Author: Dave Deriso
University of California, San Diego
BIPN 146: Computational Neurobiology
Professor: Dr. Terrence J. Sejnowski

Before reading, watch this video of a monkey controlling a robot arm with his brain:

http://www.nature.com/nature/journal/v453/n7198/extref/nature06996-s2.wmv

Abstract

The present paper discusses how neurons in the motor cortex can be decoded through a population vector algorithm (PVA) to control a motorized prosthetic arm. The PVA was computed by extracting and summing the preferred directions of each unit within the recorded population weighted by its instantaneous firing rate and then characterized into four dimensions: the 3 degrees arm’s endpoint (x,y,z) and the aperture velocity between gripper fingers (fourth dimension). Although the model was the first to offer four dimensions of control and had a surprisingly short 150ms delay between spike signals and motor movement, it was shown to have only a modest 61% success rate. My assessment of the model is that it was a great first step, but the accuracy indicates that alternative algorithms, such as the bayesian probability model, may improve the design.

Introduction

Central Question

The present experiment addressed separate neuroscientific and mathematical questions. The neuroscientific question asked if activity patterns of populations of neurons in the motor cortex  could be decoded efficiently enough to control a prosthetic arm with accuracy and speed at a near-natural, or `embodied,’ level. To this end, the authors constructed a robotic armature that was controlled by the decoded neural signals. The underlying mathematical inquiry tested the efficacy of a population vector algorithm for modeling these neural signals and the movement intentions they represent. The success rate of a monkey’s (macca mulata) feeding attempts (measured by the number of attempts to retrieve food from the end of a delivery device and maneuver it back to the mouth) was used to indicate the efficacy of the system and model.

The original population vector algorithm was proposed in a paper by Georgopoulos, Kettner, and Schwartz (1988) and described a code by which a population of motor cortical neurons could determine uniquely the direction of reaching movements in three-dimensional space. The experimenters recorded from a population consisting of several hundred directionally tuned cells, each of which were found to discharge at the highest rate with movements in its “preferred direction” and at progressively lower rates with movements in directions away from the preferred one. The model made the assumption that the cells in the population could be linearly summed as vectors, and the output would determine the intended direction of movement in space. Specifically, each cell’s preferred direction was multiplied by it’s normalized change in the firing rate, and then summed to form the “neuronal population vector” as described in the equation below:

Where M is a particular movement direction, N is the number of cells in the population, wi(M) is the weighting function computed by the number of spikes a cell will fire in a particular direction M, and Ci is the preferred direction of the ith cell.

Further work by Lukashin, A.V. and Amirikian, B.R. and Georgopoulos, A.P. (1996) showed that neural recordings in the motor cortex of monkeys could control a mechanical actuator that mimicked the movements of an arm. The experimental results indicated that the artificial interface could generate forces in close quantitative agreement with those exerted by trained monkeys, in both the temporal and spatial domains, and may be controlled by the impulse activity of as few as 15 motor cortical cells. These results were the first to show that raw neuronal signals could be used to drive artificial mechanical systems and paved the way for future research in motor based neural prosthetics.

Specific Aims

The model was designed to decode firing patterns in a population of motor cortex neurons into vectors representing intended movement in real-time. Additionally, the PVA was designed to decode the signal into four dimensions of arm control: the 3 degrees of the arm’s endpoint (x,y,z) and the velocity between the gripper fingers (fourth dimension)

Model Assumptions

The population decoding method described in Equation 1 is only effective at predicting intended movement direction when neural firing patterns fit a linear relationship such that each component of the vector can be linearly summed (see Equation 2) and enough neurons are used. Additionally, the model was simplified by assuming that firing rates were modulated equally above and below baseline rate, and the preferred directions of those neurons are uniformly distributed throughout the workspace (Dornhege et al., 2007; Georgopoulos, Kettner, & Schwartz, 1988).

Where R(t) is the neural firing rate; B0 is it’s mean firing rate; Mx(t), My(t), and Mz(t) are the x, y and z components of a unit vector pointing in the direction of movement at time t; and Bx, By, and Bz are regression coefficients that define a vector pointing in the cells preferred direction.

Lastly, a few data pre-processing steps were taken to simplify the between-unit comparisons. To decrease noise, the spike data were smoothed with a finite-impulse response filter algorithm and each neuron was normalized using each unit’s baseline rate and amplitude.

Testable Predictions

The success of the model was measured by the success rate of the monkey’s feeding behavior attempts. This was calculated as a count of how many times the monkey was able to retrieve and eat the presented food divided by the number of attempts made. 

Analysis

Findings

The authors were able to show that a PVA could be used decode movement intentions in multiple dimensions, while previous experiments only tested two. Additionally, it indicated that greater amounts of accuracy could be obtain from this method than were previously found, thereby adding more credibility to the PVA method of neural signal decoding. Finally, the work demonstrated that a real-time and near-natural “embodied” control is possible to achieve with the cortical-prosthesis interface technology.

Strengths and Weaknesses

The strength of the model is that it is inherently simple, which allows the decoding to occur in real-time with accuracy that was higher than in previous work.

However, many other studies have shown that neural firing activity has a much more complicated relationship to intended movement than is captured by the population vector algorithm. Neural rates have also been shown to relate to movement speed as well as direction (Moran & Schwartz, 1999) therefore indicating that the PVA may be oversimplified.

A limitation of the PVA, is the assumption that the basis function add linearly. This model cannot represent distributions that are sharper than the component distributions. For instance, a point in between two tuning curves will be misrepresented as being in both places. Additionally, while previous models have typically viewed the relationship between firing rates in MI and various aspects of hand motion (position, direction, speed, velocity, or acceleration) in isolation, Wu et al. (2006) found that decoding performance is improved when the encoding model simultaneously takes into account all these variables, suggesting decoding performance drops when cells are assumed to be conditionally independent.

A second class of models addresses this problem using a generative approach, where an encoding model (e.g., Poisson) is first assumed and a Bayesian decoding model is used to estimate the intended direction (or its distribution), given the state of the population (Doya, Ishii, Pouget, & Rao, 2007). This bayesian approach has been shown to be a more robust and accurate model for population vectors than the PVA (Wu, Gao, Bienenstock, Donoghue, & Black, 2006).

References

Dornhege, G., Mill´n, J., Hinterberger, T., McFarland, D., Sejnowski, T., & Müller, K. (2007). Toward brain-computer interfacing. Cambridge, Massachusetts: The MIT

Doya, K., Ishii, S., Pouget, A., & Rao, R. (2007). Bayesian brain: Probabilistic approaches to neural coding. Cambridge, Massachusetts: MIT Press.

Georgopoulos, A., Kettner, R., & Schwartz, A. (1988). Primate Motor Cortex and Free Arm Movements to Visual Targets in Three-Dimensional Space. II. Coding of the Direction of Movement by a Neuronal Population. Journal of Neuroscience, 8 (8),

Lukashin, A., Amirikian, B., & Georgopoulos, A. (1996). A simulated actuator driven by motor cortical signals. Neuroreport, 7 (15-17), 2597.

Moran, D., & Schwartz, A. (1999). Motor cortical representation of speed and direction during reaching. Journal of Neurophysiology, 82 (5), 2676.

Taylor, D., & Schwartz, A. (2004). Direct cortical control of 3d neuroprosthetic devices.

Velliste, M., Perel, S., Spalding, M. C., Whitford, A. S., & Schwartz, A. B. (2008, June). Cortical control of a prosthetic arm for self-feeding. Nature, 453 (7198), 1098–101.

Wu, W., Gao, Y., Bienenstock, E., Donoghue, J. P., & Black, M. J. (2006, January). Bayesian population decoding of motor cortical activity using a Kalman filter. Neural computation, 18 (1), 80–118.