U.S. patent application number 09/949411 was filed with the patent office on 2002-10-24 for quantification of muscle tone.
Invention is credited to de Lateur, Barbara J., Goldberg, Randal P., Kanderian, Sami S., Lenz, Fred A., Obell, Katrina Rieflin, Whitcomb, Louis L..
Application Number | 20020156399 09/949411 |
Document ID | / |
Family ID | 22864735 |
Filed Date | 2002-10-24 |
United States Patent
Application |
20020156399 |
Kind Code |
A1 |
Kanderian, Sami S. ; et
al. |
October 24, 2002 |
Quantification of muscle tone
Abstract
A method and device for the quantification of muscle tone,
particularly the wrist, wherein non-sinusoidal and non ramp
trajectories are used to drive the wrist. Equation 1 is utilized
determine the stiffness, viscosity and inertial parameters.
.tau..sub.s(t)=K.sub.H.theta.(t)+B.sub.H.theta.(t)+J.sub.T.theta.(t)+.tau.-
.sub.off [Eq. 1] wherein where .tau..sub.s is the total torque,
.tau..sub.off is the offset torque, K.sub.H and B.sub.H are the
angular stiffness and viscosity of the combined flexor and extensor
muscle groups that act on the joint, J.sub.T is the combined
inertia of the oscillating appendage, .theta. is the angular
displacement of the system, and 1 0 . and 0 are the velocity and
acceleration. In accordance with the method, the trajectory
.theta.(t) is controlled, the torque response .tau.(t) is measured
and the stiffness, viscosity, and inertial parameters are
determined using Equation 1. The method and device are particularly
suitable for use on patients with spacisityf
Inventors: |
Kanderian, Sami S.;
(Northbridge, CA) ; Goldberg, Randal P.; (Mountain
View, CA) ; Obell, Katrina Rieflin; (Ann Arbor,
MI) ; de Lateur, Barbara J.; (Baltimore, MD) ;
Whitcomb, Louis L.; (Baltimore, MD) ; Lenz, Fred
A.; (Baltimore, MD) |
Correspondence
Address: |
Edwards & Angell, LLP
P.O. Box 9169
Boston
MA
02209
US
|
Family ID: |
22864735 |
Appl. No.: |
09/949411 |
Filed: |
September 6, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60230314 |
Sep 6, 2000 |
|
|
|
Current U.S.
Class: |
600/587 |
Current CPC
Class: |
A61B 5/6824 20130101;
A61B 5/4528 20130101; A61B 5/224 20130101; A61B 5/389 20210101 |
Class at
Publication: |
600/587 |
International
Class: |
A61B 005/103; A61B
005/117 |
Claims
What is claimed is:
1. A method for quantifying muscle tone patient comprising the
steps of: moving the patient's wrist in a non-sinusoidal and non
ramp trajectory and determining the stiffness, viscosity and
inertial parameters using the following relationship 51 s ( t ) = K
H ( t ) + B H . ( t ) + J T ( t ) + off where .tau..sub.s is the
total torque, .tau..sub.off is the offset torque, K.sub.H and
B.sub.H are the angular stiffness and viscosity of the combined
flexor and extensor muscle groups that act on the joint, J.sub.T is
the combined inertia of the oscillating appendage, .theta. is the
angular displacement of the system, and 52 . and are the velocity
and acceleration.
2. A method of quantifying muscle tone in a patient comprising the
steps of: driving the patient's wrist is in arbitrary trajectory
that is neither sinusoidal nor ramp; controlling the trajectory
.theta.(t); measuring the torque response .tau.(t); and determining
the stiffness K.sub.H, viscosity B.sub.H, and inertial J.sub.T
parameters using the relationship 53 s ( t ) = K H ( t ) + B H . (
t ) + J T . ( t ) + off wherein where .tau..sub.s is the total
torque, .tau..sub.off is the offset torque, K.sub.H and B.sub.H are
the angular stiffness and viscosity of the combined flexor and
extensor muscle groups that act on the joint, J.sub.T is the
combined inertia of the oscillating appendage, .theta. is the
angular displacement of the system, and 54 . and are the velocity
and acceleration.
3. A device for quantifying muscle tone in a comprising: an
electromechanical system that drives the wrist of a patient with an
arbitrary trajectory that is neither sinusoidal nor ramp, wherein
the system includes: a housing having a top surface; a hand support
on the top surface of the housing for holding the hand in a desired
position; an arm support on the top surface of the housing for
holding the arm in a desired position relative to the hand; a motor
coupled to the hand support such that the motor moves back and
fourth tracking the desired trajectory and wherein the motor causes
the hand to move in the desired trajectory; and an automated
feedback controller for varying the torque, speed and direction of
the motor.
4. The device of claim 3, wherein a discrete set of finite data
points defining the trajectory is input into the controller, and
wherein the motor tracks these data points.
5. The device of claim 3, wherein the hand securing mechanism
comprises at least a pair of vertical bars extending upwards from
the top surface of the housing and being spaced apart so the hand
can be placed between the pair of vertical bars.
6. The device of claim 5, wherein the vertical bars have padding or
a cushion on their outer surface.
7. The device of claim 6, wherein the padding or cushion is
removable and varies in thickness for adapting the device to
various sized hands.
8. The device of claim 6, wherein the padding or cushion is
compressible and expandable to accommodate hands of varying
sizes.
9. The device of claim 5, wherein the vertical bars are slidably
attached to the housing so that the vertical bars are movable
towards each other and away from each other and locked into a
desired position for accommodating varying sized hands.
10. The device of claim 3, further comprising an arm securing
mechanism to secure the arm in place.
11. The device of claim 3 further comprising an optical encoder for
converting motion of the device and wrist into a series of digital
pulses.
12. The device of claim 3 further comprising an amplifier for
amplifying the command voltage from the controller into either a
voltage or a current to the motor.
Description
[0001] The present application claims the benefit of U.S.
provisional application No. 60/230,314, filed on Sep. 6, 2000,
incorporated herein by reference.
FIELD OF THE INVENTION
[0002] The present invention relates to a method and apparatus for
the quantification of muscle tone. More particularly, the present
invention relates to a method and device that utilize
non-sinusoidal perturbations to quantify muscle tone. The device
is, and method are particularly useful in quantifying muscle tone
in a spastic patient.
BACKGROUND OF THE INVENTION
[0003] Individual skeletal muscle cells are mechanically and
anatomically arranged in parallel. The total force produced by a
muscle is equal to the sum of the forces generated by its
constituent cells. In the normal subject, muscles that comprise the
wrist flexors and extensors are normally relaxed and are usually
recruited to generate force and movement.
[0004] Lower motor neuron paralysis occurs when muscles are
deprived of their immediate nerve supply from the spinal cord. This
occurs when a nerve between the spinal cord and a muscle is cut or
when cell bodies of the ventral horn are destroyed as in
poliomyelitis. Muscles become soft and atrophic, and reflex
response to sensory stimuli is lost. Most nerve disorders that
affect limb function are due to upper motor neuron paralysis,
wherein damage is present somewhere in the corticospinal tract that
originates in the brain and travels through the spinal cord.
[0005] Spasticity is defined as abnormal involuntary contraction of
a muscle or group of muscles due to a rate-dependent reflex
mechanism. The spindle elicits the reflex response upon
deformation. To a certain extent, these reflexes are normal and
important. In normal operation, these reflexes are suppressed to a
certain extent to allow flexibility and motion of joints. In
spasticity however, there is a disruption in the normal behavior of
the stretch reflex that causes muscles, particularly the flexors,
to be extremely resistive to passive stretch (i.e. high in tone).
As a result, motor control is severely impaired and stiffness or
tightness of the muscles may interfere with gait, movement, and
speech. Spasticity is usually found in people with some sort of
upper motor neuron paralysis, such as those with cerebral palsy,
traumatic brain injury, spinal cord injury and stroke patients.
[0006] Common symptoms of spasticity may include hypertonicity
(increased muscle tone), clonus (a series of rapid muscle
contractions), exaggerated deep tendon reflexes, muscle spasms,
scissoring (involuntary crossing of the legs) and fixed joints. The
degree of spasticity varies from mild muscle stiffness to severe,
painful, and uncontrollable muscle spasms. The condition can
interfere with rehabilitation in patients with certain disorders,
and often interferes with daily activities.
[0007] Many forms of intervention are available to reduce muscle
tone in spasticity. Biochemical pharmaceuticals such as Botox
(Botulinum Toxin Type A), Intrethecal Baclofen, and Zanaflex
(tizanidine) may be used as a biochemical form of intervention.
(See R. W. Armstrong, P. Steinbok, D. D. Cochrane, et al.
Intrathecally administered baclofen for treatment of children with
spasticity of cerebral origin. J Neurosurg; 87(3):409-414, Sep
1997; J. V. Basmajian, K. Shankardass, D. Russel: Ketazolam Once
Daily for Spasticity: Double-Blind Cross-Over Study. Arch. Phys.
Med. Rehabil. Vol. 67, pp556-557, 1986; P. J. Delwaide:
Electrophysiological Analysis of the Mode of Action of Muscle
Relaxants in Spasticity. Annals of Neurology, Vol. 17, No. 1,
January 1985, pp 90-950). These chemicals are used either to
destroy nerve endings at the neuromuscular junction, or they are
used as blocking agents which depress neuromuscular transmission by
competing with acetylcholine for receptors, thus suppressing nerve
conduction. In severe cases, microsurgery is also an option, where
incisions are made in the brainstem or anywhere in the stretch
reflex pathway. The safest form of intervention is physical
therapy, such as training, stretching exercises and casting. (J. C.
Otis, L. Root, M. A. Kroll: Measurement of Plantar Flexor
Spasticity During Treatment with Tone-Reducing Casts. Journal of
Pediatric Orthopedics 5:682-686, 1985).
[0008] Tone is defined as the degree of resistance to stretch from
an external source. An assessment of tone is important in
evaluating the degree of spasticity that a patient has. This
assessment is imperative for the clinician to decide what form of
intervention to take and to what degree. Further, continued
assessment throughout intervention is important to assess the
effectiveness of the intervention. For example, if the Botox dosage
administered is too low, it may have little or no effect in
reducing a patient's spasticity. Conversely, if the dosage is too
high, then the patient may lose the ability to control his or her
limb, as blocking too many neuromuscular junctions at the muscle
site may prevent the central nervous system from having any control
over the muscle. An assessment of tone before and after
intervention is also important as it can demonstrate the
effectiveness of the treatment.
[0009] Probably the most widely accepted clinical test for the
evaluation of tone in spasticity is the Ashworth scale shown below
in Table 1.
1TABLE 1 Grade Description 0 No increase in muscle tone. 1 Slight
increase in muscle tone, manifested by a catch and release or by
minimal resistance at the end of the range of motion when the
affected part(s) is(are) moved in flexion or extension. 2 Slight
increase in muscle tone, manifested by a catch fol- lowed by
minimal resistance through the remainder of the range of motion but
the affected part(s) is(are) easily moved. 3 More marked increase
in muscle tone through most of the range of movement, but affected
part(s) easily moved. 4 Considerable increase in muscle tone,
passive movement difficult. 5 Affected part(s) is(are) rigid in
flexion or extension. TABLE 1: Modified Ashworth scale. The
Ashworth scale is a popular, and widely accepted method of
evaluating muscle tone among clinicians. Though the grades are
numeric, they are based on a qualitative "feel" of resistance to
passive stretch movements performed by the clinician on the
patient. (Taken from Arch. Phys. Med. Rehabili. Vol 80, September
1999).
[0010] The clinician moves the subject's limbs about the joints and
then assigns a grade based on a "touchy feely" assessment of how
much resistance the clinician feels. One can easily see the problem
here. Since the test is a qualitative one, different clinicians may
assign different grades to the same test. Even the same clinician's
evaluation may change due to lack of consistency or depending on
whether he or she is optimistic or pessimistic at the time of the
test. The clinician may also be biased and may, for example, assign
a better grade if he or she has knowledge of interventions being
performed on the patient. Even putting all these issues aside, it
is difficult to get an absolute measure of tone using the Ashworth
scale. As stated in a review article "The quantification of
spasticity has been a difficult and challenging problem, and has
been based primarily on highly observer-dependent measurements. The
lack of effective measurement techniques has been restrictive,
since quantification is necessary to evaluate various modes of
treatment." (R. T. Katz, W. Rymer: Spastic hypertonia; mechanisms
and measurement. Archives of Physical Medicine and Rehabilitation.
1989; 70:144-145).
[0011] In attempt to quantify muscle tone, some have used
Electromyography (EMG) information. (See P. J. Delwaide:
Electrophysiological Analysis of the Mode of Action of Muscle
Relaxants in Spasticity. Annals of Neurology, Vol. 17, No. 1,
January 1985, pp 90-95; A. Eisen: Electromyography in Disorders of
Muscle Tone. Le Journal Canadien des Sciences Neurologiques, Vol.
14, No. 3. August 1987, pp 501-505; W. G. Tatton, P. Bawa, I. C.
Bruce, R. G. Lee: Long Loop Reflexes in Monkeys: An Interpretative
Base for Human Reflexes. Cerebral Motor Control in Man.: Long Loop
Mechanisms. Prog. clin. Neurophysiol., vol 4, Ed. J. E. Desmedt, pp
229-245, Krager Basel, 1978). EMG electrodes measure and amplify
actual action potentials sent to the muscles. Thus, they can
monitor the stretch reflex in action and the active force of
muscles can be monitored.
[0012] However, the total force of muscles is a combination of both
the active and passive forces. Active tension is due to muscle
stimulation and contraction due to crossbridge cycling. Independent
of muscle stimulation and crossbridge cycling, muscles also
experience passive tension. Like all materials, muscles experience
a passive tension when they are stretched beyond their resting
lengths. This is due to the inherent mechanical properties of
connective tissue in the muscles, such as elastin. The total force
of the muscle is the sum of the active and passive tensions, as
shown in FIG. 1. If muscles were de-innervated, then there would be
no active force and the total force would just be the passive
force.
[0013] EMG electrodes cannot monitor passive tension. Thus, the EMG
signal is correlated to the active force exhibited by the muscle
but not the total force. The most common definition of spasticity
is "a motor disorder characterized by a velocity-dependent increase
in muscle tonic stretch reflexes (muscle tone) with exaggerated
tendon jerks, resulting from hyperexcitability of the stretch
reflex, as one component of the upper motor neuron syndrome." (J.
W. Lance: Symposium Synopsis: Disordered Motor Control, R. G.
Feldman, R. R. Young, W. P. Koella, Chicago, Year Book Pulishers,
1980, pp. 485-494). However, it has also been proposed that an
increase in tone is largely caused by changes in the intrinsic
mechanical properties of the muscle tissue that causes an increase
in the passive stiffness of the muscle. This contribution of muscle
tone is independent of the stretch reflex and is not encapsulated
in the EMG signal. Still further, EMG signals are extremely noisy,
particularly if surface electrodes are used. EMG signals measured
with surface electrodes can also be influenced by hair, oil, or
lotions, and dead skin, thereby i yielding erroneous results.
Though the amplitude of the EMG signal is correlated with the
active force produced by the muscle, it is extremely difficult to
find the proper transformation between the two quantities. This
relationship differs from person to person due to physiological
differences. It is also sensitive to changes in location of the
electrode within the same subject. Thus, the use of an EMG machine
is not a good option for quantifying muscle tone, but, rather, is
more useful for monitoring the timing of reflex responses.
[0014] Still other tests, such as the pendulum test, measure the
range of motion and rate of change of motion of the joint in
response to a tendon jerk test. Though such tests may give an
indication of tone, the trajectory of a joint does not give a full
picture of muscle tone.
[0015] Tone describes the relationship of torque produced by the
muscles in response to an induced trajectory perturbation, or the
resulting trajectory given a torque perturbation. Either way, the
relationship between torque and trajectory can be described using a
mathematical model where parameters quantify tone in terms of the
viscoelastic properties of the muscles. However, it is difficult to
quantify these parameters. Unlike heart rate or blood pressure,
which are inherently physical quantities that can be measured, tone
describes a relationship between torque and displacement, as well
as the first derivative of angular displacement or velocity of the
joint based on the viscoelastic properties of the muscles. Also,
inertia of the limb has influence on the torque, which needs to be
properly isolated when determining the viscoelastic properties of
the muscles acting on a joint.
[0016] In the past, simple DC motors have been used to oscillate an
appendage about its joint while measuring the torque response due
to the external perturbation. The response of appendage movements
about the joint of rotation can be explained in terms of elastic
and viscous parameters. These parameters are dependent upon the
passive mechanical properties of muscles and the active stretch
reflex response, which has some inherent delay. A certain amount of
torque is required to move the appendage and to move the parts of
the apparatus, as every mass has a rotational inertia. Thus, the
torque response measured can be written as equation 1 shown below:
2 s ( t ) = K H ( t ) + B H . ( t ) + J T ( t ) s ( t ) = K H ( ( t
) - RP ) + B H . ( t ) + J T ( t ) s ( t ) = K H ( t ) + B H . ( t
) + J T ( t ) - K H EQ s ( t ) = K H ( t ) + B H . ( t ) + J T ( t
) + off [Eq.1]
[0017] where .tau..sub.s is the total torque sensed by the
transducer. .tau..sub.off is the offset torque and tells the
angular position the hand prefers to be in relative to the origin
or bias position. K.sub.H and B.sub.H are the angular stiffness and
viscosity of the combined flexor and extensor muscle groups that
act on the joint. J.sub.T is the combined inertia of oscillating
appendage, J.sub.H and the rotating components of the apparatus,
J.sub.A. J.sub.T=J.sub.H+J.sub.A. .theta. is the angular
displacement of the system. {dot over (.theta.)} and {umlaut over
(.theta.)} are the velocity and acceleration which are the first
and second derivatives of displacement respectively. .theta..sub.RP
is the angular position of the resting hand.
[0018] This second order differential equation has previously been
used as a model by many including Evans at al (C. M. Evans, S. J.
Fellows, P. M. H. Rack, H. F. Ross and D. K. W. Walters: Response
of the Normal Human Ankle Joint to Imposed Sinusoidal Movements. J.
Physiol. (1983), 344, pp. 483-502), Rack et al. (P. M. H. Rack, H.
F. Ross and T. I. H. Brown: Reflex Response during Sinusoidal
Movements of Human Limbs. Prog. Clin. Neurophysiol., vol. 4, Ed. J.
E. Desmedt, pp 216-228, 1978), Lehmann et al. (J. F. Lehmann, R.
Price, B. J. DeLateur, S. Hinderer, C. Traynor: Spasticity:
Quantitative Measurements as a Basis for Assessing Effectiveness of
Therapeutic Intervrntion. Arch. Phys. Med. Rehabil. Vol 70. pp
6-15, 1989), Prince et al. (R. Price, K. F. Bjornson, J. F.
Lehmann, J. F. McLaughlin, R. M. Hays: Quantitative Measurement of
Spasticity in Children with Cerebral Palsy. Developemental Medicine
and Child Neurology, 33, pp.585-595, 1991), Minders et al. (M.
Meinders, R. Price, J. F. Lehmann, K. A. Questad: The Stretch
Reflex Response in the Normal and Spastic Ankle: Effect of Ankle
Position. Arch. Phys. Med. Rehabili. Vol 77. pp 487-491, 1996). In
each case, simple sinusoidal displacements of the ankle or finger
joint were used at various frequencies. The technique of measuring
the frequency response to sinusoidal inputs to investigate
properties of second order electromechanical systems is common and
easy to do. The goal is to compute K.sub.H and B.sub.H at various
frequencies of oscillation. Since the activation stretch reflex
loop in the central nervous system is rate-dependent, one would
expect that K.sub.H and B.sub.H vary at different perturbation
speeds. Sinusouds have been chosen because they are easy to
generate by means of a unidirectional rotating wheel and crank. No
feedback loop is necessary. It has been argued that since
sinusoidal movements are continuous and smooth, they involve no
sudden impulsive movements that might synchronize a large number of
sensory receptors in an artificial or unphysiological way.
[0019] However, there is a fundamental mathematical problem in
isolating the inertia from the elastic stiffness of the muscles
when using simple sinusoidal displacements.
[0020] In this case, the displacement,
.theta.(t)=A.multidot.sin(.omega.t)- , where A is the amplitude of
the sinusoid in radians and o is the frequency of the oscillation
in rads/sec. The velocity, 3 . ( t ) = d / dt = A cos ( t )
[0021] d.theta./dt=A.omega..multidot.cos(.omega.t) and the
acceleration 4 ( t ) = d 2 / dt 2 = - A 2 sin ( t ) .
[0022]
d.sup.2.theta./dt.sup.2=-A.omega..sup.2.multidot.sin(.omega.t).
[0023] Substituting these state variables into equation 1 and
rearranging, we get:
.tau..sub.s-.tau..sub.off=K.sub.HA sin(.omega.t)+B.sub.HA.omega.
cos(.omega.t)-J.sub.TA.omega..sup.2 sin(.omega.t)
.tau..sub.s-.tau..sub.off=(K.sub.H-J.sub.T.omega..sup.2)(A
sin(.omega.t))+B.sub.H.omega.(A cos(.omega.t)) [Eq. 2]
[0024] The dominant waveform of the torque response is a sinusoid
of the same frequency but .phi. radians out of phase with the
displacement wave as shown in equation 3. After data acquisition,
A, M and .phi. are obtained by looking at the transfer functions of
the displacement and torque signals in the frequency domain to
obtain the magnitude and phases at the forced frequency .omega.
.tau..sub.s-.tau..sub.off=M sin(.omega.t+.phi.) [Eq. 3]
[0025] From the sum formula: .tau..sub.s-.tau..sub.off=M
sin(.phi.)cos(.omega.t)+M cos(.omega.)sin(.omega.)t)
[0026] If M.sub.1=M sin(.phi.) and M.sub.2=M cos(.phi.)
Then: .tau..sub.s-.tau..sub.off=M.sub.1 cos(.omega.t)+M.sub.2
sin(.omega.t) [Eq. 4]
[0027] Substituting equation 4 into equation 2:
M.sub.1 cos(.omega.t)+M.sub.2
sin(.omega.t)=(K.sub.s-J.sub.T.omega..sup.2)- (A
sin(.omega.t))+B.sub.H.omega.(A cos(.omega.t))
[0028] Thus, the total torque measured can be isolated as a
component in phase with the displacement wave and a component
quadrature with the displacement wave.
M.sub.1/A=K.sub.H-J.sub.T.omega..sup.2 [Eq. 5]
and
M.sub.2/A=B.sub.H.omega. [Eq. 6]
[0029] The amplitude of the in phase component contains both
elastic and inertial terms. Researchers have argued that a least
squares (error) fit of the in phase component and displacement
amplitude with frequency squared yields a linear relationship of
slope intercept form; y=mx +b, where y is M.sub.1/A, x is
.omega..sup.2, m is the slope and b is the intercept. They have
assumed that the slope is the total inertial and this "total
inertia" value has been used to evaluate the stiffness by
manipulating equation 5 to solve for K.sub.H at each frequency.
[0030] At first glance of equation 5, this assumption may seem
correct. After all, the total inertia does remain constant.
However, the assumption is false because the least squares fit
yields an intercept, b, that is a single approximation of K.sub.H
across all frequencies. Since the goal is to find a pair of varying
stiffness and viscosity values at each frequency, this analysis is
self-contradictory. This analysis forces the K.sub.H values to be
trendless (uncorrelated) across frequencies whose variance depends
on how well equation 5 fits to a straight line. To put it simply,
there are more unknowns than equations. If N sinusoids are used,
each at a different forcing frequency, we are looking for N
different stiffness values and one inertia value. Thus, there are
N+1 unknowns and N number of equations that resemble equation 5.
With more unknowns than equations, the system is indeterminate and
it is impossible to isolate the stiffness values from the inertia
value when only sinusoids are used.
[0031] Another way to show this problem that prevents isolation of
the stiffness and inertial values from the in phase component can
be shown using least squares regression analysis. Usually, we can
obtain the linear parameters of the model in equation 1 by
performing a least squares regression fit on the data. Given any
set of data values obtained from a given perturbation trial: 5 T s
= s ( t 1 ) s ( t 2 ) s ( t n ) nx1 and = 1 ( t 1 ) . ( t 1 ) ( t 1
) 1 ( t 2 ) . ( t 2 ) ( t 2 ) 1 ( t n ) . ( t n ) ( t n ) nx4
[0032] It is possible to obtain the set of four parameters, 6 N ~ =
off K H B H J T 4 x1
[0033] that describes the model in equation 1 7 s ( t ) = K H ( t )
+ B H . ( t ) + J T ( t ) + off [eq.1]
[0034] using the pseudo-inverse which minimizes the sum squared
error
SE=(.sub.s-.O slashed.).sup.T(.sub.s-.O slashed.)
V.sub.emf=K.sub.e
[0035] Typically, the pseudo-inverse (denoted by the function pinv
in equation 7), can be used to obtain the vector of unknowns, P, as
follows:
=pinv(.O slashed.).sub.s=(.O slashed..sup.T.O slashed.).sup.-1.O
slashed..sup.T.sub.s [eq. 7]
[0036] However, this can usually but not always be done because, in
the case of sinusoidal perturbation at a given frequency, the
acceleration waveform is always a constant multiple of the
displacement waveform by the scalar quantity -A.omega..sup.2 for
all time. Thus the displacement values and acceleration values are
linearly dependent. Since the first and third rows of .PSI. are
linearly dependent, the product of the matrices .PSI..sup.T.PSI. is
singular or very close to singular. All singular matrices are
noninvertible, thus P cannot be obtained, or the obtained values
are inaccurate.
SUMMARY OF THE INVENTION
[0037] The present invention provides a method and apparatus that
quantifies muscle by using non-sinusoidal perturbations. More
particularly, the device and method move the upper or lower
extremities of a patient in a non-sinusoidal trajectory,
.theta.(t), while measuring the torque response .tau..sub.s(t) and
utilizing Equation 1 to determine the stiffness K.sub.H, viscosity
B.sub.H and inertial J.sub.T parameters. 8 s ( t ) = K H ( t ) + B
H . ( t ) + J T ( t ) + off [Eq.1]
[0038] In an exemplary embodiment, as set out herein in more
detail, the device and method of the present invention can be
utilized to quantify the forearm muscle tone, the wrist in
particular. The device is particularly useful for quantifying
muscle tone in a spastic patient. However, it is to be understood
that the present method and device are not limited to
quantification of forearm muscle tone or to the spastic patient.
Rather, the device and method are useful on both the upper and
lower extremities including, for example, the ankle. Further, the
method and device can be used to measure muscle tone in the
non-spastic patient. For example, the method and device are useful
in evaluating patients with various types of upper or lower motor
neuron paralysis that affects skeletal muscles, such as patients
with cerebral palsy, traumatic brain injury, spinal cord injury,
stroke, or Parkinson's Disease patients. Further, the method and
device could be used in analyzing a patient's muscle tone in line
with, for example, physical therapy that the patient is undergoing
to regain control of the muscles in the legs after a spinal
accident.
[0039] More specifically, in accordance with an exemplary method of
the present invention, the wrist is driven with an arbitrary
trajectory that is neither sinusoidal nor ramp. By controlling the
trajectory .theta.(t) and measuring the torque response .tau.(t),
the stiffness, viscosity, and inertial parameters in equation 1 can
then be determined.
[0040] In general, the device in accordance with the present
invention is an automated tone assessment device that
non-invasively and properly quantifies tone. The device properly
determines the muscle tone of a person's flexors and extensors
about a appendage non-invasively. The appendage is perturbed with
arbitrary trajectories by virtue of a robotic design that uses a
closed loop automated feedback direct drive device that tracks any
arbitrary desired trajectory. The device perturbs an appendage with
any desired trajectory to properly determine the stiffness of the
flexors and extensors of an appendage. More particularly, a desired
displacement of the wrist is first determined using a set of
conditions detailed herein. A discrete set of finite points
defining this trajectory is then input into a controller, and a
motor shaft tracks these points at a certain sampling rate.
[0041] Other aspects and embodiments of the invention are discussed
infra.
BRIEF DESCRIPTION OF THE DRAWINGS
[0042] It should be understood that the drawings are provided for
the purpose of illustration only and are not intended to define the
limits of the invention. The foregoing and other objects and
advantages of the embodiments described herein will become apparent
with reference to the following detailed description when taken in
conjunction with the accompanying drawings in which:
[0043] FIG. 1 shows the total muscle tension as the sum of active
and passive tensions. (Taken from E. R. Kandel, J. H. Schwartz, and
T. M. Jessell. Principles of Neural Science, third edition,
Elsevier, New York, 1981, p. 552)
[0044] FIG. 2 shows the generation of a smooth filtered random
trajectory by limiting the maximum frequency component of a
uniformly distributed random number set of 1000 points in the
frequency domain. The signal is then taken back to the time domain
via the inverse Fourier transform. The filtered random trajectory
is selected to start and stop at the origin and finally scaled to
have an RMS value of 7000 counts (7 degrees).
[0045] FIG. 3 shows the generation of faster trajectories from the
same random number set by increasing the maximum frequency
component in the frequency domain in filtering a random number
set.
[0046] FIG. 4 shows the generation of two sets of filtered random
trajectories from two sets of random numbers. Trials I and 2 have a
maximum frequency component of 4 Hz, trials 3 and 4 have a maximum
frequency component of 5 Hz, trials 5 and 6 have a maximum
frequency component of 6 Hz, and trials 7 and 8 have a maximum
frequency component of 8 Hz. The displacements shown are relative
to the bias position or starting angle of the wrist. If the left
hand is tested instead of the right, these trajectories are flipped
or negated.
[0047] FIG. 5 shows one embodiment of the device in accordance with
the present invention.
[0048] FIG. 6 shows an optical encoder in the form of a code wheel
with a series of slits followed by opaque radial lines. The two
LED/Phototransistor pairs measure the amount of rotation by keeping
count of the number of slits that go by.
[0049] FIG. 7 shows the typical circuitry of an LED/phototransistor
pair. When light is transmitted from the LED to the phototransistor
V.sub.OUT is approximately 5V. When a opaque object blocks the
light, V.sub.OUT drops to 0V.
[0050] FIG. 8 shows the square wave outputs of two
LED/phototransistor channels. Two channels together are able to
detect the direction of rotation of the code wheel. Two channels
also increase the degree of resolution by 4.
[0051] FIG. 9 shows the theory of operation of a simple brushed
motor. (Taken from M. B Histand, and D. G. Alciatore, Introduction
to Mechatronics and Measurement Systems, WCB/McGraw-Hill, Boston,
1999, p. 315).
[0052] FIG. 10 shows the torque-speed curve of the brushless
servomotor (B-202-B-31) used in one embodiment of the present
invention.
[0053] FIG. 11 shows how a patient's arm is properly placed in one
embodiment of the device of the present invention.
[0054] FIG. 12 shows the proportional relationship between the
input voltage and the output current of the amplifier. The constant
of proportionality, or amplifier gain, was experimentally adjusted
so that the maximum range of voltage (+/-10 V) would correspond to
the maximum possible current output as listed in the manufacturer
specification sheet (+/-6 Amps).
[0055] FIG. 13 shows the proportional relationship between the
input current and the torque output of the servomotor. The constant
of proportionality, or torque constant was experimentally
determined.
[0056] FIG. 14 shows the proportional relationship between the
input voltage to the amplifier and the torque output of the
servomotor. The constant of proportionality between the two is the
product of the torque constant and the amplifier gain.
[0057] FIG. 15 is a block diagram showing components of the PD
closed loop control system used to follow the desired trajectories
in accordance with one embodiment of the present invention.
[0058] FIG. 16 shows a typical analytical frequency response and
step response of the entire closed loop system shown in FIG.
15.
[0059] FIG. 17 shows four possibilities of bias positions that
subjects were tested at in accordance with the present
invention.
[0060] FIG. 18 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial I of experiment
DMJF.
[0061] FIG. 19 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 2 of experiment
DMJF.
[0062] FIG. 20 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 3 of experiment
DMJF.
[0063] FIG. 21 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 4 of experiment
DMJF.
[0064] FIG. 22 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 5 of experiment
DMJF.
[0065] FIG. 23 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 6 of experiment
DMJF.
[0066] FIG. 24 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 7 of experiment
DMJF.
[0067] FIG. 25 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 8 of experiment
DMJF.
[0068] FIG. 26 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 9 of experiment
DMJF.
[0069] FIG. 27 shows raw data collected from optical encoder,
torque transducer and EMG electrodes in trial 10 of experiment
DMJF.
[0070] FIG. 28 shows the frequency response of the Savitsky-Golay
filter used on the encoder counts.
[0071] FIG. 29 shows the frequency response of the butterworth
filter used on the torque signal.
[0072] FIG. 30 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial I of
experiment DMJF.
[0073] FIG. 31 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 2 of
experiment DMJF.
[0074] FIG. 32 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 3 of
experiment DMJF.
[0075] FIG. 33 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 4 of
experiment DMJF.
[0076] FIG. 34 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 5 of
experiment DMJF.
[0077] FIG. 35 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 6 of
experiment DMJF.
[0078] FIG. 36 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 7 of
experiment DMJF.
[0079] FIG. 37 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 8 of
experiment DMJF.
[0080] FIG. 38 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 9 of
experiment DMJF.
[0081] FIG. 39 shows rectified data filtered from the optical
encoder, torque transducer and EMG electrodes in trial 10 of
experiment DMJF.
[0082] FIG. 40 shows the amount of residual torque when using one
set of time invariant parameters, {tilde over (.tau.)}.sub.off,
{tilde over (K)}.sub.H, {tilde over (B)}.sub.H, and {tilde over
(J)}.sub.T over the entire data set in each trial in experiment
DMJF.
[0083] FIG. 41 shows the results for control adult subject JF. JF's
right arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0084] FIG. 42 shows results for control adult subjects PW, JM, and
DD. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0085] FIG. 43 shows results for control adult subjects JF, MT, and
RP. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0086] FIG. 44 shows results for control adult subjects SN, JC, and
SB. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0087] FIG. 45 shows results for control adult subjects EK, SW, and
JH. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0088] FIG. 46 shows results for control adult subjects SP, VG, and
NM. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories
[0089] FIG. 47 shows results for control adult subjects SL, SR, and
HH. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0090] FIG. 48 shows results for control adult subjects LA, CS, and
SD. One arm was .tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0091] FIG. 49 shows results for control adult subjects RB, LA, and
HC. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0092] FIG. 50 shows results for control adult subjects KT, WZ, and
MH. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0093] FIG. 51 shows results for control adult subjects LH, DR, and
RW. One arm was tested at a bias of both 0 degrees and 30 degrees
flexion at each of the ten filtered, random trajectories.
[0094] FIG. 52 shows results for control adult subject GD. One arm
was tested at a bias of both 0 degrees and 30 degrees flexion at
each of the ten filtered, random trajectories.
[0095] FIG. 53 shows the average {tilde over (.tau.)}.sub.off,
{tilde over (K)}.sub.H and {tilde over (B)}.sub.H values across all
control adults for each trail. The eleventh bar shows the overall
average and standard deviation across all control adults, across
all ten trials.
[0096] FIG. 54 shows the results for adult subjects with hemiplegic
spasticity: AM, JS, and SH. The affected and unaffected arms were
tested at a bias of 30 degrees flexion at each of the ten filtered,
random trajectories.
[0097] FIG. 55 shows the results for adult subject BY with
hemiplegic spasticity. The affected and unaffected arms were tested
at a bias of 30 degrees flexion at each of the ten filtered, random
trajectories.
[0098] FIG. 56 shows the average {tilde over (.tau.)}.sub.off,
{tilde over (K)}.sub.H and {tilde over (B)}.sub.H values across all
adults with hemiplegic spasticity for each trail. The eleventh bar
shows the overall average and standard deviation across all adults
with spasticity, across all ten trials.
[0099] FIGS. 57-124 show block diagrams of code used in accordance
with one embodiment of the present invention.
[0100] FIG. 125 shows one embodiment of the wiring schematic of the
motor system in accordance with the present invention
[0101] FIG. 126 shows one embodiment of the wiring schematic from
the sensors to the data acquisition board in accordance with the
present invention.
[0102] FIG. 127 shows the pulse width of the embedded chip in the
US Digital decoder was decreased via the addition of a resistor as
shown. This was done because the original pulse width was wide and
the optical encoder was skipping counts at high rotational
speeds.
[0103] FIG. 128 shows an AutoCAD mechanical design drawing of one
embodiment of the motor coupling in accordance with the present
invention.
[0104] FIG. 129 shows an AutoCAD mechanical design drawing of one
embodiment of the shaft coupling in accordance with the present
invention.
[0105] FIG. 130 shows an AutoCAD mechanical design drawing of one
embodiment of the output shaft in accordance with the present
invention.
[0106] FIG. 131 shows an AutoCAD mechanical design drawing of one
embodiment of the forked wrench in accordance with the present
invention.
[0107] FIG. 132 shows an AutoCAD mechanical design drawing of one
embodiment of the hand support in accordance with the present
invention.
[0108] FIG. 133 shows an AutoCAD mechanical design drawing of one
embodiment of the hand plate in accordance with the present
invention.
[0109] FIG. 134 shows an AutoCAD mechanical design drawing of one
embodiment of the poles that secure the hand on the hand plate in
accordance with the present invention.
[0110] FIG. 135 shows an AutoCAD mechanical design drawing of one
embodiment of the arm rest attachment in accordance with the
present invention.
[0111] FIG. 136 shows an AutoCAD mechanical design drawing of one
embodiment of the Mechanical stop pin in accordance with the
present invention.
[0112] FIG. 137 shows an AutoCAD mechanical design drawing of one
embodiment of the top surface of the housing in accordance with the
present invention.
[0113] FIG. 138 shows an AutoCAD mechanical design drawing of one
embodiment of the bottom surface of the housing in accordance with
the present invention.
[0114] FIG. 139 shows an AutoCAD mechanical design drawing of one
embodiment of the back surface of the housing in accordance with
the present invention.
[0115] FIG. 140 shows an AutoCAD mechanical design drawing of one
embodiment of the left side surface of the housing in accordance
with the present invention.
[0116] FIG. 141 shows an AutoCAD mechanical design drawing of one
embodiment of the right side surface of the housing in accordance
with the present invention.
[0117] FIG. 142 shows an AutoCAD mechanical design drawing of one
embodiment of the encoder mount in accordance with the present
invention.
[0118] FIG. 143 shows an AutoCAD mechanical design drawing of one
embodiment of the motor mounting plate in accordance with the
present invention.
[0119] FIG. 144 shows an AutoCAD mechanical design drawing of one
embodiment of the front surface of the housing in accordance with
the present invention.
[0120] FIG. 145 shows an AutoCAD mechanical design drawing of one
embodiment of the bearing on the top surface of the housing in
accordance with the present invention.
[0121] FIG. 146 shows an AutoCAD mechanical design drawing of one
embodiment of the motor support column in accordance with the
present invention.
[0122] FIG. 147 shows an AutoCAD mechanical design drawing of one
embodiment of the armrest slide in accordance with the present
invention.
[0123] FIG. 148 shows an AutoCAD mechanical design drawing of one
embodiment of the bearing clamp ring in accordance with the present
invention.
[0124] FIG. 149 shows an AutoCAD mechanical design drawing of one
embodiment of the hand sub assembly in accordance with the present
invention.
[0125] FIG. 150 shows an AutoCAD mechanical design drawing of one
embodiment of the complete assembly drawing in accordance with the
present invention.
[0126] FIG. 151 shows an AutoCAD mechanical design drawing of one
embodiment of the labeled parts in accordance with the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
[0127] The present invention provides a method for quantifying
muscle tone and an apparatus that carries out the method.
[0128] In general, the device in accordance with the present
invention is an automated tone assessment device that
non-invasively and properly quantifies tone. Quantification of tone
allows a clinician to decide on the nature and degree of
intervention to administer. A pre and post-evaluation can also
determine the effectiveness of the intervention as well as track
the progress of the patient. The system software can easily be
modified to output the muscle stiffness of the patient to the
clinician in real time. The implications of this are in the
operating room where a neuro-surgeuon makes temporary lesions in
the brain while monitoring the patient's muscle tone in real time.
Once the surgeon finds the proper location in the brain that
alleviates the degree of muscle tone with out too much loss in
function, he/she can make the lesion permanent.
[0129] In an exemplary embodiment the device and method of the
present invention are utilized to quantify the forearm muscle tone,
in particular, the wrist in a spastic patient. However, it is to be
understood that the present method and device are not limited to
quantification of forearm muscle tone or to the spastic
patient.
[0130] When used to quantify muscle tone in the spastic patient,
upon determination of the muscle tone, the degree of spasticity
that the patient has can be determined, thereby allowing a
clinician to decide what form of intervention to take and to what
degree. The muscle tone can further be monitored over time to allow
the clinician to determine whether the intervention is providing
benefits to the patient.
[0131] More particularly, the present invention utilizes equation 1
to determine the stiffness, viscosity and inertial parameters. 9 s
( t ) = K H ( t ) + B H . ( t ) + J T ( t ) + off [Eq.1]
[0132] While equation 1 has been used in the past, the methods and
devices that were used to apply equation 1 utilized sinusoidal
displacements of the ankle or finger joint at various frequencies.
Using sinusoidal displacements, as set out above, leads to an
indeterminate system, and it is impossible to isolate the stiffness
values from the inertia values.
[0133] In accordance with the method of the present invention, a
desired trajectory that is non-sinusoidal and not a ramp is first
determined. The desired trajectory is then input into the device of
the present invention, which is an electromechanical system that
utilizes a feedback controller to track the desired displacement
trajectory.
[0134] In accordance with the present method, a desired
displacement of the wrist is first determined using the following
set of conditions.
[0135] (1) The trajectory is `smooth`. In other words, when
perturbing an appendage about its joint of rotation, there should
be "no sudden impulsive movements that might synchronize a large
number of sensory receptors in an artificial or unphysiological
way." (See P. M. H. Rack, H. F. Ross and T. I. H. Brown: Reflex
Response during Sinusoidal Movements of Human Limbs. Prog. Clin.
Neurophysiol., vol. 4, Ed. J. E. Desmedt, pp 216-228, 1978). As
used herein, a "smooth discrete trajectory" is mathematically
defined as follows:
[0136] .theta..sub.d(t.sub.k) is a discrete signal consisting of
set of N (1000) points that could be sampled from a continuous,
differentiable function, .theta..sub.d(t) for all time t such
that:
[0137] a. The sampling frequency (fhz.sub.mc) of the discrete
signal must be near to or greater than or equal to 100 Hz,
particularly if the maximum frequency required to represent the
discrete signal approaches or exceeds 10 Hz.
[0138] b. In the frequency domain, the maximum frequency needed to
represent the desired trajectory must be less than the smaller of
one-sixth frequency of the sampling rate of the motor controller,
fhz.sub.mc, or 15 Hz.
[0139] (2) At time, t=0, .theta..sub.d(0)=0, the motor does not
jump rapidly to the initial point.
[0140] (3) The trajectory .theta..sub.d(t) is periodic (repeatable)
and smooth for all time t>0. In other words
.theta..sub.d(t.sub.N+1) equals .theta..sub.d(t.sub.1).
[0141] (4) The trajectory has a finite range of motion with a
controllable, defined distribution.
[0142] (5) The matrix .PSI. has linearly independent columns, which
ensures that the matrix .PSI..sup.T.PSI. is nonsingular.
[0143] Filtered random trajectories are then generated using, for
example, MATLAB in the following way. There exist three discrete
signals, r.sub.a(t.sub.k), r.sub.b(t.sub.k) and r.sub.c(t.sub.k) in
the time domain which correspond to R.sub.a(.omega.),
R.sub.b(.omega.), and R.sub.c(.omega.) respectively in the
frequency domain. The time between two consecutive points given to
the controller is dt.sub.mc seconds apart.
[0144] (1) A set of N(1000) uniformly distributed numbers is
generated from -0.5 to 0.5. The frequency of the motor controller,
fhz.sub.mc, is 128 Hz, so consecutive points are dt.sub.mc=0.0078
seconds apart in time. This discrete signal is called
r.sub.a(t.sub.k).
[0145] (2) The discrete Fourier Transform of r.sub.a(t.sub.k) is
taken, R.sub.a(.omega.) to obtain the magnitude,
.vertline.R.sub.a(.omega.).vert- line. and phase,
.phi.(R.sub.a(.omega.)) of the signal in the frequency domain.
[0146] (3) Now, R.sub.b(.omega.) is generated. For all .omega.,
.phi.(R.sub.b(.omega.))=.phi.(R.sub.a(.omega.)). An .omega..sub.max
is selected such that .vertline.R.sub.b(0).vertline.=0, for
0<.omega..ltoreq..omega..sub.max,
.vertline.R.sub.b(.omega.).vertline.-
=.vertline.R.sub.a(.omega.).vertline., and for all
.omega.>.omega..sub.- max,
.vertline.R.sub.b(.omega.).vertline.=0. In FIG. 2,
.omega..sub.max=2.pi.*4 Hz.
[0147] (4) The Inverse Fourier Transform of R.sub.b(.omega.) is
taken to obtain r.sub.b(t). Note that the mean value of
r.sub.b(t.sub.k)=0.
[0148] (5) There is no guarantee that r.sub.b(0.sub.1)=0, however,
the trajectory does cross .theta.=0 at several instances in time.
The index, min_i is found where r.sub.b(tmin_i) has the lowest
absolute value which is approximately 0. Note that r.sub.b(t.sub.k)
is a continuous periodic function for all time with a period of
T.sub..theta.=dt.sub.mc*(N)=7.8125 s.
[0149] (6)
r.sub.c(t.sub.k)=.alpha.(r.sub.b(t.sub.k+t.sub.min.sub..sub.--.-
sub.i)-r.sub.b(t.sub.min.sub..sub.--.sub.i)). By shifting the
signal r.sub.b(t.sub.k) back tmin_i seconds in time, r.sub.c(0)=0.
.alpha. is a scalar number which scales the range of motion of the
trajectory. .alpha. was selected so that the root mean squared
value of r.sub.c(t.sub.k) is 7000/{square root}{square root over
(2)} counts. Thus, .alpha.=7000*RMS(r.sub.b(t.sub.k))/{square
root}{square root over (2)}
[0150] (7) Finally, each data point in r.sub.c(t.sub.k) is rounded
to the nearest integer which gives the desired trajectory,
.theta..sub.d(t.sub.k). This is done because the encoder (position
sensor) and the controller deal with an integer number of digital
counts.
[0151] The discrete set of finite data points defining the
trajectory is then inputted into the controller, and a motor shaft
tracks these points at a certain sampling rate. The desired
trajectories generated in this fashion satisfy all conditions
listed above. Faster desired trajectories can be further generated
that cover the same distribution of angular positions from the same
random number set. For example, as shown in FIG. 4, two random
number sets were used with maximum frequency components of 4, 5, 6,
7, and 8 Hz to give 10 trials.
[0152] Generally, the trajectory is determined for testing of the
right hand. However, if the left hand is to be tested, these
trajectories for the right hand can simply be flipped or negated
about the bias position, or relative origin, 0, to ensure symmetry
across contralateral limbs.
[0153] The device in accordance with the present invention is an
electromechanical system that is designed to drive the wrist with
the filtered random trajectories described above. Because these
trajectories have complex variable position and velocity profiles,
an automated feedback controller, or robot, is used which
constantly varies the torque, speed and direction of the actuator
(motor). The desired trajectory is given as input, and the actuator
moves back and fourth tracking the desired trajectory. Thus, design
of the system in accordance with the present invention includes a
mechanical design, the use of sensors and actuators, feedback
control, data acquisition and programming.
[0154] One embodiment of the electromechanical system is shown in
FIG. 5. As shown, the device includes a housing 1. The materials
used in fabricating the housing are not particularly limited
provided they supply the required structural support for holding a
patient's arm on the top surface 2 of the housing 1 during testing.
One preferred material is a metal such as aluminum. The housing 1
is shown as box-like in shape, however, the shape of the housing 1
is not limited and can come in a variety of shapes. Preferably, the
top surface 2 of the housing 1, where the patient's arm rests
during testing, is flat.
[0155] On the top surface 2 of the housing 1 is a hand securing
mechanism 3 where the patent places his hand during the test. The
hand securing mechanism 3 is designed such that the patient's hand
can be placed sideways within the hand securing mechanism 3 with
the palm facing the left (when the right hand is tested) and the
thumb facing upwards. To accommodate various sized hands, the hand
securing mechanism 3 is preferably adjustable to varying sizes.
[0156] In one preferred embodiment, as shown in FIG. 5, the hand
securing mechanism 3 is formed of two vertical bars 6 that extend
upwards from the top surface 2 of the housing 1 so that the patient
can place his or her hand between the two bars as shown in FIG. 7.
The two vertical bars 6 preferably have padding or cushions 7 on
their outer surfaces to provide comfort, as shown in FIG. 11. The
two vertical bars 6 may accommodate various sized hands by, for
example, slidably attaching the two vertical bars 6 to the housing
1 so that they can be moved inwards and outwards and locked into a
desired position. The padding or cushions 7 can also be removable
and can come in a variety of thicknesses to provide smaller and
larger openings between the two vertical bars 6, thereby
accommodating various sized hands. In yet another embodiment, the
padding or cushions 7 are compressible and expandable such that the
padding or cushions 7 compress or expand as required to hold hands
of various sizes in place.
[0157] A hand rest 4 and an arm rest 5 may further be mounted on
top surface 2 of the housing 1 to assist in providing proper
positioning of the arm and hand during testing. Preferably, the arm
rest 5 includes an arm securing mechanism 10 such as, for example,
one or more Velcro straps, as shown in FIG. 11, to secure the arm
in place during testing.
[0158] In a preferred embodiment, a motor shaft 11 drives the hand
about the wrist joint back and forth to follow the desired
trajectories. In this embodiment, a direct drive system is
preferably used wherein the hand rest 4 is directly connected to an
extension of the motor shaft 11, called the output shaft 12.
Preferably, there are no gears in between the motor shaft 11 and
the output shaft 12 so that there is no jitteriness or backlash
when the motor shaft 11 moves or changes direction. During use, the
hand is positioned on the hand rest 4, which may be in the form of
a small metal platform as shown in FIG. 6. The hand is secured as
it rotates about the wrist joint.
[0159] The hand securing mechanism 3, e.g. two vertical bars 6,
secure the area of the hand directly proximal to the first joint
between the metacarpals and phalanges so that the knuckles lie past
the hand securing mechanism 3, as shown in FIG. 11. The hand is
secured so that the patient being tested does not grasp the hand
securing mechanism 3. In fact, the patient should be completely
relaxed so that all muscle contractions are completely involuntary
due to the stretch reflex arc. Thus, the patient should not grasp
the hand securing mechanism 3 during the test, as there are muscle
groups that control flexion/extension of the wrist as well as the
fingers.
[0160] In a preferred embodiment, the hand rest 4 lies on a sliding
forked wrench 22 that is screwed into the output shaft 12. The hand
rest 4 is then secured to a position on a sliding track, such that
the axis of rotation of the wrist joint lies directly above the
axis of rotation of the output shaft 12. During the perturbation of
the hand, the remainder of the arm is secured to the arm rest 5
with the arm securing mechanism 10 as set out above. The arm rest 5
is preferably made out of low temperature thermoplastic that is
covered with a thin layer of foam for comfort. In a preferred
embodiment, the arm rest 5 is on an adjustable track, e.g. a
friction screw track, that allows for minor adjustments in the
positioning of the arm and hand if necessary.
[0161] The arm rest 5 and associated arm securing mechanism 10 hold
the arm securely in place with quick setup time and is sized to
accommodate various arm sizes. Removable cushions or pads of
varying sizes can, for example, be placed in-between the arm rest 4
and the arm to accommodate various sized arms. In one embodiment, a
compressible and expandable cushion (not shown) is mounted on the
arm rest 5 such that the cushion fits about varying sized arms by
compressing or expanding as necessary. Further, the arm rest 5 and
arm securing mechanism 10 is preferably adjustable to varying sized
arms. For example, in one embodiment, Velcro straps, which can be
quickly and easily secured tighter or looser, are used as the arm
rest arm securing mechanism 10. In another embodiment, one or more
straps having multiple snaps along the length of the straps can be
used for varying sized fits. Still further, one or more straps
similar to a belt with multiple holes can be used to provide
varying sized fits.
[0162] A torque transducer 20 (sensor) is placed between the motor
shaft 11 and the output shaft 12. The torque transducer 20 may, for
example, be placed between the motor shaft 11 and the output shaft
via two machined couplings secured with screws. Preferably, a top
coupling has a flat surface for a flat end screw to securely hold
the output shaft 12 onto the coupling. During fabrication of the
device, before the top surface 2 of the housing 1 is put in place,
an incremental optical encoder 24 (position sensor) is placed
around the output shaft 12 as shown in FIG. 5. After the top
surface 2 is secured on top of the housing 1, the inner rotating
ring 26 of the encoder 24 is secured to the output shaft 12 with,
for example, a clamp adapter ring positioned between the optical
encoder 24 and output shaft 12. In a preferred embodiment, the
rotating ring 26 is secured to the output shaft 12 via a plurality
of hex-screws with the clamp adapter ring in between the inner
rotating ring 26 of the optical encoder 24 and the output shaft 12.
A rotation of the output shaft 12 corresponds to the same amount of
rotation of the code wheel disc of the encoder 24.
[0163] The incremental optical encoder 24 is a device that converts
motion into a series of digital pulses that can be measured. A
preferred incremental optical encoder 24 in accordance with the
present invention is shown in FIG. 6 and consists of a disc with a
series of equally spaced slits or transparent segments 32 on it.
Separating these slits or segments 32 are opaque radial lines 38 of
equal arc thickness. On either side of the disk are two LED
emitters 34 paired with two phototransistors 36. The typical
circuitry of an LED/phototransistor pair is shown in FIG. 7.
[0164] Typically the forward voltage drop across the LED, V.sub.AK
is rated at around 1V at 20 mA. Since V.sub.S is 5V, the resistor,
R.sub.1 is needed to dissipate 4V. Thus by Ohm's law,
R.sub.1=4V/20 mA=200.OMEGA.
[0165] When there is no opaque object between the emitter and
detector, the light from the emitter supplies a base current to the
transistor. By Kirchoff's Voltage Law,
V.sub.C=V.sub.S=5V
[0166] The saturated collector emitter voltage, V.sub.CE is rated
at 0.2V, thus
V.sub.out=5V-0.2V=4.8V
[0167] If R.sub.2=1 M.OMEGA.,
I.sub.E=V.sub.out/R.sub.2=4.8V/1 M.OMEGA.=4.8 .mu.A
[0168] By Kirchoff's Current Law, inside the transistor the emitter
current is equal to the sum of the base and collector currents,
I.sub.E=I.sub.C+I.sub.B
[0169] Also in the transistor,
I.sub.C=h*I.sub.B
[0170] where h is some positive number. In summary, when there is
no opaque object between the LED emitter 34 and the phototransistor
36, there is some finite base current, IB from the LED emitter 34,
and V.sub.out has a reading of almost 5V (TTL high). When the
opaque radial line blocks the light between the LED emitter 34 and
the phototransistor 36, I.sub.B.apprxeq.0, and I.sub.C.apprxeq.0,
thus V.sub.out.apprxeq.0V. As the disc 30 rotates between the
transparent slits 32 and the radial lines 38, the output voltage
shifts between TTL high and TTL low respectively, resulting in a
square wave output. Typically, the number of square wave cycles
(ncypr) generated by an LED/phototransistor pair 34, 36 is equal to
the number of radial lines 38 or transparent slits 32 on the disc
30. However if more sophisticated circuitry and interpolation
techniques is used, the number of square wave cycles may be greater
than the number of radial lines 38 on the disc. The preferred
incremental optical encoder used in the present device is the
Gurley hollow shaft encoder, which has 11,250 radial lines on the
disc and generates 90,000 square wave cycles per revolution.
[0171] The more radial lines 38 (square wave cycles) that there are
on the disc 30, the higher the count resolution. The simplest way
to obtain angular position from a pair of LED emitters 34 and
phototransistors 36 is to count the number of cycles that go by,
either by counting the rising or falling edges of one square wave
output (CH A) as depicted in FIG. 8, (c) and (d). In this case, the
angular resolution is equal to the number of cycles per revolution
[ncypr] counts/rev or [360/ncypr] degrees. As shown in FIG. 8, (e)
and (f), both the rising and falling edges of CHA are counted, the
resolution can be doubled to [2*ncypr] counts/rev or [720/ncypr]
degrees.
[0172] If only one channel of square wave output is used, it is
impossible to tell the direction of rotation of the disc 30 as the
counting pattern of the clockwise and counterclockwise direction
are the same (see FIGS. 9(c) and 9(d)). To overcome this problem,
an additional LED/phototransistor pair 34, 36 is physically placed
around the disk 30 such that it's square wave output (CH B) is a
quarter cycle out of phase with that of CH A. Thus, the square wave
cycles from both channels are called quadrature signals. When the
disk 30 rotates in one direction (i.e. clockwise), CH A leads CH B
by a quarter of a cycle, but when the disk 30 rotates in the
opposite direction, CH A lags CH B by a quarter of a cycle. Another
advantage of using quadrature signals is that the count resolution
of the optical encoder 24 can be increased to [4*ncypr] counts/rev
by counting the rising and falling edges of both CH S A and CH B.
This is done using a quadrature decoder chip (for example, the
US-Digital PC-6-84-4). As shown in FIG. 8, (g) and 5(h), the count
patterns in the clockwise and counterclockwise directions are
different--they are reversed. The quadrature decoder converts the
signals from CH A and CH B into a direction (up/down pulse) and
count pulses, where a count pulse is generated every time the TTL
state of either channel changes. Since the Gurley hollow shaft
encoder, preferably used in the present device, generates 90,000
cycles per revolution in each channel, after quadrature edge
detection, the encoder gives 360,000 counts per revolution, which
is an amazing resolution of one thousandth (10.sup.-3) of a
degree.
[0173] In the setup of the present invention, the outputs of the
optical encoder 24 split and go to both the motion controller for
feedback control and to a National Instruments data acquisition
card for acquiring data. Theoretically, position information can be
obtained by interrogating the motion controller via software, in
which case, data acquisition of the position signal is not
necessary. However, when the motion controller is interrogated at a
high sampling rate, its operation and control of the motor shaft 11
is impeded. The controller software cannot both operate the
feedback loop to follow a desired trajectory and output data to the
user at 500 Hz.
[0174] The optical encoder 24 outputs three additional signals
relative to ground, not just A and B. These outputs are the index
signals, {overscore (A)}, and {overscore (B)}. Once activated, the
optical encoder 24 keeps track of angular position, in counts,
relative to the initial angular position where it started counting.
The index signal provides an absolute reference so that the
absolute position of the hand rest 4 is known in space. In addition
to the many equally spaced slits on the disk 30, there is one
additional slit that is at a different radial distance away from
its center, where the index signal is at TTL 1 only in one absolute
position using an additional LED/phototransistor pair 34, 36 as
described above. The counter value determined by channels A and B
is reset to zero where the TTL value of the index is 1 and, thus,
the index serves as an origin in space. Once this position is
found, the system knows where the absolute position of the hand
rest 4 is in real space.
[0175] As used herein, the axis of rotation of the output shaft 12
is defined as pointing upward, so that a counter clockwise rotation
is positive change in direction, and a clockwise rotation is
negative change in direction. The motion controller however,
defines a clockwise rotation as positive, and a counterclockwise
rotation as negative.
[0176] Preferably, in the device of the present invention, the
index signal is not used. Rather, in one preferred embodiment, the
reference point used to determine absolute position is the left
mechanical stop 26. A right mechanical stop 27 may further be
located opposite the left mechanical stop 26. The motor shaft 11
moves counterclockwise at a slow speed until the forked wrench of
the hand rest 4 hits the left mechanical stop 26 at which point the
motor stops. In this configuration, the mid-axis of the forked
wrench is 90 degrees (90940 counts) away from the midline, the
counter value with the motion controller is set to -90940 which is
-90.940 degrees.
[0177] Now the counter value reads, and will continue to read, the
correct absolute position until the computer that powers the
optical encoder 24 is turned off.
[0178] The output pulse width determines the minimum separation
between consecutive A and B pulses that can be detected by the
decoder chip. If the separation between consecutive A and B pulses
is less than the output pulse width of the decoder, then two output
pulses overlap and only one count is registered instead of two,
resulting in an erroneous position reading. The width of the clock
pulse is influenced by the value of the resistor between pins 1 and
3 of the LS7084 quadrature decoder chip embedded in the US-Digital
PC-6-84-4 as shown in FIG. 127. In an exemplary embodiment, an
added resister across pins 1 and 3 is used to decrease the decoder
pulse width to less than 750 ns.
[0179] An actuator is a device that converts electromechanical
force into motion. This electromechanical force can be explained by
Lorentz's Law:
{right arrow over (F)}={right arrow over (I)}.times.{right arrow
over (B)}
[0180] When a current in a conductor, {right arrow over (I)}, is
exposed to a magnetic field, {right arrow over (B)}, a force {right
arrow over (F)} is produced in the direction perpendicular to both
{right arrow over (I)} and {right arrow over (B)} as described by
the right hand rule.
[0181] Since the hand is perturbed about the wrist joint during
testing, a motor 40 was used as the actuator for this task.
Generally, the stationary outer housing of a motor, the stator, is
magnetized either by permanent magnets or by currents flowing
through coiled wires wrapped around iron cores. The rotor or
rotating shaft is also magnetized either by permanent magnets or
winded field coils. The rotor and its windings are collectively
known as armature. If the rotor is magnetized via coils, then it
has commutator segments where the current is supplied. Brushes
provide stationary electrical contact between the power source and
the moving commutator and rotor. FIG. 9 shows the theory of
operation of a simple two-pole DC motor in view of the long axis of
the rotor, wherein "DC" denotes Direct Current. The setup shown
consists of a stator that is a permanent magnet and a rotor that is
magnetized via coils. In the starting position, (i), the right
brush touches commutator segment A and the left brush touches
segment B creating a current that flows through the rotor winding.
This current magnetizes the rotor into N and S poles as shown.
Since like poles repel and opposite poles attract, the rotor
rotates in the clockwise direction as shown in (ii) and (iii). In
(iv), for a brief instant, the commutators lose contact with the
brushes, no current flows through the armature and the rotor is
demagnetized. However, the rotor continues to turn clockwise due to
momentum. In (v), the commutator contacts switch brushes and the
armature current now flows in the opposite direction, so the poles
of the rotor are switched. Thus, the motor continues rotating as
the armature current constantly switches direction, maintaining
torque in the clockwise direction. Like most motors, the motor
shown in FIG. 9 is a brush motor. Its stator is a permanent magnet
and its rotor armature has a constantly switching current provided
by an external current source through the brushes. The brushes of a
DC motor have several limitations: brush life, brush residue,
maximum speed, and electrical noise. The currents produced in the
armature produce a large amount of heat in the rotor that is
difficult to dissipate.
[0182] The brushless DC motor operates by the same principle as the
brush motor except that the rotor consists of a permanent magnet
and the stator is magnetized via rotating fields in the stator. It
is like a brush motor turned inside out. Indicative of its name,
the brushless motor eliminates the need for brushes and
commutators. Brushless DC motors are potentially cleaner, faster,
more efficient, less noisy, more reliable, produce no sparks and
the rotor does not heat up. These motors are also known as
permanent magnet motors. Motors that use feedback for a position or
trajectory control applications are called servomotors.
[0183] Preferably, the motor according to the present invention is
a brushless DC servomotor, although other types of motors are
compatible for use in the present invention. A particularly
preferred motor for use in the present invention is the B-202-B-3 1
brushless servomotor from Kollmorgen as its speed range,
torque-speed curves and maximum stall torque are acceptable for use
in the present invention. The speed torque curve shows the maximum
torque the motor can produce at a certain speed using the amplifier
of the present invention (see FIG. 10). For the present invention,
this is the torque applied by the hand in response to the
perturbations given, and, more importantly, the inertias of the
hand and the hand rest. As shown in FIG. 10, the maximum possible
operating speed of the motor is 3800 RPM. The motor can generate
torques up to 3.5 Nm while maintaining a speed fairly close to the
maximum value. If the motor is to generate torques above 3.5 N, the
maximum speed it can maintain drops very sharply until the motor
finally stops moving at the maximum torque of 4.7 Nm. This maximum
torque value where the motor shaft is stationary is called the
stall torque.
[0184] When the load torque on the motor is equal and opposite to
the toque produced by the motor while the shaft is stationary, the
motor is said to be stalling. This value is limited by the maximum
amount of current that the amplifier can supply to the motor. What
is considered a fast rotation in most industrial applications is at
least an order of magnitude larger than what one would consider a
rapid angular joint velocity. In industrial applications, motors
may move on the order of 10.sup.3 RPM. In the present invention,
the wrist joint is not expected to be moved to speeds above 25
rads/s or 238 RPM. As shown on the torque-speed curve, the motor
can produce close to the maximal stall torque through the entire
range of speeds that the present invention is operating at and,
thus, the torque-speed relation is not of concern. Rather the
concern is that the maximum toque of 4.8 Nm is sufficient for the
purpose of the present invention. To determine this, the magnitudes
of torques that the motor has to oppose must be analyzed. By
Newton's second law, 10 = m + 1 + f = J t
[0185] Rearranging to: 11 m = J t - 1 - f
[0186] wherein .tau..sub.m is the torque generated by the motor,
.tau..sub.l is the load torque applied by the passive and active
viscoelastic properties of the muscles and .tau..sub.f is the
negligible friction torque of the mechanical apperatus. J.sub.t is
the total inertia of the mechanical apperatus (arm rest) J.sub.m
plus the inertia of the human hand, J.sub.l. The signs of
.tau..sub.l and .tau..sub.f are opposite that of .tau..sub.m since
they oppose the motor torque and rotation direction, thus: 12 m = J
t - 1 - f
[0187] The majority of the torque that the motor is required to
produce is to overcome the total inertia of the system, J.sub.t.
The inertia of the typical hand was crudely estimated to be around
0.0015 kg m.sup.2. The inertia of the armrest is around 0.005 kg
m.sup.2. J.sub.t=J.sub.m+J.sub.l.apprxeq.0.0065 kg m.sup.2. Since
it is not expected that the wrist joint will be perturbed at
accelerations that exceed .+-.500 rads/s.sup.2, the maximum torque
needed to overcome inertia is 13 J t max = ( 0.0065 kgm 2 ) ( 500
rads / s 2 ) = 3.25 Nm
[0188] With the load torque applied in response to the
perturbations, the motor selected is sufficient for the present
invention because the maximum possible torque that the motor can
produce is not expected to be exceeded. Further, based on these
specifications, other suitable motors may be readily determined by
one of skill in the art. The torque capibility of the motor is
expressed in terms of the peak stall torque and the continuous
stall torque. The peak stall torque is the absolute maximum torque
that the motor can produce. This peak torque can only be maintained
for a few seconds before the torque settles down to to the
continuous stall torque.
[0189] The back emf, V.sub.emf is an induced voltage by the
rotating armature that opposes the applied voltage that is
determined by: 14 V emf = K e . or V emf ( s ) = K e ( s ) .
[0190] in the Laplace domain. [eq. 8]
[0191] K.sub.e is the emf constant of the motor and .theta. is the
angular velocity of the rotor. If the power supplied to the motor
is a voltage source and the voltage supplied at a particular time
is V.sub.m, then: 15 V m = L I . m + RI m + V emf = L I . m + RI m
+ K e . or V m ( s ) = ( Ls + R ) I m ( s ) + V emf ( s ) in the
Laplace domain [ eq . 9 ]
[0192] I.sub.m is the resulting armature current that can be
derived in terms of V.sub.m, L and R. L is the inductance, and R is
the motor resistance. I is the rate of change of the armature
current. The torque produced by the motor is proportional to the
current supplied to it:
.tau..sub.m=K.sub.tI.sub.m
[0193] or T.sub.m(s)=K.sub.tI.sub.m(s) in the Laplace domain [eq.
10]
[0194] where K.sub.t is the torque constant of the motor.
[0195] Equation 10 can be rewritten as: 16 m + 1 = B m . + J t or
T.sub.m(s)+T.sub.l(s)=(B.sub.ms+J.sub.ts.sup.2).THETA.- (s) in the
Laplace domain. [eq.11]
[0196] The amplifier is the variable power supply to the motor. It
amplifies the command voltage from the controller into either a
voltage or a current to the motor 40. The input to the amplifier is
the command voltage given by the Galil motion controller. There are
three modes of operation of an amplifier: voltage source mode,
current source mode, and velocity loop mode, all of which are
described below:
[0197] Voltage Source Mode:
[0198] In this mode, the output to the motor is a voltage, V.sub.m,
that is some unitless gain, K.sub.V, times the command voltage,
V.sub.cmd.
V.sub.m=K.sub.VV.sub.cmd [eq. 12]
[0199] The resulting armature current can be derived from equation
9. The result is quite cumbersome since equation 9 is a first order
differential equation in terms of I.sub.m and also depends on the
time varying velocity and the back emf constant, as well as the
impedance and resistance of the motor. The resulting motor toque,
.tau..sub.m is simply proportional to the current I.sub.m by the
torque constant. It is not easy to derive the torque output of the
motor given the amplifier output of V.sub.m because of the
complexity of equation 9. The transfer function that is the ratio
of motor position to voltage command V.sub.cmd is: 17 ( s ) V cmd (
s ) = K v K t J t Ls 3 + ( B m L m + J t R m ) s 2 + ( B m R m + K
t K e ) [ eq . 13 ]
[0200] Current Source Mode:
[0201] The relationship between the motor voltage, V.sub.m and
motor torque, .tau..sub.m is a complicated differential equation
with respect to many variables. In current source mode, advantage
can be taken of the simple linear relationship between the motor
current and torque output as described by the torque constant,
K.sub.t as shown in equation 10. Here the amplifier takes the
command voltage, V.sub.cmd from the Galil controller and amplifies
it to the current I.sub.m the gain K.sub.a:
I.sub.m=K.sub.aV.sub.cmd [eq. 14]
[0202] The units of K.sub.a are [Amps*RMS/Volt]. Here, the transfer
function between the motor position and voltage command is: 18 ( s
) V cmd ( s ) = K a K t J t s 2 + B m s [ eq . 15 ]
[0203] Velocity Loop Mode:
[0204] The velocity loop mode is the same as the current mode with
an added feedback component. A tachometer that senses velocity
converts the velocity into a voltage by the gain, Ku, and sends it
back to the amplifier. The units of K.sub.u are [V*s/count]. In
this mode the transfer function between the motor position and
command voltage is: 19 ( s ) V cmd ( s ) = K a K t J t s 2 + B m s
+ K u K a K t [ eq . 16 ]
[0205] A preferred amplifier for use in the present invention is
the Kollmorgen BDS4-1033-0101-202B2, which matches the desired
motor characteristics. In an illustrative embodiment, the amplifier
is set up in the current mode. This mode makes the analysis of the
control system fairly simple. The preferred power supply used for
the amplifier is the PSR4/5-112-0102, which can supply a peak
current to the above-described motor of about 6 Amps RMS, that
lasts for around 2 seconds, and a maximum continuous current of
about 3 Amps RMS, as shown by the dashed line in FIG. 12.
[0206] After setting up the system, prior to operating the motor
40, the gain of the amplifier and other adjustments are set via
tuning pots located on the chassis of the amplifier. The command
scale pot is used to adjust the velocity loop gain, K.sub.u.
However, since the velocity loop is disabled, this is not
necessary. Pin 18 on Connector C1 of the amplifier is used to
monitor the current output relative to common (pin 17). The output
is a voltage proportional to the current output where 1V 0.75 Amps
RMS. This feature is used to monitor the current supplied by the
amplifier. The balance pot is used to make sure that when 0V is
commanded from the Galil controller, the current output of the
amplifier is 0 Amps RMS and the motor produces no torque. Equation
14 above is really of the form:
I.sub.m=K.sub.aV.sub.cmd+.alpha. [eq. 14]
[0207] where .alpha. is the offset current that is adjustable with
the balance pot. With the motor enabled, the input to the
amplifier, V.sub.cmd is set to 0V and the balance pot is rotated
such that I.sub.m read 0 Amps to ensure no offset current. The
current limit pot is turned all the way clockwise to maximize the
maximum amount of current that the amplifier can supply (up to
.+-.6Amps RMS). The most important adjustment is the stability or
gain adjustment. This determines the magnitude of K.sub.a. This
adjustable amplifier gain is set experimentally so that the maximum
possible value of V.sub.cmd (10 V) would correspond to the maximum
current limit (approximately 6A) of the amplifier to take advantage
of the full range of currents. Thus, the stability pot is adjusted
so that value of K.sub.a is set to 0.6 Amps RMS/V.
[0208] An experiment was conducted where the voltage output from
the Galil controller was set from 0V to 10V at 0.5V increments. To
measure the torque output of the motor, .tau..sub.m, the motor
shaft was kept stationary using the mechanical stops. In this
state, 20 . = 0 and = 0
[0209] and
.tau..sub.m=-.tau..sub.m from equation 11.
[0210] This torque was measured with the torque transducer. The
motor torque and amplifier current was measured at each command
voltage to produce the plots shown in FIG. 12.
[0211] For each command voltage, the correspontind amplifier
currents and motor torques were plotted against each other and
K.sub.t was determined by a linear fit through the origin as shown
in FIG. 13.
[0212] The maximum torque the motor can produce is limited by the
maximum current supplied by the amplifier as defined by equation
10. Thus the peak transient torque the motor can produce is 4.86
Nm, which lasts for about 2 seconds before it drops to about 3
Nm.
[0213] The controller is the brain of the feedback system, which
consists of hardware and software. It controls the command voltage,
V.sub.cmd that is sent to the amplifier that controls the output
torque of the motor shaft since .tau..sub.m=K.sub.tK.sub.aV.sub.cmd
and K.sub.a and K.sub.t are known constants. The controller has two
inputs at any given discrete time instant, t.sub.i: the desired
position of the motor shaft, .theta..sub.d(t.sub.k) and the actual
position of the motor shaft, .theta.(t.sub.i). The encoder 24 gives
the actual position of the motor shaft 11 with a resolution
accuracy of 0.001 degrees, as there are 360,000 counts in one
revolution of the motor shaft 11. The controller deals with
positions in [counts] since that is the digital output of the
encoder/decoder. The command voltage it sends to the amplifier is
some function of the position error, .theta..sub.e where:
.theta..sub.e(t.sub.i)=.theta..sub.d(t.sub.i)-.theta.(t.sub.i)
[0214] The desired trajectory, .theta.(t.sub.k) is given as a set
of digital points dt.sub.mc seconds apart. This is the period of
one cycle of the feed back loop. A new command voltage is sent to
the amplifier every dt.sub.mc seconds. Thus the frequency of the
desired trajectory fed into the controller in Hz is 21 fhz m c = 1
dt m c
[0215] The points in the desired trajectory are either generated
offline or online. If they are generated offline, the exact points
of the trajectory have to predetermined and fed into the controller
as an array. This is what is done, for example, when the desired
trajectories are the filtered random trajectories that are
generated with MATLAB. Since the desired trajectory is periodic,
only one period of the trajectory needs to be inputted to the
controller. If the points in the desired trajectory are dependent
on some output state such as torque or continuously change with
time, then they have to be generated online within the loop. When
the desired trajectory is a sinusoid, each point of the desired
trajectory is generated online based on the time elapsed from the
start and the user defined amplitude and frequency. If the points
are to be generated within the loop, then everything from sensing
the necessary output states to computing the next desired position
or torque has to take place in less that dt.sub.mc seconds. This is
done so the sampling frequency of the controller is maintained at
128 Hz, otherwise the frequency of the controller needs to be
decreased to increase the amount of time per loop. At substantially
low sampling frequencies, the trajectory will become "choppy" and
will not be smooth as defined earlier.
[0216] Preferred components of the controller selected for the
present invention can be obtained from Galil Motion Control.
Several high-level motion controllers can be considered.
Preferably, the controllers can be interfaced and, thus, controlled
by LabVIEW software, which is the preferred code used in the
present device. Preferably, the device is entirely automated and,
thus, intervention of the user is minimal as he/she only gives
certain desired inputs such is file identifier and the desired
trajectories for the device to follow. The components of the Galil
controller include the following:
[0217] the DMC-1410 single-axis motion controller for the ISA
bus.
[0218] the ICM-1460 interconnect module.
[0219] the WSDK-32 Servo Design Kit for Windows 95, 98
[0220] the Setup-32 software for Windows 95, 98
[0221] a 37 pin connector cable from the DMC-1410 to the
ICM-1460
[0222] The controller uses a high level code, which is attached
hereto as Appendix A. Of course, controllers having similar
components and that function as required by the present invention
could also be used.
[0223] FIG. 15 shows one preferred embodiment of a block diagram of
components of the PD closed loop control system used to follow the
desired trajectories.
[0224] As shown in FIG. 15, a PD Compensator is utilized. A
preferred PD Compensator for use with the present invention has the
following specifications:
[0225] Manufacturer: Galil Motion Control
[0226] Input: position error, .theta..sub.e [counts]
[0227] Output: digital number, N.sub.d from -32767 to 32767
[0228] Description: motion control software downloaded to PLC takes
desired trajectory input and feedback from encoder to control motor
output.
[0229] Transfer Function: 22 N d e = ( K P + K D S )
[0230] Constants: K.sub.P=0.75 (chosen) K.sub.D=0.1563 s.sup.-1
(chosen)
[0231] Further shown in FIG. 15 is a Digital to Analog converter
(D/A). A preferred D/A for use with the present invention has the
following specifications:
[0232] Manufacturer: Galil Motion Control
[0233] Input: digital number, N.sub.d from -32767 to 32767.
[0234] Output: command voltage, V.sub.cmd from -10 V to 10 V.
[0235] Description: converts the digital number from -32767 to
32767 to an analog voltage output from -10 V to 10 V.
[0236] Transfer Function: 23 V cmd e = G dac
[0237] Constants: G.sub.dac=20/65535 (fixed, set by PWM &
hardware)
[0238] Further shown in FIG. 15 is an amplifier. A preferred
amplifier for use with the present invention has the following
specifications:
[0239] Manufacturer: Kollmorgen Industrial Drives
[0240] Input: command voltage, V.sub.cmd from -10 V to 10 V.
[0241] Output: motor armature current, i.sub.m, from -6.16 Amps RMS
to 6.16 Amps RMS.
[0242] Description: produces a current proportional to the input
voltage. The adjustable amplifier gain was set experimentally so
that the maximum possible value of V.sub.cmd would correspond to
the maximum current limit of the amplifier to take advantage of the
full range of currents.
[0243] Transfer Function: 24 I m V cmd = K a
[0244] Constants: K.sub.a=0.603 Amps RMS/V (experimentally set)
[0245] Further shown in FIG. 15 is a servo motor. A preferred servo
motor for use with the present invention has the following
specifications:
[0246] Manufacturer: Kollmorgen Industrial Drives
[0247] Input: motor armature current, i.sub.m, from -6.16 Amps RMS
to 6.16 Amps RMS.
[0248] Output: torque produced by motor from -5.19 Nm to 5.19
Nm.
[0249] Description: produces a torque proportional to the input
current.
[0250] Transfer Function: 25 T m I m = K t
[0251] Constants: K.sub.t=0.843 Nm/Amps RMS (fixed, experimentally
determined)
[0252] Further shown in FIG. 15 is a plant. A preferred plant for
use with the present invention has the following
specifications:
[0253] Input: motor torque, T.sub.m plus external load torque,
T.sub.l applied by human [Nm].
[0254] Output: actual motor shaft position, 0 [counts].
[0255] Description: the resulting motor shaft position is
determined by the input torques, combined viscosities and inertia
of the motor shaft, all mechanical loads attached to the motor
shaft including the arm rest B.sub.m and J.sub.m. The position is
also affected by the inertia of the hand, J.sub.l if attached.
[0256] Transfer Function: 26 ( T l + T m ) = 1 B m s + ( J l + J m
) s 2 4 N cypr 2
[0257] Note: all units in the control system are expressed in SI
units except for the angular positions which are not in radians but
in counts. (4N.sub.cypr counts=2.pi. radians)
[0258] Constants: B.sub.m=0.003 Nm s/rad experimentally
determined,
[0259] J.sub.m.apprxeq.0.0048 kg m.sup.2. The exact value slightly
varies depending on the position of the armrest on the sliding
bar.
[0260] J.sub.l.apprxeq.0.0023 kg m.sup.2. The exact value varies
depending on the mass distribution, and geometry of the hand of the
subject being tested.
[0261] N.sub.cypr=90,000. This is the number of square wave cycles
per revolution of the incremental encoder. With quadrature edge
detection, there are 4N.sub.cypr counts per revolution.
[0262] The entire closed loop PD system preferably has the
following specifications:
[0263] Input: desired motor shaft positions (trajectory),
.theta..sub.d [counts].
[0264] Output: actual motor shaft position, .theta. [counts].
[0265] Description: the system implemented is a Linear Time
Invariant second order model of the system.
[0266] Transfer Function: 27 d = ( K D G dac K a K t ) s + K P G
dac K a K t ( J l + J m ) 2 N cypr s 2 + ( K D G dac K a K t + B m
2 N cypr ) s + K P G dac K a K t = 24.256 s + 465.705 0.1239 s 2 +
24.308 s + 465.705
[0267] It is important that the system characteristic equation or
denominator of R(s), gives poles at: 28 - ( K D G dac K a K t + B m
2 N cypr ) ( K D G dac K a K t + B m 2 N cypr ) 2 - 2 ( J l + J m )
( K P G dac K a K t ) N cypr ( J l + J m ) N cypr
[0268] -87.56 and -10.73 after substitution and simplification.
Since the roots have negative real parts, it can be said that the
linear time-invariant system is bounded-input, bounded-output and
asymptotically stable. The fact that roots are unequal and have no
imaginary parts says that the system is overdamped (.zeta.>1).
In fact, for the inertia constants used above, .zeta.=1.6. For
smaller inertias, .zeta. increases slightly and for larger hand
inertias, .zeta. decreases slightly.
[0269] Using typical values for constants J.sub.m, and J.sub.l
shown above and substituting j.omega. for s, the analytical
magnitude and phase of the frequency response is shown in FIG. 16.
The analytical step response is also shown in FIG. 16.
[0270] The tuning parameters, K.sub.p and K.sub.d, are chosen so
that the system will have a fast response time without making them
too large. The torque saturates when small position and velocity
error gives rise to a large digital output N.sub.d and a command
voltage, V.sub.cmd close to +/-10V. Preferably, from 0 to 8 Hz, the
magnitude of frequency remains close to 1. The actual trajectory of
the shaft was checked for all types of desired trajectories both
analytically using the MATLAB function mypid.m (see Appendix A) as
well as experimentally by measuring the actual output position of
the shaft.
[0271] A preferred test setup and procedure in accordance with the
present invention is as follows. The patient being tested with the
device of the present invention is preferably seated in front of
the device. Two surface electrodes are placed on the patient's arm
to monitor activity of the flexors and extensors. The ground
electrode is placed on an inactive or neutral site. After the
absolute position of the motor shaft is calibrated, the seat is
adjusted such that the patent's left or right arm can be placed in
the arm rest 5. At this point, the patient's elbow is preferably at
about 145 to 160 degrees. The patient's hand is placed on the hand
rest 4 in the neutral supination/pronation position such that his
or her knuckles are slightly passed between the padded vertical
bars 6. The vertical bars 7 are moved closer together and tightened
such that the hand is comfortably secured in place. The hand rest 4
is then slid forward or backward so that the wrist joint is lined
up with the motor shaft 11. Now the subject is simply told to relax
and not to resist the robot's movement as the robot moves to the
initial bias position and follows the desired trajectories as
described above. The robot automatically cycles through the desired
trajectories (trials 1-10) while collecting torque, position and
EMG data. If an additional test is to be performed in a different
bias position, the patient's arm is preferably removed from the
apparatus for 2 or 3 minutes before the procedure is repeated at
the new initial bias position.
[0272] The bias position is the absolute initial angular position
of the wrist joint that the motor shaft 11 moves to before each
perturbation trajectory or trial is carried out. A bias position of
0 degrees corresponds to the neutral flexion/extension position. It
is also the median angular position of the trajectory. The user
selects the bias or initial position, and the motor shaft 11
automatically moves to that position before the desired trajectory
is carried out. In testing control subjects, selecting a 0-degree
bias position is not a problem as control subjects have a wide
range of motion. Almost all patients with spasticity and others
with neurological problems, however, have a limited range of
motion. Their resting position is in a hyper-flexed position and it
is painful or impossible for them to extend their hand beyond the
0-degree absolute position due to the contracted state of the
flexor muscles. Due to this constraint, subjects in the patient
population were tested in the 30 degree flexed position. Control
subjects were tested at both 0 and 30 degree flexed bias position.
Since the left or right arm may be tested, the four possible
combinations of bias positions are shown in FIG. 17.
[0273] For more detailed instructions about the procedure, please
refer to the user's manual attached hereto as Appendix B.
[0274] Next, the raw data is taken and transformed into the torque
offset, elastic stiffness, viscosity and inertia parameters
described above and represented by the variables .tau..sub.off,
K.sub.H, C.sub.H, and I.sub.T respectively. .tau..sub.off is the
offset torque, K.sub.H is the combined angular elastic stiffness of
all the muscles acting on the wrist joint, C.sub.H is the combined
angular viscosity of all the muscles acting on the wrist joint, and
I.sub.T is the moment of inertia of the moving hand as well as the
moving mechanical parts of the apparatus (hand rest).
[0275] Data obtained from subject JF (a 28 year old, male control
subject) is identified as experiment DMJF. In this experiment, the
10 trial random trajectories were run on the right hand at a bias
of 0 degrees. The entire data analysis procedure will be described
from obtaining the raw data until the computation of impendence
parameters in equation 1.
[0276] As mentioned above, for each perturbation trajectory given,
five measurements are collected and stored using LabVIEW and a
National instrument PCI-E series data acquisition board at 500 Hz.
A reading from each sensor is synchronously collected every 2 ms.
These raw data points are stored as an n.times.5 array in ASCII
format. Data is collected for 20 seconds (n=10,000) per trial. The
first data column is just a timestamp of when data from each sensor
is collected (i.e. 0 ms, 2 ms, 4 ms . . . ). The second data column
is a set of integer counts from the encoder 24, which make up the
angular position signal of the motor shaft 11 and the wrist joint.
The third data column is a list of torque readings from the torque
transducer in Nm. The fourth and fifth data columns are flexor and
extensor EMG readings respectively, in mV. Since each experiment
consists of ten filtered random trajectories, there are ten arrays
of raw data stored as DMJFI1t1, DMJFI1t2, . . . , DMJFI1t10.
[0277] The raw signals of each of the 10 trials in experiment DMJF
are shown in FIGS. 18-27.
[0278] In one preferred embodiment, the device utilizes a filter.
One preferred filter is a Savitsky-Golay filter (Savitsky &
Golay, Press et. al: Numerical Recipes). A filter can provide a
number of advantages. The discretization of position gives a finite
resolution of position based on the resolution of the encoder. In
the present invention, this resolution is 0.001 degrees. Filtering
enables displacement positions to fall between these increments.
Since the resolution is very high, this is particularly important
when using low-resolution encoders, with a low ncypr. Further,
filters can assist in the timing of data acquisition. Still
further, filters are useful in obtaining smooth first and higher
order derivatives of a discrete signal. A crude method to obtain
the derivative (slope or tangent) at a point in a discrete signal
is to take the difference between neighboring points and then
divide it by the sampling period. This is based on the assumption
that the two neighboring points are sufficiently close enough such
that the points in between lie on a straight-line between the two.
Sharp discontinuities in the derivative signal are observed using
this technique. As in most smooth signals, the present displacement
signal between any two points is actually a curve. Thus, the filter
utilizes a better technique to obtain derivatives by fitting a
polynomial through a window of neighboring points. The
Savitsky-Golay filter, for example, is a smoothing filter that is
useful when determining derivatives such as velocity and
acceleration offline when the raw displacement signal has already
been collected and stored. This smoothing technique fits a
polynomial to a moving window of data using least squares fitting.
Derivatives, as well as the function value, can be determined at
the center point of each window. Since the coefficients of the
fitted polynomial are linear in the data values, the filter
coefficients can be pre-computed. The filter coefficients are then
convoluted with the raw digital signal to obtain the actual
smoothed version of the raw waveform as well as well as its
derivatives at each center point.
[0279] The Savitsky-Golay algorithm operates as follows with the
following variables:
[0280] d.sub.raw: the column vector of actual displacement data
points
[0281] N: total number of points in the raw digital displacement
signal (rads)
[0282] ord: the order of the polynomial.
[0283] wins: the number of equally spaced points to be fit by the
polynomial, the size of the window. This number is always odd.
[0284] y.sub.i: a sub vector of d.sub.raw of length wins with i
being the index of the center point.
[0285] hw=(wins-1)/2: half width of the window.
[0286] The matrix X of dimension wins by (ord+1) is taken as 29 X
winsXord + 1 = - hw 0 - hw 1 - hw ord - 1 - hw ord - ( hw - 1 ) 0 -
( hw - 1 ) 1 - ( hw - 1 ) ord - 1 - ( hw - 1 ) ord 0 0 0 0 0 ( hw -
1 ) 0 ( hw - 1 ) 1 ( hw - 1 ) ord - 1 ( hw - 1 ) ord - hw 0 - hw 1
- hw ord - 1 - hw ord
[0287] The sum of the squared error, S, is minimized between the
elements of y.sub.i and y.sub.i, an estimate of y.sub.i:
y.sub.i=X*F*y.sub.i
[0288] where F is a (ord+1) by wins matrix. The sum of the squared
errors can be written as:
S=(y.sub.i-y.sub.i).sup.T*(y.sub.i-y.sub.i)=(y.sub.i-X*F*y.sub.i).sup.T(y.-
sub.i-X*F*y.sub.i)
[0289] A matrix F is evaluated such that the least possible
sum-squared error, S, is obtained. To do this, the derivative of S
is set with respect to F to 0, dS/dF=0. This yields the
pseudo-inverse solution,
F=(X.sup.T*X).sup.-1*X.sup.T
[0290] The columns of F are then reversed and the k.sup.th
derivative is then given by k! multiplied with the (k+1).sup.th row
of F divided by (dt_daq).sup.k convolved with the raw displacement
data. Before applying the Savitsky-Golay filter, the encoder count
signal is converted into radians. Since the resolution of the
encoder gives us 1000 counts for a degree of angle, the raw encoder
count signal is multiplied by 30 180000
[0291] to give the raw displacement data in radians in the column
vector, rawrads. In equation form, the i.sup.th element of the
k.sup.th derivative using the Savitsky-Golay filter is given as: 31
k ( r a w r a d s ) t k ( i ) = ( 1 t_ a q k ) * k ! * j = - h w h
w ( r a w r a d s i * F k + 1 , i + 1 - j )
[0292] A third order polynomial (ords=3) is used with a window size
of 21 points. Thus, F is a 4 by 21 matrix. From the equation above,
the i.sup.th element of the filtered displacement signal is given
as: 32 d i s p ( i ) = j = - 10 10 ( r a w r a d s i * F 1 , i + 1
- j )
[0293] the velocity signal is given as: 33 vel ( i ) = ( r a w r a
d s ) t ( i ) = ( 1 0.002 ) * j = - 10 10 ( r a w r a d s i * F 2 ,
i + 1 - j )
[0294] and the acceleration signal is given as: 34 acc ( i ) = 2 (
r a w r a d s ) t 2 ( i ) = ( 1 4 * 10 - 6 ) * 2 * j = - 10 10 ( r
a w r a d s i * F 3 , i + 1 - j ) .
[0295] Since the units of the elements in the raw rads vector are
in rads or radians, elements in the displacement, velocity, and
acceleration array are in rads, rads/s, and rads/s.sup.2
respectively. The beginning and the end of each vector are
truncated by a number of points equal to the half width of the
window. The frequency response of the Savitsky-Golay filter using a
third order polynomial with a window size of 21 points (0.04 s) in
the frequency domain can be seen using the freqz MATLAB function
which shows the Z-transform digital filter frequency response as
follows:
[0296] >>sav=sav_golay(3,21);
[0297] >>[h,f]=freqz(sav(1,:),1);
[0298] >>plot(f*500/(2*pi),abs(h),`k`);
[0299] This produces the frequency response plot shown in FIG. 28.
There is no phase lag since the window is symmetric with respect to
the point at which the polynomial is evaluated (center point).
[0300] Unlike digital signals, such as that from the encoder 24,
analog signals from torque transducers have high frequency noise
components that do not give a true representation of the actual
torque exerted. Low pass digital filters are often used offline to
attenuate the high frequencies in the torque signal. A zero lag
8.sup.th order digital Butterworth filter can be used to greatly
attenuate these high frequencies.
[0301] In MATLAB, [b,a]=butter(n, Wn) designs an order n lowpass
digital Butterworth filter with cutoff frequency Wn. It returns the
filter coefficients of length n+1 in row vectors b and a, with
coefficients in descending powers of z: 35 H ( z ) = B ( z ) A ( z
) = b ( 1 ) + b ( 2 ) z - 1 + + b ( n + 1 ) z - n 1 + a ( 2 ) z - 1
+ + a ( n + 1 ) z - n
[0302] The cutoff frequency is that frequency where the magnitude
response of the filter is {square root}{square root over ({fraction
(1/2)})}. For example, for MATLAB's butter function, the cutoff
frequency, Wn must be a number between 0 and 1, where 1 corresponds
to half the sampling frequency (the Nyquist frequency). A preferred
embodiment of the present invention uses a Wn of 0.075, which
corresponds to a cutoff frequency of 18.75 Hz (see getstatesgbw.m
in Appendix A). Normally, Butterworth filters have a phase response
where there is a lag between the filtered and the raw signal as a
function of frequency of the raw signal. In other words the
filtered torque signal is nonlinearly shifted in time with respect
to the original signal as a function of frequency. Thus, the
filtered torque signal also lags behind the encoder signal. These
phase lags are particularly significant in high order filters. This
lag is problematic because it is important for the torque waveform
to be synchronized with the position velocity and acceleration
waveforms in order to evaluate the parameters in the viscoelastic
model described herein. However, the filtfilt function in MATLAB is
prefereably used. y=filtfilt(b,a,x) performs zero-phase digital
filtering by processing the input data in both the forward and
reverse directions.
[0303] After filtering in the forward direction, the filtered
sequence is reversed and it runs it back through the filter. The
resulting sequence has precisely zero-phase distortion and double
the filter order (A. V. Oppenheim, and R. W. Schafer. Discrete-Time
Signal Processing. Englewood Cliffs, N.J.: Prentice Hall, 1989.
Pgs. 311-312).
[0304] Stiffness, viscosity, and inertial parameters are obtained
from position and torque signals obtained from the optical encoder
and torque transducer. Velocity and acceleration signals are also
required, as shown in equation 1. These signals are derived
inherently from the position signal via the Savitsky-Golay filter
described above. Filtering of the flexor and extensor EMG signals
is not crucial since these signals are not necessary for post
processing. However, monitoring live EMG information can be used to
monitor possible voluntary contractions. Ideally the muscle should
be fully relaxed before perturbing the wrist, since spasticity is
being measured, which is an involuntary reflex. Thus, the EMG
information can be used live to ensure proper integrity of the data
collected. Since flexor and extensor EMG activity is monitored, the
EMG data can also be collected and stored. Post processing on EMG
signals can be useful to answer more basic questions, such as the
investigating reflex delay times from the onset of single or
repetitive muscle perturbations to muscle contraction. Thus, the
total time it takes for the entire reflex loop can be measured.
Researchers have shown that two separate response times can be
measured, one due to spinal pathways to the spinal cord and back,
and one due to supra-spinal pathways which involve upper motor
neurons from the brain (See J. C. Houk: Participation of Reflex
Mechanisms and Reaction-Time Processes in the Compensatory
Adjustments to Mechanical Disturbances. Cerebral Motor Control in
Man: Long Loop mechanisms. Prog. clin. Neurophysiol., vol 4, Ed. J.
E. Desmedt, pp 193-215, Krager Basel, 1978; W. G. Tafton, P. Bawa,
I. C. Bruce, R. G. Lee: Long Loop Reflexes in Monkeys: An
Interpretative Base for Human Reflexes. Cerebral Motor Control in
Man: Long Loop mechanisms. Prog. clin. Neurophysiol., vol 4, Ed. J.
E. Desmedt, pp 229-245, Krager Basel, 1978). Naturally, the
supra-spinal response occurs after the spinal response.
[0305] EMG signals are extremely noisy, particularly if surface
electrodes are used. EMG signals measured with surface electrodes
are influenced by hair, oil, lotions and dead skin. The actual
action potentials sent to the muscles are internally amplified by
1000, typically resulting in a signal from 0 to .+-.5 V.
Preferably, internal to the Delsys 2-channel EMG unit is a 20-450
Hz band pass filter. Once the data is collected through the data
acquisition board and stored, further filtering is then performed
offline in MATLAB as follows.
[0306] First a moving root-mean-square (RMS) window is applied to
the raw output of the EMG signal where the size of the window is 15
points or 28 milliseconds. Thus, the k.sup.th sample point is of
the RMS EMG signal is equal to 36 E M G R M S ( k ) = 1 15 i = k -
7 k + 7 ( E M G R A W ( k ) ) 2
[0307] After the RMS EMG signal is obtained, it is passed through a
low pass butterworth filter as applied to the torque signal. The
result gives the final filtered EMG signal. The cutoff frequency
used in this butterworth filter is 37.5 Hz.
[0308] The displacement, velocity and acceleration signals using
the Savitsky-Golay filter on the encoder signal for each of the 10
trials are shown in FIGS. 30-29. The filtered torque and EMG
signals are also shown. Filtered data obtained from two cycles or
periods of each random displacement signal are used for further
processing.
[0309] Now all the proper state measurements 37 ( s ( t i ) , ( t i
) , . ( t i ) , and ( t i ) )
[0310] are known after the signal processing described above, and
the data can now be fit to the model of the present invention: 38 s
( t i ) = off + K H * ( t i ) + B H * . ( t i ) + J T * ( t i )
[0311] where .tau..sub.S is the filtered torque signal from the
transducer. K.sub.H and B.sub.H are the angular stiffness and
viscosity of the combined flexor and extensor muscle groups that
act on the wrist joint. J.sub.T is the combined inertia of
oscillating appendage, J.sub.H, and the rotating components of the
apparatus, J.sub.A. J.sub.T=J.sub.H+J.sub.A. .tau..sub.off, the
offset torque is equal to -K.sub.H*.theta..sub.RP as described
above. .theta. is the angular displacement of the system. 39 .
and
[0312] are velocity and acceleration, respectively which are the
first and second derivatives of displacement. The data was fit
using a linear least squares fit pseudo-inverse (See A. Bjorck,
Numerical Methods for Least Squares Problems, SIAM, Philadelphia,
1996; H. Anton, C. Rorres, Elementary Linear Algebra, Applications
version, sixth edition, Wiley & Sons, New York, 1991), as
follows. For a set of discrete samples, the following matrices are
constructed: 40 T s = | s ( t 1 ) s ( t 2 ) s ( t 3 ) s ( t n ) | n
.times. 1 and = | 1 ( t 1 ) . ( t 1 ) ( t 1 ) 1 ( t 2 ) . ( t 2 ) (
t 2 ) 1 ( t 3 ) . ( t 3 ) ( t 3 ) 1 ( t n ) . ( t n ) ( t n ) | n
.times. 4
[0313] It is possible to obtain the set of three parameters, 41 N ~
= o ^ ~ off K ~ H B ~ H J ~ T 4 .times. 1
[0314] that best fits the present model in equation 1: 42 S ( t i )
= off + K H * ( t i ) + B H * . ( t i ) + J T * ( t i )
[0315] using the pseudo-inverse which minimizes the sum squared
error, a positive scalar value. In matrix equation form the
sum-squared error can be written as:
SSE=(.sub.S-.O slashed.*).sup.T*(.sub.S--.O slashed.*)
[0316] The matrix P that minimizes SSE is evaluated as:
=pinv(.O slashed.)*.sub.S=(.O slashed..sup.T*.O slashed.).sup.-1*.O
slashed..sup.T*.sub.S [eq. 15]
[0317] First the pseudo-inverse is performed to obtain one set of
parameters utilizing all data over 2 whole periods (15.625 s or
n=7815) that construct one large .sub.S (7815.times.1) vector of
torque measurements and one large .O slashed. (7815.times.4) state
matrix. Let us denote the four evaluated parameters as {tilde over
(.tau.)}.sub.off, {tilde over (K)}.sub.H, {tilde over (B)}.sub.H,
and {tilde over (J)}.sub.T. These evaluated parameters for the
experiment DMJF whose data is shown below.
2TABLE 2 The use of overall data in each trial to obtain one set of
best-fit parameters for each trial for experiment DMJF. {tilde over
(.tau.)}.sub.off {tilde over (K)}.sub.H {tilde over (B)}.sub.H
{tilde over (J)}.sub.T Torque Offset Stiffness Viscosity Total
Inertia Trial [N * m] [N * m/rad] [N * m * s/rad] [kg * m.sup.2] 1
-0.03667 0.76224 0.05009 0.00687 2 -0.03744 0.76663 0.04372 0.00673
3 -0.03740 0.81638 0.04503 0.00682 4 -0.04743 0.89976 0.04170
0.00701 5 -0.04922 0.83478 0.04355 0.00701 6 -0.05149 0.88837
0.04229 0.00707 7 -0.06263 0.92421 0.04594 0.00720 8 -0.06939
0.89970 0.04502 0.00715 9 -0.06859 0.94812 0.05022 0.00730 10
-0.07785 1.01639 0.05268 0.00737 Average -0.05381 0.87566 0.04603
0.00705 Standard 0.01496 0.08074 0.00372 0.00021 dev.
[0318] To determine whether the model used in the present invention
to obtain overall parameters for each trial is a reasonable one,
the residual torque, .tau..sub.R is plotted. The residual torque is
the amount of torque that is unaccounted for by the model and for a
particular time sample. In equation form, it is defined as: 43 R (
t i ) = s ( t i ) - [ ~ off + K ~ H * ( t i ) + B ~ H * . ( t i ) +
J ~ T * ( t i ) ]
[0319] From the residual torque plots in FIG. 40, it is shown that
the amount of measured torque, .sub.S(t.sub.i) that is not
accounted by the model (the residual, .tau..sub.R(t)) is only about
4% on average. This demonstrates that the present model described
by equation 1 fits to the data well, even when estimating only one
set of parameters, {tilde over (.tau.)}.sub.off, {tilde over
(K)}.sub.H, {tilde over (B)}.sub.H and {tilde over (J)}.sub.T over
the entire data set in each trial. If, however the residuals are
large, this would indicate that the equation of the present model
is inadequate, or that a single set of time invariant, four
parameters applied to the state data 44 ( ( t ) , . ( t ) , and ( t
) )
[0320] over the whole trial is insufficient to describe the torque
output. In other words, if the residual is large using only one set
of time invariant parameters, the model may be good, but the
impedance parameters of torque offset, stiffness and viscosity may
be changing in time, within a given trial. To estimate how the
impedance parameters change within a given trial, rather than have
a single T.sub.S, P.sub.S and .PSI. matrix over the whole trial as
shown above, multiple T.sub.S, P.sub.S and .PSI. matrices can be
used by applying a smaller, one second moving window (501 samples)
over the data as follows. First it is assumed that the total
inertia does not change within each trial. This is a reasonable
assumption since the distribution of mass of the moving parts about
the center of the motor shaft does not change and the subject's
hand is secured in place with the vertical bars 6. For each trial,
{tilde over (J)}.sub.T is used, which is evaluated above as the
total inertia of the system. It is possible for the other three
parameters to change within a trial. For a particular point in
time, these now time varying parameters are denoted with subscripts
as .tau..sub.off(t.sub.i), K.sub.H(t.sub.i), B.sub.H(t.sub.i).
Using these time varying parameters and subtracting the torque due
to inertia results in a slightly modified equation of the model: 45
S ( t i ) - J T * ( t i ) = off ( t i ) + K H * ( t i ) + B H * . (
t i )
[0321] The torque data set with out the contribution of inertia is
now fit as follows: The data is fit using a linear least squares
fit pseudo-inverse similar to above, but this is performed multiple
times, once for each window as follows: 46 T si - J ~ T * i = s ( t
i - 250 ) - J ~ T * ( t i - 250 ) s ( t i ) - J ~ T * ( t i ) s ( t
i + 250 ) - J ~ T * ( t i + 250 ) 501 .times. 1 and i = 1 ( t i -
250 ) . ( t i - 250 ) 1 ( t i ) . ( t i ) 1 ( t i + 250 ) . ( t i +
250 ) 501 .times. 3
[0322] where i goes form 251 to 8064 that cover two periods of the
random trajectory or 15.63 seconds). For each i, the matrices 47 [
T si - J ~ T * i ]
[0323] and .O slashed..sub.i are obtained and P.sub.i is computed
for each i as follows: 48 N ~ i = ^ OFF ( t i ) K ^ H ( t i ) B ^ H
( t i ) 3 .times. 1
[0324] where P.sub.i is calculated similar to P above as
follows:
.sub.i=pinv(.O slashed..sub.i)*.sub.S.sub..sub.i=(.O
slashed..sub.i.sup.T*.O slashed..sub.i).sup.-1*.O
slashed..sub.i.sup.T*.s- ub.S.sub..sub.i
[0325] Since I goes from 251 to 8064, there are 7813 {circumflex
over (.tau.)}.sub.off, {circumflex over (K)}.sub.H, and {circumflex
over (B)}.sub.H values per trial. The mean and variance or standard
deviation of these values for each trial is determined. If the
standard deviation of these values: std{{circumflex over
(.tau.)}.sub.off(t.sub.i)}, std{{circumflex over
(K)}.sub.H(t.sub.i)}, and std{{circumflex over (B)}.sub.H(t.sub.i)}
are small, this indicates that the stiffness and viscosity of the
subject's flexors and extensors remain fairy constant within each
trial and the torque residuals of the time invariant model would be
small as shown in FIG. 40. Note also that the mean of the
time-variant impedance parameters values (denoted with the
{circumflex over (x)}) should be very close to the evaluated
time-invariant parameters (denoted with the {tilde over (x)}), that
is:
mean{{circumflex over (.tau.)}.sub.off(t.sub.i)}.apprxeq.{tilde
over (.tau.)}.sub.off;
mean{{circumflex over (K)}.sub.H(t.sub.i)}.apprxeq.{tilde over
(K)}.sub.H; and
mean{{circumflex over (B)}.sub.H(t.sub.i)}.apprxeq.{tilde over
(B)}.sub.H;
[0326] This is shown in FIG. 41.
[0327] The first row of bar plots in FIG. 41 show the results for
the torque offset, stifffiess, and viscosity parameters obtained
for each of the ten trials in experiment DMJF. The asterisk `*`
plots the values of {tilde over (.tau.)}.sub.off, {tilde over
(K)}.sub.H, and {tilde over (B)}.sub.H where one set of best-fit
parameters over the whole trial as described above. The location of
the tip of each bar graph represents mean{{circumflex over
(.tau.)}.sub.off(t.sub.i)}, mean{{circumflex over
(K)}.sub.H(t.sub.i)}, and mean{{circumflex over
(B)}.sub.H(t.sub.i)} where a set of {circumflex over
(.tau.)}.sub.off, {circumflex over (K)}.sub.H, and {circumflex over
(B)}.sub.H is obtained for each moving window of 501 data samples
as described above. The height of the error bar indicates the
standard deviation of these values, std{{circumflex over
(.tau.)}.sub.off(t.sub.i)} std{{circumflex over
(K)}.sub.H(t.sub.i)}, and std{{circumflex over
(B)}.sub.H(t.sub.i)}.
[0328] The eleventh bar shows a summary of all ten trials. The
asterisk on the eleventh bar shows the average of the ten {tilde
over (.tau.)}.sub.off, {tilde over (K)}.sub.H, or {tilde over
(B)}.sub.H values, or in equation form: 49 1 10 k = 1 10 ( ~ off
for trial k ) , 1 10 k = 1 10 ( K ~ H for trial k ) , and 1 10 k =
1 10 ( B ~ H for trial k )
[0329] The location of the tip of the eleventh bar is the average
of the height of the ten bar graphs, or in equation form: 50 1 10 k
= 1 10 ( mean { ^ off } for trial k ) , 1 10 k = 1 10 ( mean { K ~
H } for trial k ) , and 1 10 k = 1 10 ( mean { B ^ H } for trial k
)
[0330] As mentioned earlier, there are 7813 {circumflex over
(.tau.)}.sub.off, {circumflex over (K)}.sub.H, and {circumflex over
(B)}.sub.H values per trial. If all ten trials are grouped
together, then there are 78130 {circumflex over (.tau.)}.sub.off,
{circumflex over (K)}.sub.H, and {circumflex over (B)}.sub.H
values. The height of the error bar of the eleventh bar plot is the
standard deviation of all 78130 values.
[0331] Experiment DMJF was performed on the right arm of a control
adult subject tested at a bias of 0 degrees. Each control subject
was also tested at a bias position of degrees flexion. The bottom
row of graphs in FIG. 41 shows the results of parameters for two
sets of experiments, DMJF, and DNJF, as labeled on the left of the
graphs. The `M` in the parentheses, indicates that the subject JF
is a male. The bar graphs for experiment DMJF are plotted in white
(bias of 0 degrees) and bar graphs for experiment DNJF are plotted
in grey (bias of 30 degrees flexion) as indicated by the
legend.
[0332] The results of subject JF show that the stiffness values
when tested at a bias of degrees are markedly higher than when
tested at a bias of 0 degrees in all ten trials. The average {tilde
over (K)}.sub.H across all ten trials are 0.876 N*m/rad and 1.30
N*m/rad at a bias of 0 and 30 degrees respectively. The asterisks
on the eleventh bars show these values. Thus, the cumulative
stiffness of all the muscles acting on the wrist joint is 48%
higher at a bias of 30 degrees flexion.
[0333] Similarly, the viscosity values are markedly higher when
tested at a bias of 30 degrees flexion than at a bias of 0 degrees
for all ten trials. The average {tilde over (C)}.sub.H across all
ten trials are 0.0460 N*m*s/rad and 0.0714 N*m*s/rad at a bias of 0
and 30 degrees respectively and the cumulative stiffness of all the
muscles acting on the wrist joint is 55% higher at a bias of 30
degrees flexion.
[0334] The resulting torque offsets, {tilde over (.tau.)}.sub.off
tell us something very interesting. The first noticeable thing
about these values is not only that they are different in magnitude
but also opposite in sign. .tau..sub.off is an important variable
that tells us the angular position the hand prefers to be relative
to the selected bias position or origin, .theta..sub.0. If the bias
position was chosen to be the resting position of the wrist joint,
then in the equation below .theta..sub.RP=0,
.tau..sub.off=-K.sub.H*.theta..sub.RP
[0335] and ideally, .tau..sub.off would be 0 Nm. For a given
angular stiffness, the further the bias position is selected from
the preferred resting position of the wrist joint, the greater the
torque offset, .tau..sub.off will be. The preferred resting
position of the wrist joint is determined by the relative passive
stiffness of flexor muscle group to the extensor muscle group. It
should also be noted that .tau..sub.OFF is also dependent on the
stiffness K.sub.H. Since the active stiffness of muscles are
influenced when they are perturbed, .tau..sub.OFF is influenced by
these wrist perturbations or oscillations. If, however, the bias
position is very close to the resting position of the wristjoint,
.tau..sub.off will be very close to 0 Nm regardless of the
magnitude of K.sub.H since .theta..sub.RP.apprxeq.0. A positive
torque offset indicates that this contribution of torque is applied
in the clockwise direction by the subject's arm and a negative
torque offset indicates that this contribution of toque is applied
in the counter clockwise direction. This information is important
when interpreting the sign of {tilde over (.tau.)}off. The subject
JF's right arm was tested in experiments DMJF and DNJF. As shown in
the plots in FIG. 41, when tested at a bias of 0 degrees, the
torque offset values are very slightly negative. The mean overall
torque offset, {tilde over (.tau.)}.sub.off for all ten trials
shown by the asterisk on the eleventh bar is equal to -0.0538 Nm at
a bias of 0 degrees, and the contribution of torque by {tilde over
(.tau.)}.sub.off is in the counter clockwise direction. At a bias
of 30 degrees flexion, this value is equal to 0.110 Nm and the
contribution of torque by {tilde over (.tau.)}.sub.off in this case
is in the clockwise direction. This means that there is less
resistance in the wrist flexors at a bias of 0 than of 30 degrees
flexion and the resting position of the hand of the control subject
is close to the neutral flexion-extension position. The magnitude
of these numbers is small as compared to the torque offset values
in the spastic population as will be shown. It is important to note
that if contra-lateral left arm of the subject was tested instead,
then the sign of .tau..sub.off is expected to switch by virtue of
symmetry. Thus, in order to compare the left hand to the right
hand, if the left hand of a subject is tested, then the sign of
.tau..sub.off is switched. Hence, the sign of .tau..sub.off no
longer represents clockwise or counterclockwise torque. Rather, a
positive torque offset indicates that the contribution of
.tau..sub.off is in the direction towards the extension direction
of the hand being tested relative to the selected bias position.
Conversely, a negative torque offset indicates that the
contribution of .tau..sub.off is in the direction towards the
flexion direction of the hand being tested relative to the selected
bias position.
[0336] Now, the results of each individual control adult will be
shown. Either the left or right hand of 31 control adults was
tested, at a bias position of both 0 and 30 degrees flexion. 10 of
the subjects were male and 21 were female. The average age of
control subjects tested was 31.29, the youngest was 18 years of age
and the eldest was 60 years of age. The plots of the results for
each individual subject are shown in FIGS. 42-52. All graphs that
are plots of results of the same variable are plotted on the same
scale so that visual comparisons can be made.
[0337] As shown in FIGS. 42-52, when looking at the average of
{tilde over (.tau.)}.sub.off, {tilde over (K)}.sub.H and {tilde
over (B)}.sub.H over all ten trials for each experiment (denoted by
the asterisk over the eleventh bar labeled trial 11), the following
conclusions can be made. At a bias position of 0, the magnitude of
{tilde over (.tau.)}off across all ten trials, for all 31 subjects
is negligible, some being positive in value, some negative. This
indicates that the resting position of a control subject's hand is
very close to the neutral flexion/extension where muscles acting on
the wrist exhibit the least amount of tension. At a bias of 30
degrees the torque-offset values are significantly higher and
positive in sign. This indicates that the hand exhibits more
elastic tension at this bias position. The positive sign indicates
that the hand prefers to be at the neutral 0 degree bias position.
All 31 subjects had a higher stiffness at a 30 degree flexion bias
than at a 0 degree bias. 30 subjects had a higher mean viscosity
value at a 30 degree flexion bias than at a 0 degree bias. Only 1
subject (MT) had a lower mean viscosity value at a 30 degree
flexion bias than at a 0 degree bias. The average and standard
deviation (denoted by the height of the error bars) of {tilde over
(.tau.)}.sub.off, {tilde over (K)}.sub.H and {tilde over (B)}.sub.H
values across all control adults for each trail are shown in FIG.
53. The eleventh bar shows the overall average and standard
deviation across all control adults, across all ten trials.
[0338] Null-hypothesis significance tests can be used to
quantitatively test how significant these different observations
are between testing at the bias of 30 degrees flexion versus the
bias of 0 degrees. For each experiment, the mean {tilde over
(.tau.)}.sub.off, {tilde over (K)}.sub.H, and {tilde over
(B)}.sub.H are taken over the ten trials and these parameters are
separated into two groups according to bias position. Thus, there
are 31 mean{{tilde over (.tau.)}.sub.off}, mean{{tilde over
(K)}.sub.H}, and mean{{tilde over (B)}.sub.H} parameters for each
of the two bias positions. The null hypotheses test indicates that
the mean torque offsets, mean stiffnesses and mean viscosities are
not significantly higher at a bias of 30 degrees than they are at a
bias of 0 in control subjects. From the null hypothesis test, the
p-value is obtained, wherein the p-value is the probability of
observing the given result by chance given that the null hypothesis
is true. Small values of p cast doubt on the validity of the null
hypothesis. The probability of the null hypothesis stating that the
average torque offset values are higher at 0 than at 30 degrees is
true is p=9.2*10.sup.-4 The probability of the null hypothesis
stating that the average stiffness values are higher at 0 than at
30 degrees is true is p=2*10.sup.-5 The probability of the null
hypothesis stating that the average viscosity values are higher at
0 than at 30 degrees is true is p=4.2*10.sup.-5. Since a resulting
p-value of 5*10.sup.-3 is considered to be very significant, there
is no question that the increase in all three parameters {tilde
over (.tau.)}.sub.off, {tilde over (K)}.sub.H, and {tilde over
(B)}.sub.H is extremely significant when testing at a bias position
of 30 degrees flexion rather than 0 in the control adult subject
population.
[0339] Table 3 below shows the average and standard deviation of
{tilde over (.tau.)}.sub.off, {tilde over (K)}.sub.H and {tilde
over (B)}.sub.H values across all ten trials across all control
adult subjects which are indicated by the height of the 11.sup.th
bars shown in FIG. 53. Table 4 shows the range of average {tilde
over (.tau.)}.sub.off, {tilde over (K)}.sub.H and {tilde over
(B)}.sub.H values across all ten trials in the control adult
group.
3TABLE 3 {tilde over (.tau.)}.sub.off [N * m]: Bias Torque offset
{tilde over (K)}.sub.H [N * m/rad]: {tilde over (B)}.sub.H [N * m *
s/rad]: position towards extension Stiffness Viscosity 0 degrees
-0.0189 .+-. 0.0609 0.789 .+-. 0.309 0.0353 .+-. 0.0127 30 degrees
0.1667 .+-. 0.0936 1.305 .+-. 0.480 0.0512 .+-. 0.0175 flexion
[0340]
4TABLE 4 {tilde over (.tau.)}.sub.off [N * m]: Bias Torque offset
{tilde over (K)}.sub.H [N * m/rad]: {tilde over (B)}.sub.H [N * m *
s/rad]: position towards extension Stiffness Viscosity 0 degrees
-0.123 to 0.089 0.233 to 1.347 0.021 to 0.059 30 degrees 0.0241 to
0.361 0.482 to 2.345 0.0274 to 0.105 flexion
[0341] An additional observation from FIG. 53 is that when testing
at a bias of 0 degrees, the elastic stiffness increases from trial
1 to trial 10. As stated previously, trials 1 and 2 have a maximum
frequency component of 4 Hz, trials 3 and 4 have a maximum
frequency component of 5 Hz, trials 5 and 6 have a maximum
frequency component of 6 Hz, and trials 7 and 8 have a maximum
frequency component of 8 Hz. One hypothesis that can explain this
observation is that because velocities of the perturbations
increase with trial number, the primary afferents of the muscle
spindle sense these greater rates of muscle stretch in turn
activating the stretch reflex causing muscles to contract and
become stiffer. Thus, the hypothesis says that the combined active
stiffness of the muscles acting on the wrist may be increasing with
trial number. An observed increase in EMG activity at the greater
trial numbers supports this hypothesis. This trend, however, is not
shown at the bias of 30. This is likely because extensor muscles
are already active in all 10 trials as they are stretched to a
length further from the neutral position.
[0342] Many subjects with spasticity cannot be tested at a neutral
bias position of 0 degrees as they have difficulty extending their
wrist joint to that position. The resting configuration of the hand
of someone with spasticity is in the hyper-flexed position due to
hyperactivity of the flexor muscle group. Four adult patients with
hemiplegic spasticity were tested, AM, JS, SH, and BY, 3 males and
1 female. A hemiplegic patient is one where one side of his or her
body is affected by spasticity whereas the contra-lateral side is
practically unaffected or less affected. Because the contra-lateral
arm is unaffected or less affected, it can serve as a control to
the spastic arm when testing a patient with hemiplegic spasticity.
JS is a patient with Parkinson's disease, SH suffers from traumatic
brain injury due to a motorcycle accident, and BY is a patient who
severely lost function of his left hand after a stroke. AM's
affected arm was tested at a bias of 30 degrees flexion. For
subjects JS, SH, and BY the affected arms and unaffected
contra-lateral arms were tested, both at a bias of 30 degrees. The
results of these experiments are shown in FIGS. 54 and 55. Unlike
the figures showing results of the control subjects, all plots are
not on the same scale due to the large range in values. The white
bar graphs show results for the unaffected arm and the grey bar
graphs show results for the contra-lateral affected arm. Both arms
were tested at a bias of 30 degrees flexion.
[0343] Looking at the average of {tilde over (.tau.)}.sub.off,
{tilde over (K)}.sub.H and {tilde over (B)}.sub.H over all ten
trials for each experiment denoted by the asterisk over the
eleventh bar labeled trial I 1, the following conclusions can be
made. In the experiment with the unaffected hand at the bias of 30
degrees flexion, the average {tilde over (.tau.)}.sub.off across
all ten trials are comparable to what is seen in control subjects
when tested at the same bias. As in the control subjects, the
torque offset values are positive indicating that the unaffected
hand prefers to be at the neutral 0 degree bias position as in the
control subjects. However, when testing the affected, spastic side
at the 30-degree bias, the {tilde over (.tau.)}.sub.off values are
negative in sign and greater in magnitude. This indicates that the
preferred resting position of the subject's spastic wrist joint is
at a flexed position even greater than 30 degrees, as the hand is
pushing towards an even further flexed position. This phenomenon is
what is called hyper-flexion. This observation of increase in
magnitude and change in sign in the average {tilde over
(.tau.)}.sub.off across the ten trials when testing the affected
hand versus the unaffected hand is significant (p=0.0177). All 3
subjects tested on both arms have a higher average stiffness (mean
of {tilde over (K)}.sub.H across the ten trials) in their spastic
arm as compared to their contra-lateral arm (p=0.0743). When
comparing the average stiffness between contralateral arms, in
subjects JS, and SH, the difference is large. Also, in general, the
average viscosity, {tilde over (B)}.sub.H, across the ten trials is
greater in the affected hand when compared to the unaffected hand,
but the difference seen in viscosity values is not as great as the
difference seen in the stiffness values (p=0.199). Here, the
difference between the affected spastic arm is compared with the
unaffected contra lateral arm within the spastic group.
[0344] The average and standard deviation (denoted by the height of
the error bars) of {tilde over (.tau.)}.sub.off, {tilde over
(K)}.sub.H and {tilde over (B)}.sub.H values across all control
adults for each trail are shown in FIG. 56. The eleventh bar shows
the overall average and standard deviation across all control
adults, across all ten trials.
[0345] Table 5 below shows the average and standard deviation of
{tilde over (.tau.)}.sub.off, {tilde over (K)}.sub.H and {tilde
over (B)}.sub.H values across all ten FIG. 56. Table 6 below shows
the range of average {tilde over (.tau.)}.sub.off, {tilde over
(K)}.sub.H and {tilde over (B)}.sub.H values across all ten trials
in the group of adults with hemiplegic spasticity.
5TABLE 5 Hand tested {tilde over (.tau.)}.sub.off [N * m]: {tilde
over (K)}.sub.H {tilde over (B)}.sub.H (both at bias of 30 Torque
offset [N * m/rad]: [N * m * s/rad]: degrees flexion) towards
extension Stiffness Viscosity Unaffected 0.213 .+-. 0.0877 2.062
.+-. 0.820 0.0709 .+-. 0.0318 Affected -0.593 .+-. 0.471 3.858 .+-.
1.648 0.0992 .+-. 0.0447
[0346]
6TABLE 6 {tilde over (.tau.)}.sub.off [N * m]: Hand tested Torque
offset {tilde over (K)}.sub.H (both at bias of 30 towards [N *
m/rad]: {tilde over (B)}.sub.H [N * m * s/rad]: degrees flexion)
extension Stiffness Viscosity Unaffected 0.144 to 0.281 1.220 to
2.857 0.0343 to 0.0916 Affected -1.1008 to 2.606 to 6.284 0.0694 to
0.166 -0.161
[0347] Tables 5 and 6 show that at the bias position of 30 degrees
flexion, the average parameter values of the unaffected or less
affected arms of the hemiplegic population are still somewhat
higher than when compared to the control population. This
demonstrates that the tone of the less affected side of the patient
group in the is still greater on average than what would be seen in
the control group, though this difference is of course greater when
comparing the severely affected side of the hemiplegic population
with the control population. This is a fairer comparison since
subjects in the control group have no known neurological disorders.
When comparing the hemiplegic subjects to the controls, the
observation of the negation of sign and increase in magnitude of
the average torque offset values, {tilde over (.tau.)}.sub.off
across the ten trials shown by the 11.sup.th bars are extremely
significant (p=3.0*10.sup.-10). The increase in average stiffness,
{tilde over (K)}.sub.H and viscosity, {tilde over (B)}.sub.H values
across the ten trials when compared across populations are also
extremely significant (p=1.5*10.sup.-8 and p=6.5*10.sup.-5
respectively).
[0348] On average, the stiffness and viscosity values across all
trials of the control group were 1.305 N*m/rad and 0.0512 N*m*s/rad
respectively. The corresponding stiffness and viscosity values of
the severely affected side of the hemiplegic population were 3.858
N*m/rad and 0.0992 N*m*s/rad respectively. These elevated values
when compared to those of the control group are extremely
significant (p=1.5*10.sup.-8 for stiffness and p=6.5*10.sup.-5 for
viscosity).
[0349] While the device and method have been described in detail
for use in quantifying muscle tone, particularly in the wrist, in a
spastic patient, the invention is not so limited. Rather, the
device and method are useful on both the upper and lower
extremities including, for example, the ankle. Thus, for example,
the device could be modified to suit the leg and ankle accordingly.
Further, the method and device can be used to measure muscle tone
in the non-spastic patient. For example, the method and device can
be used to measure rigidity in a patient. Further, the method and
device could be used in analyzing a patient's muscle tone in line
with, for example, physical therapy that the patient is undergoing
to regain control of the muscles in the legs after a spinal
accident.
[0350] Although a preferred embodiment of the invention has been
described using specific terms, such description is for
illustrative purposes only, and it is to be understood that changes
and variations may be made without departing from the spirit or
scope of the following claims.
* * * * *