(367f) Control of a Motor Intended Neural Prosthetic Finger Using a Network of Cortical Motor Neurons

Neurophysiological systems, such as natural limbs, are partially driven by neural activities of the primary motor cortex (M1) projected to the spinal motor units [1]. Experimental evidence indicates that these M1 neural activities contain sufficient information which can be extracted to drive motor intended neural prostheses, such as artificial limbs. An interface that connects a motor intended neural prosthesis, wired or wireless, to the M1 is called brain-machine interface (BMI).

Current formulations of BMI are insufficient in providing feedback information, such as kinematic and dynamic senses of the prosthetic device movement to the brain. This information is necessary for the online error correction during the voluntary movement of the device. Micro-stimulation techniques, relatively new in BMIs application, have emerged as a promising approach in providing artificial proprioceptive feedback by stimulating the appropriate sensory areas of the brain. The aim here is to incorporate missing natural feedbacks, such as proprioception and tactile, available from the motor intended prosthetic device back to the brain. This may provide us an enhanced control over prosthetic limbs similar to our natural limbs. Although these techniques are promising for developing next generation BMIs, the experimental trial and error approach in designing appropriate sensory input currents may damage a part of the brain or modify the natural functionality of the brain. Therefore, it is appropriate to take a control-theoretic approach. To do this, we can use well established optimal feedback control theory as a parallel alternative towards developing next generation BMIs. This approach promises to provide flexibility in the design of optimal stimulating sensory input currents in addition to providing detailed analysis of the closed-loop neural prosthetic system under various conditions. Motivated by these facts as well as our previous work on the control of a prosthetic finger using a single M1 neuron [2], we extend our earlier work to provide a more generalized control-theoretic framework. Within this framework, neural activities of a network of M1 neurons are used to control a prosthetic device. We focus here on closed-loop control of a prosthetic finger about a single joint which is controlled by a small network of M1 neurons. Our framework consists of: a) a network of M1 neurons connected through seed neurons b) a decoder model which takes the instantaneous firing rate of M1 neurons and an ensemble based inter-spike interval (ISI, the time difference between two consecutive instantaneous ensemble firing of M1 neurons) and generates the encoded torque information, c) a prosthetic finger model which uses the torque to drive the finger about a single joint, and finally d) a receding horizon based optimal control strategy which uses system models as well as available feedback information, visual and proprioceptive, from the finger to generate optimal input currents needed to stimulate seed neurons.

In this presentation, we limit ourselves to consider a small network of neurons consisting of 4 seed neurons and 10 M1 neurons. Experimental evidence in neuroscience suggests that the M1 neurons interact with neurons from various other cortical areas of the brain and receive motor intended information by making synaptic connections with them. To keep our mathematical and computational formulation simple, we represent an ensemble of neurons within each cortical area of the brain by a seed neuron. Each seed neuron represents an individual cortical area namely pre-motor, somatosensory, post parietal and cerebellum. These cortical areas projects neural activities to M1 neurons by establishing synaptic connections. Each seed neuron captures firing rate behaviors of an ensemble of neurons. These seed neurons are activated by external stimuli, designed by the receding horizon based optimal control strategy using the feedback information available from the prosthetic system. Dynamic behavior of each M1 neuron is described by the Izhikevich single neuron model. Dynamic behavior of each seed neuron is described by a population based model. We define synaptic connectivity from seed neurons to M1 neurons using a well-defined feedforward model. Synaptic connectivity among M1 neurons are defined by a well-defined recurrent model. We assume that there is no synaptic connectivity among seed neurons. With time invariant synaptic connectivity and corresponding weights, we model the synaptic current to a M1 neuron in the form of the sum of alpha functions. These functions capture the effect of variability in spiking behaviors of other M1 neurons and seed neurons connected to the M1 neuron in the network. We further assume that all neurons in the network are excitatory. This means that each action potential in a presynaptic neuron, which occurs during the firing of a presynaptic neuron, makes contribution towards an increment in its postsynaptic neuron membrane potential. Thus, in terms of an input-output model, we define a small network of neurons where the inputs to the network are four current stimuli which stimulate each of the seed neurons. Outputs of the network are the number of M1 neurons emitting actions potentials at a given instant of time and the ensemble based ISI. These outputs are then used by a dynamical decoder model, developed by us, which decodes the torque information and thus actuates the prosthetic finger. The rest of the control-theoretic framework follows directly from our previous work on the design and control of an index finger using cortical activities of a single M1 neuron [2].

We consider a minimum time control problem in the receding horizon framework. The cost function for the controller is the total time required to reach the desired angular target space defined by a terminal set constraint. This cost is minimized over stimulating input currents of four seed neurons subject to two system constraints. The first constraint ensures that the resultant movement of the prosthetic finger is continuous and smooth. In terms of the firing activities of neurons, this means that the next firing of ensemble of motor neurons occurs before the initial movement generated by previous firings dies out. The second constraint defines a terminal set constraint which ensures that the goal directed voluntary movement terminates once the finger is in the region of target space defined by the terminal set constraint. At each time varying sampling time, defined as the ensemble based ISI, the controller computes four stimulating input currents. These computations utilize the information about the current position of the finger, which is available to the controller through the visual feedback. The overall control problem, at each sampling time, leads to a nonconvex nonlinear constrained optimization problem. This problem is solved numerically by implementing the infeasible interior point algorithm along with the Markov filter method.

Proprioceptive feedback carries information such as the sense of movement, position, force and effort required to move the finger which together provides the perception of the limb position to our brain. In the absence of natural proprioceptive pathways, we capture this feature of perception in a form of an artificial proprioceptive feedback current model. This model is a linear function of the torque applied at the joint and the velocity of the prosthetic finger. We project the feedback current induced by this model directly to all M1 neurons in the network such that each M1 neuron receives the same proprioceptive information. By varying time invariant gains of the proprioceptive feedback current model, we study the effect of proprioception on the activities of M1 neurons under the closed-loop framework. This study leads to an important conclusion that the firing rates of M1 neurons increase with the increase in external load opposing the direction of movement. This conclusion is consistent with the experimental observations made by Evarts and Fetz in early 70’s [1]. The adaptation of M1 neuron activities subject to an external load would be impossible in the absence of proprioceptive feedback because the visual feedback alone cannot make distinction between external loads. This observation emphasizes the necessity of including artificial proprioceptive feedback in designing next generation BMIs. The second conclusion of this talk is the importance of visual feedback in rejecting internal noises. It is now widely accepted in the neuroscience community that neurons, in general, possess stochastic characteristics due to internal fluctuations while transmitting synaptic information. Therefore we introduce randomness in synaptic weights of the interconnected network of seed and M1 neurons. With this, we study the closed-loop and the open-loop behaviors of the overall system in the absence of proprioceptive feedback. In the open-loop framework, i.e. in the absence of visual feedback, we find that the controller completely throws off the angular trajectory of the prosthetic finger from the desired path. We further study how the activities of M1 neurons are modulated by including the visual feedback which drives the final angular position of the prosthetic finger to the desired target space.

1. E. R. Kandel, J. H. Schwartz and T. M. Jessell, Principles of Neural Science, Fourth Edition, McGraw-Hill, 2000.

2. G. Kumar, V. Aggarwal, N. V. Thakor, M. H. Schieber and M. V. Kothare, An Optimal Control Problem in Closed-Loop Neuroprostheses, Submitted to the 50^th IEEE Conference on Decision and Control and European Control Conference, 2011.