(288b) Design and Control of a Closed-Loop Neural Prosthesis

Brain Machine Interfaces (BMIs) provide an interface between the brain and a machine whereby electrophysiological measurement of neuronal firing activity in the brain is interpreted by the computer in real-time and translated to provide actuation commands for a variety of motor tasks such as hand grasping in artificial arms. This interface can be used to control a prosthetic device in severely paralyzed patients or amputees using raw cortical neural activity measurements available from the patient's primary motor cortex area (M1) [1]. Current applications in neuroprosthesis use these raw cortical neural activities in ``open-loop'' controller forms to actuate the prosthetic device. Implicit or explicit feedbacks are not formally incorporated in designing the control action. To incorporate feedback information, there is a need to develop a closed-loop system [2] that is amenable to a control-theoretic study of the neuroprosthetic system.

With the goal of designing a closed-loop neural prosthesis, we present a control-theoretic study of a right hand index finger movement using neural cortical experimental data from a primate study. We assume that visual feedback, other sensory information, and motor planning activity are present in both the natural limb subject and the prosthetic limb subject for use in accomplishing natural or prosthetic finger movements respectively. We further assume that the only missing feedback information in the case of the prosthetic limb is proprioceptive feedback (available through afferent pathways from the limb to the thalamus and cerebellum to the cortex). With this feedback pathway, we propose a hypothesis towards designing a closed-loop system for a single motor cortex neuron.

We define time "T_lag = T_{1, lag} + T_{2, lag}" where T_{1, lag} is the time required the motor cortex output to reach the limb for a planned action and T_{2, lag} is the time required for proprioceptive feedback from the limb to reach the primary motor cortex. During the time period of 0 <= t < T_lag, no proprioceptive feedback information is available to the primary motor cortex and the overall system works in open-loop. During this time, outputs (action potentials) from the primary motor cortex are directly implemented on the prosthetic limb. These initial spike activities contain information such as intent of action, direction of movement, initial speed (fast / slow) of movement, final destination / position of the limb etc. and are used to provide set points to the prosthetic controller. The effect of proprioceptive feedback on the closed-loop system starts at time t = T_lag. At this time, spike activity of the motor cortex neuron is modulated using available proprioceptive feedback information to achieve the desired objective and thus form a closed-loop neural prosthesis system.

With this hypothesis, we formulate a closed-loop control problem using a single motor cortex neuron. For simplicity, we assume that information such as intention of the finger movement and the final angular position of the index finger are available prior to the design of a prosthesis based controller. We use Inter-Spike Intervals (ISIs) data recorded from a single motor neuron from a primate study [3] to design a closed-loop controller. We assume that afferent feedback information from the index finger is missing in these recorded ISIs. We use the first recorded ISIs in the duration of 0<= t < T_lag to estimate Izhikevich single neuron model parameters [4]. These estimated model parameters are kept fixed during the closed-loop control design. We use simplified index finger dynamics and compute information such as torque, angular velocity and angular position of the finger using ISIs. Using these finger dynamics along with the Izhikevich single neuron model, we design a receding horizon based non-linear control problem to estimate optimal timing of spikes (ISIs) in order to reach a pre-specified angular position during an extension of the index finger. The prediction horizon is time varying in nature and is considered as the number of action potentials required to reach the desired angular position. The control horizon is considered fixed during the initial period and eventually converges to the prediction horizon as the desired target is approached. We solve the resulting non-linear optimization problem using the primal-dual interior point method [5] in MATLAB and design the optimal input currents and optimal ISIs to reach the desired angular position. Finally, we compare our optimal closed-loop ISIs with the experimental ISIs from a primate study and propose the need for designing experiments that elucidate the difference between open loop and closed loop neuroprosthetic systems.

Reference:

[1] M. A. Lebedev and M. A. L. Nicolelis. Brain-machine interfaces: past, present and future. Trends in Neurosciences, Vol. 29, No. 9, 536-546, 2006.

[2] M. A. L. Nicolelis and M. A. Lebedev. Principles of neural ensemble physiology underlying the operation of brain-machine interfaces. Nature Reviews, Vol. 10, 530-540, 2009.

[3] Schieber, M.H. and Hibbard, L.S. How somatotopic is the motor cortex hand area? Science 261:489-492, 1993.

[4] Eugene M. Izhikevich, Dynamical Systems in Neuroscience, MIT Press.

[5] S. Boyd and L. Vandenberghe. Convex Optimization. 3^rd Edition, Cambridge University Press, 2008.