This paper studies the possible benefit that can be obtained by introducing variability into the robotic control of trajectories used to train hindlimb locomotion in adult spinal mice. The spinal cords of adult female Swiss-Webster mice were completely transected at a mid-thoracic level. Fourteen days post-transection, the spinal mice were robotically trained to step in the presence of a 5-HT agonist, quipazine, for a period of six weeks. In this pilot study nine animals were divided into three groups, each receiving a different control strategy: a fixed training trajectory (Group A), a variable training trajectory without interlimb coordination imposed (Group B) and a variable training trajectory with hindlimb bilateral coordination imposed (Group C). Preliminary results indicate that Group A recovers more slowly than the two groups receiving variable modes of robotic training. Groups B and C show higher levels of recovery than Group A in terms of the number of steps performed during testing sessions, as well as in their step periodicity and shape consistency. Group C displays a higher incidence of alternating stepping than Group B. These results indicate that variable trajectory robotic training paradigms may be more effective than fixed trajectory paradigms in promoting robust post-injury stepping behavior. Furthermore, it appears that the inclusion of interlimb coordination is an important contribution to successful training

Burdick, J. W.

Cai, L. L.

Cham, J. G.

Edgerton, V. R.

Fong, A. J.

Liang, Y. Q.

Otoshi, C. K.

Roy, R. R.

Zhong, H.

Caltech Authors - Main

EFFECTS OF CONSISTENCY VS. VARIABILITY IN 
ROBOTICALLY CONTROLLED TRAINING OF STEPPING IN 
ADULT SPINAL MICE 
L.L. Cai1; A.J. Fong1; C.K. Otoshi3; Y.Q. Liang2; J.G. Cham2; H. Zhong4; R.R. Roy5; V.R. Edgerton3,4,5; J.W. 
Burdick1,2;
1. Bioengineering, 2. Mechanical Engineering, California Institute of Technology, Pasadena, CA, USA 
3. Neurobiology, 4. Physiological Science, 5. Brain Research Institute, UCLA, Los Angeles, CA, USA 
ABSTRACT 
This paper studies the possible benefit that can be obtained 
by introducing variability into the robotic control of 
trajectories used to train hindlimb locomotion in adult 
spinal mice. The spinal cords of adult female Swiss-
Webster mice were completely transected at a mid-thoracic 
level. Fourteen days post-transection, the spinal mice were 
robotically trained to step in the presence of a 5-HT agonist, 
quipazine, for a period of six weeks. In this pilot study nine 
animals were divided into three groups, each receiving a 
different control strategy: a fixed training trajectory (Group 
A), a variable training trajectory without interlimb 
coordination imposed (Group B) and a variable training 
trajectory with hindlimb bilateral coordination imposed 
(Group C).  Preliminary results indicate that Group A 
recovers more slowly than the two groups receiving 
variable modes of robotic training. Groups B and C show 
higher levels of recovery than Group A in terms of the 
number of steps performed during testing sessions, as well 
as in their step periodicity and shape consistency. Group C 
displays a higher incidence of alternating stepping than 
Group B. These results indicate that variable trajectory 
robotic training paradigms may be more effective than fixed 
trajectory paradigms in promoting robust post-injury 
stepping behavior. Furthermore, it appears that the 
inclusion of interlimb coordination is an important 
contribution to successful training. 
INTRODUCTION 
Robotic-facilitated rehabilitative training paradigms have 
recently become more common.  Commercially available 
robotic orthotics such as the Lokomat ™ are already 
available to facilitate the rehabilitative training of spinal 
cord injuried (SCI) and stroke patients with promising 
results [1]. However, little is known about the mechanisms 
of how locomotor recovery is achieved with this type of 
rehabilitative training.  Additionally the best training 
procedure has yet to be established. 
To shed light on these issues, we have developed a robotic 
training device (Fig. 1) to study locomotor recovery after 
SCI in mice.  A mouse model is attractive due to the many 
strands of transgenic mice available.  In our previous 
experiments, we have demonstrated that fixed trajectory 
robotic training and serotonergic treatment each have 
significant independent and synergistic positive effects in 
enhancing motor performance of adult spinalized mice [2].  
Furthermore, these improvements were retained even when 
both training and drug treatment were suspended, 
suggesting that a type of learning phenomenon had 
occurred [2]. In this paper, we propose the hypothesis that 
the post SCI, spinal cord will be better able to relearn to 
step if it is constantly challenged during locomotor training 
by introducing forms of variability in the training pattern. 
The present pilot study compared the efficacy of two 
variable trajectory robotic training paradigms versus fixed 
trajectory robotic training on recovering locomotor ability 
in completely spinalized adult mice that were administered 
quipazine.  The results of the study demonstrate that 
animals given variable robotic training exhibited faster and 
more pronounced recovery than those given fixed robotic 
training.  These findings suggest that an optimal 
rehabilitation strategy can be obtained by combining an 
“assist as needed” training paradigm and pharmacological 
intervention.   
METHODS
Animals: Adult Swiss-Webster mice (mean body weight of 
21.5±1.1 g at the time of surgery) obtained from Charles 
River Laboratories (Wilmington, MA) were used. A 
complete mid thoracic spinal transection was performed at 
45 days of age. 
Quipazine Administration:  A serotonergic agonist – 
quipazine (0.5 µ g/g body weight, i.p.) was administered to 
all subjects 5 min prior to the training or testing session [3]. 
Robotic Step-Training and Measurement System:  A four 
axis robotic system was developed for position data 
collection and as an active training apparatus.  The robotic 
system consists of four major components: 1) a pair of 
robotic manipulators to guide ankle motion; 2) motion 
control hardware; 3) a treadmill; and 4) a body weight-
support device.  The main components of the mouse stepper 
are the robotic manipulators.  Each robotic manipulator is 
comprised of a leg guidance linkage (Fig. 2), a pair of 
motors that drive the linkage (2342-006CR; Micromo 
Electronics, Clearwater, FL), and a pair of optical encoders 
that record the rotational position of the motors (Agilent 
HEDM-5500; Micromo Electronics).  Ankle position is 
derived from these encoders and the linkage 
Proceedings of the 2005 IEEE
9th International Conference on Rehabilitation Robotics
June 28 - July 1, 2005, Chicago, IL, USA
0-7803-9003-2/05/$20.00 ©2005 IEEE
FrB01-05
575
Figure 1: Schematic of Current Step Training System 
geometry.  The five bar limb guidance linkage allows 
optimal motion sensing and control in a 3.5 x 3.5 cm 
workspace, which is sufficient to accommodate all step 
trajectories associated with mouse locomotion.  In addition, 
due to the geometry of the linkage, the dynamic of the two 
axes are uncoupled and approximately linear in the range of 
motions encountered during training and evaluation. 
The mice are placed into the mouse stepper using a cone-
shaped cloth harness. Once the mouse has entered the 
harness, it is secured using a binder clip, which is then 
magnetically attached to the weight-support system. 
Figure 2: Schematics of the five-bar, parallelogram-
type linkage used.  The dimension and weight of each 
link is noted.  The drawing is done at actual scale.  
Important features labeled: A) ankle attachment point; 
B) motor attachment point driving linkage 4; C) motor 
attachment point driving linkage 1. 
Fixed Trajectory Robotic Training:  In fixed robotic 
training, the robotic arms are controlled using a PID 
controller to perform a continuous trajectory tracking of a 
pre-determined pattern.  When attach to the mice, the 
robotic arms actively move the ankle points of the limbs in 
this fixed trajectory.  The imposed x and y trajectory of 
each hindlimb was obtained from a neonatally transected 
mouse that stepped well.  This pattern was recorded from 
the neonatal mouse when it was approximately the same 
age as the adult mice used in this study.  Neonatally 
transected mice can spontaneously recover functional 
stepping without pharmacological or mechanical assistance 
(unpublished observations).  The spinal mice were trained 
for 10 min. a day, 5 days per week.  
Robotic Training with Variability I (Band) Algorithm:  The 
animals in this group received a variable training paradigm 
that provided an “assist as needed” training strategy. This 
training paradigm uses velocity fields to control the 
movement of the robotic linkages.  That is, the velocity of 
the robot’s distal tip is commanded to a specific speed.  
This strategy implements two fixed boundaries: an inner 
bound and an outer bound, forming a “band” surrounding 
the desired trajectory.  Within the band, the robot follows a 
small velocity field tangent to the desired trajectory.  I.e., it 
nudges the leg along the trajectory, but does not enforce 
specific timing of leg movement.  The regions inside 
(outside) the band are filled with an outward spiraling 
(inward-spiraling) converging velocity field. When the 
ankle point of the hindlimb leaves the band, the convergent 
velocity fields will rapidly move it back into the band 
region (Fig. 3).  However, the paradigm does not impose 
interlimb constraint.  In essence the robotic device only 
actively manipulates the hindlimbs when their position 
deviates from the nominal trajectory beyond the 
predetermined boundaries.  Inside the band, the animal 
largely dictates its own motions, with a small forward bias 
provided by the robot.   The animals were trained for 10 
min. each day, 5 days a week. 
Figure 3: Variability training paradigm I (Band).  The 
desired training trajectory is shown in thick blue.  The 
dotted thin red lines represent the boundaries.  The blue 
arrows correspond to the convergent velocity fields. 
Robotic Training with Variability II (Window) Algorithm:
The third group received a variable training paradigm 
analogous to the second group, but based on a “window” 
variable training paradigm.  In this approach, a circular 
“window” moves along the desired trajectory. (Fig. 4)  
Within the window, a small velocity field tangent to the 
desired trajectory biases the robot’s motion, but doesn’t 
enforce specific timing inside window.  Outside the 
576
boundary, the robotic movement is guided by a radial force 
field that points inward with a magnitude proportional to 
the distance from the circle center. Hence, when the 
animal’s ankle deviates from the window, it is quickly 
returned to the window.  Within the window, the ankle is 
gently guided in the direction of the trajectory, thus 
providing loose timing control.  The same strategy was used 
on both hindlimbs and was timed to provide alternating 
phasing.  The animals were trained for 10 min each day, 5 
days a week. 
Figure 4: Variability training paradigm II (Window).  
The desired training trajectory is in blue and the 
moving window is highlighted in red.  The blue arrows 
correspond to the radial force fields. 
Experimental Design: Nine mice were randomly divided 
into three groups.  All three groups received a form of 
robotic training with quipazine for six weeks.  The first 
group was the control in this experiment and was trained 
with the fixed robotic training algorithm.  The two 
experimental groups were each trained with a form of 
variable training.  The second group received the “Band” 
variable training, while the third group received the 
“window” variable training for six weeks.
Data Acquisition and Formatting:  Three modes of data 
were collected for each test session.  First, using in-house 
acquisition programs written in the LabVIEWTM
development environment, we recorded position data for 
both ankles at 400 Hz.  Second, we maintained a log of all 
qualitative observations in a database.  Third, beginning 
with the third test session, we captured video footage of 
both the left and right sides of each mouse as it stepped on 
the treadmill.   
Data Analysis:  We used Fast Fourier Transform (FFT) 
analysis to quantify step periodicity.  Mice that stepped 
rhythmically exhibited a sharp and distinct fundamental 
peak in the FFT of their ankle trajectories.  The location of 
the predominant peak along the x-axis corresponds to the 
most common stepping frequency.  Conversely, mice with 
poor periodicity exhibited either a very broad fundamental 
peak in the FFT spectrum or, in extreme cases, failed to 
demonstrate a fundamental peak.  To quantify these 
observations, we measured the full width at half maximum 
(FWHM) of the fundamental peak.  A low measurement of 
FWHM corresponds to temporally consistent, rhythmic 
stepping, whereas high measurements typically indicate 
erratic stepping consistent with stumbling and foot 
dragging.   
In addition to the temporal information provided by FFT 
analysis, we also sought to study any changes in spatial 
stepping consistency throughout the study.  We suggest that 
locomotor improvement can be characterized by more 
consistent repetition of a nominal trajectory.  Principle 
components analysis (PCA) is a multivariate analysis 
technique that 1) picks out patterns (relationships) in the 
variables of a data set; and 2) reduces the dimensionality of 
the data set without significant loss of information  [4].  
Using PCA, we can calculate the percentage of the total 
variance in the data set that is captured by the first principal 
component.  Hence, a high PCA score corresponds to a 
subject that consistently executes the same stepping 
trajectory.
RESULTS 
The average total number of steps performed in a best 15 
second interval by the animals in each group is shown in 
figure 5.  The “window” and “band” groups performed 
more steps than the fixed group.  However, there does not 
seem to be any statistical difference between the two 
variable groups. 
Figure 5: Number of steps performed in 15 sec. 
interval.  Through out the experiment, both variable 
training groups perform better compare to the fixed 
group. 
In figure 6, the inverse of FWHM is plotted to emphasize 
the improvement in step rhythm throughout the study.  The 
“window” and “band” variable training groups consistently 
stepped more rhythmically than the fixed training group. 
Although the two variable groups could not be statistically 
distinguished, the “window” group seemed to recover 
faster.  A 0 score was assigned to all mice that could not 
step on test day 0. 
Test Day
0 1 2 3 4 5 6 7
N
um
be
r o
f S
te
ps
0
2
4
6
8
10
12
14
16
18
Fixed
Band
Window
577
PCA percentage is plotted in figure 7. Although the 
“window” training group appeared to recover faster, there 
was no indication of a difference between the step shape 
consistencies of the three groups. This may be due to the 
small n used. Alternatively, this supports previous findings 
that quipazine, rather than the specific training pattern, is 
primarily responsible for shape consistency [2]. A PCA 
percentage of 45% assigned to for all mice that could not 
step on test day 0. 
Figure 6: The inverse of FWHM is plotted to 
emphasize the locomotor improvement over time.  Both 
variable training groups performed better than the fixed 
training through out the experiment. 
DISCUSSION 
A key objective of this study was to ascertain whether 
providing variability in training enhances stepping 
recovery.  A significant concern is that fixed trajectory 
training strategies may drive the spinal cord into a state of 
“learned helplessness,” [5, 6] whereby the spinal cord, not 
challenged to explore potential stepping patterns on its own, 
will defer to the trainer and give up on learning.  No 
statistically significant differences were observed between 
the variable “band” and “window” training groups.  This 
may be due to the small n used. Nevertheless, both variable 
training paradigms appears to be a more effective 
rehabilitative strategy then the fixed training paradigm. 
Nevertheless, interlimb coordination must be controlled in 
order to maximize locomotor recovery [7]. We found that 
similar is true for adult spinal mice. Although mice trained 
with the “band” pattern recovered greatly in their stepping 
performance, their steps were typically arrhythmic and 
frequently interrupted by dragging.  In contrast, bouts of 
stepping executed by the “fixed” and “window” training 
groups were rhythmic and prolonged.  This is clearly 
demonstrated by the FFT data, which show that stepping in 
the latter two groups converged to a frequency near 1Hz as 
the study progressed, a result consistent with constant speed 
treadmill locomotion at 3cm/sec. 
Principal components analysis did not elucidate a difference 
in the shape consistency of the three groups.  By week 3, 
the average PCA score of all three groups was greater than 
80%, indicating that all of the mice could step rhythmically.  
This result supports our previous conclusion that quipazine 
rather than step training has the larger influence on step 
shape consistency [2].  
Figure 7: The PCA percentage score of each training 
gropu is plotted.  There were no statistically significant 
differences between the three groups after the third 
week of training. 
Sensory information is critical to motor learning [8, 9].  The 
pattern and timing of assistance provided during step 
training dictates the extent to which the injured spinal cord 
can recover motor function.  We have shown that failure to 
enforce contralateral phasing of the legs during training 
limits stepping recovery compared to mice trained with an 
alternating gait [2].  It is likely that the spinal cord is 
similarly highly sensitive to other proprioceptive cues.  As 
demonstrated here, poorly conceived or poorly 
implemented training algorithms may actually inhibit 
stepping recovery. 
This emphasizes a fundamental advantage of using robotic 
devices that can consistently and accurately apply defined 
locomotor training paradigms while simultaneously 
maintaining a thorough quantitative record of both training 
and performance parameters.  Used with data optimization 
schemes, quantitative data are teaching us which parameters 
to focus on when devising novel training strategies.  By 
developing our understanding of how sensory inputs affect 
spinal learning, we can “tune the spinal cord to learn.” 
ACKNOWLEDGEMENT 
This work is supported by the Christopher Reeve Paralysis 
Foundation (#VEC 2002-2) and the National Institutes of 
Health (1 R01 HD044830-01). 
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[1] S. Hesse, H. Schmidt, C. Werner, and A. Bardeleben, "Upper and 
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Test Day
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Effects of consistency vs. variability in robotically controlled training of stepping in adult spinal mice

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Effects of consistency vs. variability in robotically controlled training of stepping in adult spinal mice

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