Skip to main content
NCBI home page
Journal of Anatomy logoLink to Journal of Anatomy
. 2012 Oct 11;221(6):590–597. doi: 10.1111/j.1469-7580.2012.01569.x

Computational modeling of a forward lunge: towards a better understanding of the function of the cruciate ligaments

Tine Alkjær 1, Maja R Wieland 2, Michael S Andersen 2, Erik B Simonsen 1, John Rasmussen 2
PMCID: PMC3512282  PMID: 23057673

Abstract

This study investigated the function of the cruciate ligaments during a forward lunge movement. The mechanical roles of the anterior and posterior cruciate ligament (ACL, PCL) during sagittal plane movements, such as forward lunging, are unclear. A forward lunge movement contains a knee joint flexion and extension that is controlled by the quadriceps muscle. The contraction of the quadriceps can cause anterior tibial translation, which may strain the ACL at knee joint positions close to full extension. However, recent findings suggest that it is the PCL rather than the ACL which is strained during forward lunging. Thus, the purpose of the present study was to establish a musculoskeletal model of the forward lunge to computationally investigate the complete mechanical force equilibrium of the tibia during the movement to examine the loading pattern of the cruciate ligaments. A healthy female was selected from a group of healthy subjects who all performed a forward lunge on a force platform, targeting a knee flexion angle of 90°. Skin-markers were placed on anatomical landmarks on the subject and the movement was recorded by five video cameras. The three-dimensional kinematic data describing the forward lunge movement were extracted and used to develop a biomechanical model of the lunge movement. The model comprised two legs including femur, crus, rigid foot segments and the pelvis. Each leg had 35 independent muscle units, which were recruited according to a minimum fatigue criterion. This approach allowed a full understanding of the mechanical equilibrium of the knee joint, which revealed that the PCL had an important stabilizing role in the forward lunge movement. In contrast, the ACL did not have any significant mechanical function during the lunge movement. Furthermore, the results showed that m. gluteus maximus may play a role as a knee stabilizer in addition to the hamstring muscles.

Keywords: anterior cruciate ligament, computational modeling, cruciate ligaments, knee joint, posterior cruciate ligament

Introduction

Several studies have pointed out that contraction of the quadriceps muscle can cause anterior tibial translation, which in the intact knee will strain the anterior cruciate ligament (ACL) (Arms et al. 2009; Renstrom et al. 2001; Draganich & Vahey, 1988; Hirokawa et al. 1993; More et al. 2004; Macwilliams et al. 2009a). It has been suggested that co-contraction of the hamstring muscles could reduce the load on the ACL and stabilize the knee joint (Solomonow et al. 2005; Yanagawa et al. 2012). Furthermore, it has been suggested that co-contraction of the hamstring muscles would stabilize the knee during quadriceps contractions in cases of ACL deficiency (More et al. 2004). In contrast to this, other studies suggest that sagittal plane movements cannot strain the ACL severely (McLean et al. 1999) and it is the posterior cruciate ligament (PCL) rather than the ACL that may be loaded during movements in the sagittal plane (Escamilla et al. 1990,b). A possible explanation for these contradictory findings may be that many factors influence the force equilibrium in the knee and a full understanding of the role of the cruciate ligaments requires an endeavor to include all relevant factors into a model. In this study we shall establish a detailed three-dimensional musculoskeletal model performing a movement that predominantly takes place in the sagittal plane; a so-called forward lunge. For this case, we attempt to describe the complete state of equilibrium for the tibia.

The forward lunge movement is a popular and common type of movement among athletes for training and rehabilitation (Heijne et al. 2008; Jonhagen et al. 2005,b) and this movement has also been proposed as a model to study functional adaptation to ACL rupture (Alkjaer et al. ). We have observed differences in the movement pattern of a forward lunge between ACL-deficient and healthy subjects (Alkjaer et al. ). This indicates that the ACL has an important function during forward lunging, but the exact functional role of the ACL in this situation is unclear. Heijne et al. (2008) examined the ACL strain behavior in vivo during a lunge movement and observed that the ACL strain was low (below 2%) during the whole movement (range 30°–70° of knee flexion, 0° = full extension), with the highest strain observed at 30° and the lowest at peak knee flexion. In addition, Escamilla et al. (1990) estimated the knee joint loadings during a forward lunge and found that it was the PCL and not the ACL that was loaded during this movement (Escamilla et al. 1990). These observations concur with more general observations which suggest that the ACL becomes slack when the knee is flexed (Nisell et al. 2004; Beynnon & Fleming, 1984). Both Heijne et al. (2008) and Escamilla et al. (1990,b) proposed that low ACL strain values during forward lunging may be due to co-contraction of the hamstring muscles, but this was not confirmed in any of the referred studies and thus remains an open question. It is relevant to examine the loading pattern of the cruciate ligaments during forward lunging since this movement is widely used in sports, assessment of knee function and rehabilitation (Heijne et al. 2008; Mattacola et al. 2009b; Farrokhi et al. 2010a; Jonhagen et al. 2005,b; Thorlund et al. 2000).

The reaction force supported by the passive structures in the knee is the result of the external loads acting on the adjoining bones and the actions of dozens of muscles. A complete understanding of this three-dimensional equilibrium may clarify the mechanical role of the cruciate ligaments and muscle function during the forward lunge movement. It is impossible to measure all the individual muscle and ligament forces directly (Erdemir et al. 2006). Instead we shall establish a computational model of a forward lunge in which calculations of individual muscle forces are possible by solving the so-called muscle recruitment problem (Rasmussen et al. 2010; Erdemir et al. 2006). We attempt to obtain a full understanding for a musculoskeletal model of a single subject and then investigate whether the findings are sensitive to reasonable variations of the anatomical parameters and the inevitable assumptions of the model. Furthermore, rather than attempting to resolve the internal forces in the knee into the different supporting structures, we shall resolve them into directions relative to the tibial plateau, i.e. normal and shear forces. This allows for elimination of normal forces carried in bone-on-bone contact, leaving only the shear forces which are likely to load the cruciate ligaments during a lunge movement.

Materials and methods

Experimental data

Data were recorded from a healthy female (height = 1.69 m, weight = 59.6 kg, age = 20 years) who was familiar with the forward lunge movement. Three-dimensional coordinates of skin-mounted markers were obtained via five video cameras (Canon MV 600, digital video) operating at 50 Hz. The Ariel Performance Analysis System (APAS, Ariel Dynamics Inc., San Diego, CA, USA) was used for reconstruction of the three-dimensional coordinates. The skin markers were placed on the lower extremities according to the marker set-up described by Vaughan et al. (2008). The subject was instructed to perform a forward lunge according to the guidelines we use in our laboratory (Alkjaer et al. ; Henriksen et al. 2010). The subject stood in an upright position on both feet (starting position) in front of a force platform (model OR6-5-1, AMTI, Watertown, MA, USA). She was instructed to perform a forward lunge by taking one step forward, placing the foot on the force platform, flexing the knee to approximately 90° and subsequently extending the knee to return to the starting position. The subject was asked to keep her upper body perpendicular to the ground and leave the contralateral foot in contact with the ground during the whole movement (the heel was allowed to lift on this side). On the leading leg, the knee was allowed to traverse in front of the toes but the heel remained in contact with the ground during the whole movement.

Data from the movement phase of the forward lunge were extracted for further biomechanical modeling (see below). The movement phase was defined as the period of time when the foot was in contact with the ground.

Computational model

A biomechanical model of a forward lunge movement (Fig. 1) was developed using the anybody modeling system ver. 3.01 (AnyBody Technology, Aalborg, Denmark, 2008) (Damsgaard et al. 1998) and based on the lower extremity model found in the anybody model repository version 7. Scaling of the body segments was performed using the length-mass-fat scaling law (Rasmussen et al. 1994). The modeling approach applied here was inverse dynamics including muscle recruitment to estimate the individual muscle forces. The model comprised two legs including femur, crus, rigid foot segments and the pelvis. Each leg contained 27 different muscles. Some muscles had multiple insertions or origins and were therefore subdivided into separate muscle-tendon units. For example, m. gluteus maximus, m. gluteus minimus, m. gluteus medius and m. adductor magnus were split into three parts each. In the case of m. gluteus maximus, one part inserts on the proximal femur while the two other parts connect to the tibia via the ilio-tibial tract and have an ability to affect the knee joint, depending on the body posture. This resulted in 35 independent muscle units in each leg that were recruited according to a minimum fatigue criterion (also known as the min/max criterion), which builds on the assumption that muscles are recruited in a manner which postpones fatigue (An et al. 2002; Rasmussen et al. 2010). This includes all the significant muscles crossing the knee and ankle joint influencing the equilibrium of the lower leg. Excluded muscles were m. adductor brevis, mm. gemelli inferior et superior, m. obturator internus, m. pectineus, m. peroneus longus, m. peroneus tertius, m. plantaris, m. popliteus and m. quadratus femoris. These muscles were omitted because of their reduced force productive capacity due to small physiological cross-sectional area or because their effect was considered to be very limited in the lunge movement. A forward lunge is a closed kinetic chain movement which primarily takes place in the sagittal plane, whereas internal/external rotations of the ankle, knee and hip are limited.

Fig. 1.

Fig. 1

Open in a new tab

The lunge model (here shown at time step 5) constructed in the anybody modeling system (anybody 3.0, AnyBody Technology, Aalborg, Denmark). Each leg in the model contained 27 muscles, some subdivided into more muscle-tendon units, which in total resulted in 35 muscle-tendon units in each leg (see text for further explanation).

The chosen muscle model was a Hill-type including contractile, parallel-elastic and serial-elastic elements. The hip was modeled as a spherical joint, the knee as a modified hinge joint and the ankle as a universal joint. The joint assumptions for the ankle and hip are close to the anatomical reality, whereas the anatomical knee is obviously significantly more complex than a hinge joint. However, for the purpose of emulating the conditions for the surrounding muscles, the simple approximation will suffice. The net load in the knee was subsequently resolved into its different components as described below in detail.

The quadriceps muscles (comprising the mm. vastii and m. rectus femoris) passed over points representing the patella and on to their mutual insertion on the tibia. This system, collectively representing the patella and patella ligament, was designed to ensure an anatomical insertion angle of the patella tendon on the tibia (Fig. 2), an anatomical moment arm of the quadriceps muscle over the knee joint and a mechanically correct transfer of the patella wrapping forces to the distal end of the femur.

Fig. 2.

Fig. 2

Open in a new tab

Patella tendon angle with respect to the tibia as a function of the knee flexion angle. Comparison of the experimental results of Herzog & Read (2004), Baltzopoulos (2010) and the lunge model from the present study. 0° on the y-axis indicated that the patella tendon angle was parallel to the longitudinal axis of the tibia. Positive/negative patella tendon angle values indicated the potential effect of quadriceps activity to translate the tibia anteriorly/posteriorly.

The magnitudes of the vertical and shear components of the quadriceps muscle force depend on the angle between the pulling direction of the patellar ligament and the longitudinal axis of the tibia, which varies with the actual knee joint angle (Buff et al. 1995; Herzog & Read, 2004; Baltzopoulos, 2010). Herzog & Read (2004) identified the lines of action in the sagittal plane of the major force-carrying structures crossing the human knee. These were determined as a function of the knee joint angle and were expressed using polynomial regression equations. The patella tendon insertion angle varied remarkably between five cadavers. Thus, the knee joint angle at which the patella tendon was perpendicular to the tibial plateau, i.e. the angle of transition from anterior to posterior drag from the quadriceps, was in the range 60°–90° (Herzog & Read, 2004). The patella tendon angle as a function of the knee joint angle determined by Herzog & Read (2004) can be seen in Fig. 2 together with the patella tendon angle measured by Baltzopoulos (2010) and the angle from the present lunge model. The patella tendon angle was given as the smallest angle between the tendon and a line perpendicular to the tibial plateau.

The knee joint angle was measured as the angle between the local y-axes of the femur and the tibia, which were in the longitudinal direction of the bones (positive was in the proximal direction). Full extension corresponded to zero angle and flexion angles were positive.

As mentioned, the knee model was a simple hinge joint. However, the organization of the model was such that the local reference frame of the joint, and therefore also the joint reaction forces, referred to the tibia, making it possible to dissolve the reaction forces into a y component normal to the tibial plateau, an anterior/posterior x component parallel with the tibial plateau, and a medial/lateral z component also parallel with the tibial plateau. The organization of the model guaranteed that compression forces in the y direction could only be carried by contact between the tibial plateau and the femoral condyles. Reaction forces in the local x direction were shear forces between the bones and hence balanced either by the ligaments and/or by the menisci. Disregarding the possible effect of the menisci will therefore conservatively estimate the shear force carried by the cruciate ligaments. Because cruciate ligament elements were assumed to be unilateral, the direction of the shear force determined which of the cruciate ligaments were loaded at any time. Positive knee reaction forces in the x direction indicate an anterior drag on tibia by the PCL, whereas negative knee reaction forces indicate a posterior drag on the tibia caused by the ACL.

The cruciate ligaments were simulated by two unilateral reaction forces in the local x (i.e. shear) direction of the knee joint. The first unilateral reaction prevented posterior translation of the femoral condyles on the tibial plateau and therefore emulated the effect of the ACL. The second unilateral reaction prevented anterior translation of the femoral condyles on the tibial plateau and therefore emulated the effect of the PCL. It is important to stress that these reaction forces were used as proxies for the true loadings of the cruciate ligaments. The difference was that the ACL and PCL formed an angle with the tibial plateau (Herzog & Read, 2004). The simulated reaction forces were therefore smaller than the actual ligament forces. The latter were easy to compute by simple trigonometry if the ligaments' angles with the tibial plateau were known. However, this was not necessary for the purpose of this investigation, as will be demonstrated later.

Note that the unilateral nature of the two reaction forces allowed for selective elimination of the effect of the ACL or PCL in the model.

Kinematics and external kinetics

The marker trajectories obtained from the experiment were processed by means of an optimization algorithm (Andersen et al. 2009, 1984) in order to determine the movement pattern and scaling of the model segments to fit the experimental data accurately. The output channels from the force platform were combined and converted into a three-dimensional moving center-of-pressure (CoP) relative to the center of the force platform (Winter, 2005). The local coordinates of the CoP were then transformed into the global coordinate system. The CoP, ground reaction force (GRF) vector and moment around the vertical axis were stored on text files as time histories. The force platform was implemented as a massless segment in the anybody model and driven kinematically by the CoP data. The GRF force vector and moment were applied in the model to this virtual platform, and a kinetic constraint was established between the foot and the platform in all six mutual degrees-of-freedom. Please note that it is a special feature of the anybody modeling system which allows for separation of kinematic and kinetic boundary conditions. The position, i.e. the position of the CoP, is driven while the measured and subsequently applied forces are balanced by a kinetic connection to the foot. This has the effect of transferring the measured ground reaction forces into the foot at the corresponding moving CoP.

The movement sequence was divided into 41 time steps. The first time step was defined as heel strike of the right foot and at this instant the right knee was flexed 39.5°. Peak knee flexion of 116° was reached at the 23rd time step (Fig. 3).

Fig. 3.

Fig. 3

Open in a new tab

Knee flexion angle of the right knee during a forward lunge. Five time steps (steps 9, 16, 23, 30 and 37) were selected for further analysis of the mechanical equilibrium between reaction forces and muscle-tendon forces acting on the tibia.

Outcome measures

The dynamic analysis of the lunge model computed the forces in the muscle-tendon units and the reaction forces in the knee and ankle joints (Rasmussen et al. 2010). Each force on the tibia from the muscles and joints was transformed into the local coordinate system of the tibia, thereby allowing for the construction of a full free body diagram, comprising all forces acting on the tibia and analysis of the mechanical equilibrium between joint reaction forces and muscle-tendon forces. The forces were normalized in terms of the total anterior and posterior force, respectively. In the interest of legibility, force contributions < 10% of the total shear force acting on the tibia were omitted from the result figures but were included in the computation. Finally, the absolute magnitude of the shear component of the quadriceps drag on the tibia was reviewed.

Results

The principal muscle and joint reaction forces pulling on the tibia in the anterior or posterior (x) direction are displayed in Fig. 4. In all five selected time steps the knee joint reaction force was positive, indicating that the PCL pulled the tibia in the anterior direction. The ACL did not contribute to the equilibrium at any time during the movement (Fig. 4). At peak knee flexion the knee reaction force (shear force component) reached a magnitude of 2880 N (Fig. 6). This anterior drag on the tibia was primarily counterbalanced by m. gluteus maximus (Fig. 4). At peak knee flexion, m. gluteus maximus was responsible for 67% of the posterior drag on the tibia (−1940 N). The quadriceps muscle was responsible for < 25% (< 430 N) of the total anterior drag on the tibia in the beginning and the end of the forward lunge movement, whereas it created a posterior drag on the tibia (−3%, −98.4 N) at the time of peak knee flexion (Fig. 4). M. semimembranosus accounted for < 20% (< −460 N) of the posterior drag on the tibia during the whole lunge movement (Fig. 4). The remaining hamstring muscles (m. semitendinosus, m. biceps femoris) did not contribute significantly to the posterior drag on the tibia. The ankle reaction force contributed 7–11% (∼ −155 N to −301 N) of the posterior drag on the tibia in all time steps (Fig. 4).

Fig. 4.

Fig. 4

Open in a new tab

Principal muscle forces normalized to the total shear force (QUA, m. quadriceps; SM, m. semimembranosus; GM1 and GM2, m. gluteus maximus) and joint reaction forces projected on the local x-axis (anterior direction) of the tibia as a function of the knee joint angles in selected time steps (see Fig. 3). A positive force value would cause an anterior drag on the tibia, whereas a negative value would cause a posterior drag. The omitted forces were small in magnitude compared with the included forces (< 10%), and since inertial forces were relatively small in this case, the positive and negative columns for each time step in the figure must roughly cancel each other out for the tibia to be in equilibrium.

Fig. 6.

Fig. 6

Open in a new tab

The total knee reaction shear force component (N) during the forward lunge movement. Peak knee flexion occurred at time step 23.

To verify the result, the unilateral reaction force representing the ACL was removed from the model simulating complete ACL deficiency. This did not cause any change in the force equilibrium, thus confirming that the ACL did not contribute any force to the equilibrium.

The quadriceps force acting on the tibia (Fig. 5) confirmed the posterior drag of the quadriceps near maximum knee flexion and revealed a maximum contribution to a local anterior drag of < 500 N (Fig. 5).

Fig. 5.

Fig. 5

Open in a new tab

The quadriceps force acting on the tibia. The x-axis is the knee flexion angle. In local tibia coordinates, the quadriceps shear force component was negative for positions close to maximum knee flexion.

Discussion

The present study aimed at contributing to an understanding of the force equilibrium in the lower leg by establishing a musculoskeletal model of the forward lunge. The intention was to computationally investigate the mechanical force equilibrium of the knee to provide a full understanding of the loading pattern of the cruciate ligaments and muscle function during the movement. Previous studies have investigated ACL and PCL loading during the forward lunge but these studies were based on experimental approaches, which makes quantification of individual muscle and ligament forces difficult and thus does not provide a full overview of the equilibrium. The studies by Heijne et al. (2008), who measured the strain of the ACL during lunging in vivo, and by Escamilla et al. (1990,b), who estimated the ACL loading by a biomechanical model including six muscles of which the individual forces were estimated by the electromyographic (EMG) force relationship, showed that the ACL was not significantly loaded during the forward lunge. The unloading of the ACL was not completely explained or confirmed in these studies, although the hamstring muscles were assumed to be responsible for the ACL unloading (Heijne et al. 2008; Escamilla et al. 1990,b). In the present study, we applied a musculoskeletal model comprising 35 independent muscle units to understand and explain the loading pattern of the knee structures during the movement. The advantage of this was that it provided the opportunity to explore the effect of several muscles and structures contributing to the mechanical equilibrium at the knee joint. The mechanical force equilibrium revealed that the hamstring muscles had a limited effect on the posterior drag on the tibia, whereas m. gluteus maximus dominated the posterior drag on tibia during the lunge movement. This was surprising, as the hamstring muscles are commonly thought to be the primary stabilizers of the knee by counteracting the potential effect of the quadriceps muscle to strain the ACL in dynamic situations (Solomonow et al. 2005; Hirokawa et al. 1993; Macwilliams et al. 2009a; Alkjaer et al. ). Thus, the effect of the hamstring muscles with respect to stabilizing the knee joint regarding anterior translation relative to femur may be overestimated for this specific movement. In line with this, the capacity of the hamstring muscles to protect the ACL during a side-cutting maneuver has been shown to be limited (Simonsen et al. 1986).

Surprisingly, the present results showed that gluteus maximus contributed considerably to the posterior drag on the tibia during the lunge, suggesting that this muscle is important with respect to knee joint stability. Most of the muscle fibers of the gluteus maximus inserts into the iliotibial tract, which inserts laterally on the tibia (Gerdy's tubercle) (Standring, 1987) and when the knee is flexed this muscle acts as a knee flexor via this insertion. Decreased neuromuscular activity of gluteus maximus during landing has been observed in women compared with men (Zazulak et al. 2002). This has been interpreted as limited ability to control the limb position, which has been suggested to add to the increased risk of ACL injuries observed in women (Hewett et al. 2009). Escamilla et al. (2007) mentioned further the gluteus maximus as a possible muscle to unload the ACL but did not include this muscle in their biomechanical knee model. In addition to this, increased activity in gluteus maximus has been observed in ACL-reconstructed subjects during a counter movement jump (Nyland et al. 1993). It is possible that this reflects an adaptive response in ACL reconstructed subjects which may benefit the knee joint stability in dynamic situations. Thus, the gluteus maximus seems to be important for knee joint stability and future investigations should look into the potential knee-stabilizing effect of this muscle.

The lunge model is subject to assumptions that might influence the result. First, the model morphology is an approximation of human anatomy, of which the most important is the angle at which the patella tendon inserts on the tibia. A larger angle in addition to possible alterations of the muscle recruitment pattern may lead to a larger local anterior component of the quadriceps force. However, it is evident from Fig. 2 that the angle of the model between the patella tendon and the tibia is conservative with respect to the findings of Herzog & Read (2004) and Baltzopoulos (2010), making it unlikely that the true angle would be larger than the model assumption. Secondly, the choice of optimality criterion used to resolve the muscle forces in the lunge model influences the muscle recruitment pattern. However, when the net moment is dominated by the knee extensors, all significant extensor muscle contributions are assembled in the patella tendon, and the patella tendon force therefore has a high degree of independency with respect to the distribution of forces among the individual knee extensors caused by the recruitment criterion. Additional co-contraction of the hamstrings might increase the quadriceps force, but Fig. 5 shows clearly that the kinematics of the patella tendon is such that even significant tendon forces do not give rise to much anterior drag, if any, in the local tibia coordinate system. Finally, muscle model features such as fiber lengths, tendon slack lengths and pennation angles may influence the result. However, as mentioned above, the fact that the patella ligament collects all knee extensor moment contributions in combination with the requirement for fulfillment of the equilibrium equations ensures that the knee equilibrium cannot deviate much from the identified solution. An exception could be the case of excessive passive muscle forces resulting from overly short tendon slack lengths. To avoid this, the computational procedure includes a calibration procedure which fits the tendon slack lengths to the size of the model.

The present results showed that the quadriceps muscle contributed with an anterior drag on the tibia during the beginning and at the end of the forward lunge. This concurs with other studies which observed that it is only at knee joint angles close to full extension that the quadriceps has the potential to drag the tibia anteriorly (Arms et al. 2009). As can be observed in Fig. 5, an appreciation of the complex force equilibrium of the tibia in conjunction with the change of direction of the local coordinate system of the tibia as the motion progresses is important for a full understanding of the force equilibrium. When these factors are taken into account, the net result is that the anterior drag of the quadriceps on the tibia is modest. In contrast, the present results suggest that the PCL is loaded during the forward lunge and that the peak load reached a value of 2880 N at the time point of peak knee flexion (Fig. 6). In the current model, the cruciate ligaments were assumed to be parallel to the tibial plateau, which is not anatomically correct. The angle between the PCL and the tibial plateau has been reported to be a function of the knee joint angle (Herzog & Read, 2004). If we account for the angle between PCL and the tibial plateau, the peak PCL force increases to 4243 N. The PCL has been reported to have a maximal strength of 4000 N (Race & Amis, 1986). Thus, the present results seem to overestimate the true PCL force value, which obviously must be lower than the predicted value. We assume that the high level of PCL loading observed in the present study is due to the assumption that the knee cruciate ligaments solely carried the shear force and thus the knee shear force was used as a proxy for the ligament forces in the current model, whereas all other structures, such as soft tissue, joint capsule, menisci (Standring, 1987) as well as the concavity of the tibial plateau (Hashemi et al. 2010b, 2008), which also act to resist the shear forces, were neglected. Further studies are needed to reveal the effects of these other structures in relation to cruciate ligament loading.

Conclusion

The present study provides an understanding of the mechanical force equilibrium of the knee joint during a forward lunge. A detailed musculoskeletal model with a high level of robustness against the major modeling assumptions such as patella ligament insertion angle and muscle recruitment criterion was successfully established. The results confirm that the PCL has an important mechanical function in the lunge movement, whereas the mechanical function of the ACL seems to be insignificant for this specific type of movement. Furthermore, the m. gluteus maximus was suggested to have an important stabilizing function with respect to anterior tibial translation. This muscle was found to be responsible for loading the PCL, whereas the effect of the hamstring muscles was limited.

References

  1. Alkjaer T, Simonsen EB, Peter Magnusson SP, et al. Differences in the movement pattern of a forward lunge in two types of anterior cruciate ligament deficient patients: copers and non-copers. Clin Biomech (Bristol, Avon) 2002;17:586–593. doi: 10.1016/s0268-0033(02)00098-0. [DOI] [PubMed] [Google Scholar]
  2. Alkjaer T, Henriksen M, Dyhre-Poulsen P, et al. Forward lunge as a functional performance test in ACL deficient subjects: test-retest reliability. Knee. 2009;16:176–182. doi: 10.1016/j.knee.2008.11.011. [DOI] [PubMed] [Google Scholar]
  3. An KN, Kwak BM, Chao EY, et al. Determination of muscle and joint forces: a new technique to solve the indeterminate problem. J Biomech Eng. 1984;106:364–367. doi: 10.1115/1.3138507. [DOI] [PubMed] [Google Scholar]
  4. Andersen MS, Damsgaard M, Rasmussen J. Kinematic analysis of over-determinate biomechanical systems. Comput Methods Biomech Biomed Engin. 2009;12:371–384. doi: 10.1080/10255840802459412. [DOI] [PubMed] [Google Scholar]
  5. Andersen MS, Damsgaard M, MacWilliams B, et al. A computationally efficient optimisation-based method for parameter identification of kinematically determinate and over-determinate biomechanical systems. Comput Methods Biomech Biomed Engin. 2010;13:171–183. doi: 10.1080/10255840903067080. [DOI] [PubMed] [Google Scholar]
  6. Arms SW, Pope MH, Johnson RJ, et al. The biomechanics of anterior cruciate ligament rehabilitation and reconstruction. Am J Sports Med. 1984;12:8–18. doi: 10.1177/036354658401200102. [DOI] [PubMed] [Google Scholar]
  7. Baltzopoulos V. A videofluoroscopy method for optical distortion correction and measurement of knee-joint kinematics. Clin Biomech (Bristol, Avon) 1995;10:85–92. doi: 10.1016/0268-0033(95)92044-m. [DOI] [PubMed] [Google Scholar]
  8. Beynnon BD, Fleming BC. Anterior cruciate ligament strain in-vivo: a review of previous work. J Biomech. 1998;31:519–525. doi: 10.1016/s0021-9290(98)00044-x. [DOI] [PubMed] [Google Scholar]
  9. Buff HU, Jones LC, Hungerford DS. Experimental determination of forces transmitted through the patello-femoral joint. J Biomech. 1988;21:17–23. doi: 10.1016/0021-9290(88)90187-x. [DOI] [PubMed] [Google Scholar]
  10. Damsgaard M, Rasmussen J, Christensen ST, et al. Analysis of musculoskeletal systems in the AnyBody Modeling System. Simul Model Pract Theory. 2006;14:1100–1111. [Google Scholar]
  11. Draganich LF, Vahey JW. An in vitro study of anterior cruciate ligament strain induced by quadriceps and hamstrings forces. J Orthop Res. 1990;8:57–63. doi: 10.1002/jor.1100080107. [DOI] [PubMed] [Google Scholar]
  12. Erdemir A, McLean S, Herzog W, et al. Model-based estimation of muscle forces exerted during movements. Clin Biomech (Bristol, Avon) 2007;22:131–154. doi: 10.1016/j.clinbiomech.2006.09.005. [DOI] [PubMed] [Google Scholar]
  13. Escamilla RF, Zheng N, Macleod TD, et al. Cruciate ligament forces between short-step and long-step forward lunge. Med Sci Sports Exerc. 2010a;42:1932–1942. doi: 10.1249/MSS.0b013e3181d966d4. [DOI] [PubMed] [Google Scholar]
  14. Escamilla RF, Zheng N, MacLeod TD, et al. Cruciate ligament tensile forces during the forward and side lunge. Clin Biomech (Bristol, Avon) 2010b;25:213–221. doi: 10.1016/j.clinbiomech.2009.11.003. [DOI] [PubMed] [Google Scholar]
  15. Farrokhi S, Pollard CD, Souza RB, et al. Trunk position influences the kinematics, kinetics, and muscle activity of the lead lower extremity during the forward lunge exercise. J Orthop Sports Phys Ther. 2008;38:403–409. doi: 10.2519/jospt.2008.2634. [DOI] [PubMed] [Google Scholar]
  16. Hashemi J, Chandrashekar N, Gill B, et al. The geometry of the tibial plateau and its influence on the biomechanics of the tibiofemoral joint. J Bone Joint Surg Am. 2008;90:2724–2734. doi: 10.2106/JBJS.G.01358. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Hashemi J, Chandrashekar N, Mansouri H, et al. Shallow medial tibial plateau and steep medial and lateral tibial slopes: new risk factors for anterior cruciate ligament injuries. Am J Sports Med. 2010;38:54–62. doi: 10.1177/0363546509349055. [DOI] [PubMed] [Google Scholar]
  18. Heijne A, Fleming BC, Renstrom PA, et al. Strain on the anterior cruciate ligament during closed kinetic chain exercises. Med Sci Sports Exerc. 2004;36:935–941. doi: 10.1249/01.mss.0000128185.55587.a3. [DOI] [PubMed] [Google Scholar]
  19. Henriksen M, Alkjaer T, Simonsen EB, et al. Experimental muscle pain during a forward lunge – the effects on knee joint dynamics and electromyographic activity. Br J Sports Med. 2009;43:503–507. doi: 10.1136/bjsm.2008.050393. [DOI] [PubMed] [Google Scholar]
  20. Herzog W, Read LJ. Lines of action and moment arms of the major force-carrying structures crossing the human knee joint. J Anat. 1993;182(Pt 2):213–230. [PMC free article] [PubMed] [Google Scholar]
  21. Hewett TE, Zazulak BT, Myer GD, et al. A review of electromyographic activation levels, timing differences, and increased anterior cruciate ligament injury incidence in female athletes. Br J Sports Med. 2005;39:347–350. doi: 10.1136/bjsm.2005.018572. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Hirokawa S, Solomonow M, Lu Y, et al. Anterior-posterior and rotational displacement of the tibia elicited by quadriceps contraction [see comments] Am J Sports Med. 1992;20:299–306. doi: 10.1177/036354659202000311. [DOI] [PubMed] [Google Scholar]
  23. Jonhagen S, Ackermann P, Saartok T. Forward lunge: a training study of eccentric exercises of the lower limbs. J Strength Cond Res. 2009a;23:972–978. doi: 10.1519/JSC.0b013e3181a00d98. [DOI] [PubMed] [Google Scholar]
  24. Jonhagen S, Halvorsen K, Benoit DL. Muscle activation and length changes during two lunge exercises: implications for rehabilitation. Scand J Med Sci Sports. 2009b;19:561–568. doi: 10.1111/j.1600-0838.2007.00692.x. [DOI] [PubMed] [Google Scholar]
  25. Macwilliams BA, Wilson DR, DesJardins JD, et al. Hamstrings cocontraction reduces internal rotation, anterior translation, and anterior cruciate ligament load in weight-bearing flexion. J Orthop Res. 1999;17:817–822. doi: 10.1002/jor.1100170605. [DOI] [PubMed] [Google Scholar]
  26. Mattacola CG, Jacobs CA, Rund MA, et al. Functional assessment using the step-up-and-over test and forward lunge following ACL reconstruction. Orthopedics. 2004;27:602–608. doi: 10.3928/0147-7447-20040601-17. [DOI] [PubMed] [Google Scholar]
  27. McLean SG, Huang X, Su A, et al. Sagittal plane biomechanics cannot injure the ACL during sidestep cutting. Clin Biomech (Bristol, Avon) 2004;19:828–838. doi: 10.1016/j.clinbiomech.2004.06.006. [DOI] [PubMed] [Google Scholar]
  28. More RC, Karras BT, Neiman R, et al. Hamstrings – an anterior cruciate ligament protagonist. An in vitro study. Am J Sports Med. 1993;21:231–237. doi: 10.1177/036354659302100212. [DOI] [PubMed] [Google Scholar]
  29. Nisell R, Nemeth G, Ohlsen H. Joint forces in extension of the knee. Analysis of a mechanical model. Acta Orthop Scand. 1986;57:41–46. doi: 10.3109/17453678608993213. [DOI] [PubMed] [Google Scholar]
  30. Nyland J, Klein S, Caborn DN. Lower extremity compensatory neuromuscular and biomechanical adaptations 2 to 11 years after anterior cruciate ligament reconstruction. Arthroscopy. 2010;26:1212–1225. doi: 10.1016/j.arthro.2010.01.003. [DOI] [PubMed] [Google Scholar]
  31. Race A, Amis AA. The mechanical properties of the two bundles of the human posterior cruciate ligament. J Biomech. 1994;27:13–24. doi: 10.1016/0021-9290(94)90028-0. [DOI] [PubMed] [Google Scholar]
  32. Rasmussen J, Damsgaard M, Voigt M. Muscle recruitment by the min/max criterion – a comparative numerical study. J Biomech. 2001;34:409–415. doi: 10.1016/s0021-9290(00)00191-3. [DOI] [PubMed] [Google Scholar]
  33. Rasmussen J, de Zee M, Damsgaard M, et al. Proceedings of the 10th International Symposium on Computer Simulation in Biomechanics. Cleveland, OH: 1986. A general method for scaling musculoskeletal models. 28-30 July 2005. [Google Scholar]
  34. Renstrom P, Arms SW, Stanwyck TS, et al. Strain within the anterior cruciate ligament during hamstring and quadriceps activity. Am J Sports Med. 2005;14:83–87. doi: 10.1177/036354658601400114. [DOI] [PubMed] [Google Scholar]
  35. Simonsen EB, Magnusson SP, Bencke J, et al. Can the hamstring muscles protect the anterior cruciate ligament during a side-cutting maneuver? Scand J Med Sci Sports. 1987;10:78–84. doi: 10.1034/j.1600-0838.2000.010002078.x. [DOI] [PubMed] [Google Scholar]
  36. Solomonow M, Baratta R, Zhou BH, et al. The synergistic action of the anterior cruciate ligament and thigh muscles in maintaining joint stability. Am J Sports Med. 2000;15:207–213. doi: 10.1177/036354658701500302. [DOI] [PubMed] [Google Scholar]
  37. Standring S. Gray's Anatomy: The Anatomical Basis of Clinical Practice. Edinburgh: Elsevier, Churchill & Livingstone; 2008. [Google Scholar]
  38. Thorlund JB, Damgaard J, Roos EM, et al. Neuromuscular function during a forward lunge in meniscectomized patients. Med Sci Sports Exerc. 2005;44:1358–1365. doi: 10.1249/MSS.0b013e31824c315b. [DOI] [PubMed] [Google Scholar]
  39. Vaughan CL, Davis BL, O'Connor JC. Dynamics of Human Gait. Champaign, IL: Human Kinetics Publishers; 2012. [Google Scholar]
  40. Winter DA. Biomechanics and Motor Control of Human Movement. Hoboken: John Wiley & Sons, Inc; 2002. [Google Scholar]
  41. Yanagawa T, Shelburne K, Serpas F, et al. Effect of hamstrings muscle action on stability of the ACL-deficient knee in isokinetic extension exercise. Clin Biomech (Bristol, Avon) 1992;17:705–712. doi: 10.1016/s0268-0033(02)00104-3. [DOI] [PubMed] [Google Scholar]
  42. Zazulak BT, Ponce PL, Straub SJ, et al. Gender comparison of hip muscle activity during single-leg landing. J Orthop Sports Phys Ther. 2005;35:292–299. doi: 10.2519/jospt.2005.35.5.292. [DOI] [PubMed] [Google Scholar]

Articles from Journal of Anatomy are provided here courtesy of Anatomical Society of Great Britain and Ireland

RESOURCES