Download Application of a large-scale musculoskeletal upper limb model

APPLICATION OF A LARGE-SCALE MUSCULOSKELETAL UPPER LIMB
MODEL: ANALYSIS OF FORCES AT THE GLENOHUMERAL JOINT
Iain W. Charlton and Garth R. Johnson
Centre for Rehabilitation and Engineering Studies (CREST), Department of Mechanical, Materials &
Manufacturing Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK
INTRODUCTION
There is currently little knowledge of the loading patterns of the bones and muscles of the shoulder girdle.
Despite the existence of complex upper limb models, they have only recently been used to study the
loading of the joints during tasks of daily living. Studying activities of daily living is vital in
understanding the range of kinematics, load bearing and stability required of the upper limb in order to
assess, rehabilitate and repair the variety of injuries and disabilities which can effect function.
A previous study of ten important everyday tasks (Murray, 1999) yielded kinematic and dynamic data for
the shoulder, elbow and wrist. This dynamic model has been extended to include the clavicle and scapula
and is used in conjunction with a large-scale musculoskeletal model in the calculation of joint contact
forces.
Applying such a complex, large-scale musculoskeletal model containing many and varied muscles,
ligaments, bones and joints presents unique challenges.
METHODS
A musculoskeletal model was developed using SIMM (Musculographics, IL, USA) and morphometric
data available in the literature. 74 muscular elements crossing the glenohumeral and scapulothoracic
joints were included, plus the coracoclavicular and costoclavicular ligaments. Skeletal geometry was
derived from the Visible Human data set, yielding bone surface models and geometry parameters defining
joint centres and muscle wrapping shapes.
Clavicle and scapula kinematics were simulated using regression equations developed by Marchese
(2000) and Barnett (1996) respectively. A model input optimisation algorithm was used to close the
scapulothoracic joint (modelled as an ellipsoid fitted to the posterior rib cage) and simulate the effect of
the conoid ligament on clavicle axial rotation by maintaining it at a fixed length.
Following calculation of the net forces and moments by the recursive Newton-Euler method, equations of
motion were formed using muscle vector output from SIMM.
The primary difficulty in large scale musculoskeletal modelling is of course redundancy. A unique
solution to the equations of motion for muscle and joint forces was found in this case by minimising the
sum of square muscle stresses.
Ligament forces are also allowed in the model, being included as variables in the optimisation, (but not in
the cost function). Upper and lower bounds on ligament forces were imposed based on the most severe
and more conservative proposed stress-strain characteristics found in the literature respectively.
Further consideration is given to glenohumeral stability by incorporating a constraint allowing the contact
force to pass only through the glenoid. Dynamic muscle properties, excitation and activation are also
accounted for by solving a combined 2nd order ODE to give upper and lower bounds on muscle force
based on the previous state of the model.
RESULTS AND DISCUSSION
Figure 1 shows the glenohumeral force for a single subject to be of around 400N for most tasks and 400N
to 800N for those involving heavy objects (lifting a 0.5kg block to head height).
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Gamma ( )
Force (N)
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Time (% cycle)
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X
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Total
(a) Reach from Table to Opposite Side of Neck.
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Gamma( )
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Force (N)
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Time (% cycle)
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Beta ( )
(b) Lifting a 0.5kg Block to Shoulder Height.
Figure 1. Glenohumeral Contact Force during Tasks of Daily Living (expressed in the global
frame: X = lateral, Y = superior and Z = posterior). The polar illustrates the locus of the contact
force (glenoid rim shown as an ellipse).
The magnitude of the glenohumeral force is quite constant, as is its direction, passing mainly through the
central part of the glenoid for low intensity tasks. Interaction with objects gave a larger range of force
magnitude although the “envelope” of the glenohumeral force vector remained surprisingly constant,
although shifted more towards the posterior portion of the glenoid. This suggests that the normal
glenohumeral joint is remarkably stable during tasks of moderate load bearing.
The influence of individual morphology on the results is rather less distinct; the result of simply morphing
a single data set to each subject anthropometrically is as yet unknown. The effect of subtle changes in,
particularly the rotator cuff muscles, is to be established through a sensitivity study.
Two important aspects of the data capture and processing have a possible impingement upon the model
results - the accuracy of the capture method itself and the model input optimisation algorithm. The
sensitivity of the input optimisation algorithm to the estimation of the shape of the scapulothoracic joint is
demonstrated in Figure 2. The shape of the underlying rib cage is estimated from 3 external
measurements of the maximum thorax width, depth at this level and vertical distance from this level to
C7. Sensitivity of the kinematics results for the mean measurements to plus and minus the SD (N=3) is
illustrated using the mean RMS differences between the kinematics of the modified thorax model and the
“average” model for abduction and forward flexion tasks.
O
Mean RMS Difference +SD ( )
3.5
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Clavicle Axial
Rotation
Clavicle
Protraction
Clavicle
Elevation
Width
Scapula
Backward Tip
Depth
Scapula
Protraction
Scapula
Lateral
Rotation
Height
Figure 2. Sensitivity of the Model Input Optimisation Algorithm to External Thorax Measurements
(mean RMS difference explained in text).
This confirms that the lateral rotation of the scapula (i.e. the scapulohumeral rhythm) and axial rotation of
the clavicle are affected very little by subtle changes in the input optimisation algorithm parameters.
Despite this, there is no guarantee that the variations actually correspond to “real” inter-subject
differences in the kinematics and individually measuring the shoulder girdle kinematics of each subject
would be invaluable in future studies. However, the influence of small changes in angles in the SC, AC
and GH joints is unlikely to have a dramatic effect on the muscle and joint forces calculated due to the
(probably) small changes in muscle moment arms they will cause.
One other modelling issue was found to be of significance: ligament modelling. Firstly the conoid
ligament is essential in maintaining clavicular equilibrium against the axial rotation moments of the
deltoid and trapezius muscles. Secondly, the trapezoid ligament force was found to prevent the force in
the AC joint from being too far out of alignment with the long axis of the clavicle and was hence shear
limiting. The costoclavicular ligament was found to have a similar effect on the SC joint. Finally,
excessive forces in the trapezoid ligament, which can be due to overestimation of the modulus or
underestimation of the rest length, had an interesting effect on scapular equilibrium. The excessive
backward tipping moment caused by the ligament gives rise to much higher contact forces in the
scapulothoracic joint at the inferior angle and a loss of contact force at the superior angle to balance this.
Finally, the dynamic constraints used in the calculation of muscle and joint forces appear to be of little
importance in, rather slow, everyday tasks: the pure time delays in excitation and active state and the
muscle force-velocity relationship become rate limiting only at higher joint velocities. For faster, more
ballistic, tasks, these dynamic constraints have been shown to be useful, but good results depend on wellconditioned, high sampling frequency data. There is obviously some trade-off in such studies between the
necessity of using a high sampling frequency and the consequent detriment to computing time.
ACKNOWLEDGMENT
This project is funded by an EPSRC CASE award in conjunction with DePuy International Ltd.
REFERENCES
Barnett, N.D. (1996) Measurement and modelling of three dimensional scapulohumeral kinematics. Ph.D.
Thesis, University of Newcastle upon Tyne, UK.
Marchese, S.S. (2000) Sterno-clavicular kinematics - a new measurement system. Ph.D. Thesis,
University of Newcastle upon Tyne, UK.
Murray, I.A. (1999) Upper limb kinematics and dynamics during every day tasks. Ph.D. Thesis,
University of Newcastle upon Tyne, UK.