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MODEL OF THE KNEE FOR UNDERSTANDING THE SQUAT MOVEMENT BIOMECHANICS
MODEL OF THE KNEE FOR UNDERSTANDING THE SQUAT MOVEMENT BIOMECHANICS
Guillaume Agnesina, Redha Taïar, William Bertucci, Alain Lodini
Laboratoire d'Analyse des Contraintes Mécaniques (LACM – EA 3304) UFR STAPS Université de Reims, Moulin de la Housse 51100 Reims, France
Abstract: By means of MSC Adams- BRG LifeMOD software, a three dimensional lower extremity model has been developed in this study. This model take into account 16 muscles, 4 ligaments, 2 tendons in order to quantify forces and contacts (patello-femoral and tibio-femoral) during muscular training movement (e.g. a squat) with various raised loads (0, 20 and 30 kg). The first results showed the importance of the relationships between muscle activations (e.g. Quadriceps, Hamstrings) and ligament forces (e.g. Anterior and Posterior Cruciate Ligaments). Copyright © 2006 IFAC Keywords: Model, Human Reliability, Estimation, Force, Knee.
1. INTRODUCTION The means whereby we can understand and predict the normal knee motion is by reconstructing and modelling this joint taking into account the ligaments and tendons. There have been many studies about the relationships between knee loading and ligament tension or strain (Ahmed et al., 1992, Markolf et al., 1993, Renstrom et al., 1986, Takai et al., 1993, Wascher et al. 1993, Bendjaballah et al. 1995). Furthermore, numerous studies have investigated the effects of muscle forces on ligament loading (Draganisch and Vahey, 1990, Kurosawa et al., 1991, Pandy and Shelburne, 1997, Hsieh and Draganich, 1997, Shelburne and Pandy, 1997, Abdel-Rahman and Hefzy, 1998). All the studies as mentioned above are very complete and the different models developed integrate well the complete knee motion. For instance those of Pandy and Shelburne in 1997. Even if it is a twodimensional model (sagittal plane), they were be able to estimate the anterior cruciate ligament (ACL) and the posterior cruciate ligament (PCL) tensions according to the flexion-extension movements of the knee. They estimate also the patellar-tendon force
and the tibiofemoral-contact force with the aim to minimize ACL force. In order to study the knee movement, we developed a new three dimensional model joint. The aim of our study can be divided in two parts. In the first one, we studied the forces of the muscles, ligaments and contacts (patello-femoral and tibio-femoral) during movement of muscular training (e.g. a squat) with various raised loads. In the second one, we predicted ACL and PCL forces, lateral collateral ligament (LCL) and medial collateral ligament (MCL) forces as a function of loads, knee flexion and muscular contribution. The results obtained can help us to limit injuries bound to this joint.
2. METHODS In this study, MSC ADAMS - BRG LifeMOD 2005 software was used in order to create the new model. A healthy subject was chosen with the physical conditions: a man, 40 years old, 1.74 m height and 85 kg weight. The leg model is created for simulation. The model consists of a single leg, adding masses at the hip location (It represents the mass of the upper body more the mass of the raised loads).
Contact ellipsoids are created to describe the tibiofemoral and patello-femoral contact elements. They are installed on the distal end of the femur to provide contact between the femur and the tibia. Thus, contact forces can be predicted between these condyles and the tibial plateau. To create these segments, we used a value of 1400 kg/m3 for the osseous density. Also, the patella is created as a separate segment with the aim to predict contact forces between this segment and the condyles of the femur (Fig. 1).
In our study, 16 muscles have been generated. There are: Gluteus Maximus 1 and 2, Gluteus Medius 1 and 2, Adductor Magnus, Semitendinosus, Vastus Medialis, Vastus Lateralis, Biceps Femoris 1 and 2, Rectus Femoris, Iliacus, Gastrocnemius 1 and 2, Soleus and Tibialis Anterior. (Fig. 3)
Front view
Back view
Fig 3. Insertion of muscles (in red). Fig 1. Location of the patella and condyles ellipsoids. In blue, there are lateral and medial condyles segments, in red, there is the patella condyle segment. The joint is stabilized by adding ligaments and patellar tendon. In this study, four ligaments are represented: MCL, LCL, ACL and the LCL. (Fig. 2) Mechanical ligament properties are provided from the studies of Woo et al. (1982) and Wilson et al. (1988).
To create the flexion movement of the knee, a motion agent (Fig. 4) is added to the lower leg model. This motion agent is removed for the inverse-dynamics simulation (the muscle contraction histories has been recorded). We can now use the active muscle formulation to produce a force to recreate the motion history.
Fig 4. Insertion of a motion agent. This motion agent allows the flexion of the knee.
Front view
Back view
Fig 2. Insertion of ligaments and tendons. In blue, the four ligaments (MCL, LCL, ACL, LCL), in yellow, the tendon. To model muscles, LifeMOD uses a force in order to replicate the desired body motion, while staying within each muscle's physiological limits. The calculation muscle forces uses the physiological cross sectional area (pCSA). The muscle geometry data (pCSA) was developed by amongst others Eycleshymer et al. (1970). The upper limit of the muscle force (Fmax) is generated by multiplying pCSA for each muscle to a maximum tissue stress (Mstress) value derived from Hatze (1981).
To simulate the movement of a squat in muscular training we applied two different masses on the lower torso (Pelvis) to have three analyses and results. In the calculation, we divided these masses by two, because we have one leg. We made an analysis with: - no mass, the squat movement is made without load. - with a mass of 20 kg, - with a mass of 30 kg.
3. RESULTS We made the analysis and we obtained the following results. Firstly, we can analyze the ACL behaviour. At 1.8 seconds, we have the maximal knee flexion (90°).
Knee Flexion Max Knee Flexion Max
Fig 5. Anterior Cruciate Ligament behaviour
Fig 7. Gastrocnemius Muscle behaviour
We have the ACL maximal tension just before the bottom dead centre (when the model is still moving). For a 30 kg load, the ACL tension is maximal compared to without load and 20 kg load. (Fig 5)
This result can be explained by examining the equilibration of the forces of the model. Indeed, for a squat movement without load, the model can directly pick up on the gastrocnemius muscle but with a load (20 or 30 kg) this muscle is not sufficient. With the action of the others muscles (e.g. Vastus Medialis, Biceps Femoris), the activity of the gastrocnemius muscle decreases. When we compare one agonist and antagonist muscle we see how the movement is made. (Fig 8 and 9) For two muscles of the thigh (the Biceps Femoris and the Vastus Medialis), we can explain this movement of a squat (muscular training). For instance, when the Vastus Medialis tension is lower, the Biceps Femoris tension is higher (during the downward phase). Furthermore, when we are at the dead centre the tension in each muscle is roughly equilibrated (For a 30 kg load, at the dead centre we have 490 N for the Biceps Femoris muscle and 440 N for the Vastus Medialis muscle).
Knee Flexion Max
Fig 6. Posterior Cruciate Ligament behaviour For the PCL tension (Fig. 6), we can make the same diagnostic findings. The major difference is in the tension value (in Newton). We see the PCL is more solicited than the ACL. The very interesting result that we can see is the behaviour of some muscles. For instance, we analyzed the Vastus Medialis (which is a part of the quadriceps muscle), the Biceps Femoris (which is a part of the hamstrings muscle) and the gastrocnemius muscle. For the gastrocnemius muscle, its activity is maximal when the knee flexion is about 90°. (Fig. 7) Furthermore, for a 30 kg load, this muscle has a tension less significant than with a 20 kg load.
Fig 8. Vastus Medialis Muscle behaviour
Knee Flexion Max
decreased for instance the quadriceps contribution muscles (Vastus Medialis and Lateralis muscles, Rectus Femoris Muscle). The result obtained showed an ACL tension diminution and pathologies of the subject .
Knee Flexion Max
Fig 9. Biceps Femoris Muscle behaviour What is very interesting is to analyze the tibiofemoral contact forces in the vertical axis (Fig. 10). This figure showed the relationships between forces and knee angle during flexion and extension. We observed during the first phase (until 1.83s) the high force values in function to the raised loads. In the second phase (until 3.5s) the force values decreased as a function of the no load movement. In addition these values increased for the other raised loads. During flexion and extension, we observed a link between the contact forces and the PCL (or ACL) tension. Indeed, if this contact is high, the PCL (or ACL) tension becomes higher.
Fig 11. ACL tension with two different contribution muscles These observations are in agreement with the results shown by Pandy and Shelburne (1997) and more recently Mesfar and Shirazi-Adl (2005). In the horizontal component (Fig.12) we observed the similarity of the forces values as a function of the raised loads during extension (2.5 and 3.2s). This result indicates the good equilibrium of the subject.
TIBIO-FEMORAL CONTACT FORCES (VERTICAL-AXIS)
Knee Flexion Max
Fig 10. Tibio-femoral contact forces in the vertical axis The same relation was found between muscle activation and ligament tension in our study. (Fig 11) For the same movement with no load, and taking into account the possibilities of our software, we
Fig 12. Tibio-femoral contact forces in the horizontal axis
4. DISCUSSION The objectives of this first study were to determine the behaviour of the knee joint: more precisely the ligaments and the muscles of the lower extremity and the contact forces in the knee during muscular training activity (the squat). The results are in good agreement with other studies covering the same subject. We have found, for instance, the interest to interpret the quadriceps or hamstring tensions in the aim of limiting cruciate ligament forces. Moreover, the contact forces allowed us to appreciate these cruciate ligament forces. The originality of our study is to take for first time into account the real weight of the subject and the various raised loads representing the movement. The model developed in this study made possible the estimation of the knee movement for high level athletes or a pathological subject and permit a good estimation for muscle coordination during movement. For this first approach, there are some limitations: The menisci are not integrated in our model and the condylar surfaces have been simplified by ellipsoids. In the future we will integrate twelve ligament bundles in Abdel-Rahman and Hefzy’s study (1998) in comparison to the fourth created in our study and will study the shear contact forces between Tibia and Femur. All the results that we can obtain permit a better knee joint understanding in order to decrease the pathologies of subjects.
REFERENCES Abdel-Rahman EM, Hefzy MS. (1998) Threedimensional dynamic behaviour of the human knee joint under impact loading. Medical Engineering and Physics. 20: 276-290 Ahmed AM, Burke DL, Duncan NA, Chan KH. (1992) Ligament tension pattern in the flexed knee in combined passive anterior translation and axial rotation. Journal of Orthopaedic Research. 10: 854-867. Bendjaballah MZ, Shirazi-Adi A, Zukor DJ. (1995) Biomechanics of the human knee joint in compression: reconstruction, mesh generation and finite element analysis. The Knee Vol. 2.2: 69-79. Draganisch LF, Vahey JW. (1990) An in-vitrostudy of anterior cruciate ligament strain induced by quadriceps and hamstrings forces. Journal of Orthopaedic Research. 8: 57-63 Eycleshymer AC, Shoemaker D.M. (1970). A crosssection anatomy. New York: Appleton-CenturyCrofts Hatze H, (1981). Estimation of myodynamics parameter values from observations on isometrically contracting muscle groups. European Journal of Applied Physiology and Occupational Physiology. 46: 325-338. Hsieh YF, Draganich LF. (1997) Knee kinematics and ligament lengths during physiologic levels of isometric quadriceps loads. The Knee. 4: 145154 Kurosawa H, Yamakoshi KI, Yasuda K, Sasaki T. (1991) Simultaneous measurement of changes in
length of the cruciate ligaments during knee motion. Clin Orthop. 265: 233-240. Mesfar W and Shirazi-Adl A. (2005) Biomechanics of the knee joint in flexion under various quadriceps forces The Knee. 12(6): 424-434. Markolf KL, Wascher DC, Finerman GAR. (1993) Direct in vitro measurement of forces in the cruciate ligaments. Part II: The effects of section of the posterolateral structure. Journal of bone and joint surgery. 75A: 387-394. Pandy MG, Shelburne KB. (1997) Dependence of cruciate-ligament loading on muscle forces and external load. Journal of biomechanics. 30: 1015-1024 Renstrom P, Arms SW, Stanwyck TS, Johnson RJ, Pope MH. (1986) Strain within the anterior cruciate ligament during hamstring and quadriceps activity. American journal of sports medicine. 14: 83-87. Shelburne KB, Pandy MG. (1997) A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions. Journal of Biomechanics. 30: 163-176. Takai S, Adams DJ, Livesay GA, Woo SL-Y. (1993) Determination of the in situ loads on the human anterior cruciate ligament. Journal of Orthopaedic Research. 11: 686-695. Washer DC, Markolf KL, Shapiro MS, Finerman GAR. (1993) Direct in vitro measurement forces in the cruciate ligaments of the knee. Part I: The effects of multiplane loading in the intact knee. Journal of bone and joint surgery. 75: 377-386. Wilson C.J, Dahners LE. (1988) An examination of the mechanisms of ligament contracture. Clinical Orthopaedics and Related Research, 227: 286291. Woo SLY, Gomez MA, Woo YK., Akeson WH. (1982) Mechanical properties of tendons and ligaments. II:The relationships of immobilization and exercise on tissue remodeling. Biorheology. 19(3): 397-408.
Guillaume Agnesina, Redha Taïar, William Bertucci, Alain Lodini
Laboratoire d'Analyse des Contraintes Mécaniques (LACM – EA 3304) UFR STAPS Université de Reims, Moulin de la Housse 51100 Reims, France
Abstract: By means of MSC Adams- BRG LifeMOD software, a three dimensional lower extremity model has been developed in this study. This model take into account 16 muscles, 4 ligaments, 2 tendons in order to quantify forces and contacts (patello-femoral and tibio-femoral) during muscular training movement (e.g. a squat) with various raised loads (0, 20 and 30 kg). The first results showed the importance of the relationships between muscle activations (e.g. Quadriceps, Hamstrings) and ligament forces (e.g. Anterior and Posterior Cruciate Ligaments). Copyright © 2006 IFAC Keywords: Model, Human Reliability, Estimation, Force, Knee.
1. INTRODUCTION The means whereby we can understand and predict the normal knee motion is by reconstructing and modelling this joint taking into account the ligaments and tendons. There have been many studies about the relationships between knee loading and ligament tension or strain (Ahmed et al., 1992, Markolf et al., 1993, Renstrom et al., 1986, Takai et al., 1993, Wascher et al. 1993, Bendjaballah et al. 1995). Furthermore, numerous studies have investigated the effects of muscle forces on ligament loading (Draganisch and Vahey, 1990, Kurosawa et al., 1991, Pandy and Shelburne, 1997, Hsieh and Draganich, 1997, Shelburne and Pandy, 1997, Abdel-Rahman and Hefzy, 1998). All the studies as mentioned above are very complete and the different models developed integrate well the complete knee motion. For instance those of Pandy and Shelburne in 1997. Even if it is a twodimensional model (sagittal plane), they were be able to estimate the anterior cruciate ligament (ACL) and the posterior cruciate ligament (PCL) tensions according to the flexion-extension movements of the knee. They estimate also the patellar-tendon force
and the tibiofemoral-contact force with the aim to minimize ACL force. In order to study the knee movement, we developed a new three dimensional model joint. The aim of our study can be divided in two parts. In the first one, we studied the forces of the muscles, ligaments and contacts (patello-femoral and tibio-femoral) during movement of muscular training (e.g. a squat) with various raised loads. In the second one, we predicted ACL and PCL forces, lateral collateral ligament (LCL) and medial collateral ligament (MCL) forces as a function of loads, knee flexion and muscular contribution. The results obtained can help us to limit injuries bound to this joint.
2. METHODS In this study, MSC ADAMS - BRG LifeMOD 2005 software was used in order to create the new model. A healthy subject was chosen with the physical conditions: a man, 40 years old, 1.74 m height and 85 kg weight. The leg model is created for simulation. The model consists of a single leg, adding masses at the hip location (It represents the mass of the upper body more the mass of the raised loads).
Contact ellipsoids are created to describe the tibiofemoral and patello-femoral contact elements. They are installed on the distal end of the femur to provide contact between the femur and the tibia. Thus, contact forces can be predicted between these condyles and the tibial plateau. To create these segments, we used a value of 1400 kg/m3 for the osseous density. Also, the patella is created as a separate segment with the aim to predict contact forces between this segment and the condyles of the femur (Fig. 1).
In our study, 16 muscles have been generated. There are: Gluteus Maximus 1 and 2, Gluteus Medius 1 and 2, Adductor Magnus, Semitendinosus, Vastus Medialis, Vastus Lateralis, Biceps Femoris 1 and 2, Rectus Femoris, Iliacus, Gastrocnemius 1 and 2, Soleus and Tibialis Anterior. (Fig. 3)
Front view
Back view
Fig 3. Insertion of muscles (in red). Fig 1. Location of the patella and condyles ellipsoids. In blue, there are lateral and medial condyles segments, in red, there is the patella condyle segment. The joint is stabilized by adding ligaments and patellar tendon. In this study, four ligaments are represented: MCL, LCL, ACL and the LCL. (Fig. 2) Mechanical ligament properties are provided from the studies of Woo et al. (1982) and Wilson et al. (1988).
To create the flexion movement of the knee, a motion agent (Fig. 4) is added to the lower leg model. This motion agent is removed for the inverse-dynamics simulation (the muscle contraction histories has been recorded). We can now use the active muscle formulation to produce a force to recreate the motion history.
Fig 4. Insertion of a motion agent. This motion agent allows the flexion of the knee.
Front view
Back view
Fig 2. Insertion of ligaments and tendons. In blue, the four ligaments (MCL, LCL, ACL, LCL), in yellow, the tendon. To model muscles, LifeMOD uses a force in order to replicate the desired body motion, while staying within each muscle's physiological limits. The calculation muscle forces uses the physiological cross sectional area (pCSA). The muscle geometry data (pCSA) was developed by amongst others Eycleshymer et al. (1970). The upper limit of the muscle force (Fmax) is generated by multiplying pCSA for each muscle to a maximum tissue stress (Mstress) value derived from Hatze (1981).
To simulate the movement of a squat in muscular training we applied two different masses on the lower torso (Pelvis) to have three analyses and results. In the calculation, we divided these masses by two, because we have one leg. We made an analysis with: - no mass, the squat movement is made without load. - with a mass of 20 kg, - with a mass of 30 kg.
3. RESULTS We made the analysis and we obtained the following results. Firstly, we can analyze the ACL behaviour. At 1.8 seconds, we have the maximal knee flexion (90°).
Knee Flexion Max Knee Flexion Max
Fig 5. Anterior Cruciate Ligament behaviour
Fig 7. Gastrocnemius Muscle behaviour
We have the ACL maximal tension just before the bottom dead centre (when the model is still moving). For a 30 kg load, the ACL tension is maximal compared to without load and 20 kg load. (Fig 5)
This result can be explained by examining the equilibration of the forces of the model. Indeed, for a squat movement without load, the model can directly pick up on the gastrocnemius muscle but with a load (20 or 30 kg) this muscle is not sufficient. With the action of the others muscles (e.g. Vastus Medialis, Biceps Femoris), the activity of the gastrocnemius muscle decreases. When we compare one agonist and antagonist muscle we see how the movement is made. (Fig 8 and 9) For two muscles of the thigh (the Biceps Femoris and the Vastus Medialis), we can explain this movement of a squat (muscular training). For instance, when the Vastus Medialis tension is lower, the Biceps Femoris tension is higher (during the downward phase). Furthermore, when we are at the dead centre the tension in each muscle is roughly equilibrated (For a 30 kg load, at the dead centre we have 490 N for the Biceps Femoris muscle and 440 N for the Vastus Medialis muscle).
Knee Flexion Max
Fig 6. Posterior Cruciate Ligament behaviour For the PCL tension (Fig. 6), we can make the same diagnostic findings. The major difference is in the tension value (in Newton). We see the PCL is more solicited than the ACL. The very interesting result that we can see is the behaviour of some muscles. For instance, we analyzed the Vastus Medialis (which is a part of the quadriceps muscle), the Biceps Femoris (which is a part of the hamstrings muscle) and the gastrocnemius muscle. For the gastrocnemius muscle, its activity is maximal when the knee flexion is about 90°. (Fig. 7) Furthermore, for a 30 kg load, this muscle has a tension less significant than with a 20 kg load.
Fig 8. Vastus Medialis Muscle behaviour
Knee Flexion Max
decreased for instance the quadriceps contribution muscles (Vastus Medialis and Lateralis muscles, Rectus Femoris Muscle). The result obtained showed an ACL tension diminution and pathologies of the subject .
Knee Flexion Max
Fig 9. Biceps Femoris Muscle behaviour What is very interesting is to analyze the tibiofemoral contact forces in the vertical axis (Fig. 10). This figure showed the relationships between forces and knee angle during flexion and extension. We observed during the first phase (until 1.83s) the high force values in function to the raised loads. In the second phase (until 3.5s) the force values decreased as a function of the no load movement. In addition these values increased for the other raised loads. During flexion and extension, we observed a link between the contact forces and the PCL (or ACL) tension. Indeed, if this contact is high, the PCL (or ACL) tension becomes higher.
Fig 11. ACL tension with two different contribution muscles These observations are in agreement with the results shown by Pandy and Shelburne (1997) and more recently Mesfar and Shirazi-Adl (2005). In the horizontal component (Fig.12) we observed the similarity of the forces values as a function of the raised loads during extension (2.5 and 3.2s). This result indicates the good equilibrium of the subject.
TIBIO-FEMORAL CONTACT FORCES (VERTICAL-AXIS)
Knee Flexion Max
Fig 10. Tibio-femoral contact forces in the vertical axis The same relation was found between muscle activation and ligament tension in our study. (Fig 11) For the same movement with no load, and taking into account the possibilities of our software, we
Fig 12. Tibio-femoral contact forces in the horizontal axis
4. DISCUSSION The objectives of this first study were to determine the behaviour of the knee joint: more precisely the ligaments and the muscles of the lower extremity and the contact forces in the knee during muscular training activity (the squat). The results are in good agreement with other studies covering the same subject. We have found, for instance, the interest to interpret the quadriceps or hamstring tensions in the aim of limiting cruciate ligament forces. Moreover, the contact forces allowed us to appreciate these cruciate ligament forces. The originality of our study is to take for first time into account the real weight of the subject and the various raised loads representing the movement. The model developed in this study made possible the estimation of the knee movement for high level athletes or a pathological subject and permit a good estimation for muscle coordination during movement. For this first approach, there are some limitations: The menisci are not integrated in our model and the condylar surfaces have been simplified by ellipsoids. In the future we will integrate twelve ligament bundles in Abdel-Rahman and Hefzy’s study (1998) in comparison to the fourth created in our study and will study the shear contact forces between Tibia and Femur. All the results that we can obtain permit a better knee joint understanding in order to decrease the pathologies of subjects.
REFERENCES Abdel-Rahman EM, Hefzy MS. (1998) Threedimensional dynamic behaviour of the human knee joint under impact loading. Medical Engineering and Physics. 20: 276-290 Ahmed AM, Burke DL, Duncan NA, Chan KH. (1992) Ligament tension pattern in the flexed knee in combined passive anterior translation and axial rotation. Journal of Orthopaedic Research. 10: 854-867. Bendjaballah MZ, Shirazi-Adi A, Zukor DJ. (1995) Biomechanics of the human knee joint in compression: reconstruction, mesh generation and finite element analysis. The Knee Vol. 2.2: 69-79. Draganisch LF, Vahey JW. (1990) An in-vitrostudy of anterior cruciate ligament strain induced by quadriceps and hamstrings forces. Journal of Orthopaedic Research. 8: 57-63 Eycleshymer AC, Shoemaker D.M. (1970). A crosssection anatomy. New York: Appleton-CenturyCrofts Hatze H, (1981). Estimation of myodynamics parameter values from observations on isometrically contracting muscle groups. European Journal of Applied Physiology and Occupational Physiology. 46: 325-338. Hsieh YF, Draganich LF. (1997) Knee kinematics and ligament lengths during physiologic levels of isometric quadriceps loads. The Knee. 4: 145154 Kurosawa H, Yamakoshi KI, Yasuda K, Sasaki T. (1991) Simultaneous measurement of changes in
length of the cruciate ligaments during knee motion. Clin Orthop. 265: 233-240. Mesfar W and Shirazi-Adl A. (2005) Biomechanics of the knee joint in flexion under various quadriceps forces The Knee. 12(6): 424-434. Markolf KL, Wascher DC, Finerman GAR. (1993) Direct in vitro measurement of forces in the cruciate ligaments. Part II: The effects of section of the posterolateral structure. Journal of bone and joint surgery. 75A: 387-394. Pandy MG, Shelburne KB. (1997) Dependence of cruciate-ligament loading on muscle forces and external load. Journal of biomechanics. 30: 1015-1024 Renstrom P, Arms SW, Stanwyck TS, Johnson RJ, Pope MH. (1986) Strain within the anterior cruciate ligament during hamstring and quadriceps activity. American journal of sports medicine. 14: 83-87. Shelburne KB, Pandy MG. (1997) A musculoskeletal model of the knee for evaluating ligament forces during isometric contractions. Journal of Biomechanics. 30: 163-176. Takai S, Adams DJ, Livesay GA, Woo SL-Y. (1993) Determination of the in situ loads on the human anterior cruciate ligament. Journal of Orthopaedic Research. 11: 686-695. Washer DC, Markolf KL, Shapiro MS, Finerman GAR. (1993) Direct in vitro measurement forces in the cruciate ligaments of the knee. Part I: The effects of multiplane loading in the intact knee. Journal of bone and joint surgery. 75: 377-386. Wilson C.J, Dahners LE. (1988) An examination of the mechanisms of ligament contracture. Clinical Orthopaedics and Related Research, 227: 286291. Woo SLY, Gomez MA, Woo YK., Akeson WH. (1982) Mechanical properties of tendons and ligaments. II:The relationships of immobilization and exercise on tissue remodeling. Biorheology. 19(3): 397-408.