Virtual palaeontology: Gait reconstruction of extinct vertebrates using high performance computing

Abstract

Gait reconstruction of extinct animals requires the integration of palaeontological information obtained from fossils with biological knowledge of the anatomy, physiology and biomechanics of extant animals. Computer simulation provides a methodology for combining multimodal information to produce concrete predictions that can be evalu- ated and used to assess the likelihood of competing locomotor hypotheses. However, with the advent of much faster supercomputers, such simulations can also explore a wider range of possibilities, allowing the generation of gait hypotheses de novo. In this paper we document the use of an 8000 core computer to produce mechanically and physiologically plausible gaits and trackway patterns for a sub-adult dinosaur (Edmon- tosaurus annectens), evaluating a large range of locomotor possibilities in terms of running speed. The anatomical reconstruction presented is capable of running and hopping bipedal gaits; trot, pace and single foot symmetrical quadrupedal gaits; and asymmetrical galloping gaits. Surprisingly hopping is the fastest gait (17 ms-1), fol- lowed by quadrupedal galloping (16 ms-1) and bipedal running (14 ms-1). Such a hop- ping gait is considered unlikely for this animal, which would imply that either our anatomical and physiological reconstruction is incorrect or there are important con- straints such as skeletal loading and safety factor that are currently not included in our simulation. The most likely errors are in joint ranges of motion, combined with the lengths of muscle fibres and tendons since these values are difficult to reconstruct. Thus the process of gait simulation is able to narrow down our predictions of unknown features of the extinct animal using a functional bracket. Trackway geometries derived from the gait models are currently very basic due to the simplicity of the ground/foot contact model used, but demonstrate the future potential of this technology for inter- preting and predicting trackway geometry.

Full text

Palaeontologia Electronica
http://palaeo-electronica.org
PE Article Number: 12.3.13A
Copyright: Paleontological Association December 2009
Submission: 15 November 2008. Acceptance: 2 July 2009
Sellers, W.I., Manning, P.L., Lyson, T., Stevens, K., and Margetts, L., 2009. Virtual Palaeontology: Gait Reconstruction of Extinct
Vertebrates Using High Performance Computing. Palaeontologia Electronica Vol. 12, Issue 3; 11A: 26p;
http://palaeo-electronica.org/2009_3/180/index.html
VIRTUAL PALAEONTOLOGY: GAIT RECONSTRUCTION OF EXTINCT
VERTEBRATES USING HIGH PERFORMANCE COMPUTING
W.I. Sellers, P.L. Manning, T. Lyson, K. Stevens, and L. Margetts
ABSTRACT
Gait reconstruction of extinct animals requires the integration of palaeontological
information obtained from fossils with biological knowledge of the anatomy, physiology
and biomechanics of extant animals. Computer simulation provides a methodology for
combining multimodal information to produce concrete predictions that can be evalu-
ated and used to assess the likelihood of competing locomotor hypotheses. However,
with the advent of much faster supercomputers, such simulations can also explore a
wider range of possibilities, allowing the generation of gait hypotheses de novo. In this
paper we document the use of an 8000 core computer to produce mechanically and
physiologically plausible gaits and trackway patterns for a sub-adult dinosaur (Edmon-
tosaurus annectens), evaluating a large range of locomotor possibilities in terms of
running speed. The anatomical reconstruction presented is capable of running and
hopping bipedal gaits; trot, pace and single foot symmetrical quadrupedal gaits; and
asymmetrical galloping gaits. Surprisingly hopping is the fastest gait (17 ms
-1
), fol-
lowed by quadrupedal galloping (16 ms
-1
) and bipedal running (14 ms
-1
). Such a hop-
ping gait is considered unlikely for this animal, which would imply that either our
anatomical and physiological reconstruction is incorrect or there are important con-
straints such as skeletal loading and safety factor that are currently not included in our
simulation. The most likely errors are in joint ranges of motion, combined with the
lengths of muscle fibres and tendons since these values are difficult to reconstruct.
Thus the process of gait simulation is able to narrow down our predictions of unknown
features of the extinct animal using a functional bracket. Trackway geometries derived
from the gait models are currently very basic due to the simplicity of the ground/foot
contact model used, but demonstrate the future potential of this technology for inter-
preting and predicting trackway geometry.
W.I. Sellers. Lecturer in Integrative Vertebrate Biology, Faculty of Life Sciences, The University of
Manchester, Jackson's Mill, PO Box 88, Sackville Street, Manchester M60 1QD, UK,
William.Sellers@manchester.ac.uk
P.L. Manning. Senior Lecturer in Palaeontology, School of Earth, Atmospheric and Environmental
Sciences, University of Manchester, Manchester, M13 9PL, UK.
T. Lyson. Graduate Student, Department of Geology and Geophysics, Yale University, New Haven, USA.
K. Stevens. Professor of Computer Science, Department of Computer and Information Science, Deschutes
Hall, University of Oregon, Eugene, OR 97403.

Sellers et al.: Gait Reconstruction
2
L. Margetts . Visiting Lecturer in Geology, School of Earth, Atmospheric and Environmental Sciences,
University of Manchester, Manchester, M13 9PL, UK.
Keywords: locomotion; dinosaur; Hadrosaur; robotics; simulation
INTRODUCTION
Computational techniques are now regularly
used to investigate the locomotion of extinct spe-
cies. For example finite element analysis is now
frequently used to investigate the strength of skele-
tal elements under load (Rayfield et al. 2001; Man-
ning et al. 2006; Sereno et al. 2007), and imaging
techniques such as LIDAR are powerful tools in the
analysis of fossil trackways of vertebrates (Bates et
al. 2008). However the most directly applicable
technique is locomotor modelling. Models vary
from the highly theoretical (e.g., Alexander 1992;
McGeer 1992; Minetti and Alexander 1997; Srini-
vasan and Ruina 2006) to more realistic simula-
tions (e.g., Yamazaki et al. 1996; Sellers et al.
2003; Nagano et al. 2005), and these approaches
have been used both to understand the fundamen-
tal mechanics of terrestrial gait and also to predict
gait parameters: either those internal values that
are difficult to measure directly or for fossil verte-
brates where experimentation is impossible.
Simple models have the great advantage of
being straightforward to understand and unequivo-
cal in their predictions. More complex models
depend on a much greater number of modelling
parameters and are therefore more difficult to inter-
pret. However, because they are based more
closely on real organisms they can be directly
tested through comparison of their predictions to
those obtained experimentally. For example Srini-
vasan and Ruina’s recent model (Srinivasan and
Ruina 2006) predicts that there are three types of
stable, efficient bipedal locomotion that they
describe as walking, pendular running and running.
The model itself is highly simplified with mass-less,
linear sprung limbs and a point mass body, and so
its predictions cannot be tested experimentally.
More realistic models are similarly able to produce
these gaits spontaneously (Sellers et al. 2004; Sell-
ers et al. 2005) but because they are more closely
modelled on the morphology of experimental sub-
jects, their predictions are more accurate and can
be directly compared with experimental data.
The earliest musculoskeletal models for use in
reconstructing gait in vertebrate fossils date back
to the pioneering work of Yamazaki et al.
(Yamazaki et al. 1996) who produced a highly
sophisticated neuromusculoskeletal simulation to
investigate the evolution of bipedality in humans
and other primates. Indeed it is early human fossils
that have received the most attention with a num-
ber of models of extinct bipeds having been pro-
duced (Crompton et al. 1998; Kramer 1999; Sellers
et al. 2004; Nagano et al. 2005; Sellers et al. 2005;
Ogihara and Yamazaki 2006). However, the study
of terrestrial vertebrate locomotion has also
involved computer simulations: terror birds (Blanco
and Jones 2005) and dinosaurs (Gatesy et al.
1999; Stevens 2002; Hutchinson et al. 2005; Sell-
ers and Manning 2007).
Simulations require a musculoskeletal model
and are either kinematically based where a move-
ment pattern is provided for the animal based on
either trackway data or motion-capture information
from extant species, or kinetically based where the
simulation is driven by muscular forces usually with
a global optimisation criterion to produce efficient
models of high speed locomotion. The latter
approach is particularly valuable in situations
where there are no suitable modern analogues
(usually because a particular morphological form is
no longer found) or where there is little trackway
data (for example most forms of high speed loco-
motion). Simulation technology is now relatively
mature with a range of both commercial [e.g.,
SC.ADAMS (www.mscsoftware.com), SDFast
(www.sdfast.com), MADYMO (www.tass-
safe.com)] and open-source [e.g., Dynamechs
(dynamechs.sourceforge.net), ODE
(opende.sourceforge.net), PhysSym (phys-
sim.sourceforge.net) and Tokamac (www.tokamak-
physics.com)] along with front ends that allow
simplified construction of biomechanical models
[e.g., SIMM (www.musculographics.com), Open-
SIMM (www.simmtk.org), Marilou Robotics Studio
(www.anykode.com), and LifeMod (www.lifemod-
eler.com)]. Gait production also requires gait con-
trollers, and for complex models it is impractical to
explore exhaustively the whole solution space so a
selective search is needed to find suitable control-
ler parameters. Popular techniques are to use finite
steps within the search space (Srinivasan and
Ruina 2006); to constrain parts of the model using
functional linkage and pre-designed neural net-

PALAEO-ELECTRONICA.ORG
3
works (Yamazaki et al. 1996); and to use genetic
algorithms to explore selectively profitable areas of
the search space (Sellers et al. 2003). These
approaches are frequently combined with genetic
algorithms and this combined approach is particu-
lar popular in robotics leading to the term evolution-
ary robotics (Nolfi and Floreano 2000).
Hadrosaurian dinosaurs are an ideal study
animal for gait reconstruction given they were par-
ticularly diverse, and their fossil remains relatively
abundant (Horner et al. 2004). Trackway interpre-
tations have suggested that they were gregarious
(Carpenter 1992; Lockley and Matsukawa 1999).
Their gait is particularly interesting because there
has been a debate on the function of their well-
developed ossified tendons arrayed along their spi-
nal columns (Organ 2006), and also as to whether
they were quadrupedal, bipedal or indeed faculta-
tively able to switch between the two gaits (Galton
1970; Maryańska and Osmólska 1984; Lockley
1992; Meyer and Thuring 2003). Added to that a
number of extraordinarily well-preserved speci-
mens have been found with probable soft tissue
preservation (for review see Manning 2008). One
particular aspect of gait that has received consider-
able attention is the prediction of maximal running
speed. Chasing down prey is a vital factor in the
lives of extant predators, as is the avoidance of
being captured for prey animals. It is, therefore, of
little surprise that speed estimation is of such inter-
est to vertebrate palaeobiologists. Recent work
estimating dinosaur maximum running speeds
(Sellers and Manning 2007) provided a good
match between predicted and simulated top
speeds of extant bipeds. However, the results for
bipedal dinosaurs were surprising in that there was
a strong inverse relationship between body mass
and top speed. Theoretical considerations have
suggested that maximal running speed should be
independent of body mass (Hill 1950) or should
increase with body mass (Blanco and Gambini
2007). However, experimental and observational
data suggest that there is an optimum body size for
running speed at about 100 kg with both smaller
and larger animals running slower (Garland 1983).
These data suggest that simple theoretical models
are unable to adequately represent the diversity of
physical processes involved in maximal speed run-
ning and in particularly the differences associated
with varying gaits (bipedal, quadrupedal, symmetri-
cal and asymmetrical), and it is this aspect that is
the focus of this paper.
METHODS
Following on from previous work, we used the
GaitSym simulation system based on the Open
Dynamics Engine (ODE) (Sellers and Manning
2007). To produce the musculoskeletal model, a
mounted skeleton of a juvenile Edmontosaurus
annectens (BHI 126950) was photographed (Fig-
ure 1) and measured, and selected elements were
laser scanned using a Polhemus FastSCAN sys-
tem (complete hindlimb and forelimb, limb girdles,
skull and representative vertebrae and ribs). This
system allows detailed scanning using a short-
range laser scanner with the advantage that both
the scanning head and the object being scanned
can be freely moved, which is especially useful
when scanning complex objects such as vertebrae
FIGURE 1. Edmontosaurus annectens, composite cast of sub-adult based upon remains from Corson County (South
Dakota, USA) in the Hell Creek Formation (BHI 126950).

Sellers et al.: Gait Reconstruction
4
and skulls. The raw scan files were exported from
the proprietary FastSCAN software in .obj format
and imported into Maya (www.autodesk.com)
where bone outlines were fitted to the scans (Fig-
ure 2). This process allows correcting for distortion,
and the idealised geometries produced have a
much lower polygon count, which allows them to
be used efficiently for later visualisation, animation
and modelling. The individual, re-inflated bones are
then articulated within Dinomorph (www.dino-
morph.com) where joint centres and ranges of
motion are defined, and the rearticulated model is
re-exported to Maya to allow the construction of the
body segment geometry and to define origin and
insertion points of muscles (Figure 3) for import
into GaitSym. A detailed description of the recom-
mended workflow for creating models can be found
in the GaitSym user manual available at www.ani-
malsimulation.org.
With current technology it is relatively easy to
simulate the contraction of a large number of mus-
cles, but treating each muscle as a separate entity
(or even functionally subdividing muscles) pro-
duces extremely complex gait controllers, and our
current system cannot find suitable contraction pat-
terns in a reasonable length of time. The complex-
ity can be reduced considerably by grouping
functionally equivalent muscles. The hindlimb mus-
culature was taken from Dilkes (2000) and the fore-
limb musculature from Schachner (2005) and
FIGURE 2. Reconstruction of Edmontosaurus foot using Maya. Left shows scanned bones with uncorrected tapho-
nomic distortion, Centre shows combined fossil and re-inflated bone, Right shows a re-inflated foot ready to be used
in a musculoskeletal model.
FIGURE 3. Reconstructing the Edmontosaurus skeleton. TL rearticulation; TR joint definition; BL defining body
hoops; BR lofting estimated body surfaces.

PALAEO-ELECTRONICA.ORG
5
composite muscle groupings produced depending
on action (groupings named after Carrano and
Hutchinson 2002). Deciding the muscle mass to
assign is problematic, but for consistency with pre-
vious work we chose a figure of 30% of body mass
for extensor musculature (Hutchinson 2004;
Hutchinson 2004; Sellers and Manning 2007) and
20% of body mass for flexor muscle mass (Sellers
and Manning 2007). However, we note that these
values are likely to be towards the upper end of
plausible muscle mass estimates (Grand 1977;
Hutchinson and Garcia 2002). Dividing this total
muscle mass among even a simplified range of
muscles is similarly difficult and so the pragmatic
solution of dividing equally among the joints of
each leg was chosen and in the case of the qua-
drupedal simulation an arbitrary division was made
such that 30% of the muscle mass was in the fore-
limb and 70% in the hindlimb reflecting the covaria-
tion in limb geometry for Edmontosaurus. Even
then there are muscle groups that have an action
over more than one joint, and in these cases they
receive a mass proportion from each joint. The
fibre lengths and tendon lengths were calculated
by measuring the minimum and maximum length of
each composite muscle obtained by moving the
joints through their full ranges of motion and using
the length change for the fibre length and the mean
overall length minus the fibre length as the tendon
length. This is likely to be a fairly optimal length for
any muscle since vertebrate muscles are typically
able to generate force from approximately 60% to
160% of their resting length (McGinnis 1999).
Using length change through joint range of motion
as a way of defining fibre length also eliminates
any uncertainty over moment arm since the lever-
age gain of a larger moment arm is exactly bal-
anced by the force production loss for a given
mass of muscle. Physiological cross section area
is calculated from fibre length and muscle volume
assuming a muscle density of 1056 kg m
-3
(Winter
1990). All muscle information is shown in Table 1.
Segmental mass properties were generated auto-
matically from the body outlines using a body den-
sity of 1000 kg m
-3
(Henderson 1999). The total
volume was also used to estimate a total body
TABLE 1. Per limb muscle proportions for quadrupedal and bipedal models. BM - Body Mass, PCA - Physiological
Cross-section Area, FL - Fibre Length, TL - Tendon Length, FD - Flexor Digitorum, ED - Extensor Digitorum. FL and TL
are the same in both quadrupedal and bipedal models.
Quadruped Biped
% BM (kg) PCA (m
2
) FL (m) TL (m) % BM (kg) PCA (m
2
)
Hindlimb Deep Dorsal Group 2.33% 0.152 0.104 0.082 3.33% 0.217
Triceps Femoris Group 1.75% 0.018 0.664 0.201 2.50% 0.026
Caudo Femoralis Group 3.50% 0.063 0.375 0.496 5.00% 0.090
Femoro Tibialis Group 1.75% 0.076 0.157 0.470 2.50% 0.108
Flexor Cruris Group 2.33% 0.030 0.521 0.289 3.33% 0.043
Gastrocnemius Lateralis +
FD
1.75% 0.055 0.215 0.623 2.50% 0.079
Tibialis Anterior + ED 2.33% 0.191 0.083 0.369 3.33% 0.272
Gastrocnemius Medialis 1.75% 0.252 0.047 0.649 2.50% 0.359
Forelimb Shoulder Flexors 1.00% 0.027 0.246 0.267 0% 0
Triceps Brachii 0.75% 0.030 0.171 0.239 0% 0
Shoulder Extensors 1.50% 0.162 0.063 0.485 0% 0
Biceps Brachii 0.50% 0.021 0.160 0.302 0% 0
Elbow Flexors 0.50% 0.035 0.098 0.016 0% 0
Elbow Extensors 0.75% 0.108 0.047 0.138 0% 0
Wrist Flexors 1.00% 0.252 0.027 0.298 0% 0
Wrist Extensors 1.50% 0.323 0.031 0.353 0% 0

Sellers et al.: Gait Reconstruction
6
mass of 715.3 kg. Limited experimentation was
performed using alternative densities and including
air sacs (Alexander 1989) but the differences found
were small and have therefore been ignored since
the uncertainty in the body outlines is likely to be a
much larger source of error. The models are fully
three-dimensional but all joints are hinge joints
allowing only parasagittal rotation to keep the
model at manageable levels of complexity. The full
specification of each model as a human readable
XML file is available for download from http://
www.animalsimulation.org. The version for gallop-
ing is included in the Appendix.
The muscles were activated by a 5-phase pat-
tern. This was applied to each muscle for a fixed
duration, and then the left and right hand side pat-
terns were swapped and reapplied. A complete
gait cycle thus consisted of 5 distinct activation pat-
terns for 32 muscles plus the cycle duration: a total
of 161 parameters. The musculoskeletal model as
placed in a stationary, upright pose with the fore-
limb tightly flexed in the bipedal models but
extended in the quadrupedal model, and this was
used as the starting condition for the genetic algo-
rithm optimisation process. This process has been
described in detail elsewhere (Sellers et al. 2003;
Sellers and Crompton 2004; Sellers et al. 2005) but
in brief it proceeds by cycling through a testing
phase, a selection phase and a reproduction
phase. We start with 1000 random activation pat-
terns, and these patterns are tested by applying
these to the model and running the simulation to
see how far that activation pattern can drive the
model forward in 5 seconds of simulated time. This
test evaluates the fitness of these patterns with the
fittest being able to drive the model a little further
forward than the others. This procedures is then
followed by a selection phase where 'roulette
wheel' algorithm (Davis 1991) is used to select
which of the original 1000 patterns is used as a
model, which means that the best of the previous
patterns are more likely to contribute to subse-
quent patterns, and the best 100 patterns are
retained for subsequent generations in any case.
In this algorithm the roulette wheel is biased so the
likelihood of random selection is proportional to the
forward distance achieved by the pattern.
In the reproduction phase another 1000 pat-
terns are then created using the selected patterns
as models and then adding a small amount of ran-
dom variation or by merging parts of two patterns
(this alteration process is sometimes referred to as
mutation). The new patterns are then entered into
the cyclic process again where they are tested,
selected and reproduced as before. There is a rea-
sonable likelihood that one of the new patterns will
work better than the ones in the previous genera-
tion. This process is repeated 1000 times or until
no improvement has been detected for 100
repeats. At the end of this process, from a standing
start, some form of forward locomotion will have
been generated. Rather than begin again from a
standing start with a new random set of patterns, a
new set of initial conditions are generated from the
simulation by taking a snapshot of the model state
after one gait cycle. This state is now a dynamic
starting condition with velocities as well as posi-
tions for all the segments and enables us to boot-
strap the simulation process since we are aiming to
simulate steady state locomotion rather than accel-
eration. We also use the previous best set of pat-
terns as the starting set of patterns since these are
likely to be good patterns for the new starting con-
ditions. The whole process (1000 batches of new
patterns) is then repeated, and this process of
restarting from a new set of initial conditions gener-
ated from a previous run is repeated 20 times. This
simulation has potentially been run 20 × 1000 ×
1000 times although usually because of the termi-
nation after no improvement rule it is usually about
half this value i.e., 10,000,000 repeats. In this par-
ticular project this process was performed for both
the bipedal model and for the quadrupedal model,
and each model was repeated 10 times. Given that
the simulator runs in roughly half real time, over
10,000 days of CPU time is represented. Fortu-
nately the system is able to run on multiple com-
puters simultaneously so this amount of computing
power is relatively manageable.
After optimisation, the best runs are chosen
from each of the 20 top level repeats, and these
are visualised and the gait classified. The gaits are
generated randomly, and the same selective effort
has been put into each case so these should be an
unbiased estimate of the locomotor capabilities of
the quadrupedal and bipedal forms. The random
noise added is normally distributed so given long
enough each run can theoretically explore the
whole of the gait search space. Experience has
shown that with this amount of computational effort
it will tend to stabilise around a local rather than a
global optima that allows it to find a range of sub-
optimal gaits but to produce high quality gait within
these sub-optima. However, it was hoped that with
10 repeats it would be possible to detect patterns
of preferred gait: gaits that either occupy a large
proportion of the search space or that produce con-
sistently higher speed than other gaits. The gait

PALAEO-ELECTRONICA.ORG
7
types produced were visually identified. Selected
gaits were also further optimised using a lower total
run time (3 seconds) to see whether the require-
ments of stability were hampering their maximum
running speed.
RESULTS
All runs produced effective forward gait but
there was a surprisingly large variation in the gaits
generated and the maximum speeds. Table 2 sum-
marizes the results.
The quadrupedal model never generated a
completely bipedal run but in 3 out of 10 occasions
the contribution of the forelimb was minimal: brush-
ing along the ground momentarily at some point in
the gait cycle. The other seven gaits generated
were quadrupedal, and the full range of symmetri-
cal gaits were demonstrated: trot, pace and single
foot (Hildebrand 1965). However, given the essen-
tially symmetrical nature of the muscle pattern gen-
erator it was surprising that the highest speed gait
discovered was the asymmetrical gallop. The
enforced bipedal model generated a range of hop-
ping and primarily running gaits. The surprising
finding was that the fastest gait seen was a kanga-
roo style hop.
Of these gaits, three were identified as inter-
esting and were re-optimised for a 3 second dura-
tion rather than a 5 second duration to reduce the
effects of stability that seemed to particularly effect
the bipedal runs. All top speeds increased (bipedal
run 14.0, quadrupedal gallop 15.7, bipedal hop
17.3) but the biggest increase was for the bipedal
run. The bipedal run and gallop as well as the qua-
drupedal gallop can be seen as pre-rendered mov-
ies (Movie 1, 2 and 3).
The simulator can also calculate the ground
reaction force generated by the model, which can
be rendered as a virtual trackway (Figure 4). The
foot/substrate contact model is highly simplified
being represented as contact spheres attached to
the distal ends of the digits. To produce the contact
maps, these point forces have been smeared over
a larger area to be more representative of a hadro-
TABLE 2. Descriptions of the gaits generated by the simulator including the top speed attained.
Quadrupeded
V
(ms
-1
) Description
8.0 Skipping hindlimb with minimal forelimb contribution
10.4 Trotting gait
10.5 More of less bipedal with odd skipping gait, minimal forelimb contribution
10.6 Diagonal single foot gait
11.4 More or less bipedal run, no regular forelimb contribution
12.0 More or less bipedal run, no regular forelimb contribution
12.4 Pacing gait
12.6 Gallop but without a very organised or consistent forelimb contribution
13.1 Pacing gait
13.7 Galloping gait
Biped 6.3 Irregular hop/skip
7.2 Irregular run
7.4
Irregular run
8.4
Run
9.0 Run
9.3 Slightly irregular run
10.8 Slightly irregular run
11.1 Slightly irregular hop/skip
11.5 Hop
16.5 Hop

Sellers et al.: Gait Reconstruction
8
MOVIE 2. Bipedal running gait generated by the simulator. Playback is at approximately quarter speed (24 fps from
a 100 fps original).
MOVIE 3. Quadrupedal galloping gait generated by the simulator. Playback is at approximately quarter speed (24
fps from a 100 fps original).
MOVIE 1. Bipedal hopping gait generated by the simulator. Playback is at approximately quarter speed (24 fps from a
100 fps original).

PALAEO-ELECTRONICA.ORG
9
saur foot. However the differences between the dif-
ferent trackway types can be clearly seen.
DISCUSSION
The simulator has clearly been able to find a
large range of gaits that are both physiologically
and anatomically possible given the constraints of
the model. The fastest gait is the bipedal hop, fol-
lowed by the quadrupedal gallop and finally the
bipedal run. The question then becomes which of
these gaits would the animal have chosen?
Bipedal hopping would seem to be the obvious
answer but this interpretation of the findings would
be very bold. It is true that hopping has been
described in dinosaurs based on trackway evi-
dence, and an ichniospecies has even been pro-
posed based on a putatively hopping gait:
Saltosauropus latus (Bernier et al. 1984). However
the current interpretation of these ostensibly hop-
ping tracks is that they are swimming traces proba-
bly produced by a large turtle (Lockley 2007). The
largest hopping mammals are probably the Pleisto-
cene megafaunal species of macropodid Procopt-
odon goliah with a mean estimated body mass of
232 kg (Helgen et al. 2006) so a 715 kg hopper is
not an impossibility but identification of hopping
based on morphological features is not straightfor-
ward. Whilst kangaroos are highly anatomically
specialised, other hopping animals are less obvi-
ous: Otolemur garnettii and Galago crassicaudatus
are morphologically very similar bushbabies and
yet one is a habitual hopper when on the ground
whereas the other employs a bounding gallop
(Oxnard et al. 1990). However, what is more likely
is that the simulation is able to tell us that our
reconstruction is incorrect: features of the model
that are insufficiently constrained have allowed it to
develop a highly effective hopping gait that would
not be available for the animal itself.
There are several possibilities here. Firstly
hopping may put higher loads on the skeleton than
running, and this is not currently incorporated into
the simulation. Secondly, ranges of motion on joint,
muscle fibre lengths or tendon lengths may allow
hopping to occur. Thus the question becomes why
could this animal not hop as the simulation shows
the current configuration could do so effectively. In
the former case the question of skeletal loading
during locomotion has received considerable atten-
tion. Initial work used beam theory to explain
observed differences in skeletal robusticity with
body size (McMahon 1973), and this has been
used to estimate the athletic ability of dinosaurs
(Alexander 1985). More recent work has made
considerable use of finite element analysis (FEA)
to investigate the detailed loading of individual
skeletal elements (Rayfield et al. 2001; Rayfield
2005; Manning et al. 2006; Sereno et al. 2007).
Musculoskeletal models allow these numerical
analyses to be taken to their next logical step since
they calculate the forces in individual muscles and
muscle groups as well as the reaction forces and
torques around joints. Thus the full in vivo loading
environment of skeletal elements is available, and
following on from work elsewhere (Smith et al.
2007) we are curretnly developing software to inte-
grate high speed FEA of skeletal loading into the
current simulation system.
In the latter case, however, diagnosing hop-
ping would require considerably more experimental
work on a wide range of extant hopping animals
including the development of hopping simulators
that match experimental results. However as a pre-
liminary investigation of the current results, we per-
formed a simple beam mechanic analysis of the
loads on the femur and humerus based solely on
the joint reaction forces calculated by the model
(Alexander 1974). This ignores much of the com-
plexity of the actual shape, loading and movement
of the bones but does serve to illustrate potential
loading differences associated with each gait that
may explain actual gait choice. The bones were
modelled as thick-walled cylinders using the mea-
sured mean external radius and assuming an inter-
nal radius half the external radius as is typical for
load-bearing bones in mammals (Garcia and da
TABLE 3. Peak mid-shaft skeletal loading for each of the models. Positive values represent peak compres-
sive stress and negative values peak tensile stress. All values are in MPa.
Bipedal Hop
16.5 ms
-1
Bipedal Run (MPa)
14.0 ms
-1
Quadrupedal Gallop
13.7 ms
-1
Femur Min -555 -253 -357
Femur Max 574 269 373
Humerus Min -710
Humerus Max 716

Sellers et al.: Gait Reconstruction
10
Silva 2006). In this form of analysis, the bone is
assumed to be stationary and fixed at the mid-
shaft. Loading is calculated as compressive, and
lateral bending components can be combined to
estimate the peak tensile and compressive loads.
Table 3 shows the results for the three high-speed
gait types. It is clear that in this simulation both
hopping and galloping generate very high skeletal
loads, and the bipedal running results are much
lower. The breaking stress of bone is approxi-
mately 240 MPa for a 1000 kg animal (Biewener
1982) but it is highly dependent on loading rate,
and considerably higher values can be withstood
for high strain rates (Reilly and Burstein 1974).
However, experimentally measured peak stress
values for running animals are much lower than
this with typical strain values of 2000 to 3000
microstrain which equates to 40 to 60 MPa (Rubin
and Lanyon 1984). This value would suggest that
bipedal running is the most likely gait but it must be
remembered that the optimisation did not take
skeletal loading into account when generating gait.
There may be very similar results in terms of top
speed that have much lower skeletal loads associ-
ated. This area is clearly where research effort
needs to be focussed.
The results might be interpreted as weakly
supporting bipedal running as the preferred high-
speed locomotor mode for Edmontosaurus. It is
certainly true that recent finds show friction cal-
luses on the manus (Figure 5) but the weight of
current thought proposes hadrosaurs to be primar-
ily bipedal with facultative quadrupedalism at low
speeds (Galton 1970; Meyer and Thüring 2003).
The simulations show that the animal can certainly
facultatively switch between bipedalism and qua-
drupedalism but in fact at high speeds bipedalism
was likely to be preferable. However the quadrupe-
dal mode is much more stable than the bipedal one
as judged by the much closer range of speed esti-
mates in the 10 independent repeats. The highest
speed gallop is faster than the fastest bipedal run
even though the amount of locomotor muscle is the
same in both cases. Added to that, the quadrupe-
dal gait might be expected to have a better turning
speed since it allows force to be applied to the sub-
strate at an increased distance from the centre of
mass leading to a greater possible torque
(although counter to this argument is the fact that
the anterior muscle mass would increase the
moment of inertia so that a greater impulse would
be required to affect a turn). Turning speed in ani-
mals is currently poorly understood.This is an area
where there is very little experimental data for com-
parison. Certainly if an animal has forelimbs that
can touch the ground there is very little point in not
using them although it is clear that care might be
necessary to maintain skeletal loading within
acceptable limits. Galloping gaits are unsurpris-
ingly preferred at high speeds, and such gaits are
adopted by most high-speed quadrupeds. The idea
that an animal might rear-up onto its hind limbs at
Bipedal Hop
X (m)
Y (m)
0 2 4 6 8 10 12 14 16 18 20
−1
0
1
0
5000
10000
Bipedal Run
X (m)
Y (m)
0 2 4 6 8 10 12 14 16 18 20
−1
0
1
0
5000
10000
Quadrupedal Gallop
X (m)
Y (m)
0 2 4 6 8 10 12 14 16 18 20
−1
0
1
0
5000
10000
FIGURE 4. Contour plots of the ground reaction forces generated by the model for the three fastest gait
types. Top: bipedal hop; middle: bipedal run; bottom quadrupedal gallop.

PALAEO-ELECTRONICA.ORG
11
high speed confuses acceleration that might tend
to tilt the animal backwards with steady state high-
speed running. In terms of medium speed gaits
there is overlap between the bipedal and symmetri-
cal gaits with the pace slightly preferred to the trot
or single foot. Bipedalism has more appeal at low
speed, both because it is supported by trackway
evidence (Lockley 1992) and also because that is
when the extra mobility in head, neck and cranial
trunk may be useful both for predator search
behaviour and foraging. The predicted top speeds
themselves are entirely reasonable. They are
faster than our previous estimates for predatory
dinosaurs (Sellers and Manning 2007) but rather
slower than modern quadrupeds of equivalent
body size. For example, horses are quoted as hav-
ing running speeds of 70 km/h (19.4 ms
-1
) (Gar-
land 1983). One could certainly argue that a life-
lunch cost-benefit analysis would always assume
that a prey animal should invest more in predator
avoidance than a prey animal should invest in prey
capture.
The virtual trackways should be considered a
proof-of-concept rather than being particularly use-
ful. They do show the effects of spacing changes
with gait as a function of speed rather well but the
current state of ground-substrate interaction simu-
lation within the model is insufficient to provide a
good footprint indent. However there is no reason
why future versions of the model could not incorpo-
rate the improved models currently being devel-
oped (Manning 2004; Falkingham et al. In Press).
Such simulations would provide a highly effective
way of reconstructing the locomotor behaviour of
track-makers as well as providing force/time pro-
files for footprint simulations. It is possible that this
technique may allow more accurate estimates of
track-maker’s speed (Sellers et al. 2005) but the
biggest source of uncertainty is always the identity
and stature of the track-maker and computer simu-
lation can only help in that area once track simula-
tions have improved.
CONCLUSION
This paper demonstrates what can be
achieved with the current level of computer simula-
tion technology. The simulations do demonstrate a
wide range of possible locomotor modes and
shows (a) that 10 independent repeats is probably
insufficient for a quadrupedal gait analysis and (b)
that there are major gaps in our understanding of
gait choice that are highlighted by this process.
Whilst bipedality is currently the most likely option,
a high-speed quadrupedal hadrosaur should not
be ruled out as a serious locomotor possibility for
this group of dinosaurs.
ACKNOWLEDGEMENTS
We would like to thank National Geographic,
EPSRC and NERC for their financial support for
this project. We also wish to thank the Marmarth
FIGURE 5. Edmontosaurus sp. manus from MRF-03 showing pad structure (to left) and 3-dimensional
(collapsed) skin envelope (Scale bar in cm).

Sellers et al.: Gait Reconstruction
12
Research Foundation for access to MRF-03 and
the Black Hills Institute of Geological Research for
access to the cast of the sub-adult Edmontosau-
rus.
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PALAEO-ELECTRONICA.ORG
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Appendix
Complete specification of the hadrosaur model. This version includes the driver
values required to generate galloping.
<?xml version="1.0"?>
<GAITSYMODE>
<STATE SimulationTime="0"/>
<IOCONTROL OldStyleInputs="false"/>
<GLOBAL IntegrationStepSize="1e-4"
GravityVector="0.0 0.0 -9.81" ERP="0.2"
CFM="1e-10" ContactMaxCorrectingVel="100"
ContactSurfaceLayer="0.001"
AllowInternalCollisions="false" BMR="0"
TimeLimit="5" MetabolicEnergyLimit="0"
MechanicalEnergyLimit="0"
FitnessType="DistanceTravelled"
DistanceTravelledBodyID="HT"/>
<INTERFACE TrackBodyID="HT"
EnvironmentAxisSize="1 1 1"
EnvironmentColour="0.5 0.5 1.0 1.0"
BodyAxisSize="0.1 0.1 0.1" BodyColour=".275
.725 .451 .9" JointAxisSize="0.1 0.1 0.1"
JointColour="0 1 0 1" GeomColour="0 0 1 0.5"
StrapColour="1 0 0 1" StrapRadius="0.005"
StrapForceColour="1 0 0 0.5"
StrapForceRadius="0.01"
StrapForceScale="0.000001"
StrapCylinderColour="0 1 1 0.5"
StrapCylinderLength="0.1"
DrawingOrder="Environment Joint Muscle Geom
Body"/>
<ENVIRONMENT Plane="0 0 1 0"/>
<BODY ID="HT" GraphicFile="ht_hull.obj"
Scale="1" PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10"
Offset="0.071370853363158349 -
9.4219898522232949e-05 -1.4276420322582368"
Mass="571.91967814278394"
MOI="35.467054948732468 443.45901409449215
420.93678159649011 -0.46274408883735624
50.392194389226113 0.015575301414043233"
Density="-1" Position="World 0 0
1.3716550848989824" Quaternion="World
0.99770454359839089 -0.0043580001230305752 -
0.067532375554171992 -0.0024555590126144737"
LinearVelocity="12.401420201193885
0.048234022799837663 0.10113881627253112"
AngularVelocity="-0.29817868392487623
0.74649964861457019 0.12217124622782705"/>
<BODY ID="LeftThigh"
GraphicFile="left_thigh_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10"
Offset="0.44524259230361951 -
0.24267163006437489 -1.272116959478172"
Mass="42.37400036566666"
MOI="2.5494657883395786 2.886681458017534
0.52041527044607561 0.038217851162187462
0.4548132296108659 0.086986222471630556"
Density="-1" Position="World -
0.37944703501216193 0.24289876746329406
1.1596809720856798" Quaternion="World
0.99986327261642338 -0.0042251998040302337 -
0.015761032859227461 -0.0026783581916058796"
LinearVelocity="15.101513650062664 -
0.074312204189691131 0.66081062823457881"
AngularVelocity="-0.35033975328662725 -
8.7455374217370725 0.20143992993130427"/>
<BODY ID="LeftShank"
GraphicFile="left_shank_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10"
Offset="0.44784536956295701 -
0.25423894995604207 -0.66910018074046107"
Mass="15.081917241166668"
MOI="0.40764307257214594 0.44731405191911799
0.10632384970216729 -0.00092403911851659582 -
0.11183436002002527 -0.0020490408577721669"
Density="-1" Position="World -
0.52622752335635958 0.25147080094670915
0.70525449985165201" Quaternion="World
0.92939438744127789 -0.0028742484102449212
0.36905426185928236 -0.0040942755437635772"
LinearVelocity="18.620440188079865 -
0.25255160703693524 0.33871368111170563"
AngularVelocity="-0.32994527847390576 -
5.0344330009691989 0.17044241076909039"/>
<BODY ID="LeftFoot"
GraphicFile="left_foot_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10"
Offset="0.52824217186034217 -
0.24345652133462703 -0.2240724416016866"
Mass="6.3933479319999984"
MOI="0.084445760114794419 0.073878881997155407
0.030202243625299819 0.00025059024321312826
0.018202696755688058 -0.0084908119161335813"
Density="-1" Position="World -
0.87176488592125878 0.24030293245971721
0.43249829554078117" Quaternion="World
0.95579207042555125 -0.0031906748516766469
0.29400083797348059 -0.0038529179228283432"
LinearVelocity="20.268774352243 -
0.40326729794103922 -1.4378887468610126"
AngularVelocity="-0.34280777481409103 -
7.375260285790926 0.18999672261409037"/>
<BODY ID="RightThigh"
GraphicFile="right_thigh_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10"
Offset="0.44524212936624091 0.24267148598192351
-1.2721175597186958" Mass="42.37395754700001"
MOI="2.5494597643557939 2.8866708375447456
0.52041099469890195 -0.038217910113828357
0.45480205383710109 -0.086988165315726326"
Density="-1" Position="World -
0.27650685048111701 -0.24272401444901404
1.1966569471328932" Quaternion="World

Sellers et al.: Gait Reconstruction
16
0.98060023557473763 -0.0046389024823999328 -
0.19595447424316556 -0.0018715230729268615"
LinearVelocity="12.133491965222774 -
0.037543534858323804 0.29223810443447162"
AngularVelocity="-0.29479753052919266
1.3617851706492758 0.11703303143883377"/>
<BODY ID="RightShank"
GraphicFile="right_shank_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
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MOI="0.40761068903493353 0.44720317310237018
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AngularVelocity="-0.40700591501061589 -
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<BODY ID="RightFoot"
GraphicFile="right_foot_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10"
Offset="0.52807215606083047 0.24342356711426938
-0.22404605213970355" Mass="6.3937735455000002"
MOI="0.084436566792715259 0.073882384716655508
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Density="-1" Position="World -
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LinearVelocity="25.568918884634968 -
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AngularVelocity="-0.41293641523648095 -
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<BODY ID="LeftArm"
GraphicFile="left_arm_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10" Offset="-
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MOI="0.049907087247126614 0.079018136000938294
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Density="-1" Position="World
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LinearVelocity="12.108183324816498 -
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AngularVelocity="-0.30507012850762633 -
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<BODY ID="LeftForearm"
GraphicFile="left_forearm_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10" Offset="-
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MOI="0.015799437534319779 0.023132047750820964
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Density="-1" Position="World
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LinearVelocity="12.279446120262486 -
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AngularVelocity="-0.30648053007596443 -
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<BODY ID="LeftHand"
GraphicFile="left_hand_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10" Offset="-
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MOI="0.0052284097176611482
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0.00030556638302727424 0.0021898187004173834 -
0.00061144454414326836" Density="-1"
Position="World 0.95750867503413684
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Quaternion="World 0.99973028835854072 -
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LinearVelocity="12.476158375805969 -
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<BODY ID="RightArm"
GraphicFile="right_arm_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
PositionHighBound="1000 1 10" Offset="-
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MOI="0.049911250361925487 0.079032126492164678
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Density="-1" Position="World
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LinearVelocity="15.202922808338712 -
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AngularVelocity="-0.37455743828203869 -
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<BODY ID="RightForearm"
GraphicFile="right_forearm_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
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MOI="0.015812845847471755 0.023148464008991565
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Density="-1" Position="World 1.1080156569819755
-0.17683331645915912 0.39625102157648717"

PALAEO-ELECTRONICA.ORG
17
Quaternion="World 0.9681273686119497 -
0.0047363509108884578 -0.25040841443568651 -
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LinearVelocity="20.017255376366556 -
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AngularVelocity="-0.45038335112683603 -
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<BODY ID="RightHand"
GraphicFile="right_hand_hull.obj" Scale="1"
PositionLowBound="-10 -1 0.0"
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MOI="0.0052250846912375876
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Position="World 1.3767149851085376 -
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Quaternion="World 0.96762629135170053 -
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AngularVelocity="-0.22471623764284532
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<JOINT ID="RightHip" Type="Hinge"
Body1ID="HT" Body2ID="RightThigh"
ParamLoStop="-0.785398163"
ParamHiStop="0.785398163" HingeAnchor="HT -
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0.14970796774176209" HingeAxis="HT 0 1 0"
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<JOINT ID="RightKnee" Type="Hinge"
Body1ID="RightThigh" Body2ID="RightShank"
ParamLoStop="-1.570796327" ParamHiStop="0"
HingeAnchor="RightThigh 0.10294212936624075
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HingeAxis="RightThigh 0 1 0"
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<JOINT ID="RightAnkle" Type="Hinge"
Body1ID="RightShank" Body2ID="RightFoot"
ParamLoStop="0" ParamHiStop="0.785398163"
HingeAnchor="RightShank -0.13192425625332455
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HingeAxis="RightShank 0 1 0"
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<JOINT ID="LeftHip" Type="Hinge" Body1ID="HT"
Body2ID="LeftThigh" ParamLoStop="-0.785398163"
ParamHiStop="0.785398163" HingeAnchor="HT -
0.40112914663684152 0.15390578010147773
0.14970796774176209" HingeAxis="HT 0 1 0"
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<JOINT ID="LeftKnee" Type="Hinge"
Body1ID="LeftThigh" Body2ID="LeftShank"
ParamLoStop="-1.570796327" ParamHiStop="0"
HingeAnchor="LeftThigh 0.10294212936624036 -
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HingeAxis="LeftThigh 0 1 0"
StartAngleReference="-0.78751619016521479"/>
<JOINT ID="LeftAnkle" Type="Hinge"
Body1ID="LeftShank" Body2ID="LeftFoot"
ParamLoStop="0" ParamHiStop="0.785398163"
HingeAnchor="LeftShank -0.13192425625332443 -
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HingeAxis="LeftShank 0 1 0"
StartAngleReference="0.1591647497700302"/>
<JOINT ID="RightShoulder" Type="Hinge"
Body1ID="HT" Body2ID="RightArm" ParamLoStop="-
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HingeAnchor="HT 0.8960208533631584 -
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HingeAxis="HT 0 1 0"
StartAngleReference="0.48180187316424339"/>
<JOINT ID="RightElbow" Type="Hinge"
Body1ID="RightArm" Body2ID="RightForearm"
ParamLoStop="-0.785398163"
ParamHiStop="0.785398163" HingeAnchor="RightArm
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0.10160853358313515" HingeAxis="RightArm 0 1 0"
StartAngleReference="-0.11076054718322098"/>
<JOINT ID="RightWrist" Type="Hinge"
Body1ID="RightForearm" Body2ID="RightHand"
ParamLoStop="-0.785398163" ParamHiStop="0"
HingeAnchor="RightForearm 0.090571838643254909
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HingeAxis="RightForearm 0 1 0"
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<JOINT ID="LeftShoulder" Type="Hinge"
Body1ID="HT" Body2ID="LeftArm" ParamLoStop="-
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HingeAxis="HT 0 1 0" StartAngleReference="-
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<JOINT ID="LeftElbow" Type="Hinge"
Body1ID="LeftArm" Body2ID="LeftForearm"
ParamLoStop="-0.785398163"
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0.10160853358313438" HingeAxis="LeftArm 0 1 0"
StartAngleReference="0.19932938422182639"/>
<JOINT ID="LeftWrist" Type="Hinge"
Body1ID="LeftForearm" Body2ID="LeftHand"
ParamLoStop="-0.785398163" ParamHiStop="0"
HingeAnchor="LeftForearm 0.090571838643260016 -
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HingeAxis="LeftForearm 0 1 0"
StartAngleReference="1.1990408665951691e-11"/>
<GEOM ID="RightFootPP1Contact" Type="Sphere"
BodyID="RightFoot" Radius="0.018"
SpringConstant="2e6" ContactSoftERP="0.1"
Mu="1.0" Abort="false" Position="RightFoot
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<GEOM ID="RightFootPP2Contact" Type="Sphere"
BodyID="RightFoot" Radius="0.00179"
SpringConstant="2e6" ContactSoftERP="0.1"
Mu="1.0" Abort="false" Position="RightFoot
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<GEOM ID="RightFootPP3Contact" Type="Sphere"
BodyID="RightFoot" Radius="0.0219"
SpringConstant="2e6" ContactSoftERP="0.1"

Sellers et al.: Gait Reconstruction
18
Mu="1.0" Abort="false" Position="RightFoot
0.15507215606083047 -0.11787643288573055 -
0.20214605213970357" Quaternion="RightFoot 1 0
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<GEOM ID="LeftFootPP1Contact" Type="Sphere"
BodyID="LeftFoot" Radius="0.018"
SpringConstant="2e6" ContactSoftERP="0.1"
Mu="1.0" Abort="false" Position="LeftFoot
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0"/>
<GEOM ID="LeftFootPP2Contact" Type="Sphere"
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Mu="1.0" Abort="false" Position="LeftFoot
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<GEOM ID="LeftFootPP3Contact" Type="Sphere"
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Mu="1.0" Abort="false" Position="LeftFoot
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0"/>
<GEOM ID="RightHandPP1Contact" Type="Sphere"
BodyID="RightHand" Radius="0.013"
SpringConstant="2e6" ContactSoftERP="0.1"
Mu="1.0" Abort="false" Position="RightHand
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<GEOM ID="RightHandPP3Contact" Type="Sphere"
BodyID="RightHand" Radius="0.013"
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Mu="1.0" Abort="false" Position="RightHand
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<GEOM ID="LeftHandPP1Contact" Type="Sphere"
BodyID="LeftHand" Radius="0.013"
SpringConstant="2e6" ContactSoftERP="0.1"
Mu="1.0" Abort="false" Position="LeftHand
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<GEOM ID="LeftHandPP3Contact" Type="Sphere"
BodyID="LeftHand" Radius="0.013"
SpringConstant="2e6" ContactSoftERP="0.1"
Mu="1.0" Abort="false" Position="LeftHand
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="TwoPoint" ID="RightDeepDorsalGroup"
OriginBodyID="HT" InsertionBodyID="RightThigh"
PCA=" 0.151664796 " FibreLength=" 0.104205 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
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<MUSCLE Type="MinettiAlexanderExtended"
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ID="RightTricepsFemorisGroup" OriginBodyID="HT"
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FibreLength=" 0.663802 "
ForcePerUnitArea="300000" VMaxFactor="8"
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CylinderRadius="0.10000000000000001"
CylinderQuaternion="RightShank -
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="CylinderWrap"
ID="RightFemoroTibialisGroup"
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InsertionBodyID="RightShank"
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CylinderRadius="0.10000000000000001"
CylinderQuaternion="RightShank -
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="TwoPoint" ID="RightCaudoFemoralisGroup"
OriginBodyID="HT" InsertionBodyID="RightThigh"
PCA=" 0.063139805 " FibreLength=" 0.375458 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
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ActivationKinetics="false"
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="TwoPoint" ID="RightFlexorCrurisGroup"
OriginBodyID="HT" InsertionBodyID="RightShank"
PCA=" 0.030344782 " FibreLength=" 0.520822 "

PALAEO-ELECTRONICA.ORG
19
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
ParallelStrainAtFmax="0.6"
ActivationKinetics="false"
TendonLength="0.41878636000000002" Origin="HT -
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="CylinderWrap"
ID="RightGastrocnemiusLateralis+FD"
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InsertionBodyID="RightFoot"
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FibreLength=" 0.214724 "
ForcePerUnitArea="300000" VMaxFactor="8"
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Insertion="RightFoot -0.040527843939169528 -
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CylinderRadius="0.059999999999999998"
CylinderQuaternion="RightFoot
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<MUSCLE Type="MinettiAlexanderExtended"
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ID="RightGastrocnemiusMedialis"
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FibreLength=" 0.047105 "
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<MUSCLE Type="MinettiAlexanderExtended"
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FibreLength=" 0.082897 "
ForcePerUnitArea="300000" VMaxFactor="8"
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ActivationKinetics="false"
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Insertion="RightFoot 0.0045721560608305012 -
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="TwoPoint" ID="LeftDeepDorsalGroup"
OriginBodyID="HT" InsertionBodyID="LeftThigh"
PCA=" 0.151664796 " FibreLength=" 0.104205 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
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ActivationKinetics="false"
TendonLength="0.06232791" Origin="HT -
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="CylinderWrap"
ID="LeftTricepsFemorisGroup" OriginBodyID="HT"
InsertionBodyID="LeftShank"
CylinderBodyID="LeftShank" PCA=" 0.017856488 "
FibreLength=" 0.663802 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
ParallelStrainAtFmax="0.6"
ActivationKinetics="false"
TendonLength="0.128012601" Origin="HT -
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CylinderRadius="0.10000000000000001"
CylinderQuaternion="LeftShank -
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="CylinderWrap"
ID="LeftFemoroTibialisGroup"
OriginBodyID="LeftThigh"
InsertionBodyID="LeftShank"
CylinderBodyID="LeftShank" PCA=" 0.075716382 "
FibreLength=" 0.156547 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
ParallelStrainAtFmax="0.6"
ActivationKinetics="false"
TendonLength="0.39132054599999999"
Origin="LeftThigh 0.075142129366240373 -
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Insertion="LeftShank 0.14707574374667554
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="TwoPoint" ID="LeftCaudoFemoralisGroup"
OriginBodyID="HT" InsertionBodyID="LeftThigh"
PCA=" 0.063139805 " FibreLength=" 0.375458 "
ForcePerUnitArea="300000" VMaxFactor="8"

Sellers et al.: Gait Reconstruction
20
ActivationK="0.17" SerialStrainAtFmax="0.06"
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ActivationKinetics="false"
TendonLength="0.53659248699999995" Origin="HT -
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<MUSCLE Type="MinettiAlexanderExtended"
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ActivationK="0.17" SerialStrainAtFmax="0.06"
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<MUSCLE Type="MinettiAlexanderExtended"
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ID="LeftGastrocnemiusLateralis+FD"
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InsertionBodyID="LeftFoot"
CylinderBodyID="LeftFoot" PCA=" 0.055201899 "
FibreLength=" 0.214724 "
ForcePerUnitArea="300000" VMaxFactor="8"
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ActivationKinetics="false"
TendonLength="0.68294359500000001"
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="CylinderWrap"
ID="LeftGastrocnemiusMedialis"
OriginBodyID="LeftShank"
InsertionBodyID="LeftFoot"
CylinderBodyID="LeftFoot" PCA=" 0.251633001 "
FibreLength=" 0.047105 "
ForcePerUnitArea="300000" VMaxFactor="8"
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CylinderRadius="0.059999999999999998"
CylinderQuaternion="LeftFoot
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="TwoPoint" ID="LeftTibialisAnterior+ED"
OriginBodyID="LeftShank"
InsertionBodyID="LeftFoot" PCA=" 0.190648998 "
FibreLength=" 0.082897 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
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Insertion="LeftFoot 0.0045721560608300571
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<MUSCLE Type="MinettiAlexanderExtended"
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OriginBodyID="HT" InsertionBodyID="RightArm"
PCA=" 0.027493045 " FibreLength=" 0.246362 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
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ActivationKinetics="false"
TendonLength="0.29325024999999999" Origin="HT
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<MUSCLE Type="MinettiAlexanderExtended"
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ID="RightShoulderExtensors" OriginBodyID="HT"
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ActivationKinetics="false"
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<MUSCLE Type="MinettiAlexanderExtended"
Strap="CylinderWrap" ID="RightTricepsBrachii"
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ActivationK="0.17" SerialStrainAtFmax="0.06"
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TendonLength="0.23191341900000001" Origin="HT
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0.10957816135674514 -0.019710035981314711

PALAEO-ELECTRONICA.ORG
21
0.14202774699567011"
CylinderPosition="RightForearm -
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0.17122774699567006"
CylinderRadius="0.029999999999999999"
CylinderQuaternion="RightForearm
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<MUSCLE Type="MinettiAlexanderExtended"
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InsertionBodyID="RightForearm"
CylinderBodyID="RightArm" PCA=" 0.021103596 "
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<MUSCLE Type="MinettiAlexanderExtended"
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ForcePerUnitArea="300000" VMaxFactor="8"
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<MUSCLE Type="MinettiAlexanderExtended"
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InsertionBodyID="RightForearm"
CylinderBodyID="RightForearm" PCA=" 0.107989436
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ForcePerUnitArea="300000" VMaxFactor="8"
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ActivationKinetics="false"
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0.14202774699567011"
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CylinderRadius="0.029999999999999999"
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<MUSCLE Type="MinettiAlexanderExtended"
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OriginBodyID="RightForearm"
InsertionBodyID="RightHand"
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FibreLength=" 0.026842 "
ForcePerUnitArea="300000" VMaxFactor="8"
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<MUSCLE Type="MinettiAlexanderExtended"
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<MUSCLE Type="MinettiAlexanderExtended"
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OriginBodyID="HT" InsertionBodyID="LeftArm"
PCA=" 0.027493045 " FibreLength=" 0.246362 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
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ActivationKinetics="false"
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<MUSCLE Type="MinettiAlexanderExtended"
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FibreLength=" 0.06283 "
ForcePerUnitArea="300000" VMaxFactor="8"
ActivationK="0.17" SerialStrainAtFmax="0.06"
ParallelStrainAtFmax="0.6"

Sellers et al.: Gait Reconstruction
22
ActivationKinetics="false"
TendonLength="0.485243588" Origin="HT
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0.322242032258238" Insertion="LeftArm
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<MUSCLE Type="MinettiAlexanderExtended"
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ActivationKinetics="false"
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<MUSCLE Type="MinettiAlexanderExtended"
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<MUSCLE Type="MinettiAlexanderExtended"
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<MUSCLE Type="MinettiAlexanderExtended"
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<MUSCLE Type="MinettiAlexanderExtended"
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<MUSCLE Type="MinettiAlexanderExtended"
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CylinderRadius="0.040000000000000001"

PALAEO-ELECTRONICA.ORG
23
CylinderQuaternion="LeftHand -
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<DRIVER Type="Cyclic"
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<DRIVER Type="Cyclic"
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<DRIVER Type="Cyclic"
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Sellers et al.: Gait Reconstruction
24
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PALAEO-ELECTRONICA.ORG
25
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Sellers et al.: Gait Reconstruction
26
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