Abstract
Our studies have
recently demonstrated that a proportional and derivative (PD) feedback
controller can effectively generate a control command that precedes body sway
by 0.1 to 0.2s. We also identified gain pairs that ensured a robust system with
a dynamic behaviour similar to the one observed in quiet standing experiments.
The purpose of the present study was to experimentally demonstrate that the PD
controller can facilitate stable quiet standing. The real-time control system
consisted of a center of mass (COM) position sensor, functional electrical
stimulation regulated by the PD controller and a subject who had difficulty
maintaining balance during quiet standing due to a neurological disorder called
von Hippel-Lindau disease. Our stability analysis using common COM and center
of pressure measures revealed that body sway could significantly be reduced
with the PD control effort. In consequence, it can be concluded that the
proposed feedback control system is capable of improving human balance during
quiet stance in subjects with certain neuromuscular disabilities. Additionally,
the observed effectiveness of the PD controlled feedback system supports our
findings that the CNS adopts a control strategy that relies highly on the body’s
velocity information.
1. INTRODUCTION
Open- and closed-loop applications of functional electrical stimulation
(
2. METHODS
2.1. Experimental Setup
The PD controlled
system received its input from a laser sensor (
The applied
stimulation pulses had a constant frequency (35Hz) as well as pulse width
(300μs), and were controlled by amplitude variation (mA). In order to
produce the torque as calculated by the controller, we determined the
amplitude-torque relationship of the subject in a preliminary experiment. The
complete real-time system was executed by a C++-based kernel (MS Visual C++
5.0), while a National Instruments data acquisition board (PCI-MIO-16E-4)
performed the necessary A/D and D/A conversions. The closed-loop time delay of
the feedback circuit was ensured to lie within the range of 80-135 ms that
corresponds to the physiological closed-loop time delay observed in able-bodied
subjects during quiet standing.
2.2. Control System
The PD controller
capable of compensating for the neurological delay times by producing a motor
command that precedes body sway by 100 to 200 ms has been shown to have a
relatively high velocity component [2]. In systematic simulations following
this conclusion, we determined PD gains that not only evoked the preceding
motor command, but also ensured a robust system with dynamic features observed
in able-bodied standing [3]. The real-time system
implementing this velocity accentuated controller regulated the level of
necessary ankle torque and consisted of the following main components:
·
Butterworth 3rd
order low-pass filter with 10 Hz cut-off frequency
·
PD controller with gains set to
Kp = 750 Nm∙rad-1and Kd = 350 Nm∙s∙rad-1 [3]
·
Limits for minimum (0 Nm)
and maximum torque (52 Nm)
The positive values of the controller output represented the torque that
was expected to be generated by the plantar flexors. By contrast, the negative
values represented the torque that the dorsiflexor muscles were meant to
produce. Since we only stimulated plantar flexors, only positive values of the
controller output were delivered while negative values had no effect.
2.3. Procedure
In order to determine whether the proposed system is capable of improving
balance during quiet standing, we compared the subject's performance for three
different treatments:
·
NTR: Trials without stimulation
·
CST: Trials with constant stimulation
·
CTR: Trials with controlled stimulation
For every treatment,
three trials of 120 seconds each were recorded. In each trial, the subject was
asked to stand still and maintain a balanced position with eyes open. The
signals of the COM and COP fluctuation were logged at a sampling frequency of 1
kHz, filtered (4th order Butterworth, 5 Hz cut-off frequency [4])
and analyzed using a one-way ANOVA (α = 0.10). In order to adequately
characterize the performance for each treatment, the COM and COP fluctuation
was analyzed by means of measures of postural steadiness as suggested by Prieto
et al. [4]: I) Distance measures
(MDIST: mean distance, RDIST: rms distance, RANGE); II) velocity measures
(MVELO: mean velocity, RVELO: rms velocity); and III) frequency measures
(CFREQ: centroidal frequency). Furthermore, the results were related to
respective values of able-bodied subjects performing quiet standing (not
shown).
2.4. Subject
The proposed system
was tested with a male subject that has difficulty keeping balance during quiet standing due to a neurological disorder called von
Hippel-Lindau disease (VHL). The subject was 36 years of age, had height 173
cm, mass 59 kg, and experienced VHL from birth on. VHL is a rare genetic
multi-system disorder characterized by the abnormal growth of tumors in certain
parts of the body including the nervous system. The subject of our study had
balance problems and impaired gait due to partial loss of sensation and
proprioception. Furthermore, he experienced dizziness and muscle weakness in
the legs.
3. RESULTS
Figure 1 shows the subject’s
COM fluctuation for three trials, each representing a different treatment.
Already evident by a simple visual inspection, the body sway in CTR had a
smaller magnitude than it did in NTR (dashed lines: ±1 SD). Note that the constant
stimulation used in CST (33.0 mA) was of the same order as the average
stimulation current provided by the control system in CTR (33.9 mA).
Figure 1: COM
fluctuation without stimulation (NTR), with constant stimulation (CST), and
with controlled stimulation (CTR).
The marked portion of the controlled treatment in Figure 1 (black
rectangle) is also shown in Figure 2a. Here, the COM fluctuation is related to
the controller output and to the fluctuation of the resulting stimulation
current (Fig. 2b). It can be seen that the control effort stabilized the system
and that the fluctuation of the control and stimulation signals preceded the
fluctuation of the COM. The maximum stimulation current of the complete trial
was 36 mA, generating approximately 21 Nm per ankle.
Figure 2: Excerpt from the COM fluctuation
for CTR (a) and resulting stimulation current (b).
Table 1 summarizes the results
of the COM and COP analysis. The trials using a controlled level of stimulation
had the smallest average value (bold font) for all COM measures except for the
frequency at which the spectral mass is centered (CFREQ). The COP analysis on
the other hand revealed that the distance measures were smallest for CTR
whereas the velocity and frequency measures were smallest for NTR and largest
for CTR. The differences in treatment were significant
for eight measures (*).
Table 1:
Average stability results for each treatment
|
|
COM |
NTR |
CST |
CTR |
|
I |
MDISTAP
* |
0.852
cm |
1.101
cm |
0.690 cm |
|
RDISTAP
* |
1.112
cm |
1.321
cm |
0.898 cm |
|
|
RANGEAP |
6.642
cm |
6.795
cm |
5.575 cm |
|
|
II |
MVELOAP
* |
0.938
cm/s |
0.881
cm/s |
0.776 cm/s |
|
RVELOAP
* |
1.240
cm/s |
1.132
cm/s |
1.020 cm/s |
|
|
III |
CFREQAP
* |
0.312
Hz |
0.298 Hz |
0.345
Hz |
|
|
COP |
NTR |
CST |
CTR |
|
I |
MDISTAP
* |
1.093
cm |
1.188
cm |
0.856 cm |
|
RDISTAP
* |
1.405
cm |
1.486
cm |
1.102 cm |
|
|
RANGEAP |
9.820
cm |
8.854
cm |
7.673 cm |
|
|
II |
MVELOAP
|
2.611 cm/s |
2.705
cm/s |
2.778
cm/s |
|
RVELOAP
|
3.546 cm/s |
3.589
cm/s |
3.774
cm/s |
|
|
III |
CFREQAP
* |
0.562 Hz |
0.615
Hz |
0.721
Hz |
4. DISCUSSION AND CONCLUSIONS
Due to the fact
that all COM time domain measures are smallest for CTR, body sway has evidently
been reduced during this treatment. The stated difference between the COP
distance and velocity measures can be explained by their meaning during quiet
standing: Distance measures have been related to the effectiveness of, or the
stability achieved by, the postural control system; and velocity measures have
been related to the amount of regulatory activity associated with this level of
stability [4]. Hence, it can be concluded that during CTR the postural control
system is achieving a higher level of stability (lower distance measures) by
applying a higher level of regulatory activity (higher velocity measures).
The question of
whether a feedback system can control unsupported standing was also addressed
by Gollee et al. They established and
evaluated a feedback system regulated by a torque controller [1]. The inner
loop provided feedback control of muscle moment, while the outer loop
controlled the angl
The findings presented
herein strongly suggest that human balance can be improved by means of a PD
controlled feedback system that successfully mimics the physiological control
task of an intact CNS. Furthermore, the system’s effectiveness verifies our
hypothesis that the CNS adopts a control strategy that relies highly on the
velocity information [2]. Future research will test the control system with a
larger group of subjects and will also consider the
less dominant negative torque by including a stimulation branch for
dorsiflexors.
References
[1] Gollee H, Hunt KJ, and Wood DE.
New results in feedback control of unsupported standing in paraplegia. IEEE Trans Neural Sys Rehab Eng, 12:
73-80, 2004.
[2] Masani K, Popovic MR, Nakazawa K, et al. Importance of body sway velocity
information in controlling ankle extensor activities during quiet stance. J Neurophysiol, 90: 3774-3782, 2003.
[3] Masani K, Vette AH, Popovic MR. Controlling
balance during quiet standing: Proportional and derivative controller generates
preceding motor command to body sway position. Gait and Posture, in press.
[4] Prieto TE, Myklebust JB, and Hoffmann RG, et al. Measures of postural steadiness: Differences between healthy
young and elderly adults. IEEE Trans
Biomed Eng, 43: 956-966, 1996.
Acknowledgements
Canadian Fund for Innovation;