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Objectives. Brain-machine interfaces (BMIs) aim to help people with motor disabilities by interpreting brain signals into motor intentions using advanced signal processing methods. Currently, BMI users require intensive training to perform a pre-defined task, not to mention learning a new task. Thus, it is essential to understand neural information pathways among the cortical areas in task learning to provide principles for designing BMIs with learning abilities. We propose to investigate the relationship between the medial prefrontal cortex (mPFC) and primary motor cortex (M1), which are actively involved in motor control and task learning, and show how information is conveyed in spikes between the two regions on a single-trial basis by computational models. Approach. We are interested in modeling the functional relationship between mPFC and M1 activities during task learning. Six Sprague Dawley rats were trained to learn a new behavioral task. Neural spike data was recorded from mPFC and M1 during learning. We then implement the generalized linear model, the second-order generalized Laguerre-Volterra model, and the staged point-process model to predict M1 spikes from mPFC spikes across multiple days during task learning. The prediction performance is compared across different models or learning stages to reveal the relationship between mPFC and M1 spike activities. Main results. We find that M1 neural spikes can be well predicted from mPFC spikes on the single-trial level, which indicates a highly correlated relationship between mPFC and M1 activities during task learning. By comparing the performance across models, we find that models with higher nonlinear capacity perform significantly better than linear models. This indicates that predicting M1 activity from mPFC activity requires the model to consider higher-order nonlinear interactions beyond pairwise interactions. We also find that the correlation coefficient between the mPFC and M1 spikes increases during t

Brain-machine interfaces (BMIs) help people to control external devices using the digital commands based on interpreted brain states from multi-scale neural data. Existing methods have extracted brain states using principal component analysis and clustering. However, they work on the spike count data, fail to exploit the full information of spike timings, and result in a relatively coarse time resolution. Quick-response BMIs call for fine temporal resolution brain states estimation. The high-temporal resolution can be achieved by directly operating on spike timings. A cross-intensity (CI) kernel family facilitate this by mathematically describing the spike timings in a functional reproducing kernel Hilbert space (RKHS). In this paper, we applied a CI kernel distance-based clustering method on multi-neuron spike trains for brain state estimation. We tested this method on the neural data from the primary motor cortex of a Sprague Dawley rat performing lever-press tasks. The spike trains are grouped into several clusters by proposed method. We found the timings of clustered brain states to be highly correlated to specific stages of lever-press process. We compared CI-based clustering with L1-norm based clustering on multi-neuron spike trains, and found that CI-based clustering on average has 24.3% improvement on the correlation with lever-press states. These clustered brain states can be used to correlate local field potentials, and this correlation potentially helps build long-term stable BMIs. © 2021 IEEE.

Neuroprosthesis refers to implantable medical devices which can replace injured biological functions in the brain. One of the core problems in neuroprosthesis study is to construct a neural signal transformation model from one cortical area to another. Since the brain encodes and transmits information in spike trains, spiking neural network (SNN) can be an ideal choice for neuroprosthesis modeling. This paper proposes a spiking neuron point-process model (SNPM), which receives spike times as input, and is capable of modeling nonlinear interactions between cortical areas. The proposed SNPM can be implemented on neuromorphic chips for low-energy computing, thus has potential for clinical applications. Experiments show that SNPM can accurately reconstruct functional relationships from PMd (dorsal premotor cortex) to M1 (primary motor cortex) areas. © 2021 IEEE.

The medial prefrontal cortex (mPFC) and primary motor cortex (M1) are both actively involved in the reward guided learning. However, how the information is conveyed in spike trains between these two regions has not been investigated. Spike prediction models have been developed to predict the spike trains between two cortical areas, for example, CA3 to CA1 in hippocampus, as well as premotor to M1. In this paper, we investigate the co-activation between mPFC and M1 by comparing three spike prediction models with different nonlinear capacity. Our data was collected from the mPFC and M1 of a rat when it was learning a two-lever discrimination task. The mPFC spike trains are served as the input of models and M1 spike trains as the desired output. We compare the spike prediction performances of three models, including generalized linear model (GLM), second order GLM, and staged point-process model. Our results show that all three model outputs have similar discrete-time rescaling Kolmogorov-Smirnov test results and similar correlation coefficient (0.42 on average across neurons). The paired t-tests across neurons also show the lack of significant difference. The preliminary results indicate possible linear co-activation between the M1 and mPFC during the learning stage.

A neural prosthesis is designed to compensate for cognitive functional losses by modeling the information transmission among cortical areas. Existing methods generally build a generalized linear model to approximate the nonlinear transformation among two areas, and use the temporal information of the neural spike with low efficiency. It is essential to efficiently model the nonlinearity embedded in spike generation and transmission for the real-time. This paper proposes a nonlinear point-process model to describe spike-in and spike-out transformation using the theory of reproducing kernel Hilbert space (RKHS) and the binless kernel on spike trains. The binless kernel efficiently maps exact spike timing information to the RKHS to describe nonlinear transformations with global minimum regardless of the weight initialization. A streaming K-medoids algorithm is introduced to select typical and important features in this nonlinear binless kernel for further modeling. We test our model on the nonlinearly generated synthetic neural spike trains, and compare with the existing spike transformation methods, such as Volterra model and staged point-process model. The results show that our model has higher goodness-of-fit evaluated by Kolmogorov-Smirnov test and less variance on the prediction results, which indicates the potential better modeling approach for neural prosthesis application. © 2019 IEEE.

Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than