1940 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 11, NOVEMBER 2007
OpenSim: Open-Source Software to Create and
Analyze Dynamic Simulations of Movement
Scott L. Delp*, Frank C. Anderson, Allison S. Arnold, Peter Loan, Ayman Habib, Chand T. John,
Eran Guendelman, and Darryl G. Thelen
Abstract—Dynamic simulations of movement allow one to study
neuromuscular coordination, analyze athletic performance, and
estimate internal loading of the musculoskeletal system. Simu-
lations can also be used to identify the sources of pathological
movement and establish a scientific basis for treatment planning.
We have developed a freely available, open-source software system
(OpenSim) that lets users develop models of musculoskeletal
structures and create dynamic simulations of a wide variety of
movements. We are using this system to simulate the dynamics of
individuals with pathological gait and to explore the biomechan-
ical effects of treatments. OpenSim provides a platform on which
the biomechanics community can build a library of simulations
that can be exchanged, tested, analyzed, and improved through a
multi-institutional collaboration. Developing software that enables
a concerted effort from many investigators poses technical and
sociological challenges. Meeting those challenges will accelerate
the discovery of principles that govern movement control and
improve treatments for individuals with movement pathologies.
Index Terms—Computed muscle control, forward dynamic sim-
ulation, musculoskeletal modeling, open-source software.
I. INTRODUCTION
M
ANY elements of the neuromusculoskeletal system in-
teract to enable coordinated movement. Scientists fasci-
nated by human movement have performed an extensive range
of studies to describe these elements. As a result, there is a
wealth of data that characterize the mechanics of muscle, the
geometric relationships between muscles and bones, and the
motions of joints. Clinicians who treat movement abnormali-
ties in individuals with cerebral palsy, stroke, osteoarthritis and
Parkinson’s disease have examined the neuromuscular excita-
tion patterns and movement kinematics of literally thousands
Manuscript received August 10, 2006. This work was supported in part by
the National Institutes of Health through the NIH Roadmap for Medical Re-
search Grant U54 GM072970 and through NIH Grants HD33929, HD046814,
and GM63495. Asterisk indicates corresponding author.
*S. L. Delp is with the Departments of Bioengineering and Mechanical En-
gineering, Stanford University, Clark Center, Room S-170, 318 Campus Drive,
Stanford, CA 94305-5450 USA (e-mail: delp@stanford.edu).
F. C. Anderson, A. S. Arnold, and E. Guendelman are with the Department
of Bioengineering, Stanford University, Stanford, CA 94305 USA (e-mail:
fca@stanford.edu; asarnold@alum.mit.edu; erang@stanford.edu).
P. Loan is with the MusculoGraphics Division of Motion Analysis Corpora-
tion, Chicago, IL 60640, USA (e-mail: peter@musculographics.com).
A. Habib is with Stanford University, Stanford, CA 94305 USA (e-mail:
ahabib@stanford.edu).
C. T. John is with the Computer Science Department, Stanford University,
Stanford, CA 94305 USA (e-mail: ctj@stanford.edu).
D. G. Thelen is with the Mechanical Engineering Department, University of
Wisconsin-Madison, Madison, WI 53706 USA (e-mail: thelen@engr.wisc.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TBME.2007.901024
of patients, both before and after treatment interventions. How-
ever, synthesizing detailed descriptions of the elements of the
neuromusculoskeletal system with measurements of movement
to create an integrated understanding of normal movement and
to establish a scientific basis for correcting abnormal movement
remains a major challenge.
Using experiments alone to understand movement dynamics
has two fundamental limitations. First, important variables,
including the forces generated by muscles, are not generally
measurable in experiments. Second, it is difficult to establish
cause-effect relationships in complex dynamic systems from
experimental data alone. As a result, elucidating the functions
of muscles from experiments is not straightforward. For ex-
ample, electromyographic (EMG) recordings can indicate when
a muscle is active, but examination of EMG recordings does
not allow one to determine which motions of the body arise
from a muscle’s activity. Determining how individual muscles
contribute to observed motions is difficult because a muscle
can accelerate joints that it does not span and body segments to
which it does not attach [1].
A theoretical framework is needed, in combination with ex-
periments, to uncover the principles that govern the coordination
of muscles during normal movement, to determine how neuro-
muscular impairments contribute to abnormal movement, and
to predict the functional consequences of treatments. To achieve
these goals, the theoretical framework must reveal the cause-ef-
fect relationships between neuromuscular excitation patterns,
muscle forces, and motions of the body.
A dynamic simulation of movement that integrates models
describing the anatomy and physiology of the elements of the
neuromusculoskeletal system and the mechanics of multijoint
movement provides such a framework. Muscle-driven dynamic
simulations complement experimental approaches by providing
estimates of important variables, such as muscle and joint
forces, which are difficult to measure experimentally. Simu-
lations also enable cause-effect relationships to be identified
and allow “what if?” studies to be performed in which, for
example, the excitation pattern of a muscle can be changed and
the resulting motion can be observed.
Although the value of dynamic simulations of movement is
broadly recognized [2]–[8], the field is fragmented. Many labo-
ratories develop their own simulation software, and do not pro-
vide this software to others; thus, it is difficult for a simula-
tion to be used or evaluated outside the laboratory where it is
developed. The inability to reproduce results is a major limi-
tation to advancing the science of biomedical simulation. Indi-
vidual investigators have made elegant contributions to simula-
tion technology, including the development of novel methods to
model muscle [9]–[11], simulate contact [12], [13], and repre-
0018-9294/$25.00 © 2007 IEEE
DELP et al.: OPENSIM: OPEN-SOURCE SOFTWARE TO CREATE AND ANALYZE DYNAMIC SIMULATIONS OF MOVEMENT 1941
sent musculoskeletal geometry [14]–[16], but it is difficult for
others to make use of these new techniques because the soft-
ware that implements them is generally unavailable. Since soft-
ware tools are not freely accessible to assist in the development,
analysis, and control of musculoskeletal dynamic simulations,
researchers typically must spend a great deal of time imple-
menting each new simulation and creating tools to analyze it.
Developing dynamic simulations of movement is technically
challenging, and many movement science laboratories lack the
resources or technical expertise to generate their own simula-
tions. These conditions create a major barrier to advancing sim-
ulation technology and achieving the scientific potential of mus-
culoskeletal simulations.
In the early 1990s, Delp and Loan introduced a muscu-
loskeletal modeling environment, called SIMM [17]–[19], that
lets users create, alter, and evaluate models of many different
musculoskeletal structures [20]–[22]. This software is now used
by hundreds of biomechanics researchers to create computer
models of musculoskeletal structures and to simulate move-
ments such as walking [23]–[25], cycling [26]–[28], running
[29], [30], and stair climbing [31]. Using SIMM, models of the
lower and upper extremities were developed to examine the
biomechanical consequences of surgical procedures including
tendon surgeries [32]–[38], osteotomies [39]–[41] and total
joint replacements [42]–[44]. A lower-extremity model was
used to estimate muscle-tendon lengths, velocities, moment
arms, and induced accelerations during normal and pathologic
gait [45]–[52]. Studies have been conducted to investigate the
treatment of individuals with spinal cord injury [53]–[56], to
analyze joint mechanics in subjects with patellofemoral pain
[57], [58], to calculate forces at the knee during running [59]
and cutting [60], to examine the influence of foot positioning
and joint compliance on the occurrence of ankle sprains [61],
[62], and to investigate causes of abnormal gait [63]–[65].
These studies have demonstrated the utility of musculoskeletal
models and dynamic simulations for analyzing the causes of
gait abnormalities and the effects of various treatments. SIMM
has helped bring simulation to biologists who have created
computational models of the frog [66], [67], Tyrannosaur [22],
cockroach [68], and other animals.
Although SIMM helps users formulate models of the muscu-
loskeletal system and dynamic simulations of movement, it pro-
vides no assistance with the computation of muscle excitations
that produce coordinated movement and has limited tools for an-
alyzing the results of dynamic simulations. Furthermore, SIMM
and other commercial packages, such as Visual 3-D (C-Motion
Inc.), Anybody (Anybody Technology) or Adams (MSC Soft-
ware Corp.), do not provide full access to source code, which
makes it difficult for biomechanics researchers to extend their
capabilities. Over the past decade, new software engineering
methods have emerged that enable the development of software
systems that are more extensible. We view this as an opportunity
to develop a simulation platform that engages a broader spec-
trum of the biomechanics community.
We have established an open-source simulation environment,
called OpenSim, to accelerate the development and sharing of
simulation technology and to better integrate dynamic simula-
tions into the field of movement science (Fig. 1). Open-source
software development has become a successful strategy for
Fig. 1. Schematic of OpenSim, an open source software system for modeling,
simulating, and analyzing the neuromusculoskeletal system. OpenSim is built
on top of core computational components that allow one to derive equations
of motion for dynamical systems, perform numerical integration, and solve
constrained non-linear optimization problems. In addition, OpenSim offers
access to control algorithms (e.g., computed muscle control), actuators (e.g.,
muscle and contact models), and analyses (e.g., muscle-induced accelerations).
OpenSim integrates these components into a modeling and simulation plat-
form. Users can extend OpenSim by writing their own plug-ins for analysis or
control, or to represent neuromusculoskeletal elements (e.g., muscle models).
In a graphical user interface, the user is able to access a suite of high-level tools
for viewing models, editing muscles, plotting results, and other functions. Sim-
Track, one of the OpenSim tools, enables accurate muscle-driven simulations
to be generated that represent the dynamics of individual subjects. OpenSim
is being developed and maintained on Simtk.org; all of the software is freely
available.
both commercial and academic efforts (e.g., the Linux operating
system). Making source code available enables researchers to
reproduce results produced by other laboratories and to make
improvements and adapt code to meet their needs. Modern
plug-in technology, which we have adopted, lets users extend
software functionality and allows new tools to be shared more
easily. We believe that the biomechanics community will
benefit from a greater degree of collaboration as a result of an
open-source effort.
Enticing researchers to help develop and test open-source
software requires the initial developers to provide tools that
others can use and extend. OpenSim provides two. The first
comprises a set of modeling and analysis tools that complement
those included in SIMM [17], [19]. The second, SimTrack, en-
ables researchers to generate dynamic simulations of movement
from motion capture data.
This article first provides a brief overview of OpenSim. We
then focus on SimTrack and how simulations that characterize
the dynamics of individual subjects can assist in treatment plan-
ning. We describe a method to generate subject-specific simula-
tions and present a case study, in which we used a dynamic simu-
lation of a subject with stiff-knee gait to understand the causes of
1942 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 11, NOVEMBER 2007
his abnormal movement and the effects of possible treatments.
We close with a review of the challenges for the field.
II. W
HAT
IS
OPENSIM?
OpenSim is an open-source platform for modeling, sim-
ulating, and analyzing the neuromusculoskeletal system. It
includes low-level computational tools that are invoked by
an application (Fig. 1). A graphical user interface provides
access to key functionality. OpenSim is being developed and
maintained on Simtk.org by a growing group of participants.
Simtk.org serves as a public repository for data, models, and
computational tools related to physics-based simulation of
biological structures.
The software is written in ANSI C++, and the graphical user
interface is written in Java, allowing OpenSim to compile and
run on common operating systems. Open-source, third-party
tools are used for some basic functionality, including the Xerces
Parser from the Apache Foundation for reading and writing
XML files (xml.apache.org/xerces-c) and the Visualization
Toolkit from Kitware for visualization (www.vtk.org). Use of
plug-in technology allows low-level computational components
such as dynamics engines, integrators, and optimizers to be
updated as appropriate without extensive restructuring. For
example, OpenSim initially used SDFast (Parametric Tech-
nology Corp.) as its dynamics engine; however, current releases
will allow Simbody
to be used as well. Simbody™ is an
open-source order-n dynamics engine under development at
Simtk.org.
The plug-in architecture of OpenSim encourages users to
extend functionality by developing their own muscle models,
contact models, controllers, and analyses. For example, about
a dozen analysis plug-ins, authored by different users, are
available in OpenSim. These analysis tools calculate joint
forces, muscle-induced accelerations, muscle powers, and other
variables. Although these analyses were developed for different
musculoskeletal models, they have general applicability and
can be used with any OpenSim model. The plug-in architecture
of OpenSim thus provides a means of rapidly disseminating
new functionality to the biomechanics community.
To add a plug-in (e.g., an analysis), a user must write a
new C++ class (e.g., InducedAcceleration) derived from the
appropriate base class (e.g., Analysis), implement a number
of required methods, and compile the class into a dynamically
linked library. The new plug-in (e.g., the InducedAcceleration
analysis) can then be used in simulations and shared with
other users. Independently, plug-ins can also be developed to
enhance the capabilities of the graphical user interface. The
user interface gets nearly all its functionality from plug-ins. For
example, the modules for motion viewing, plotting, and muscle
editing are all plug-ins. A user interface plug-in example is
provided with OpenSim that users can adapt to extend the
functionality of the graphical interface. Like the low-level C++
plug-ins for analyses, muscle models, controllers, etc., user
interface plug-ins can be shared with other users.
The OpenSim graphical user interface includes a suite of tools
for analyzing musculoskeletal models, generating simulations,
and visualizing results (Fig. 2). Some of the basic functionality
of SIMM is available in OpenSim, including, for example, the
Fig. 2. Screenshot from OpenSim. Models of many different musculoskeletal
structures, including the lower extremity, upper extremity, and neck, can be
loaded, viewed and analyzed. Muscles are shown as red lines; virtual markers
are shown as blue spheres.
ability to edit muscles and plot variables of interest. In addi-
tion, SIMM joint (*.jnt) and muscle (*.msl) files [18] can be
imported. OpenSim provides simulation and control capabilities
that complement SIMM. SimTrack, in particular, is a tool ca-
pable of generating muscle-actuated simulations of subject-spe-
cific motion quickly and accurately, as described below.
III. S
IMTRACK:AN OPENSIM TOOL FOR GENERATING
DYNAMIC SIMULATIONS
To create a muscle-driven simulation of a movement, one
must first formulate a dynamic model of the musculoskeletal
system and its interactions with the environment. The elements
of the musculoskeletal system are modeled by sets of differential
equations that describe muscle contraction dynamics, muscu-
loskeletal geometry, and body segmental dynamics. These equa-
tions characterize the time-dependent behavior of the muscu-
loskeletal system in response to neuromuscular excitation. Once
a dynamic model of the musculoskeletal system is formulated,
the next step is to find a pattern of muscle excitations that pro-
duce a coordinated movement. Excitations may be found by
solving an optimization problem in which the objective of a
motor task is defined (e.g., jumping as high as possible) or in
which the objective is to drive a dynamic model to “track” ex-
perimental motion data [69]. Simulations are generally evalu-
ated by how well they agree with experimentally measured kine-
matics, kinetics, and EMG patterns. Once a simulation is created
and its accuracy is tested, it can be analyzed to examine the con-
tributions a muscle makes to the motions of the body and the
consequences of a simulated treatment.
Determining a set of muscle excitations that produce a coor-
dinated movement is one of the major challenges in creating a
dynamic simulation. Historically, the computational cost of gen-
erating coordinated muscle-actuated simulations of movement
has been high, requiring days, weeks, or months of computer
time [23], [65], [70]. Recent breakthroughs in the application
DELP et al.: OPENSIM: OPEN-SOURCE SOFTWARE TO CREATE AND ANALYZE DYNAMIC SIMULATIONS OF MOVEMENT 1943
Fig. 3. Steps for generating a muscle-driven simulation of a subject’s motion with SimTrack. The inputs are a dynamic musculoskeletal model, experimental
kinematics (i.e., x-y-z trajectories of marker data, joint centers, and joint angles), and experimental reaction forces and moments obtained from a subject. In Step
1, the experimental kinematics are used to scale the musculoskeletal model to match the dimensions of the subject. In Step 2, an inverse kinematics (IK
) problem
is solved to find the model joint angles that best reproduce the experimental kinematics. In Step 3, a residual reduction algorithm (RRA) is used to re
fine the
model kinematics so that they are more dynamically consistent with the experimental reaction forces and moments. In Step 4, a computed muscle control
(CMC)
algorithm is used to find a set of muscle excitations that will generate a forward dynamic simulation that closely tracks the motion of the subject.
of robotic control techniques to biomechanical simulation have
dramatically reduced the time needed to generate such simu-
lations [28], [71]. For example, the computed muscle control
technique determines muscle excitations that reproduce mea-
sured pedaling dynamics in just ten minutes [28]; this is over
two orders of magnitude faster than conventional dynamic op-
timization techniques. Thelen and Anderson extended this ap-
proach to compute muscle excitation patterns that drove a 21-de-
gree-of-freedom, 92-muscle model to track experimental gait
data of 10 healthy adults [25]. A simulation of a half-cycle
of gait was generated in approximately 30 minutes. The speed
of this technique makes it practical to generate subject-specific
simulations of a wide variety of movements.
SimTrack guides users through four steps to create a dy-
namic simulation (Fig. 3). As input, SimTrack takes a dynamic
model of the musculoskeletal system and experimentally-mea-
sured kinematics and reaction forces and moments. While
this approach is general, we will describe it in the context of
generating simulations of gait, since this is one of the most
challenging applications.
In Step 1, a dynamic musculoskeletal model (e.g., a SIMM
model [19]) is scaled to match the anthropometry of an indi-
vidual subject. The dimensions of each body segment in the
model are scaled based on relative distances between pairs of
markers obtained from a motion-capture system and the corre-
sponding virtual marker locations in the model (e.g., see blue
spheres in Fig. 2). The mass properties of the body segments are
scaled proportionally so that the total measured mass of the sub-
ject is reproduced. Muscle fiber lengths and tendon slack lengths
of the muscle-tendon actuators are scaled so that they each re-
main the same percentage of total actuator length.
In Step 2, an inverse kinematics (IK) problem is solved
to determine the model generalized coordinate values (joint
angles and translations) that best reproduce the raw marker
data obtained from motion capture. Step 2 is formulated as
a least-squares problem that minimizes the differences be-
tween the measured marker locations and the model’s virtual
marker locations, subject to joint constraints [72]. If the ex-
perimental kinematics includes a set of joint centers or joint
angles produced by motion-capture software, these may also
be included in the formulation. Therefore, for each frame in the
experimental kinematics, the inverse kinematics problem is to
minimize the weighted squared error
(1)
where
and are the three-dimensional posi-
tions of the
th marker or joint center for the subject and model,
and are the values of the th joint angle for the
subject and model, and
and are factors that allow markers
and joint angles to be weighted differently.
Due to experimental error and modeling assumptions,
measured ground reaction forces and moments are often dy-
namically inconsistent with the model kinematics. In Step 3,
a residual reduction algorithm (RRA) is applied to make the
model generalized coordinates (joint angles and translations)
computed in Step 2 more dynamically consistent with the
measured ground reaction forces and moments. From Newton’s
second law, the following equation relates the measured ground
reaction force and gravitational acceleration to the accelerations
of the body segments
(2)
where
is the measured ground reaction force minus the
body weight vector,
is the translational acceleration of the
center of mass of the
th body segment, is the mass of the
th body segment, and is the residual force. An analo-
gous equation relates the ground reaction moment to the model
kinematics and the residual moment. In the absence of exper-
imental and modeling error, the residual force should be zero
(i.e.,
). In practice, this is never the case. Through
a combination of slight, controlled perturbations to the motion
trajectory, and small adjustments to the mass parameters of the
model, it is possible to reduce the residual forces and moments
required for dynamic consistency. To reduce the residual forces
1944 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 11, NOVEMBER 2007
and moments, the residuals are computed and averaged over the
duration of the movement. Based on these averages, the algo-
rithm recommends changes in the model mass parameters, such
as the location of the center of mass of the trunk, that reduce the
average values of the residuals over the duration of the move-
ment. Following any adjustments to the mass parameters, a con-
trol problem is solved in which all degrees of freedom of the
model are actuated. In particular, the joints are actuated by ide-
alized joint moments, and, in addition, three residual forces and
three residual moments are applied to a chosen segment of the
model to control the six degrees of freedom between the model
and the ground (i.e., three translations and three rotations). If
no limits are placed on the residuals, the kinematics can be
tracked with little or no error. However, at the user’s discretion,
upper limits can be placed on the magnitudes of the residuals, in
which case the motion of the model is altered yielding a new set
of kinematics that are dynamically consistent with the limited
residuals. A performance criterion is used to distribute tracking
errors across the joint angles
(3)
where
is a factor weighting the relative importance of the th
joint, and
is the desired acceleration of the th degree
of freedom given by a proportional-derivative control law [28].
The values for the model degrees of freedom and mass proper-
ties output by the residual reduction algorithm are used as input
to Step 4.
In Step 4, computed muscle control (CMC) is used to gen-
erate a set of muscle excitations that produce a coordinated
muscle-driven simulation of the subject’s movement. Computed
muscle control uses a static optimization criterion to distribute
forces across synergistic muscles and proportional-derivative
control to generate a forward dynamic simulation that closely
tracks the kinematics derived in Step 3 [25]. Although a static
performance criterion is used, the full state equations repre-
senting the activation and contraction dynamics of the muscles
are incorporated into the forward dynamic simulation. Activa-
tion dynamics is modeled by relating the time rate of change
of muscle activation
to muscle activation and excitation
(4)
where
and are the time constants for activation
and deactivation. Musculotendon contraction dynamics is
described by a lumped-parameter model that accounts for the
force-length-velocity properties of muscle and the elastic prop-
erties of tendon. In particular, the time rate of change of muscle
length
is related to muscle length , musculotendon
actuator length
, and muscle activation
(5)
where
is the force velocity relation for muscle. In our cur-
rent implementation, the force between the foot and the ground
is not modeled; rather, the measured ground reaction forces and
moments are applied directly to the foot. When analyzing a sim-
ulation, as described in the case study below, spring-damper el-
ements are introduced between the foot and the ground to allow
the reaction forces and moments to respond to perturbations
(e.g., altered muscle forces).
IV. C
ASE
STUDY
We have generated dynamic simulations of individual sub-
jects with abnormal gait using computed muscle control [25]
to examine the causes of their abnormal walking pattern and to
simulate treatment options. This case study demonstrates how
simulations can provide insight into the causes of stiff-knee
gait, a condition in which swing-phase knee flexion is sub-
stantially diminished. Reduced knee flexion is often attributed
to excessive excitation of the rectus femoris during the swing
phase [73]. However, factors that limit knee flexion velocity
just before swing, such as excessive force in vasti or rectus
femoris, or diminished force in iliopsoas or gastrocnemius,
may also reduce knee flexion during swing [74]. Determining
which, if any, of these factors limit an individual’s knee flexion
is challenging because current diagnostic methods cannot
evaluate how forces produced by the rectus femoris or other
muscles influence swing-phase knee motions.
There are several options for treatment of stiff-knee gait.
One option, botulinum toxin injection, theoretically decreases
the hip and knee moments generated by the rectus femoris. A
second option, rectus femoris transfer, theoretically decreases
the muscle’s knee extension moment while leaving its hip
flexion moment intact. At present, the mechanisms responsible
for patients’ improvements in swing-phase knee flexion fol-
lowing these treatments are not well understood. In this case
study, we generated and analyzed a dynamic simulation of a
subject with stiff-knee gait to determine the biomechanical
cause of his diminished knee flexion and the potential conse-
quences of different treatment options (Fig. 4).
The subject was a 12-year-old male diagnosed with spastic
cerebral palsy. His left lower limb exhibited limited knee flexion
during swing and abnormal activity of rectus femoris (preswing
and swing) and vasti (preswing). We represented the subject’s
musculoskeletal system by a scaled, 21-degree-of-freedom
linkage actuated by 92 muscles and generated a forward dy-
namic simulation of the subject’s gait. The simulated joint
angles reproduced the subject’s measured knee flexion angle to
within 2
(Fig. 5, “simulated”).
We evaluated the contributions of rectus femoris, vasti, and
other muscles to knee flexion by altering muscle excitations in
the simulation and computing the resulting changes in peak knee
flexion. Analysis of the subject’s dynamic simulation suggested
that excessive activity of the knee extensors in preswing was
the major cause of his stiff-knee gait. Decreasing the excitation
of rectus femoris or vasti during preswing increased peak knee
flexion substantially (Fig. 5, curves A and B). Decreasing the
excitation of rectus femoris in early swing had a negligible effect
on peak knee flexion (Fig. 5, curve C).
We examined the potential biomechanical consequences
of botulinum toxin injection and rectus femoris transfer.
Botulinum toxin injection was simulated by decreasing the
excessive excitation of rectus femoris while leaving its passive
