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Knee joint biomechanics in open-kinetic-chain flexion exercises
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Clinical Biomechanics 23 (2008) 477–482 www.elsevier.com/locate/clinbiomech
Knee joint biomechanics in open-kinetic-chain flexion exercises W. Mesfar a, A. Shirazi-Adl b,* b
a Laboratory of Biomechanical Orthopedics, E´cole Polytechnique Fe´de´rale de Lausanne, Switzerland Department of Mechanical Engineering, E´cole Polytechnique, P.O. Box 6079, Station Centre-Ville, Montre´al, Que´bec, Canada H3C 3A7
Received 1 October 2007; accepted 23 November 2007
Abstract Background. Different rehabilitation exercises such as open-kinetic-chain flexion and extension exercises are currently employed in non-operative and post-operative managements of joint disorders. The challenge is to strengthen the muscles and to restore the near-normal function of the joint while protecting its components (e.g., the reconstructed ligament) from excessive stresses. Methods. Using a validated 3D nonlinear finite element model, the detailed biomechanics of the entire joint in open-kinetic-chain flexion exercises are investigated at 0°, 30°, 60° and 90° joint angles. Two loading cases are simulated; one with only the weight of the leg and the foot while the second considers also a moderate resistant force of 30 N acting at the ankle perpendicular to the tibia. Findings. The addition of 30 N resistant force substantially increased the required hamstrings forces, forces in posterior cruciate and lateral collateral ligaments and joint contact forces/areas/stresses. Interpretation. At post-anterior cruciate ligament reconstruction or injury period, the exercise could safely be employed to strengthen the hamstrings muscles without a risk to the anterior cruciate ligament. In contrast, at post-posterior cruciate/lateral collateral ligaments reconstructions or injuries, the open-kinetic-chain flexion exercise should be avoided under moderate to large flexion angles and resistant forces. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Open-kinetic-chain flexion exercise; Knee joint; Finite elements; Ligaments; Hamstrings
1. Introduction In various occupational and recreational activities, the human knee joint is exposed to large loads and deformations and, hence, to high risk of injuries and degeneration. The joint stiffness and stability is provided by different components such as menisci, ligaments and musculature. Any weakness, injury or alteration in one of these structures would influence the biomechanical role of the remaining components and the entire joint that in turn predisposes the joint to the risk of additional injury and degeneration. Different rehabilitation exercises are currently employed in non-operative and post-operative managements of joint disorders. Athletic training and performance enhancement programs also take advantage of such exercises. Evidently, *
Corresponding author. E-mail address: [email protected] (A. Shirazi-Adl).
0268-0033/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.clinbiomech.2007.11.016
the challenge is to exercise and strengthen the muscles and to restore the near-normal function of the joint while protecting its components (e.g., the reconstructed ligaments) from excessive stresses. Irrgang and Fitzgerald (2000) suggested that the rehabilitation for a patient with a ligament injury should aim to reduce pain and swelling, restore range of motion, strength and endurance, and enhance proprioception and dynamic stability of the knee. The open-kinetic-chain (OKC) and closed-kinetic-chain (CKC) exercises generate, as expected, different patterns of muscle activities and ligament forces (Escamilla et al., 1998; Lutz et al., 1993; Wilk, 1994). The CKC programs activate antagonistic muscle groups across multiple joints and as such cannot be used to isolate or examine a single muscle group (Lutz et al., 1993; Salem et al., 2003). Conversely, the OKC exercises isolate specific muscle groups for strengthening and evaluation purposes. These latter exercises involve the leg-extension which strengthens
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quadriceps while extending the knee against a resistance and the leg-flexion which strengthens hamstrings while flexing the knee against an opposing force. Knowledge of the strain in the joint ligaments during such exercises is vital if the knee is to be protected properly after a ligament reconstruction (Yasuda and Sasaki, 1987; Draganich and Vahey, 1990). Biomechanical and clinical investigations have suggested that OKC extension exercises produce large forces in the anterior cruciate ligament (ACL) especially near full extension (Escamilla et al., 1998; Draganich and Vahey, 1990; Mesfar and Shirazi-Adl, 2008; Shoemaker and Markolf, 1985). In contrast, CKC exercises have been recommended to be safer in post-ACL reconstruction period (Lutz et al., 1993; Palmitier et al., 1991; Shelbourne and Nitz, 1990). Recent studies, however, advocate both OKC and CKC exercises as effective regimens to restore and enhance performance of joint normal function (Andersen et al., 2006; Fitzgerald, 1997; Perry et al., 2005; Witvrouw et al., 2004). Using a combined model-measurement study, Cohen et al. (2001) reported that the patellofemoral contact stresses were of the same order of magnitude in both CKC and OKC extension exercises. Since hamstrings are important joint stabilizers in the ACL-deficient or injured knees, the OKC flexion exercises are crucial in augmenting hamstrings strength and coordination (Butler et al., 1985; Za¨tterstro¨m, 1999). These exercises, however, produce net posterior shear forces that may overload the posterior cruciate ligament (PCL) especially following a PCL injury or reconstruction (Wilk, 1994; Smidt, 1973). In such cases, OKC extension exercises to strengthen quadriceps may be preferable (Wilk, 1994; Mesfar and Shirazi-Adl, 2008). For adequate strengthening of both muscle groups following a ligament injury, the challenge remains as to identify exercises for the quadriceps that place safe forces on the ACL and those for the hamstrings that produce safe forces in the PCL. Proper knowledge of detailed knee biomechanics under various exercise regimens is therefore crucial for the design of effective rehabilitation programs. In an earlier model study, the detailed biomechanics of the entire knee joint in OKC extension exercises were investigated at 0°, 30°, 60° and 90° joint angles with and without a resistant force of 30 N acting at the ankle perpendicular to the tibia (Mesfar and Shirazi-Adl, 2008). In post-ACL reconstruction period or in the joint with ACL injury, it was recommended to avoid exercises under larger resistant force and at near full extension positions. In the absence of earlier detailed model studies, the current work aims hence to employ the previously validated 3D knee model to investigate biomechanics of the entire joint in OKC flexion exercises (leg curl exercise) as well. Two loading cases are considered; one with no external load accounting only for the weight of the leg and the foot while the second one also incorporated a moderate resisting force of 30N acting at the ankle perpendicular to the tibia. For the joint angles of 0°, 30°, 60° and 90°, biomechanics of the knee joint including required hamstrings forces, joint moment, flexor
lever arm, tibiofemoral contact forces/areas and joint ligament forces are computed and compared with those in OKC extension exercises under similar loads. 2. Methods The knee joint model consists of three bony structures (tibia, femur, and patella) and their articular cartilage layers, menisci, six principal ligaments (collaterals LCL/MCL, cruciates ACL/PCL, and medial/lateral patellofemoral ligaments), patellar tendon, quadriceps muscle force vectors (divided into three components; vastus lateralis/rectus femoris-vastus intermidus medialis/vastus medialis obliqus) and hamstrings muscle force vectors (divided into three components; biceps femoris/sartorius-gracilis-semitendinosus (TRIPOD)/semimembranosus) (Fig. 1). Ligaments are each modeled by a number of uniaxial elements with different prestrains and nonlinear material properties (no compression) (Fig. 2) (Butler et al., 1986; Atkinson et al., 2000; Mesfar and Shirazi-Adl, 2006a; Moglo and ShiraziAdl, 2003a, 2003b; Sta¨ubli et al., 1999). In the current study due to the isolated activity in hamstrings, the patellofemoral joint/ligaments and patellar tendon are not considered. Additional details of the model are available elsewhere (e.g., Mesfar and Shirazi-Adl, 2005). The relative forces in hamstrings muscle components are taken from the study of Kwak et al. (2000); biceps femoris: semimembranosus:TRIPOD=1:1:(35/87). At full extension and in the frontal plane, biceps femorisis oriented 11.8° medially, semitendinosus is 7° laterally and the TRIPOD is 7.1° medially relative to the tibial axis. In the sagittal plane, biceps femoris is parallel to the tibial axis whereas semitendinosus and TRIPOD are respectively 16.1° and 18.7° posteriorly to the axis (Aalbersberg et al., 2005; Hillman, 2003). The forgoing muscle orientations subsequently altered with joint flexion angle (Mesfar and Shirazi-Adl, 2006b). For stable and fully unconstrained boundary conditions in flexion, the femur is fixed while the tibia is left completely free. The joint reference configuration at full extension is initially established under ligament prestrains (Mesfar and Shirazi-Adl, 2006a). To account for the weight of the leg and the foot, two gravity forces of 29.3 N and 7.85 N, respectively, are applied at their mass centres based on anthropometric data of female subjects (De Leva, 1996) since our finite element model was originally constructed based on a female knee joint (Bendjaballah et al., 1995) (Fig. 1). For the cases simulating flexion against an opposing force, an additional (extensor) force of 30 N is applied normal to the tibia at the ankle situated at a lever arm of 372 mm to the tibial plateau (De Leva, 1996) (Fig. 1). The joint flexion angles of 0°, 30°, 60° and 90° are considered for both loading conditions. To circumvent the likely adverse effect of changes in the medial–lateral positioning of forgoing gravity and external forces on results (e.g., TF internal–external rotations), the coupled tibial internal–external rotations are fixed when these external loads
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Fig. 1. Finite element model of the entire knee joint showing cartilage layers, menisci, ligaments, patellar tendon (PT) and hamstrings muscles. Bony structures are assumed rigid and not shown. Quadriceps components and patella are not however considered in the current simulation of the OKC flexion exercises. Hamstrings components are BF: biceps femoris, SM: semimembranous and the TRIPOD composed by SR: sartorius, GR: gracilis and ST: semitendinosus. On the left, the OKC flexion exercise is schematically shown in two joint positions with gravity and resistant forces.
OKC-F
28
OKC-F +30N
24
1000 800
20 16
600
12
400
8 200
4
0
0 0
30 60 Flexion Angle (Deg)
90
Fig. 2. Computed hamstrings forces at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N). The ratios to the leg and foot weight are also shown (right axis).
are applied. After the application of ligament prestrains and at each joint flexion angle, the model iteratively searches for the hamstrings forces that maintain equilibrium under the gravity alone or combined with the resistant force. In this manner, OKC flexion exercises are simulated at four joint angles and two loading conditions. The nonlinear analyses are performed using ABAQUS 6.4 (Hibbit, Karlsson & Sorensen, Inc., Pawtucker, RI) finite element package program.
3. Results
strings forces of 1122 N and 473 N were computed at 0° flexion under gravity with and without resistant force of 30 N, respectively. These forces diminished to 263 N and 31 N at 90° flexion, respectively. The joint moment, supported primarily by foregoing hamstrings forces, followed similar trends; it markedly increased in presence of the external load at the ankle but diminished substantially with flexion angle in both loading conditions (Fig. 3). The effective flexor lever arm of the joint estimated as the ratio of the tibial flexor moment to associated hamstrings force was found to increase with joint flexion angle under both loading conditions, except between 60° and 90° under gravity alone where a small decrease was computed (Fig. 4). The increase in the lever arm with joint flexion angle was more pronounced in the presence of resistant force. Due to the posterior translation of the tibia under hamstrings activity, ACL force remained negligible <6 N throughout joint flexion (Fig. 5). On the contrary, PCL 25 Tibial Moment (N-m)
32 Ratio to Leg Weight
Hamstrings Force (N)
1200
OKC-F
20
OKC-F +30N
15 10 5 0 0
In OKC flexion simulations, the total hamstrings force required to counterbalance the extension moment of gravity with and without resistant force substantially decreased as joint flexed from 0° to 90° (Fig. 2). The maximum ham-
30 60 Flexion Angle (Deg)
90
Fig. 3. Net joint moment at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
W. Mesfar, A. Shirazi-Adl / Clinical Biomechanics 23 (2008) 477–482
1200
OKC-F OKC-F +30N
40
TF Contact Force (N)
Lever Arm (mm)
50
30 20 10 0 0
30 60 Flexion Angle (Deg)
90
PCL Force (N)
300
200
ACL Force (N)
400
4
OKC-F (ratio)
800
OKC-F +30N (ratio)
3 600 2 400 1
200 0
0 30 60 Flexion Angle (Deg)
90
Fig. 7. Computed total resultant tibiofemoral contact forces at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N). The ratios to the corresponding hamstrings forces are also shown for both cases (right axis).
8 4 0 0
30
60
90
OKC-F OKC-F +30N
100
0 0
30
60
90
Flexion Angle (Deg) Fig. 5. Computed forces in the posterior and anterior (inlay figure) cruciate ligaments at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
contributions initiated at 30° and reached large values (maximum of 334 N at 60°) especially under the 30 N resistant force (Fig. 6). In both loading cases, PCL force
decreased from 60° to 90° flexion. The force in LCL ligament (Fig. 6) also substantially increased with joint flexion especially so in presence of resistant force; it reached maximums of 35 N and 125 N without and with resistant force, respectively. Forces in the MCL remained relatively small <15 N in all cases. Total tibiofemoral contact forces for different cases followed the same trend as those of hamstrings forces (Fig. 7). The maximum tibiofemoral contact forces of 1056 N and 466 N were computed at 0° flexion that diminished to 429 N and 136 N at 90° with and without resistant force, respectively. On the contrary, the ratio of tibiofemoral contact forces to corresponding hamstrings forces increased with joint flexion especially so under gravity alone in which case it varied from the minimum of 0.98 at 0° to the maximum of 4.44 at 90°. Total tibiofemoral contact area followed the same trend as that of contact force. Under the same loading conditions respectively, tibiofemoral contact area decreased from its maximums of 1027 mm2 and 812 mm2 at full extension to its minimums of 665 mm2 and 466 mm2 at 90° flexion. 4. Discussion
150 OK C- F
120 LCL Force (N)
1000
0
Fig. 4. Computed equivalent flexor lever arm (defined as the ratio of joint moment over the hamstrings force) at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
5
OKC-F OKC-F +30N
Ratio to Hamstrings Force
480
OK C- F +3 0N
90 60 30 0 0
30 60 Flexion Angle (Deg)
90
Fig. 6. Computed forces in the lateral collateral ligament at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
Detailed biomechanics of the entire knee joint at different flexion positions were investigated under OKC flexion exercises with and without a 30 N resistant load at the ankle. For this purpose a validated 3D nonlinear model of the knee joint was used to compute hamstrings forces, joint moments, effective lever arms, forces in various joint ligaments and contact forces/areas. Due to the marked decrease in muscle forces as the joint flexed, the joint moment decreased substantially from 0° to 90°; by nine-fold under gravity alone and by two-fold under combined load (Fig. 3). A negligible portion (<1 Nm) of these moments are, however, due to the passive resistance of the joint itself (Mesfar and Shirazi-Adl, 2005). The associated effective flexor lever arm of the flexor mech-
W. Mesfar, A. Shirazi-Adl / Clinical Biomechanics 23 (2008) 477–482
anism (estimated as the ratio of the joint moments over hamstrings forces) substantially increased by 80% under gravity loading alone and by 155% when resistant force was also added as flexion angle varied from 0° to 90°. In contrast and under almost the same joint moment magnitudes, the extensor lever arm decreased by 28% and 18%, respectively, in OKC extension cases under similar loading conditions (Mesfar and Shirazi-Adl, 2008). These differences in the joint lever arms in OKC flexion and extension exercises, despite the posterior shift in tibial contact in flexion (Dennis et al., 2005; Scarvell et al., 2005), are due primarily to the changes in orientations and displacements of tibial insertions of the patellar tendon and hamstrings muscles during joint flexion. The estimated hamstrings forces diminished by 77% as joint flexed to 90° under resistant force and by 94% when gravity alone was considered (Fig. 2). In order to counterbalance the additional moment of the 30 N resistant force, hamstrings force increased by as much as 650 N at 0° flexion but by only 232 N at 90° flexion. Accordingly, observation of variations in hamstrings forces and joint moments with flexion angles or equivalently of changes in the associated flexor lever arms demonstrates that moment-generating capacity of hamstrings muscles improves with joint flexion. This corroborates our earlier findings that hamstrings are much more efficient in resisting moments at larger flexion angles in contrast to quadriceps muscles that are more efficient at smaller flexion angles (Mesfar and Shirazi-Adl, 2008, 2006b). The computed variations in hamstrings forces with joint flexion are in good agreement with those reported by Shelburne and Pandy (1997). Very small ACL forces (<6 N) were computed throughout joint flexion angles and that despite the presence of gravity and resistant forces acting on the tibia in the anterior direction especially at near extension positions. The results, hence, advocate the use of OKC flexion exercises at all joint angles and resistant force levels in post-ACL reconstruction periods or in joints following an ACL injury. In contrast to ACL ligament, large forces were computed in the PCL at and beyond 30° flexion reaching their maximum at 60° flexion. Our earlier studies under isolated constant hamstrings force indicated similar PCL forces that monotonically increased with flexion angle up to 90° (Mesfar and Shirazi-Adl, 2006b). The addition of 30 N resistant force further increased PCL force by 141 N at 30°, 198 N at 60° and 275 N at 90°. Relatively large forces were also generated in LCL ligament at large flexion angles under the resistant force. The current results, hence, advocate the use of OKC flexion exercise in the post-PCL/LCL reconstruction period or in the joint with PCL/LCL injury preferably at near full extension positions and that in presence of rather small resistant forces. The foregoing negligible ACL forces at near full extension that disappear with flexion and large PCL forces that increase with flexion are in agreement with predictions of Shelburne and Pandy (1997).
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Under both loading cases, tibiofemoral contact forces decreased with joint flexion. These changes in contact forces during joint flexion, despite increases in PCL and LCL forces, were due to substantial decreases in hamstrings forces. The computed tibiofemoral contact force at full extension in this study reached a value two-fold greater than that in OKC extension exercise under identical load magnitudes (Mesfar and Shirazi-Adl, 2008). Similarly, mean tibiofemoral contact stresses decreased throughout flexion and reached values larger than the corresponding contact stresses in OKC extension exercises which remained nearly constant throughout flexion (Mesfar and Shirazi-Adl, 2008). In OKC flexion, the mean tibiofemoral contact stresses varied from 0.57 MPa (at 0°) to 0.29 MPa (at 90°) under gravity alone and from 1.03 MPa (at 0°) to 0.65 MPa at 90° knee flexion under 30 N resistant force in contrast to corresponding stresses computed in OKC extension exercises that remained nearly constant throughout flexion, 0.35 MPa and 0.65 MPa, respectively for cases without and with resistant load. These computed tibiofemoral contact stresses are within the range of values reported for contact stresses under similar compression loads (Bendjaballah et al., 1995; Ahmed et al., 1983; Meyer et al., 1997) and much smaller than reported ultimate cartilage stress values (Flachsmann et al., 2001; Vener et al., 1992). Finally, no excessive force or stress in various joint components, with the exception of the PCL and to some extent LCL, was found in the OKC flexion exercises under moderate resistant force of 30 N considered in this study. The magnitude of this resistant force plays a crucial role by substantially increasing the required hamstrings forces, forces in PCL/LCL ligaments, and joint contact forces/stresses. At post-ACL reconstruction period or in the joint with ACL injury, the exercise could safely be used to strengthen the hamstrings muscles without a risk to the ACL. In contrast, at post-PCL/LCL reconstruction or injury, the OKC flexion exercise should be avoided under moderate to large resistant forces and knee flexion angles. Our current and earlier studies (Mesfar and Shirazi-Adl, 2008) are helpful in the design of efficient OKC exercises in rehabilitation periods as well as performance enhancement programs. Acknowledgements The financial supports of the Natural Science and Engineering Research Council of Canada (NSERC-Canada) and the Canadian Institute of Health Research (CIHR) are gratefully acknowledged. The earlier efforts of M.Z. Bendjaballah and K.E. Moglo in development of the model are also acknowledged. References Aalbersberg, S., Kingma, I., Ronsky, J.L., Frayne, R., van Diee¨n, J.H., 2005. Orientation of tendons in vivo with active and passive knee muscles. J. Biomech. 38, 1780–1788.
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Ahmed, A.M., Burke, D.L., Yu, A., 1983. In-vitro measurement of static pressure distribution in synovial joint – Part II: Retropatellar surface. J. Biomech. Eng. Trans. ASME 105, 226–236. Atkinson, P., Atkinson, T., Huang, C., Doane, R., 2000. A comparison of the mechanical and dimensional properties of the human medial land lateral patellofemoral ligaments. In: Trans. 46th Ann. Meet. Orthop. Res. Soc., Orlando, p. 776. Andersen, L.L., Magnusson, S.P., Nielsen, M., Haleem, J., Poulsen, K., Aagaard, P., 2006. Neuromuscular activation in conventional therapeutic exercises and heavy resistance exercises: implications for rehabilitation. Phys. Ther. 86, 683–697. Bendjaballah, M.Z., Shirazi-Adl, A., Zukor, D.J., 1995. Biomechanics of the human knee joint in compression: reconstruction, mesh generation and finite element analysis. The Knee 2, 69–79. Butler, D.L., Grood, E.S., Noyes, F.R., Sodd, A.N., 1985. On the interpretation of our anterior cruciate ligament data. Clin. Orthop. 196, 26–34. Butler, D.L., Kay, M.D., Stouffer, D.C., 1986. Comparison of material properties in fascicle-bone units from human patellar tendon and knee ligaments. J. Biomech. 19, 425–432. Cohen, Z.A., Roglic, H., Grelsamer, R.P., Henry, J.H., Levine, W.N., Mow, V.C., Ateshian, G.A., 2001. Patellofemoral stresses during open and closed kinetic chain exercises. An analysis using computer simulation.. Am. J. Sport. Med. 29, 480–487. De Leva, P., 1996. Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. J. Biomech. 29, 1223–1230. Dennis, D.A., Mahfouz, M.R., Komistek, R.D., Hoff, W., 2005. In vivo determination of normal and anterior cruciate ligament-deficient knee kinematics. J. Biomech. 38, 241–253. Draganich, L.F., Vahey, J.W., 1990. An in vitro study of anterior cruciate ligament strain induced by quadriceps and hamstrings forces. J. Orthop. Res. 8, 57–63. Escamilla, R.F., Fleisig, G.S., Zheng, N., Barrentine, S.W., Wilk, K.E., Andrews, J.R., 1998. Biomechanics of the knee during closed kinetic chain and open kinetic chain exercises. Med. Sci. Sport. Exer. 30, 556– 569. Fitzgerald, G.K., 1997. Open versus closed kinetic chain exercise: issues in rehabilitation after anterior cruciate ligament reconstructive surgery. Phys. Ther. 77, 1747–1754. Flachsmann, R., Broom, N.D., Hardy, A.E., 2001. Deformation and rupture of the articular surface under dynamic and static compression. J. Orthop. Res. 19, 1131–1139. Hillman, S.K., 2003. Interactive Functional Anatomy. Primal pictures, London, U.K. Irrgang, J.J., Fitzgerald, G.K., 2000. Rehabilitation of the multipleligament-injured knee. Clin. Sport. Med. 19, 545–571. Kwak, S.D., Ahmad, C.S., Gardner, T.R., Grelsamer, R.P., Henry, J.H., Blankevoort, L., Ateshian, G.A., Mow, V.C., 2000. Hamstrings and iliotibial band forces affect knee kinematics and contact pattern. J. Orthop. Res. 18, 101–108. Lutz, G.E., Palmitier, R.A., An, K.N., Chao, E.Y., 1993. Comparison of tibiofemoral joint forces during open-kinetic-chain and closed-kineticchain exercises. J. Bone Joint Surg. Am. 75, 732–739. Mesfar, W., Shirazi-Adl, A., 2005. Biomechanics of the knee joint in flexion under various quadriceps forces. The Knee 12, 424–434. Mesfar, W., Shirazi-Adl, A., 2006a. Biomechanics of changes in ACL and PCL materials properties or prestrains in flexion under muscle forceimplications in ligament reconstruction. Comp. Meth. Biomech. Biomed. Eng. 9, 201–209.
Mesfar, W., Shirazi-Adl, A., 2006b. Knee joint mechanics under quadriceps-hamstrings muscle forces are influenced by tibial restraint. Clin. Biomech. 21, 841–848. Mesfar, W., Shirazi-Adl, A., 2008. Computational biomechanics of knee joint in open-inetic chain extension exercises. Comp. Meth. Biomech. Biomed. Eng. 11, 55–61. Meyer, S.A., Brown, T.D., Pedersen, D.R., Albright, J.P., 1997. Retropatellar contact stress in simulated patella infera. Am. J. Knee Surg. 10, 129–138. Moglo, K.E., Shirazi-Adl, A., 2003a. On the coupling between anterior and posterior cruciate ligaments, and knee joint response under anterior femoral drawer in flexion: a finite element study. Clin. Biomech. 18, 751–759. Moglo, K.E., Shirazi-Adl, A., 2003b. Biomechanics of passive knee joint in drawer: load transmission in intact and ACL-deficient joints. The Knee 10, 265–276. Palmitier, R.A., An, K.N., Scott, S.G., Chao, E.Y., 1991. Kinetic chain exercise in knee rehabilitation. Sport. Med. 11, 402–413. Perry, M.C., Morrissey, M.C., King, J.B., Morrissey, D., Earnshaw, P., 2005. Effects of closed versus open kinetic chain knee extensor resistance training on knee laxity and leg function in patients during the 8- to 14-week post-operative period after anterior cruciate ligament reconstruction. Knee Surg. Sport. Traum. Arthr. 13, 357–369. Salem, G.J., Salinas, R., Harding, F.V., 2003. Bilateral kinematic and kinetic analysis of the squat exercise after anterior cruciate ligament reconstruction. Arch. Phys. Med. Rehabil. 84, 1211–1216. Scarvell, J.M., Smith, P.N., Refshauge, K.M., Galloway, H., Woods, K., 2005. Comparison of kinematics in the healthy and ACL injured knee using MRI. J. Biomech. 38, 255–262. Shelbourne, K.D., Nitz, P., 1990. Accelerated rehabilitation after anterior cruciate ligament reconstruction. Am. J. Sport. Med. 18, 292–299. Shelburne, K.B., Pandy, M.G., 1997. A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions. J. Biomech. 30, 163–176. Shoemaker, S.C., Markolf, K.L., 1985. Effects of joint load on the stiffness and laxity of ligament-deficient knees. An in vitro study of the anterior cruciate and medial collateral ligaments. J. Bone Joint Surg, 136–146. Smidt, G.L., 1973. Biomechanical analysis of knee flexion and extension. J. Biomech. 6, 79–92. Sta¨ubli, H.U., Schatzmann, L., Brunner, P., Rincon, L., Nolte, L.P., 1999. Mechanical tensile properties of the quadriceps tendon and patellar ligament in young adults. Am. J. Sport. Med. 27, 27–34. Vener, M.J., Thompson Jr., R.C., Lewis, J.L., Oegema Jr., T.R., 1992. Subchondral damage after acute transarticular loading: an in vitro model of joint injury. J. Orthop. Res. 10, 759–765. Wilk, K.E., 1994. Rehabilitation of isolated and combined posterior cruciate ligament injuries. Clin. Sport. Med. 13, 649–677. Witvrouw, E., Danneels, L., Van Tiggelen, D., Willems, T.M., Cambier, D., 2004. Open versus closed kinetic chain exercises in patellofemoral pain: a 5-year prospective randomized study. Am. J. Sport. Med. 32, 1122–1130. Yasuda, K., Sasaki, T., 1987. Exercise after anterior cruciate ligament reconstruction. The force exerted on the tibia by the separate isometric contractions of the quadriceps or the hamstrings. Clin. Orthop. 220, 275–283. Za¨tterstro¨m, R., 1999. The Injured Anterior Cruciate Ligament and Neuromuscular Rehabilitation. Doctoral thesis, University of Lund, Sweden.
Clinical Biomechanics 23 (2008) 477–482 www.elsevier.com/locate/clinbiomech
Knee joint biomechanics in open-kinetic-chain flexion exercises W. Mesfar a, A. Shirazi-Adl b,* b
a Laboratory of Biomechanical Orthopedics, E´cole Polytechnique Fe´de´rale de Lausanne, Switzerland Department of Mechanical Engineering, E´cole Polytechnique, P.O. Box 6079, Station Centre-Ville, Montre´al, Que´bec, Canada H3C 3A7
Received 1 October 2007; accepted 23 November 2007
Abstract Background. Different rehabilitation exercises such as open-kinetic-chain flexion and extension exercises are currently employed in non-operative and post-operative managements of joint disorders. The challenge is to strengthen the muscles and to restore the near-normal function of the joint while protecting its components (e.g., the reconstructed ligament) from excessive stresses. Methods. Using a validated 3D nonlinear finite element model, the detailed biomechanics of the entire joint in open-kinetic-chain flexion exercises are investigated at 0°, 30°, 60° and 90° joint angles. Two loading cases are simulated; one with only the weight of the leg and the foot while the second considers also a moderate resistant force of 30 N acting at the ankle perpendicular to the tibia. Findings. The addition of 30 N resistant force substantially increased the required hamstrings forces, forces in posterior cruciate and lateral collateral ligaments and joint contact forces/areas/stresses. Interpretation. At post-anterior cruciate ligament reconstruction or injury period, the exercise could safely be employed to strengthen the hamstrings muscles without a risk to the anterior cruciate ligament. In contrast, at post-posterior cruciate/lateral collateral ligaments reconstructions or injuries, the open-kinetic-chain flexion exercise should be avoided under moderate to large flexion angles and resistant forces. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Open-kinetic-chain flexion exercise; Knee joint; Finite elements; Ligaments; Hamstrings
1. Introduction In various occupational and recreational activities, the human knee joint is exposed to large loads and deformations and, hence, to high risk of injuries and degeneration. The joint stiffness and stability is provided by different components such as menisci, ligaments and musculature. Any weakness, injury or alteration in one of these structures would influence the biomechanical role of the remaining components and the entire joint that in turn predisposes the joint to the risk of additional injury and degeneration. Different rehabilitation exercises are currently employed in non-operative and post-operative managements of joint disorders. Athletic training and performance enhancement programs also take advantage of such exercises. Evidently, *
Corresponding author. E-mail address: [email protected] (A. Shirazi-Adl).
0268-0033/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.clinbiomech.2007.11.016
the challenge is to exercise and strengthen the muscles and to restore the near-normal function of the joint while protecting its components (e.g., the reconstructed ligaments) from excessive stresses. Irrgang and Fitzgerald (2000) suggested that the rehabilitation for a patient with a ligament injury should aim to reduce pain and swelling, restore range of motion, strength and endurance, and enhance proprioception and dynamic stability of the knee. The open-kinetic-chain (OKC) and closed-kinetic-chain (CKC) exercises generate, as expected, different patterns of muscle activities and ligament forces (Escamilla et al., 1998; Lutz et al., 1993; Wilk, 1994). The CKC programs activate antagonistic muscle groups across multiple joints and as such cannot be used to isolate or examine a single muscle group (Lutz et al., 1993; Salem et al., 2003). Conversely, the OKC exercises isolate specific muscle groups for strengthening and evaluation purposes. These latter exercises involve the leg-extension which strengthens
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quadriceps while extending the knee against a resistance and the leg-flexion which strengthens hamstrings while flexing the knee against an opposing force. Knowledge of the strain in the joint ligaments during such exercises is vital if the knee is to be protected properly after a ligament reconstruction (Yasuda and Sasaki, 1987; Draganich and Vahey, 1990). Biomechanical and clinical investigations have suggested that OKC extension exercises produce large forces in the anterior cruciate ligament (ACL) especially near full extension (Escamilla et al., 1998; Draganich and Vahey, 1990; Mesfar and Shirazi-Adl, 2008; Shoemaker and Markolf, 1985). In contrast, CKC exercises have been recommended to be safer in post-ACL reconstruction period (Lutz et al., 1993; Palmitier et al., 1991; Shelbourne and Nitz, 1990). Recent studies, however, advocate both OKC and CKC exercises as effective regimens to restore and enhance performance of joint normal function (Andersen et al., 2006; Fitzgerald, 1997; Perry et al., 2005; Witvrouw et al., 2004). Using a combined model-measurement study, Cohen et al. (2001) reported that the patellofemoral contact stresses were of the same order of magnitude in both CKC and OKC extension exercises. Since hamstrings are important joint stabilizers in the ACL-deficient or injured knees, the OKC flexion exercises are crucial in augmenting hamstrings strength and coordination (Butler et al., 1985; Za¨tterstro¨m, 1999). These exercises, however, produce net posterior shear forces that may overload the posterior cruciate ligament (PCL) especially following a PCL injury or reconstruction (Wilk, 1994; Smidt, 1973). In such cases, OKC extension exercises to strengthen quadriceps may be preferable (Wilk, 1994; Mesfar and Shirazi-Adl, 2008). For adequate strengthening of both muscle groups following a ligament injury, the challenge remains as to identify exercises for the quadriceps that place safe forces on the ACL and those for the hamstrings that produce safe forces in the PCL. Proper knowledge of detailed knee biomechanics under various exercise regimens is therefore crucial for the design of effective rehabilitation programs. In an earlier model study, the detailed biomechanics of the entire knee joint in OKC extension exercises were investigated at 0°, 30°, 60° and 90° joint angles with and without a resistant force of 30 N acting at the ankle perpendicular to the tibia (Mesfar and Shirazi-Adl, 2008). In post-ACL reconstruction period or in the joint with ACL injury, it was recommended to avoid exercises under larger resistant force and at near full extension positions. In the absence of earlier detailed model studies, the current work aims hence to employ the previously validated 3D knee model to investigate biomechanics of the entire joint in OKC flexion exercises (leg curl exercise) as well. Two loading cases are considered; one with no external load accounting only for the weight of the leg and the foot while the second one also incorporated a moderate resisting force of 30N acting at the ankle perpendicular to the tibia. For the joint angles of 0°, 30°, 60° and 90°, biomechanics of the knee joint including required hamstrings forces, joint moment, flexor
lever arm, tibiofemoral contact forces/areas and joint ligament forces are computed and compared with those in OKC extension exercises under similar loads. 2. Methods The knee joint model consists of three bony structures (tibia, femur, and patella) and their articular cartilage layers, menisci, six principal ligaments (collaterals LCL/MCL, cruciates ACL/PCL, and medial/lateral patellofemoral ligaments), patellar tendon, quadriceps muscle force vectors (divided into three components; vastus lateralis/rectus femoris-vastus intermidus medialis/vastus medialis obliqus) and hamstrings muscle force vectors (divided into three components; biceps femoris/sartorius-gracilis-semitendinosus (TRIPOD)/semimembranosus) (Fig. 1). Ligaments are each modeled by a number of uniaxial elements with different prestrains and nonlinear material properties (no compression) (Fig. 2) (Butler et al., 1986; Atkinson et al., 2000; Mesfar and Shirazi-Adl, 2006a; Moglo and ShiraziAdl, 2003a, 2003b; Sta¨ubli et al., 1999). In the current study due to the isolated activity in hamstrings, the patellofemoral joint/ligaments and patellar tendon are not considered. Additional details of the model are available elsewhere (e.g., Mesfar and Shirazi-Adl, 2005). The relative forces in hamstrings muscle components are taken from the study of Kwak et al. (2000); biceps femoris: semimembranosus:TRIPOD=1:1:(35/87). At full extension and in the frontal plane, biceps femorisis oriented 11.8° medially, semitendinosus is 7° laterally and the TRIPOD is 7.1° medially relative to the tibial axis. In the sagittal plane, biceps femoris is parallel to the tibial axis whereas semitendinosus and TRIPOD are respectively 16.1° and 18.7° posteriorly to the axis (Aalbersberg et al., 2005; Hillman, 2003). The forgoing muscle orientations subsequently altered with joint flexion angle (Mesfar and Shirazi-Adl, 2006b). For stable and fully unconstrained boundary conditions in flexion, the femur is fixed while the tibia is left completely free. The joint reference configuration at full extension is initially established under ligament prestrains (Mesfar and Shirazi-Adl, 2006a). To account for the weight of the leg and the foot, two gravity forces of 29.3 N and 7.85 N, respectively, are applied at their mass centres based on anthropometric data of female subjects (De Leva, 1996) since our finite element model was originally constructed based on a female knee joint (Bendjaballah et al., 1995) (Fig. 1). For the cases simulating flexion against an opposing force, an additional (extensor) force of 30 N is applied normal to the tibia at the ankle situated at a lever arm of 372 mm to the tibial plateau (De Leva, 1996) (Fig. 1). The joint flexion angles of 0°, 30°, 60° and 90° are considered for both loading conditions. To circumvent the likely adverse effect of changes in the medial–lateral positioning of forgoing gravity and external forces on results (e.g., TF internal–external rotations), the coupled tibial internal–external rotations are fixed when these external loads
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Fig. 1. Finite element model of the entire knee joint showing cartilage layers, menisci, ligaments, patellar tendon (PT) and hamstrings muscles. Bony structures are assumed rigid and not shown. Quadriceps components and patella are not however considered in the current simulation of the OKC flexion exercises. Hamstrings components are BF: biceps femoris, SM: semimembranous and the TRIPOD composed by SR: sartorius, GR: gracilis and ST: semitendinosus. On the left, the OKC flexion exercise is schematically shown in two joint positions with gravity and resistant forces.
OKC-F
28
OKC-F +30N
24
1000 800
20 16
600
12
400
8 200
4
0
0 0
30 60 Flexion Angle (Deg)
90
Fig. 2. Computed hamstrings forces at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N). The ratios to the leg and foot weight are also shown (right axis).
are applied. After the application of ligament prestrains and at each joint flexion angle, the model iteratively searches for the hamstrings forces that maintain equilibrium under the gravity alone or combined with the resistant force. In this manner, OKC flexion exercises are simulated at four joint angles and two loading conditions. The nonlinear analyses are performed using ABAQUS 6.4 (Hibbit, Karlsson & Sorensen, Inc., Pawtucker, RI) finite element package program.
3. Results
strings forces of 1122 N and 473 N were computed at 0° flexion under gravity with and without resistant force of 30 N, respectively. These forces diminished to 263 N and 31 N at 90° flexion, respectively. The joint moment, supported primarily by foregoing hamstrings forces, followed similar trends; it markedly increased in presence of the external load at the ankle but diminished substantially with flexion angle in both loading conditions (Fig. 3). The effective flexor lever arm of the joint estimated as the ratio of the tibial flexor moment to associated hamstrings force was found to increase with joint flexion angle under both loading conditions, except between 60° and 90° under gravity alone where a small decrease was computed (Fig. 4). The increase in the lever arm with joint flexion angle was more pronounced in the presence of resistant force. Due to the posterior translation of the tibia under hamstrings activity, ACL force remained negligible <6 N throughout joint flexion (Fig. 5). On the contrary, PCL 25 Tibial Moment (N-m)
32 Ratio to Leg Weight
Hamstrings Force (N)
1200
OKC-F
20
OKC-F +30N
15 10 5 0 0
In OKC flexion simulations, the total hamstrings force required to counterbalance the extension moment of gravity with and without resistant force substantially decreased as joint flexed from 0° to 90° (Fig. 2). The maximum ham-
30 60 Flexion Angle (Deg)
90
Fig. 3. Net joint moment at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
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1200
OKC-F OKC-F +30N
40
TF Contact Force (N)
Lever Arm (mm)
50
30 20 10 0 0
30 60 Flexion Angle (Deg)
90
PCL Force (N)
300
200
ACL Force (N)
400
4
OKC-F (ratio)
800
OKC-F +30N (ratio)
3 600 2 400 1
200 0
0 30 60 Flexion Angle (Deg)
90
Fig. 7. Computed total resultant tibiofemoral contact forces at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N). The ratios to the corresponding hamstrings forces are also shown for both cases (right axis).
8 4 0 0
30
60
90
OKC-F OKC-F +30N
100
0 0
30
60
90
Flexion Angle (Deg) Fig. 5. Computed forces in the posterior and anterior (inlay figure) cruciate ligaments at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
contributions initiated at 30° and reached large values (maximum of 334 N at 60°) especially under the 30 N resistant force (Fig. 6). In both loading cases, PCL force
decreased from 60° to 90° flexion. The force in LCL ligament (Fig. 6) also substantially increased with joint flexion especially so in presence of resistant force; it reached maximums of 35 N and 125 N without and with resistant force, respectively. Forces in the MCL remained relatively small <15 N in all cases. Total tibiofemoral contact forces for different cases followed the same trend as those of hamstrings forces (Fig. 7). The maximum tibiofemoral contact forces of 1056 N and 466 N were computed at 0° flexion that diminished to 429 N and 136 N at 90° with and without resistant force, respectively. On the contrary, the ratio of tibiofemoral contact forces to corresponding hamstrings forces increased with joint flexion especially so under gravity alone in which case it varied from the minimum of 0.98 at 0° to the maximum of 4.44 at 90°. Total tibiofemoral contact area followed the same trend as that of contact force. Under the same loading conditions respectively, tibiofemoral contact area decreased from its maximums of 1027 mm2 and 812 mm2 at full extension to its minimums of 665 mm2 and 466 mm2 at 90° flexion. 4. Discussion
150 OK C- F
120 LCL Force (N)
1000
0
Fig. 4. Computed equivalent flexor lever arm (defined as the ratio of joint moment over the hamstrings force) at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
5
OKC-F OKC-F +30N
Ratio to Hamstrings Force
480
OK C- F +3 0N
90 60 30 0 0
30 60 Flexion Angle (Deg)
90
Fig. 6. Computed forces in the lateral collateral ligament at different flexion angles under two OKC flexion loading cases of gravity alone (OKC-F) or gravity with a 30 N resistant force (OKC-F + 30 N).
Detailed biomechanics of the entire knee joint at different flexion positions were investigated under OKC flexion exercises with and without a 30 N resistant load at the ankle. For this purpose a validated 3D nonlinear model of the knee joint was used to compute hamstrings forces, joint moments, effective lever arms, forces in various joint ligaments and contact forces/areas. Due to the marked decrease in muscle forces as the joint flexed, the joint moment decreased substantially from 0° to 90°; by nine-fold under gravity alone and by two-fold under combined load (Fig. 3). A negligible portion (<1 Nm) of these moments are, however, due to the passive resistance of the joint itself (Mesfar and Shirazi-Adl, 2005). The associated effective flexor lever arm of the flexor mech-
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anism (estimated as the ratio of the joint moments over hamstrings forces) substantially increased by 80% under gravity loading alone and by 155% when resistant force was also added as flexion angle varied from 0° to 90°. In contrast and under almost the same joint moment magnitudes, the extensor lever arm decreased by 28% and 18%, respectively, in OKC extension cases under similar loading conditions (Mesfar and Shirazi-Adl, 2008). These differences in the joint lever arms in OKC flexion and extension exercises, despite the posterior shift in tibial contact in flexion (Dennis et al., 2005; Scarvell et al., 2005), are due primarily to the changes in orientations and displacements of tibial insertions of the patellar tendon and hamstrings muscles during joint flexion. The estimated hamstrings forces diminished by 77% as joint flexed to 90° under resistant force and by 94% when gravity alone was considered (Fig. 2). In order to counterbalance the additional moment of the 30 N resistant force, hamstrings force increased by as much as 650 N at 0° flexion but by only 232 N at 90° flexion. Accordingly, observation of variations in hamstrings forces and joint moments with flexion angles or equivalently of changes in the associated flexor lever arms demonstrates that moment-generating capacity of hamstrings muscles improves with joint flexion. This corroborates our earlier findings that hamstrings are much more efficient in resisting moments at larger flexion angles in contrast to quadriceps muscles that are more efficient at smaller flexion angles (Mesfar and Shirazi-Adl, 2008, 2006b). The computed variations in hamstrings forces with joint flexion are in good agreement with those reported by Shelburne and Pandy (1997). Very small ACL forces (<6 N) were computed throughout joint flexion angles and that despite the presence of gravity and resistant forces acting on the tibia in the anterior direction especially at near extension positions. The results, hence, advocate the use of OKC flexion exercises at all joint angles and resistant force levels in post-ACL reconstruction periods or in joints following an ACL injury. In contrast to ACL ligament, large forces were computed in the PCL at and beyond 30° flexion reaching their maximum at 60° flexion. Our earlier studies under isolated constant hamstrings force indicated similar PCL forces that monotonically increased with flexion angle up to 90° (Mesfar and Shirazi-Adl, 2006b). The addition of 30 N resistant force further increased PCL force by 141 N at 30°, 198 N at 60° and 275 N at 90°. Relatively large forces were also generated in LCL ligament at large flexion angles under the resistant force. The current results, hence, advocate the use of OKC flexion exercise in the post-PCL/LCL reconstruction period or in the joint with PCL/LCL injury preferably at near full extension positions and that in presence of rather small resistant forces. The foregoing negligible ACL forces at near full extension that disappear with flexion and large PCL forces that increase with flexion are in agreement with predictions of Shelburne and Pandy (1997).
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Under both loading cases, tibiofemoral contact forces decreased with joint flexion. These changes in contact forces during joint flexion, despite increases in PCL and LCL forces, were due to substantial decreases in hamstrings forces. The computed tibiofemoral contact force at full extension in this study reached a value two-fold greater than that in OKC extension exercise under identical load magnitudes (Mesfar and Shirazi-Adl, 2008). Similarly, mean tibiofemoral contact stresses decreased throughout flexion and reached values larger than the corresponding contact stresses in OKC extension exercises which remained nearly constant throughout flexion (Mesfar and Shirazi-Adl, 2008). In OKC flexion, the mean tibiofemoral contact stresses varied from 0.57 MPa (at 0°) to 0.29 MPa (at 90°) under gravity alone and from 1.03 MPa (at 0°) to 0.65 MPa at 90° knee flexion under 30 N resistant force in contrast to corresponding stresses computed in OKC extension exercises that remained nearly constant throughout flexion, 0.35 MPa and 0.65 MPa, respectively for cases without and with resistant load. These computed tibiofemoral contact stresses are within the range of values reported for contact stresses under similar compression loads (Bendjaballah et al., 1995; Ahmed et al., 1983; Meyer et al., 1997) and much smaller than reported ultimate cartilage stress values (Flachsmann et al., 2001; Vener et al., 1992). Finally, no excessive force or stress in various joint components, with the exception of the PCL and to some extent LCL, was found in the OKC flexion exercises under moderate resistant force of 30 N considered in this study. The magnitude of this resistant force plays a crucial role by substantially increasing the required hamstrings forces, forces in PCL/LCL ligaments, and joint contact forces/stresses. At post-ACL reconstruction period or in the joint with ACL injury, the exercise could safely be used to strengthen the hamstrings muscles without a risk to the ACL. In contrast, at post-PCL/LCL reconstruction or injury, the OKC flexion exercise should be avoided under moderate to large resistant forces and knee flexion angles. Our current and earlier studies (Mesfar and Shirazi-Adl, 2008) are helpful in the design of efficient OKC exercises in rehabilitation periods as well as performance enhancement programs. Acknowledgements The financial supports of the Natural Science and Engineering Research Council of Canada (NSERC-Canada) and the Canadian Institute of Health Research (CIHR) are gratefully acknowledged. The earlier efforts of M.Z. Bendjaballah and K.E. Moglo in development of the model are also acknowledged. References Aalbersberg, S., Kingma, I., Ronsky, J.L., Frayne, R., van Diee¨n, J.H., 2005. Orientation of tendons in vivo with active and passive knee muscles. J. Biomech. 38, 1780–1788.
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