Modulation depth estimation and variable selection in state-space models for neural interfaces

Abstract

Rapid developments in neural interface technology are making it possible to record increasingly large signal sets of neural activity. Various factors such as asymmetrical information distribution and across-channel redundancy may, however, limit the benefit of high-dimensional signal sets, and the increased computational complexity may not yield corresponding improvement in system performance. High-dimensional system models may also lead to overfitting and lack of generalizability. To address these issues, we present a generalized modulation depth measure using the state-space framework that quantifies the tuning of a neural signal channel to relevant behavioral covariates. For a dynamical system, we develop computationally efficient procedures for estimating modulation depth from multivariate data. We show that this measure can be used to rank neural signals and select an optimal channel subset for inclusion in the neural decoding algorithm. We present a scheme for choosing the optimal subset based on model order selection criteria. We apply this method to neuronal ensemble spike-rate decoding in neural interfaces, using our framework to relate motor cortical activity with intended movement kinematics. With offline analysis of intracortical motor imagery data obtained from individuals with tetraplegia using the BrainGate neural interface, we demonstrate that our variable selection scheme is useful for identifying and ranking the most information-rich neural signals. We demonstrate that our approach offers several orders of magnitude lower complexity but virtually identical decoding performance compared to greedy search and other selection schemes. Our statistical analysis shows that the modulation depth of human motor cortical single-unit signals is well characterized by the generalized Pareto distribution. Our variable selection scheme has wide applicability in problems involving multisensor signal modeling and estimation in biomedical engineering systems.

Figures

Fig. 1

Schematic representation of variable selection scheme and behavioral task design for neural recordings. (a) Decoder in a neural interface with optimal variable subset selection based on MD ranking. (b) Open-loop center-out-back task for recording neural activity under motor imagery, with four peripheral targets and a computer-controlled cursor. Bounding rectangle represents the computer screen, and scale bar is in units of visual angle.

Fig. 2

MD of human motor cortical single-unit spike rates. (a) Distribution of MD (radial length) and preferred direction (angle) of 39 individual channels (single units) recorded in one research session. (b) Cumulative MD as a function of optimal subset size. Blue, red, and green dashed lines: number of channels required to achieve at least 50%, 90%, and 95% of total MD, respectively.

Fig. 3

Decoding using optimal channel subset. (a)Open-loop center-out-back task with rightward peripheral target (gray circle). Blue line: computer cursor trajectory from home position outward to target and back; red line: cursor trajectory estimated by decoding neural activity of the m best channels ranked by MD; black rectangle: computer screen location and dimensions; scale bar in units of visual angle. (b) Decoding of the system’s hidden state (imagined cursor velocity) from neural activity using m best channels. The trials, each of 12 s duration, start with target onset at time 0. Blue arrow: direction of selected target relative to home position.

Fig. 4

Effect of neural channel MD on decoding performance. (a) Relation of MD to open-loop decoding correlation of true computer cursor velocity with velocity estimate obtained by decoding each neural channel individually. Shaded region: 95% CI of chance-level decoding correlation. (b) Improvement in decoding correlation with increasing channel subset size chosen using the specified scheme. (c) Normalized BIC as a function of channel subset size chosen by MD. Red circle: optimal subset size with lowest BIC.

Fig. 5

Effect of dropping some of the highest modulated channels on decoding performance. (a) Decrease in total MD (top) and open-loop decoding correlation between true and estimated cursor velocity (bottom) when the specified number of the best channels are removed from the neural decoder. Shaded region: 95% CI of chance-level decoding correlation. (b) Open-loop center-out-back cursor trajectories decoded from m channels with the lowest MD. Blue lines: computer cursor trajectory; red lines: imagined velocity decoded from neural channel subset; black rectangle: computer screen.

Fig. 6

Statistical characterization of single-unit MD. (a) Distribution of MD of various channels in each of five research sessions. Red line: median; box: interquartile range [q1, q3]; whiskers: extreme points that are not outliers and lie within the range q3 ± 1.5 (q3 − q1); red circles: outliers. (b) (Left) Histogram of MD data from five research sessions, along with the scaled best-fit generalized Pareto probability density function. (Right) Cumulative distribution function of MD data and best-fit generalized Pareto distribution.