rsif.royalsocietypublishing.org
Research
Cite this article: Rankin JW, Rubenson J,
Hutchinson JR. 2016 Inferring muscle
functional roles of the ostrich pelvic limb
during walking and running using computer
optimization. J. R. Soc. Interface 13: 20160035.
http://dx.doi.org/10.1098/rsif.2016.0035
Received: 14 January 2016
Accepted: 7 April 2016
Subject Category:
Life Sciences–Engineering interface
Subject Areas:
biomechanics
Keywords:
musculoskeletal model, inverse dynamics,
forward dynamics, OpenSim, static
optimization, computed muscle control
Author for correspondence:
Jeffery W. Rankin
e-mail: jrankin@rvc.ac.uk
Electronic supplementary material is available
at http://dx.doi.org/10.1098/rsif.2016.0035 or
via http://rsif.royalsocietypublishing.org.
Inferring muscle functional roles of the
ostrich pelvic limb during walking and
running using computer optimization
Jeffery W. Rankin1, Jonas Rubenson2,3 and John R. Hutchinson1
1Structure and Motion Laboratory, Department of Comparative Biomedical Sciences, The Royal Veterinary
College, Hawkshead Lane, Hatfield, Herts, UK
2Department of Kinesiology, Pennsylvania State University, University Park, PA, USA
3School of Sport Science, Exercise and Health, The University of Western Australia, Perth, Western Australia,
Australia
JWR, 0000-0002-6639-8280; JRH, 0000-0002-6767-7038
Owing to their cursorial background, ostriches (Struthio camelus) walk and
run with high metabolic economy, can reach very fast running speeds and
quickly execute cutting manoeuvres. These capabilities are believed to be
a result of their ability to coordinate muscles to take advantage of specialized
passive limb structures. This study aimed to infer the functional roles of
ostrich pelvic limb muscles during gait. Existing gait data were combined
with a newly developed musculoskeletal model to generate simulations of
ostrich walking and running that predict muscle excitations, force and mech-
anical work. Consistent with previous avian electromyography studies,
predicted excitation patterns showed that individual muscles tended to be
excited primarily during only stance or swing. Work and force estimates
show that ostrich gaits are partially hip-driven with the bi-articular hip–
knee muscles driving stance mechanics. Conversely, the knee extensors
acted as brakes, absorbing energy. The digital extensors generated large
amounts of both negative and positive mechanical work, with increased
magnitudes during running, providing further evidence that ostriches
make extensive use of tendinous elastic energy storage to improve economy.
The simulations also highlight the need to carefully consider non-muscular
soft tissues that may play a role in ostrich gait.
1. Introduction
Ostriches (Struthio camelus) walk and run with high metabolic economy [1–3],
can reach very fast running speeds [4,5], and quickly execute cutting (turning)
manoeuvres [6]. The ability to achieve such impressive performance is thought
to largely arise from morphological specializations within the pelvic limbs as
result of their cursorial and secondarily flightless evolutionary background.
Like other birds, ostriches use three-dimensional limb joint motions during
locomotion [6–8] and have specialized passive structures at the hip, including
bony stops (e.g. the antitrochanter), which play an unclear role during move-
ment [9–14]. The distal limb muscles are also highly specialized, consisting
of extremely long tendons that cross mobile metatarsophalangeal (MTP)
joints. Experimental studies of these features in ostriches and other birds
support the inference that they improve gait performance and economy
[2,15–18]. However, these adaptations also contribute to the extremely complex
ostrich pelvic limb musculoskeletal structure, which consists of more than
30 muscles—the majority of which are multiarticular—that cross joints with
multiple degrees of freedom (DOF). As a result, little can be intuitively inferred
about specific functional roles that individual pelvic limb muscles perform in
ostriches (or many other birds) during gait. Obtaining the data required to
& 2016 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution
License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original
author and source are credited.
determine muscle function is further limited owing to the
numerous challenges associated with the required experimental
techniques (e.g. electromyography (EMG), sonomicrometry,
tendon buckles). To date, these factors have obscured how
ostriches and other birds successfully meet the biomechanical
demands of walking and running.
During a movement, the functional role of a muscle–
tendon unit (MTU) can be established based on a combination
of muscular force generation and muscle and tendon length
trajectories [19–21]. If an MTU generates high force and posi-
tive power (concentric contraction) during the movement,
then energy is added to the system and the MTU can be classi-
fied as a ‘motor’. In contrast, an MTU that generates high force
but negative power (eccentric contraction) removes energy
from the system and acts as a ‘brake’. In some cases, an
MTU may generate high forces but produce very little positive
or negative power (i.e. no length change) during the move-
ment. In this case, the MTU has not added or removed
energy from the system and acts as a joint stabilizer or ‘strut’.
Last, an MTU may generate high force and switch from nega-
tive to positive power production. In this case, the net energy
provided to the system is again near zero. However, the
MTU has undergone a systematic change in length and likely
acts as a ‘spring’, storing energy from an earlier portion of
the movement that can be released later. To define an MTU’s
functional role(s) in this study, muscle excitation timing is
first used to classify whether or not a muscle primarily contrib-
utes to ‘stance’ (i.e. when the foot is in contact with the ground)
or ‘swing’ (i.e. no foot–ground contact) movements, when
possible [22,23]. Following this classification, specific muscle
roles (i.e. motor, brake, strut or spring) during stance and
swing are then determined using MTU force and length.
These roles can then be used to infer how individual muscles
contribute to the overall mechanical energy flow during gait.
Because the aforementioned difficulties associated with
experimental approaches limit their usefulness, an alternative
approach is to use realistic, detailed musculoskeletal models
and simulations. The first simple ostrich model was developed
over 35 years ago by Alexander et al. [4] to estimate muscle and
bone stress during running. More recently, two-dimensional
ostrich models have been developed to investigate postural
effects on running joint mechanics [5] and to validate running
posture [24] and maximal speed [25] predictions for various
extinct taxa. Until very recently, only a single model of loco-
motion has included muscle geometry, which was limited to
six muscles [25]. However, we have just published a highly
detailed musculoskeletal model of an ostrich’s pelvic limbs,
building on prior efforts [26]. Similar approaches have been
successfully used to address many questions in human
gait: providing insights into muscle function [27–29] and
form–function relationships [30,31].
Like most animal musculoskeletal systems, the ostrich pelvic
limb has many more muscles than DOF. As a result, multiple
muscle excitation patterns exist to produce identical joint mech-
anics. Knowing how to correctly ‘parse’ the different muscle
contributions to the net joint mechanics during movement is
critical to understanding muscle functional roles. Two distinct
approaches have been used to overcome this major challenge:
static and dynamic optimization [32–34]. Static optimization
(SO) addresses each instant in time as an independent data
point, reducing computational cost but ignoring time-dependent
quantities such as activation–deactivation dynamics and tendon
strain energy. Dynamic optimization techniques can account for
these time-dependent quantities, but incur a high computational
cost. There remains considerable debate over which (if either) is
more suitable than another for studying muscle function during
movement, in large part because a gold standard (i.e. empirical
dataset) is not readily available for comparison. For example,
Anderson & Pandy [35], after simulating half-gait cycles of
human walking, suggested that static and dynamic optimization
solutions were ‘practically equivalent’, but qualified their state-
ment and provided scenarios in which dynamic optimization
may be necessary. Later comparisons between the two
approaches in other human movements have been inconclusive
in determining a preferred technique for predicting muscle
activity [36–38]. Because of the large number of differences
that exist between humans and ostriches in both limb mor-
phology and gait mechanics [2], determining how sensitive
muscle functional roles (and by extension structure–function
relationships) between these two techniques during ostrich
gait could help future comparative research focused on
movement in different species.
The primary purpose of this study was to determine the
functional roles that individual pelvic limb muscles have in
ostriches during walking and running. Existing biomechanical
data were combined with a newly developed, detailed ostrich
musculoskeletal model [39] to generate computer simulations
that estimate MTU excitation, length and force during the
two gaits. A secondary purpose was to assess how sensitive
muscle functional roles are to choice of optimization approach
(static versus dynamic) using a model that widely diverges in
morphology from humans and a higher speed movement than
those investigated previously. These two purposes are linked,
because methodological assumptions of static versus dynamic
analysis [5,25,35] might influence biological conclusions about
the functions of particular muscles, which can be tested by
achieving these two major aims.
2. Methods
A detailed musculoskeletal model of the ostrich pelvic limb [39]
was combined with experimental data obtained from a represen-
tative walking and running trial [2,8,39] within OpenSim [40] to
generate six different simulations (three for each motion, table 1).
Two simulations (WSO, RSO) were performed using OpenSim’s
SO routine [41]. Two additional simulations (WCMCC, RCMCC)
were then generated using OpenSim’s computed muscle control
(CMC) routine [42]. The final two simulations (WCMCR, RCMCR)
were generated using CMC, but tendons were constrained to
be rigid in order to provide a direct comparison with the SO sol-
ution, which did not incorporate tendon dynamics, whereas the
other two CMC simulations (WCMCC, RCMCC) did. The simulations
estimated MTU excitation patterns, force and length, which
were used to infer muscle function. Details of the musculo-
skeletal model, optimization framework and experimental data
are given below.
2.1. Musculoskeletal model
The original musculoskeletal model was created using muscle
and tendon architecture, digitized muscle paths and computed
tomography (CT) scan data collected via dissection [39]. The
left pelvic limb was generated by mirroring the right-side
segments, joint definitions and muscle tendon paths about the
sagittal plane. The model consisted of nine rigid body segments
representing the pelvis and left and right-side femur, tibiotarsus,
tarsometatarsus and pes (figure 1). The original model’s segment
mass and inertia values were scaled using the original ostrich’s
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
2
body mass (65.3 kg) and mass of the bird that provided the
experimental data (78.7 kg; see §2.3).
Each pelvic limb had 8 DOF representing the hip (3 DOF),
knee (3 DOF), ankle (1 DOF) and MTP (1 DOF) joints. In the orig-
inal model, both the ankle and MTP joints were modelled as
3 DOF (ball-and-socket) joints. However, minimal long axis
rotation and ad/abduction have been observed in the avian
ankle and MTP during walking and running [7,8,43,44] and
these DOFs were constrained to match experimental mid-stance
values. The pelvis moved freely relative to the ground (i.e. three
translational and three rotational DOFs).
Model segments were driven by a combination of musculo-
tendon and idealized joint (coordinate) actuators (figure 1).
Thirty-four of the 35 musculotendon actuators from the original
model were retained on the right side, which represented the
major muscles in the ostrich pelvic limb (FCLA was removed
due to its very low maximum force [39]). Musculotendon actua-
tors were modelled using a Hill-type model that included
intrinsic force–length–velocity relationships [45]. Because walking
and running are everyday activities and critical to survival, it
is likely that MTU properties are tuned so force and power gener-
ation are near optimal during these movements [46,47]. However,
many muscles in the original model did not reflect this, with nor-
malized fibre lengths exceeding the physiological operating range
of 0.5–1.5 optimal fibre lengths in some postures. In the original
model, tendon slack lengths (Ltsl) were estimated based on joint
range of motion [39,48], which may not reflect tuning for major
activities like gait. To correct for this inconsistency, the original
model’s Ltsl were systematically adjusted, so that muscle fibre
lengths operated over a more optimal range (i.e. 0.75–1.25 optimal
fibre length) in the joint ranges of motion defined by the exper-
imental gait kinematics. New Ltsl were within 10% of the
original model values for all actuators except for M. iliotibialis
(ILa, ILp, 19%) and M. femorotibialis intermedius (FMTIM,
19%). Maximum isometric forces were scaled using the mass
ratio between the original model and experimental subject
(table 2). For all musculotendon actuators, maximum contraction
velocity was set to 14 Lfopts21 [49]. Excitation–activation dynamics
were represented by a first-order differential equation with acti-
vation and deactivation time constants of 10 and 15 ms. As the
left side’s movement was assumed to be symmetric with the
right side (see §2.3 Experimental data), the model was simplified
by having the left side’s joints actuated by eight idealized torque
actuators—one for each DOF.
Six additional actuators were used to compensate for residual
forces and moments at the pelvis during the motion and eight
torque actuators—one for each DOF in the right limb—were
used to compensate for mechanical work that could not be satis-
fied by the muscles alone (reserve actuators). Each optimization
was tasked with minimizing the use of these reserve actuators,
ensuring that, at each joint, the required joint moments were
satisfied primarily through muscle force.
2.2. Simulations
Three simulations were generated from the experimental walking
data. Each simulation used the same experimental data and mus-
culoskeletal model as inputs, but used a different optimization
framework to estimate MTU excitation, force and length changes.
Three additional simulations were then generated from the exper-
imental running data using the same model and optimization
frameworks (table 1).
Simulations were first generated using the SO routine
included in OpenSim. SO determines MTU excitation patterns
by optimizing a predetermined objective criterion subject to the
biomechanical constraints associated with the motion. The objec-
tive criterion used here minimized muscle activation squared,
(b)
(a)
Figure 1. Musculoskeletal model at mid-stance during running. The arrow (blue) indicates the direction and location (centre of pressure) of the ground reaction
force. Muscle–tendon actuators (red lines) of the left limb were replaced by idealized joint actuators. (a) Sagittal view. (b) Frontal view.
Table 1. Names and description of the six simulations performed.
Simulations were performed for either a walking or running motion (rows)
using three different optimization frameworks (columns).
simulation
motion
static
optimization
computed
muscle
control (rigid
tendon)
computed
muscle control
(compliant
tendon)
walking
WSO
WCMCR
WCMCC
running
RSO
RCMCR
RCMCC
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
3
Table 2. Muscle–tendon actuator properties. Optimal ﬁbre lengths and pennation angles are from the original model by Hutchinson et al. [39] but provided
for reference.
abbreviation
muscle name
maximum isometric
force (Fiso, N)
optimal ﬁbre
length (Lfopt, m)
tendon slack
length (Ltsl, m)
pennation
angle (88888)
IC
M. iliotibialis cranialis
889
0.174
0.0451
0
ILa
M. iliotibialis lateralis (cranial part)
1265
0.174
0.2432
0
ILp
M. iliotibialis lateralis (caudal part)
1265
0.174
0.3099
0
AMB1
M. ambiens, ventral (pubic) head
971
0.039
0.1648
10
AMB2
M. ambiens, dorsal (iliac) head
1793
0.044
0.3941
15
FMTL
M. femorotibialis lateralis
1434
0.088
0.1746
15
FMTIM
M. femorotibialis intermedius
1706
0.084
0.1863
25
FMTM
M. femorotibialis medialis
1089
0.089
0.0603
30
ILFBa
M. ilioﬁbularis (cranial part)
1254
0.176
0.2134
0
ILFBp
M. ilioﬁbularis (caudal part)
1254
0.176
0.2733
0
ITCa
M. iliotrochantericus caudalis
(cranial part)
897
0.064
0.0469
25
ITCp
M. iliotrochantericus caudalis
(caudal part)
897
0.064
0.038
25
IFE
M. iliofemoralis externus
479
0.025
0.0667
25
ITM
M. iliotrochantericus medius
181
0.058
0.0241
0
ITCR
M. iliotrochantericus cranialis
330
0.053
0.0488
10
IFI
M. iliofemoralis internus
410
0.041
0.0533
0
FCM
M. ﬂexor cruris medialis
1109
0.036
0.435
35
FCLP
M. ﬂexor cruris lateralis
pars pelvica
544
0.24
0.2449
0
ISF
M. ischiofemoralis
419
0.033
0.0816
15
PIFML
M. puboischiofemorales
medialis þ lateralis
816
0.089
0.1669
15
OM
M. obturatorius medialis
3124
0.055
0.1651
25
CFP
M. caudofemoralis pars pelvica
(et caudalis)
1125
0.108
0.215
15
GL
M. gastrocnemius pars lateralis
1836
0.12
0.5818
20
GIM
M. gastrocnemius pars intermedius
798
0.125
0.507
15
GM
M. gastrocnemius pars medialis
3124
0.094
0.5957
20
FL
M. ﬁbularis longus
2270
0.081
0.9633
20
FDL
M. ﬂexor digitorum longus
1130
0.048
1.0366
20
FPPD3
M. ﬂexor perforans et perforatus
digitorum 3
1154
0.025
1.0737
30
FPD3
M. ﬂexor perforans digitorum 3
3210
0.017
1.02
35
FPD4
M. ﬂexor perforans digitorum 4
1434
0.026
1.004
20
FHL
M. ﬂexor hallucis longus
469
0.04
1.0939
25
EDL
M. extensor digitorum longus
833
0.049
0.8512
30
TCf
M. tibialis cranialis
(femoral head)
686
0.045
0.4791
25
TCt
M. tibialis cranialis
(tibial head)
686
0.045
0.4215
25
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
4
summed across all muscles at each time step [33]
J ¼ min
X
34
m¼1
a2
m,
ð2:1Þ
where am is the activation level of the mth muscle. The time step
was set to 0.005 s and MTU excitation, force and length time his-
tories were obtained over the gait cycle. MTU force calculations
included intrinsic muscle force–length–velocity relationships
[45]. Because each time step is solved independently within the
SO framework, there is neither energy transfer between time
steps (e.g. tendon energy storage and return) nor muscle
excitation–activation dynamics. Passive fibre force generation is
also ignored, and tendons are assumed rigid with all MTU
length changes occurring in the muscle fibres.
The second optimization framework used to generate simu-
lations was OpenSim’s CMC routine [42]. CMC is a hybrid
forward–inverse approach, with muscle excitations for each
time step determined using the same objective criterion as the
SO routine. However, like purely forward dynamic simulations,
the model state from a previous time step (e.g. joint angles,
muscle activation level, tendon strain) influences the optimal
solution for the current step. Because time steps are linked, this
approach incorporates muscle excitation–activation dynamics
and non-rigid tendon characteristics. Passive muscle fibre force
generation is also accounted for.
In order to reduce the potentially confounding factors of differ-
ent tendon and muscle models when directly comparing between
SO and CMC, a third optimization framework was implemented.
This approach was identical to the previous CMC framework, with
the exception that, like SO, a rigid tendon model was implemented,
and muscle passive force generation was removed. Using rigid
tendons eliminates tendon–muscle fibre dynamics and partially
negates the ability of a forward dynamics optimization to account
for time-dependent muscle interactions (e.g. tendon energy storage
and return). As a result, using this framework would not be a realistic
choice under normal circumstances. However, eliminating these
potentially confounding factors allows for a more direct comparison
between the SO and CMC frameworks.
2.3. Experimental data
Experimental data for a representative walking (1.2 ms21; 0.66
duty factor) and running trial (3.5 ms21; 0.40 duty factor) were
taken from a single adult bird (78.7 kg) of a previously collected
dataset [2,8,39]. Three-dimensional segment and joint kinematics
were calculated from retro-reflective marker clusters located on
the pelvis, right-side femur, tibiotarsus and tarsometatarsus, and
a single marker on digit III. Marker locations were recorded at
200 Hz using high-speed video (Peak Performance; Centennial,
CO). Ground reaction forces were simultaneously collected
using a Kistler force plate (model 9865E, Kistler, Winterthur,
Switzerland). Data were filtered in OpenSim using a low-pass fre-
quency of 10 Hz. Because only right-side data were collected
experimentally, left-side motion and force data were estimated
by mirroring the right-side data about the sagittal plane and
phase-shifting the data 1808 to generate a complete gait cycle.
2.4. Analysis
In each simulation, muscle excitation onset and offset timings
were determined from the predicted muscle excitation patterns,
with muscles considered to be excited when the values exceeded
a 0.1 (i.e. 10% of maximum excitation) threshold. A period of
excitation was then determined by first identifying the onset
time as the closest previous time step where excitation fell
below 0.05. Offset time was then identified as the first subsequent
point that excitation fell below 0.05. Stance (i.e. foot in contact
with the ground) and swing phases were identified and timing
values were used to group muscles into ‘stance’ or ‘swing’
groups. Predicted muscle excitation onset and offset times were
then normalized to the entire gait cycle and compared with
existing avian EMG data [22,23] as a form of indirect validation.
MTU force and length time histories were used to generate com-
parisons among the six simulations. First, average muscle forces
were calculated as the mean force value during stance and swing.
An ‘integrated activation’ (iAct) value was also calculated for the
two phases. To calculate iAct, the stance and swing phases were
first normalized to per cent phase. The activation trajectory was
then integrated over the entire phase to generate a single activity
value ranging from 0 (no activity) to 100 (maximally active over
the entire phase). Net MTU work was calculated for each muscle
from the instantaneous MTU force and velocity values over the
entire gait cycle. Positive and negative work were calculated for
stance and swing by integrating only the positive and negative por-
tions of the power curves of each MTU within each phase. Muscles
were grouped based on anatomical location, creating seven distinct
groups: (i) hip rotators (ITCa, ITCp, ITCR, ITM), (ii) biarticular
hip–knee (ILa, ILp, ILFBa, ILFBp, FCLP, FCM), (iii) knee extensors
(FMTL, FMTIM, FMTM), (iv) gastrocnemius (GL, GIM, GM), (v)
digital flexors (FDL, FHL, FL, FPPD3, FPD3, FPD4), (vi) ankle flexors
(EDL, TCf, TCt) and (vii) other (proximal) muscles (OM, IFE, IFI, ISF,
PIFML, CFP, AMB1, AMB2, IC).
To evaluate the influence that reserve actuators may have had
on simulation results, average and peak reserve actuator values
were compared with the peak net joint torques (obtained via
OpenSim’s inverse dynamics analysis). Reserve actuator work
was also calculated from the actuator torque and joint angle trajec-
tories, analysed in the same manner as MTU work and then
compared with the total amount of mechanical work generated
by the muscles in each corresponding simulation. In addition,
for the CMC simulations, which were not explicitly constrained
to follow the experimental joint kinematics, root mean square
(RMS) differences between the experimental and simulation joint
kinematics were calculated for the entire movement.
3. Results
The three optimization frameworks were able to successfully
generate simulations of walking and running, with all six
simulations generating a solution. In the CMC simulations,
peak errors in simulated joint trajectories were within 28
of experimental angles and RMS errors well below 0.18 (see
electronic supplementary material, table S1).
3.1. Reserve actuators
In all six simulations, average reserve actuator values remained
below 10% of the inverse dynamics moment with the exception
of hip ad–abduction, knee ad–abduction and ankle flexion–
extension (table 3, average reserve torque). Knee ad–abduction
was below 10% for all simulations but WCMCC (15%). Hip ad–
abduction had by far the highest average reserve actuator
values, accounting for up to 90% of the inverse dynamics
moment. Average ankle flexion–extension moments were con-
sistent between all simulations, ranging from 9.1 to 16.3%.
Peak reserve actuator values were more variable across the
different simulations. Peak knee rotation and knee flexion–
extension reserve values fell below 10% of the inverse dynamics
torques in all simulations except for WCMCC. Peak hip flexion–
extension reserve values were below 10% in all but RSO (12%)
and RCMCR (15%). Peak hip rotation reserve actuator values all
fell below 15%. Ankle flexion–extension and MTP flexion–
extension peak reserve values were high in most of the
simulations. The hip ad–abduction reserve actuator was highest
in all six simulations (table 3).
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
5
Even though the hip ad–abduction reserve actuator had
the highest average and peak reserve actuator values, its con-
tribution to limb mechanical work over the gait cycle was
small (less than 6% of total muscle work) in all simulations
(table 3 and figure 2). Knee ad–abduction reserve actuator
work was consistently positive, with values ranging from
2.89 (2%; WCMCR, WSO) to 18.09 J (13%; WCMCC). The highest
net values were generated by the ankle and MTP reserve
actuators, with magnitudes reaching 31.71 J (24%; table 3
and figure 2). The other reserve actuators had low net
mechanical work (less than 5%) over the simulation.
3.2. Muscle excitation and activation
Muscle timing data were similar across all six simulations, with
the majority of muscles having a single excitation period that
occurred primarily in either stance or swing (figure 3).
The major hip, knee and ankle extensors (e.g. M. flexor cruris
lateralis pars pelvica, FCLP; M. femorotibialis, FMTIM;
M. gastrocnemius, GL), many hip rotators (e.g. Mm. iliotrochan-
tericus, ITCp, ITCr) and the digital flexors (M. flexor digitorum
longus, FDL) were primarily excited during stance. The uniarti-
cular hip extensors, M. caudofemoralis pars pelvica (CFP) and
M. puboischiofemoralis (PIFML) were excited from mid-
to-late swing through mid-stance. Owing to their large origin
sites, the M. iliotibialis lateralis and M. iliofibularis were parti-
tioned into cranial and caudal regions in the model. In both
muscles, the caudal portions (ILp, ILFBp) tended to be excited
during stance whereas the cranial portions (Ila, ILFBa) were
excited during swing (figure 3). The hip and ankle flexors
(e.g. M. iliotibialis cranialis, IC; M. tibiocranialis, TC) were
primarily excited during swing. In both running and walking
ISF is not excited. IFE, IFI and FHL are only excited during
the running simulations.
Although no ostrich EMG data are available for direct com-
parison, simulation results compare favourably to previous
Table 3. Average and peak moments as well as net mechanical work generated by the reserve actuators for each of the six simulations. Shaded columns are
for the three walking simulations. Moment values are presented in Nm and parenthetical values indicate the per cent of the inverse dynamic analysis joint
torque. Work values are presented in joules (J) and parenthetical values are percentages relative to the total muscle–tendon unit mechanical work generated in
each simulation. Positive values indicate hip/knee extension, adduction and medial rotation, and ankle/MTP ﬂexion moments. Positive/negative mechanical work
indicates energy being added/removed from the limb.
degree of freedom
WSO
WCMCR
WCMCC
RSO
RCMCR
RCMCC
average reserve torque in Nm (%)
hip ﬂexion–extension
20.8 (,1)
20.9 (,1)
22.6 (2)
23.7 (1)
24.3 (2)
21.8 (,1)
hip ad–abduction
47.7 (77)
43.7 (71)
57.9 (94)
37.1 (77)
32.7 (68)
28.4 (59)
hip rotation
3.8 (4)
3.2 (3)
3.3 (3)
20.3 (,1)
0.2 (,1)
1.0 (,1)
knee ﬂexion–extension
0.5 (,1)
0.8 (,1)
11.3 (9)
0.5 (,1)
1.0 (,1)
1.8 (1)
knee ad–abduction
0.1 (,1)
1.1 (,1)
18.8 (15)
24.2 (2)
25.6 (2)
4.3 (2)
knee rotation
20.5 (1)
20.5 (1)
22.0 (5)
20.5 (,1)
20.1 (,1)
0.3 (,1)
ankle ﬂexion–extension
9.4 (14)
6.5 (10)
6.1 (9)
11.2 (16)
9.2 (13)
9.6 (14)
MTP ﬂexion–extension
23.1 (4)
22.1 (3)
4.0 (5)
29.4 (6)
212.5 (8)
27.0 (4)
peak reserve torque in Nm (%)
hip ﬂexion–extension
23.1 (3)
23.7 (3)
28.0 (7)
232.9 (12)
239.1 (15)
210.9 (4)
hip ad–abduction
130.7 (212)
138 (224)
133.5 (217)
170.3 (353)
127.4 (263)
112.4 (233)
hip rotation
13.5 (14)
13.4 (14)
10.9 (11)
29.3 (5)
14.6 (8)
12.0 (6)
knee ﬂexion–extension
2.4 (2)
2.9 (2)
86.0 (69)
8.9 (5)
12.2 (7)
8.7 (5)
knee ad–abduction
12.3 (10)
13.7 (11)
129.2 (104)
243.4 (16)
277.3 (29)
27.0 (10)
knee rotation
1.8 (4)
21.8 (4)
219.1 (43)
25.7 (10)
22.9 (5)
2.2 (4)
ankle ﬂexion–extension
32.7 (49)
29.5 (44)
19.4 (29)
66.7 (97)
66.9 (97)
46.8 (68)
MTP ﬂexion–extension
211.7 (15)
29.2 (12)
45.1 (57)
267.9 (43)
291.0 (58)
256.3 (36)
net mechanical work (J)
hip ﬂexion–extension
0.44 (,1)
0.27 (,1)
20.28 (,1)
0.91 (,1)
0.39 (,1)
20.19 (,1)
hip ad–abduction
7.50 (6)
5.08 (4)
27.32 (5)
22.65 (1)
26.05 (3)
24.96 (3)
hip rotation
0.83 (,1)
0.12 (,1)
0.18 (,1)
0.45 (,1)
0.01 (,1)
20.49 (,1)
knee ﬂexion–extension
20.03 (,1)
20.25 (,1)
6.11 (5)
22.51 (1)
23.61 (2)
0.48 (,1)
knee ad–abduction
2.89 (2)
2.89 (2)
18.09 (13)
6.16 (2.8)
7.67 (3.5)
4.89 (3)
knee rotation
20.06 (,1)
20.14 (,1)
21.37 (1)
0.26 (,1)
0.16 (,1)
0.16 (,1)
ankle ﬂexion–extension
14.71 (11)
7.30 (5)
28.34 (6)
22.31 (10)
12.13 (6)
8.36 (5)
MTP ﬂexion–extension
2.50 (2)
0.80 (,1)
31.71 (24)
16.06 (7)
18.7 (8.5)
26.8 (4)
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
6
comprehensive studies of guinea fowl limb muscle activity
(figure 3; [22,23]). Except for small timing changes that are to
be expected owing to comparisons being performed between
different avian species, the simulated muscle excitation pat-
terns were consistent with the empirical data: most muscles
had a single period of EMG activity in either the stance or
swing phase. Nonetheless, there were a few notable exceptions.
Similar to EMG recordings [23], CFP was excited during mid-
stance. However, either an additional period of excitation or
an extended single period occurred during late swing in the
simulations that was not evident in the EMG data. The CFP
may have been preferentially used to slow down hip flexion
and assist in hip extension prior to foot strike. Digital flexor
and ankle extensor onset times occurred in early stance in the
simulations, but EMG recordings suggest an earlier onset
during late swing (e.g. FPD4, FDL, GL). Last, EMG recordings
for the ITCR suggest that this muscle is excited during swing.
However, the simulations consistently excited ITCR during
mid-stance, likely to oppose the high hip lateral rotation
moment. Instead, ITCp was excited during both mid-swing
and stance in the simulations, whereas EMG data indicate
that this muscle only has a single excitation period beginning
in late-swing through stance. The ITCa, ITCR and ITCp are
all medial hip rotators and discrepancies could be owing to
comparing different species. This will remain uncertain until
ostrich EMG data become available, even though EMG patterns
in avians measured to date generally are conservative [23,50].
When averaged across all muscles, iAct was always
greater during stance than swing in both gaits, with the smal-
lest difference occurring in WCMCC (21.2 versus 16.7). The
running simulations also consistently required more muscle
activity than during walking (e.g. RCMCC, 21.5; WCMCC,
19.6). In both gaits, the PIFML and CFP muscles were
active during both phases. However, stance phase iAct was
much larger during running than walking (figure 4). The
medial hip rotators ITCa, ITCp, ITCR and ITM and the lateral
hip rotator OM had similar activity levels in all simulations,
with the medial rotators primarily active during stance and
OM active during swing. Conversely, many of the biarticular
muscles crossing the hip and knee (i.e. ILp, ILFBp, FCLP,
FCM) had noteworthy changes in iAct between the two
gaits (figure 5). Even though muscle activity primarily
occurred during stance for both gaits, iAct values for
ILFBp, FCLP and FCM were markedly lower in the walking
motion. Similar to their excitation patterns, ILa and ILFBa
had notable iAct values during both the stance and swing
phases in running (figure 5). AMB1 and AMB2 had similar
activity levels during swing in both gaits, but had increased
activity during stance in running. The IC, a hip flexor
and knee extensor, had consistent iAct values across all
simulations, which were highest during swing.
In both gaits, the uniarticular knee extensors FMTL and
FMTIM had larger iAct values during stance than swing,
whereas the converse was true for FMTM (figure 6). Knee
extensor iAct values differed greatly between simulations,
with the CMC compliant tendon simulations (i.e. WCMCC
and RCMCC) producing higher values during swing com-
pared with the other four simulations. The major ankle
extensors (Mm. gastrocnemius: GL, GIM, GM) had higher
integrated muscle activity during stance in the running simu-
lations. Ankle flexor (TCf, TCt) iAct was comparable between
running and walking (e.g. figure 6, TCf: WSO versus RSO).
However,
the
CMC
simulations
consistently
estimated
higher overall ankle flexor activity than the SO simulations,
with the greatest differences occurring during swing in the
CMC
rigid
tendon
simulations.
Digital
flexor
(FPPD3,
FPD3, FPD4, FDL) muscle activity occurred almost exclu-
sively during stance (figure 7). Differences in FPPD3, FPD3
stance
−20
0
0
20
40
−40
−20
0
20
40
−40
−20
0
0
20
40
−40
−20
0
20
40
−40
−20
0
0
20
40
−40
−20
0
20
40
−40
swing
gait cycle
negative work (J)
positive work (J)
net work (J)
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
hip extension
hip abduction
hip rotation
knee extension
knee abduction
knee rotation
ankle extension
MTP extension
hip extension
hip abduction
hip rotation
knee extension
knee abduction
knee rotation
ankle extension
MTP extension
hip extension
hip abduction
hip rotation
knee extension
knee abduction
knee rotation
ankle extension
MTP extension
negative work (J)
positive work (J)
net work (J)
hip extension
hip abduction
hip rotation
knee extension
knee abduction
knee rotation
ankle extension
MTP extension
sum
hip extension
hip abduction
hip rotation
knee extension
knee abduction
knee rotation
ankle extension
MTP extension
sum
hip extension
hip abduction
hip rotation
knee extension
knee abduction
knee rotation
ankle extension
MTP extension
sum
Figure 2. Positive, negative and net mechanical work generated by the reserve actuators in each simulation. Positive/negative work indicates energy ( joules) added
to/removed from the limb during the movement. Sum: total of all reserve actuators.
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
7
and FPD integrated activity occurred between the two gaits,
with running simulations consistently having higher values.
The digital extensor EDL was primarily active during
swing but did have a small amount of activity during stance.
3.3. Muscle force and work
Average muscle forces tended to follow the same trends as
activation, but there was higher variability between optimiz-
ation frameworks, with the compliant tendon simulations
using CMC (RCMCC, WCMCC) regularly generating larger
forces than the other simulations (figures 8–11). Among all
the uniarticular hip muscles, the medial hip rotators and
the hip extensors (PIFML, CFP) had the greatest forces
during stance (figure 8). During swing, the PIFML and CFP
had large forces in the compliant tendon CMC simulations.
The lateral hip rotator OM consistently had larger forces in
running. Except for the AMB1 and AMB2 muscles—which
clearly generated more force during running—the biarticular
hip–knee muscles had similar amounts of force in both gaits
(figure 9). Swing phase forces were consistent across simu-
lations and movements, with the IC, AMB1 and AMB2
muscles generating the largest average forces. The uniarticu-
lar knee extensors FMTL and FMTIM and the digital flexor
FL had the greatest forces during stance (figures 10 and 11).
The GM and GL had large average stance forces in running,
but much lower values in walking. The ankle flexors (TCf,
TCt) had small forces during both stance and swing in the
0
25
50
75
100
CFP
PIFML
AMB1
IC
ILa
ILp
ILFBa
ILFBp
FCLP
ITCp
ITCR
FMTIM
TC
GL
FDL
FPD4
Marsh
Gatesy
stance
swing
per cent gait cycle
RSO
RCMCC
Figure 3. Example simulated muscle excitation timings during running. Blue (dark grey) and green (light grey) bars indicate periods of excitation for the RSO and
RCMCC solutions, respectively. For comparison, onset and offset timing obtained from EMG studies of guinea fowl during slower [20] (Gatesy, 1.0 m s21, hatched
bars) and faster [21] (Marsh, 1.5 m s21, striped bars) running are provided. Owing to differences in stance and swing times between the studies, stance and swing
phases were normalized to 50% of the gait cycle. Zero per cent (0%) of gait cycle indicates the beginning of the stance phase. The other four simulations had
similar excitation patterns.
0
25
50
75
100
swing
0
25
50
75
100
ITCa
ITCp
ITCR
ITM
OM
IFE
IFI
ISF
PIFML
CFP
stance 
integrated activation (iAct)
integrated activation (iAct)
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
Figure 4. Integrated muscle activation values of the uniarticular hip muscles during the swing and stance phases for each of the six simulations. Solid bars, running
simulations; striped bars, walking simulations.
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
8
CMC simulations, with the compliant tendon simulations
generating the highest average forces (figure 10). Digital
flexor muscles’ forces had a clear distinction between stance
and swing, with much smaller swing forces compared
with stance (figure 10). The digital extensor EDL primarily
generated force during swing.
Total MTU mechanical work had similar patterns between
walking and running (figure 12). The hip rotators (ITCa and
ITCp), knee extensors (FMTL and FMTIM), AMB2, FL and
FPPD3 consistently produced negative work, whereas many
of the biarticular hip extensors (e.g. ILFB, FCLP, FCM), the
hip flexor IC, and ankle extensor (GL) generated positive
work in the simulations. In contrast, the mechanical work gen-
erated by the ankle flexors TCf and TCt varied greatly between
simulations, with no clear pattern. The remaining muscles
tended to generate little positive or negative net mechanical
work (figure 12).
The total amount of positive and negative muscle work
generated during swing was much lower than that genera-
ted during stance (figure 13). There were increases in both
positive and negative mechanical work generated by the
M. gastrocnemius, digital flexors and ankle flexors in
WCMCC and RCMCC relative to the other simulations. During
stance, the biarticular hip–knee muscles generated the
majority of the positive work in both gaits, amounting to
more than twice their negative work (figure 13). The digital
flexors generated large amounts of both positive and negative
work, with similar amounts of negative work predicted by
all six simulations. However, the amount of positive work
generated by the digital flexors increased dramatically in
0
25
50
75
100
swing
0
25
50
75
100
stance 
AMB1
AMB2
IC
ILa
ILp
ILFBa
ILFBp
FCLP
FCM
integrated activation (iAct)
integrated activation (iAct)
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
Figure 5. Integrated muscle activation values of the biarticular muscles crossing the hip and knee during the swing and stance phases for each of the six
simulations. Solid bars, running simulations; striped bars, walking simulations.
0
25
50
75
100
swing
0
25
50
75
100
stance 
FMTL
FMTIM
FMTM
GL
GIM
GM
TCf
TCt
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
integrated activation (iAct)
integrated activation (iAct)
Figure 6. Integrated muscle activation values for the uniarticular and biarticular knee and ankle muscles during the swing and stance phases for each of the six
simulations. Solid bars, running simulations; striped bars, walking simulations.
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
9
RCMCC and WCMCC simulations. On the other hand, the knee
extensors generated a large amount of negative work and
very little positive work. The gastrocnemius group generated
very little work in walking, but consistently produced a small
amount of positive work in running.
3.4. Muscle functional roles
To act as a motor that drives motion, muscles must produce
force during concentric contractions and generate positive
work. In both gaits, the muscles identified as motors were
the same (table 4). The IC and AMB2 provided much of the
energy required during swing, whereas the biarticular hip
and knee muscles (ILFBa, ILFBp, FCM, FCLP) and lateral gas-
trocnemius (GL) provided energy during stance (figures 11
and 12 and table 3). In contrast, the hip rotators (ITCa, ITCp,
ITM, ITCR), FMTM, AMB1, ankle flexors (TCf, TCt, EDL)
and uniarticular hip extensors (PIFML, CFP) all acted as
struts, generating moderate to high forces but little positive
or negative work. Furthermore, the digital flexors acted
primarily as springs during stance, first absorbing energy
(negative work) in early stance and then generating positive
work during late stance (figure 13 and table 4). Finally, the
FDL also generated force during an eccentric contraction in
early stance, resulting in net negative limb work (i.e. a
brake). Likewise, the knee extensors FMTM and FMTL acted
as brakes, absorbing energy from the limb during stance
(figure 13 and table 4). A few differences in functional roles
between gaits were evident. During walking, the IL and GM
acted as brakes and absorbed energy from the limb during
swing
stance 
EDL
FDL
FHL
FL
FPPD3
FPD3
FPD4
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
0
25
50
75
100
0
25
50
75
100
integrated activation (iAct)
integrated activation (iAct)
Figure 7. Integrated muscle activation values for the muscles crossing the metatarsophalangeal (MTP) joint during the swing and stance phases for each of the six
simulations. All of these muscles are either biarticular (ankle–MTP) or multiarticular (knee–ankle–MTP). Solid bars, running simulations; striped bars, walking
simulations.
swing
stance 
average force (N)
average force (N)
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
0
400
500
600
0
400
600
ITCa
ITCp
ITCR
ITM
OM
IFE
IFI
ISF
PIFML
CFP
 
200
200
300
100
100
300
500
Figure 8. Average muscle force values of the uniarticular hip muscles during the swing and stance phases for each of the six simulations. Solid bars, running
simulations; striped bars, walking simulations.
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
10
stance. However, these muscles acted primarily as struts
during running, generating force but very little work. Muscles
with a second excitation period during running did not alter
the functional roles of the comparable excitation periods
between the two gaits. Instead, the additional excitation
periods added an additional role to the muscle during the
movement. The AMB1 and AMB2 had additional roles as a
strut and brake, respectively, during stance in running,
whereas the ITCa and ILFBa had additional roles of strut
and brake, respectively, during swing.
4. Discussion
Combining detailed musculoskeletal models and simulations
with empirical data allows for the estimation of quantities that
can greatly enhance our understanding of specific functional
roles during dynamic movements [28,29,51]. Although anatom-
ical and EMG studies can provide insight into muscle
classification relative to gait events (e.g. stance versus swing
phase), a detailed understanding of a muscle’s functional
role(s) requires additional quantities that are not readilyobtained
using experimental techniques. The musculotendon force and
mechanical work data generated in this study enable the deter-
mination of specific muscle mechanical roles such as motor,
brake, strut or spring during gait [19–21]. These roles provide
important information regarding how energy flows through
the limb and generates the required external work during move-
ment. Muscle functional roles were also mainly insensitive to
optimization approach or gait type (table 4).
However, there were some subtle differences between the
SO and computed muscle control compliant tendon (CMCC)
simulations, especially among muscles with long tendons
that were classified as mechanical springs (table 4). These
swing
stance 
average force (N)
average force (N)
0
450
750
900
0
300
450
900
AMB1
AMB2
IC
ILa
ILp
ILFBa
ILFBp
FCLP
FCM
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
600
750
300
150
150
600
Figure 9. Average muscle force values of the biarticular muscles crossing the hip and knee during the swing and stance phases for each of the six simulations.
Solid bars, running simulations; striped bars, walking simulations.
swing
stance 
average force (N)
average force (N)
0
300
600
900
1200
0
300
600
900
1200
FMTL
FMTIM
FMTM
GL
GIM
GM
TCf
TCt
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
Figure 10. Average muscle force values for the uniarticular and biarticular knee and ankle muscles during the swing and stance phases for each of the six simu-
lations. Solid bars, running simulations; striped bars, walking simulations.
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
11
differences were most evident in the digital flexors (FL,
FPPD3, FPD3, FPD4) during running, where the magnitude
of the net mechanical work produced by these muscles was
lower in CMCC than SO (figure 12). On the other hand, the
amount of negative and positive work generated by these
muscles in CMCC was higher than SO (figure 13). Ideal
mechanical springs have zero net mechanical work; all
absorbed energy is stored and returned. An MTU acting in a
spring-like fashion will exhibit high amounts of positive and
negative work but have a low net mechanical work. Although
the digital flexors exhibited these spring-like characteristics in
both optimization approaches, the CMCC simulations more
clearly indicated that the muscles were acting as springs.
Using CMCC may be more helpful in other situations, where
functional roles are not as easily identified.
For example, the ankle flexor group produced close to
zero net mechanical work during stance in all simulations
(figure 13). The total negative and positive mechanical
work varied greatly between simulations, however. Positive
and negative mechanical work were near zero in the SO
simulations, defining these muscles as struts during stance.
However, the positive and negative values were many
times greater in the CMCC simulations, resulting in a func-
tional role of a spring for these muscles (figure 13). Based
on their anatomical features (i.e. short muscle fibres and
long tendons), it is likely that the ankle extensor MTUs
truly do act as springs as suggested by the CMCC simu-
lations.
Interestingly,
the
computed
muscle
control
simulations incorporating a rigid tendon (CMCR) generated
results similar to the SO simulations. Thus, the incorporation
average force (N)
average force (N)
0
600
900
1200
1500
0
600
900
1200
1500
EDL
FDL
FHL
FL
FPPD3
FPD3
FPD4
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
300
300
swing
stance 
Figure 11. Average muscle force values for the muscles crossing the metatarsophalangeal (MTP) joint during the swing and stance phases for each of the six
simulations. All of these muscles are either biarticular (ankle–MTP) or multiarticular (knee–ankle–MTP). Solid bars, running simulations; striped bars, walking
simulations.
ITCa
ITCp
ITCR
ITM
OM
IFE
IFI
ISF
PIFML
CFP
IC
ILa
ILp
ILFBa
ILFBp
FCLP
FCM
AMB1
AMB2
FMTL
FMTIM
FMTM
GL
GIM
GM
TCf
TCt
EDL
FDL
FHL
FL
FPPD3
FPD3
FPD4
−50
−30
−20
−10
0
10
net work (J)
–10
0
10
20
30
50
net work (J)
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
−40
40
Figure 12. Net mechanical work for each musculotendon unit over an entire gait cycle. Positive/negative work indicates work added/removed from the bio-
mechanical system. Solid bars, running simulations; striped bars, walking simulations.
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
12
of both (i) a flexible tendon and (ii) the ability to account for
energy storage and return may be important when inferring
whether a muscle acts as a strut or spring.
Relative to the hip, the knee undergoes greater joint
excursions during walking and running in birds. As a
result, studies of avian gait have historically characterized
muscles crossing the knee as critical to driving movement
[52]. On the other hand, models of human walking and run-
ning have found muscles crossing the knee to primarily act as
brakes, absorbing energy during stance [53,54]. Ostriches are
uniquely situated—as birds they likely use similar mechanics
to smaller cursorial birds but are larger in size and thus may
require similar mechanics to larger bipedal animals such as
humans. An examination of muscular roles provides evi-
dence that ostrich gait is at least partly hip-driven, with the
major biarticular hip-to-knee muscles acting as motors and
generating much of the positive work in both gaits (table 4
and figure 12: ILFB, FCLP, FCM). Bi-articular muscles
are thought to act primarily to transfer energy across joints
(i.e. as a strut) and the function of the ostrich bi-articular
hip extensors as a motor may be greater than previously
inferred. In contrast, despite generating large forces, the uni-
articular hip extensors (PIFML, CFP) had mechanical work
values near zero and acted as struts. This result is consistent
with previous inverse dynamics analyses (i.e. joint-level ana-
lyses) that predict little hip joint work [2]. However the
muscle-level analysis performed here, which includes work
done by multi-joint muscles, shows that total hip muscle
work may be disproportionate to joint-level estimates and
suggests that ostriches may use more complex hip–knee
interactions than humans to drive their limbs. The major
knee extensors (FMTL, FMTIM) acted as brakes during
stance, suggesting that ostriches, like humans, employ these
muscles to assist in maintaining whole-body stability. Of
the muscles active in swing, only IC and AMB2 acted as
motors, indicating that these muscles are the key drivers of
swing phase mechanics, especially limb protraction.
Avian distal limb muscles are remarkably specialized, con-
sisting of extremely long tendons that have high energy storage
and return potential [2,15,17,18]. In this study, regardless of the
type of simulation, the lateral gastrocnemius (GL) and digital
flexors generated large but nearly equal amounts of negative
and positive work, resulting in near zero net mechanical work
in both gaits (figures 7 and 11–13). These muscles acted as
springs, first absorbing energy during early stance and then
returning this energy during late stance. The magnitudes of
0
–35
–70
0
35
70
negative work (J)
positive work (J)
0
35
70
positive work (J)
0
–35
–70
negative work (J)
stance
hip 
rotators
biarticular
hip/knee
knee 
extensors
gastrocnemius
digital 
flexors
ankle 
flexors
other
muscles
swing
hip 
rotators
biarticular
hip/knee
knee 
extensors
gastrocnemius
digital 
flexors
ankle 
flexors
other
muscles
RSO
RCMCR
RCMCC
WSO
WCMCR
WCMCC
Figure 13. Positive and negative musculotendon work generated by different muscle groups over the stance and swing phases of a gait cycle. Positive/negative
work indicates work added/removed from limb and were calculated from the corresponding portion of the power curves. Muscles were grouped as either hip rotators
(ITCa, ITCp, ITCR, ITM), biarticular hip/knee (ILa, ILp, ILFBa, ILFBp, FCLP, FCM), knee extensors (FMTL, FMTIM, FMTM), gastrocnemius (GL, GIM, GM), digital flexors
(FDL, FHL, FL, FPPD3, FPD3, FPD4), ankle flexors (EDL, TCf, TCt) or other muscles (OM, IFE, IFI, ISF, PIFML, CFP, AMB1, AMB2, IC). Solid bars, running simulations;
striped bars, walking simulations.
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
13
positive and negative work generated by these MTUs were also
greater during running than walking (e.g. 266.5 versus 237.8 J
and 49.6 versus 44.0 J; RCMCC versus WCMCC), congruent with
the notion that these MTUs are acting as springs that use
tendon energy storage and return (figure 13). The increased
distal limb muscle activity and work observed in the running
simulations is consistent with the widely held notion that
ostriches increase their reliance on these specialized elastic
structures during higher speed movements to improve running
economy [2,17].
In both gaits, individual muscle excitation timing and
integrated muscle activity occurred primarily during either
stance or swing, suggesting that primary muscle functional
roles may be associated with gait phases (figures 3–7).
These data allowed for general muscle classification, which
was found to be insensitive to simulation type and generally
Table 4. Muscle functional roles based on muscle–tendon unit excitation, force and mechanical work. Differences in roles between walking and running are
shown in italics. Muscles performing roles in both swing and stance have roles that are separated by a colon (:) with their role in swing ﬁrst (e.g. AMB2 acts
as a motor during swing, then acts as a brake during stance).
muscle
abbreviation
classiﬁcation
primary role
running
walking
running
walking
M. iliotibialis cranialis
IC
swing
swing
motor
motor
M. iliotibialis lateralis (cranial part)
ILa
swing
stance
strut
brake
M. iliotibialis lateralis (caudal part)
ILp
stance
stance
strut
brake
M. ambiens, ventral (pubic) head
AMB1
both
swing
strut : strut
strut
M. ambiens, dorsal (iliac) head
AMB2
both
swing
motor : brake
motor
M. femorotibialis lateralis
FMTL
stance
stance
brake
brake
M. femorotibialis intermedius
FMTIM
stance
stance
brake
brake
M. femorotibialis medialis
FMTM
swing
swing
strut
strut
M. ilioﬁbularis (cranial part)
ILFBa
both
stance
brake : motor
motor
M. ilioﬁbularis (caudal part)
ILFBp
stance
stance
motor
motor
M. iliotrochantericus caudalis (cranial part)
ITCa
stance
stance
strut
strut
M. iliotrochantericus caudalis (caudal part)
ITCp
both
stance
strut : strut
strut
M. iliofemoralis externus
IFE
stance
off
strut
M. iliotrochantericus medius
ITM
stance
stance
strut
strut
M. iliotrochantericus cranialis
ITCR
stance
stance
strut
strut
M. iliofemoralis internus
IFI
swing
off
strut
M. ﬂexor cruris medialis
FCM
stance
stance
motor
motor
M. ﬂexor cruris lateralis pars pelvica
FCLP
stance
stance
motor
motor
M. ischiofemoralis
ISF
off
off
M. puboischiofemorales medialis þ lateralis
PIFML
stance
stance
strut
strut
M. obturatorius medialis
OM
swing
swing
strut
strut
M. caudofemoralis pars pelvica (et caudalis)
CFP
stance
stance
strut
strut
M. gastrocnemius pars lateralis
GL
stance
stance
motor
motor
M. gastrocnemius pars intermedius
GIM
stance
stance
strut
strut
M. gastrocnemius pars medialis
GM
stance
stance
strut
brake
M. ﬁbularis longus
FL
stance
stance
brake
brake
M. ﬂexor digitorum longus
FDL
stance
stance
spring
spring
M. ﬂexor perforans et perforatus digitorum 3
FPPD3
stance
stance
spring
spring
M. ﬂexor perforans digitorum 3
FPD3
stance
stance
spring
spring
M. ﬂexor perforans digitorum 4
FPD4
stance
stance
spring
spring
M. ﬂexor hallucis longus
FHL
stance
off
spring
M. extensor digitorum longus
EDL
swing
swing
strut
strut
M. tibialis cranialis (femoral head)
TCf
swing
swing
strut
strut
M. tibialis cranialis (tibial head)
TCt
swing
swing
strut
strut
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
14
consistent between the two gaits; only seven of the 34 muscle
actuators had gait-specific classifications (table 4). In all seven
muscles with gait-specific classifications, the running gaits
had additional excitation periods that were not observed in
the walking simulations. For example, AMB1 was excited
during swing in both gaits. In running, AMB1 also had an
additional excitation period during stance (figure 5). These
findings may be due to the higher mechanical demands
associated with running and muscles may take on additional
roles to assist with meeting these demands.
Although a broad division based on gait phases could be
identified for individual muscles, this division did not scale
to anatomical groups. For example, within the femorotibialis
muscle group, FMTM and FMTL were classified as stance
phase muscles but FMTIM was classified as a swing phase
muscle based on excitation timing. Similarly, the cranial por-
tions of M. iliofibularis (ILFBa) and M. iliotibialis lateralis
(ILa) had different classifications from the caudal portions
(ILFBp, ILp) during running (table 4). Previous EMG studies
have also suggested that muscles within anatomical groups
are differentially excited. Marsh et al. [22] showed that the
Mm. femorotibialis and M. iliofibularis usually had two exci-
tation periods during running—one during stance and a
second during swing. Gatesy [23] also found the cranial
and caudal compartments of the M. iliotibialis lateralis to
have distinct activity patterns. Our study, combined with
the previous EMG work, highlights the need to exercise cau-
tion when assuming that anatomically similar muscles also
have similar functions during movement. In addition, the
present results further suggest that even general classification
of muscles based solely on excitation relative to stance or
swing phase mechanics may be too simplistic. For example,
despite their primary activity being clearly associated with
either stance or swing, many limb muscles in this study
also had small amounts of excitation over transition regions
(e.g. late stance to early swing) [22,43]. The reasons for this
low level excitation are less clear: activity may be associated
with a secondary minor functional role or may be a result
of time delays between muscle activity and force gener-
ation—future work directed at resolving this uncertainty
(e.g. combining simulations with induced acceleration and/
or segment power analyses [55–57]) is warranted.
When constructing optimizations designed to reproduce
experimental data, OpenSim allows the user to apply ‘reserve
actuators’ to each joint in the model to compensate for any
mechanical forces that could not be satisfied by the muscles
alone. Because the optimization framework only uses these
actuators when muscle forces are insufficient, the actuator
values can provide a rough estimate of how experimental
data and musculoskeletal model inaccuracies influence a simu-
lation. During human movements, a threshold value of 5% of
the net joint moments for reserve actuator values (average and
peak) has been suggested as one indicator of a high-quality
simulation [58]. In this study, average reserve actuators fell
below 10% of net joint moments in 37 of the 48 cases
(table 3, average). The most notable exception occurred in
the average hip ad–abduction moment, which exceeded 50%
in all six simulations. Peak values were more variable but
hip ad–abduction, ankle and MTP flexion–extension reserve
actuators were high in most of the simulations (table 3). One
plausible reason for the high average and peak reserve actua-
tor values is that they are compensating for unmodelled
passive tissues and structures. Functionally, passive tissues
act primarily as struts or springs, generating high forces but
little mechanical work. To further assess whether the reserve
actuators represent unmodelled passive structures, the posi-
tive, negative and net mechanical work generated by each
actuator was calculated. Except for ankle and MTP flexion–
extension, net mechanical work was generally low (i.e. less
than 5% of the 134.7–224 J in total muscle work; table 3 and
figures 2 and 12), suggesting that most reserve actuators
likely represented passive structures.
Ostriches, like most birds, have remarkably few hip adduc-
tor muscles [9,59]. This is not surprising, because inverse
dynamics analyses have shown that the intersegmental hip
abduction moment is less than half the hip extension
moment during stance in running [2]. However, many of the
biarticular hip extensors and knee flexors, which are the
main drivers during gait (table 4 and figure 13), also have
large hip abduction moment arms. Therefore, these muscles
generate a very large hip abduction moment during stance
that cannot be counteracted by adductor muscles alone.
Instead, passive mechanisms, such as bony contact between
the femur and antitrochanter and strong ligaments [12–14]
likely oppose this abduction moment. In our study, the hip
ad–abduction reserve actuator was used to represent these
passive mechanisms that are not explicitly modelled. Both the
net mechanical work generated and the pattern of work gener-
ation exhibited by this reserve actuator were consistent with it
representing passive tissues. During stance, this actuator gener-
ates an equal amount of negative and positive work, resulting
in little net mechanical work during the modelled motions. In
addition, the negative work associated with the hip ab–
adduction actuator was generated during early stance and the
positive work was generated during mid-to-late stance, consist-
ent with the expected energetics of a passive structure that can
stretch to absorb and then return energy (table 3 and figure 2).
To further test if the hip ad–abduction reserve actuator
represented unmodelled passive tissues and better under-
stand how these tissues may influence muscle coordination,
a series of post hoc simulations using CMCC were generated
in which the hip adduction reserve actuator was systemati-
cally reduced (i.e. reducing passive tissue contributions). As
passive force contributions decreased, the muscle IC, despite
acting as a hip flexor, was increasingly recruited during
stance owing to its small hip adduction moment. After
IC was maximally recruited, hip extension muscle activity
was
decreased
to
reduce
the
induced
hip
abduction
moment by these muscles, replaced by increasing the
torque generated by the hip extension reserve actuator.
Both the recruitment of IC during stance, which has been
found to be active exclusively during swing in other birds
[22,23], and the increased reliance on the hip extension
reserve actuator to power the motion suggest that passive
hip structures are important during ostrich gait. The avian
hip is an excellent example of a joint where non-muscular
soft tissues and bony stops deserve careful consideration in
dynamic analyses of locomotion.
However, rigorously implementing sufficiently accurate
passive structures introduces additional challenges when
building
models
and
simulations.
Rigid
body
contact
models exist that could be implemented to model bony
stops
[60–63].
However,
implementing
these
contact
models is difficult as detailed information of both the under-
lying contact geometry and detailed joint motion data are
necessary (i.e. subject-specific models), which are rarely
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
15
available. In addition, contact models can be computationally
expensive, especially when implemented at multiple joints,
further increasing the time required to generate an optimal
simulation. Similar constraints and limitations are associated
with modelling other non-muscular passive tissues, where
detailed knowledge of joint and tissue geometry is necessary.
One alternative approach that has been used successfully in
numerous human studies is to quantify the total passive
behaviour of a joint using regression equations [64–66].
These equations are usually generated in the form of a net
passive torque as a function of a single joint angle. However,
creating these characteristic regression functions requires
extensive cadaver-based work, especially when trying to
characterize how the tissues interact between multiple DOF
at a joint.
On the other hand, the ankle and MTP reserve actuators
generated a substantial amount of positive work, suggesting
that they did not represent passive structures but were
compensating for muscle deficiencies. Peak MTP reserve
actuator values occurred during mid-stance to assist the digi-
tal flexors, whereas peak ankle reserve values occurred
during mid-swing to assist the ankle flexors. To confirm
that muscle weakness was responsible for the simulations
requiring these reserve actuators, an additional RCMCC run-
ning simulation was performed in which the maximum
isometric force of the digital flexors and ankle flexors was
doubled. Doubling the strength of the digital flexors elimi-
nated the need for the MTP reserve actuator, confirming
that these muscles appear to be weak relative to the motion
requirements. This result is consistent with findings in pre-
vious human running studies, where models of the plantar
flexor
muscles
were
incapable
of
generating
sufficient
torque to overcome the mechanical demands at the ankle
joint [5,67]. Surprisingly, doubling the maximum isometric
force of the ankle muscles did not reduce the required
ankle flexion reserve torque—in fact, the required reserve
torque was higher in this simulation. Further inspection
revealed that the antagonistic digital flexors were passively
generating force during mid-swing owing to muscle fibres
operating at fibre lengths greater than the optimal fibre
length. In the model, the ankle flexors cannot counteract
these passive muscle forces using the current force ratio
between the two muscle groups. In general, muscle fibre
excursions tended to be larger than might be expected
empirically, especially over regions where the joints also
underwent large angle changes such as those found in
swing
(electronic
supplementary
material,
figure
S1).
Lumped-parameter
muscle
models,
like
the
Hill-type
muscle model used here, tend to overestimate fibre excur-
sions, which may explain why the digital flexors produce
passive force during swing [45,68].
Despite these model inconsistences, all six simulations
predicted overall muscle coordination patterns consistent
with previously collected guinea fowl EMG data (figure 3,
[20,21]). In addition, the percentage of muscle activity
that occurs during swing (13.9–38.6%; see electronic sup-
plementary material, table S2) compares favourably with
previous muscle blood flow data suggesting that one quarter
of the energetic cost of running occurs during swing
in guinea fowl [22]. Combined with the good excitation
timing comparisons in the vast majority of the muscles,
these data indicate that the excitation patterns predicted by
the simulations in this study are, in general, biologically
reasonable and realistic. The high level of similarity bet-
ween the predicted ostrich muscle coordination patterns
and those of smaller cursorial birds also suggests that,
despite
experiencing
a
large
change
in
size,
ostriches
appear to have conserved a gait coordination pattern inher-
ited from a common avian ancestor, which is unsurprising
given the apparent conservatism in avian pelvic limb
muscle activity [23,50].
Although muscle functional roles were found to be insen-
sitive to the three different optimization frameworks, there
were some subtle differences in muscle quantities. During
both walking and running, total muscle activity was consist-
ently lower in the SO simulations than in both CMC
simulations. This is most likely a direct result of the CMC
simulations including excitation–activation dynamics, which
can increase muscle co-contraction. The CMCC simulations
also generated greater muscle forces despite having similar
iAct values to the other simulations (e.g. figures 5 and 9;
TCf, TCt), with differences likely due to the incorporation of
fibre–tendon dynamics that create substantial changes in the
force generation properties of muscle. Caution should be
taken when eliminating muscle–tendon dynamics from bio-
mechanical analyses, especially when investigating specific
muscle quantities, motions that require large changes in joint
motion, or muscles with relatively long tendons. Further
tests against a gold standard (i.e. muscle fibre length measure-
ments
obtained
via
sonomicrometry
or
tendon
force
measurements via tendon buckles) should provide additional
insight into how sensitive specific muscle quantities may be
to muscle–tendon dynamics and optimization approach.
Our study shows how combining detailed musculoskeletal
models with optimization techniques can provide a rich and
varied dataset that complements and enhances existing
empirical
methods
used
in
comparative
biomechanics
research. Similar to reductionist models [69,70], these models
are well suited to theoretical studies that can elucidate under-
lying
principles
and
constraints
governing
motion.
For
example, this study has generated estimates of muscle exci-
tation, force and musculotendon work during walking and
running in an ostrich, which were used to identify muscle
functional roles. Muscle roles were found to be insensitive to
optimization approach, with the bi-articular hip and knee
muscles acting as motors and digital flexors acting as springs
during stance. The IC and AMB2 were the main drivers of the
swing motion. Passive tissues at the hip also appear to play an
important role in ostrich running, acting as a strut to prevent
excessive hip abduction. Future models should incorporate
non-muscular soft tissues and bony stops, which also deserve
careful consideration when modelling or performing dynamic
analyses of locomotion of fossil taxa.
Data accessibility. The musculoskeletal model and motion data used in
this study are available via Dryad at http://dx.doi.org/10.5061/
dryad.fh3h6.
Author contributions.
J.W.R. modified the original musculoskeletal
model, ran computer simulations, performed the analyses and
drafted the manuscript. J.R. and J.R.H. assisted in study conception
and design, helped interpret the study findings, and provided
comments on manuscript drafts. All authors gave final approval for
publication.
Competing interests. We have no competing interests.
Funding. This project was partially supported by BBSRC and NERC
grants (grant no. BB/I02204X/1 and NE/K004751/1 to J.R.H.) and
fellowships from the NSF (to J.R.H.) and the Vice Principal of
Research at the Royal Veterinary College (to J.W.R.).
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
16
Acknowledgements. We thank Thor Besier, David Lloyd, Paul Fornier
and Denham Heliams for their contribution to ostrich gait data
collection and the two anonymous reviewers who provided very
helpful suggestions during the review process.
References
1.
Watson RR, Rubenson J, Coder L, Hoyt DF, Propert
MWG, Marsh RL. 2011 Gait-specific energetics
contributes to economical walking and running
in emus and ostriches. Proc. R. Soc. B 278,
2040–2046. (doi:10.1098/rspb.2010.2022)
2.
Rubenson J, Lloyd DG, Heliams DB, Besier TF,
Fournier PA. 2011 Adaptations for economical
bipedal running: the effect of limb structure on
three-dimensional joint mechanics. J. R. Soc.
Interface 8, 740–755. (doi:10.1098/rsif.2010.0466)
3.
Rubenson J, Heliams DB, Lloyd DG, Fournier PA.
2004 Gait selection in the ostrich: mechanical and
metabolic characteristics of walking and running
with and without an aerial phase. Proc. R. Soc.
Lond. B 271, 1091–1099. (doi:10.1098/rspb.
2004.2702)
4.
Alexander RM, Maloiy GMO, Njau R, Jayes AS. 1979
Mechanics of running of the ostrich (Struthio
camelus). J. Zool. 187, 169–178. (doi:10.1111/j.
1469-7998.1979.tb03941.x)
5.
Hutchinson JR. 2004 Biomechanical modeling
and sensitivity analysis of bipedal running
ability. I. Extant taxa. J. Morphol. 262, 421–440.
(doi:10.1002/jmor.10241)
6.
Jindrich DL, Smith NC, Jespers K, Wilson AM. 2007
Mechanics of cutting maneuvers by ostriches
(Struthio camelus). J. Exp. Biol. 210, 1378–1390.
(doi:10.1242/jeb.001545)
7.
Kambic RE, Roberts TJ, Gatesy SM. 2014 Long-axis
rotation: a missing degree of freedom in avian
bipedal locomotion. J. Exp. Biol. 217, 2770–2782.
(doi:10.1242/jeb.101428)
8.
Rubenson J, Lloyd DG, Besier TF, Heliams DB,
Fournier PA. 2007 Running in ostriches (Struthio
camelus): three-dimensional joint axes alignment
and joint kinematics. J. Exp. Biol. 210, 2548–2562.
(doi:10.1242/jeb.02792)
9.
Hutchinson JR, Gatesy SM. 2000 Adductors,
abductors, and the evolution of archosaur
locomotion. Paleobiology 26, 734–751. (doi:10.
1666/0094-8373(2000)026,0734:AAATEO.2.0.
CO;2)
10. Hutchinson JR, Allen V. 2009 The evolutionary
continuum of limb function from early theropods to
birds. Naturwissenschaften 96, 423–448. (doi:10.
1007/s00114-008-0488-3)
11. Souter T, Cornette R, Pedraza J, Hutchinson J, Baylac
M. 2010 Two applications of 3D semi-landmark
morphometrics implying different template designs:
the theropod pelvis and the shrew skull. C.R.
Palevol. 9, 411–422. (doi:10.1016/j.crpv.2010.
09.002)
12. Hertel F, Campbell KE. 2007 The antitrochanter of
birds: form and function in balance. Auk 124, 789.
(doi:10.1642/0004-8038(2007)124[789:TAOBFA]2.0.
CO;2)
13. Firbas W, Zweymu¨ller K. 1971 Uber des Hu¨ftgelenk
der Ratiten. Geg. Morph. Jrb. 116, 91–103.
14. Tsai HP, Holliday CM. 2015 Articular soft tissue
anatomy of the archosaur hip joint: structural
homology and functional implications. J. Morphol.
276, 601–630. (doi:10.1002/jmor.20360)
15. Biewener AA. 1998 Muscle function in vivo: a
comparison of muscles used for elastic energy
savings versus muscles used to generate mechanical
power. Am. Zool. 38, 703–717. (doi:10.1093/icb/
38.4.703)
16. Wilson AM. 2000 Optimization of the muscle–
tendon unit for economical locomotion in cursorial
animals. In Skeletal muscle mechanics (ed. W
Herzog), pp. 517–547. Chichester, UK: Wiley & Sons.
17. Smith NC, Wilson AM. 2013 Mechanical and
energetic scaling relationships of running gait
through ontogeny in the ostrich (Struthio camelus).
J. Exp. Biol. 216, 841–849. (doi:10.1242/jeb.
064691)
18. Roberts TJ, Marsh RL, Weyand PG, Taylor CR. 1997
Muscular force in running turkeys: the economy of
minimizing work. Science 275, 1113–1115. (doi:10.
1126/science.275.5303.1113)
19. Dickinson MH, Farley CT, Full RJ, Koehl MA, Kram R,
Lehman S. 2000 How animals move: an integrative
view. Science 288, 100–106. (doi:10.1126/science.
288.5463.100)
20. Higham TE, Biewener AA, Delp SL. 2011 Mechanics,
modulation and modelling: how muscles actuate
and control movement. Phil. Trans. R. Soc. B 366,
1463–1465. (doi:10.1098/rstb.2010.0354)
21. Roberts TJ, Azizi E. 2011 Flexible mechanisms: the
diverse roles of biological springs in vertebrate
movement. J. Exp. Biol. 214, 353–361. (doi:10.
1242/jeb.038588)
22. Marsh RL, Ellerby DJ, Carr JA, Henry HT, Buchanan
CI. 2004 Partitioning the energetics of walking and
running: swinging the limbs is expensive. Science
303, 80–83. (doi:10.1126/science.1090704)
23. Gatesy SM. 1999 Guineafowl hind limb function. II:
Electromyographic analysis and motor pattern
evolution. J. Morphol. 240, 127–142. (doi:10.1002/
(SICI)1097-4687(199905)240:2,127::AID-JMOR
4.3.0.CO;2-Q)
24. Gatesy SM, Ba¨ker M, Hutchinson JR. 2009
Constraint-based exclusion of limb poses for
reconstructing theropod dinosaur locomotion.
J. Vertebr. Paleontol. 29, 535–544. (doi:10.1671/
039.029.0213)
25. Sellers WI, Manning PL. 2007 Estimating dinosaur
maximum running speeds using evolutionary
robotics. Proc. R. Soc. B 274, 2711–2716. (doi:10.
1098/rspb.2007.0846)
26. Bates KT, Schachner ER. 2012 Disparity and
convergence in bipedal archosaur locomotion.
J. R. Soc. Interface 9, 1339–1353. (doi:10.1098/rsif.
2011.0687)
27. Liu MQ, Anderson FC, Pandy MG, Delp SL.
2006 Muscles that support the body also
modulate forward progression during walking.
J. Biomech. 39, 2623–2630. (doi:10.1016/j.
jbiomech.2005.08.017)
28. McGowan CP, Kram R, Neptune RR. 2009
Modulation of leg muscle function in response to
altered demand for body support and forward
propulsion during walking. J. Biomech. 42,
850–856. (doi:10.1016/j.jbiomech.2009.01.025)
29. Zajac FE, Neptune RR, Kautz SA. 2003 Biomechanics
and muscle coordination of human walking: part II:
lessons from dynamical simulations and clinical
implications. Gait Posture 17, 1–17. (doi:10.1016/
S0966-6362(02)00069-3)
30. Lee SSM, Piazza SJ. 2009 Built for speed:
musculoskeletal structure and sprinting ability. J. Exp.
Biol. 212, 3700–3707. (doi:10.1242/jeb.031096)
31. Miller RH, Umberger BR, Caldwell GE. 2012
Limitations to maximum sprinting speed imposed
by muscle mechanical properties. J. Biomech. 45,
1092–1097. (doi:10.1016/j.jbiomech.2011.04.040)
32. An KN, Kwak BM, Chao EY, Morrey BF. 1984
Determination of muscle and joint forces: a new
technique to solve the indeterminate problem.
J. Biomech. Eng. 106, 364–367. (doi:10.1115/1.
3138507)
33. Kaufman KR, An KW, Litchy WJ, Chao EY. 1991
Physiological prediction of muscle forces
I. Theoretical formulation. Neuroscience 40,
781–792. (doi:10.1016/0306-4522(91)90012-D)
34. Erdemir A, McLean S, Herzog W, van den Bogert AJ.
2007 Model-based estimation of muscle forces
exerted during movements. Clin. Biomech. (Bristol,
Avon) 22, 131–154. (doi:10.1016/j.clinbiomech.
2006.09.005)
35. Anderson FC, Pandy MG. 2001 Static and dynamic
optimization solutions for gait are practically
equivalent. J. Biomech. 34, 153–161. (doi:10.1016/
S0021-9290(00)00155-X)
36. Miller RH, Umberger BR, Caldwell GE. 2009 Muscle
forces in the lower limb predicted by static and
dynamic optimization. In American Society of
Biomechanics 33rd Annual Meeting, State College,
Pennsylvania, PA, 26–29 August. See http://
www.asbweb.org/conferences/2009/937.pdf.
37. Lin Y-C, Dorn TW, Schache AG, Pandy MG. 2012
Comparison of different methods for estimating
muscle forces in human movement. Proc. Inst.
Mech. Eng. Part H J. Eng. Med. 226, 103–112.
(doi:10.1177/0954411911429401)
38. Morrow MM, Rankin JW, Neptune RR, Kaufman KR.
2014 A comparison of static and dynamic
optimization muscle force predictions during
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
17
wheelchair propulsion. J. Biomech. 47, 3459–3465.
(doi:10.1016/j.jbiomech.2014.09.013)
39. Hutchinson JR, Rankin JW, Rubenson J, Rosenbluth
KH, Siston RA, Delp SL. 2015 Musculoskeletal
modelling of an ostrich (Struthio camelus) pelvic
limb: influence of limb orientation on muscular
capacity during locomotion. PeerJ 3, e1001. (doi:10.
7717/peerj.1001)
40. Delp SL, Anderson FC, Arnold AS, Loan P, Habib A,
John CT, Guendelman E, Thelen DG. 2007 OpenSim:
open-source software to create and analyze
dynamic simulations of movement. IEEE Trans.
Biomed. Eng. 54, 1940–1950. (doi:10.1109/TBME.
2007.901024)
41. DeMers MS, Pal S, Delp SL. 2014 Changes in
tibiofemoral forces due to variations in muscle
activity during walking. J. Orthop. Res. 32,
769–776. (doi:10.1002/jor.22601)
42. Thelen DG, Anderson FC. 2006 Using computed
muscle control to generate forward dynamic
simulations of human walking from experimental
data. J. Biomech. 39, 1107–1115. (doi:10.1016/j.
jbiomech.2005.02.010)
43. Gatesy SM. 1999 Guineafowl hind limb function. I:
Cineradiographic analysis and speed effects.
J. Morphol. 240, 115–125. (doi:10.1002/(SICI)1097-
4687(199905)240:2,115::AID-JMOR3.3.0.CO;2-Y)
44. Nyakatura JA, Andrada E, Grimm N, Weise H, Fischer
MS. 2012 Kinematics and center of mass mechanics
during terrestrial locomotion in northern lapwings
(Vanellus vanellus, Charadriiformes). J. Exp. Zool.
Part A Ecol. Genet. Physiol. 317, 580–594. (doi:10.
1002/jez.1750)
45. Millard M, Uchida T, Seth A, Delp SL. 2013 Flexing
computational muscle: modeling and simulation of
musculotendon dynamics. J. Biomech. Eng. 135,
021005. (doi:10.1115/1.4023390)
46. Burkholder TJ, Lieber RL. 2001 Sarcomere
length operating range of vertebrate
muscles during movement. J. Exp. Biol. 204,
1529–1536.
47. Lichtwark GA, Wilson AM. 2007 Is Achilles tendon
compliance optimised for maximum muscle
efficiency during locomotion? J. Biomech. 40,
1768–1775. (doi:10.1016/j.jbiomech.2006.07.025)
48. Manal K, Buchanan TS. 2004 Subject-specific
estimates of tendon slack length: a numerical
method. J. Appl. Biomech. 20, 195–203.
49. Spector SA, Gardiner PF, Zernicke RF, Roy RR,
Edgerton VR. 1980 Muscle architecture and force–
velocity characteristics of cat soleus and medial
gastrocnemius: implications for motor control.
J. Neurophysiol. 44, 951–960.
50. Gatesy SM. 1994 Neuromuscular diversity in
archosaur deep dorsal thigh muscles. Brain Behav.
Evol. 43, 1–14. (doi:10.1159/000113619)
51. Rankin JW, Richter WM, Neptune RR. 2011
Individual muscle contributions to push and
recovery subtasks during wheelchair propulsion.
J. Biomech. 44, 1246–1252. (doi:10.1016/j.
jbiomech.2011.02.073)
52. Gatesy S. 1990 Caudefemoral musculature and the
evolution of theropod locomotion. Paleobiology 16,
170–186.
53. Roberts TJ, Belliveau RA. 2005 Sources of mechanical
power for uphill running in humans. J. Exp. Biol. 208,
1963–1970. (doi:10.1242/jeb.01555)
54. Pires NJ, Lay BS, Rubenson J. 2014 Joint-level mechanics
of the walk-to-run transition in humans. J. Exp. Biol.
217, 3519–3527. (doi:10.1242/jeb.107599)
55. Kimmel SA, Schwartz MH. 2006 A baseline of
dynamic muscle function during gait. Gait Posture
23, 211–221. (doi:10.1016/j.gaitpost.2005.02.004)
56. Zajac FE, Neptune RR, Kautz SA. 2002 Biomechanics
and muscle coordination of human walking. Part I:
introduction to concepts, power transfer, dynamics
and simulations. Gait Posture 16, 215–232. (doi:10.
1016/S0966-6362(02)00068-1)
57. Neptune RR, Kautz SA, Zajac FE. 2001 Contributions
of the individual ankle plantar flexors to support,
forward progression and swing initiation during
walking. J. Biomech. 34, 1387–1398. (doi:10.1016/
S0021-9290(01)00105-1)
58. Hicks JL, Uchida TK, Seth A, Delp SL. 2015 Is my
model good enough? Best practices for verification
and validation of musculoskeletal models and
simulations of movement. J. Biomech. Eng. 137,
020905. (doi:10.1115/1.4029304)
59. Gangl D, Weissengruber GE, Egerbacher M,
Forstenpointner G. 2004 Anatomical description
of the muscles of the pelvic limb in the ostrich
(Struthio camelus). Anat. Histol. Embryol. 33,
100–114. (doi:10.1111/j.1439-0264.2003.00522.x)
60. Guess TM, Liu H, Bhashyam S, Thiagarajan G. 2013
A multibody knee model with discrete cartilage
prediction of tibio-femoral contact mechanics.
Comput. Methods Biomech. Biomed. Engin. 16,
256–270. (doi:10.1080/10255842.2011.617004)
61. Bei Y, Fregly BJ. 2004 Multibody dynamic
simulation of knee contact mechanics. Med. Eng.
Phys. 26, 777–789. (doi:10.1016/j.medengphy.
2004.07.004)
62. Lerner ZF, DeMers MS, Delp SL, Browning RC. 2015
How tibiofemoral alignment and contact locations
affect predictions of medial and lateral tibiofemoral
contact forces. J. Biomech. 48, 644–650. (doi:10.
1016/j.jbiomech.2014.12.049)
63. Delp SL. 2001 Three-dimensional dynamic
simulation of total knee replacement motion during
a step-up task. J. Biomech. Eng. 123, 599. (doi:10.
1115/1.1406950)
64. Silder A, Whittington B, Heiderscheit B, Thelen DG.
2007 Identification of passive elastic joint
moment–angle relationships in the lower
extremity. J. Biomech. 40, 2628–2635. (doi:10.
1016/j.jbiomech.2006.12.017)
65. Davy DT, Audu ML. 1987 A dynamic optimization
technique for predicting muscle forces in the swing
phase of gait. J. Biomech. 20, 187–201. (doi:10.
1016/0021-9290(87)90310-1)
66. Domalain M, Vigouroux L, Berton E. 2010 Determination
of passive moment–angle relationships at the
trapeziometacarpal joint. J. Biomech. Eng. 132, 071009.
(doi:10.1115/1.4001397)
67. Hof AL, Van Zandwijk JP, Bobbert MF. 2002
Mechanics of human triceps surae muscle in
walking, running and jumping. Acta Physiol.
Scand. 174, 17–30. (doi:10.1046/j.1365-201x.2002.
00917.x)
68. Blemker SS, Delp SL. 2006 Rectus femoris
and vastus intermedius fiber excursions predicted
by three-dimensional muscle models. J. Biomech.
39, 1383–1391. (doi:10.1016/j.jbiomech.2005.04.
012)
69. Srinivasan M, Ruina A. 2006 Computer optimization
of a minimal biped model discovers walking and
running. Nature 439, 72–75. (doi:10.1038/
nature04113)
70. Usherwood JR, Channon AJ, Myatt JP, Rankin JW,
Hubel TY. 2012 The human foot and heel-sole-toe
walking strategy: a mechanism enabling an inverted
pendular gait with low isometric muscle force?
J. R. Soc. Interface 9, 2396–2402. (doi:10.1098/rsif.
2012.0179)
rsif.royalsocietypublishing.org
J. R. Soc. Interface 13: 20160035
18

Inferring muscle functional roles of the ostrich pelvic limb during walking and running using computer optimization.
Rankin, Jeffery W,Rubenson, Jonas,Hutchinson, John R