Walking and running in the red-legged running frog, Kassina maculata
Concord Field Station, MCZ, Harvard University, Old Causeway Road, Bedford, MA 01730, USA
* Author for correspondence (e-mail: aahn{at}oeb.harvard.edu)
Accepted 21 October 2003
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Summary |
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Key words: walking, running, gait, locomotion, biomechanics, Kassina maculata, anuran
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Introduction |
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Classically, the definitions of walking versus running gaits have
been based on duty factor, or the fraction of the stride during which the
animal's limb is in contact with the ground. Duty factors of >0.5 provide a
kinematic characterization of walking gaits. By contrast, duty factors of
<0.5 typically characterize running gaits (Alexander,
1977,
1989
;
Hildebrand, 1985
), during
which a reference limb of an animal contacts the ground for <50% of the
stride cycle. This method of gait determination allows the evaluation of
locomotion with a single video camera and has been used to examine gaits in
mammals, amphibians and birds (Muybridge,
1957
; Alexander,
1977
; Hildebrand,
1985
; Ashley-Ross,
1994
; Gatesy,
1999
; Reilly and Biknevicius,
2003
; Hutchinson et al.,
2003
).
In mechanical terms, differences in the patterns of the kinetic
(Ek) and potential energy (Ep)
fluctuations of an animal's COM during locomotion have also been used to
distinguish walking and running gaits. By examining the Ek
and Ep fluctuations of the COM of an animal, walking can
be modeled as a rolling egg, with the limbs and body functioning like an
inverted pendulum, whereas running can be modeled as a bouncing ball, with the
limbs and body functioning like a simple spring-mass system
(Cavagna et al.,
1977). During the stance phase of walking, the animal's COM vaults
over each limb following an upward then downward trajectory. Correspondingly,
the fluctuations in Ek and Ep of its
COM are largely out of phase (Cavagna et
al., 1977
). By contrast, during running, the COM
generally loses height in phase with the animal's deceleration during the
first half of limb support. The COM then rises in phase with the animal's
acceleration during the second half of limb support. This downward then upward
trajectory of the COM is accomplished with the compression and re-extension of
the spring-like legs during the stance phase of running, which results in the
largely in-phase fluctuations of the Ek and
Ep of the animal's COM. Similar to a bouncing ball, energy
can be conserved through elastic storage and release in the muscles, tendons
and joint ligaments of the animal's legs
(Cavagna et al., 1977
). A
force platform is used to measure the instantaneous ground reaction forces of
the whole animal during terrestrial locomotion. From these measurements, the
movements of the animal's COM are determined to provide a mechanical basis for
the principles of energy exchange that distinguish terrestrial walking and
running gaits. This mechanical method is most useful when examining animals
with varying leg number, leg orientation, body shape or skeletal type and has
been used to identify the walking and running gaits of a variety of mammals,
birds, crabs, insects and lizards (Cavagna
et al., 1977
; Heglund
et al., 1982
; Blickhan and
Full, 1987
; Full and Tu,
1991
; Muir et al.,
1996
; Farley and Ko,
1997
; Parchman et al.,
2003
).
Walking and running gaits are rarely studied in frogs, mainly because past
research has focused on their swimming and jumping abilities
(Calow and Alexander, 1973;
Zug, 1978
;
Emerson, 1979
;
Marsh, 1994
;
Lutz and Rome, 1994
;
Kamel et al., 1996
;
Peters et al., 1996
;
Peplowski and Marsh, 1997
;
Gillis and Biewener, 2000
).
Although most frog species are specialized for hopping and swimming,
Kassina maculata primarily uses a third locomotor mode: a gait during
which the animal's left and right fore- and hindlimbs alternate over a broad
range of speeds. Some frogs also use gaits with alternating hindlimbs during
swimming (Nauwelaerts and Aerts,
2002
) and when walking at very slow speeds
(Gray, 1968
;
Walton and Anderson, 1988
;
Anderson et al., 1991
).
However, Kassina uses this walking/running-type gait as its primary
mode of locomotion at all speeds on land
(Fig. 1; see Results).
|
In the present study, we examine the kinematics and mechanics of
Kassina's locomotion to determine whether these frogs use a walking
or running gait (or both) and how speed influences their gait.
Kassina's alternating limb gait does not appear to change as they
increase speed (Fig. 1). Unlike
gait changes that are clear and easily discernible in mammalian quadrupeds,
Kassina's gait at fast speeds appears simply to be a faster version
of its gait at slow speeds. More typical patterns in mammals show drastic
changes in the footfall patterns accompanying the gait changes from walking to
trotting to galloping with increasing speed
(Alexander, 1977;
Biewener, 2003
). We test the
general hypothesis that Kassina does not change gait with speed.
Based on the uniform visual appearance of Kassina's locomotion at
slow and fast speeds (Fig. 1),
we hypothesize that Kassina uses a vaulting or walking gait at all
speeds. Based on previous studies that show animals can use a bouncing,
running gait without aerial phases, however, an alternative hypothesis is that
Kassina uses a bouncing or running gait at all speeds
(McMahon et al., 1987
;
Full and Tu, 1990
).
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Materials and methods |
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Kinematic variables
Speed, duty factor and limb phase of the animals were determined from the
video recordings. High-speed digital video data were recorded at 125 frames
s-1 (Redlake PCI-500 MotionScope) as the animals moved over the
force platform. The video camera was positioned to obtain a direct lateral
view of the animal, but, additionally, a mirror placed at an angle allowed a
simultaneous dorsal view so that all four limbs were visible in the video
recordings (Fig. 1).
Speed
The mean speed of each trial was calculated from the digital video
sequences by dividing the length of the force platform (0.12 m) by the time
taken by the animal to cross the platform using the animal's eye movement as a
reference. With the exception of speeds obtained from treadmill trials
(Fig. 2), all data presented
were obtained from force platform trials.
|
Treadmill data were obtained to determine the upper boundary of Kassina's locomotory speeds and to determine whether the speeds recorded during the force platform trials were indicative of the maximal, steady-state speeds of the animals. Therefore, the only trials recorded and analyzed on the treadmill were those at faster speeds. The treadmill (0.21 mx0.60 m working space) was much larger than the animal in order to avoid constraining the animal within a confined area. Although Kassina tended to move intermittently, the animals often moved at relatively constant or steady-state speeds during the bursts, staying in one position on the moving treadmill belt. The speeds for these constant-speed bursts on the treadmill were compared with the speeds recorded when the animals moved over the force platform (Fig. 2).
Duty factor
Duty factor was the main kinematic parameter used to distinguish between
walking and running gaits. For each force platform trial, duty factor was
calculated as the percentage of the stride cycle during which one reference
limb was on the ground. According to Hildebrand's model of symmetrical gaits
(Hildebrand, 1985), if a
single reference limb contacted the ground for more than 0.50 of the cycle,
then the animal used a walking gait. By contrast, if a single limb contacted
the ground for less than 0.50 of the stride cycle, then the animal used a
running gait. For the present study, the duty factor measurements were
averaged between the right fore- and hindlimbs of a trial, resulting in a
representative duty factor for that trial. Duty factor measurements did not
differ between fore- and hindlimbs (P=0.82; paired
t-test).
Limb phase
Diagonal limb (DL) and same-side limb (SSL) phases were calculated as the
percentage difference between the times at which the diagonal-side or
same-side limbs came into contact with the ground during a stride. For DL
phases, the front left and hind right limbs were used for analysis. For SSL
phases, we analyzed the side during which the forelimbs contacted the ground
first during the stride.
Mechanics of the center of mass
Miniature force platform
To determine the kinetic (Ek) and potential energy
(Ep) fluctuations of the animal's center of mass (COM),
force platform and digital video data were obtained simultaneously as the
animals (N=12; mass=8.38±1.55 g;
SVL=0.044±0.004 m) moved across a custom-built miniature force
platform (Heglund, 1981;
Biewener and Full, 1992
). A
2.12 m-longtrack was constructed with three wooden walls and one Plexiglas
wall, through which the animals were filmed. The miniature force platform
(0.12 m long x 0.06 m wide) was positioned midway along the length of
the running track and set flush to the running surface. The animals moved
across the force platform into a darkened cardboard box placed approximately 3
cm from the other end of the force platform. We attempted to collect multiple
trials from each animal at varying speeds. However, the animals mostly moved
to escape gentle prodding, with many of the fastest and slowest trials tending
to include very large accelerations or decelerations. The criteria we used to
determine acceptable trials included: (1) the animal completed an entire
stride while on the force platform, (2) the relative magnitudes of the
Ek and Ep were within a single order
of magnitude of each other and (3) the net horizontal change in velocity was
less than 50% of the average velocity across the force platform. Change in
velocity, determined from the horizontal force recordings for each trial, was
calculated by dividing the difference between the final and initial horizontal
velocities by their mean and then multiplying this fraction by 100. Although a
±50% change in velocity is a generous criterion for steady-state
locomotion, the nine trials for which the change in velocity was between 25%
and 50% showed patterns of kinematics and COM energy changes much like those
trials with less than 25% changes in velocity (P=0.22-0.96; unpaired
t-tests).
The force platform consisted of a rectangular (0.12 m x 0.06 m), 2
mm-thick panel of honeycomb aluminum bonded to two brass beams that were
supported over an aluminum base. The front and rear brass beams were machined
with three independent, single spring blade elements on either side, allowing
vertical, horizontal (fore-aft), and medio-lateral forces to be recorded
separately. For the purposes of this study, only the vertical and horizontal
components of the ground reaction forces were resolved, because the lateral
forces generated by the animal were too small to be measured by the force
platform. Since lateral forces have been recorded to be less than 5% of the
fore-aft horizontal forces in sprawled quadrupeds that laterally undulate
during locomotion (Farley and Ko,
1997), omitting the lateral forces would be unlikely to influence
the conclusions of the present study. Forces were measured using a pair of
single-element, metal foil strain gauges (type FLA-1-11; Tokyo Sokki Kenkyujo
Co., Tokyo, Japan) bonded to both sides of each of the 12 spring blades (three
spring blades for each of the four corners of the platform). Cross-talk
between vertical and horizontal outputs did not exceed 3.1%. Loads in the
range of those generated by the animal (0.02-0.2 N) produced a linear response
with a maximum variation across the platform of 3.4%
(r2=0.99 for vertical and horizontal directions). The
sensitivity of the channel outputs in the vertical direction was 0.56 N
V-1 and the horizontal direction was 0.63 N V-1. The
natural, unloaded frequency of the platform equaled 125 Hz. Raw force signals
were amplified through Vishay conditioning bridge amplifiers (model 2120;
Measurement Group, Don Mills, Ontario, Canada) and collected using
data-acquisition software at 5 kHz (Axoscope 8.0; Axon Instruments, Inc.,
Foster City, CA, USA) on a PC. The data were filtered using a recursive,
lowpass Butterworth filter with a cut-off frequency of 25 Hz. The video
recordings were post-triggered and synchronized with the force recordings for
each trial.
Energy calculations
The vertical and horizontal forces recorded over a complete stride were
used to calculate the mechanical energies of the COM of each animal as it
traveled across the miniature force platform
(Cavagna, 1975). These forces
were first integrated to obtain the instantaneous vertical and horizontal
velocities. Whereas the integration constant in the vertical direction was
zero, the mean speed of the animal was used as the integration constant to
calculate changes in horizontal velocity. To ensure correct calculations, the
horizontal velocities calculated from force platform data were compared with
the velocities determined from video data. The instantaneous horizontal and
vertical velocities were then used to calculate the instantaneous vertical
kinetic energy (Ekv) and horizontal kinetic energy
(Ekh) using the formula: kinetic
energy=0.5Mv2, where M is the mass of the
animal and v is its velocity. The sum of these energies determined the
instantaneous total kinetic energy (Ek). An additional
integration of the instantaneous vertical velocity gave the instantaneous
vertical displacement (h) of the COM to calculate changes in the
gravitational potential energy
(Ep=Mgh, where
M is the mass and g represents acceleration due to
gravity) of the animal. The total mechanical energy of the COM of the animal
at each instant was obtained by adding Ek and
Ep. Percentage change in velocity was calculated by
dividing the difference between the final horizontal velocity and initial
horizontal velocity by the mean horizontal velocity for the trial and then
multiplying this fraction by 100.
Phase shift
The phase shift between Ek and Ep
was the main mechanical determinant used to distinguish between walking and
running gaits. Typically, a 180° phase shift between the
Ek and Ep of the COM has defined a
walking gait (Cavagna et al.,
1977; Farley and Ko,
1997
), and a 0° phase shift of the COM energies has defined a
running gait (Cavagna et al.,
1977
; Full and Tu,
1990
). For the present study, trials during which the phase shift
approximated 180° (or >135°) were classified as walks, and trials
during which the phase shift approximated 0° (or <45°) were
classified as runs. The mechanical energy phase shift was determined by
dividing the time between the absolute minima of Ek and
Ep by the time of a complete stride and multiplying it by
360°.
Percentage recovery
%Recovery, defined as the energy exchanged between Ek
and Ep, has been used to evaluate the magnitude of
mechanical energy saved by this energy exchange of the COM based on an
inverted pendulum model of walking gaits
(Cavagna et al., 1976).
Because of changes in the relative phases of Ek and
Ep during walking (out-of-phase) versus running
(in-phase), %Recovery would be expected to be high during walking and low
during running. Following Cavagna et al.
(1977
), %Recovery was
calculated as:
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For the present study, we did not use %Recovery to classify walks
versus runs. Instead, we examined %Recovery only as a correlate of
gait, relying on the phase relationship between the Ek and
Ep of the animal's COM as the mechanical determinant of a
gait (Full and Tu, 1990;
Farley and Ko, 1997
). In
trials for which the relative magnitudes of the fluctuations in
Ek and Ep of the COM were similar
(within one order of magnitude), the %Recovery and the phase shift would be
expected to positively correlate. A low %Recovery would accompany an in-phase
or near-zero phase shift, while a high %Recovery would accompany an
out-of-phase or near-180° phase shift.
Percentage congruity
For the present study, %Congruity was defined as the proportion of the
cycle during which the Ek and Ep of
the COM changed similarly in direction, recognizing that these two
mechanical energies were never completely in- or out-of-phase. We adopted
%Congruity to provide an additional quantitative approach for assessing how
the relative timing of the fluctuations in Ek and
Ep correspond to walking versus running gaits.
Ideally, %Congruity would be 0% for a walking trial and 100% for a running
trial. Lower values of %Congruity indicated a gait that was more like a walk,
and higher values of %Congruity indicated a gait that was more like a run. In
determining %Congruity for each trial, the instantaneous rate of change of the
energy was calculated by differentiating Ek and
Ep with respect to time during a stride. When the product
of the instantaneous changes in Ek and
Ep was greater than zero, the two energies were congruent.
Conversely, when the product of the instantaneous changes in
Ek and Ep was equal to or less than
zero, the energies were incongruent. %Congruity was calculated as the sum of
the portions of the cycle during which the two energies changed in similar
directions (i.e. when the product of the rates of energy change was greater
than zero) divided by the cycle time and multiplied by 100. Although
%Congruity neglected the relative magnitudes of the fluctuations in
Ek and Ep of COM, it quantifies the
relative changes in Ek and Ep
throughout the entire stride cycle.
Statistics
All reported values represent means ± S.D. If more than
one trial was obtained for an individual, the data were averaged to represent
that individual to avoid pseudo-replication. Comparisons were tested with
unpaired t-tests. Differences were considered to be statistically
significant when P<0.05. Linear regressions, however, were
obtained from pooled data (n=32) because three trials or fewer were
obtained from 10-12 individuals. The linear regressions obtained from pooled
data did not result in different conclusions from regressions of averaged
data, for which a single data point or a single regression line represented an
individual.
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Results |
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Kassina mainly increased speed by increasing stride frequency (Fig. 3). As the speed of the animals increased threefold, stride frequency approximately doubled from 1.8 Hz to 3.8 Hz (stride frequency=11.0v+0.84; r2=0.67; P<0.0001). The additional increase in speed was achieved by a more modest increase in stride length from 0.05 m to 0.08 m (stride length=0.097v+0.05; r2=0.24; P=0.004).
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Kinematics-footfall patterns
Duty factor
The duty factors of the animals locomoting over the force platform
indicated that the frogs used only a walking gait
(Fig. 4). Although duty factor
(averaged between fore- and hindlimbs) never measured less than 0.5, it
decreased with increasing speed (duty factor=-1.03v+0.88;
r2=0.62; P<0.05) and ranged from 0.77 to 0.59
(mean=0.69±0.05; N=12 individuals) over the speed range
recorded. On the treadmill, the two fastest trials observed (0.28 m
s-1 and 0.33 m s-1) also exhibited duty factors
indicative of walking gaits (0.67 and 0.69, respectively).
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Limb phase
Diagonal limb (DL) phase and same-side limb (SSL) phase were both nearly
independent of forward speed (Fig.
5).DL phase ranged from 4.8% to 16.1% (mean=11.5±2.4%;
N=12 individuals) and was independent of speed (DL
phase=-9.71v+13.26; r2=0.02; P=0.44).
SSL phase ranged from 31.4% to 48.9% (mean=38.4±4.2%; N=12
individuals) and varied slightly with speed (DL phase=52.39v+28.78;
r2=0.25; P=0.0035). A DL phase of 0% and an SSL
phase of 50% would indicate a trot-like running gait. The limb phases observed
here, however, showed that these frogs used a gait that was slightly offset
from a trot, during which the diagonal limbs contacted the ground at slightly
different times. Although the limb phase data failed to discriminate whether
the animals `walked' or `ran', they did suggest that the gait used did not
change with speed.
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Mechanical energies of the COM
Walking frogs
Four of the 32 trials showed that three animals used a mechanical walking
gait, during which the phase shift between Ek and
Ep exceeded 135° (Figs
6A,
7A). In these trials, the phase
shift between the minima of Ek and Ep
ranged from 147° to 200° (mean=170±26°; N=3
individuals). These trials during which the phase shift approximated 180°
indicate that the minimum Ek occurred simultaneously with
the maximum Ep (e.g.
Fig. 6A), consistent with the
pattern of energy exchange expected for an inverted pendulum. Although speed
did not strictly determine gait, walking tended to occur at slower speeds in
Kassina (<2 m s-1).
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|
Running frogs
In 21 of the 32 trials examined, the phase shift between
Ek and Ep was less than 45° (Figs
6B,
7A), indicating that nine
animals used a bouncing or mechanical running gait. In these trials, the phase
shift between the minima of the mechanical energies ranged from 3° to
33° (mean=12±9°; N=9 individuals; P<0.05
when compared with phase shift during walking), indicating that the
Ek fluctuations correlated closely with the fluctuations
in Ep (Fig.
6B). As with walking, speed did not strictly determine gait in
Kassina. However, the fastest trials observed consisted of only
running trials.
An intermediate gait
In the remaining seven trials, the phase shift between
Ek and Ep was between 45° and
135°, indicating that these seven animals did not use a well-defined
vaulting or bouncing gait (Fig.
7A). In these trials, the phase shift between the minima of the
mechanical energies ranged from 47° to 131° (mean=88±31°;
N=7 individuals; P<0.05 when compared with phase shift
during walking and running), indicating that the Ek
fluctuations were neither consistently in-phase nor outof-phase with the
fluctuations in Ep
(Fig. 7A).
Percentage recovery
%Recovery generally decreased with increasing speed in Kassina
(Fig. 7B). %Recovery, on
average, was higher in walking trials (range, 21.9-44.2%;
mean=32.0±10.9%; N=3) than in running trials (range,
3.9-28.0%; mean=15.4±6.3%; N=9; P<0.05), but
considerable overlap existed in terms of both speed and %Recovery values.
Moreover, %Recovery for the trials during which the animals used an
intermediate gait did not differ from %Recovery during walking and running
trials (range, 6.6-39.1%; mean=25.8±11.8%; N=7;
P>0.05).
Percentage congruity
%Congruity increased linearly with forward speed
(%Congruity=200.5v+19.5; r2=0.34;
P<0.05; Fig. 7C)
and matched closely the (inverse) pattern observed for %Recovery
(Fig. 7B). When using phase
shift to differentiate walking from running, %Congruity was lower during
walking (range, 32.0-44.6%; mean=36.5±5.2% of the stride; N=3)
than during running (range, 46.5-75.1%; mean=62.4±7.9%; N=9;
P<0.05). In general, the mechanical energies during all walking
and most of the intermediate gait trials showed opposing directional changes
in Ek and Ep of the animal's COM,
indicating a vault-like gait. By contrast, higher values of %Congruency
indicated similar directional changes in Ek and
Ep of an animal's COM and a bouncing gait
(Fig. 7C). However, many of the
trials, including those defined as walking and running using the phase shift
definition, exhibited congruities near 50%, characterizing a gait that likely
combined the vaulting and bouncing mechanisms within a single stride. Through
a large range of intermediate speeds, the animal's COM often exhibited
vaulting mechanics in addition to bouncing mechanics
(Fig. 8), during which
Ek and Ep fluctuated out-of-phase or
in-phase during different periods of the stride cycle.
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Discussion |
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Kinematic evaluation of gait
From an evaluation of Kassina's footfall patterns, we found that
these frogs use only a walking gait (Fig.
9). At very slow speeds, Kassina attains static stability
with duty factors that approximate 0.75 of the stride
(Fig. 4), as has been observed
in other frogs and quadrupeds (Gray,
1968; Alexander,
1977
). With increasing speed, the time that each limb contacts the
ground decreases, but each limb always remains in contact with the ground for
greater than half the stride (duty factor >0.59) over the observed speeds
and conditions. Even at the fastest speeds, Kassina never exhibits an
aerial phase. Although animals can use a bouncing-type of gait, such as a
trot, without an aerial phase, the footfall pattern of Kassina shows
that the diagonal limbs contact the ground at slightly offset times
(Fig. 5). Albeit `trot-like',
this footfall pattern contrasts the trotting patterns typically seen in
mammals and some reptiles (Hildebrand,
1985
; Farley and Ko,
1997
). Based on their footfall patterns, we conclude that
Kassina walks at all speeds.
|
Mechanical evaluation of gait
Mechanical energy fluctuations
Although Kassina's gait does not change kinematically with speed,
the Ek and Ep of Kassina's
COM during locomotion suggest that these frogs not only use both walking and
running gaits but also a gait mechanically equivalent to a mammalian gallop.
Kassina uses the same two basic mechanisms observed previously in
mammals, birds, reptiles and arthropods
(Cavagna et al., 1977;
Heglund et al., 1982
;
Blickhan and Full, 1987
;
Full and Tu, 1990
;
Farley and Ko, 1997
). At
slower speeds, Kassina occasionally uses a vaulting or walking gait
when moving, as indicated by the Ek and
Ep of its COM changing out-of-phase and incongruously
(Figs 6A,
7). At faster speeds,
Kassina occasionally uses a running gait, much like a spring-mass
system or bouncing ball, during which the Ek and
Ep of its COM change mostly in-phase during a stride (Figs
6B,
7). More often, at many of the
speeds observed in the lab, Kassina employs a gait that combines the
mechanics of a vaulting gait and a bouncing gait, during which %Congruity
between Ek and Ep of the animal's COM
approximates 50%. This combined gait is mechanically similar to a mammalian
gallop at slow speeds (Fig. 8;
Cavagna et al., 1977
).
In the present study, we use two criteria to examine the mechanical
distinctions between walking and running (Figs
7,
10). The main criterion, the
phase shift between the minima of Ek and
Ep, has been used to distinguish walking from running in
insects, reptiles and mammals (Fig.
7A; Full and Tu,
1990; Farley and Ko,
1997
; Parchman et al.,
2003
). Additionally, we calculate a secondary criterion,
%Congruity, to examine more completely the relative fluctuations in
Ek and Ep of the COM throughout the
entire stride cycle (Fig. 7C).
%Congruity, or the proportion of the cycle during which the
Ek and Ep of the COM change
similarly in direction, indicates whether the COM behaves
mechanically more like a vaulting system or more like a bouncing system.
Unlike bipeds, the existence of fore- and hindlegs in quadrupeds may
complicate the movements of the COM. For example, elephants locomote at faster
speeds by vaulting with their forelimbs, during which their forelimbs move
upwards then downwards during stance, and bouncing with their hindlimbs, which
move downwards then upwards during the stance phase of fast locomotion
(Hutchinson et al., 2003
). As
would be expected for elephants, %Congruity during walking or running in
Kassina does not show ideal vaulting or ideal bouncing behavior.
Instead, mechanical energies of its COM are 36% congruent for walking frogs
and 62% congruent for running frogs (Fig.
7C). %Congruity, thus, may be an additional, useful measure of
gait type when the COM energies do not fluctuate like those of ideal
point-mass systems, which probably would not occur in any animal system.
|
Mechanical work to lift and accelerate the COM
As the product of positive work per stride and stride frequency, the total
external mechanical power required to lift and accelerate the COM increases
with speed (Fig. 11). On a
mass-specific basis, Kassina expends 1.5 J kg-1 to travel
1 m, which is similar to that required for Coleonyx and
Eumeces lizards (1.5 J kg-1 m-1;
Farley and Ko, 1997). This
value also falls within the range observed in other walking and running
animals, such as birds, mammals, crabs and insects (0.13-1.7 J kg-1
m-1; Heglund et al.,
1982
; Blickhan and Full,
1987
; Full and Tu,
1990
), and excludes the internal mechanical work needed to move
the limbs relative to the COM. This consistent range of mass-specific
mechanical energy values required to move a given distance in such diverse
group of animals suggests very similar and general principles underlying the
mechanism of legged, terrestrial locomotion
(Heglund et al., 1982
;
Full, 1989
).
|
Resolving differences between terrestrial gait definitions
The discrepancy between gait definitions based on kinematics
versus mechanics is not new. Early locomotion studies showed that
mammals use a vaulting gait with high duty factors (walk) at slow speeds and
then switch to a bouncing gait with low duty factors (run or trot) at faster
speeds (Fig. 9;
Muybridge, 1957;
Cavagna et al., 1977
;
Hildebrand, 1985
). Several
subsequent studies, however, have shown this distinction between gaits to be
less ubiquitous. For example, McMahon et al.
(1987
) showed that humans who
run with bent legs (i.e. `groucho running') use a mechanical bouncing gait,
even without an aerial phase. Insects (Full and Tu,
1990
,
1991
) and opossums
(Parchman et al., 2003
) also
use bouncing gaits based on their COM mechanics without including an aerial
phase. By contrast, lizards employ a trotting footfall pattern even though
they use a walking gait based on their COM mechanics
(Farley and Ko, 1997
).
Although the basic patterns and principles of walking and running gaits were
defined decades ago, exceptions to the basic rules continue to surface, which
may simply reflect the earlier bias towards the study of cursorial mammals and
birds.
Gait transitions
Regardless of its locomotor gait or the definition used to determine its
locomotor gait, Kassina does not appear to exhibit a clear
terrestrial gait transition. The walk-run transition typically occurs at a
distinct speed for a given species (Hoyt
and Taylor, 1981; Heglund and
Taylor, 1988
; Farley and
Taylor, 1991
; Kram et al.,
1997
). In mammalian quadrupeds, this transition is often
associated with a distinct change in the slope of the relationship between
stride frequency and speed (Heglund and
Taylor, 1988
). In Kassina, however, stride frequency and
duty factor vary linearly and continuously with speed (Figs
3,
4). Neither parameter exhibits
a change in slope or a curvilinear relationship as observed in quadrupedal
mammals and avian bipeds (Gatesy and
Biewener, 1991
; Gatesy,
1999
). Furthermore, diagonal limb phase does not depend on speed
and exhibits no change in slope. Mechanically, Kassina uses a walking
gait at slower speeds and a running gait at faster speeds, but there also
exists a large range of intermediate speeds over which Kassina uses a
gait that combines the mechanics of vaulting and bouncing gaits (Figs
7C,
8). This gait, which approaches
50%Congruity, is mechanically similar to the slow gallop of quadrupedal
mammals (Cavagna et al.,
1977
). Although Kassina clearly does not gallop like
cursorial mammals, these frogs may be utilizing a locomotory mode between
walking and running gaits. Unlike cursorial animals, the gait transition
between walking and running occurs over a broader range of speeds in frogs and
lizards (Fig. 7;
Farley and Ko, 1997
).
Although Kassina primarily utilizes a gait with an alternating
hindlimb sequence of footfall patterns, it also hops and swims like many other
anuran species. With increasing speed, Kassina tends to walk/run
faster rather than resort to jumping. By contrast, Fowler's toads (Bufo
woodhousei fowleri) change gaits from walking to hopping by gradually
decreasing the relative frequency of walking steps to hops with increasing
speed (Anderson et al., 1991).
Anderson et al. (1991
) suggest
that toads cannot maintain moderate and high speeds of locomotion by only
walking because their shorter forelimbs and longer hindlimbs prevent them from
increasing stride length sufficiently. Likewise, Kassina also
increases stride frequency more than stride length to move faster, but without
resorting to jumping at faster speeds (Fig.
3). Even though Fowler's toads are 2.5x larger than
Kassina in body size, Kassina is able to achieve much faster
speeds (0.1-0.3 m s-1) than the toads (<0.1 m s-1;
Anderson et al., 1991
) using an
alternating hindlimb sequence gait.
Conclusions
Although Kassina maculata appears to use only one terrestrial gait
based on footfall patterns, it uses two mechanical mechanisms to move at
different speeds and, thereby, may be considered to be using at least two
gaits. Like other limbed animals, Kassina uses a strut-like mechanism
to walk and a bouncing, spring-mass-like mechanism to run. Unlike many other
terrestrial mammals and birds that walk and run, Kassina never
achieves an aerial phase and its footfall patterns do not change substantially
with speed. At slower speeds, during a mechanically defined walk, the
Ek and Ep of Kassina's COM
are 170° out-of-phase and 37% congruent. At a broad range of intermediate
speeds, Kassina combines the mechanics of both walking and running
gaits. Finally, at faster speeds, Kassina uses a bouncing or
mechanical running gait during which the Ek and
Ep of its COM are largely in-phase (mean 12° phase
difference) and 62% congruent. During running, energy is conserved by its
storage and release in the elastic elements of the animal's musculoskeletal
system with each `bounce' or stride
(Cavagna et al., 1977).
Therefore, Kassina's switch to a bouncing gait at faster speeds may
be energetically favorable compared with hopping, as hopping in toads has been
found to be energetically more costly compared with running in other
terrestrial animals (Anderson et al.,
1991
). The kinematic and mechanical patterns of Kassina
are similar to those observed in a variety of other terrestrial animals such
as lizards, opossums, cockroaches and `groucho-running' humans. Although the
basic COM mechanisms identified for walking and running gaits apply to a
diversity of terrestrial animals, the kinematics associated with them can be
quite varied and may not reflect distinct gait transitions in terms of limb
movement patterns. Thus, Kassina's common name, the red-legged
running frog, is apt in terms of its locomotor body mechanics but not in terms
of its limb kinematics.
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Acknowledgments |
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