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First published online January 18, 2008
Journal of Experimental Biology 211, 433-446 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.012385
Neuromechanical response of musculo-skeletal structures in cockroaches during rapid running on rough terrain
Department of Integrative Biology, University of California, Berkeley, CA 94720, USA
* Author for correspondence (e-mail: sponberg{at}berkeley.edu)
Accepted 26 November 2007
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: locomotion, motor control, muscle
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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; Cruse et al.,
2007; Pearson,
2004). In a dynamic, unpredictable environment, a muscle and its
tendon or apodeme often must do more than generate the force and work required
for steady-state locomotion (Dickinson et
al., 2000). These musculo-skeletal structures
(Delp and Loan, 1995;
Zajac, 1989) must stabilize
locomotion by managing any energetic deviations from steady state produced by
perturbations from the environment (Holmes
et al., 2006; Koditschek et
al., 2004). A stable solution may demand that a structure produce,
absorb, store and return and/or transfer energy
(Biewener and Daley, 2007;
Biewener and Gillis, 1999;
Full et al., 1998). A given
structure can respond with no change in its neural activation from steady
state or by adjusting the neural signals to the muscle. A structure that is
passive with no activation or one with unaltered rhythmic feedforward
activation from a central pattern generator (CPG) can provide stabilization
through mechanical feedback. These responses are sometimes referred to as
preflexes (Brown and Loeb,
2000). A structure that reacts to a perturbation through sensory
modulation of the efferent motor code or neural feedback can provide
stabilization using reflexes. In the present study, we focus on rapid running
that may limit the bandwidth of neural feedback
(Koditschek et al., 2004), as
well as the time a musculo-skeletal structure has to generate force and relax
for the next cycle (Marsh and Bennett,
1985; Swoap et al.,
1993). In addition, while there is a growing understanding of the
control strategies that animals employ in response to single perturbations
(Biewener and Daley, 2007;
Daley et al., 2006;
Jindrich and Full, 2002;
Kohlsdorf and Biewener, 2006;
Revzen et al., 2005;
Watson et al., 2002a),
locomotion is typically characterized by negotiation of irregular terrain that
repeatedly perturbs the steady state locomotor limit-cycle
(Spagna et al., 2007). Our
primary objective was to measure the activation of musculo-skeletal structures
during rapid running on rough, irregular versus flat, regular terrain
to determine the type of feedback a musculo-skeletal structure employs for
stabilization.
We selected musculo-skeletal structures of an insect that are exclusively
innervated by a single motor neuron, because their identifiable muscle action
potentials (MAPs) provide the simplest possible characterization of muscle
activation. The cockroach Blaberus discoidalis possesses a pair of
dorsal/ventral femoral
extensors1 (178 and
179) (Carbonell, 1947) that
are putative control muscles and innervated only by a single fast motor neuron
(Df) (Pearson and Iles, 1971;
Pipa and Cook, 1959). A single
action potential in Df produces one, relatively large MAP in its target
muscles, resulting in nearly identical patterns of activation in both
extensors muscles (Ahn et al.,
2006; Full et al.,
1998; Watson and Ritzmann,
1995). When first recruited during running, these femoral
extensors have been hypothesized to shorten the transition from flexion to
extension and possibly increase joint angular velocity at higher speeds
(Levi and Camhi, 1996;
Watson and Ritzmann, 1998b).
The relatively rapid force development in response to Df action potentials (10
ms latency and 30 ms to peak force) (Full
et al., 1998; Watson and
Ritzmann, 1995), compared with the much longer time (225 ms) to
first movement in `slow' Ds motor neuron activation
(Watson and Ritzmann, 1995),
could enable effective neural feedback control in these extensors at higher
running speeds. Quantifying energy management in these muscles has shown that
they are capable of producing, storing and returning and/or absorbing energy
depending on activation level (i.e. the number of MAPs), phase of activation
and strain (Ahn et al., 2006;
Full et al., 1998). The low
twitch to tetanus ratio (0.2) found in the ventral femoral extensor (179)
permits a fine gradation of force, suggesting considerable control potential
via neural feedback. Here, we directly compare the activation pattern
of these musculo-skeletal structures as cockroaches run at their preferred
speed over flat versus rough terrain containing randomized block-like
obstacles up to three times `hip' height (1.5 cm). We hypothesize a change in
MAP number, inter-stimulus interval, burst phase and/or interburst period
reflecting the use of neural feedback to stabilize rough terrain locomotion.
Alternatively, no change from the feedforward motor activation pattern would
support the hypothesis that these structures contribute to stability by
mechanical feedback.
Connecting feedback provided by individual musculo-skeletal structures to
higher level, task-relevant variables remains a challenge
(Biewener and Daley, 2007;
Cappellini et al., 2006;
Flash and Hochner, 2005;
Todorov et al., 2005).
Although approaches correlating muscle activation patterns with kinematic
variables have been successful at reducing dimensions
(Ivanenko et al., 2005;
Wang et al., 2006), we must
ultimately find the mechanistic link between musculo-skeletal structures'
responses to a perturbation and the recovery dynamics of the body or center of
mass (Biewener and Daley, 2007;
Holmes et al., 2006;
Ting, 2007). By comparing a
musculo-skeletal structure's perturbation response to that of the whole
animal, we can begin to understand how the mechanical and neural feedback of
individual structures couple to result in task-level stability. Therefore, our
secondary objective was to determine if a gait change during perturbed and
unperturbed locomotion is consistent with the mechanical and/or neural
feedback response measured at the level of the individual musculo-skeletal
structures.
To characterize the task-level feedback response of the animal, we measured
speed, pitch, roll and yaw of the body, static stability margin, duty factor,
stance initiation phase and stance termination phase for cockroaches running
on flat versus rough terrain. If cockroaches are perturbed on the
rough terrain, then pitch, yaw and roll and static stability margin should
show greater variation and perhaps a different pattern than on flat terrain.
If animals can negotiate this rough terrain by completing the course without
large decrements in speed, then they must be recovering from perturbations.
Significant alterations in gait could point to an important role of neural
feedback to musculo-skeletal structures for recovery
(Cruse, 1976;
Pearson and Franklin, 1984).
This would be particularly true if animals showed a shift away from the
typical steady state alternating tripod gait or demonstrated compensatory
corrections on a step-by-step basis. We tested the latter hypothesis by
determining whether cockroaches use a follow-the-leader (FTL) gait on rough
terrain where each posterior foot is placed on the secure foothold used by a
more anterior leg on the same side (Song
and Choi, 1989). Alternatively, animals running over rough terrain
that rely on collections of mechanically controlled musculo-skeletal
structures might show little change in the feedforward alternating tripod gait
generated during unperturbed locomotion and demonstrate no evidence of precise
stepping (Spagna et al.,
2007).
Characterizing the mechanical and neural feedback contributions from a musculo-skeletal structure in the context of the body's response to perturbations is a necessary step to understand how responses at lower levels interact to produce control at higher levels of the hierarchy. Yet, we view this approach as one of a suite of approaches. Complementing perturbation studies with characterization of musculo-skeletal structures' capabilities in isolation, direct manipulation of their motor and sensory neural code during locomotion, and modeling using a dynamical systems approach, will enable a far more complete understanding of the control of locomotion.
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MATERIALS AND METHODS |
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Rough and level terrain track
To simulate cockroaches running over natural, rough terrain, we constructed
an artificial wooden terrain with a random distribution of surface heights to
ensure that no regularity in the substrate would contribute to stabilization.
The rough terrain surface was constructed using 1 cmx1 cm variable
height blocks of wood formed into a track 22 cm long by 10 cm wide
(Fig. 1A). The height of each
block was randomly assigned to a value selected from a Gaussian distribution
with a mean of zero and a standard deviation of 0.5 cm (i.e. near cockroach
`hip' or coxa-body joint height), so that perturbations in the running surface
reached up to three times the cockroach's hip height
(Fig. 1).
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Kinematics
We video recorded the cockroaches running over rough and flat terrains with
two cameras (Ektapro Model 2000 cameras, Eastman Kodak, Rochester, NY, USA)
recording at 500 frames s–1 with a resolution of
512x384. Large mirrors were placed at a 15–30° incline along
the terrain to reflect the image. The position of each camera above the
trackway was oriented 5–10° off-center to provide both a view of the
track and a reflected view of the cockroach in one of the mirrors. This
arrangement provided four views distributed in a 60° arc above the
terrain.
We used a flood lamp (Lowel, Brooklyn, NY, USA) located adjacent to the cameras to illuminate the surface and two double goose-neck lights located on either end of the arena to reduce shadows and provide more even lighting particularly on the rough terrain. Images were buffered through the camera memory until post-triggering, after which a 1024 frame (2048 ms) clip from each camera was reviewed and cropped to the relevant time segment (usually 1000–1600 ms). Frames were then downloaded as a series of images (.tiff) and converted to movie files (.avi) for digitization. All video capture, downloading, and conversion were done with a software program (MotionCentral v2.7.5; Redlake MASD, Tuscon, AZ, USA).
Muscle action potentials (MAPs)
We recorded the activation patterns of the muscle 179
(Carbonell, 1947) that
parallels the proximal-distal axis of the coxa on the medio-ventral side. Its
dorsal counterpart, muscle 178, receives identical activation from the same
motor neuron, Df (Ahn et al.,
2006). Muscle action potential recordings follow previously
published methods (Ahn and Full,
2002; Watson and Ritzmann,
1998a; Watson and Ritzmann,
1998b). Briefly, we created two small holes in the cuticle using
size 0 insect pins. Two 50 µm silver wires (California Fine Wire Company,
Grover Beach, CA, USA), whose tips were stripped of insulation and formed into
small balls, acted as a bipolar electrode directly under the exoskeleton along
the proximal–distal axis of the coxa. The silver wires were kept in
place by making the balls slightly larger than the holes and covering the
insertion points with a small quantity of dental wax. Care was taken to
prevent wax from contacting joints. A third wire was placed in the third or
fourth most posterior abdominal segment to serve as the reference for the
bipolar recording. Finally, we epoxied the three wires to the dorsal abdominal
surface to prevent entanglement with the legs during running.
MAP signals coming from the running cockroach were collected differentially using an AC pre-amplifier (Grass-Telefactor, West Warwick, RI, USA) and amplified 2000x with 30 Hz low pass, 1 kHz high pass and 60 Hz line-in filters. We acquired the data through an acquisition board (National Instruments, BNC 2090, Austin, TX, USA) and PCI card using custom programs (Matlab, MathWorks, Natick, MA, USA). The electrophysiological recording synchronized with the video via a custom external trigger box. We imported the resulting raw data into a program (Spike2 v5.07, Cambridge Electronic Design, Cambridge, England) for analysis and applied a 60 Hz notch filter (alpha=1). Thresholding and peak finding searches discriminated spikes from the recording. The resulting spike times were exported and synchronized with the kinematic data.
Experimental protocol
In preparation for experimentation, cockroaches were cold-anesthetized,
although direct contact with ice was avoided by placing the cockroach in a
submerged plastic well. After motion ceased in about 30 min, we removed the
specimen from the bath. The distal regions of both pairs of wings were removed
to expose the dorsal side of the abdomen. Kinematic markers were composed of
small dots of white liquid paper and one was placed on the tarsus of each leg.
Markers were placed on the distal and proximal extremes of each tibia to
provide additional reference points to determine leg movement during tracking.
Finally, markers were added on the dorsal side of the cockroach body. One
marker was added on the center of the pronotum (referred to as the head
point), one on the second thoracic segment, and three along the abdomen. To
measure pitch, roll and yaw during traversal, we affixed three cockroaches
with a balsa wood cross above the COM with a fifth arm rising above the
cockroach. Matching a three-dimensional model of the cross to the recovered
cross markers in the resulting videos enabled calculation of body rotations
about all three axes.
If the cockroach was not motionless after marking, it was returned to the ice bath for 15–30 min. We then secured the specimen to a rubber platform using staple-shaped pins to hold the body and coxa in proper orientation for MAP wire insertion. At no time was the cockroach's cuticle pierced except to create the holes required for the recording wires. A small amount of ice was placed around the cockroach during operation to keep the air cool and maintain sedation. Cockroaches were allowed at least 1.5 h to recover at room temperature prior to running trials.
After recovery, we released the cockroach onto the approach track and elicited rapid running by gently probing the posterior abdominal segments and cerci with a small rod. Cockroaches quickly ran down the track and traversed either the rough or flat terrain before entering a shaded region at the end of the exit ramp. If the cockroach stopped or attempted to climb the wall of the track, we repositioned it manually on the approach track. After a successful trial, the cockroach had at least 5 min to recover as the video was downloaded from the camera buffer. The track was illuminated only during recording to encourage the cockroaches to remain stationary in between trials and to prevent a change in temperature.
We randomly chose whether each animal would first run on flat or rough terrain. We continued recording until six trials were obtained that met our operational definition and then switched to the other terrain type. There was at least a 30 min transition time between the two terrain types. Occasionally, the animal would snare and break the long trailing recording wire during the experiment, resulting in fewer than six trials on the second terrain. We analyzed only individuals with at least one flat and one rough terrain run.
We recorded a trial when a cockroach made one complete traversal of the
rough or flat terrain. Each trial was divided into constituent strides, which
are considered individually. We defined a stride as starting when the hind
left leg, from which we recorded MAPs, first initiated stance. Since we wished
to test cockroaches' stability in the face of repeated perturbations to
high-speed running, some strides were not included in our analysis.
Specifically, we rejected strides under four conditions. We rejected strides
when the cockroach's body contacted one of the mirrored side walls. In these
trials, cockroaches could experience a lateral perturbation due to contact and
often the tarsi were obscured throughout the analysis. Secondly, under normal
and perturbed running the cockroach would naturally yaw, but cockroaches would
occasionally exhibit substantial turns, often in response to contacting and
tracking the wall (Camhi and Johnson,
1999). We therefore removed strides in which the cockroach
exhibited turns of greater than 15°. Thirdly, we excluded strides in which
the cockroach started or ended with a velocity of zero (i.e. when the animals
stopped). Finally, strides occasionally occurred in which one leg failed to
make contact with the ground throughout the entire stride (duty factor=0) due
to the leg being placed in a large trough formed by the rough blocks. We
separately consider the few strides containing these mis-steps
(N=6).
Kinematic analysis
After the experiments, we imported uncompressed videos (.avi) of each run
into a commercial motion analysis software package (Peak Motus v8.5, Peak
Performance Technologies division of Vicon, Centennial, CO, USA) for
digitization. We analyzed the actual image (non-reflected) from whichever
video provided the least obscured view of the animal. Other views were used to
confirm placement of legs and visually corroborate our analysis.
We used a 9.6x8.0 cm calibration object (Lego blocks, Lego Systems, INC., Enfield, CT, USA) with 24 digitization points. In all images at least 16 calibration points were visible. Distances between each pair of points provided references to calibrate the video images. The calibration object was large enough to fill approximately half of the camera screen to ensure distortion in the image did not significantly affect the calibration.
All markers on the cockroach's body and legs were digitized in each frame. The resulting data were exported to a spreadsheet editor (Excel, Microsoft Corp., Redmond, WA, USA) and synchronized with the MAP data. We used custom scripts (Matlab) to represent the trajectory of each leg and stance onset was operationally defined as the time when leg movement relative to the surface went to zero. We constructed gait diagrams from the leg timing data. Steps in which the stance timing of the hind left leg could not be determined due to occlusion were not used in the analysis. Absolute footfall position and the block where foot placement occurred were recorded for analysis of FTL stepping.
To calculate running speed on a stride-to-stride basis, we took the linear distance between the thoracic body marker at the time of stance initiation in the hind left leg in two subsequent steps and divided by the stride time between them. We also calculated the yaw angle of the cockroach in each camera frame as the angle between the line segment formed by the head and thorax markers on the cockroach and a line segment oriented along the long axis of the terrain that was constant for each run. The difference in this angle between subsequent stance initiation times of the hind left leg determined the stride-to-stride heading adjustment of the animal.
MAP analysis
Each stride had a corresponding set of MAPs defined by their peak spike
times associated with the hind left leg. Since both number of spikes and their
timing affect muscle activation, it was important to characterize several
variables to determine if the neural activation patterns were changing from
flat to rough terrain running (Fig.
2A). Therefore, we analyzed the number of spikes occurring in each
step, the time between spikes (interspike interval, ISI), the relative phase
of the burst of spikes with respect to the initiation of stance in that leg,
and the timing between the initiations of bursts (interburst interval, IBI;
Fig. 2B). Since the number of
spikes per stride is categorical and ordinal, we performed
2-tests for statistical differences. Interspike interval,
burst phase and interburst interval are all continuous variables for which we
compared means and variances across the two terrain types. Since stepping
speed impacted the timing between bursts and spikes and each animal shifted
its activation phase slightly, we used partial t-tests from multiple
regressions of the timing variables with respect to terrain, speed, and/or
individual. We implemented all statistics in a data analysis program (JMP
v5.1, SAS Institute, Inc., Cary, NC, USA) except for multiple regressions,
which were accomplished with another program (STATA v8.1, Stata Corp., College
Station, TX, USA).
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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System level perturbations
We intended the rough terrain treatment to significantly perturb
steady-state running behavior. The repeated surface height perturbations
increased body pitch (Fig. 3A),
roll (Fig. 3B), and yaw
(Fig. 3C) when cockroaches ran
on the rough terrain. Comparing across all flat and rough terrain trials from
the three animals with the tracking cross, pitch, roll and yaw all showed
statistically significant greater variation while on the rough terrain
(F tests for equivariance, P<0.0001).
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). Both the
degree of static stability, defined as the actual distance between the COM and
the nearest edge of the support tripod, and the ideal margin of stability, the
maximum possible degree of static stability, were significantly lower while
traversing the rough terrain (t-tests, P<0.0001,
Kruskal–Wallis tests, P<0.0001). Cockroaches running on both
rough and flat terrains showed significant periods of static instability where
the COM fell outside of the tripod of support, but the rough terrain treatment
significantly increased the time spent statically unstable (t-test,
P<0.0001, Kruskal–Wallis test, P<0.0001). This
necessitates that inertial effects preserve posture through dynamic stability
(Ting et al., 1994) or
external forces (e.g. adhesion/friction) counteract the destabilizing
gravitational effects. Taken together the pitch, roll and yaw as well as the
static stability data confirm the visual observation that cockroaches running
over the randomly rough terrain experienced significant system level
perturbations.
Musculo-skeletal structure activation response to perturbations
MAP spikes per burst
We could not show any significant difference in the distribution of the
number of MAPs between flat and rough terrain trials for the hindleg femoral
extensors (Fig. 4A). During
flat terrain running, MAP recordings of muscle 179 demonstrated a stereotyped
pattern of 2–3 spikes during each stance period. Occasionally steps
occurred with 1 or 4 spikes. Despite repeated perturbations to body height and
orientation, a contingency analysis of spike counts found that the
distribution of spike number did not significantly vary between flat and
perturbed running (Pearson 2-test, P=0.25; Likelihood
ratio test, P=0.26). We note that a contingency analysis is sensitive
to differences in both the mean number of spikes and, more importantly, the
variance of spike occurrences. Therefore, if a significant number of rough
terrain steps demonstrated both increases and decreases in activation, as
might be expected from the random nature of the perturbation, then these tests
would show significant differences (P<0.05) in the distribution of
spike activity.
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When we further challenged the dynamic requirements of the running
cockroach with larger initial (Fig.
4B) and final steps (Fig.
4C), neural activation did change. Prior to moving across the
rough terrain, we required the cockroaches to first ascend a large step. The
cockroaches had to descend an equally large downwards step when leaving the
rough terrain track. The initial and terminal step varied from 2 to 4 cm in
height, depending on the section of the track the cockroach encountered. Motor
activation patterns elicited by ascending
(Fig. 4B) and descending
(Fig. 4C) steps showed
significant changes in per step spike count from flat terrain running.
Ascending steps demonstrated a significant increase in spikes per burst
(2-test, P<0.0001) with up to seven spikes being
recorded, whereas the plurality of descending steps required only a single Df
spike and the overall motor activation pattern was significantly decreased
(2-test, P<0.0001).
Interspike interval
The number of MAPs per burst does not solely determine muscle force and
power output, which can also depend on the amount of time between spikes or
interspike interval (ISI). ISI decreased as speed increased bringing the
spikes closer together in time as stance period decreased (regression
F test, P<0.0001, r2=0.40). However,
mean ISI did not vary significantly between flat and rough terrain running
independently of speed differences (Fig.
5, partial t-test, P=0.46). To control for
non-normal distributions of ISIs, we also tested for statistical differences
under Poisson and logarithmic transformations as well as the non-parametric
Kruskal–Wallis test. No alternative method affected the statistical
outcome. ISI means remained statistically indistinguishable for flat and rough
terrain (Poisson transform: t-test, P=0.33; log transform;
t-test, P=0.33; Kruskal–Wallis test, P=0.26).
Additionally, no differences were detectable when we considered all ISIs as
coming from the same sample or separated them into groups depending on which
spikes in the burst were being analyzed (e.g. ISI between spike 1 and 2, ISI
between spike 2 and 3 etc.).
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Burst-to-burst period and phase
Since the burst of MAPs occurs during stance, the period of bursting may
depend strongly on speed, which was not constrained from step to step. We
therefore normalized the period from the first spike of one burst to the first
spike of the subsequent burst with respect to speed. No significant difference
in the corrected interburst interval (IBI) mean or variance was observable
between flat and rough terrain running
(Fig. 6A, partial
t-test, P=0.58; non-parametric Kruskal–Wallis test,
P=0.64, F test for equivariance, P=0.27).
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Mis-steps
During six steps of the 150 analyzed for rough terrain running, cockroaches
experienced a particularly large elevation difference between blocks. The
resulting orientation of the cockroach's body and the roughness of the
surfaces caused one of the hindlegs to swing through its stride without making
contact with the surface at any time. We analyzed these events as particularly
extreme perturbations to steady-state running. In the instances where the hind
left leg missed its step completely, we observed a normal feedforward pattern
of Df activation, despite the duty factor of the leg being reduced to zero
(Fig. 7A,B). To test if there
was feedback occurring during or following the missed steps, we compared the
stride period two strides prior to the perturbation, following the
perturbation, and two strides subsequent to the perturbation
(Fig. 7C). Compared to the
normal period (0.119±0.022 s, mean ± s.d.), the period
significantly increased by 30.9% in the stride immediately following the
perturbation (0.158±0.047 s, mean ± s.d; t-test,
P<0.004). After recovery, the period returned to a level
indistinguishable from its original value (0.130±0.013 s, mean ±
s.d.; t-test, P=0.57). This transient increase in stride
period requires neural feedback, as the timing of the cyclical neural
activation of the muscles must change
(Revzen et al., 2005).
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System level response to perturbations
Gait and leg phasing
We measured the duty factors and relative phasing of the legs with a phase
of zero set at the moment of stance initiation in the hind left leg. Gait
analysis (duty factors and statistics in
Table 1; gait phases in
Table 2) demonstrated no
detectable change in duty factor, stance initiation phase or stance
termination phase for any leg between flat and rough terrain running.
Throughout flat and rough terrain trials, the cockroach maintained an
alternating tripod gait.
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Follow-the-leader gait and interleg coordination
A follow-the-leader (FTL) gait occurs when the organism targets a posterior
leg to land on the successful foothold that the ipsilateral leg anterior to it
used in a previous step (Song and Choi,
1989; Spagna et al.,
2007). Functionally it constitutes feeding back information of
stable foot placement to guide the following leg movements. On the rough
terrain, a simple FTL gait would predict that cockroach foot placements should
minimally occupy the same 1 cmx1 cm equiplanar block. Using the
definition that posterior tarsi gain purchase on the same block as their
anterior ipsilateral partner, we found that only 23.3% and 25.5% of the hind
left and hind right legs, respectively, followed in the footsteps of the
preceding middle leg (Fig. 8)
on the rough terrain. The percentage for middle legs following front legs was
higher (29.5 and 30.1% for left and right, respectively), but the vast
majority of steps still resulted in footholds on completely different blocks
(Fig. 8).
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Despite not targeting the same foothold block, cockroaches could attempt to
use FTL stepping, but often fail given the challenging substrate. This
strategy would still target posterior foot placements to land near the
successful anterior placement. Determination of how close placement has to be
to constitute FTL stepping requires definition. Since the posterior leg cannot
coincide exactly with anterior placement without the cockroach stepping on
itself, a strict criterion for a posterior leg targeting a successful foothold
would be placement within one-foot-length of the anterior leg, as is observed
in biological FTL gaits (Song and Choi,
1989). In this case, the strict criterion would be the long
dimension of the cockroach's tarsus, which is 
3 mm. A reasonable minimal
criterion is the half-width of a rough terrain block and, therefore the target
area of constant surface height for the posterior foot, assuming ideal
anterior foot placement in the center of the block. For the rough terrain
condition, this minimal criterion is 5 mm, which is 15% of the body
length and 25% of the stride length of the cockroach.
We calculated the absolute magnitude of the deviation between the placement
of each anterior and posterior pair of tarsi
(Fig. 9B). In 95.1% of rough
terrain steps, the deviation from precise FTL stepping exceeded the longest
dimension of the tarsus (3 mm), whereas 85.1% exceeded the 5 mm minimal
FTL criterion. Flat terrain running exceeded these criteria in 91.4% and 76.4%
of steps, respectively. FTL deviation did not differ in terms of means (rough
8.40±3.75 mm, mean ± s.d.; flat 8.80±5.83 mm;
t-test, P=0.13). Additionally, foot placement variance was
larger during rough terrain running (F test for equivariance,
P<0.0001), indicating less precise stepping during perturbed
conditions, counter to the FTL hypothesis of decreasing variation in
challenging environments.
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Interestingly, the direction of systematic deviation in foot placement
depended on which pair of legs was compared
(Fig. 9A). On the left side of
the body middle legs tended to fall to the left of front leg foothold with
hindlegs stepping progressively further left. A mirror image pattern was
observed for the right legs. These results indicate that more posterior legs
assume more sprawled footholds. This constant offset suggested that leg
placement may be coordinated as in walking stick insects
(Cruse, 1979;
Dean and Wendler, 1982;
Dean and Wendler, 1983).
Indeed, the variation in body-centered posterior foot placement is correlated
with anterior foot placement for all pairs of legs (regression F
tests, P<0.05), although the strength of this coordination is weak
(r2=between 0.05 and 0.55).
The cockroach could possibly accomplish this coordination through neural
feedback, as in the stick insect (Buschges,
2005; Cruse et al.,
2007), but mechanical coupling between the legs could also produce
significant correlation. In fact, simple geometry of the running animal
suggests that as the body yaw angles away from a leg pair or the body pitches
up, both foot placements in an anterior/posterior pair should move forward and
lateral in world coordinates centered about the COM. We can partially test for
a mechanical basis for the coordination observed by including yaw in the
coordination regression. In nearly all coordination comparisons, yaw accounts
for a significant portion of foot placement correlation (14 of 16 cases,
partial correlation and restriction F tests, P<0.05) and
in 8 of the 16 cases is sufficient to explain all of the coordination (partial
correlation of the posterior foot position to anterior position is no longer
significant, P>0.05). Further, coordination was generally weaker
and more completely explained by yaw mechanics during rough terrain running
than on flat terrain, rejecting more careful neural coordination operating
during perturbed running. Overall, while coordination itself does not
necessarily indicate that the system is adopting a neural or mechanical
feedback strategy, our results are consistent with simple mechanical
models.
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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). A mode is
a direction of recovery that can be as simple as a dynamic response in a
single degree of freedom, such as rolling to the left after a rightward
perturbation. They can also be more complex, involving coupled degrees of
freedom and energy production, absorption or exchange, such as a pitching
moment and vertical acceleration mode driven by increased stress in a muscle
in response to sudden loading. Modes that decay rapidly are more likely
influenced by mechanical feedback, whereas those that are slower or recover
with a significant gait change may require neural feedback
(Full et al., 2002).
Musculo-skeletal structures acting alone or in concert to enable these
recovery modes can be considered control modalities. Control modalities can
include a neural feedback strategy if muscle activation is altered in response
to a perturbation, or adopt a primarily mechanical feedback strategy if there
is no alteration in the rhythmic feedforward activation from a CPG.
Musculo-skeletal structure activation response to perturbations
A hypothesized mechanical control modality over rough terrain The hindleg
musculo-skeletal structures (femoral extensors, 178 and 179) of cockroaches
appear to be operating as a mechanical control modality during rapid running
over rough terrain with large unpredictable perturbations in surface height.
Data showed no significant difference in the distribution of the number of
MAPs, the interspike interval, burst phase or interburst period between flat
and rough terrain trials (Figs
4,
5,
6).
Locomotion over the rough terrain likely caused considerable variation in
the ground reaction force during the stance phase. Yet, the summed forces were
sufficient to produce stable running over the rough terrain with only a small
decrease in speed. While some steps resulted in secure footholds by the tarsi
similar to those used on flat terrain, many steps showed contact with the
blocks distributed along the leg. The resulting shift in contact point and
moment arms will alter the force output of a given activation pattern.
Contacting the block nearer the joint can increase force output resulting in
destabilizing pitch, yaw and roll of the body. This effect has been shown in a
physical model, a hexapedal robot (RHex) attempting to run over a pile of
bricks (Weingarten et al.,
2004). Rapid neural feedback to the dorsal/ventral pair of femoral
extensors altering their activation patterns has the potential to modulate
forces that enhance stability, but we found no changes in the neural code
during typical rough terrain traversal.
Generating stabilizing neural feedback in dorsal/ventral femoral extensors
during a step may be challenging at high speeds due to bandwidth limitations
and muscle properties. For speeds greater than 20 cm s–1,
stance and swing duration decrease to less than 40 ms
(Fig. 10). Sensory response
latencies measured in American cockroaches Periplaneta americana
range from 6 to 15 ms (Ridgel et al.,
2001; Wilson,
1966). Adding to this reflex delay is the 10 ms required for
dorsal/ventral femoral extensors to begin to generate force following
stimulation (Ahn et al., 2006).
Therefore, the fastest reflex response following a leg perturbation is not
likely to occur before 16–20 ms have lapsed, nearly one-half the stance
duration. This prediction is supported by Schaefer et al.
(Schaefer et al., 1994), who
report the latency between tactile leg stimulus and first leg movement in the
American cockroach at 17 ms. In situ measurements of these muscles
show that their twitch kinetics might further limit their effective changes of
force development (Ahn et al.,
2006; Full et al.,
1998). The time to peak isometric force for muscles 178 and 179
stimulated with 2–3 MAPs is 47 ms. The time to 50% relaxation in force
after the peak is 62–66 ms. Even though shortening deactivation will
decrease the duration of twitches
(Josephson and Stokes, 1989;
Rome and Swank, 1992), femoral
extensor kinetics do not allow peak force development and recovery to occur
within the duration of a half-cycle. As a result, when muscle 178 is cycled to
mimic rapid running, stimulation at the beginning of stance results in peak
force being attained at the end of stance
(Ahn et al., 2006). Work and
power are generated during extension in the stance phase, but an equal amount
of energy is absorbed during the swing phase as force declines.
|
;
Full et al., 1998). Muscle 178
does develop force and produce energy during extension in the stance phase,
but absorbs an equal amount of energy during the swing phase
(Ahn et al., 2006). Despite
being activated by the same motor neuron at the beginning of stance, muscle
179 generates no power during stance and only absorbs energy during the swing
phase (Full et al., 1998).
Perhaps, the dorsal/ventral pair of femoral extensors responds to
perturbations in both stance and swing by absorbing, storing and returning,
and transferring energy.
For example, legs frequently struck blocks on the rough terrain during the
swing phase. Perturbation studies of the isolated legs of B.
discoidalis give us insight into how these femoral extensors may be
contributing to mechanical feedback. Dudek and Full
(Dudek and Full, 2007) imposed
large, dorsal-ventrally directed impulsive perturbations to isolated hindlegs.
These sagittal plane perturbations were out of the plane of coxa–femur
joint rotation, so any response resulted from the passive properties of the
exoskeleton alone. Leg position attained its peak amplitude within 4–6
ms following an impulse. Position was recovered completely within 16–47
ms, depending on leg configuration. Feedforward activation of muscles 178 and
179 could set an effective stiffness that allows rapid rejection of
perturbations in the plane of joint rotation through mechanical feedback.
Our conclusion that hindleg musculo-skeletal structures 178 and 179 are functioning as a mechanical control modality for rough terrain running is not a result of an inability to detect changes in the neural motor code. Detectable changes in neural activation are produced when the cockroach encountered the even larger step perturbations at the beginning and end of the rough terrain track. MAP number increased when cockroaches ascended steps above 1.5 cm (Fig. 4B) and decreased when they descended from similar height blocks (Fig. 4C).
A hypothesized neural control modality for the largest perturbations – mis-steps
Mis-steps during rough terrain running occurred when one leg of the
cockroach failed to make contact with the surface throughout its stride,
completely eliminating the stance phase. This is equivalent to a duty factor
of zero. Stepping through a hole where no footfall occurs can offer further
insight into neuromechanical control of musculo-skeletal structures. Earlier
experiments on stick insects and cockroaches
(Blaesing and Cruse, 2004a;
Blaesing and Cruse, 2004b;
Duerr, 2001;
Tryba and Ritzmann, 2000a;
Tryba and Ritzmann, 2000b)
moving more slowly demonstrate a neural feedback strategy for negotiating
mis-steps that involves a foothold searching behavior, where the leg is
repeatedly retracted and protracted until surface contact is established. By
contrast, cockroaches running at rapid speeds did not exhibit this behavior,
but continued to swing the leg throughout retraction before resuming a normal
swing protraction (Fig. 7A).
The failure to make contact during its normal gait cycle resulted in the
largest perturbation. Rhythmic activation of Df persisted for one step,
despite the lack of stance initiation, suggesting a continuation of the
feedforward, clock-like signal (Fig.
7B). However, in the next step, neural feedback acted to delay
stance initiation (Fig. 7C).
During these very large perturbations, the dorsal/ventral femoral extensors
operated as a neural control modality that used sensory information, not to
adjust within a step, but to shift the phase of the CPG's clock-like signal in
the subsequent stride.
Running speed and perturbation size
The response of the dorsal/ventral femoral extensors likely depends on both
running speed and the magnitude of the perturbation. At the slowest 1/6 of the
cockroach's speed range (<10 cm s–1), the fast motor
neuron (Df) stimulating muscles 178 and 179 is not active
(Fig. 10). At these slow
speeds, particularly during exploratory walking behaviors, neural control
modalities seem to dominate locomotor control primarily through the `slow'
motor neuron (Ds) that innervates two other femoral extensors, muscles 177d
and 177e (Pearson and Iles,
1970; Pearson and Iles,
1971; Pipa and Cook,
1959; Watson and Ritzmann,
1998a; Watson and Ritzmann,
1998b; Watson et al.,
2002a). Load sensing (Noah et
al., 2004; Ridgel et al.,
2001; Zill et al.,
2004), proprioceptive hair plates
(Pearson et al., 1976) and
antennal/visual detection of obstacles
(Watson et al., 2002a) can all
alter these femoral extensors' activity patterns. Ds activity is correlated
with a graded increase in joint velocity when activated in isolation during
slow locomotion (Watson and Ritzmann,
1998a; Watson and Ritzmann,
1998b). Cutting the descending inputs to the thoracic ganglia of
cockroaches adversely affects walking including Ds firing
(Ridgel and Ritzmann, 2005).
However, thoracic circuits are still capable of generating locomotion.
As running speeds reach 1/3 maximal speed (10–20 cm
s–1) and dynamics become increasingly more important in
locomotor control, single Df spikes activate the dorsal/ventral femoral
extensors. Df also innervates femoral extensor muscles 177d and 177e, where it
acts on top of persisting Ds activity
(Levi and Camhi, 1996;
Pearson and Iles, 1970;
Pipa and Cook, 1959;
Watson and Ritzmann, 1998b).
At these speeds, Df activation in these femoral extensors is correlated with
the shortening of the transition from flexion to extension
(Watson and Ritzmann,
1998b).
At one-half maximal speed (0.30 cm s–1; the speed measured
in the present study), stance and swing duration approach their minimum values
(Fig. 10). In situ
measurements of the dorsal/ventral femoral extensors mimicking running show
that one muscle generates power in the stance phase, but both muscles show
significant energy absorption during the swing phase
(Ahn et al., 2006;
Full et al., 1998). At this
speed, the musculo-skeletal structures may assist in rejecting relatively
large perturbations resulting from changes in ground reaction forces or forces
imposed in the plane of joint motion when the leg collides with an obstacle.
Effective within step, rapid stabilization appears to result from a
visco-elastic, mechanical feedback response set by the feedforward activation
of these structures, since no changes in the activation pattern occurred (Figs
4,
5,
6). When perturbed outside this
already surprisingly large region of mechanical stability, neural feedback can
alter the activation levels or the timing of the feedforward motor pattern in
the next step (Fig. 7). This
nested approach to neuromechanical control relies on stride-to-stride neural
feedback to set the general activation `state' of the control modalities,
while rejecting moderate within-stride perturbations with rapid mechanical
feedback in these modalites that might include damping
(Dudek and Full, 2007), energy
exchange (Ahn et al., 2006;
Full et al., 2002), energy
storage and return (Dudek and Full,
2006), distributed contact
(Spagna et al., 2007) and/or
momentum trading (Holmes et al.,
2006; Kubow and Full,
1999; Seipel and Holmes,
2006).
From moderate speed to the cockroaches' maximal speed, the function of the
femoral extensors, or any muscle, is unknown. At these speeds, cycle period no
longer decreases (Fig. 10).
Speed instead increases by taking longer strides
(Full and Tu, 1990). This
transition may arise from functional constraints, but our hexapedal model
(Seipel et al., 2004) supports
a different view that relates to stability. The dynamic model shows that an
increase in stride frequency with speed provides stability at slower speeds,
but the resulting gaits become unstable or graze the stability boundary near
mid-speed where cockroaches attain their maximum stride frequency. When foot
touchdown positions are modified to approximate the increased stride lengths
measured at speeds greater than mid-speed, then the mechanical feedback
stability boundary moves further out and a reasonable dynamic stability margin
is obtained throughout the speed range. Increased Df activation to the femoral
extensors could enable this mechanical stability by increasing stride length.
Indeed, Df activity during escape response has been correlated with increased
coxa-trochanter-femur joint excursion in the American cockroach
(Levi and Camhi, 1996). Still,
unraveling the causal control potential of Df activation on task-level
dynamics, particularly in this speed range, will likely require direct
manipulation of the motor code.
System level response to perturbations
The system level response to rapid running over rough terrain perturbations
was consistent with the mechanical feedback response of the musculo-skeletal
structures. Despite large perturbations to the body
(Fig. 3), variations in ground
reaction forces and legs striking obstacles during swing, animals successfully
negotiated unpredictable terrain with less than a one-fifth reduction in
speed. Cockroaches retained the use of the alternating tripod gait on the
rough terrain with no significant changes in duty factor
(Table 1) or leg phase
(Table 2).
We found no evidence that cockroaches used a feedback dependent
follow-the-leader gait (Figs 8
and 9) that enforces precise
stepping through perception of limb placement to aid in negotiation of the
rough terrain (Song and Choi,
1989). Even under the broadest definition of a FTL gait, where
some minimal amount of information concerning effective footholds in the
surrounding environment is passed to posterior legs, only a small percentage
of steps satisfied the condition. This does indicate that such a gait is not
physically constrained by leg geometry at high speeds, but simply that it
occurred infrequently (Fig.
9).
Anterior-posterior pairs of legs did demonstrate coordinated variation in
tarsus placement, but much or all of this variation could be accounted for by
the animal's variation in yaw. While it is likely that the cockroach's body
pose can provide mechanical coupling to coordinate the legs, the neural or
mechanical basis of coordination cannot be fully resolved without separate
experiments similar to those revealing the intricate neural coordination of
walking sticks and other organisms (reviewed in
Buschges, 2005;
Cruse et al., 2007;
Pearson, 2004). Rather, we can
reject any of the FTL hypotheses that the animal is providing useful
coordination to reference effective foot placements by preceding legs.
A similar absence of FTL stepping and gait change was discovered when
cockroaches and spiders run over surfaces possessing a very low probability of
contact (Spagna et al., 2007).
Animals attained high running speeds on a simulated terrain made of wire mesh
with 90% of the surface contact area removed. These arthropods appear to
simplify control on low contact surfaces by rapid running that uses kinetic
energy to bridge gaps between footholds. Using dynamics for stability was
possible because these many-legged arthropods can take advantage of
distributed mechanical feedback, resulting from passive contacts along legs
positioned by CPG pre-programmed trajectories favorable to their attachment
mechanisms. Distributed mechanical feedback appeared to play the same role for
traversing rough terrain. Recovery from system level perturbations during
rapid running on challenging terrain is consistent with the use of mechanical
feedback for self-stabilization during controlled lateral perturbations in
cockroaches (Jindrich and Full,
2002) and dynamic models
(Kubow and Full, 1999;
Schmitt et al., 2002;
Schmitt and Holmes, 2000a;
Schmitt and Holmes, 2000b;
Seipel and Holmes, 2006;
Seipel et al., 2004).
We envision several important next steps if we are to understand how
musculo-skeletal structures contribute to system level locomotor stability at
high speeds. Characterization of the body's recovery using dynamical systems
approaches can provide directions along which recovery of system level
variables occurs (Full et al.,
2002). Groups of musculo-skeletal structures that act together to
stabilize the body along these particular directions (or modes) can be thought
of as a control modality. We contend that control modalities can be composed
of musculo-skeletal structures that provide mechanical and/or neural feedback.
As we identify control modalities, it will be advantageous if we can determine
the feedback strategy employed by the musculo-skeletal structures that
contribute to stability. Typically, only muscles that respond by neural
feedback are considered part of the controller, whereas passive or feedforward
responses are relegated to body mechanics (i.e. the plant). Yet mechanical
feedback acting to these musculo-skeletal structures can be integral to
stability. To gain a deeper understanding of both of the performance and
morphology enabling controlled behavior, the concept of control must include
musculo-skeletal structures that reject perturbations by mechanical
feedback.
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