A STATIC DYNAMOMETER MEASURING SIMULTANEOUS
TORQUES EXERTED AT THE UPPER LIMB
P Boissy, M.Sc.1-2 , D Bourbonnais, PhD 1-2, D Gravel, PhD1-2, AB Arsenault,
PhD1-2 & M Leblanc Eng, MA
1- Research Center, Montreal Rehabilitation Institute
2- School of Rehabilitation, Faculty of Medicine, University of Montreal
Please address correspondence and requests for reprints to:
Dr. Daniel Bourbonnais
Research center,
Montreal Rehabilitation
Institute
6300 Av. Darlington,
Montreal, Quebec,
Canada
H3S 2J4
Phone number (514) 343-2094
Fax number (514) 343-2105
This work was supported by the FRSQ and NHRDP
Running title: Static dynamometer
ABSTRACT
The majority of available dynamometers are designed to measure force or
torque in one specific direction, one joint at a time. For the quantification of
motor incoordination in neurological patient populations, these dynamometers
provide limited information about the global behavior of the limb under
investigation. This report describes the potential use and function of a static
dynamometer measuring torques exerted simultaneously at the shoulder (flexionextension, abduction-adduction, internal-external rotation), elbow (flexionextension) and forearm (pronation-supination).
Orthogonal forces were measured at the arm and wrist using strain gauge
transducers interfaced with a laboratory computer.
The lever arms were
specified to a software program and the joint torques were calculated in real time
according to static equilibrium equations.
The use of the dynamometer is
illustrated by characterizing for one hemiparetic subject, the joint torques
recorded at the shoulder, elbow and forearm during isolated submaximal grip
exertions at different force levels on both sides. The torques generated at the
shoulder, elbow and forearm during the hand grip tasks on the affected side were
significantly higher than those obtained on the non-affected side and increased
with the grip force level.
These differences probably reflect the loss of movement selectivity observed
following a lesion in the central nervous system. Further studies are currently
being undertaken in neurological patient populations to characterize and quantify
motor deficits using this dynamometer. As a long term goal, we hope that the
method and technologies described here will contribute to the evaluation and
rehabilitation of these populations.
INTRODUCTION
Dynamometry is widely used in the assessment of muscle function in normal
and pathological populations [1-6].
Isometric grip and pinch strength
assessments are commonly used to evaluate hand strength for disability ratings
and to assess responses to various forms of therapy [7-9].
Isokinetic
dynamometry allows for the measurement and improvement of muscular
performance of various muscle groups in dynamic conditions [10-13]. Clinically,
hand-held dynamometry is now increasingly employed to measure motor
performance in patients with neurological disorder [14-17].
While these dynamometers provide accurate and reliable readings, generally
they can only measure forces or torques exerted in a single plane of movement
and in one joint at a time. In order to quantify neuromuscular deficits at the upper
limb, a static dynamometer allowing simultaneous measurement of shoulder
torques (flexion-extension, abduction-adduction, internal-external rotation), elbow
torques (flexion-extension) and forearm torques (pronation-supination) was
developed. The design of this dynamometer was adapted from previous work
[18]. In this report, the original characteristic of this dynamometer, namely the
simultaneous multidirectional measurement of joint torques at the shoulder,
elbow and forearm will be illustrated by recording torques on the affected and
non-affected upper limbs of one hemiparetic subject during hand grip tasks.
Some details of the dynamometer have been presented in abstract form [19].
METHOD
Overview
The subject was seated in a wheelchair with his trunk secured with straps. The
wheelchair is positioned on a uniform X-Y grid marked off on the support surface
and immobilized by a breaking mechanism limiting forward and backward sways.
A back support system was used to ensure that the subject’s back remained
straight. The upper limb was placed and secured in two fixation rings (Figure 1).
These rings were made of two semi-circular padded metallic structures tightened
together with a Velcro strap. Two sets of rings with different diameters were
used depending on the girth of the subject’s upper limb. The rings were rigidly
mounted by means of force transducers to plates attached to a metallic structure
bolted on the floor. The anchor points fixing the transducers to the plates are
spaced 12mm apart in the X and Y axis. The plates themselves can be moved
horizontally and vertically. In order to accommodate subjects with different
anthropometric characteristics, the position and angulation of the transducers on
the plates and the plates themselves can be changed. The range of possible
joints configurations goes from 0° to 135° in elbow flexion and from 0° to 90° in
shoulder abduction and shoulder flexion. For repeated measurements, the
anterior-posterior and lateral positions of the center of the wheelchair chair in
relation to the force transducers as well as the positions of the force transducers
on the plates are recorded by taking the X-Y coordinates of the transducers on
the plates and the position of the wheelchair on the floor. This allows us to place
the subject in approximatively the same position (i.e. coordinates) from one
experiment to another.
-INSERT FIGURE 1 AROUND HERE-
Force transducers
Two force transducers, using strain gauge technology, recorded forces
exerted proximally at the distal end of the humerus arm level and distally at the
wrist. The arm transducer consisted of a dynamometric ring measuring forces in
the Z-direction and a cantilever structure measuring forces in the X and Y
directions. The mechanical dimensions of the transducer were 60 mm for the
width of the inner ring, 4.5 mm for the thickness of this ring and 22.7 mm for the
thickness of the cantilever rod. These dimensions permitted the measurement of
force components up to 900 N in X, Y, Z axis. The voltage output from the
transducer was evaluated during successive loading of each orthogonal axis of
transducers (X, Y, Z). Linear regression analysis was used to compute factors
(intercept and slope) converting voltage output to force values for the axis tested.
This transducer was found to be linear, reliable and accurate and showed no
cross-sensitivities. The hysteresis of the transducers was estimated to be 0.2%.
Further details on this transducer characteristics can be found elsewhere [18].
Distally, a tridimensional sensor (AMTI, MC3-6-500) was used to quantify
forces exerted at the lower end of the forearm as well as the forearm torques in
pronation-supination.
The cross-sensitivities for each orthogonal axis of this
commercial transducer were corrected using the sensitivity matrix provided by
the company. The maximal force component of this transducer in the two axes
used was 1100 N. The maximal force component of both transducers is well over
the range of typical maximal static upper limb force recorded in normal
populations. The gain of the amplifiers in the different axes were set to
approximatively 31 N/V. Since the range of the voltage input of the 12 bits
resolution A/D card (Metrabyte Dash 10) range from -10 V to 10 V, the resolution
of the system is estimated at 0.2 N/Analog-to-digital converter units or according
to the equation :
10V − (− 10V )
2
12bits
= 4.88 mV ADCu X 31 N V = 0.2N
Mechanical model
Coordinate systems
The joint torques exerted in each anatomical plane of movement at the
shoulder, elbow and forearm were calculated according to equilibrium equations
derived from static force analysis.
The coordinate systems used in the
mechanical analysis are illustrated in Figure 2. Three body coordinate systems
are defined (scapula, elbow and wrist). For the local coordinate system of the
scapula, with the upper limb straight, forearm in neutral position with the thumb
pointing forward (Figure 2 frontal view), the Y axis is oriented along the
longitudinal axis of the arm and the X axis is oriented anteriorly while the Z axis is
orthogonal to the X and Y axes. The origin of the system of coordinates of the
scapula is the center of rotation of the glenohumeral joint (i.e. scapula X0, Y0, Z0).
Force vectors at the arm and wrist transducers are defined as FX’, FY’, FZ’and
EX’’, EY’’, EZ’’ respectively. The torque in pronation-supination at the forearm
transducer is defined as Ty.
Angles and lever arms
The angle β is the abduction angle of the shoulder defined by the Y and Z
axes (Figure 2 frontal view), the angle α is the flexion angle of the shoulder
defined by the X and Y axes (Figure 2 lateral view) and the angle λ is the
rotation angle of the shoulder defined by the X and Z axes (Figure 2 upper view).
The angle A (Figure 2 lateral view) is the flexion angle of the elbow defined in
the X and Y axes and C is the angle of pronation-supination of the forearm
defined in the X and Z axes (Figure 2 upper view). With the wrist in a neutral
position, the lateral epicondyle of the elbow is considered as a projection of the
center of rotation of the elbow. The position situated at 1 cm lower to the upper
limit of the head of the humerus is considered as the projection of the center of
rotation of the shoulder. The lever arm l is defined as the distance between the
transducer at the wrist and the center of rotation of the elbow, LL as the distance
between the center of rotation of the elbow and the center of rotation of the
shoulder and L as the distance between the arm transducer and the center of
rotation of the shoulder.
-INSERT FIGURE 2 AROUND HERE-
Rotational matrix
Using this system of reference, transformation equations were computed to
calculate torques, expressed in reference to the system of origin (X0, Y0, Z0),
according to forces measured at the forearm transducer (FX’, FY’, FZ’) and arm
transducer (EX’’, EY’’, EZ’’). The rotational sequence used to determine the
transformation equations starts with a rotation around the Z axis, followed by a
rotation around the Y axis and ends with a rotation around the X axis.
Forces were transposed from forearm to elbow with the following matrix:

cos χ cosα

[X′
′
,Y ′
′
,Z ′
′
]− sinα cos β + sinβ sin χ cos α
 sin α sin β + cos β sin χ cos α

cos χ sinα
cosα cos β + sin β sin χ sin α
− cosα sin β + cos β sin χ sinα
− sin χ 

X′
, Y′
, Z′
]
sin β cos χ  = [

cos β cos χ
Where the forces are transposed from the elbow to the shoulder with the
following matrix:
cos C cos A
[X ′
,Y ′
, Z′
] − sin A

sinC cos A
cos C sin A
cos A
sin C sin A
− sin C 

0
X, Y, Z ]
=[

cos C 
Simplified equations
In this experiment, the elbow was flexed (A = 90o) with the shoulder at a
position where C= 0o,α=0o, β=30o and the forearm supinated (C=30o).
angles were measured with a manual goniometer.
All
In these conditions, the
general static equilibrium equations can be simplified. The simplified equations
used in this experiment to compute the torques exerted at the shoulder, elbow
and forearm in respect to the coordinates system of the scapula are defined
below where:
a) The muscular torque exerted in flexion-extension of the shoulder is
expressed as:
S1′= l
(E x cosC + E z sinC )− LL E y + l F x
(Equation 1)
b) The muscular torque exerted in abduction-adduction of the shoulder is
expressed as:
S 2 ′= − LL(E z cos C −
(Equation 2)
E x sin C )−
Ty − L
Fz
c) The muscular torque exerted in internal-external rotation of the shoulder is
expressed as:
(E z cosC − E x sin C)
S 3′
=−l
(Equation 3)
d) The muscular torque exerted in flexion-extension of the elbow is expressed
as:
E1′= l(E x cos C +
E z sin C )
(Equation 4)
e) The muscular torque exerted in pronation-supination of the forearm is
expressed as:
E 2 ′= [
− Ty]
(Equation 5)
Torque computation
As required by the mechanical analysis, the lever arms of the arm (L, LL) and
forearm (l) were measured following the subject’s limb positioning in the fixation
rings and then specified to the computer program. The lever arms were identified
by positioning markers on pre-determined locations (anatomical sites identified
by palpation and positions on the force transducers) and measuring the distance
between each marker with an antropometrical caliper [Lafayette Instrument,
Model 01290]. Using a desktop computer (IBM-AT) and an acquisition card
(Labmaster, model PGH), voltage values from the strain gauge amplifiers were
digitized at a frequency of 50 Hz. The computer program, using lever arms and
force values converted from calibration factors, calculates, in real time, muscular
torques exerted in each specific anatomical plane of movement of the shoulder,
elbow, and forearm according to static equilibrium equations.
Correction for Ty
In addition, the value of Ty was recalculated to take into account the geometry
of the structure of the transducer at the wrist. Indeed, the component of the force
in flexion-extension of the elbow (Ex) will produce a torque at the wrist transducer
in supination and pronation respectively. This torque will be proportional to the
magnitude of the force Ex and to the distance between the wrist and the
reference point of the AMTI transducer which is fixed in the experiment at 15 cm.
Therefore, the torque in pronation-supination is calculated by substracting the
torque measured by the transducer from the product of the force in flexionextension of the elbow and the constant value of the lever arm.
Protocol
To illustrate the use of the dynamometer, ipsilateral torques produced at the
shoulder, elbow and forearm were recorded in one hemiparetic during isolated
grip tasks at different levels of maximal voluntary grip force (MVGF) executed
alternatively on both sides (affected vs non-affected). From clinical observations,
these isolated grip tasks have been shown to trigger involuntary movements (or
net joint torques) in the affected upper extremity of spastic hemiparetic subjects.
It was expected that the present dynamometer would be able to characterize the
muscular torques associated with these involuntary movements.
The subject is a 42 years old male who suffered an hemoragic left cortical
lesion resulting in a right side hemiparesis 6 years ago. His motor performance,
as evaluated by the Fugl-Meyer Upper limb scale [22] was 28 out of 66 and he
showed a marked increase in elbow, wrist and finger flexor tone. The MVGF of
the subject was determined as the mean of three trials realized two minutes
apart. Using this value as a reference, targets representing 65%, 75% and 85%
of the MVC grip were displayed alternatively on a monitor in front of the subject.
The subject was asked to reach the target and maintain it for 5 seconds using
visual feedback on the grip force signals. Three trials were repeated at oneminute intervals and the second trial was kept for analysis.
Analysis
For each experimental condition, the torques recorded in the first 200 ms of
each exertion were not considered in the analyses and net joint torques were
averaged during the interval ranging from 0.2 s to 5 s. Ipsilateral torques at the
shoulder, elbow and forearm during hand grip exertions on the affected side and
on the non-affected side for one hemiparetic subject at three force levels are
compared in figure 3. The spider graphs were plotted using averaged torques
computed in each anatomical plane of movement of the shoulder, elbow and
forearm from a constant time interval (i.e. 0.2 s- 5 s). Each radial axis
corresponds to a specific upper limb torque direction. In these graphs, the
amplitude of each ipsilateral torque appears on the concentric lines. The outer
limit of the graphs for the non-affected and affected sides corresponds to 10 Nm
and 30 Nm respectively.
RESULTS
For both sides evaluated, the pattern of ipsilateral torques observed during the
grip tasks was similar with the exception of the torque in shoulder flexionextension which was in flexion for the unaffected side and in extension for the
affected side.
The results indicate that the amplitude of the torques at the
shoulder, elbow and forearm during a grip task varied according to the side
(affected vs non-affected) on which the subject executes the task.
-INSERT FIGURE 3 AROUND HEREWhereas the highest mean torque on the non-affected side was generated in
elbow flexion (9.2 Nm) at 85% of the MVGF, mean torques generated in internal
rotation and abduction of the shoulder and flexion of the elbow on the affected
side at 85% MVGF reached 29.7 Nm, 20.1Nm and 17.5 respectively. The
amplitude of the torques also varied with the level of grip force exerted.
In
general, the torque values on both sides, with the exception of the torque
obtained in shoulder extension on the affected side, increased with the level of
grip force exerted. On the non-affected side, the torque increases were less
evident and there was no obvious pattern of torque combinations across force
levels.
DISCUSSION
Sources of error for torques computations
Lever arm
The sources of errors in the measurements of the external lever arms are the
estimation of the position of the center of rotation of the joints in relation to the
external anatomical markers and the measurement of the lever arms itself. The
measurement of the lever arms assumes that the center of rotation of the
glenohumeral joint, elbow joint and radius-cubital joint corresponds to a
determined set of external anatomical markers (cf Figure 1). The actual positions
of the center of rotations in relation to these anatomical markers are prone to
errors. Furthermore, the lever arm values are measured by taking the distance
from one external anatomical marker to another or distances from one
anatomical marker to the center of rotation of the force transducers with an
antropometrical caliper. Difficulties, particularly when trying to localize the head
of the humerus in subjects with thick cutaneous tissues can arise and results in
errors.
Forces
The most important source of errors for force measurements are the angular
and translational displacements of the upper limb segments due to the shift of
soft tissues within the fixation rings. Theses displacements can produce errors in
the measurement of the resultant forces within the rings because forces may be
applied in other planes than the reference planes of the transducers. In addition,
they change the lever arm values taken from one anatomical marker to the
center of rotation of the transducers.
Fast casting of
wrist segment has shown promising results in limiting
movement of soft tissues at forearm attachment. It can also drastically improve
the comfort of the subject in the forearm fixation ring. Unfortunately, this practice
is time consuming. Since installation in the dynamometer, adjustment of upper
limb segment, measurement of lever arms and angles require a substantial
amount of time, casting is best prescribed for repeated measurements where the
cast can be done once and re-used on numerous occasions.
Error estimates
Although, force measurements using the transducers are prone to errors,
these errors are negligible assuming accurate calibration [18]. However, due to
slight angular displacements of the upper limb within the fixation rings during
exertion, the resultant forces within the ring may be applied in other planes than
the references planes of the transducers. We estimate that these shifts of force
components from one plane to the other are of the order of 15°, introducing an
error of 3 % on the force. The axial displacements of the upper limb within the
fixation rings also contribute to an error in the value of lever arm. The
approximate displacements observed (n=5 subjects) at the wrist and arm fixation
attachments during upper limb exertions in the X axis are 1 and 2 cm for the
forearm transducer and the arm transducer respectively. This error contributes
approximatively to an error ranging from 4% to 10% depending on the value of
the lever arm measured.
Total relative error
To summarize, the total relative error on upper limb torque measurements
during exertion can be determined as the root mean square of the relative errors
in force (3%) and lever arm measurements used in the torque computations (4%,
6% %, 10%). For example, the total relative error for torque computed in elbow
flexion or shoulder internal-external rotation according to static equilibrium
2
2
equations would be equal to 3.98 + 3 = 4.98% . As the number of lever
arms used in the equations rises so does the total relative error of the computed
torque. For torques computed in shoulder flexion-extension and abductionadduction, the total relative error is estimated to be 10 % and 12 % respectively.
Clearly the accuracy of torque measurement would be greatly enhanced by both
a more accurate measurement of the lever arm and a more secure positioning of
the upper limb in the fixation rings.
Applications of the apparatus
This dynamometer offers attractive perspectives for the quantification and
analysis of upper limb muscular coordination.
In this paper, the use of the
dynamometer was illustrated by characterizing shoulder, elbow and forearm
torques during hand grip exertions performed bilaterally at different grip force
levels in one hemiparetic subject. While performing the hand grip tasks on his
unafected side, the hemiparetic subject was generally capable of executing an
isolated power grip with little or no extraneous activity at other joints. In contrast,
significant torques, particularly in shoulder abduction, shoulder internal rotation
and elbow flexion were observed when he performed the same tasks with his
affected limb. These torques also increased with the levels of grip force exerted.
Individuals with hemiparesis often exhibit difficulty performing selective
movements [20].
Movements are rather executed in global and inflexible
patterns closely related to the spastic posture of the subject. Torques produced
on the affected side may appear locked or bound in a stereotyped pattern. In
contrast, healthy subjects can perform selective and coordinated movements that
are adapted to the task requirement. In this study, the differences in the patterns
of the torques generated during the hand grip tasks on the affected side and on
the non-affected side of the hemiparetic subject reflect the loss of movement
selectivity on the affected side following a lesion in the central nervous system.
Obviously, this multi-directional and bi-articular dynamometer could also serve
as a tool to characterize and evaluate single efforts in hemiparetic and normal
subjects. The dynamometer was used successfully to study the EMG power
spectrum of the biceps brachii during linearly increasing static elbow exertions in
normal subjects and hemiparetic subjects [21]. This apparatus is also suitable for
the evaluation and characterization of global synkineses seen in hemiparetic
patients.
Global
synkineses
are
pathological
non-purposive
associated
movements on the involved side of hemiparetic subjects that are triggered during
a voluntary movement. Although it is generally considered that the capacity of
hemiparetic subjects to control synkineses is an index of their motor performance
[22], few studies have used quantitative measures to characterize them. A recent
study using this dynamometer provided a quantitative assessment of the
kinematic and electromyographic patterns of global synkineses in hemiparetic
patients and their correlates with clinical observations [23].
An interesting avenue for the use of this dynamometer is to reeducate motor
performance of the upper limb in hemiparetic patients by providing feedback of
the involuntary torques generated simultaneously at the shoulder, elbow and the
forearm during multi-joint efforts.
With the increasing successful use of
biofeedback in the treatment of motor deficits in neurological patient populations
[24], the characteristics offered by this dynamometer may help to improve
function of the upper limb in these populations. A pilot study to assess the
efficacy of a reeducation program based on the use of the dynamometer on
chronic hemiparetic patients is now underway [25].
We hope that the
characteristics of this dynamometer will prove useful in promoting not only gains
in upper limb strength but also have an impact, through increased coordination,
on the control of voluntary movement.
CONCLUSION
This paper presents a bi-articular dynamometer that allows the simultaneous
measurement of multidirectional torques exerted at the shoulder, elbow and
forearm. The dynamometer was used to contrast control strategies of upper limb
segments of an hemiparetic subject during hand grip exertions. For similar level
of grip force produced, the torque amplitude and pattern at the shoulder and
elbow were different depending on the side of the grip tasks. This new method
offers interesting research potential in motor control, motor learning and
evaluative research in rehabilitation sciences and can also be used in
biofeedback therapies for treatment of upper limb motor deficits in neurological
patient populations.
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ACKNOWLEDGMENTS
The authors wish to thank P. Duval for his technical assistance. This project
was funded by the FRSQ and NHRDP. P. Boissy and D. Bourbonnais are
supported by the FRSQ.
FIGURE CAPTIONS
FIGURE 1. General overview of the static bi-articular dynamometer.
FIGURE 2. Coordinates systems for the derivation of the static equilibrium
equations used to compute the torques.
FIGURE 3. Typical pattern of ipsilateral upper limb torques (Nm) exerted during
a hand grip on the non-affected side and on the affected side at a) 65%, b)
75%, c) 85% of the maximal voluntary contraction for one hemiparetic subject.