Kinematics of 90° running turns in wild mice
Department of Biology, University of Utah, Salt Lake City, Utah 84112, USA
e-mail: walter{at}biology.utah.edu
Accepted 27 February 2003
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Summary |
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Key words: agility, maneuverability, moment of inertia, locomotion, running, mouse, Mus musculus
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Introduction |
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Although specific kinematics may vary in conjunction with body
configuration, the mechanics of all successful running turns in which final
and initial speed are the same consist of two components: (1) the center of
mass must decelerate in the initial direction and accelerate in the new
direction, and (2) the body must be rotated to face the new direction
(Jindrich and Full, 1999). The
force required to decelerate the center of mass in the original direction is
equal to the decrease in momentum (mass x change in velocity) in this
direction divided by the time allotted for this deceleration. Similarly, the
force required for acceleration equals the mass multiplied by the
acceleration. The torque (
) required to rotate the body is equal to its
rotational inertia (I) times the required angular acceleration
(
).
Any feature reducing rotational inertia would, therefore, reduce the torque
required to achieve a given level of angular acceleration and may improve
turning agility. Rotational inertia is a body's resistance to rotation about
an axis. It is defined as the differential elements of a body's mass
(m) multiplied by their distances from the rotational axis
(r) squared (I=mr2)
(Halliday et al., 1993
). Eilam
(1994
) studied the kinematics
of walking turns in wolves, polecats and honey badgers and found that each of
these animals behaves in ways unique to its body plan to reduce the effective
rotational inertia during the turn. Wolves tilt their heads down and bend
laterally to reduce rotational inertia about a central turning axis, whereas
long-bodied pole cats use the pelvic and pectoral girdles as two separate
turning axes, and honey badgers rear up on their hindlimbs to reduce
rotational inertia about the pelvic girdle
(Eilam, 1994
). Many possible
variations also exist for running turns, and these may vary between groups of
animals depending on gait, body configuration, size, flexibility and muscular
strengths. This study focuses specifically on 90° turns executed by
bounding mice. It addresses whether mice behaviorally reduce their rotational
inertia during turns or take advantage of the fluctuations in rotational
inertia inherent to a bounding gait by rotating when it is minimized. Mice are
particularly convenient subjects for kinematic analysis as their small body
size allows multiple strides to be filmed from below with a single camera.
Also of interest is the effect of turning on the stride cycle. Greene and
McMahon (1979) studied the
gait parameters of human subjects running along paths of varying radii. They
found that neither stride frequency nor step length (the distance traveled
during ground contact) varied with path radius. Based on these results, and
the known forces of gravity and centripetal acceleration that must be overcome
to complete a turn, they made several predictions about how speed and
ballistic air time should vary with path radius for humans running at maximal
speed. Mice, with their very different body configuration and gait kinematics,
must still overcome the same forces of gravity and centripetal acceleration to
complete a turn. In this study, changes in gait parameters with path radius in
mice are compared to those observed in humans and to the predictions of Greene
and McMahon (1979
).
A further question of this study concerns the timing of the deflection in
heading of the center of mass relative to the rotation of the body axis.
Jindrich and Full (1999) found
that in cockroaches, the change in direction of heading led body rotation by
an average of 5°. They noted that the lateral forces applied during
straight-ahead running were sufficient to generate the perpendicular forces
that changed the direction of heading in turns. Further, despite the greater
contributions of the outside legs to turning, they found no difference in duty
factors during turns. In mice, where the forelimbs are used mainly for
deceleration and the hindlimbs for acceleration in straight running
(Heglund et al., 1982
), it was
hypothesized that the forelimbs might have a greater duty factor just prior to
the turn as the mouse decelerates in the original direction, and the hindlimbs
might have a greater duty factor just after the turn as the mouse accelerates
in the new direction. Thus, duty factors of the fore- and hindlimbs were also
compared just prior to and after the center of the turn.
This paper describes the kinematics of running turns in wild mice, focussing specifically on changes in posture that influence resistance to body rotation, how gait parameters vary in running turns versus straight running, and the timing in deflection in heading of the center of mass relative to the rotation of the body axis. These observations suggest that for running turns in mice: (1) body rotation coincides with the portion of the stride in which rotational inertia is minimized, (2) crouched limb posture may allow relatively higher velocities to be maintained, and (3) rotating the body prior to changing the direction of heading may facilitate rapid acceleration in the new direction.
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Materials and methods |
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Setup and procedure
Mice were videotaped from below at 250 Hz while performing 90° running
turns in a 0.6 mx0.6 m L-shaped track, 10.2 cm wide, made of Plexiglas.
Plexiglas was used as the running surface to allow video recording of the
underside of the mouse throughout the turn. This greatly improved resolution
of limb support, duty factors, stride frequency and lateral bending of the
trunk. To induce mice to run, doors at either end of the trackway were opened
and the mice were blown on if necessary. Runs in both directions were
recorded. The Plexiglas at either end of the trackway was covered on the
outside with dark-colored paper to motivate mice to run all the way to the end
and to stay there until induced to run again. Each mouse made 2030 runs
on the trackway on each of 3 different days. The six fastest performances
(determined by counting the number of video frames required to cover the
trackway), in which the mouse made no contact with the side walls of the
track, were digitized and analyzed for each mouse. Because only the fastest
runs were used, all turns analyzed consisted of bounding locomotion. In the
majority of trials no apparent foot slippage occurred, and those trials in
which mice did slip were excluded from the analysis. Nevertheless, it seemed
possible that subjects might modify their stride parameters or run more
slowly, with increased caution, on the Plexiglas. To control for this
possibility, the trackway was carpeted and four of the mice performed 30
control runs on each of two days. Carpeted control runs were filmed from above
at 250 Hz and the fastest control run for each mouse was then analyzed and
compared to experimental trials.
Stride frequency and duty factors
Stride frequency and proportion of stride time spent unsupported were
compared over the two strides in the middle of the turn to those of mice
running along a straight trajectory. The unsupported portion of the stride is
the same as the ballistic air time referred to by Greene
(1985) and encompasses both
flight phases. Duty factors of the fore- and hindlimbs were compared between
the first and second strides centered upon the apex of the turn, and between
turns and straight runs. The apex of the turn refers to the point at which the
velocity in the new direction becomes equal to that in the original direction,
i.e. when the center of mass is moving at a 45° angle relative to the
initial heading. Duty factors and flight phases were determined by recording
whether the hindlimbs or forelimbs were in contact with the ground for each
frame of the videotape. Because the videotape was recorded at 250 Hz and
contact phases ranged from 2540 ms, whereas flight phases could be as
short as 4 ms, there was some error inherent in this data. To control for
this, reported duty factors were averaged over the six turns for each mouse
and then over the six mice. Stride and step lengths were determined by
multiplying the mean stride velocity by the stride time and total ground
contact time (forelimb + hindlimb support), respectively. For measurements on
the straight trajectory, five of the mice were videotaped from below at 250 Hz
while they ran in a similar Plexiglas enclosure 1.22 m in length and 10.2 cm
in diameter without the 90° turn. Two strides from the middle of the
trackway were analyzed from six runs for each mouse. Straight runs were
selected for analysis such as to obtain as wide a range of bounding speeds as
possible, including the fastest straight run for each mouse.
Measurement and analysis of rotation and angle of deflection
To study rotation of the body during the turn and to measure the extent of
lateral bending, it was necessary to know the angles that various `segments'
of the mouse's body made with the axis of the track throughout the turn. To
determine this, four black markings for digitizing were placed ventrally along
the sagittal axis of the mouse in the following locations: (1) tip of chin,
(2) throat, (3) caudal end of rib cage and (4) just cranial to anus. Using
these markings, each mouse's body was divided into four segments: (i) the head
and neck from marking 1 to 2, (ii) the thoracic segment from marking 2 to 3,
(iii) the abdomen and hindquarters from marking 3 to 4 and (iv) the
postcranial body from marking 2 to 4. The angle made by each of these segments
with the track axis was then calculated for each frame of the video.
To determine the extent to which head rotation preceded that of the postcranial body, the difference in angles made by each of these two segments with the track axis was measured for each frame and averaged over the two strides centered at the apex of each turn (Fig. 1A). These values were then averaged over the six turns from each mouse and the mean of these means was calculated. If the head tended to rotate prior to the body, this mean value would be significantly positive. This procedure was repeated using the upper and lower body segments to determine whether lateral bending of the trunk occurred to a significant extent.
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To determine when in the stride cycle the majority of angular displacement occurred, the stride was divided into six phases: the first and second halves of forelimb and hindlimb support, flight phase 1 from hindlimb to forelimb support and flight phase 2 from forelimb to hindlimb support (see Fig. 5). The angle rotated by the head/neck and postcranial body during each of these phases was then calculated for the two strides centered at the apex of each turn. To determine the mean and maximal angles turned in bouts of rotation, it was first necessary to locate the beginning and end of each bout. To do this angular velocity (determined from the angular displacement through the same derivation as used to determine linear velocity and explained below) was plotted over time and bouts were measured between minima. The amount of body rotation occurring in each bout was then determined by integrating the area under this curve.
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The angle of deflection, described by Jindrich and Full
(1999) as the angle between
the instantaneous and original directions of travel of the center of mass, was
also measured throughout the turn. This was calculated as the angle between a
segment connecting the location of the center of mass in two consecutive video
frames and the track axis. Because this measurement was subject to fluctuating
error, measured values were smoothed using fourth-order central differences
(Lanczos, 1956
) as explained
below for velocity. The extent to which body rotation preceded deflection in
heading was then determine by averaging the difference between the body angle
and the angle of deflection over the two strides centered at the apex of the
turn.
Calculating speed
To calculate the speed of the center of mass, its location was approximated
as the third marking, at the caudal end of the rib cage, based on previous
measurements (Walter and Carrier,
2002). Because the actual location of the center of mass varies
throughout the stride cycle, and the mouse's skin moves relative to its body,
this estimate introduces some error. To reduce this error, speed was averaged
over a stride cycle. Linear velocities (Vx and
Vy) in the original and new directions were calculated by
first smoothing positional data using fourth-order central differences and
then taking the derivatives using moving regressions
(Lanczos, 1956
):
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As noted in many previous studies (e.g.
Walker, 1998), there is some
error inherent in positional data obtained through digitizing. Previous
studies point out that this error is multiplied when taking the derivatives to
obtain velocity data. With the magnification and video speed used, Walker
(1998
) observed the mean error
in velocity derived from digitized positional data to be less than 10%, while
maximum velocity values were not overestimated by more than 25% in 90% of
trials.
Measurement of rotational inertia
While rotational inertia of mice in the lateral (yaw) direction for
standing/trotting postures has previously been measured
(Walter and Carrier, 2002),
the extent to which it varies throughout the stride cycle in bounding mice was
unknown. To estimate this variation, the rotational inertia of three mice
frozen in each of the following three bounding postures (9 in total) was
measured: (1) with trunk and limbs maximally extended, (2) maximally flexed,
and (3) midway between as in a standing posture. Rotational inertia was
determined by oscillating each mouse as a pendulum about a rod passing
dorsalventrally through its sagittal plane and timing the pendulum's
period (method described in Walter and
Carrier, 2002
). Each mouse oscillated about two separate axes,
allowing for two separate estimations of the rotational inertia about the
center of mass using the parallel axis theorem. These two estimates, which
differed by less than 15% in all cases, were averaged. To account for the
slight variations in mass of the nine mice, assumptions of geometric
similarity were used to scale each rotational inertia value to an 18.5 g
mouse. Rotational inertia values for the three mice in each posture were then
averaged.
Statistical analysis
Paired Student's t-tests were used to determine whether
differences in velocity and gait parameters were significant between each
mouse's fastest trial turning on Plexiglas versus carpet, and turning
versus straight running. t-tests were used to determine
whether differences between the rotational inertia values for each of the
three limb postures were significant. In all comparisons, parameters were
assumed to be significantly different if the P values were less than
or equal to 0.05. Student's t-tests were also used to determine
whether average leads in head and body angles over the deflection angle were
significantly different from zero.
As it was not possible to coerce mice to run along the straight trajectory
at exactly the same speeds used in turns, the mean speeds and gait parameters
of the six mice over their turns were averaged and compared to reduced major
axis (RMA) regressions of the various parameters against speed. RMA regression
lines (Sokal and Rohlf, 1997)
were fitted to plots of stride frequency and proportion of stride unsupported
versus straight path speed. 95% confidence intervals
(Sokal and Rohlf, 1997
) for
means of 36 samples (turns) were also calculated.
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Results |
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Comparison of turns on Plexiglas with carpeted controls
The Plexiglas surface on which the mice ran had a minimal effect on speed
and stride parameters. On average, mice ran only 10% faster during carpeted
control runs than on Plexiglas. No significant differences were found in gait
parameters including stride frequency, proportion of the stride spent
unsupported, and fore- and hindlimb duty factors between the fastest carpeted
and Plexiglas runs. Because the differences in speed between carpeted and
Plexiglas runs, though significant, were relatively small, and there were no
significant differences in other gait parameters, it seems reasonable to
assume that the biomechanics and kinematics of the mice's gait were not
substantially altered by the low frictional surface of the Plexiglas.
Comparison of stride parameters between turns and straight runs
Maximum speed and gait parameters did differ, however, between the fastest
turns and straight runs of the mice when they ran on Plexiglas. Maximum speeds
during straight runs were on average 1.37 times greater than maximum speeds
over the two strides surrounding the apex of the turn, but stride frequencies
did not differ significantly (Table
1). Mice spent a smaller portion of the stride period unsupported
in the maximum speed turns and a greater portion supported by the
forelimbs.
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On average, mice had higher stride frequencies during turns than would be expected for straight runs at similar speeds (Fig. 2). The percentage of stride spent unsupported for the stride prior to the apex of the turn was not significantly different from that predicted for same speed straight runs. A slightly greater portion of the stride after the apex of the turn was spent unsupported than would be predicted for same speed straight runs (Fig. 3). Although mice ran more slowly just after the apex of turns than before, other stride parameters including proportion of stride spent unsupported, stride frequency and duty factors, did not differ between the two turning strides (Table 1).
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Body rotation and rotational inertia
Postcranial body rotation did not occur in one continuous motion, but
rather in bouts interspersed with periods in which little or no body rotation
occurred (Fig. 4A). These bouts
of increased angular velocity were synchronized with the stride cycle
(Fig. 4B) and resulted in body
rotations of 1553° (Fig.
4C). Thus the total body rotation of 90° was usually completed
in two or three strides. The greatest amount of body rotation occurred during
the period from the second half of forelimb support to the first half of
hindlimb support (Fig. 5). The
rotational velocity during the intervening flight phase 2 was lower than that
during the second half of forelimb support, but not significantly different
from that during the first half of hindlimb support. However, because of its
short duration or absence in many of the strides, a smaller percentage of the
total rotation occurred during it. The period from the end of forelimb to the
beginning of hindlimb support is also the portion of the stride in which the
mouse's body is maximally flexed and rotational inertia is minimized.
Rotational inertia of a maximally extended 18.5 g mouse
(1.14x105±4.5x1012) was
1.54 times greater than that of a fully flexed mouse
(7.41x106±9.0x1013) and
1.39 times greater than that of a standing or intermediately postured mouse
(8.24x106±1.0x1012).
The difference in rotational inertia between flexed and intermediately
postured mice was not significant.
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Averaged over the two strides centered at the apex of the turn, rotation of the head/neck segment preceded that of the body by 8° and preceded the deflection of heading by 11° (Table 2). Rotation of the thoracic segment did not significantly precede that of the hindquarters. Body rotation preceded deflection of heading by an average of 3°. Thus, mice tended to rotate both their heads and trunks to face the new direction before their centers of mass began moving in this direction.
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Discussion |
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Predicting relative speed from turn radius
Although the finding that the maximum speed of mice is lower in turns than
in straight runs is rather intuitive, an explanation for the magnitude of the
decrease in speed is not obvious. Greene and McMahon
(1979) related the decrease in
maximal velocity to path radius by assuming that the average total force
(horizontal and vertical combined) applied during ground contact is maximized
for an individual running at maximum speed. Based on this assumption, as path
radius decreases and greater horizontal force is required, the average
vertical force applied during ground contact must decrease proportionately.
This decrease in average vertical force necessitates spending larger portion
of the stride in contact with the ground at decreased radii. Greene and
McMahon further assumed that stride frequency and step length at maximum speed
were independent of curve radius. They thus proposed that the observed
decrease in speed around curves was due to an increase in ground contact time
without a corresponding increase in distance traveled during ground contact
(Greene and McMahon, 1979
).
Greene related path radius to relative velocity through the dimensionless
reciprocal Froude number
(rg/vo2)
(Greene, 1985
;
Fig. 6):
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So are the assumptions of Greene's equation reasonable, and do they apply
to mice as well as humans? The equation assumes that the vector sum of the
average foreaft, lateral and vertical forces applied during ground
contact remain constant. If, however, different muscle groups that were
capable of functioning concurrently produced these forces, one might expect
the average total ground force during the stance phase of turns to be much
greater. Electromyograph analyses on humans by Rand and Ohtsuki
(2000) and Neptune and
colleagues (1999
) have in fact
shown that the activity patterns of various lower limb muscle groups differ in
turns from straight-ahead running. Despite this, Chang et al.
(2001
) measured a decrease in
net ground force production during turns in humans, primarily in the inside
leg. These findings are not consistent with the assumption that total force
production is independent of turn radius in humans. Because ground forces were
not measured in this study, it is not possible to evaluate the effects of
curve radius on total ground force production in running mice. The second
assumption, that stride frequency and step length are independent of path
radius, was empirically demonstrated to be true for humans
(Greene and McMahon, 1979
). In
mice, step length and stride frequency also did not differ significantly
between maximum speed turns and straight runs
(Table 1).
Because the Froude number (vo2/rg) is dimensionless, Greene's equation should be equally applicable to animals of all sizes. The radii required for similar inverse Froude numbers are proportionately smaller in smaller animals because their maximum speeds are lower. For an inverse Froude number of 0.5, Greene's human subjects used a radius of 3.1 m, which was approximately 20 times larger than the average radius for mice (0.153±0.005 m; mean ± S.E.M., N=5). In other words, because the humans and mice were running along curves of equivalent radii for their maximum speed, their speeds should have been affected to the same extent.
The speeds of human subjects running along curves of various radii, showed
close agreement with Greene and McMahon's prediction at larger radii, but fell
below the predicted curve at reciprocal Froude numbers <1
(Greene, 1985;
McMahon, 1984
). For reciprocal
Froude numbers from 0.30.65, human velocities fell below the curve by
an average of 17% whereas mice velocities, on average, fell below the curve by
only 3.9% (calculated from Greene,
1985
; Fig. 6). Thus
at these small Froude numbers, mice were able to run closer to their maximum
speeds than humans.
It is possible that being quadrupedal versus bipedal confers some
advantage in turning. The bounding gait used by the mice places outside and
inside limbs in contact with the ground simultaneously. Thus if mice exhibited
the same decrease in force production by the inner legs as do humans
(Chang et al., 2001), it might
be partially ameliorated by the concurrent force production of the outside
legs. Alexander (2002
)
suggested that at very small radii humans might run slower than predicted by
Greene and McMahon because they are limited by friction rather than their
muscular ability to produce force.
Biewener (1983) suggested
that the crouched posture of small quadrupedal mammals might increase their
maneuverability by increasing the summed length of their limb segments
relative to their hip or shoulder heights. This would allow them to exert
ground forces over a longer contact period. Another possible advantage of the
crouched posture in turning is the mechanical advantage at the limb joints in
applying horizontal ground forces. Whereas an upright posture confers a much
greater mechanical advantage in producing the vertical ground reaction forces
needed to counteract gravity (Biewener,
1989
), it decreases the mechanical advantage for horizontal ground
forces (Fig. 7). For instance,
when humans perform running turns, much of the deflection in linear momentum
is produced by braking and medio-lateral forces of the vastus medialis and
other thigh muscles of the outer leg (Rand
and Ohtsuki, 2000
). Given the long lever arm of the nearly
straight lower limb and the very short lever arm of the muscles' insertions in
humans, these muscles are clearly operating at a very low mechanical advantage
(Fig. 7). In contrast, mice,
with their crouched posture, would be likely to apply the necessary horizontal
forces at a much greater mechanical advantage, thereby giving them an
advantage in turns of smaller radii. Greene and McMahon's over-prediction of
human performance at smaller radii may be because their estimate does not
account for the difference in mechanical advantage at which horizontal and
vertical forces are produced. This possibility is supported by the improved
turning performance of humans along banked curves observed by Greene
(1987
). A banked surface would
allow a runner to apply part of the horizontal ground force through the same
mechanism and mechanical advantage through which vertical force is normally
applied. In mice, the more comparable mechanical advantage for horizontal and
vertical force production might contribute to the closer agreement of their
performance with Greene's prediction at smaller radii.
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Duty factor compared between strides of the turn
There is a division of labor in mammals in which the forelimbs are
primarily used for deceleration and hindlimbs are primarily used for
acceleration (Heglund et al.,
1982). Because of this, it seemed likely that mice might have a
longer forelimb support phase in the stride prior to the apex of the turn,
when more deceleration in the original direction is likely to occur, and a
longer hindlimb support phase in the stride just after the apex, when more
acceleration in the new direction is likely to occur. Although there was a
trend in this direction (Table
1), there were no significant differences in forelimb and hindlimb
support phase lengths between the two strides. Force plate data during running
turns would be of great interest, as it would allow more exact timing of force
application by the limbs involved.
Turning mice rotate when rotational inertia is minimized
Turning mice rotated their body axes in a series of discrete bouts of
1553°, interspersed with periods where no rotation occurred
(Fig. 4A). These bouts of
angular rotation generally coincided with the end of forelimb support and the
beginning of hindlimb support (Fig.
5). This suggests a division of labor in which the forelimbs
provide more of the torque to rotate the body, after which the hindlimbs are
used to accelerate the body in the new direction.
At the end of forelimb support and the beginning of hindlimb support, when
the majority of body rotation occurs, the mouse has reached a maximum in
sagittal bending. The appendages and caudal region are located most closely to
the turning axis, such that the rotational inertia is only 65% of that when
the mouse is fully extended (Fig.
6). Thus the torque required to rotate the mouse's body at a given
angular acceleration is 35% less than would be required if the mouse were to
rotate during the period of maximum extension. Having a phasic stride cycle
that includes periods of increased and decreased rotational inertia is a
novelty of the bounding gait of quadrupedal mammals and might explain the
discontinuous body rotation observed in mice. In cockroaches, where rotational
inertia varies little over the stride cycle, body rotation is less abrupt
(Jindrich and Full, 1999).
Rotation of the head and neck was smoother than rotation of the body,
showing less variation in angular velocity within a given turn
(Fig. 5). Head rotation
occurred early in the forelimb duty phase and preceded the sharper rotations
of the body axis as well as the deflection in heading
(Table 2). Many studies on
walking turns in humans have similarly found head rotation to precede body
rotation and deflection in heading (e.g. Grasso et al.,
1996,
1998
;
Patla et al., 1999
;
Imai et al., 2001
;
Hollands et al., 2001
).
Hollands and colleagues (2001
)
suggested that, through neurons which fire selectively based on head
orientation, turning head to the new travel direction could be used by the CNS
as an allocentric reference frame to reorient the body. Turning the sensory
organs to face the new direction first would also increase the time available
for the both humans and mice to perceive the environment they must navigate
through. This extra reaction time is likely to be important in a flight
situation. In portions of some mice turns, head and body rotation appear to be
out of phase. This may be advantageous as it would reduce the maximum torque
required at a given instant.
Lateral bending might allow axial muscles to aid the appendicular skeleton in creating the torque necessary for rotation by bending and straightening the body. In contrast, if the body were held laterally rigid, although axial muscle activity would be required to maintain this rigidity, appendicular muscles would have to create more of the torque through concentric contractions. Rotation of the thoracic region, however, did not precede that of the abdominal region (Table 2), suggesting that lateral bending did not occur to a significant extent. It is also possible, however, that periods in which thoracic rotation preceded that of the hindquarters occurred, but were approximately equal to periods in which rotation of the hindquarters preceded that of the thoracic region. In this case, although a significant amount of lateral bending may have occurred, the average lead of the thoracic region would be insignificant.
Eilam (1994) described three
possible methods of behaviorally reducing rotational inertia: bending the
body, rearing up on one set of limbs, and rotating about multiple axes.
Although mice did not rear up or bend laterally, the sagittal bending of their
bounding gait did tend to bring the trunk and limb mass closer to the
rotational axis during the periods of maximal body rotation. Further, the
early rotation of the head may have allowed it to be rotated about a more
proximal axis than the rest of the body.
Body rotation precedes deflection of heading angle in mice
Jindrich and Full (1999)
describe the angle of deflection as the difference between the direction in
which the center of mass is traveling at a given instant and its original
direction. This deflection in heading must be created by ground forces that
are perpendicular to the original direction. These ground forces could be
generated by an animal facing the original direction applying medio-lateral
forces, or by an animal that has already rotated to face the new direction
applying forces parallel to its body axis. In cockroaches, where rotation of
the foreaft axis lags an average of 5° behind the angle of heading
(Jindrich and Full, 1999
),
medio-lateral ground forces are applied to change heading. In mice, however,
rotation of the body axis led the angle of heading by an average of 3.2°
(Table 2). Rotating the body
before deflecting the heading of their center of mass would allow mice to use
forces applied parallel to their body axis to change their heading. This
difference makes sense given the differences in limb configuration and running
gait between mice and cockroaches. The parasagittal limb posture and
bilaterally symmetrical gait of bounding mice yields reduced leverage for
lateral force production. In contrast, the sprawled posture and alternating
tripod gait of cockroaches is much more conducive to generating lateral force.
Compared to the changes in heading seen in mice
(Fig. 4A), the changes in
heading observed by Jindrich and Full in cockroaches were much more abrupt
(1999
). In fact, Jindrich and
Full (1999
) mention that the
lateral force impulses applied by a cockroach during straight-ahead running
are sufficient to generate the perpendicular forces observed in turning. The
fact that mice rotate into the new turn direction earlier in the turn also
makes sense, in that mice may be using distant visual cues to a greater extent
to enable them to maneuver through the terrain.
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Conclusions |
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List of symbols |
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Acknowledgments |
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References |
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Alexander, R. M. (2002). Stability and maneuverability of terrestrial vertebrates. Int. Comp. Biol. 42,158 -164.
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