Developing a quantifier of the neural control of motion is extremely useful in characterizing motor disorders and personalizing the model equations using data. We approach this problem using a top-down optimal control methodology, with an aim that the quantity estimated from the collected data is representative of the underlying neural controller. For this purpose, we assume that during the flexion of an arm, human brain optimizes a functional. A functional is defined as a function of a function that returns a scalar. Generally, in forward problems, this functional is chosen to be a function of metabolic energy spent, jerkiness, variance of motion, etc., integrated throughout the trajectory of motion. Current states (angular configuration and velocity) and torque applied can approximately determine the motion of a joint. Therefore, any internal cost functional optimized by the brain has to have its effect in the control of the torque. In this work, we study the flexion of the arm in normals and patient groups and intend to find the cost functionals governing the motion. To achieve this, we parametrize the cost functional governing the motion into the variables θp and ωp , which are then estimated using marker data obtained from the subjects. These parameters are shown to vary significantly for the normal and patient populations. The θp values were shown to be significantly higher in the case of patients than in the case of normals and ωp values showed an exactly opposite trend. We also studied how these cost functionals govern the applied torques in both subject groups and how is it affected while perturbed with sinusoidal frequencies. A time frequency analysis of the resulting solutions revealed a distinguishing pattern for the normals compared with the patient groups.
Keywords: arm model; cost functionals; early detection; motor disorders; optimal control.