Whole-body mechanics and gaits in the gray short-tailed opossum Monodelphis domestica: integrating patterns of locomotion in a semi-erect mammal
1 Department of Biological Sciences, College of Arts and Sciences, Ohio
University, Athens OH 45701, USA
2 Department of Biomedical Sciences, College of Osteopathic Medicine, Ohio
University, Athens OH 45701, USA
* Author for correspondence (e-mail: reilly{at}ohiou.edu)
Accepted 27 January 2003
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Summary |
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Key words: kinematics, kinetics, locomotion, opossum, Monodelphis domestica, marsupial
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Introduction |
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Another way to quantify patterns of locomotion is by describing gaits; for
centuries `gait' has referred to footfall patterns (e.g.
Gioffon and Vincent, 1779; see
review in Reilly and Biknevicius,
2003
). In the well-established gait model proposed by Hildebrand
(1976
,
1977
,
1980
,
1985
), the walk/run transition
occurs at a 50% duty factor (Table
1). Specific walking and running gaits are then defined by the
phase relationships of the limbs (relative timing of fore- and hindfoot
falls). From gait analyses of numerous species spanning the postural and
phylogenetic range of terrestrial vertebrates, Hildebrand proposed that
vertebrates almost universally use the more stable walking gaits at slower
speeds and either transition into specific running gaits dominated by
coordinated limb couplets (such as the trot,
Table 1), or switch to
asymmetrical gaits (such as the bound or gallop) to increase speed. Gait
studies of lizards (White and Anderson,
1994
; Reilly and Delancey,
1997
), alligators (Reilly and
Elias, 1998
; Renous et al.,
2002
) and mammals (Dagg,
1973
; Pridmore,
1992
; White, 1990
)
have supported this hypothesis. Thus, vertebrate footfall patterns can be
categorized as walking or running gaits based on duty factor
(Table 1), and specific gaits
are determined by limb phase. Note that `walk' and `run' are often used by
students of mechanics as synonyms for pendular and spring mechanics,
respectively. However, we retain Hildebrand's formal definition for walk and
run (Hildebrand, 1976
) as they
relate to footfall patterns, because of priority of formal definition
(Reilly and Biknevicius, 2003
)
and because it has not been demonstrated how these mechanical patterns relate
to gait patterns.
Remarkably, the two perspectives on quantifying locomotion (center-of-mass
fluctuations versus footfall patterns) have been largely explored
independently (see Reilly and Biknevicius,
2003). Consequently, gaits used during mechanical energy studies
are often vaguely described, and kinematic studies rarely obtain data
appropriate for assessing locomotor mechanics. The relationships between gaits
and mechanical energy patterns have not been examined in any quantitative way
and therefore, we know little about how neuromuscular movements of axial and
appendicular systems control movements of the center of mass. Neuromuscular
control of the limbs produces the gait patterns that carry the center of mass.
Thus, to understand locomotion we have to know more than what the center of
mass is doing. Details of locomotor mechanics and gaits are particularly
lacking in non-cursorial mammals. Therefore, the goal of this study is to
quantify both the kinematic gaits and mechanical energy patterns employed by a
generalized, semi-erect mammal as a means to address three general questions.
First, do small, semi-erect mammals employ the energy-saving pendular and
spring mechanics used by erect mammals? Second, do opossums exhibit the
walk/run gait transitions proposed as the primitive condition for tetrapods by
Hildebrand? Third, how well do mechanical locomotor patterns correlate with
kinematic gaits? Specifically, we want to test the hypothesis
(Reilly and Biknevicius, 2003
)
that gaits (walks, runs) correlate with mechanical patterns (pendular and
spring mechanics, respectively).
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Materials and methods |
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Data collection
All procedures followed approved animal care and use protocols. Footfall
data and ground reaction forces were collected simultaneously as possums moved
down a trackway and across a force platform. During data collection, the
opossums were allowed to freely choose the speed and gait with which they
crossed the force platform. Our goal in recording kinematic and force data was
to sample the full range of velocities (and therefore, we presumed, mechanical
patterns and gaits) that the opossums would use. After numerous trials
revealed the general range of speeds at which the opossums chose to move, we
attempted to extend the range of speeds for analysis by chasing the animals
with our hands to invoke faster trials. We also spent considerable time simply
hiding and waiting for the animals to use even slower speeds. Neither of these
approaches extended the range of speeds that the opossums would move at a
steady speed.
Each trial was filmed at 120 Hz by a digital video camera (JVC GR-DVL 9800) mounted 0.85 m directly above the center of the force platform. Two Monarch-Nova strobe lights (233.3 Hz) provided adequate lighting to visualize all four feet. Two mirrors, mounted on the angled walls of each side of the platform, provided lateral views of the animals so that each video frame included a dorsal and two lateral views. The three separate views allowed us to verify whether or not the animal ran straight across the platform and to clearly visualize the interaction of each limb with the force platform. The videos were downloaded to a computer using Studio DV (version 1.04.100), and the motion analysis program APAS (version 1.0) was then used to review each trial in order to eliminate those in which opossums failed to move at a steady speed and direction. Footfall times of valid trials were recorded. For each trial, the touchdown time of the first limb to contact on the platform was aligned with the onset of vertical ground reaction forces on the platform to synchronize footfall data with force data.
The force platform was based on a spring-blade design similar to that
described in Bertram et al.
(1997). The platform surface
measured 0.11 m wide by 0.36 m long, a length that allowed ground reaction
forces to be recorded for 2-3 complete strides per trial. The platform was
inserted flush to the surface of a 2.44 m trackway and then the platform and
trackway were covered with a thin layer of fine grit sandpaper for traction. A
dark enclosure was placed at the end of the trackway to entice the opossums to
cross the platform.
Ground reaction forces were measured in the three orthogonal directions (vertical, craniocaudal and mediolateral) with four separate outputs: one each for craniocaudal and mediolateral and two for the verticals (at cranial and caudal ends of the platform). By assessing the relative output of each vertical sensor, the craniocaudal position of the center of pressure was determined. The movement of the position of the center of pressure during each step was used to calculate mean velocity for each step.
Ground reaction force data were collected at 500 Hz for 4 s periods. Analog
outputs were amplified (National Instruments SCXI 1000 and 1121) and then
converted to a digital format (National Instruments NB-M10-16L). Voltage
changes were recorded with a LabView 5.1 (National Instruments) virtual
instrument data acquisition program. A second LabView program scaled the
voltage data to forces (in N), based on calibration factors for the three
directions of force and the craniocaudal position of center of pressure; our
calibration protocols followed Bertram et al.
(1997), adapted for a single
platform. Finally, a third LabView program extracted ground reaction force
data for each step and determined external mechanical energy profiles, phase
shifts, and percentage energy recoveries for these steps (see below).
Video data analysis
The gaits (footfall patterns) for each step analyzed were described using
Hildebrand's model of symmetrical gaits (Hildebrand,
1976,
1977
,
1980
,
1985
;
Reilly and Biknevicius, 2003
).
Duty factor is the percentage of the stride that the reference hindlimb was on
the ground: a 50% or greater duty factor defines a walking gait whereas
running gaits have duty factors that fall below 50%
(Table 1). Limb phase was
determined as the duration between footfalls of the reference hindlimb to the
ipsilateral forelimb, as a percentage of total stride duration. The limb phase
variable very conveniently describes symmetrical gaits generally (diagonal
versus lateral sequence) and in specific terms (pace, singlefoot and
trot, as well as lateral and diagonal couplet walking gaits; see
Reilly and Biknevicius, 2003
for details).
External mechanical energy analysis
The change in the position of the center of pressure (distance traveled)
during the step and step duration of the diagonal couplet (taken from the
videos) were used to calculate the average velocity for each couplet step
under analysis. From the initial sample of steps, only those in which the
differences in velocity at the beginning and end of the step were within
±5% of mean velocity were subjected to mechanical analysis.
Consequently, a total of 90 steps were analyzed, representing individual
samples of 16, 11, 20, 8, 15, 15 and 5 steps for the seven opossums.
External mechanical energy profiles for each diagonal couplet step were
determined following procedures given by Blickhan and Full
(1992). Accelerations of the
center of mass in vertical, craniocaudal and mediolateral directions were
obtained by dividing ground reaction forces by body mass (body weight was
first subtracted in vertical records). Velocity changes of the center of mass
for each direction were estimated by taking the first integration of
acceleration. The integration constants for the craniocaudal direction were
set to mean forward velocity (Cavagna et
al., 1977
; Blickhan and Full,
1992
), and for the vertical and lateral records they were
estimated as the mean values from calculated velocity profiles
(Donelan et al., 2002
). These
velocities were then used to calculate kinetic energies
(KE=1/2mv2, where m is body mass in kg)
in the vertical (KEV), craniocaudal
(KECC) and mediolateral (KEML)
directions. Total kinetic energy of the center of mass
(KETOT) during the step was then calculated as:
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Finally, changes in the vertical displacement of the center of mass (h) were determined by integrating vertical velocity (integration constant estimated as the mean vertical displacement) and were used to determine changes in gravitational potential energy during the step (PE=mgh, where g is gravitational acceleration or 9.81 m s-2).
The phase shift between fluctuations in PE and
KETOT was used to determine whether the center of mass
exhibited pendular or spring mechanics during each step
(Cavagna et al., 1977;
Farley and Ko, 1997
). Phase
shifts were calculated as the time interval between minima in PE and
KETOT divided by step duration and multiplied by 360°.
Perfect pendular mechanics are characterized by a phase shift of 180°,
indicating that the two energies are precisely out of phase, and spring
mechanics are characterized by a phase shift around 0° (in phase).
The efficacy with which an animal was utilizing pendular mechanics was
calculated as the percentage energy recovery
(Cavagna et al., 1977;
Farley and Ko, 1997
):
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Results |
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Gaits
Gait plots for all steps analyzed in Monodelphis domestica are
presented in Fig. 1 and means
for velocity, duty factor and limb phase are presented in
Table 2. Duty factors ranged
from 29.0% to 53.6% and averaged 41.45%. Only eight
(Fig. 1, squares) of the 90
steps had duty factors of 50% or higher, thus, according to the Hildebrand
(1980) model, only these steps
were defined as walks and the remainder were scored as runs
(Fig. 1, circles). The
limb-phase relationship between the reference hindlimb and ipsilateral
forelimb was 37.4-59.2%, mean 47.81% (Table
2). The majority of the trials (76 of 90) had limb-phase variables
between 44% and 56% and were clearly categorized as trots (with the footfalls
and lift-offs of diagonal couplets tightly coordinated in time, following
Hildebrand's model). 14 trials had limb-phase variables between 44% and 37.4%,
which indicates that the footfall and lift-off times of the feet of the
diagonal couplet were becoming less synchronized.
|
|
Aerial phases (identified from gait diagrams or when vertical force records decrease to zero between steps) were never observed in walking strides. Among the 82 running strides, 54 contained aerial phases between steps (Fig. 1, solid circles). In the remaining 28 running strides, the forelimbhindlimb couplets were sufficiently unsynchronized that no aerial phases were recorded even though the duty factors for these trials were less than 50% (Fig. 1, open circles).
The velocity vector, indicating how speed increases in the sample of steps analyzed, is also presented in Fig. 1. This is the superimposition of the direction of velocity increase, taken from a velocity versus duty factor versus limb phase plot, onto the 2-D Hildebrand plot. Comparison of the velocity vector with the appearance of an aerial phase indicates that the aerial/non-aerial transition lies perpendicular to the velocity vector.
Ground reaction forces and step mechanics
The typical ground reaction forces observed during the support duration of
a diagonal couplet are illustrated in Fig.
2A. Vertical forces during a diagonal couplet tended to either
start at 0 N, if there was an aerial phase between the two couplets, or very
close to 0 N. The vertical force increased throughout the first half of the
step to reach about one and a half times body weight around midstance and then
decreased more rapidly back towards 0 N during the second half of the step.
The craniocaudal forces show an initial breaking impulse during the first half
of the step, followed by an equivalent propulsive impulse throughout the last
half of the stance phase. Mediolateral forces observed over a diagonal couplet
were small in comparison to the vertical and craniocaudal forces and
fluctuated slightly around zero with no discernable pattern across the
sample.
|
Among the velocities, craniocaudal velocities, which fluctuated about the mean forward velocity, were of greatest magnitude (Fig. 2A). In every step, the center of mass started at its maximum height relative to the ground, decreased to its minimum height at midstance, and then increased back to its maximum height throughout the remainder of the stance phase. Vertical fluctuations in the center of mass ranged between 1 and 4 mm.
Consistent patterns of fluctuations in total kinetic, gravitational potential and total mechanical energies were found across all trials (Fig. 2B). Kinetic and gravitational potential energies decreased to their minima at midstance and then increased throughout the remainder of the stance phase. Consequently, total mechanical energy profiles similarly displayed maxima at the beginning and ending of a step with minima at midstep. Fluctuations in total kinetic and gravitational potential energies of the center of mass remained closely in phase with one another across the full range of velocities (Fig. 3A, Table 2). The phase shift between the minimum values of kinetic and potential energies ranged from -44.00° to 46.96°, mean 13.72°. No significant change in phase shift was seen with velocity (P=0.797), thus, all 90 steps were categorized as spring mechanics.
|
A trivial amount of external mechanical energy was recovered through pendular mechanisms during the support phase of each diagonal couplet that was analyzed (Fig. 3B, Table 2). Percentage recovery ranged from 0 to 9.41%, mean 3.42%; such low values are indicative of spring mechanics. In addition, no significant change in percentage recovery was seen with velocity (P=0.630).
Effects of an aerial phase
No significant differences were found in percentage recovery or phase shift
in the ANOVA comparing steps grouped into walking, non-aerial running and
aerial running gaits (Table 2;
three groups in Fig. 1). Walks
and non-aerial runs occurred at the same speed while aerial runs occurred at
significantly higher velocities (Table
2), as indicated by the velocity vector
(Fig. 1). Walks and aerial runs
maintained coordinated limb couplets (limb phases near 50%,
Table 2). The non-aerial runs
differed from walks and aerial runs in having significantly lower limb phase
values, indicating that the limb couplets were less tightly coordinated. Thus,
as duty factor decreased, walks changed to aerial runs when more synchronized
trotting gaits were maintained. Non-aerial runs occur in slower runs with less
coordinated limb contact times.
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Discussion |
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Contrary to these predictions, our results show that Monodelphis domestica preferentially utilizes running trots for steady-speed locomotion on flat surfaces. Over the fivefold range of speeds where the opossums used uniform linear locomotion, limb phases of most strides were around 50%, indicating that diagonal limbs were tightly coordinated; that is, they were trotting. And while limb phases of 14 strides were slightly lower (44-37%, with less synchronized touch-downs and lift-offs of the fore- and hindlimbs), these runs were still dominated by diagonal couplet movements. All but eight steps analyzed had duty factors that fell below 50%, and thus 90% of the steps were characterized as running trots. The remaining steps fell just into the zone describing walking trots (50-54% duty factors; 45-55% limb phase). Although it is clear that opossums are dedicated to trotting gaits across their full range of speeds, evidence for a clear gait transition between walking and running is not obvious given the round shape of the overall cloud of steps in Fig. 1.
We are not suggesting that Monodelphis is incapable of performing
other walking gaits (besides trots). Indeed, Monodelphis moved at
slower speeds on the trackway but these locomotor bouts were brief and
erratic, never lasting for more than a step or two before the animal turned or
stopped. This intermittent locomotor behavior resembled foraging activity (as
opposed to steady-state locomotion as when Monodelphis preferentially
ran with coordinated diagonal limb couplets). Intermittent locomotion at slow
speeds has been reported for squirrels, chipmunks and even cockroaches
(Biewener, 1983;
Full and Tu, 1990
;
Heglund et al., 1982
).
Interestingly, non-trotting walks (lateral-sequence diagonal-couplets walks
and singlefoot walks) have been observed in Monodelphis during slow
treadmill locomotion (Pridmore,
1992
; S. M. Reilly and T. D. White, unpublished data). It is
possible that the movement of the belt on the treadmill inspired more linear
locomotion, but it is also important to note that kinematic stride variables
of treadmill locomotion are not precisely equivalent to overground locomotion.
For example, horses on treadmills tend to increase stance duration, have
earlier forelimb footdowns, and greater fore- and hindlimb retractions
(Buchner et al., 1994
). If
these also characterize slow treadmill locomotion in Monodelphis,
then greater stance durations would yield higher duty factors (walks) and
earlier forelimb footdowns would shift walking gaits further into the lateral
sequence singlefoot range of the Hildebrand gait plot. In addition,
observations of arboreal locomotion in Monodelphis have verified that
lateral sequence diagonal couplets walks and singlefoot walks are normal parts
of their locomotor repertoire (Lammers,
2001
). In terms of Hildebrand's hypothesis that primitive
tetrapods should transition from walking to running gaits with speed, it
appears that opossums do transition from singlefoot and lateral-sequence
diagonal-couplets walks (when moving intermittently and at low unsustained
speeds) to fast walking and running trots for more continuous locomotion and
higher speeds.
Finally, aerial phases were not a necessary characteristic of running
gaits. In our sample, about a third of the running strides lacked aerial
phases. These trials had duty factors that fell below 50%, but were, on
average, equivalent in speed to the walking strides
(Table 2). The aerial phases
were lost when forelimbhindlimb couplets became slightly unsynchronized
during the slower running trots. This is comparable to the condition found
among gaited horses (such as the Tennessee walking horse breed), which employ
a variety of 4-beat symmetrical gaits and also lose aerial phases at the lower
running speeds (Hildebrand,
1965; Harris,
1993
). As gaited horses run faster, the duty factor of each limb
decreases further and an aerial phase is achieved.
Locomotor mechanics in walking and running gaits
Our analysis of whole-body ground reaction forces clearly shows that
Monodelphis domestica preferentially utilized the spring mechanics at
all speeds of steady state locomotion on level terrestrial substrates. The
force and velocity patterns seen over the duration of a diagonal couplet were
similar to those that have been observed in spring mechanics in larger, erect
animals such as horses, dogs and kangaroos
(Biewener et al., 1981;
Budsberg et al., 1987
;
Cavagna et al., 1977
;
Kimura and Endo, 1972
). Phase
shifts between the minima of total kinetic and gravitational potential
energies were scattered around 0°, ranging from -42 to 47°, clearly
indicating the in-phase relationships of spring mechanics. In addition,
percentage recoveries across trials were small (mean 3.5%), indicating that
the animals were not utilizing pendular mechanics as an effective
energy-saving mechanism, even in walking trots. Furthermore, neither
percentage recovery nor phase shift changed with speed
(Table 2), revealing that
Monodelphis domestic maintained the same locomotor mechanics over the
fivefold range of speeds used for sustained locomotion. Thus, there was no
evidence that they were beginning to transition out of spring mechanics at
either end of the speed range. Consequently, very little
kineticgravitational energy transfer took place in Monodelphis
during walking trots. The intermittent locomotor behavior of
Monodelphis at even slower speeds probably interrupts pendular
mechanisms so that these, too, would be likely to lack efficient energy
exchange and transfer.
This is the first study to explore the relationship between whole body
mechanics and Hildebrand gaits explicitly, so we can examine how these two
locomotor paradigms can be integrated. Reilly and Biknevicius
(2003) predicted that running
trots should be associated with spring mechanics and that spring mechanics may
extend into the walking trot gait as well. Both of these predictions are true
for opossums. In Monodelphis, the Hildebrand trotting gaits from fast
walking trots to running trots are clearly associated with spring mechanics
(Table 2).
The prediction that fast walking trots might have characteristics in common
with spring mechanics (Reilly and
Biknevicius, 2003) was based on data displayed in previous studies
that suggest that this apparent inconsistency may not be unusual. For example,
the fastest walking trials of skinks, rams and turkeys recover very little
mechanical energy through pendular mechanisms (see fig. 7 in
Cavagna et al., 1977
; figs 6
and 7 in Farley and Ko, 1997
).
Unfortunately these studies did not report gaits, so the relationship between
gait and changes in mechanics cannot be directly examined. Among
invertebrates, slow and fast locomotion of cockroaches have been variously
described as `walking' or `running'
(Hughes, 1952
;
Kozacik, 1981
) yet only the
energy fluctuation patterns associated with bouncing gaits have been reported
(Blickhan and Full, 1987
;
Full and Tu, 1990
), suggesting
that cockroaches use spring mechanics at nearly all speeds as well.
Additionally, lizards use spring mechanics in trots with greater than 50% duty
factors (S. M. Reilly and K. L. Hickey, unpublished data) and non-aerial
spring mechanics can be obtained in humans when they `Groucho walk'
(McMahon et al., 1987
).
Furthermore, locomotor data on Monodelphis, together with those on
lizards (S. M. Reilly and K. L. Hickey, unpublished data) and cockroaches
(Full and Tu, 1990
), reveal
that while steps with aerial phases are usually associated with spring
mechanics, the lack of an aerial phase does not exclude a gait from having
in-phase energy fluctuations. Thus, the time course of mechanical energy
fluctuations characteristic of spring mechanics can occur in both walking and
running trotting gaits. Further work is needed to examine how far spring
mechanics can extend into slower walking, trotting gaits and if slower trots
can have pendular mechanics.
Why is Monodelphis dedicated to spring mechanics and trotting
gaits?
The key to saving energy with spring-like limbs is the use of elastic
elements of the musculoskeletal system, and several have been identified
(Biewener and Baudinette, 1995;
Biewener and Roberts, 2000
).
Although elastic recoil of cross-bridges in muscles may save some mechanical
energy, the most likely sources of elastic energy recovery are tendons and
ligaments in the limbs (Alexander et al.,
1982
; Biewener and Baudinette,
1995
; Cavagna et al.,
1977
). The tendons and ligaments of species that display the
greatest specialization for elastic energy recovery (ungulates, dogs, hopping
kangaroos and humans) are typically long and slender
(Biewener et al., 1998
;
Cavagna et al., 1977
; Ker et
al., 1987
,
1988
), a condition that also
increases locomotor efficiency by reducing distal limb mass
(Biewener and Baudinette,
1995
). Elastic strain energy, stored and then released from these
`biological springs', reduces significantly the amount of work that muscles
must supply in order to efficiently locomote at high speeds and for long
distances. Energy savings via elastic recoil may be as high as 30-50%
(Biewener et al., 1995, 1998
;
Farley et al., 1993
).
Although the spring-mass model has gained general acceptance for larger,
cursorial mammals, it is believed that the tendons of smaller and less
cursorially adapted mammals may not be capable of storing large amounts of
elastic strain energy as their shortness and relative thickness render them
poor springs at best (Biewener et al.,
1981). Furthermore, to date, there is no empirical support for
significant energy savings by summing small amounts of potential energy stored
in serially arranged elastic elements. Acknowledging that Monodelphis
is a small mammal (<150 g) with a semi-erect, crouched posture, it seems
improbable that their tendons are capable of storing sufficient energy for
useful elastic energy recovery when running. Nonetheless, Monodelphis
clearly prefer to use spring mechanics with coordinated diagonal couplets over
their entire range of steady-state locomotor speeds. One possible explanation
is that Monodelphis does not use biological springs for energy
recovery to any significant extent, that is, it may simply pay for running
with muscular work.
Support for this hypothesis comes from recent studies of abdominal muscle
function during locomotion in marsupials. Didelphid opossums (and probably
most marsupials possessing epipubic bones) have a unique cross-couplet body
stiffening mechanism powered by muscles
(Reilly and White, 2003).
Electromyographical patterns of abdominal muscles (extending from the rib cage
on one side through the midline to the contralateral epipubic bone and femur)
are activated asymmetrically across a couplet in concert with the stance
period of the diagonal limbs of that couplet. The asymmetrical firing of these
muscles in conjunction with the elevation of the movable epipubic bone
effectively forms a tightening sling across each diagonal limb couplet as the
animal bounces on it. This functional mechanism appears to stiffen the trunk
across each couplet during the step. Perhaps Monodelphis prefers the
running trot gait rather than other possible gaits because it employs this
unique cross-couplet firing mechanism. It is possible that the cross-couplet
support mechanism largely restricts Monodelphis to using
couplet-dominated trotting gaits for any kind of sustained locomotion. Indeed,
Monodelphis in this study continued to use a running trot at speeds
three times greater than the speed at which rats shift to a gallop
(Gillis and Biewener, 2001
).
We hypothesize that use of the cross-couplet muscle linkage produces the
mechanical energy patterns characteristic of a spring mechanics. Thus,
Monodelphis appears to simply pay for locomotion with muscular
activity, and this involves both appendicular and abdominal muscles.
Spring mechanics are highly correlated with a running gait in Monodelphis, but the assumption that spring mechanics are associated with passive spring storage appears to be tenuous for non-cursorial mammals with semi-erect postures. Paying for locomotion with muscular work may be the primitive condition for mammals. Further work on animal locomotor dynamics should look for other possible ways that semi-erect and sprawling forms may be choosing gaits and coping with the costs typically associated with bouncing mechanics. Future studies integrating mechanics with gaits will begin to illuminate the energetic consequences of particular gaits, why certain gaits are preferred, and how the neural control of an array of musculoskeletal systems can move the limbs to modulate patterns of whole body mechanics.
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Acknowledgments |
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