Proceedings of the 26th Annual International Conference of the IEEE EMBS San Francisco, CA, USA • September 1-5, 2004
Closed-Loop Neural Control of Cursor Motion using a Kalman Filter W. Wu∗ A. Shaikhouni† J. P. Donoghue† M. J. Black‡
∗ Division of Applied Mathematics, Brown University, Providence, RI, USA † Department of Neuroscience, Brown University, Providence, RI, USA ‡ Department of Computer Science, Brown University, Providence, RI, USA
Abstract— Recently, we proposed a Kalman filter method to model the probabilistic relationship between neural firing in motor cortex and hand kinematics. In this paper, we demonstrate on-line, closed-loop, neural control of cursor motion using the Kalman filter. In this task a monkey moves a cursor on a computer monitor using either a manipulandum or their neural activity recorded with a chronically implanted micro-electrode array. A number of advantages of the Kalman filter were explored during the on-line tasks and we found that the Kalman filter had superior performance to previously reported linear regression methods. While the results suggest the applicability of the Kalman filter for neural prosthesis applications, we observed the decoded cursor position was nosier under brain control as compared with manual control using the manipulandum. To smooth the cursor motion without decreasing accuracy we propose a method that smoothes the neural firing rates. This smoothing method is described and its validity is quantitatively evaluated with recorded data. Index Terms— neural prosthesis, neural control, brainmachine interface, closed-loop control, primary motor cortex, Kalman filter.
I. I NTRODUCTION Real-time neural decoding algorithms are necessary for the development of neural motor prostheses. A variety of algorithms have been proposed to convert neural activity into a voluntary control signal [1]–[4]. In our recent work, we proposed a Kalman filter to decode the neural firing rate obtained from multi-electrode recordings [5], [6] to produce an estimate of hand kinematics. We showed that the method has a number of benefits for neural prosthesis applications: 1) it requires only a small amount of “training” data; 2) the computational cost for the parameter estimation (learning) of the model is negligible; 3) it provides accurate and efficient state estimation (less than 10ms for each time step). Because of these advantages, we argued that the Kalman filter could be used for closed-loop neural control. This paper is a continuation of our recent work; here, for the first time, we demonstrate the Kalman filter in a closed-loop neural control task. The experimental paradigm required a monkey to control the two-dimensional (2D) motion of a feedback cursor viewed on a video monitor. The animal’s task was to move the cursor to hit targets that appeared at random locations on the screen. In the This work was supported by the DARPA BioInfoMicro Program, NIHNINDS #NS25074, and NSF ITR #0113679. Correspondence: W. Wu (
[email protected])
0-7803-8439-3/04/$20.00©2004 IEEE
experiment, a single macaque monkey was implanted with an electrode array and the Kalman filter was used to decode the neural activity in real time to estimate the cursor position. By closed-loop we mean that the brain directly controls the cursor and the visual feedback to the animal about the cursor position closes the loop. To evaluate the performance of the method we compared the animal’s ability to hit targets with both the Kalman filter and a simple linear regression method which has been widely used for neural decoding. We also evaluated the accuracy of the method in off-line data analysis. While the advantages of the Kalman filter have been clearly described in our previous work [5], [6] here we show that the Kalman filter outperforms the linear regression method in the closedloop neural control task. Though accurate and efficient, the estimates produced by the Kalman filter are not as smooth as those observed under manual control using a manipulandum. While the significance of this is unclear from the viewpoint of neural control, we explored various methods to produce smooth neural decodings that more closely approximate the motion under manual control. In previous work the decoded hand position produced by the linear regression method was smoothed using a simple windowed average method [2]. In this paper, we propose an on-line smoothing approach that instead smoothes the neural firing rate data. This results in smooth reconstructions of hand motion while providing a good balance between bias (accuracy) and the variance (smoothness) [7]. II. M ETHODS A. Experimental paradigm Simultaneous recordings of spikes are acquired from an array consisting of 100 micro-electrodes chronically implanted in the arm area of primary motor cortex (MI) in a Macaque monkey [8]. Multi-unit firing activity on each channel is detected using simple filtering and thresholding. We use the behavioral paradigm described in [2] for two tasks described below. Manual-control task: The behavioral task for the monkey is referred to as a step-tracking task, or more intuitively, a pinball task which is designed to test direct neural control performance [2]. During the task, a target dot was shown on the screen in front of the monkey and the monkey moved a manipulandum on a 2D tablet that was parallel to the floor.
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Fig. 1. Reconstruction for the x and y-position using the Kalman filter: first row: x-position; second row: y-position; dashed lines: true trajectories; solid lines: reconstructed trajectories. 30
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The position of the manipulandum (same as the hand) was shown as a feedback cursor on the same screen. The monkey was required to move this cursor to “hit” the target (within a pre-specified distance). When the target was acquired, it disappeared and then reappeared in a new random location. Each time the target appeared, the monkey moved to hit the new location. The hand trajectory and the neural activity were recorded simultaneously. The spiking activity was detected via empirically determined threshold settings and a firing rate was computed using non-overlapping 70ms time bins [6]. The position, velocity, and acceleration of the hand were also computed every 70ms. Neural-control task: In the closed-loop neural control task the experiment remained the same except that the motion of the cursor was controlled by the decoded neural signals. This decoding was performed using a Kalman filter. To quantitatively compare with related work, the same procedure was repeated using a linear regression method for decoding. These two methods are described below. Recordings were made during experiments over several months and details of the experiments are described in Section III.
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1) Kalman filter: Here, we briefly describe the Kalman filter model and its decoding algorithm. The details can be found in our recent work [5], [6]. In general, decoding involves estimating the state of the hand at the current instant in time; i.e. xk = [x, y, vx , vy , ax , ay ]Tk representing x-position, y-position, x-velocity, y-velocity, x-acceleration, and y-acceleration at time tk = k∆t where ∆t = 70ms in our experiments. The Kalman filter model assumes the state is linearly related to the observations zk ∈
