An information-theoretic approach for evaluating probabilistic tuning functions of single neurons

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

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.

Eye Velocity Gain Fields in MSTd During Optokinetic Stimulation

Lesion studies argue for an involvement of cortical area dorsal medial superior temporal area (MSTd) in the control of optokinetic response (OKR) eye movements to planar visual stimulation. Neural recordings during OKR suggested that MSTd neurons directly encode stimulus velocity. On the other hand, studies using radial visual flow together with voluntary smooth pursuit eye movements showed that visual motion responses were modulated by eye movement-related signals. Here, we investigated neural responses in MSTd during continuous optokinetic stimulation using an information-theoretic approach for characterizing neural tuning with high resolution. We show that the majority of MSTd neurons exhibit gain-field-like tuning functions rather than directly encoding one variable. Neural responses showed a large diversity of tuning to combinations of retinal and extraretinal input. Eye velocity-related activity was observed prior to the actual eye movements, reflecting an efference copy. The observed tuning functions resembled those emerging in a network model trained to perform summation of 2 population-coded signals. Together, our findings support the hypothesis that MSTd implements the visuomotor transformation from retinal to head-centered stimulus velocity signals for the control of OKR.

Neuronal variability of MSTd neurons changes differentially with eye movement and visually related variables

Neurons in macaque cortical area MSTd are driven by visual motion and eye movement related signals. This multimodal characteristic makes MSTd an ideal system for studying the dependence of neuronal activity on different variables. Here, we analyzed the temporal structure of spiking patterns during visual motion stimulation using 2 distinct behavioral paradigms: fixation (FIX) and optokinetic response. For the FIX condition, inter- and intra-trial variability of spiking activity decreased with increasing stimulus strength, complying with a recent neurophysiological study reporting stimulus-related decline of neuronal variability. In contrast, for the optokinetic condition variability increased together with increasing eye velocity while retinal image velocity remained low. Analysis of stimulus signal variability revealed a correlation between the normalized variance of image velocity and neuronal variability, but no correlation with normalized eye velocity variance. We further show that the observed difference in neuronal variability allows classifying spike trains according to the paradigm used, even when mean firing rates (FRs) were similar. The stimulus-dependence of neuronal variability may result from the local network structure and/or the variability characteristics of the input signals, but may also reflect additional timing-based mechanisms independent of the neuron's mean FR and related to the modality driving the neuron.