Authors of clinical reports4,7,18,19,23 suggest patients with anterior cruciate ligament (ACL)-deficient knees have an increased incidence of knee osteoarthritis (OA) relative to an uninjured population. In addition, authors of some studies1,10 imply there are rotational kinematic changes during walking after ACL injury. These observations suggest kinematic changes as a possible factor in the initiation of osteoarthritis.2
Although increased mechanical force at the knee has been related to higher rates of progression of knee OA,20 it remains unclear whether load is the primary mechanical factor initiating degenerative changes to cartilage. In healthy knees the ratio of medial compartment to lateral compartment cartilage thickness is greater in subjects with higher adduction moments during walking,2 suggesting the higher load on the medial side24 is associated with thicker cartilage in healthy knees.15 Conversely, patients with medial-compartment knee OA show more cartilage thinning with higher loads during walking.2,15,20 Indeed, the outcomes of load-modifying interventions for medial compartment knee OA, such as high tibial osteotomy,22 have been associated with the loads during walking; patients with lower loads on the medial compartment preoperatively have better clinical outcomes than patients that have higher loads.
The kinematic changes during walking in ACL- deficient knees1,10 and the high loads at the knee that occur during the initial phase of the gait cycle24 (between heel strike and the weight acceptance phase) suggest a possible mechanism for the initiation of cartilage breakdown after ACL injury.2 In particular, a shift towards internal tibial rotation has been reported1,10 to occur during walking in patients with ACL-deficient knees. It also has been reported2 that in the ACL-intact knee the thickest cartilage in the weightbearing regions of the tibia and femur align in the medial and lateral compartments when the knee is near full extension, as occurs during the initial phase of the gait cycle when the highest axial loads occur. These observations raise the possibility that the kinematic changes after ACL injury introduce a change in the load bearing characteristics of the tibiofemoral joint by shifting the loads to unconditioned regions of cartilage, thus initiating cartilage breakdown prematurely compared with a knee with normal kinematics.
Computer simulation of the in vivo conditions associated with ACL-deficient knees offers a unique opportunity to explore the feasibility of the hypothesis that kinematic changes can lead to initiation and/or progression of knee OA. There have been numerous studies3,6,11 using computer simulation to explore general characteristics of the mechanical response of articular cartilage to loading; however, there have been relatively few previous cartilage studies using three-dimensional (3-D) knee models with physiologic geometry8,11 and authors of these studies have not examined the influence of kinematic changes on cartilage loss after ACL injury.
In this study, we used computer simulation to examine the hypothesis that the 5° internal tibial rotational shift in the knee during walking after ACL injury accelerates cartilage thinning relative to a healthy knee.
MATERIALS AND METHODS
Briefly, the model was designed to predict the progression of cartilage loss as a function of time past initial cartilage breakdown2 based on the type and magnitude of stress in the cartilage (Fig 1). Three-dimensional geometry of the femoral and tibial articular cartilage was derived from magnetic resonance (MR) images. The loads and kinematics incorporated into the model were derived from experimental gait data from the initial phase of the gait cycle.24 The coefficient of friction at the contact interface was set higher than for normal cartilage to simulate fibrillation.9,26 An iterative algorithm then was used to calculate the cartilage thinning. At each iteration step, the stress distribution was calculated using a nonlinear finite-element model. The model did not attempt to relate the iterations to walking cycles. The cartilage was then thinned according to this stress distribution using an octahedral shear stress criterion as described below. The rate of cartilage thinning for the kinematics associated with the ACL-deficient and the intact knee were compared to test the hypothesis.
Applying previously reported methods for cartilage segmentation,15 we created a 3-D cartilage model from MR images and quantified the cartilage thickness throughout the model (Fig 2). These images were acquired using a 3-D spoiled gradient-echo sequence using parameters previously reported.15,25 Cartilage surface models were obtained by segmenting the MR images using a B-Spline Snakes14 method and then assembling the segmented images for 3-D reconstruction of the femoral and tibial cartilage. The thickness of the cartilage surface models were calculated by finding the Euclidian distance between the subchondral bone surface and the articular surface.
Solid meshes of the femoral and tibial cartilage were generated using MSC Patran (MSC Software, Santa Ana, CA). The model (Fig 2) consisted of 8037 nodes (5295 for femoral cartilage, 2742 for tibial cartilage) and 5040 eight-node linear brick elements (3312 for femoral cartilage, 1728 for tibial cartilage). The cartilage was assumed to behave as a linear elastic, isotropic solid with a Young's modulus of 6 MPa and Poisson's ratio of 0.47.3 The subchondral bone interfaces were modeled as rigid. Contact was defined between the two articular surfaces, as well as between the articular surfaces and the rigid bone; however, the contact interactions between the articular surfaces and the rigid bones were applicable only when full-thickness defects occurred. For each of the three contact pairs, master and slave surfaces were defined. To enforce the contact constraint, Lagrange multiplier forces were applied to any slave nodes found to penetrate the master surface. The resulting stress distributions and contact area were calculated for each analysis using ABAQUS version 6.4 (ABAQUS, Inc., Pawtucket, RI).
We used a coefficient of friction at the articular surface of 0.1 to simulate conditions of initial cartilage break down.9,26 The kinematic and load measurements used as input were derived from a previously reported study of subjects with ACL-deficient and healthy knees.1,10 The alignment of the ACL-deficient knee was modeled by rotating the tibia 5° internally from the normal knee.1 To study the differences in cartilage thinning between knees in healthy and ACL-deficient patients, the thinning simulation analysis was conducted for a normal knee2 and a rotated (ACL-deficient) knee. The medial-lateral load ratio applied to both models was derived from methods described by Schipplein et al,24 who used the joint axial load, flexion angle, adduction moment, and flexion moment from experimental gait data to calculate the total compressive load and the medial-lateral load distribution within the joint. The medial-lateral load ratio at the instant of first peak adduction moment during the initial phase of the gait cycle was used in this study as a representative load distribution in the knee for the gait cycle, because the first peak adduction moment has been shown to be associated with the progression of knee OA.20 This resulted in a 5.15:1 medial- lateral load ratio, which was distributed in a 100 N compressive load. Identical loads were applied to both the normal and the ACL-deficient models.
At each step of the simulation, the femoral and tibial cartilage were thinned based on the octahedral shear stress distribution, which was chosen because high shear stress conditions have been shown to cause a decrease in cartilage biosynthetic activity.13,16 The cartilage was thinned by translating the nodes through the cartilage thickness closer to the subchondral bone surface. The amount of thinning at each node depended linearly on the octahedral shear stress calculated at the node so that the nodes with higher stresses were thinned more than the nodes with lower stress values. When regions of cartilage thickness fell below a threshold value of 0.05 mm, the mesh elements in that region were removed from the mesh to a emulate full thickness defect and expose the subchondral bone.
In addition to comparing the thinning rates between the ACL- intact (idiopathic OA) and ACL-deficient models, the validity of the basic assumptions of the model was evaluated qualitatively by comparing the thinning pattern predicted by the model with both a previous report,12 as well as to a 3-D cartilage thickness map of an end-stage osteoarthritic patient (thickness map obtained using the segmentation method described above) (Fig 3).15
The rotational offset1 introduced into the ACL-deficient knee caused a higher rate of cartilage loss than the knee with the ACL intact without any change in the loading on the joint (Fig 4), with a 44% increase in loss after eight iterations. While the rate of cartilage loss was accelerated for the ACL-deficient knee, both knees showed similar spatial patterns of cartilage loss.
The predicted regions of cartilage thinning for the ACL-deficient and intact knee started in the central load bearing region of the medial compartment and then shifted to the medial boundary of the medial compartment where the first full-thickness defects occurred (Fig 5). On the femur, the primary degeneration occurred on the medial side, with a secondary thinning center on the lateral side. On the tibia, the degeneration was almost entirely in the anterior portion of the medial side.
The model also predicted a greater rate of cartilage loss in the medial compartment relative to the lateral, as shown by the curve of cumulative volume loss versus simulation time (Fig 6). The slopes of the medial and lateral tibial cartilage loss with time were greater than their mating femoral condyles. In addition, the rate of loss on the me- dial tibial cartilage increased with time as the cartilage loss moved to the medial boundary of the medial compartment (Fig 6). This greater loss on the medial side resulted in a drift to varus alignment as the simulation progressed.
The model used in this study was developed to examine the potential for the rotational changes reported in ACL-deficient knees to accelerate the rate of cartilage thinning relative to knees with an intact ACL (idiopathic OA). The data support the hypothesis that altered gait kinematics contribute to accelerated cartilage thinning. The rotational change associated with the ACL-deficient knee shifted the load bearing to thinner regions of cartilage, resulting in increased stresses in the cartilage and accelerated the loss of cartilage relative to the intact knee (Fig 4). In addition, the results of this study suggest a mechanical basis for understanding the increased incidence of medial compartment knee OA after ACL injury. In particular, the morphologic variations in cartilage thickness and the differences in the conformity between the medial and lateral compartments make the medial compartment more vulnerable than the lateral compartment with kinematic changes. The thickest regions of cartilage in the medial compartment are located in a relatively small region of the load bearing area of the joint compared with the lateral compartment (Fig 2). These observations are consistent with authors of other studies who suggest2,29 that the altered contact mechanics in the ACL-deficient knee lead to cartilage loss.
The results should be considered in light of the simplifying assumptions used to generate the model. The model thinning predictions were based solely on mechanical principles that focused on the influence of the contact mechanics of the joint, the variation in cartilage thickness, and the mechanical environment at the knee during the initial phase of the gait cycle. Octahedral shear stress was chosen as the thinning parameter based on previous studies that have suggested that high shear stress conditions at the tissue13 and cellular16 level are detrimental to the cartilage phenotype. In addition, the model incorporated a linear elastic model for cartilage, did not include a meniscus, and applied only a scaled physiologic load. The use of the multiphasic model of cartilage,21 incorporating a meniscus, and applying a more physiologic load would influence the absolute magnitude of the stresses calculated with this type of model, but would not likely alter the results of this study due to its comparative nature. Moreover, the features included in this model were sufficient to predict more rapid progression of medial-compartment knee OA2 and regional patterns of cartilage volume loss that were consistent with a previous clinical reports,12,27 as well as one of our own clinical cartilage degeneration patterns (Fig 5).
The model also showed the higher sensitivity to changes in kinematics of the medial compartment compared with the lateral compartment. To understand the sensitivity of the medial compartment it is important to examine the greater contact conformity (concave tibial surface) in the medial compartment relative than the lateral compartment (convex tibial surface). The higher conformity of the medial compartment will cause a substantially larger shift in the location of this tibiofemoral contact than the lateral compartment for the same kinematic change (Fig 7). Furthermore, the more focal region of thick cartilage in the medial compartment relative to the lateral compartment with a broader region of thicker cartilage (Fig 3) support the observations that cartilage thickness and mechanical properties are related to regions of functional load bearing5,17,28 where highly loaded regions show increased thickness and enhanced mechanical properties. A rotational shift at the beginning of the gait cycle where the knee is near full extension will cause loading to shift to regions that typically sustain lower loads. Therefore the greater conformity and focal thickened regions in the medial compartment make this compartment more vulnerable to kinematic changes whereas the nonconforming contact on the lateral cartilage would allow for a broader range of movement without substantial changes in contact stress.
The modeling approach presented here attempted to help to explain the relationship between specific gait characteristics, cartilage morphology, and the cartilage loss associated with ACL injury. The model showed that under identical loading, the rotational offset associated with the ACL-deficient knee will accelerate cartilage thinning, with predominant thinning in the medial compartment. These results highlight the importance of correcting for rotational gait patterns during ACL reconstruction. Further clinical and experimental studies should be done to verify these findings.
1. Andriacchi TP, Dyrby CO. Interactions between kinematics and loading during walking in the normal and ACL-deficient knee. J Biomech
2. Andriacchi TP, Mundermann A,Smith RL. Alexander EJ, Dyrby CO, Koo S. A framework for the in vivo pathomechanics of osteo- arthritis at the knee. Ann Biomed Eng. 2004;32:447-457
3. Beaupre GS, Stevens SS, Carter DR. Mechanobiology in the development, maintenance, and degeneration of articular cartilage. J Rehabil Res Dev
4. Buckland-Wright J, Lynch J, Dave B. Early radiographic features in patients with anterior cruciate ligament rupture. Ann Rheum Dis
5. Bullough PG. The pathology of osteoarthritis. In: Moskowitz R, Howell D, Goldberg V, eds. Osteoarthritis: Diagnosis and Medical/Surgical Management
Philadelphia, PA: WB Saunders; 1992:36-69.
6. Carter DR, Wong M. Modelling cartilage mechanobiology. Philos Trans R Soc Lond B Biol Sci
7. Daniel DM, Stone ML, Dobson BE, Fithian DC, Rossman DJ, Kaufman KR. Fate of the ACL-injured patient. A prospective outcome study. Am J Sports Med
8. Donahue TLH, Hull ML, Rashid MM, Jacobs CR. A finite element model of the human knee joint for the study of tibio-femoral contact. J Biomech Eng. 2002;124:273-280
9. Forster H, Fisher J. The influence of continuous sliding and subsequent surface wear on the friction of articular cartilage. Proc Inst Mech Eng. 1999;213:329-345
10. Georgoulis AD, Papadonikolakis A, Papageorgiou CD, Mitsou A, Stergiou N. Three-dimensional tibiofemoral kinematics of the anterior cruciate ligament-deficient and reconstructed knee during walking. Am J Sports Med
11. Han SK, Federico S, Epstein M, Herzog W. An articular cartilage contact model based on real surface geometry. J Biomech
12. Harman MK, Markovich GD, Banks SA, Hodge WA. Wear patterns on tibial plateaus from varus and valgus osteoarthritic knees. Clin Orthop Relat Res
13. Heiner A, Martin M. Cartilage responses to a novel triaxial mechanostimulatory culture system. J Biomech
14. Kass M, Witkin A, Terzopoulos D. Snakes: active contour models. Int J Comput Vis
15. Koo S, Gold GE, Andriacchi TP. Considerations in measuring cartilage thickness using MRI: Factors influencing reproducibility and accuracy. Osteoarthritis Cartilage
16. Lee MS, Trindade MC, Ikenoue T, Goodman SB, Schurman DJ, Smith RL. Regulation of nitric oxide and bcl-2 expression by shear stress in human osteoarthritic chondrocytes in vitro. J Cell Biochem
17. Li G, Park SE, DeFrate LE, Schutzer ME, Ji L, Gill TJ, Rubash HE. The cartilage thickness distribution in the tibiofemoral joint and its correlation with cartilage-to-cartilage contact. Clin Biomech (Bristol, Avon)
18. Lohmander LS, Ionescu M, Jugessur H, Poole AR. Changes in joint cartilage aggrecan after knee injury and in osteoarthritis. Arthritis Rheum
19. Lohmander LS, Roos H. Knee ligament injury; surgery and osteoarthrosis: truth or consequences. Acta Orthop Scand
20. Miyazaki T, Wada M, Kawahara H, Sato M, Baba H, Shimada S. Dynamic load at baseline can predict radiographic disease progression in medial compartment knee osteoarthritis. Ann Rheum Dis
21. Mow VC, Guo XE. Mechano-electrochemical properties of articular cartilage: their inhomogeneities and anisotropies. Ann Rev Biomed Eng. 2002;4:175-209
22. Prodromos CC, Andriacchi TP, Galante JO. A relationship between gait and clinical changes following high tibial osteotomy. J Bone Joint Surg
23. Roos H, Adalberth T, Dahlberg L, Lohmander LS. Osteoarthritis of the knee after injury to the anterior cruciate ligament or meniscus: The influence of time and age. Osteoarthritis Cartilage
. 1995;3: 261-267.
24. Schipplein OD, Andriacchi TP. Interaction between active and passive knee stabilizers during level walking. J Orthop Res
. 1991;9: 113-119.
25. Stammberger T, Eckstein F, Englmeier KH, Reiser M. Determination of 3D cartilage thickness data from MR imaging: computational method and reproducibility in the living. Magn Reson Med
26. Wang H, Ateshian GA. The normal stress effect and equilibrium friction coefficient of articular cartilage under steady frictional shear. J Biomech
27. Weidow J, Pak J, Kärrholm J. Different patterns of cartilage wear in medial and lateral gonarthrosis. Acta Orthop Scand
28. Wong M, Siegrist M, Cao X. Cyclic compression of articular cartilage explants is associated with progressive consolidation and altered expression pattern of extracellular matrix proteins. Matrix Biol
29. Wu JZ, Herzog W, Epstein M. Joint contact mechanics in early stages of osteoarthritis. Med Eng Phys