The development of methods for improving accuracy and validity of musculoskeletal modelling of the lower limb

Abstract

The aim of present study was to address limitations in model design, anatomical data, and implementation of muscle force-length and force velocity relationships for the purpose of improving accuracy and validity of musculoskeletal modelling. To achieve these a comprehensive three dimensional musculoskeletal model of the leg was developed and implemented in the analysis of gait.

The following were achieved: i) Anatomical data for 48 muscle elements of the lower limb, including skeletal coordinate data to define muscle-tendon paths and moment arms throughout joint movements. ii) Optimisation of muscle model parameters to changes in muscle belly lengths to define an optimal fibre length and force-length relationship. iii) Equations describing muscle model geometry, force-length and force-velocity relationships to describe muscle model contraction dynamics. iv) A cost function which minimised the sum of squared normalised muscle forces with soft constraints on maximum and minimum muscle force, which allowed for the unconstrained minimisation of the cost function. v) An optimisation procedure that combined the equipollence equations, muscle excitation and contraction dynamics and muscle force limits in the minimisation of the cost function.

The limitations identified include: i) Accuracy of velocity data achieved was not sufficient to determine muscle contraction dynamics which relied on muscle contractile element velocity to determine maximum muscle forces; ii) Calculation of moment arms from muscle-tendon co-ordinate data was extremely sensitive to errors including : • accurate location of body-fixed axes from external markers; • relative motion of muscle point co-ordinates and joint centres; • the use of straight as opposed to curved-line tendon paths; • accuracy of three dimension segment location during movement. iii) The muscle model predicted contractile element velocities larger than those modelled by the present force-velocity equations, indicating a need to scale force-velocity relationships to the maximum contractile element velocities. iv) The optimisation approach predicted consistent forces for the 48 muscle elements of the lower limb, however limitations were: • determining initial muscle force estimates in accordance with the equipollence equations; • minimisation of the cost function did not change muscle forces significantly from their initial estimated values.

Improvements suggested include: i) Improvements in moment arm prediction by: • use of pre-trial functional evaluations of predicted centres of rotation to improve location of body fixed axes; • improved location of muscle point co-ordinates to define muscle lines of action at varying joint angles. ii) Optimise the muscle model parameters to the range of muscle lengths determined by the end-range of motion instead of the motion within a trial to achieve a more realistic optimal fibre length and force-length relationship by considering the change in fibre lengths as an approximation of the maximum changes in fibre lengths. iii) Improve the validity of the joint models to: • determine moments to be balanced by muscular forces. • improve the optimisation procedure to obtain muscle forces. • increase accuracy of muscle force prediction. iv) Review the force-velocity relationship, the dynamic response of the muscle model, and assess the validity of the muscle model in predicting maximum muscle forces; v) Improved initial muscle force estimates which meet the equipollence equations and achieve convergence to a global minimum. vi) Apply the optimisation procedures to movements involving higher muscle forces, where accurate prediction of maximum muscle forces, modelling of joint passive forces, and excitation dynamics become more critical.

While the present study succeeds in many respects, its succeeds most in identifying the complexity of the process and proposing methods to achieve greater success.