joint such as the knee. This likely sustains high fluid pressure, even in the case of degenerative material properties, and reduces the mechanical demands on the solid components. It must also be recognized that the applied force was unchanged between models and that this must be balanced by the tissue stress and pressure. Thus the main effect of degeneration in this model is the change in load sharing between the tissue components. It is likely that a mechanical explanation for osteoarthritic degeneration requires additional insult to the joint. In the hip, this could include abnormal contact stresses due to morphological deformities as in femoroacetabular impingement (Ganz et al., 2008) or dysplasia (Chegini et al., 2009), or due to external trauma. In these cases changes to the periarticular tissues could amplify the effects of the associated abnormal contact stresses. This study examined the loading of individual cartilage constituents in the high-curvature model of the hip joint. The external load is supported primarily by the fluid pressure, but is slowly transferred to the solid component with cyclic loading. Changes in tissue properties were selected to simulate moderate degeneration. Subchondral sclerosis was found to have a larger influence on cartilage stresses, pressure and consolidation than cartilage degeneration, although differences from the healthy model may not be sufficient to explain mechanically-induced damage. Further work is required to assess the influence of degenerative changes in the presence of joint incongruities such as femoroacetabular impingement deformities in three dimensional models.
Conflict of interest The authors have no conflicts of interest.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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Acknowledgements This study was supported by Canadian Institutes of Health Research (MOP 97778) and Natural Sciences and Engineering Research Council of Canada. References Amin, A.K., Huntley, J.S., Simpson, A.H.R.W., Hall, A.C., 2009. Chondrocyte survival in articular cartilage: the influence of subchondral bone in a bovine model. J. Bone Jt. Surg. Br. 91, 691–699. Anderson, A.E., Ellis, B.J., Maas, S.A., Weiss, J.A., 2010. Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J. Biomech. 43, 1351–1357. Arkill, K.P., Winlove, C.P., 2008. Solute transport in the deep and calcified zones of articular cartilage. Osteoarthr. Cartil. 16, 708–714. Armstrong, C.G., Mow, V.C., 1982. Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content. J. Bone Jt. Surg. Am. 64, 88–94. Athanasiou, K., Agarwal, A., Dzida, F.J., 1994. Comparative study of the intrinsic mechanical properties of the human acetabular and femoral head cartilage. J. Orthop. Res. 12, 340–349. Basalo, I.M., Raj, D., Krishnan, R., Chen, F.H., Hung, C.T., Ateshian, G.a., 2005. Effects of enzymatic degradation on the frictional response of articular cartilage in stress relaxation. J. Biomech. 38, 1343–1349. Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A., Strauss, J., Duda, G.N., 2001. Hip contact forces and gait patterns from routine activities. J. Biomech. 34, 859–871. Brandt, K.D., Dieppe, P., Radin, E.L., 2008. Etiopathogenesis of osteoarthritis. Rheum. Dis. Clin. N. Am. 34, 531–559. Brown, S.J., Pollintine, P., Powell, D.E., Davie, M.W.J., Sharp, C.A., 2002. Regional differences in mechanical and material properties of femoral head cancellous bone in health and osteoarthritis. Calcif. Tissue Int. 71, 227–234. Brown, T.D., Radin, E.L., Martin, R.B., Burr, D.B., 1984. Finite element studies of some juxtarticular stress changes due to localized subchondral stiffening. J. Biomech. 17, 11–24. Brown, T.D., Vrahas, M.S., 1984. The apparent elastic modulus of the juxtarticular subchondral bone of the femoral head. J. Orthop. Res. 2, 32–38. Chegini, S., Beck, M., Ferguson, S.J., 2009. The effects of impingement and dysplasia on stress distributions in the hip joint during sitting and walking: a finite element analysis. J. Orthop. Res. 27, 195–201. Chegini, S., Ferguson, S.J., 2010. Time and depth dependent Poisson's ratio of cartilage explained by an inhomogeneous orthotropic fiber embedded biphasic model. J. Biomech. 43, 1660–1666. Dar, F.H., Aspden, R.M., 2003. A finite element model of an idealized diarthrodial joint to investigate the effects of variation in the mechanical properties of the tissues. Proc. Inst. Mech. Eng. Part H J. Eng. Med. 217, 341–348. Démarteau, O., Pillet, L., Inaebnit, A., Borens, O., Quinn, T.M., 2006. Biomechanical characterization and in vitro mechanical injury of elderly human femoral head cartilage: comparison to adult bovine humeral head cartilage. Osteoarthr. Cartil. 14, 589–596. 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. J. Biomech. 32, 1037–1047. Ewald, F.C., Poss, R., Pugh, J., Schiller, a.L., Sledge, C.B., 1982. Hip cartilage supported by methacrylate in canine arthroplasty. Clin. Orthop. Relat. Res. 171, 273–279. Federico, S., La Rosa, G., Herzog, W., Wu, J.Z., 2004. Effect of fluid boundary conditions on joint contact mechanics and applications to the modeling of osteoarthritic joints. J. Biomech. Eng. 126, 220. Ferguson, S.J., Bryant, J.T., Ganz, R., Ito, K., 2000. The influence of the acetabular labrum on hip joint cartilage consolidation: a poroelastic finite element model. J. Biomech. 33, 953–960. Frank, E.H., Grodzinsky, A.J., 1987. Cartilage electromechanics—II. A continuum model of cartilage electrokinetics and correlation with experiments. J. Biomech. 20, 629–639. Ganz, R., Leunig, M., Leunig-Ganz, K., Harris, W.H., 2008. The etiology of osteoarthritis of the hip: an integrated mechanical concept. Clin. Orthop. Relat. Res. 466, 264–272. Hayes, W.C., Keer, L.M., Herrmann, G., Mockros, L.F., 1972. A mathematical analysis for indentation tests of articular cartilage. J. Biomech. 5, 541–551. Kellgren, J.H., Lawrence, J.S., 1957. Radiological assessment of osteo-arthritis. Ann. Rheum. Dis. 16, 494–502. Korhonen, R.K., Laasanen, M.S., Tö yräs, J., Lappalainen, R., Helminen, H.J., Jurvelin, J. S., 2003. Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage. J. Biomech. 36, 1373–1379. Krishnan, R., Park, S., Eckstein, F., Ateshian, G.A., 2003. Inhomogeneous cartilage properties enhance superficial interstitial fluid support and frictional
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Med. 215, 487–496. Warner, M.D., Taylor, W.R., Clift, S.E., 2004. Cyclic loading moves the peak stress to the cartilage surface in a biphasic model with isotropic solid phase properties. Med. Eng. Phys. 26, 247–249. Wei, H.-W., Sun, S.-S., Jao, S.-H.E., Yeh, C.-R., Cheng, C.-K., 2005. The influence of mechanical properties of subchondral plate, femoral head and neck on dynamic stress distribution of the articular cartilage. Med. Eng. Phys. 27, 295–304. Williamson, A.K., Chen, A.C., Masuda, K., Thonar, E.J.-M. a, Sah, R.L., 2003. Tensile mechanical properties of bovine articular cartilage: variations with growth and relationships to collagen network components. J. Orthop. Res. 21, 872–880. Wilson, W., van Donkelaar, C.C., van Rietbergen, B., Ito, K., Huiskes, R., 2004. Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J. Biomech. 37, 357–366. 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Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration Andrew D. Speirs a,n, Paul E. Beaulé b, Stephen J. Ferguson c, Hanspeter Frei a a
Department of Mechanical and Aerospace Engineering, Carleton University, 3135 Mackenzie, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6 Division of Orthopaedic Surgery, Ottawa Hospital, Ottawa, Canada c Institute for Biomechanics, ETH Zurich, Zurich, Switzerland b
art ic l e i nf o
a b s t r a c t
Article history: Accepted 17 April 2014
The understanding of load support mechanisms in cartilage has evolved with computational models that better mimic the tissue ultrastructure. Fibril-reinforced poroelastic models can reproduce cartilage behaviour in a variety of test conditions and can be used to model tissue anisotropy as well as assess stress and pressure partitioning to the tissue constituents. The goal of this study was to examine the stress distribution in the fibrillar and non-fibrillar solid phase and pressure in the fluid phase of cartilage in axisymmetric models of a healthy and osteoarthritic hip joint. Material properties, based on values from the literature, were assigned to the fibrillar and poroelastic components of cartilage and cancellous and subchondral compact bone regions. A cyclic load representing walking was applied for 25 cycles. Contact stresses in the fibrillar and non-fibrillar solid phase supported less than 1% of the contact force and increased only minimally with load cycles. Simulated proteoglycan depletion increased stresses in the radial and tangential collagen fibrils, whereas fibrillation of the tangential fibrils resulted in increased compressive stress in the non-fibrillar component and tensile stress in the radial fibrils. However neither had an effect on fluid pressure. Subchondral sclerosis was found to have the largest effect, resulting in increased fluid pressure, non-fibrillar compressive stress, tangential fibril stress and greater cartilage consolidation. Subchondral bone stiffening may play an important role in the degenerative cascade and may adversely affect tissue repair and regeneration treatments. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Cartilage Bone Osteoarthritis Finite element analysis Hip joint
1. Introduction Articular cartilage can transmit large joint loads while allowing motion with very low friction. To accomplish this, the tissue has a complex multi-phase structure of water and macromolecules, primarily type II collagen and proteoglycan (Muir, 1978). Viscous and electrostatic forces between water and proteoglycan molecules impairs fluid exudation (Frank and Grodzinsky, 1987; Mow et al., 1980), resulting in elevated fluid pressures that support a substantial portion of the joint loads (Donzelli et al., 1999; Macirowski et al., 1994; Mak et al., 1987; Mow et al., 1980). This decreases the load supported by stresses in the solid component, reducing wear processes in the joint (Basalo et al., 2005). Collagen fibrils act primarily in tension, but interact with the proteoglycan network and influence the compressive properties of the tissue (Li et al., 1999; Williamson et al., 2003). Analysis of the interactions of these constituents and their role in supporting compressive
n
Corresponding author. Tel.: þ 1 613 520 5089; fax: þ 1 613 520 5715. E-mail address: [email protected] (A.D. Speirs).
loads will improve our understanding of the biomechanics of cartilage and degeneration. Stress analysis of cartilage has evolved from early linear elastic material models (Brown et al., 1984; Hayes et al., 1972; Wei et al., 2005) to viscoelastic (Zhu et al., 1993), poroelastic (Mow et al., 1980; Wu et al., 1998) and poro-viscoelastic (Suh and Bai, 1998) to better reproduce in vitro experimental data under various loading conditions. Coupled stress-fluid flow analysis in poroelastic models can provide proteoglycan stresses and fluid pressures to study load transmission through the tissue. A transversely isotropic poroelastic model predicted regions of high stress which correspond to sites of failure, and was more sensitive to surface curvature compared to isotropic models (Donzelli et al., 1999). Fibril reinforcement of poroelastic models can also provide depth- and orientation-dependent behaviour observed in cartilage (Chegini and Ferguson, 2010; Krishnan et al., 2003; Li et al., 2009; Pierce et al., 2013a, 2013b; Wilson et al., 2004). These models better reproduce in vitro experimental results under a variety of loading conditions compared to homogeneous or isotropic models. Furthermore, separation of material behaviour to mimic tissue ultrastructure in computational models allows analysis of stresses within the different cartilage constituents (Chegini and Ferguson,
http://dx.doi.org/10.1016/j.jbiomech.2014.04.031 0021-9290/& 2014 Elsevier Ltd. All rights reserved.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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2010; Li et al., 2009). However analyses using fibril-reinforcement have been mostly limited to models representing cartilage plugs or cartilage regions with low curvature (Chegini and Ferguson, 2010; Li et al., 2009; Mononen et al., 2011). Donzelli et al. (1999) showed that increased curvature shifts the location of peak stress from the cartilage surface to the cartilage-bone interface, as well as away from the centre of contact compared to planar surfaces. Thus the goal of this study was to analyse stress and pressure in a poroelastic, fibril-reinforced cartilage model in the highly curved hip joint. The role in load support of the fibrillar and poroelastic components was examined by comparing stress and pressure in a healthy joint, as well as changes in load sharing with cyclic loading. The influence of typical osteoarthritic degenerative changes in the periarticular tissues on load sharing between cartilage constituents and consolidation was examined by simulating proteoglycan depletion, collagen fibrillation and subchondral sclerosis.
2. Methods A generic axisymmetric hip joint model was created (Fig. 1). All analyses were performed in Abaqus (v6.10, Dassault Systèmes) using the non-linear solver to account for contact and finite strain formulations. The femoral head subchondral bone surface was arbitrarily based on a sphere of 26 mm and the acetabular subchondral surface had a radius 2.5 mm larger (Anderson et al., 2010). The femoral and acetabular cartilage layers were 1 mm thick, similar to cartilage on the superior femoral head (Athanasiou et al., 1994) resulting in a minor incongruity at the periphery (Menschik, 1997; Neusel et al., 1996). Cartilage regions were modelled with bi-linear poroelastic elements (CAX4P). Each cartilage region consisted of 25 elements in the depth direction and 800 elements in the tangential direction. The subchondral compact bone layer was 2 mm thick and consisted of bi-linear elements (CAX4). The cancellous regions consisted of both four and three node linear elements (CAX3 and CAX4).
2.1. Material models An elastic modulus of 1.37 GPa was assigned to compact bone regions (Brown and Vrahas, 1984) and 247 MPa to the cancellous regions (Brown et al., 2002). The cartilage layers were modelled as a fibril-reinforced poroelastic material (Chegini and Ferguson, 2010) with properties based on data reported from the human femoral head. In a poroelastic model, the solid and fluid phases are assumed to be incompressible. Thus any macroscopic compression of the tissue results in changes in the pore volume only and requires outflow of the fluid. The fluid flow is impeded by fluid-solid interactions such as viscous shear and hydrostatic forces, measured by the permeability. The poroelastic non-fibrillar component, simulating proteoglycan and water, was governed by the modulus (E), Poisson's ratio (v) and permeability (k), which were assumed to be uniform and
isotropic. For the initial “healthy” model, E¼ 1.64 MPa and v ¼0.3 (Démarteau et al., 2006). Poisson's ratio was calculated from the relationship between elastic and aggregate moduli since the observed Poisson's ratio is influenced by the collagen fibrils (Chegini and Ferguson, 2010). Permeability decreases exponentially with cartilage consolidation (Lai et al., 1981). A permeability–void ratio relationship was determined from data reported for femoral head cartilage (Démarteau et al., 2006; Li et al., 1999): k ¼ 1:0610 17 expf2:0eg where e is the void ratio. For an initial void ratio of 2.7, i.e. water content of 73% (Démarteau et al., 2006), the permeability in the unloaded state was 2.3 10 15 m4/N s. The fibrillar component was modelled with a strain- and depth-dependent, tensile-only modulus defined in a user subroutine (UMAT). Mesh regions were created for the fibrillar component with the same mesh density as the poroelastic component. The tensile-only strain-dependent modulus of the tangential fibrils was calculated at each material point (Korhonen et al., 2003): Et ¼ sð1:0εt þ 190Þ
for
εt 40
where εt is the strain in the tangential direction and s is a scale factor. The scale factor was 1.0 at the bearing surface to provide maximum tensile stiffness tangent to the surface. It decreased linearly to 0.38 at the tidemark to simulate the preferred fibril orienation such that fibril stiffness in the tangential direction at the tidemark was reduced by 62% (Chegini and Ferguson, 2010; Verteramo and Seedhom, 2004). For compressive strains, the modulus was arbitrarily set to 0.00001 MPa to improve solver convergence. Comparable data was not available for radial fibrils. However, since fibril density is approximately the same in deep and superficial zones, a similar continuum model was implemented for radial fibrils. The modulus was calculated from the radial strain and linearly scaled from 100% stiffness at the tidemark to 38% at the bearing surface. These were applied as tangent moduli to increment the fibril stress from the strain increment. It was assumed that all off-diagonal shear terms of the fibril stress tensor were zero. 2.2. Constraints Due to identical mesh geometry, the nodes of the fibril mesh regions were coincided with and displacements were constrained to the nodes of the underlying poroelastic regions. Adjacent mesh regions were fully constrained along the common boundary (TIE constraint) and the cartilage/bone boundary was impermeable. Contact at the bearing surfaces was modelled with a non-linear penalty formulation. Free draining of open cartilage surfaces was implemented with an adaptive seepage algorithm in a user subroutine (FLOW) to create a more physiological boundary condition (Federico et al., 2004; Ferguson et al., 2000; Pawaskar et al., 2010; Warner et al., 2001). A surface material point was closed if the contact stress at the closest surface node was greater than zero, or open otherwise. Seepage from an open surface maintained the surface pore pressure close to zero simulating a free-draining boundary condition. 2.3. Loading and boundary conditions All nodes at the outer edge of the acetabulum were constrained to have no displacement in the vertical or horizontal directions. The hip contact force was applied through a single node on the symmetry axis which was kinematically coupled to all nodes on the upper bone surface of the femur region. The hip contact force was applied to the femur to simulate normal walking. The time-varying force measured in a patient over a 1.04 s gait cycle was applied, which varied from 266 N to 2072 N (31–241% of body weight) (Bergmann et al., 2001). The load profile was repeated for 25 cycles. 2.4. Simulation of degeneration In order to investigate the role of degenerative changes in peri-articular tissues in the hip model, associated changes in properties were applied. Proteoglycan depletion and collagen fibrillation (Muir, 1978) and increased subchondral bone density i.e. sclerosis (Kellgren and Lawrence, 1957; Tö nnis, 1976) have been reported in osteoarthritic joints. Four different models were used to investigate the effects of changes in the biomechanical properties of periarticular tissues. Each model is described relative to the healthy reference model:
Fig. 1. The generic axisymmetric model of the hip was based on the cross section in the oblique sagittal slice of a computed tomography scan, outlined in blue (right). The compact bone layers are highlighted in red. The material properties were assigned for each region identified. A time-varying cyclic force, F, was applied to the femoral head. Fibril preferred stiffness directions are defined relative to the locally radial (R) and tangential (T) directions of the cartilage tissue shown by the black lines (left). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
1. Proteoglycan depletion: the poroelastic modulus (E) was decreased by 15% for moderate degeneration. Permeability (k) was correspondingly increased by 20% (Armstrong and Mow, 1982). 2. Fibrillation: due to a lack of reference data, the modulus (Et) of the tangential fibrils was arbitrarily decreased by 50% from the calculated value while the modulus of the radial fibrils was not modified. 3. Subchondral sclerosis: the modulus of all bone regions was increased by 50%, corresponding to differences predicted by bone mineral density changes in the hip (Speirs et al., 2013).
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
A.D. Speirs et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 4. Tidemark advancement: the two layers of cartilage adjacent to the bone, representing a thickness of 0.08 mm, were converted to bone material to simulate tidemark duplication (Brandt et al., 2008). In this model the bone was assigned the properties as in the healthy model. The influence of degenerative changes was assessed by comparing the maximum fluid pressure, proteoglycan (non-fibrillar) compressive stress, radial and tangential fibril stresses and cartilage consolidation, defined as the volumetric strain. Volumetric strains measure the local change in volume of the tissue as well as the loss in fluid, and are independent of orientation.
3. Results
3
Within the fibrils, peak stresses occurred near the edge of the contact region where pore pressure decreased (Fig. 2) in both radial and tangential fibrils. The superficial tangential stresses were highest in the acetabular cartilage whereas the deep radial stresses were higher in the femoral cartilage. The actions of the fibril stresses were primarily to resist tension perpendicular to the minimum principal stresses in the proteoglycan at the corresponding locations. Changes in stresses in the three components, i.e. proteoglycan, water and collagen fibrils, near the edge of contact on the acetabular cartilage surface over the 25 cycles are shown in Fig. 3. As water was exuded the superficial proteoglycan component was gradually
A mesh sensitivity analysis showed a change in maximum pressure of 0.6% and in minimum principal stress of 0.4% when the mesh size was increased from 12,000 to 20,000 elements in each cartilage region, which we considered acceptable. 3.1. Healthy cartilage model The distribution of fluid pressure and minimum principal stress in the poroelastic component at the peak of the 25th load cycle is shown in Fig. 2. A pressure of 1.16 MPa was observed at the symmetry axis, however the highest pressures, of up to 1.5 MPa, were observed approximately one third of the circumference from the symmetry axis. Pore pressure was approximately constant through the tissue thickness, except near the free-draining boundaries. Peak compressive stresses in the proteoglycan reached 0.13 MPa on the femoral side and 0.11 MPa on the acetabular side, corresponding to the location of decreasing pore pressure (Fig. 2). This occurred at the bone/cartilage boundary in both the femoral and acetabular cartilage, whereas the stresses at the bearing surface were lower.
Fig. 3. Fluid pressure gradually decreased with cyclic loading as fibril tensile stress and proteoglycan (PG) compressive stress magnitude increased. Data is shown for a location on the acetabular surface near the peak tangential fibril stress.
Fig. 2. Top: Fluid pressure (left) and minimum principal stress (right) in the poroelastic component of the reference model at the instant of maximum hip force during the final load cycle. Bottom: Tensile stress in radial fibrils (left) and tangential fibrils (right). Note that fluid pressure was high near the central portion of the joint (symmetry axis) and tapered near the edge of contact where stresses in the solid components were higher.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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compressed, resulting in a slow increase in compressive stress from a peak of 0.018 MPa in the first cycle to 0.063 MPa in the last cycle. The peak tensile stress in the tangential fibrils increased from 0.029 MPa to 0.18 MPa over 25 cycles. This prevented tangential expansion, effectively decreasing the apparent Poisson's ratio in order to sustain fluid pressure. The fluid pressure gradually decreased with load cycles, from a peak of 1.1 MPa in the first cycle to 1.0 in the last cycle. Over the whole contact surface, the proportion of the external load supported by the proteoglycan increased slightly, from 0.76% to 0.79%, while fluid pressure accounted for the remainder. Peak radial fibril stresses were highest at the femoral cartilage/ bone interface. At a corresponding location in the femur, the peak increased from 0.011 MPa to 0.11 MPa. 3.2. Proteoglycan depletion Simulated proteoglycan depletion primarily resulted in increased fibril stresses (Fig. 4). The highest minimum principal stresses in the proteoglycan component at the peak of the 25th load cycle differed by less than 0.1% compared to the healthy model (Fig. 4). However higher compressive strains were observed in the PG-depleted model due to the lower modulus. At the cartilage/bone interface the highest minimum principal strains were 0.113 in the PG-depleted model compared to 0.099 in the healthy reference model, an increase in the magnitude of 14%. The highest pore pressure was unaffected by proteoglycan depletion, with a difference less than 1%. Volumetric strain exhibited the largest differences between the models (Fig. 4). The highest volumetric strains were observed at the edge of the contact region due to exudation of water from the nearby cartilage surface. Here the highest volumetric strain was 0.0415 in the PG-depleted model compared to 0.038 in the healthy reference model, an increase of 9%. Volumetric strains near the symmetry axis were 0.015 in the PG-depleted model compared to 0.0086 in the Reference model, and were lower in both cases due to high fluid pressure in the region. The peak radial and tangential fibril stresses increased by 8% and 10%, respectively, compared to the reference model. The proportion of the applied peak load borne by the proteoglycan in the final cycle decreased to 0.74%, compared to 0.79% for the base model as described above. 3.3. Fibrillation Simulated fibril weakness similarly had little effect on peak fluid pressure, with a difference of 0.8%. However the peak minimum principal stress of the poroelastic component was 6%
Fig. 4. Changes in maximum pressure, stresses and consolidation in the cartilage components due to simulated degenerative changes. Values are normalized to the corresponding maximum value in the healthy reference model.
higher than in the reference model. Furthermore, weakening of the tangential fibrils resulted in a 12% increase in the maximum stress in the radial fibrils. Volumetric strains were 9% higher than in the reference model at the symmetry axis and 12% higher at the edge of contact. 3.4. Subchondral sclerosis Stiffening of the subchondral bone resulted in a 10% increase in fluid pressure and a 11% increase in the minimum principal stress of the poroelastic component compared to the reference model. Peak stresses in the superficial tangential fibrils increased by 11%, however the radial fibril stresses were only 2% higher than in the reference model. Volumetric strain increased by 7% at the symmetry axis and up to 26% near the edge of contact. 3.5. Tidemark advancement Simulated tidemark advancement had almost no influence on peak fluid pressure, with a difference of only 1% from the reference model, and minimum principal stresses decreased by 4%. The largest effects were seen in the tangential fibril stress (þ7%) and the maximum volumetric strain (þ11%).
4. Discussion This study examined stresses, pore pressure and consolidation in a fibril-reinforced poroelastic model of cartilage in a simplified axisymmetric hip model with realistic material properties and under physiological loading. Cyclic loading resulted in localized consolidation of the cartilage and increased stresses in the fibrillar and poroelastic components, i.e. collagen and proteoglycan, respectively. At the cartilage surface, compressive stress in the poroelastic solid component supported less than 1% of the hip contact force, with the remainder supported by fluid pressure. Minor redistribution to the poroelastic solid component occurred due to fluid exudation and consolidation over the 25 load cycles, although the tangential fibrils bore higher stresses (Fig. 3). Consistent with other studies, fluid pressure was approximately constant through the depth of the cartilage within the area of joint contact, but varied near the edge of contact as the surface fluid was able to drain from the cartilage (Krishnan et al., 2003; Warner et al., 2004). The study also demonstrated the influence of bone and cartilage property changes on loading of the individual cartilage components. Simulated proteoglycan depletion resulted in increased stress in the fibrils, whereas fibrillation resulted in increased compressive stress in the proteoglycan matrix. Both models of degeneration resulted in large regions of high volumetric strains compared to the reference model, with increases of 7–12% in the maximum volumetric strain. Early cartilage degeneration was not found to substantially influence fluid pressure. Global changes in the subchondral bone regions resulted in increased fluid pressure (þ10%), proteoglycan compressive stress (þ11%), tangential fibril stress (þ11%), as well as up to 26% higher volumetric strains. The models exhibited differences in cartilage tissue stresses, however the simulation was a simplification of the natural hip joint. The fibril-reinforced poroelastic model of cartilage greatly simplifies the complex structure and interactions of the molecular network in cartilage such as cross-linking between collagen fibrils and proteoglycan (van der Rest and Mayne, 1988; Wu and Eyre, 1995). We assumed an arbitrary reduction in tangential fibril stiffness due to a lack of experimental data. However the influence on tissue component stresses was small, suggesting that substantial fibrillation is required to affect tissue stresses. We assumed an isotropic permeability for the model although anisotropy in the permeability is known to exist, particularly at the bearing and tidemark surfaces.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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Within the area of joint contact, fluid was constrained to flow in the tangent direction due to the impermeable bone and opposing cartilage such that anisotropy is likely to have little effect. At the edge of contact where flow patterns are more complex the anisotropy may have a stronger but localized effect. Tissue consolidation and loading of chondrocytes in this region could be investigated in the future using anisotropic permeability and multi-scale models. However this material model has reproduced in vitro cartilage behaviour under a variety of conditions (Chegini and Ferguson, 2010; Korhonen et al., 2003; Li et al., 1999). Another limitation is the simplified joint geometry and lack of tangential motion due to joint rotation. The geometry of the pelvis approximated the crosssection of the acetabulum, however the model did not include the acetabular fossa, which is assumed to be non-load bearing. The bearing surfaces were assumed to be spherical with a small incongruity between the acetabulum and femur which may occur in the hip joint (Menschik, 1997; Neusel et al., 1996). Anderson et al. (2010) reported large changes in the maximum contact pressure due to the assumed shape of the joint. However the effect may be overestimated since that study assumed a modulus of 17 GPa in the subchondral bone compared to 1.37 GPa used in the current study and reported in human femoral subchondral bone (Brown and Vrahas, 1984). Patient-specific models derived from medical imaging scans may be used to estimate values of pressure and stress in the cartilage of those patients, however image partial-volume effects, practical limits of image resolution and inter-patient variability may obscure differences due to material properties. The model used in this study did not include the effects of the labrum, which can maintain high fluid pressure within the joint space thereby reducing cartilage consolidation (Ferguson et al., 2000). A damaged labrum in a degenerated joint would result in a lower pressure allowing greater fluid exudation and therefore larger differences between the degenerated and healthy model results could be expected. Difficulties were encountered with the finite element solver due to many non-linear effects in the model, especially due to the adaptive surface seepage used to allow free-draining of open cartilage surfaces (Pawaskar et al., 2010). Abaqus requires the highest volume flux in an increment to be less than 0.5% of the time- and spatially-averaged volume flux to accept an equilibrium solution. Since the volume flux near the contact region was several orders of magnitude higher than in the rest of the model, residuals were also large, and the default equilibrium tolerance was relaxed from the default 0.5% to 5% in order to obtain a solution. When this tolerance was changed from 2% to 10%, the maximum pressure difference on the bearing surface was 0.02 MPa, and the mean difference was 0.0001 MPa compared to a nominal pressure of 1.6 MPa. Differences in stresses were similarly small. Previous studies have examined cartilage stresses with varying degrees of geometric and material complexity. Preferred stiffness directions of collagen fibres through the tissue depth result in a nonuniform stress and pressure distribution (Krishnan et al., 2003; Li et al., 2009; Mononen et al., 2012; Pierce et al., 2013a, 2013b) as seen in this study. Donzelli et al. (1999) showed that a transversely isotropic model of cartilage resulted in high stresses in joint regions where cartilage failure is seen. In the current study, simulation of the constituents of cartilage in a fibril-reinforced poroelastic model achieved a similar effect, but also provided stresses and pressure in the individual components. Similar to Donzelli et al. (1999), the highest proteoglycan stresses were seen in the convex femoral cartilage near the cartilage–bone interface. The influence of subchondral bone changes has been reported with conflicting results, although previous studies have implemented a linear elastic cartilage region. Brown et al. (1984) showed that increased subchondral bone stiffness had only a minor influence on cartilage stresses, although increased compressive stress of up to 50% was seen adjacent to localized stiffening of the subchondral bone. Wei et al. (2005)
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showed that doubling subchondral bone stiffness resulted in a 7.5% increase in the cartilage compressive stress. Dar and Aspden (2003) similarly showed that subchondral bone stiffness has a minor influence on cartilage stress in compression. However in the current study the boundary conditions of the pelvis result in a bending mode. This can be seen in the high fluid pressures and stresses offset from the symmetry axis where the structural stiffness of the acetabulum is higher. The current study found bone stiffness had a larger influence on fluid pressure, proteoglycan compressive stress, and cartilage consolidation compared to cartilage degeneration, as well as a large influence on the tangential fibril stress. These phenomena cannot be examined with the elastic models of previous studies of the hip. In a canine experimental model, Ewald et al. (1982) found that replacement of femoral head cancellous bone with stiffer polymethylmethacrylate cement induced cartilage degeneration, in agreement with the current findings, although nutritional, toxicity or thermal factors may have been involved in that study. Although this study demonstrated differences in cartilage behaviour due to cartilage degeneration and increased bone stiffness, the specific conditions at the molecular or cellular level that induce degeneration are not known. The loading conditions in the hip are below the typical gel diffusion rate of cartilage, in which case chondrocyte death may occur due to extensive tissue consolidation i.e. high volume strain, possibly as a result of dehydration (Morel and Quinn, 2004). Alternatively, increased strains may directly alter chondrocyte activity through mitochondria (Wolff et al., 2013). Non-mechanical factors may also influence chondrocyte survival such as impaired nutrient supply (Arkill and Winlove, 2008) or disruption of cellular signalling as a result of thickening of the compact subchondral bone layer (Amin et al., 2009). It is not clear whether the differences in tissue stresses observed in this study are sufficient to induce or sustain degeneration, and in fact are smaller than might be expected. The confining, concave shape of the acetabulum helps reduce fluid loss from the joint space compared to a more open joint such as the knee. This likely sustains high fluid pressure, even in the case of degenerative material properties, and reduces the mechanical demands on the solid components. It must also be recognized that the applied force was unchanged between models and that this must be balanced by the tissue stress and pressure. Thus the main effect of degeneration in this model is the change in load sharing between the tissue components. It is likely that a mechanical explanation for osteoarthritic degeneration requires additional insult to the joint. In the hip, this could include abnormal contact stresses due to morphological deformities as in femoroacetabular impingement (Ganz et al., 2008) or dysplasia (Chegini et al., 2009), or due to external trauma. In these cases changes to the periarticular tissues could amplify the effects of the associated abnormal contact stresses. This study examined the loading of individual cartilage constituents in the high-curvature model of the hip joint. The external load is supported primarily by the fluid pressure, but is slowly transferred to the solid component with cyclic loading. Changes in tissue properties were selected to simulate moderate degeneration. Subchondral sclerosis was found to have a larger influence on cartilage stresses, pressure and consolidation than cartilage degeneration, although differences from the healthy model may not be sufficient to explain mechanically-induced damage. Further work is required to assess the influence of degenerative changes in the presence of joint incongruities such as femoroacetabular impingement deformities in three dimensional models.
Conflict of interest The authors have no conflicts of interest.
Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i
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Please cite this article as: Speirs, A.D., et al., Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.031i