Altered Knee Joint Mechanics in Simple Compression Associated with Early Cartilage Degeneration

The progression of osteoarthritis can be accompanied by depth-dependent changes in the properties of articular cartilage. The objective of the present study was to determine the subsequent alteration in the fluid pressurization in the human knee using a three-dimensional computer model. Only a small compression in the femur-tibia direction was applied to avoid numerical difficulties. The material model for articular cartilages and menisci included fluid, fibrillar and nonfibrillar matrices as distinct constituents. The knee model consisted of distal femur, femoral cartilage, menisci, tibial cartilage, and proximal tibia. Cartilage degeneration was modeled in the high load-bearing region of the medial condyle of the femur with reduced fibrillar and nonfibrillar elastic properties and increased hydraulic permeability. Three case studies were implemented to simulate (1) the onset of cartilage degeneration from the superficial zone, (2) the progression of cartilage degeneration to the middle zone, and (3) the progression of cartilage degeneration to the deep zone. As compared with a normal knee of the same compression, reduced fluid pressurization was observed in the degenerated knee. Furthermore, faster reduction in fluid pressure was observed with the onset of cartilage degeneration in the superficial zone and progression to the middle zone, as compared to progression to the deep zone. On the other hand, cartilage degeneration in any zone would reduce the fluid pressure in all three zones. The shear strains at the cartilage-bone interface were increased when cartilage degeneration was eventually advanced to the deep zone. The present study revealed, at the joint level, altered fluid pressurization and strains with the depth-wise cartilage degeneration. The results also indicated redistribution of stresses within the tissue and relocation of the loading between the tissue matrix and fluid pressure. These results may only be qualitatively interesting due to the small compression considered.


Introduction
Osteoarthritis (OA) is the most prevalent cause of disability among the elderly [1][2][3] . Among all joints, the knee has the highest incidence of OA [1,4,5]. e onset and progression of OA is related to the mechanical environment of articular cartilage [6]. In fact, the cartilage morphology, biosynthesis, and pathogenesis are strongly associated with its mechanical loading [7]. erefore, the better the mechanical behavior of cartilage is understood, the better treatment and prevention strategies could be planned.
Osteoarthritis has been reported to initiate with deterioration from cartilage surface or cartilage-bone interface [8]. e former is believed to be a result of surface wear or splitting and the latter a result of high stiffness gradient at cartilage-bone interface [8,9]. An altered mechanical environment, such as by stress, strain, and �uid �ow, affects the biosynthesis of chondrocytes [10] and eventually leads to tissue degeneration and loss and exposure of bone surface to direct joint contact.
When OA is initiated from the surface, it progresses layer by layer from the super�cial zone to the middle and eventually deep zones [11]. During this process, each layer of the tissue suffers from an altered mechanical environment; for example, the stress, strain, and �uid pressure in the deeper layer can be altered by degenerated super�cial layers.
e mechanics of depth-wise (layer by layer) progression of OA in the knee joint must be affected by the multiple contacts between the cartilaginous tissues, including femoral cartilage, meniscus, and tibial cartilage. A few factors may be important in the contact mechanics of the knee. First, the 3D geometry of these tissues is obviously a dominant parameter that determines the contact area and distribution of contact loading. �econd, the �uid pressurization in these tissues plays an essential role in the mechanical functions of the knee, because the knee compression is associated with high �uid pressure in these cartilaginous tissues �12]. Additionally, the depth-dependent tissue properties, oen being characterized by three discrete zones, may also affect the mechanical behavior of the joint. Great progress has been made in computational OA modeling, with major simpli�cations on the geometry including unrealistic boundary conditions and on the material properties including absence of �uid and �ber properties. For those studies with �uid pressure considered, some assumed a spherical contact in the knee with no meniscus [13][14][15]� others modeled uncon�ned compression testing only. e effect of PG depletion and collagen degradation was investigated by reducing the modulus of the two constituents, respectively [16]. �ncon�ned geometry was used with a �bril reinforced model [17]. In another study, OA was modeled in a depth-dependent manner [18]. e depth-dependent properties were used for cartilage based on values reported in the literature [19]. Again, uncon�ned compression geometry was used in the study. A major progress was made recently in knee OA modeling when both 3� geometry and �uid pressure in articular cartilage were implemented [20]. In this latest study the �uid �ow in the menisci was ignored, which could possibly affect the prediction of the contact mechanics of the joint. Furthermore, the depth-dependent mechanical properties were not incorporated in the study.
Computer modeling may provide an effective tool to examine the effect of cartilage degeneration on contact mechanics and especially �uid pressure within the intact joint. We attempted to study the contact mechanics with an anatomically accurate �nite element (F�) model of the normal and osteoarthritic knee joint. e material model for the cartilaginous tissues included non�brillar matrix, �bers, �uid, and depth-dependent properties. We hypothesized that, due to perturbations induced by OA, the �uid pressure in the tissue would be reduced with a given knee compression (displacement-control). To examine this hypothesis a normal model was compared with case studies whereby depth-wise progression of cartilage degeneration was implemented.
As a �rst step for our OA modeling of the knee, cartilage degeneration was assumed in the high load-bearing region of the medial condyle. is is one of the regions where the lesions are more likely progressed to deep layers [9,21,22], although OA lesions were also found in other sites of femoral cartilage [21,23]. e medial condyle was chosen because it was believed to carry higher load compared to the lateral condyle [24]. e medial condyle was reported to be more susceptible to OA development in both normal [25] and ligament-de�cient knees [26][27][28]. e medial condyle experienced the most rapid lesion progression [29].

Methods
e geometry of the model was reconstructed from MRI images of the right knee of a 27-year-old male subject, who had no symptoms of OA (SPGR sequence, 625 × 625 m resolution, sagittal scan). e model included the distal femur, femoral cartilage, meniscus, tibial cartilage, and proximal tibia ( Figure 1). e maximum thickness of the femoral cartilage was approximately 2.8 mm, and the maximum thickness of the menisci was 8.4 mm [30].
e cartilaginous tissues, that is, femoral cartilage, menisci, and tibial cartilage, were assumed as �brilreinforced �uid-saturated materials. A �bril-reinforced constitutive law was used which models the solid of the tissue as a linear non�brillar matrix that is reinforced by a nonlinear �brillar matrix [17]. Hence, two material properties were required to de�ne the non�brillar matrix, that is, the elastic modulus and Poisson's ratio . e �brillar matrix was characterized by elastic moduli in three orthogonal directions. For the case of small deformations considered in the present study, these moduli were simpli�ed as linear functions of the corresponding tensile strain, for example, for the local direction e compressive stiffness of the �brillar matrix was neglected because the �bers mainly support tensile loading. Note that the direction could be oriented in different directions for different sites. erefore, a 3D collagen orientation could be thus incorporated. In order to describe the interstitial �uid �ow, an orthotropic hydraulic permeability was introduced per Darcy's law, for example, for the local direction where is the -component of the permeability, which is the negative ratio of the -component of the �uid velocity, , and the -component of the �uid pressure gradient, , . Simply replacing the subscript in (1) and (2) with or would obtain the relevant equations for the or direction. e depth-dependent properties were incorporated for the femoral cartilage; that is, the tissue properties varied with the super�cial, middle, and deep zones, in the way approximated previously [31]. In the super�cial zone, the �bers were oriented according to the split lines recorded from the surface ([32]; adopted from Figure 2 in [30]). In the middle zone, the �bers did not have any speci�c orientation. In the deep zone, they were vertical to the cartilage-bone interface. In the meniscus, the primary �bers were oriented in the circumferential direction. No preferred �ber directions were considered for the tibial cartilage due to lack of data.
e surface-to-surface contact was de�ned between articulating surfaces using ABAQUS 6.10. Namely, contact was de�ned between femoral cartilage and meniscus, femoral cartilage and tibial cartilage, and meniscus and tibial cartilage. No �uid �ow was assumed between cartilage and bone. e cartilages and bones were meshed independently. However, in reality, the cartilage is �rmly attached to the bone. ere is no relative motion at the cartilage-bone interface. is interface condition was modeled using the TIE contact option provided by ABAQUS; that is, femoral cartilage was tied to femur, medial and lateral tibial cartilages were tied to tibia, and meniscus horns were tied to the tibial cartilage at both ends of each meniscus.
A ramp compression of 0.1 mm was applied in 1 s on top of the femur while the bottom of the tibia was �xed. e knee was in full extension. As a boundary condition, the free articulating surface (which was not in contact) was assigned to zero �uid pressure.
e consolidation procedure in ABAQUS was used to analyze the quasistatic problem. For cartilaginous tissues, porous elements with �uid pressure were used. e 20-node quadratic elements were used for the femoral cartilage, and the 8-node linear elements were used for tibial cartilage and meniscus. e choice of using different element types for the cartilages was a result of compromise between faster contact convergence and better �uid pressure distribution. e 20node elements provide better numerical accuracy for the �uid pressure but signi�cantly slow down the contact convergence. We used the 20-node elements for the femoral cartilage, because that was the focus for results. e bones were meshed with solid elements. e �uid pressure in the bones was not considered, because it is less signi�cant in load support as compared to that in cartilaginous tissues due to a 3-order higher stiffness of the bones.
In order to understand the mechanics of the depth-wise progression of OA, the normal and three degenerative case studies were implemented computationally. In Case 1, the perturbations were implemented only in the super�cial zone. In Case 2, the perturbations were implemented in super�cial and middle zones, and in Case 3, the perturbations were implemented in all three zones. As discussed earlier, local cartilage degeneration was implemented within the high load-bearing region of the medial condyle of the femoral cartilage ( Figure 2, bounded by the dash line). All other tissues were assumed normal. ese three cases simulated the onset of cartilage degeneration from the super�cial zone and progression to the deep zone.
e following perturbations were implemented for the degenerated cartilage: the permeability was increased by 50%, �oung's modulus of �brillar matrix was decreased by 70%, �oung's modulus of non�brillar matrix was decreased by 65%, and the orientation of �bers was not set in any particular direction. e material properties of normal tissues are summarized in Table 1, which were mainly based on previous �bril-reinforced modeling with tissue explants [31,33]. We assumed no changes in the thickness of the degenerated cartilage, because only early degeneration was considered. erefore, the same tissue geometry was used for the normal and three case studies.

Results
All results presented here are for the end of ramp compression prior to relaxation. e �uid pressure in the femoral cartilage is shown in Figure 2 for a super�cial layer and Figure 3 for a deep layer. �n either layer, no signi�cant alteration in the pressure was seen in the lateral condyle (le in �gure) when cartilage degeneration advanced in the medial condyle from the super�cial to middle and then deep �ones (�ormal → Case 1 → Case 2 → Case 3). e pore pressure in the medial condyle was substantially reduced with the progression of degeneration. is again was true for the �uid pressure in either super�cial or deep layer. e depth variation of the �uid pressure in the degeneration site is shown in Figures 4, 5, and 6. e pressure decreased with the tissue depth in all cases. However, the pressure gradient in the tissue thickness direction reduced progressively with cartilage degeneration for a given knee compression, with larger reduction in the super�cial �one ( Figure 4). e depth variation was also site-speci�c� it can be more easily seen in the high load-bearing region ( Figures  5 and 6).
e distribution of normal strain along the tissue depth was also altered with degeneration in the medial condyle ( Figure 7). is strain was associated with the lateral expansion of the tissue when compressed in the thickness direction. e strain was smaller in the super�cial �one because more tangentially oriented �bers there restrained the lateral expansion. However, the �rst principal strain was actually higher T 1: Material properties for the normal tissues (modulus: MPa; permeability: 10 −3 mm 4 /Ns). e x is the primary �ber direction, that is, the split-line direction for the super�cial zone, the depth direction for the deep zone for articular cartilage, and the circumferential direction for the meniscus. e y and z are normal to the primary �ber direction. e properties are the same in the y and z directions.  in the super�cial zone than in the middle and most deep zones due to high shear strains at the surface (not shown). e �rst principal strain in the deepest layer was the largest in Case 3 (Figure 8), mostly because of large shear strains at the cartilage-bone interface in Case 3 (the lateral strain shown in Figure 7 was not the largest at the deepest layer). As compared to the normal case, the shear strains at the cartilage-bone interface were reduced by cartilage degeneration in the super�cial zone ( Figure 9, Case 1 versus Normal) and further reduced when degeneration progressed into the middle zone (Figure 9, Case 2 versus Case 1). However, the shear strains were eventually raised above normal when cartilage degeneration progressed into the deep zone ( Figure  9, Case 3 versus Normal). Note that these shear strains were associated with shear stresses and , which might cause shear failure at the cartilage-bone interface ( is the tissue thickness direction).

Discussion
e �uid pressurization in all cartilaginous tissues was considered in the proposed model of cartilage degeneration in the human knee with anatomically accurate geometry of the joint. e zonal differences were considered in order to simulate the progression of degeneration from the super�cial to deep zones. Our hypothesis was positively tested: for a given compression (displacement-control), the model predicted reduced �uid pressurization (Figures 2-6) although water content increased with cartilage degeneration. e �uid pressure can support a large portion of the load applied to cartilage [12], which is believed to be part of the mechanism to reduce the joint friction [34] and thus to reduce the chances of OA initiation from the tissue surface. Furthermore, the reduction in the �uid pressure observed in the present study for the case of displacement-control indicated increased joint friction and increased load support by the tissue matrix in the case of joint-force-control. Both may cause further progression of OA and deterioration of the tissue.
e onset of cartilage degeneration in an upper zone also resulted in reduced �uid pressure in the lower zone; for example, a degenerated super�cial zone would reduce the �uid pressure in both middle and deep zones (Figure 4, Case 1). �ince �uid pressurization bears high loading for the tissue, this result agrees with the protective role of the surface layer for the deep layer, as suggested by both experimental and computational studies [35,36].
Furthermore, the �uid pressure reduced �uickly when the degeneration started from the super�cial zone and progressed to the middle zone, then reduced at a lower rate when the degeneration advanced to the deep zone ( Figure  4). is was most likely a conse�uence of different �ber orientations in the three zones. �n the super�cial zone, the �bers are oriented tangentially to resist lateral expansion under knee compression and thus great �uid pressure is produced. �ome tangential �bers in the middle zone should also contribute to increased �uid pressure. �n the deep zone, however, the vertical �bers are in compression, and thus do not signi�cantly contribute to �uid pressurization. erefore, collagen degeneration in the deep zone would cause less �uid pressure change in the tissue than degeneration in the super�cial and middle zones.  Figure 2. is is an inferior view of the right knee; that is, the medial condyle is on the right.
e shear strains at the cartilage-bone interface were increased substantially with cartilage degeneration to the deep zone (Figure 9, Case 3 versus Normal). is was probably because cartilage degeneration in the deep zone further increased the high gradient of the material properties from deep cartilage to underlying bone. Great shear strains at the cartilage-bone interface could cause microfractures, which eventually lead to OA [37][38][39]. e high gradients of material properties are believed to increase the possibility of damage to the cartilage-bone interface [8,37]. Surprisingly, the shear strains at the interface were reduced in Cases 1 and 2 prior to the progression of degeneration into the deep zone ( Figure 9, Case 1 or 2 versus Normal). e reason was probably due to the reduction of �uid pressure and its gradient in the tissue depth direction while the material properties in the deep zone remained unchanged in Cases 1 and 2. Note that knee compression was given in the present study (displacement-control). e shear strains might not have been reduced in Cases 1 and 2, if the joint force had been given (force-control).
Lower Young's moduli and higher permeability were used in the present study to simulate cartilage degeneration, in agreement with data from the literature [40,41] e compressive modulus of cartilage was reduced, respectively, by 18% and 87.5%, and the water content was increased, respectively, by 79.9-81.6% and 84.1%, in moderate and advanced OA [41,42]. According to another study, as a result of OA, the compressive and tensile moduli of human articular cartilage were decreased by 55-68% and 72-83%, respectively, and the permeability was increased by 60-80% [43]. For the human tibial cartilage, the compressive stiffness was decreased by 29% [44]; the compressive compliance was increased by 71% as a result of OA [45]. Six months aer anterior cruciate ligament transection, the compressive modulus of canine cartilage was decreased by 25%, while the permeability was increased by ∼48% twelve weeks aer the surgery [46,47]. We have used moderate values from these measurements.
�educed surface �uid pressure with OA was also reported in the only similar existing study [20]. It was found in that study that the stress distribution through cartilage depth was also in�uenced by the orientation of super�cial �bers. e additional features of the present study included the �uid pressure in all cartilaginous tissues and full consideration of the depth-dependent mechanical properties. We further simulated the depth-wise cartilage degeneration from the super�cial to deep zones. As a consequence, the present results suggest that not only the degeneration in the super-�cial layer reduced the �uid pressure in the deeper layers, which agrees with the existing study [20], but also the degeneration in the deeper layers lowered the �uid pressure in the super�cial layer.
A major limitation of the present study was due to the small knee compression (100 m) that was applied at a rather low rate (100 m/s) in the computer simulation. Our choice was a consequence of slow contact convergence and high demand in computational time resulting from a high resolution of element mesh associated with the zonal differences. Eight layers of elements were meshed in the tissue thickness direction so there were 2, 4, and 2 layers of elements, respectively, for the super�cial, middle, and deep zones. is mesh required several times more computational time, as compared to the previous 4-layer mesh when the zonal differences were ignored [30,48]. It took about a week to complete 1 s simulation on a 4 CPU workstation. In addition, we sometimes failed to obtain convergent results when larger or faster compressions were applied. Further veri�cations are in progress. Because of the small compression considered, one primary concern is whether the results were compromised by the geometrical errors introduced during MRI segmentation and element meshing, such as errors in surface curvature and tissue thickness. While such errors indeed existed, they were probably at a lower level as compared to 100 m. (e quality of surface construction can be positively seen from the continuous variation in pore pressure. e errors in geometry construction have been examined by independent research groups, e.g., [49].) Other limitations included the omission of osmotic pressure and the use of lab loading conditions. e same compression was used in the present study; that is, a displacement-control was used for comparison. While the force-control loading protocol is oen considered more realistic, a knee joint with different stages of OA may not experience the same force. As the OA develops, the patient tends to apply lower load on the diseased side [50]. On the other hand, it is more convenient and easier to interpret the results when using a displacement-control in both computer simulations and lab tests. eoretically, the results from displacement-control can be qualitatively interpreted to that of force-control. erefore, we chose the displacement-control for simplicity.
e results presented here should be qualitatively correct, although the magnitudes are not realistic because of the use of small and slow compression in the present study. e alterations due to degeneration would be ampli�ed in the case of a physiologically realistic compression. is is because of the nonlinear and compression-rate dependent load response of the joint. If a larger compression was applied, the �uid pressure in the healthy cartilage would nonlinearly increase due to the normal collagen network in the tissue, while the pressure in the degenerated cartilage would increase more slowly due to a weak collagen network. For the same reason, if the same compression was applied faster, the �uid pressure would increase faster in the healthy cartilage than in the degenerated cartilage. In other words, the difference in the �uid pressurization in the healthy and degenerated cartilages would be enlarged with the compression magnitude and compression rate. is is understood from previous studies on cartilage explants: both nonlinearity and strain-rate dependence of the load response of cartilage are predominantly determined by the properties of collagen network [17,51,52].
e results of this investigation shed light on the effect of perturbation of material properties and �bers orientation on knee joint mechanics, in the course of progression of OA from cartilage surface to the cartilage-bone interface. Clinical studies suggest the depth of cartilage defect as a parameter that characterizes OA severity [53]. Computational modeling can be used to study the effect of this parameter on the mechanics of knee joint. Furthermore, the role of defect depth in knee joint mechanics can be better understood if computational models consider depth-dependent properties embedded in an anatomical accurate geometry, as this study showed. e �ndings of this study could be implemented in characterizing OA severity based on the depth of cartilage injury. In fact, the development of OA is a multifactorial phenomenon including alteration of tissue mechanical properties, perturbation of �ber orientation, cartilage tissue loss, and the size and location of cartilage lesion [20,[53][54][55]. In this study, the effect of the �rst two parameters was investigated whereas the importance of other factors will be investigated in future.
In summary, we have determined the alterations of �uid pressure and strains in articular cartilage for the local tissue degeneration in the medial condyle of the femur. ese results may provide new information in understanding the progression of osteoarthritis. As discussed earlier, cartilage degeneration resulted in reduced capability of �uid pressurization and reduced pressure gradients in the tissue, which suggest reduced lubrication in the joint and increased load support for the tissue matrix. Results also suggest that once cartilage degeneration is initiated from the articulating surface, it will eventually advance to the deep layer. is facilitation is achieved through the reduction of �uid pressurization in all three zones with greater reduction in the super�cial zone and damage to the depth-dependent structure of the tissue. In particular, cartilage degeneration in the super�cial zone may increase the possibility of damage to cartilage-bone interface.
�on��ct of �nterests e authors have no con�ict of interests to disclose.