Quarterly Progress Report N01-NS-1-2333 Restoration of Hand and Arm Function by Functional Neuromuscular Stimulation

A large-scale, three dimensional model of the upper extremity that combines the advantages of forward and inverse dynamics is under development. The model uses inversedynamic optimization to calculate an optimal set of neural excitations for a given movement. These excitations can be used as the starting point for investigations using a forward-dynamic model, which would otherwise be prohibitively expensive in terms of computational cost. Initial results show that the algorithm is successful in providing muscle excitations which produce the desired movement. Introduction The application of biomechanical modelling can helpfully be divided into two categories: fundamental research into human function, and analysis of clinical problems. Much insight can be gained into human function by the use of simple models that illustrate certain principles of movement or motor control. When applied to the evaluation of specific clinical problems, Quarterly Progress Report #13 N01-NS-1-2333 7/30/04 PI: R.F. Kirsch, Ph.D. 2 however, a large-scale three-dimensional model is essential. Only such a comprehensive model allows for the validation that is essential to clinical application, and the ability to make patientspecific predictions of clinical outcome. This allows sophisticated models to be used for the analysis of clinical problems, improvement of current treatments and the development of new procedures. This work focuses on the further development of such a model that will allow its use in the solution of clinical problems. Methods The Delft Shoulder and Elbow Model (DSEM) as first described by van der Helm (1994) is an inverse-dynamic model of the complete shoulder mechanism. The recorded motions of the bones are used as inputs to the model, together with the external loading, and internal forces and moments are calculated using an inverse-dynamics method. The musculo-skeletal system is indeterminate; that is, there are many more muscles crossing a degree of freedom than equations of motion governing it. Thus, some kind of optimization must be carried out to calculate individual muscle forces. The 'load-sharing problem' was solved by a non-linear optimization routine involving the minimization of the sum of the squared muscle stresses. Muscle forcelength relationships are also accounted for by the inclusion of muscle architecture parameters. Output from the model consists of the resulting joint contact forces, ligament forces and muscle forces, lengths and moment arms. The model has been used by a number of authors for the study of activities such as wheelchair propulsion (van der Helm and Veeger 1996, Veeger et al. 2002), the examination of surgical interventions such as tendon transfer (Magermans et al. 2004A, Magermans et al. 2004B) and the treatment of scapular fracture (Chadwick et al. (in press)), and for the design of a neuroprosthetic system by Kirsch et al. (2001). The motion of the upper limb is subject to a number of constraints which complicate the modelling process. The most obvious of these is the closed-chain nature of the shoulder girdle. That is, the thorax, scapula and clavicle form a closed-chain kinematic mechanism which restricts the motion of the shoulder. In modelling terms, this must be accounted for by a reduction in the number of degrees of freedom, and leads to a mismatch in the kinematics observed in a subject and that which is shown by the model. This can be accounted for by scaling of the bones in the model, or by adjustment of the input data. A further reduction in the freedom of the shoulder girdle is assumed to be caused by the conoid ligament, which couples the rotations of the clavicle and the scapula due to its high stiffness. The inverse-dynamic (ID) model is quasi-dynamic in that segment velocities and accelerations are accounted for, but muscle dynamics are not. The equations of motion can thus be solved independently for each time-step, and so the model is computationally efficient. This does not allow studies to be made of the effects of muscle dynamics on function, however, and the post-operative kinematics resulting from a given intervention must be known a priori. When analyzing an existing normal or pathological motion this is fine, but for speculative studies about the effects of certain interventions, it is a serious limitation. In this, the advantages of a forwarddynamic model, in which the input muscle activations result in output motions, are clear. Forward-dynamic (FD) models have the great advantage that no a priori knowledge of kinematic is necessary, but are less common in the literature for one reason in particular: computational cost. The optimization of the neural excitations which produce a desired limb trajectory involve the repeated integration of the state equations at each step, which leads to enormous simulation times for large-scale, three-dimensional models. One further advantage that Quarterly Progress Report #13 N01-NS-1-2333 7/30/04 PI: R.F. Kirsch, Ph.D. 3 FD models have over their ID counterparts is the ability to model stiff structures such as ligaments. These structures are often of such stiffness that the accuracy required of displacement estimates to ensure realistic force changes is unachievable. In order to take advantage of the possibilities offered by forward-dynamic models, a 'hybrid' model is under development. This model combines inverse and forward dynamics to allow FD simulations to be carried out in a feasible time frame. The model employs static optimization of muscle forces (inverse dynamics) together with feedback and feedforward control to drive an FD model towards some desired trajectory. The ID model is used to calculate optimum muscle forces which produce the desired motion, and an inverse muscle model calculates muscle excitations. These excitations are then used to drive an FD model, and the error in predicted kinematics is fed back to the ID model as a controller. This produces an optimum set of muscle excitations for a given motion, which can be used as a starting point for FD studies. Results Simulations of simple motions such as abduction and anteflexion of the humerus have been successfully carried out, with approximately two hours needed to simulate one second of movement. While this is still slow, it is much faster than a full-scale forward-dynamic optimization would be on a model of this scale. The controller was able to produce a set muscle excitations which led to the correct motion being produced by the FD model. Errors between the kinematics of the ID and FD models were of the order of 2o. However, without the controller, the FD model is not stable, and discretization errors and other numerical instabilities are catastrophic. Next quarter The next step in the development of the model is to achieve gains in speed. This can be done with the implementation of a faster integrator and a simpler muscle model, and these possibilities will be investigated. Furthermore, evaluation of the model needs to be done by comparison of the predicted muscle excitations with measured EMG signals. Refinement of the predicted excitations can then be done by modification of the cost function used in the muscle force optimization.