ovid_ glenohumeral joint kinematics and kinetics for three coordinate system representations during...

[Research Articles]

American Journal of Physical Medicine & Rehabilitation

Número: Volume 78(5), September/October 1999, pp 435-446

Copyright: © 1999 Lippincott Williams & Wilkins, Inc.

Tipo de publicación: [Research Articles]

ISSN: 0894-9115

Registro: 00002060-199909000-00006

Palabras clave: Wheelchair, Spinal Cord Injury, Three-Dimensional Kinematics, Inverse Dynamics, Repetitive Strain Injury

GLENOHUMERAL JOINT KINEMATICS AND KINETICS FOR THREE COORDINATE SYSTEM

REPRESENTATIONS DURING WHEELCHAIR PROPULSION1

Cooper, Rory A. PhD2; Boninger, Michael L. MD; Shimada, Sean D. PhD; Lawrence, Brad M. MS

Información sobre el autor1 From the Human Engineering Research Laboratories; Veterans Affairs Pittsburgh Healthcare System (RAC, MLB, BML),

Pittsburgh, Pennsylvania; Departments of Rehabilitation Science and Technology (RAC, MLB), and Bioengineering (RAC, MLB),

University of Pittsburgh, Pittsburgh, Pennsylvania; Division of Physical Medicine and Rehabilitation, Department of Orthopaedic

Surgery (RAC, MLB), University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania; and Biomechanics Laboratory (SDS),

Department of Health and Physical Education, California State University, Sacramento, California.

This research was partially supported by the U.S. Department of Veterans Affairs, Rehabilitation Research and Development

Service (B869-RA), Paralyzed Veterans of America, and Eastern Paralyzed Veterans of America.

2 All correspondence and reprint requests should be addressed to: Human Engineering Research Laboratories (151-R1), VA

Pittsburgh Healthcare System, 7180 Highland Drive, Pittsburgh, PA 15206.

ABSTRACT

The shoulder plays a very important role during manual wheelchair propulsion. Unfortunately, substantial

numbers of manual wheelchair users eventually develop shoulder injury or pain. Recently, studies have begun to

investigate the etiology of wheelchair user shoulder injuries. This study compared three coordinate systems used

to represent the shoulder during wheelchair propulsion. Our results show statistically significant differences

between the three shoulder representations analyzed. Differences are seen for individuals and for the subjects as

a group. Based upon our results, the fixed-z model appears preferable over the other representations due to its

simplicity, low hardware requirements, and the similarity of the results to the free representation. This article

also provides some insight into maximal shoulder joint forces and moments recorded during manual wheelchair

propulsion. Future work should include more sophisticated models of the shoulder complex.

Manual wheelchair propulsion is an important form of mobility for millions of people with lower extremity

impairments. To maximally benefit from a manual wheelchair, the interaction with the user must be optimized.

Optimization requires proper measurement, selection of features, positioning, and training.1-3 Only recently have

the tools become available to thoroughly study the biomechanics of wheelchair propulsion. These tools include

devices for measuring the pushrim forces in three-dimensions,4-6 system for simulating wheelchair propulsion,7, 8

and a system for measuring the motions of the arms in three dimensions.9 The data acquisition and control of

these systems must be coordinated to obtain valid and clinically useful data.

The shoulder is a complex joint that plays an important role in manual wheelchair propulsion. Investigators

have been working for several years to characterize shoulder kinematics and kinetics to address the injuries

experienced by manual wheelchair injuries and to improve propulsion efficiency. Few studies have presented

motions of the shoulder during wheelchair propulsion.10, 19 There have been studies that have described

wheelchair propulsion technique and analyzed wheelchair propulsion efficiency.11-15 Pushrim forces have also

been reported.8, 11, 15-18, 27, 28 A few articles address the dynamic forces borne by the wrist during wheelchair

propulsion.6, 8, 15, 27 Data have been published on a quasi-static study of the complex shoulder model that

included the scapula and clavicle.18 Limited data regarding dynamic shoulder forces and moments during

wheelchair propulsion have been reported.19, 28

This investigation had the following purposes:

1. to represent shoulder kinematics and kinetics during manual wheelchair propulsion using a sternum-based rigid-

body reference;

2. to calculate glenohumeral joint motion motion, shoulder net forces, and shoulder net moments in 3-D; and

3. to compare the representation of the glenohumeral joint presented in this article with methods restricting

trunk motion to the sagittal plane and to a fixed global reference frame.

For the purposes of this study, we refer to the three coordinate system representations as free, global, and

fixed-z. The free coordinate system representation is developed in a later section and detailed in the Appendix.

This representation assumes that shoulder motion can be referenced to a rigid-body fixed at the sternum. The

global coordinate system representation refers to the common practice of assuming that the trunk is fixed to a

laboratory reference (i.e., vertical, horizontal, and transverse). The fixed-z coordinate system representation is

used to define shoulder motion when the trunk is restricted to move in the sagittal plane only (i.e., no trunk

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rotation). During this study, we concentrated on glenohumeral joint motion. We did not attempt to investigate or

represent movements of the scapula, clavicle, or thoracic gliding. Our simple ball and socket model of the

shoulder with the resulting net forces and moments may be all that is necessary to adapt wheelchair designs to

reduce the incidence of shoulder injuries.

This study was designed to test the following hypotheses:

1. peak glenohumeral joint net forces would be significantly (p < 0.05) different for the three coordinate system

representations;

2. peak glenohumeral joint net moments would be significantly (p < 0.05) different for the three coordinate

system representations; and

3. the range of glenohumeral joint angles would be significantly (p < 0.05) different for the three coordinate

system representations.

Representing and recording shoulder motion during wheelchair propulsion is important for understanding the

mechanisms that contribute towards injuries. Moreover, this information should lead to new therapies, better

positioning, and improved wheelchair design.

EXPERIMENT DESIGN

Subjects

We only used data from people who used wheelchairs as their primary means of mobility. This population was

selected as the long-term goal of this research is to improve wheelchair design and set-up, and previous studies

have shown that there are differences between propulsion technique among people with and without disabilities.

Data from six subjects with paraplegia due to complete spinal cord injury were used to examine the methods

presented in this article. The three women and three men had spinal cord injuries below T-4, which ensured that

arm motion was not neurologically impaired. Each subject gave informed consent to voluntarily participate in his

study. Before participating in this study, each subject completed a medical history questionnaire. The average

age of the subjects tested was 31.7 ± 6.1 yr. The subjects had been using a wheelchair an average of 11.3 ± 2.0

yr. The mean body mass for the subjects was 80.0 ± 14.4 kg. Each subject propelled his or her personal

wheelchair during testing.

Anthropometric Model

Segment lengths were determined using the anatomical landmarks recommended by Drillis et al., who showed

measurements based upon palpable bony landmarks are highly correlated with measurements from a cadaver

study.21 The dimensions obtained from the palpable bony landmarks were then used to develop the segment

mass, segment center of mass, and segment inertial properties from Hanavan's model utilizing Clauser et al.'s

multistep weight distribution regression equations.23 Hanavan developed a 15-segment model based on modeling

segments as an ellipsoid: head, elliptical cylinders; upper and lower trunk, solid spheres; hands and frustra of

right circular cones, the remaining portions of the arms and all segments of the legs.22 Hanavan also used Barter's

regression equations to develop a set of equations for determining individual segment center of mass locations

and moments of inertia about the three principal axes of each segment. A set of anthropometric data including

lengths, diameters, and circumferences were required to determine segment parameters for individual subjects.

Our study included the mass, center of mass, and inertias of the hand, forearm, and upper-arm. This

anthropometric model is not specific to individuals with spinal cord injury. However, it is among the best

available, given that anthropometric data specific to people with spinal cord injuries are unavailable.

Kinematics for Inverse Dynamic Model

Anatomical glenohumeral motion is defined by motion of the humerus with respect to the trunk. To

determine three-dimensional glenohumeral motion, both humerus and trunk (sternum) local coordinate systems

must be defined. The humerus coordinate system was defined by three unit basis vectors; is, js, and ks (see Fig.

1). The unit vector, js, lies along the long axis of the humerus which is defined using markers 2 and 3 as shown in

Figure 2. Equation (1).



Figure 1. Diagrams showing the global and local coordinate systems used to describe shoulder net joint forces and

moments.

Figure 2. Marker placement for analysis of shoulder motion during wheelchair propulsion.

Equation 1

The unit vector, ks, is defined as the vector perpendicular to the plane that is formed by the humerus and

forearm. The unit vector, ks, is calculated by the cross-product of the unit vector, js, and a unit vector lying

along the forearm segment. The final unit vector, is, is defined by the cross-product of js and ks: Equation (2).

Equation 2

The second local coordinate system defines the trunk segment. The markers creating a vertical vector on the



trunk rigid body (markers 5 and 6), defines the first unit vector: Equation (3).

Equation 3

The unit vector, kt, is calculated by the cross-product of the unit vector jt and the unit vector lying along

the horizontal line on the sternum rigid body (marker 4 and 5). The last unit vector, it, is defined as the cross-

product between jt and kt: Equation (4). Now since we have defined the two local coordinate systems: Equation

(5).

Equation 4

Equation 5

We can calculate simplified shoulder anatomical flexion/extension, abduction/adduction, and horizontal

flexion/extension angles by rotating the humerus, is, into the trunk coordinate system, see equation (6). Because

the coordinates defining the orientation of the humerus are orthogonal, any one of the basis vectors can be used

to determine the angles examined in this paper.1, 20, 27 Equation (6). The result of equation (6) can be

represented by equation (7). Equation (7) Simple shoulder flexion/extension is described by: Equation (8) while,

simple shoulder abduction/adduction is defined as: Equation (9). The simple shoulder horizontal flexion/extension

angle was also calculated. The angle is defined as: Equation (10).

Equation 6

Equation 7

Equation 8

Equation 9

Equation 10

The internal/external angle of the simplified shoulder is described by rotating the humerus so that it is in

alignment with the unit vector, kt. This is done in two rotations. First we must rotate the humerus parallel to the

it and kt plane by finding the angle [sigma]: Equation (11). Using the rotation matrix 1, 20, Rk, Equation (12), we

then rotate the humerus by: Equation (13). Then the angle, [delta], is calculated in order to rotate the humerus

parallel to the jt and kt plane: Equation (14). Using the rotation matrix Rj, Equation (15), we rotate the humerus

once again by: Equation (16).



Equation 11

Equation 12

Equation 13

Equation 14

Equation 15

Equation 16

Finally, the rotated unit vector, ks, is projected into the it and jt components of the trunk coordinate

system. This defines internal/external rotation: Equation (17).

Equation 17

This technique transforms the three-dimensional motion that is involved with internal/external rotation into a

two-dimensional motion. This method simplifies the description of internal/external rotation.

Kinetics from a Global Framework

To calculate the net joint kinetics of the glenohumeral joint, the masses, center of masses, and inertias of

the limb segments of the arm are required. In addition, a model of each of the joint of the arm is required. For

this study, ball and socket joints were used. The limb segments were assumed to be rigid with constant

anthropometric parameters (e.g., mass and center of mass). Furthermore, the linear and angular positions, angular

velocities, and linear and angular accelerations must be known as time-series. Lastly, the external forces acting

on the limbs must be known. Net joint force/moment equations can be derived from the free-body diagrams of

link segment models. However, the equations of motion can be programmed in any number of forms: some more

efficient than others. A numerically stable algorithm for efficiently computing three-dimensional net muscle

moments and net joint forces for n-degree of freedom link-segment models will be presented. A matrix approach

was used to develop an algorithm for computing three-dimensional net muscle moments and net joint forces. The

similarity of the structure of the free-body diagrams for link-segment models was exploited.

The inertia's (Ip) about the x, y, and z axis of the fixed reference (i.e., global frame) frame are related to the

inertia's (Is) of the segment about axes fixed to the limb by a homogeneous rotation matrix. The vector triad

(iworld, jworld, kworld) is fixed to the reference along laboratory x, y, z axes and another orthogonal triad (isegment,

jsegment, ksegment) is fixed to the moving segment, any arbitrary finite rotation can be expressed in terms of the

Euler angles ([psi], [theta], [script phi]) (see Fig. 3).1, 20 Equation (18)



Figure 3. Relationships of angles and axes between a body segment and the global coordinate system.

Equation 18

The angular accelerations about the proximal end, [alpha]x, [alpha]y, [alpha]z, are the second derivatives of

each segment absolute angle about the appropriate axis. The centripetal acceleration component of the

moments is found from the cross-product of the inertia matrix with the angular velocity vector. Equation (19)

Equation 19

The joint reaction forces and moments can be determined using a matrix equation with the following

definitions: Equation (20) The variables defined above can be combined to form a single matrix equation. Equation

(21)

Equation 20



Equation 21

Equation (21) can be used to calculate three-dimensional net muscle moments and joint reaction forces for a

particular "snap-shot" of a single segment.1 Currently, post processing is the only means of determining muscle

moments and joint reaction forces. This is due to limitations in image processing systems, and the integration of

kinetic and kinematic data. When post processing, all of the anthropometric, kinematic, and most distal link

segment kinetic data are available. Most systems store this data in matrix format. The kinetic data set for the

most distal link-segment is defined as the reaction matrix. Equation (22)

Equation 22

The accelerations (linear and angular) for each joint segment can be written as an acceleration matrix.

Equation (23)

Equation 23

The mass and moment arms of the Earth's gravitation can be combined into a single matrix for each joint-

segment. Equation (24)

Equation 24

Selecting the form of the kinematic data matrix can improve the efficiency of the algorithm. Equation (25)

Equation 25

All of the matrices are of the proper dimension to calculate the muscle moments and joint reaction forces.

However, the reaction matrix requires some preconditioning which makes the post-processing algorithm slightly

more complex than the real-time algorithm. Equation (26) end (Equation 29) end

Equation 26



Equation 29

The variable q represents the joint-segment index, and n is the number of joint-segments of interest in the

model. The most distal joint-segment is defined as joint 1, typically a metacarpophalangeal joint. The algorithm in

equation (26) would be run to calculate the joint reaction vector for joint-segments of interest. This approach is

computationally efficient because the matrix structure takes advantage of computer data structures. The

algorithms only require simple matrix multiplication and addition. The matrices are triangular or block diagonal

which further simplifies computation. All transformations are numerically stable. The algorithms were implemented

in Matlab (The Mathworks Inc., Natick, MA).

Net Glenohumeral Joint Kinetics in an Anatomical Reference System

The reaction forces at the shoulder are referenced to the humerus (see Fig. 1). These forces are determined

using the results from the absolute joint reaction forces, which are a product of the algorithm presented in

equation (21) and the coordinate transformation matrix for the shoulder local coordinate system presented in

equation (5). The shoulder joint reaction forces, referenced to the trunk (sternum), may be determined using

equation (27), Equation (27)

Equation 27

The net moments about the shoulder joint were expressed in terms of the humerus coordinate system (see

Fig. 1). This is accomplished by using the results of equation (21) and the homogeneous transformation matrix for

the trunk presented in equation (5). The shoulder joint net reaction moments, referenced to the trunk, may be

determined using equation (28), Equation (28)

Equation 28

Both equation (27) and equation (28) contain homogeneous rotation matrices. This is because the local

coordinate systems for the trunk and humerus can be viewed as rotated versions of the global coordinate system

with all axes sharing a common origin at the glenohumeral joint.1 This is possible because the net joint forces and

moments for the shoulder are first calculated in the global coordinate frame. With this foundation, the net forces

and moments can be transformed from one coordinate system to another in order to provide more clinically

relevant orientations. The "right-hand rule" was used to define positive forces and moments.

Experimental Protocol and Kinetic Data Collection and Conditioning

Pushrim force/moment data were collected from the SMARTWheel at 240 Hz and filtered at 30 Hz.25 The

kinetic data filter was an eighth-order, zero-phase digital Butterworth type. For the purposes of this study, the

propulsion phase was defined as the period when the moment about the hub, Mz, deviated more than 5% from

baseline, until it once again returned to baseline and remained within 5%. We have previously described two- and

three-dimensional versions of a force and torque sensing SMARTWheel.4, 6 During this experiment, a standard

polished and anodized aluminum pushrim of 0.2667 m radius was mounted to each wheel. Standard gray rubber

tires 61 cm (i.e., 24 inch) diameter with width 3.5 cm (i.e., 1.375 inches) were used. A foam insert was used in

place of a pneumatic tube. Each subject propelled his/her own wheelchair attached with a SMARTWheel at 1.8 m/s

(4 mph) on a wheelchair dynamometer for 5 min. The wheel position, wheel alignment, and wheel camber were

the same as those for the subject's standard wheelchair wheels. The resistance of the dynamometer was set

equivalent to rolling over a smooth tile floor.24 Subjects were asked to propel their wheelchair on the

dynamometer for at least 5 min to become accommodated to the experimental set-up. After the accommodation



period, subjects were asked to propel their wheelchairs at 1.8 m/s with a power output of 15 W. Data were

collected for 20 s after the person had maintained the desired speed for at least 10 s.

Kinematic Data Collection and Conditioning

Motion data were collected with a six-camera OptoTrac active infrared marker motion analysis system

(Northern Digital Inc., Waterloo, Ontario, Canada) at 60 Hz and filtered at 6 Hz. The motion data filter was an

eighth-order, zero-phase digital Butterworth type. The filter type, order, and cut-off frequency were determined

using the discrete-Fourier-transform and power-spectral density estimate. Linear and angular velocities and

accelerations were determined using finite difference methods based upon a Taylor-series expansion. We used a

computer-generated synchronization pulse to align sampling of motion and pushrim force/moment data. The

kinematic data were selected coincident with the propulsion phase defined by the kinetic data. This eliminated

the need to estimate from kinematic data whether the hand was in contact with the pushrim. Markers were

placed over each subject's acromion process, lateral epicondyle, olecranon process, ulnar styloid, radial styloid,

second metacarpophalengeal joint, and fifth metacarpophalangeal joint (see Fig. 2). These makers locations have

been used successfully in previous studies. There is a theoretical potential for "gimble-lock" (i.e., an

indeterminent axial rotation), but this unlikely due to anatomical constraints. Two carbon fiber composite rigid

bodies, which included three infrared LED markers each, were used to track and record head and sternum

motion (see Fig. 2). The markers on the rigid body used to record sternum motion are approximately 10 cm apart

from one another. The sternum rigid body was designed to rest firmly against the sternum for both male and

female subjects. The motion analysis system was calibrated before each use with a rigid body aligned with the

vertical, horizontal, and transverse axes of the laboratory. This permitted us to track the head and sternum rigid

bodies with respect to laboratory coordinates. Before recording motion data, each subject was filmed with the

markers in a static position, and a rigid-body stylus was used to identify anatomical landmarks with respect to the

markers. These data were used to compensate for joint centers and determine the location of anatomical

landmarks in laboratory coordinates.

Statistical Analysis

Joint angles and the anatomically based forces and moments in three dimensions were analyzed for 10

propulsion strokes. Variables were analyzed among individual subjects across the three coordinate system

representation and for the six subjects as a group. During the group analysis each subject's data for the 10

strokes were averaged. The average across the 10 strokes was used to represent a subject. Each stroke is not an

independent variable; collecting multiple strokes and averaging yields a stroke that is representative of that

individual. Therefore, each subject's data could be treated as being independent when comparing models.26 A

two-step approach was used to determine the reliable parameters across multiple strokes.26 First, the interstroke

reliability was evaluated by interclass correlation coefficients ([rho]). A parameter was considered reliable and

consistent if the interclass [rho] was greater than 0.60.26, 27 Second, for parameters that met the inter-stroke

reliability coefficient criteria, Cronbach's coefficient alpha was computed to determine the increased reliability

of creating aggregated scores across multiple strokes. A summed score was considered to have high reliability if

alpha was greater than 0.80.26, 27 The apriori selection of the acceptable [rho] and Cronbach's coefficient alpha

was based upon a previous study of the wrist.27 Analysis of variance (ANOVA) with Scheffé post-hoc analysis was

used to compare reliable shoulder angle, force, and moment variables between the three models. A P < 0.05 was

considered statistically significant. The same global data were used to represent each subject. Therefore, the

differences in the results for an individual are due solely to the representation chosen.

RESULTS

All of the variables proposed in the introduction for comparison had interclass correlation coefficients ([rho])

greater than 0.60 and Cronbach's coefficient alphas greater than 0.80. Therefore, no variables were excluded

from further analysis.

Shoulder Angles

The mean and standard deviation of the maximum angles from all subjects for each of the three shoulder

angle coordinate representations are presented in Table 1. ANOVA found significant differences among the group

in maximum shoulder abduction between the free model and global representations (P = 0.007) as well between

the free and the fixed-z representations (P = 0.026). Our data also indicated significant difference between the

free and the global representations for maximum external rotation (P = 0.038) and between the global and fixed-z

representations for maximum internal rotation (P = 0.044) among the group of subjects. The group showed no

significant differences between the three representations (i.e., free, global, fixed-z) for maximum sagittal

extension, maximum sagittal flexion, and maximum horizontal flexion. None of the subjects went into shoulder

adduction or horizontal extension with any of the three representations.

TABLE 1 Maximum angles for shoulder motion using selected models for wheelchair propulsion

When the maximum shoulder joint angles for the three representations were compared for each individual,

several statistically significant differences were detected, see Table 2. At least one subject showed a significant

difference for every maximum shoulder angle across all representations. The greatest number of differences (n =

32) were observed between the global and the fixed-z representations. There were also 29 cases where the free



representation resulted in significant differences with respect to the global representation. The greatest number

of differences (n = 17) were recorded for sagittal extension angles.

TABLE 2 Significant differences (P < 0.05) between shoulder angles for the three models for each subject

individually

Glenohumeral Joint Net Forces

The mean and standard deviation of the maximum forces from all subjects for each of the three shoulder

coordinate representations are presented in Table 3. Statistical analysis revealed significant differences between

the free and both other representations (P < .001) for maximum compressive forces (i.e., forces acting on the

shoulder in the medial direction) among the group data. No other significant differences were found.

TABLE 3 Maximum forces in Newtons for shoulder motion using selected models for wheelchair propulsion

ANOVA revealed a number of significant differences (P < 0.05) between the maximum shoulder forces among

individuals across representations (e.g., free, global, fixed-z). The largest number of differences (n = 20) were

recorded between the free and the global representations (see Table 4). The second largest number of

differences were observed between the global and fixed-z representations. The greatest number of differences

(n = 16) were demonstrated for the maximum posterior to anterior force.

TABLE 4 Significant differences (P < 0.05) between shoulder forces for the three models for each subject

individually

Glenohumeral Net Joint Moments

The mean and standard deviation of the maximum moments from all subjects when resolved with each of the

three shoulder coordinate system representations are presented in Table 5. There were no significant

differences (P < 0.05) between the maximum moments between any of the models used in the study among this

group of subjects.

TABLE 5 Maximum moments in Newton · meters for shoulder motion using selected models for wheelchair

propulsion

The analysis of shoulder maximum moments among individuals across strokes revealed several statistically

significant differences (P < 0.05). The greatest number (n = 15) of differences were recorded between the free

representation and the global representation (Table 6). The next greatest number of differences were observed

between the free and the fixed-z representations. Most differences between coordinate systems for individual

subjects were attributable to the maximum adduction moments.

TABLE 6 Significant differences (P < 0.05) between shoulder moments for the three models for each subject

individually

DISCUSSION

A primary focus of our work is on the investigation of injury mechanisms. With this focal point in mind,

representing the shoulder must lead to consistent biomechanical variables that are alterable and that are

correlated with injury mechanisms. The goal is to find consistent biomechanical variables that when optimized will

lead to a lower probability of developing a shoulder injury. This study contributes to the development of robust

methodologies that enable forces, moments, and motion at the shoulder to be characterized for wheelchair

propulsion. All of the variables selected for comparison in this study had interclass correlation coefficients

greater than 0.60 and Cronbach's coefficient alpha greater than 0.80.



In the current study, all forces and moments were recorded at the pushrim with 7 degrees of freedom. In

addition, all measurements were made in each subject's personal wheelchair, whereas previous studies used

either a standardized wheelchair or ergometer. We know of no other wheelchair study that fulfills all of these

criteria. The time-series data for the shoulder angles, forces, and moments exhibited similar shapes for all

subjects. The greatest similarity was between the fixed-z and the free coordinate systems. One would expect the

force and moment time-series curves to be similar for the three representations when the angle time-series

curves are similar. There were no apparent differences in the timing of the maxima across the three selected

coordinate systems. The shoulder angle time-series data for each stroke produced a single hump or valley,

whereas the force and moment time-series data during each stroke showed more oscillatory behavior with two or

more local maxima. In nearly all cases, the shoulder forces and moments expressed a minima or maxima coincident

with the minima or maxima of the shoulder angles. The relationship between angle and force/moment minima and

maxima should be investigated further in a future study.

During a study of 16 manual wheelchair users propelling at a freely chosen speed, Rao et al. found humeral

elevation (i.e., abduction-adduction) to vary from 22.5 to 56.6°.10 As in our study, their subjects did not go into

adduction. The humeral plane angle (i.e., sagittal flexion-extension) was found to vary between -57.3 and 23.2° on

average. They found internal rotation to exhibit a maximum mean of 86.2°. Their data did not present external

rotation on average as did ours. The mean of the peak values are similar to those found in present study and are

closest to those results for the global model, which is similar to the shoulder model used in their study. The

differences are likely due to changes in marker systems, differences in speed, and variations in the fit of the

wheelchairs.

While investigating wheelchair propulsion with fatigue, Rodgers et al. reported shoulder kinetic and kinematic

data.19 They found shoulder flexion/extension range of motion (ROM) to be between 60 and 70°. Our shoulder

flexion/extension data are similar. They found shoulder abduction/adduction ROM to be about 20°. This is about

half the ROM exhibited by our subjects. This difference could be due to the smaller pushrim size (radius = 0.19 m)

and altered seating position used in their study. It is not possible to compare the kinetic data because of the way

they presented their data.

There is no "gold standard" for wheelchair propulsion kinematics and kinetics. All studies (including this one)

of the shoulder have made simplifying assumptions for trunk motion due to the inability to accurately record

trunk motion in three dimensions. To attempt to address this limitation, we developed a carbon-fiber rigid-body

that attaches to a subject's sternum. The light weight and stiffness of the rigid-body makes accurate

measurement of sternum motion possible without causing discomfort for the subject or altering motion patterns.

This permits trunk motion at the sternum to be recorded in three dimensions, eliminating the need to fix the

trunk to a global coordinate system. The orientation of the rigid-body with respect to the laboratory coordinate

system must be determined apriori using static calibration against a known three-dimensional reference. Without

a trunk mounted marker system (e.g., rigid-body), investigators have either fixed the trunk to a global coordinate

system (i.e., no trunk flexion/extension and no trunk rotation) or fixed the trunk to the global transverse axis

(i.e., trunk flexion/extension but no trunk rotation). Our methods relax these assumptions and allow for greater

trunk motion. However, the results of the fixed-z representation and the free representation are similar in many

cases. This would suggest that for some studies the fixed-z representation may be desirable, because of its

greater simplicity. Moreover, the fixed-z representation can be applied without using a sternum mounted rigid-

body. However, the free model provides results more similar to those of more complex shoulder

representations.29

None of the studies reviewed, including our work, directly measured the forces and moments in the

shoulder. For our study a ball and socket model was used. Net forces and moments are relevant, but only

represent limited information. All biomechanical models give an approximation of the net joint forces and

moments. More detailed representations of the shoulder complex may be necessary to determine injury

mechanisms. Van der Helm and Veeger have been developing more complex models of the shoulder that lead to

greater understanding of shoulder joint degeneration during wheelchair propulsion.29 Their approach is to

attempt to obtain more accurate estimates of the internal forces acting upon the shoulder. It is certainly

valuable research to develop more complex models of the shoulder. However, greater complexity does not, in

itself, guarantee greater accuracy or clinical relevancy.

The use of body-mounted markers inherently introduces some measurement error. Methods must continue to

be developed to reduce this error. The reliance on anthropometric studies of people who were not wheelchair

users or who had no physical disability limits the accuracy of net joint moment and force estimates during manual

wheelchair propulsion. Another limitation of this study is the small sample size, which reduces its generalizability

and statistical power. Additional reliable parameters could be found with a larger sample size and a greater

number of strokes. However, all of the variables selected apriori for comparison during this study were found to

be consistent (i.e., interclass correlation coefficients greater than 0.60 and Cronbach's coefficient alpha greater

than 0.80). Our model clearly makes simplifying assumptions for the shoulder. However, it is a step toward

reducing the number of constraints and providing clinically meaningful data. The approach taken in this study

could serve as a beginning for standardized data collection and presentation. This will allow all members of the

research community to benefit from the increasing pool of data that could help to address shoulder pain and

injury among manual wheelchair users. The results of this paper provide a contribution to the normative data for

wheelchair propulsion shoulder forces and moments.

Future studies must address whether the variables presented in this study are sufficient in discriminating

between activities (e.g., speed, starting, turning) and if they are correlated with the development of injuries or

pain (e.g., longitudinal clinical trials). It is also important to determine whether the variables are alterable through



available interventions (e.g., positioning, pushrim changes, wheel changes, and training). This study shows that

the forces and moments for the three representations are similar. However, the individual data are more variable.

A larger sample of subjects must be tested to determine whether interindividual differences are significant. The

majority of reports in wheelchair propulsion have used body-mounted markers and not rigid-body markers. This

may have an effect on the accuracy of the motion recorded. However, investigators must weigh the clinical

efficacy of their methods against the complexity of them.

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Documentos Enlace OPAC Enlaces Bibliograficos [Context Link]

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(Appendix) [Context Link]



APPENDIX Definition of Variables and Symbols



APPENDIX No caption available.



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APPENDIX No caption available.

Key Words: Wheelchair; Spinal Cord Injury; Three-Dimensional Kinematics; Inverse Dynamics; Repetitive Strain

Injury

GALERÍA DE IMÁGENES

Figure 1

Figure 2

Equation 1



Equation 2

Equation 3

Equation 4

Equation 5 Equation 6

Equation 7

Equation 8 Equation 9 Equation 10

Equation 11

Equation 12

Equation 13

Equation 14

Equation 15

Equation 16

Equation 17

Figure 3

Equation 18

Equation 19

Equation 20

Equation 21

Equation 22 Equation 23 Equation 24

Equation 25

Equation 26

Equation 29

Equation 27 Equation 28

Table 1

Table 2 Table 3 Table 4



Table 5 Table 6

APPENDIX Definition ...

APPENDIX No caption ...

APPENDIX No caption ...

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