Crouched posture maximizes ground reaction forces generated by muscles
Hoa X. Hoang, Jeffrey A. Reinbolt*
Department of Mechanical, Aerospace, & Biomedical Engineering, The University of Tennessee, Knoxville, TN, USA
Crouch gait, a common condition among children with cerebral
palsy, decreases walking efficiency due to the increased knee and
hip flexion during the stance phase of gait . Excessive knee
flexion increases the energy requirements of walking  which can
deteriorate joints and lead to chronic knee pain [3,4]. If left
untreated, these symptoms can worsen over time . The lifetime
costs for persons born in 2000 with cerebral palsy in the United
States are estimated to total $11.5 billion in 2003 US dollars and
place great demands on the healthcare system .
The disadvantages of crouch gait are well known; however, it
remains challenging to elucidate mechanisms that lead to a
crouched posture . Several factors have been linked with crouch
gait, including muscle weakness, spasticity, tightness [8–10],
decreased motor control , and skeletal deformities .
Despite being studied for decades, a cause and effect relationship
between these factors and crouch gait remains unknown, due to
the complexity of the musculoskeletal system [10,13–16].
Crouch gait is generally considered to be a negative symptom of
cerebral palsy; however, it may afford biomechanical advantages
that lead some patients to adopt a crouch gait. Previous study has
shown that a crouched posture reduces the capacity of muscles to
extend the hip and knee , but only in the vertical direction. An
athlete gets lower to increase the ability to produce movement in
all directions. Similarly, a standing passenger on a moving train
gets lower to increase the ability to resist movement. In each case,
the movement was produced or resisted by generating ground
reaction forces in the transverse plane. A link between crouched
gait postures and the capacity of muscles to generate ground
reaction forces has several clinical implications. If a crouched
posture reduces the capacity of muscles to generate ground
reaction forces, patients may have to spend more energy to
maintain a crouched posture compared to an upright posture.
However, if a crouched posture increases this capacity, patients
may be better suited to produce or resist movements to avoid
injuries from falling or tripping.
In this study, we used musculoskeletal modeling and optimi-
zation to evaluate one such possible advantage of crouch gait. The
objective was to determine if posture influences muscles capacity
to generate ground reaction forces in the transverse plane during
initial, middle, and final stance of a gait cycle. We hypothesized
that a crouched posture allows the largest force profile area among
postures from upright to severe crouch. Identifying the relation-
ship between posture and ground reaction forces may show an
advantage to adopting a crouched posture to compensate for
impairments associated with cerebral palsy.
A three-dimensional musculoskeletal model with 15 degrees-of-freedom and 92
muscles-tendon actuators was created in OpenSim . The model consists of a
Gait & Posture 36 (2012) 405–408
A R T I C L E
I N F O
Received 16 September 2011
Received in revised form 21 March 2012
Accepted 27 March 2012
A B S T R A C T
Crouch gait decreases walking efficiency due to the increased knee and hip flexion during the stance
phase of gait. Crouch gait is generally considered to be disadvantageous for children with cerebral palsy;
however, a crouched posture may allow biomechanical advantages that lead some children to adopt a
crouch gait. To investigate one possible advantage of crouch gait, a musculoskeletal model created in
OpenSim was placed in 15 different postures from upright to severe crouch during initial, middle, and
final stance of the gait cycle for a total of 45 different postures. A series of optimizations was performed
for each posture to maximize transverse plane ground reaction forces in the eight compass directions by
modifying muscle forces acting on the model. We compared the force profile areas across all postures.
Larger force profile areas were allowed by postures from mild crouch (for initial stance) to crouch (for
final stance). The overall ability to generate larger ground reaction force profiles represents a mechanical
advantage of a crouched posture. This increase in muscle capacity while in a crouched posture may allow
a patient to generate new movements to compensate for impairments associated with cerebral palsy,
such as motor control deficits.
? 2012 Elsevier B.V. All rights reserved.
* Corresponding author at: The University of Tennessee, Nathan W. Dougherty
Engineering Building, Room 207, 1512 Middle Drive Knoxville, TN 37996-2210,
USA. Tel.: +1 865 974 5308; fax: +1 865 974 5274.
E-mail address: firstname.lastname@example.org (J.A. Reinbolt).
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Gait & Posture
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head, trunk, pelvis, and a right and left femur, tibia, and foot segments. The lower
extremity joints were modeled as follows: the subtalar and ankle joint were
revolute joints, each knee was a planar joint, and the hip was a ball-and-socket joint.
The head and torso were included in the model and were articulated with the pelvis
through a ball-and-socket joint. The foot and floor contact was modeled as a weld
joint similarly to Anderson and Pandy . The arms were not included in the
musculoskeletal model, but the mass of the arms was included in the head and
Upright and crouch gait kinematics were recorded in the database at the Center
for Gait and Motion Analysis at Gillette Children’s Specialty Healthcare, St. Paul, MN
and obtained from a previous study . Subjects with cerebral palsy (aged six or
older) had to walk with a crouch gait to be included in the study. Arnold et al. 
defined crouch gait as walking with a knee flexion angle greater than 158
throughout the stance phase and a minimum of 208 at initial contact. Joints angles
of the subjects walking over an entire gait cycle were calculated using a standard
clinical protocol to track 3D motion of markers placed on the lower extremity. Joint
angles were normalized to a percentage of the gait cycle and averaged for each
group. In this study, we used data from the crouch group that exhibit an average of
408 of knee flexion at initial contact. Normal (upright) posture was defined from the
average gait data of 83 able-bodied subjects walking at self selected speeds while
crouch was defined from the average gait data of 100 subjects with cerebral palsy
and crouch gait (Fig. 1).
Knee flexion angles for crouch gait shows that subjects adopt a range of gait
patterns for walking with a crouch gait; the musculoskeletal model was placed in 15
different postures from upright to severe crouch during initial stance at 14% of the
gait cycle, middle stance at 32% of the gait cycle, and final stance at 50% of the gait
cycle. We linearly interpolated nine additional postures between upright and
crouched postures from the experimental data during initial, middle, and final
stance (Fig. 2). We extrapolated four additional postures (severe crouch) with knee
flexion angles greater than crouch. For the initial, middle, and final period of the
stance phase, we numbered each posture accordingly: #1 is experimental upright
posture, #2 through #10 are interpolated postures, #11 is experimental crouched
posture, #12 through #15 are extrapolated postures (severe crouch). The model
was placed in a total of 45 postures (15 for each of the three periods) for the study.
All of our postures had joint angles that were within 2 standard deviations from the
mean joint angles of crouch or upright.
To determine the relationship between posture and ground reaction forces, a
series of optimizations was performed for each postures from upright to severe
crouch during initial, middle, and final stance. An interior point optimizer (IPOPT)
was implemented to maximize the ground reaction forces for the eight compass
directions in the transverse plane by modifying muscle forces acting on the model.
Each optimization was subject to a set of constraints requiring the center of
pressure to be under the stance foot, the vertical ground reaction force to be greater
than or equal to zero, and each muscle force was constrained to be less than or equal
to its maximum isometric force. A ground reaction force profile was generated for
each posture by finding the area of the forces generated in the eight compass
directions (Fig. 2). Using the generated force profile area from initial, middle, and
final stance, the results were interpolated to show the force profile areas over the
entire stance phase of gait. We evaluated our hypothesis by comparing the force
profile area between postures.
A range of crouched postures allowed the largest ground
reaction force profile area during the stance phase of gait (Fig. 3
and Table 1). Over the stance phase, the maximum force profile
areas occurred between mild crouch (#5) and severe crouch
postures (#12) from initial stance to final stance. During initial
stance, interpolated postures (#4–6) between upright and crouch
allowed the largest ground reaction force profiles. These postures
produced force profile areas within 1% of each other, with posture
#5 being the largest (2.582 kN2). Comparatively, experimental
upright (#1) and experimental crouched (#11) postures had 12–
13% (2.265 and 2.272 kN2, respectively) smaller force profile areas,
and severe crouch (#15) was roughly 23% smaller (1.999 kN2). The
crouched posture (#11) during middle stance produced the largest
force profile areas (2.676 kN2) with this trend continuing to final
stance. Postures #8–12 produced force profile area within 2% of
each other. During final stance, a posture between crouch and
severe crouch (#12) allowed the largest ground reaction force
profiles (2.514 kN2); however, this force profile area was less than
2% larger compared to crouch (#11). The force profile area
(2.487 kN2) of experimental crouch was 7.3% higher compared to
Fig. 1. Average joint kinematics for upright and crouch gait for the whole gait cycle.
The solid line shows the mean values for a group of 83-able bodied children. The
dotted line shows the mean values for a group of 100 subjects with cerebral palsy
who walked in a crouch gait. Classification of crouch gait is based on the knee
flexion angle at initial contact. The bands around both lines show ?1 standard
deviation of the mean values. Experimental postures for upright and crouch were taken
from the mean values of each group at initial, middle, and final stance. Joint angles for
around 80% of our postures were within 1 standard deviation of the mean joint angles
for crouch or upright, while all of the postures were with within 2 standard deviations
of the mean joint angles for crouch.
Fig. 2. Three-dimensional musculoskeletal models placed in 4 (of 15 total) postures during middle stance at 32% gait cycle shown with maximum horizontal ground reaction
force profiles in the transverse plane: (a) experimental upright posture, (b) interpolated posture between experimental upright and crouch data, (c) experimental crouched
posture, (d) and extrapolated posture from experimental upright and crouch data (severe crouch). The average vertical ground reaction force is also shown for each posture.
This trend of decreasing vertical ground reaction forces is consistent with Hicks et al. .
H.X. Hoang, J.A. Reinbolt / Gait & Posture 36 (2012) 405–408
experimental upright and 4% higher than severe crouch during
This study examined how posture influences ground reaction
forces generated by muscles. We found that the force profile areas
for initial stance was highest for postures near mild crouch and
decreases as postures move towards upright and crouch. The force
profile area increased during middle stance as postures change
from mild crouch to crouch and decreased as postures move
beyond crouch to severe crouch. The trend for final stance was
similar to that of middle stance except that upright showed a slight
increase. Our results show that postures between mild crouch and
severe crouch postures were able to produce the largest force
profile area during the stance phase of gait.
Our study is fundamentally different from Hicks et al. ,
which examined the effect of crouch postures on the capacity of
muscles to extend the hip and knee joints. Their study used
induced acceleration analysis  to determine the joint angular
accelerations towards extension resulting from the application of
1 N muscle force to the musculoskeletal model. The joint angular
accelerations resulting from the induced acceleration analysis
reflects the influence of muscle geometry and posture on the
capability of each muscle’s contribution to extend the hip and knee
joints. Their study showed almost all of the major hip and knee
extensors’ capacities were reduced in crouch gait. This finding
suggests a reduction in the ability to generate vertical ground
reaction force. In our case, we used optimization to maximize
horizontal ground reaction forces in the transverse plane without
regard for the vertical ground reaction force. However, a vertical
ground reaction force is necessary to achieve the horizontal ground
reaction forces (Fig. 2). Our finding suggests an increase in the
ability to generate these horizontal forces. Furthermore, our
vertical ground reaction forces generated are consistent with the
findings in Hicks et al.  that crouched posture reduces the
ability to generate vertical ground reaction force (Fig. 2).
There were several challenges present in our study and the
results should be interpreted in context with our research
challenges. First, the optimization procedure implemented to
calculate the maximum ground reaction force was static rather
than dynamic optimization. Dynamic optimization involves
minimizing or maximizing the cost objective function over a
period of time; this was not implemented in our study as the model
was placed in a given posture while the muscles were able to
generate force. Hence, static optimization was better suited for our
study. Anderson and Pandy  showed that static optimization
was equivalent to dynamic optimization in biomechanics. Second,
our musculoskeletal model did not incorporate any skeletal
abnormalities, such as tibial torsion , commonly seen in
children with cerebral palsy walking with crouch gait. Our study
was focused on examining the different postures and their
influence on ground reaction forces. Incorporating bone deformi-
ties such as tibial torsion would add additional variables to the
investigation, making it difficult to elucidate the effects of ground
reaction force relating to the different postures. Hicks et al. 
showed that deformities such as tibial torsion in patients with
cerebral palsy reduces the capacity of the muscles to extend the hip
and knee body during the single limb of stance phase. Future
studies could include these skeletal deformities in the musculo-
skeletal model to verify the trends seen from this study across
postures during stance phase of gait. Third, several of our postures
Fig. 3. Areas of ground reaction force profiles across three parts of stance and across all postures (intermediate force profile areas between initial-middle-final generated with
a cubic spline interpolation). Force profile areas throughout stance are from lowest (blue) to highest (red). During early stance, mild crouched postures (#4–6) allowed the
greatest forces. During late stance, crouched postures (#9–11) allowed greater forces compared to upright. (For interpretation of the references to color in this figure legend,
the reader is referred to the web version of this article.)
Three largest force profile areas for each part in the stance phase of gait.
Force profile area (kN2) – [posture #]
2.581 – 
2.676 – 
2.514 – 
2.573 – 
2.661 – 
2.488 – 
2.572 – 
2.653 – 
2.502 – 
H.X. Hoang, J.A. Reinbolt / Gait & Posture 36 (2012) 405–408
were interpolated to find gait data between crouched and normal
gait. We also extrapolated some additional postures to look at gait
even more severe than crouched. About 80% of our postures,
however, were within 1 standard deviation from the mean joint
angle of crouched or upright gait. All of our postures’ joint angles
were within 2 standard deviations. Finally, the arms in our
musculoskeletal model were omitted due to the lack of an upper
extremity model with muscles. However, the mass properties of
the arms were included in the torso. In a running simulation ,
the arms accounted for less than 1% of both the maximum
horizontal and vertical mass center acceleration and therefore its
contribution to propulsion and support were minimal.
Despite these challenges, we can draw several conclusions from
this study. First, the overall ability to generate larger ground
reaction forces and force profile areas represents a mechanical
advantage of a crouched posture. This advantage results from an
increased capacity of muscles to generate ground reaction forces.
This increase in muscle capacity while in a crouched posture may
allow a patient to generate new movements to compensate for
impairments associated with cerebral palsy, such as motor control
deficits. Furthermore, this increase in muscle capacity to generate
horizontal ground reaction forces may also rationalize the
advantage an athlete gains when adopting a crouch posture in
sports. This work can be implemented into future studies to study
other bipedal animals, such as birds, to understand why they adopt
a crouch gait versus an upright gait as in humans.
We are grateful to Scott Delp, Ajay Seth, and Jennifer Hicks for
helpful discussions. This research was supported by The University
of Tennessee, Knoxville and NIH roadmap for Medical Research
U54 GM072 970.
Conflict of interest statement
The authors do not have any financial or personal relationships
with other people or organizations that could inappropriately
influence this work.
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