Introduction
Stability of the knee during walking is determined by the balance of muscle, ligament, joint contact, and
ground reaction forces applied to the leg. Muscles, in particular, are able to actively adapt to changes in
external and intraarticular loading conditions to maintain knee stability during locomotion. Indeed, many
gait analysis studies have identified specific muscular adaptations in the walking patterns of chronic ACLdeficient (ACLd) individuals.[3,4,9,17] Some studies have shown that ACLd individuals adapt their gait
patterns either by reducing the extensor moment at the knee in stance (a quadriceps reduction
pattern[6,9,11,28] or by eliminating it altogether (a quadriceps avoidance pattern.[3,4] One possible explanation
for the observed decrease in knee extensor moment is an adaptive change in thigh muscle force, brought
about by the need to reduce anterior tibial translation (ATT) in the ACLd knee. Support for this idea is
provided by EMG data acquired during gait, which show an increase in the level of hamstrings activation
concomitant with a decrease in the magnitude of knee extensor moment.[26,31] Because the quadriceps
and hamstrings apply opposite (anterior and posterior) shear forces to the tibia [13,20,27] it is widely
acknowledged that control of these muscles may be adapted to stabilize the knee during dynamic
weightbearing activity. What is not known, however, is whether an isolated change in either quadriceps or
hamstrings muscle force is sufficient to stabilize the ACLd knee during gait.
Although many studies have applied computer modeling and simulation to understand muscle
coordination of walking[1,5,34] to our knowledge only one has quantified the effect of muscle compensation
on knee instability in ACLd gait. Using a two-dimensional model of the lower limb, Liu and Maitland[15]
found that 56% of peak isometric hamstrings force was necessary to restore ATT in the ACLd knee to the
amount observed in normal gait. Their analysis was performed for a single instant of the gait cycle (heel
strike) and considered only the effect of hamstrings muscle action on ATT when people walked at their
preferred (normal) speeds.
The overall goal of the present study was to test the hypothesis that an isolated change in either
quadriceps or hamstrings muscle force is sufficient to stabilize the ACLd knee during walking. A threedimensional (3D) model of the lower limb was used to calculate muscle, ligament, and joint-contact forces
at the knee during gait. The model simulations were designed to address two questions. First, can
isolated changes in quadriceps or hamstrings muscle force stabilize the ACLd knee during walking, and if
so, what changes in muscle force are needed to provide knee stability? Second, how do quadriceps and
hamstrings muscle adaptations affect the net extensor moment developed at the knee during gait?
Methods
A three-step approach was used to determine the muscle forces needed to restore ATT in the ACLd
knee. First, joint motion, ground-reaction forces, and muscle forces for normal walking were obtained from
a forward dynamic simulation.[1] Second, these data were input into a model of the lower limb that
included a detailed 3D model of the knee. A static equilibrium problem was then solved at 23 points of the
gait cycle to determine ATT over the full gait cycle for both an intact and ACLd knee.[24,25] Third, using the
muscle forces obtained for normal gait as a baseline, two further static equilibrium problems were solved
over the whole gait cycle to determine the quadriceps and hamstrings forces needed to restore ATT in the
ACLd knee to first the intact level and then the maximum allowable level. Intact ATT was defined as the
amount of ATT calculated for normal walking in the intact knee.[24] Maximum allowable ATT was defined
as the amount of ATT calculated for maximum isometric contractions of the quadriceps (i.e., maximum
isometric knee extension) in the intact knee.[23] Maximum allowable ATT was used as the upper limit of
knee instability because some researchers have shown that ACLd subjects often perform activities with
ATT levels above those observed in the healthy knee.[10,32] Thus, maximum allowable ATT represents the
limit of ATT that a healthy knee might comfortably achieve.[33] Maximum allowable ATT was calculated
with the lower extremity model (see below) by simulating a seated maximum isometric knee extension. In
these simulations, the model knee was placed at joint angles corresponding to those found in walking, the
quadriceps muscles were maximally activated, and a constraint was applied at the level of the ankle to
prevent the knee from extending.[23]
A 3D model of the body was used to determine lower-limb muscle forces during normal walking. The
skeleton was modeled as a 10-segment, 23- df articulated chain. Each hip was represented as a 3- df
ideal ball-and-socket joint, each knee as a 1- df hinge joint, each ankle as a 2- df universal joint, and each
metatarsal joint as a 1- df hinge.[1] The model was actuated by 54 musculotendinous units, each unit
represented as a three-element muscle in series with tendon. The dynamic optimization problem was to
find the muscle excitation histories, muscle forces, and body motions subject to minimum metabolic
energy consumed per unit of distance moved. The joint angles, ground reaction forces, and muscle
activation patterns obtained from the simulation were similar to the same measures obtained from healthy
subjects who walked at their preferred speeds.[1,2] Details concerning the walking model and dynamic
optimization solution obtained for normal gait are reported by Anderson and Pandy. [1,2]
Anterior tibial translation of the intact and ACLd knee was calculated using another model of the lower
limb that included a detailed 3D model of the knee (the lower-limb model). Five segments were used to
represent the lower limb in this model: thigh, shank, patella, hindfoot, and toes. These segments were
connected together by five joints: hip, tibiofemoral joint, patellofemoral joint, ankle, and metatarsal joint
(Fig. 1). The hip, ankle, and metatarsal joints were represented in exactly the same way as in the walking
model. At the knee, six generalized coordinates described the movements of the tibia relative to the
femur, and another six coordinates described the movements of the patella relative to the femur. A
complete description of the model can be found in Shelburne et al.. [24]
Figure 1.
A. The muscles of the leg were modeled by 13 actuators:[24] vastus medialis (VasMed), vastus intermedius
(VasInt), vastus lateralis (VasLat), rectus femoris (RF), biceps femoris long head (BFLH), biceps femoris
short head (BFSH), semimembranosus (MEM), semitendinosus (TEN), medial gastrocnemius (GasMed),
lateral gastrocnemius (GasLat), and tensor fascia latae (TFL). Also included in the model but not shown
are sartorius and gracilis. B. The ligaments of the tibiofemoral joint were modeled by thirteen elastic
bundles:[24] anterior (aACL) and posterior (pACL) bundles of the anterior cruciate ligament, the anterior
(aPCL) and posterior (pPCL) bundles of the posterior cruciate ligament, the anterior (aMCL), central
(cMCL), and posterior (pMCL) bundles of the superficial medial collateral ligament, the anterior (aCM) and
posterior (pCM) bundles of the deep medial collateral ligament, the lateral collateral ligament (LCL), the
anterolateral structures (ALS), and the medial (Mcap) and lateral (Lcap) posterior capsule.
The geometry of the distal femur, proximal tibia, and patella was based on parasagittal sections of the
bones obtained from 23 cadaveric knees. The contacting surfaces of the femur and tibia were modeled as
deformable.[19] The model of patellofemoral mechanics was based on the assumptions that the patellar
tendon was inextensible and that interpenetration between the facets of the patella and the patellar
surfaces of the femur can be neglected.
The geometry of the cruciate and collateral ligaments, posterior capsule, and anterolateral structures of
the knee was modeled using 13 elastic elements (Fig. 1B). Thirteen muscles were represented in the
lower-limb model (Fig. 1A). The paths of all muscles, except vasti, hamstrings, and gastrocnemius, were
identical with those incorporated in the walking model. Whereas vasti, hamstrings, and gastrocnemius
were each represented as one muscle in the walking model, the separate portions of each of these
muscles were included in the lower-limb model.[18,19]
The relative positions of the femur, tibia, and patella in the intact knee were found by assuming the lower
limb was in static equilibrium at each instant during the simulated gait cycle; thus, the inertial contributions
of the shank, patella, hindfoot, and toe segments were neglected in these calculations. Specifically,
muscle forces, ground reaction forces, joint angles of the hip, ankle, and metatarsals, and the flexionextension angle of the knee obtained from the walking simulation were used as inputs to the model. The
unknown translations and rotations of the bones at the knee were found by performing a forward
integration of the equations of motion at each time step of the walking simulation until the accelerations
and velocities of all the joints approached zero.[24] These calculations were repeated with the ACL
removed from the model to estimate the amount of ATT during ACLd gait.[25]
Four simulations of ACL-deficient walking were performed. The model of the lower limb was used for
these calculations. In each simulation a static equilibrium problem was solved at 23 points of the gait
cycle (as described above for the intact and ACL-deficient knee) subject to the following conditions. In the
first two simulations, quadriceps force was decreased to determine whether this change alone could
reduce ATT in the ACLd knee first to the amount calculated for the intact knee (intact ATT; simulation 1),
and second, to the amount calculated for maximum isometric knee extension (maximum allowable ATT;
simulation 2). In each of these simulations, quadriceps force was decreased by decreasing the force in
each of the three vasti (medialis, intermedius, and lateralis) as a percentage of its peak isometric
strength. The forces in all three muscles were decreased by the same percentage each time. The output
of simulations 1 and 2 were a decrease in quadriceps force and the resultant change in extensor moment.
In the next two simulations, hamstrings force was increased to determine whether this change alone
could restore ATT in the ACLd knee first to the amount calculated for the intact knee (simulation 3), and
second, to the amount calculated for maximum isometric knee extension (simulation 4). In each of these
simulations, hamstrings force was increased by increasing the force in each of three hamstrings (biceps
femoris long head, semimembranosus, and semitendinosus) as a percentage of its peak isometric
strength. The forces in all three muscles were increased by the same percentage each time.
Experimental evidence suggests that a hamstrings facilitation strategy is characterized by increased
activity of both the medial and lateral hamstring muscles.[14] The output of simulations 3 and 4 were an
increase in hamstrings force and the resultant change in extensor moment.
Results
In the absence of any muscular compensation, ATT increased throughout the stance phase of ACLd gait
relative to that calculated for normal gait (Fig. 2). Peak ATT for the intact and ACLD knee occurred at
contralateral toe off, which coincided with the occurrence of peak knee extensor moment (see Fig. 3B).
Maximum allowable ATT was always greater than that calculated for normal gait, and at times was even
greater than that estimated for ACLd gait (Fig. 2, compare lightly shaded region and solid line around
50% of gait cycle).
Figure 2.
ATT of the normal ( intact ) and ACLd knee during walking. ATT of the healthy knee during maximum
isometric knee extension for the same knee angles as walking ( maximum allowable ). The change in
hamstrings and quadriceps muscle force was predicted that brought ATT of the ACLd knee (gray line) to
the ( maximum allowable ) (gray) and intact (black) levels. The dashed black line shows the amount ATT
of the ACLd knee exceeded that of the intact knee when a quadriceps avoidance strategy was simulated
(simulation 1).
The model simulation results showed that it was not entirely possible to restore ATT in the ACLd knee to
the amount calculated for normal gait merely by reducing the magnitude of quadriceps force (Fig. 3A,
gray solid line). There were periods near heel strike and in midstance when the lower limit of quadriceps
force (zero force) was reached, and yet ATT in the ACLd knee was greater than that obtained for the
intact knee (Fig. 2, black dashed line). The simulation results also showed that it was not entirely possible
to restore ATT in the ACLd knee to the maximum allowable level by reducing quadriceps force alone (Fig.
3A, gray dashed line). In this case, there was a brief period during midstance when the lower limit of
quadriceps force was reached, and yet ATT was greater than that incurred during maximum isometric
extension (Fig. 2, black dashed line exceeds the gray region during midstance).
Figure 3.
A. Quadriceps force for normal gait[1] compared with that needed to achieve intact and maximum
allowable ATT during ACLd gait (maximum quadriceps force in the lower limb model was 9356 N [19]). B.
Knee extensor moment for the healthy knee[1] compared with that calculated when quadriceps force was
decreased to achieve intact and maximum allowable ATT during ACLd gait.
Complete elimination of the knee extensor moment (a quadriceps avoidance pattern) was needed to
restore ATT in the ACLd knee to the level calculated for normal gait (Fig. 3B, gray solid line). In contrast,
some (positive) net extensor moment was predicted when ATT in the ACLd knee was restricted to the
maximum allowable limit (Fig. 3B, gray dashed line).
The simulation results showed that it was possible to reduce ATT exactly to the level calculated for the
intact knee merely by increasing the magnitude of hamstrings force (Fig. 4A). As expected, the increase
in hamstrings force needed to bring ATT in the ACLd knee to the maximum allowable level was less than
that needed to bring ATT to the intact level (Fig. 4A, compare gray dashed and solid lines). An increase in
hamstrings force led to a decrease in the knee extensor moment, but this effect was noticeably less than
that obtained when quadriceps force was reduced (compare gray lines in Fig. 3B and 4B).
Figure 4.
A. Hamstrings force for normal gait[1] compared with that needed to achieve intact and maximum
allowable ATT during ACLd gait (peak hamstrings force in the lower limb model was 4162 N9[1]). B. Knee
extensor moment for the healthy knee[1] compared with that calculated when hamstrings force was
increased to achieve intact and maximum allowable ATT during ACLd gait.
The strongest hamstrings muscle, semimembranosus, applied the largest posterior shear force to the
knee when the hamstrings were used to restore ATT in the ACLd knee to the level calculated for normal
gait (Fig. 5). Semitendinosus applied a larger shear force than biceps femoris long head as the knee
approached extension, which was surprising in view of the fact that semitendinosus is the weaker of the
two muscles in the model (Fig. 5, compare gray solid and dashed lines from 30 to 50%).
Figure 5.
Posterior shear force applied to the tibia by the biarticular hamstrings muscles when increased
hamstrings force was used to restore ATT in the ACLd knee to the level calculated for normal walking.
Peak isometric forces of the semimembranosus, biceps femoris long head, and semitendinosus were
assumed to be 1480, 960, and 640 N, respectively.[19]
Discussion
The purpose of this study was to test the hypothesis that an isolated change in either quadriceps or
hamstrings muscle force is sufficient to stabilize the ACLd knee during walking. A 3D model of the lower
limb was used to determine the decrease (increase) in quadriceps (hamstrings) force needed to keep
ATT in the ACLd knee within a stable limit. The model simulation results showed that decreasing
quadriceps force (quadriceps reduction/avoidance) is an effective method for stabilizing the knee during
most of the stance phase, except for a brief period around midstance when the knee is nearly extended.
The analysis also showed that increasing hamstrings force (hamstrings facilitation) is a more effective
method for stabilizing the ACLd knee during gait. The model results suggest, therefore, that each of these
muscular adaptation strategies is capable of independently stabilizing the ACLd knee, even when the
pattern of lower-limb joint movement is assumed to be the same as that observed in normal walking.
Before interpreting the results of this study, it is important to consider the limitations of the analysis
performed. The limitations associated with estimating muscle forces during walking have been described
by Anderson and Pandy[1] whereas those pertaining to the knee model used to calculate ligament and
joint-contact forces have been outlined by Pandy et al.[19] and Shelburne et al..[24] It was assumed in this
study that the amount of ATT incurred during maximum isometric knee extension represents the
maximum allowable limit that a healthy knee might comfortably achieve. A maximum allowable limit was
chosen as the upper limit of knee instability because some in vivo studies have shown that some subjects
who cope with ACL deficiency commonly experience levels of ATT that are greater than those found in
the healthy knee.[10,32] The peak maximum allowable ATT (9.6 mm) calculated here is comparable to the
value of peak ATT measured by Kvist and Gillquist[10] in the ACLd knee during walking (8.3 ± 3.8 mm).
Perhaps a more significant limitation was the assumption of normal kinematic profiles in the simulation of
ACLd gait. Whereas some studies have shown that many ACLd patients walk with increased knee
flexion[6] the results presented here do not take these gait alterations into account. We specifically chose
to exclude alterations in joint kinematics from the analysis, because we wanted to examine the effects of
adaptations in quadriceps and hamstrings muscle action alone and also because there is currently no
consensus regarding the existence of a general adaptive strategy in this patient group. [28] Our overall goal
was to test the hypothesis that a change in either quadriceps or hamstrings muscle force is sufficient to
stabilize the ACLd knee during walking. By increasing or decreasing thigh muscle force in the static
equilibrium calculations and keeping all other conditions the same, we were able to isolate this effect.
More research is needed to evaluate the effects of simultaneous changes in joint kinematics and thigh
muscle force on ATT during ACLd gait.
The increase in ATT predicted by the model is consistent with measurements made on the ACLd knee in
a number of in vitro and in vivo experiments.[7,10,32] Similar to the results of Figure 2, the in vivo
measurements of Kvist and Gillquist[10] reveal an increase in ATT relative to that measured during the
stance phase of normal gait. The peak change in ATT occurred in early stance and coincided with the
time of peak knee extensor moment in both the experiments[10] and model simulations. The relationship
between peak knee extensor moment and peak ATT suggests that quadriceps reduction/avoidance is a
viable strategy for ACLd patients to adopt, if the goal is to reduce ATT during gait.
The knee moments predicted for quadriceps or hamstrings compensation in the present study are
consistent with those measured for ACLd subjects during gait. The quadriceps avoidance pattern
observed in some subjects was described by a knee-joint moment that was predominantly flexor in early
stance.[4,31] This pattern is similar to both patterns of knee moment illustrated in Figure 3B, which were
obtained by reducing quadriceps force to decrease ATT in the ACLd knee. Distinct from the quadriceps
avoidance pattern, other studies[11] have reported only a small decrease in knee extensor moment in early
stance during ACLd gait. This pattern is similar to those shown in Figure 4B, which were obtained by
assuming a hamstrings facilitation strategy. Still others have found no significant change in the knee
extensor moment measured for ACLd gait compared to that estimated for normal gait.[21,28] Interestingly,
the knee moment shown in Figure 4B for maximum allowable ATT is within the standard deviation of
measurements reported by Roberts et al.[21] and Torry et al.[28] for healthy subjects. This suggests that in
vivo measurements of knee-joint moment during ACLd gait may not be sensitive enough to detect the
utilization of a hamstrings facilitation strategy, where a relatively small increase in hamstrings force may
be all that is needed to restrict ATT to a safe limit.
Berchuck et al.[4] have suggested that a reduction in knee extensor moment via quadriceps avoidance is
an effective strategy for limiting ATT during ACLd gait. The results of the present analysis are consistent
with this claim. Whereas the advantages and disadvantages of a quadriceps avoidance strategy may still
be debated, a reduction in quadriceps moment[6,11] has been shown to be related to quadriceps
weakness.[11,29] Weakness is thought to be associated with an increase in the knee adductor moment [30]
and with degeneration of the knee joint[8] which is one reason why many knee rehabilitation protocols
emphasize maintenance of quadriceps strength.[22] For these reasons, a hamstrings facilitation strategy
may be a more desirable adaptation in respect to general knee health.
The simulation results suggest that hamstrings facilitation is more effective in restoring knee stability than
is quadriceps avoidance. In the calculations, the hamstrings facilitation strategy was more effective than
quadriceps avoidance for three reasons. First, the hamstrings provided a greater change in ATT per unit
change in muscle force during the time of peak ATT in the ACL-deficient knee (roughly between 10 and
30% of the gait cycle). The reason is because the hamstrings are more steeply inclined to the long axis of
the tibia than is the patellar tendon during this time. Second, hamstrings facilitation caused a modest
decrease in the knee extensor moment, whereas quadriceps avoidance necessitated complete
elimination of this moment for much of the stance phase. The hamstrings gave a smaller change in
extensor moment per unit change in muscle force because the hamstrings moment arm is smaller than
that of the patellar tendon during gait. Third, the capacity of the quadriceps avoidance strategy is limited
by the amount of quadriceps force in normal gait. For example, the simulation for walking predicts normal
quadriceps force to be less than 3% of maximum from 35 to 40% of the gait cycle (Fig. 3A). Thus, there is
little span for reducing quadriceps force at that time. For this reason, reducing quadriceps force to zero
did not return ATT of the ACLd knee to intact levels over portions of the gait cycle in which quadriceps
force was normally low (Fig. 3A between 0-10% and 35-40% of the gait cycle).
Given the path of the hamstrings relative to the knee, it was questionable whether these muscles would
be able to stabilize the knee near extension. The model simulations showed that at critical regions of the
gait cycle, such as midstance to late stance when the knee was near extension, the ACLd knee could be
stabilized by applying a hamstrings force that was no more than 13% of the peak isometric strength of
these muscles (Fig. 4A, gray solid line).
Of the three hamstrings muscles included in the model, semimembranosus was the most effective in
limiting ATT in the ACLd knee. Because semimembranosus is the strongest of the hamstrings muscles,
the fact that it contributed most to posterior shear force was not unexpected. The effectiveness of
semimembranosus in limiting ATT was due not only to its size but also to its inclination relative to the long
axis of the tibia.
This is best illustrated by the fact that the smallest hamstrings muscle in the model, semitendinosus, often
applied a larger posterior shear force than did biceps femoris long head, which is considerably stronger.
The reason is that the geometry of semitendinosus is such that it is better suited to pulling the tibia
backward when the knee is nearly extended. This finding suggests that it may be important to preserve
the semitendinosus in surgical procedures involving ACL reconstruction. [16]
In summary, although our results support the contention that either isolated quadriceps or hamstrings
muscle action can stabilize the ACLd knee during walking, they also suggest that the latter is more
effective in reducing ATT during ACLd gait. Given that quadriceps avoidance is usually accompanied by
quadriceps muscle weakness, which has been associated with medial compartment joint degeneration [12]
a hamstrings facilitation pattern would appear to be more effective on these grounds as well. We suggest
that the inability of gait studies to identify a consistent ACLd adaptive strategy may be due to the fact that
these patients have at their disposal a continuum of compensatory mechanisms ranging from quadriceps
avoidance to hamstrings facilitation. Each individual adopts a certain strategy on the basis of tolerable
knee stability as perceived by an allowable amount of ATT, which may or may not require a significant
change in lower-limb joint kinematics.
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Funding Information
Financial support was provided in part by the Steadman Hawkins Research Foundation.
Reprint Address
Kevin Shelburne, Ph.D., Steadman Hawkins Research Foundation, Vail, CO 81657; E-mail:
kevin.shelburne@shsmf.org .
Kevin B. Shelburne,1 Michael R. Torry,1 and Marcus G. Pandy2
1
2
Steadman Hawkins Research Foundation, Biomechanics Research Laboratory, Vail, CO
Department of Biomedical Engineering, University of Texas at Austin, Austin, TX