Population decoding of motor cortical activity using a generalized linear model with hidden states

Abstract

Generalized linear models (GLMs) have been developed for modeling and decoding population neuronal spiking activity in the motor cortex. These models provide reasonable characterizations between neural activity and motor behavior. However, they lack a description of movement-related terms which are not observed directly in these experiments, such as muscular activation, the subject's level of attention, and other internal or external states. Here we propose to include a multi-dimensional hidden state to address these states in a GLM framework where the spike count at each time is described as a function of the hand state (position, velocity, and acceleration), truncated spike history, and the hidden state. The model can be identified by an Expectation-Maximization algorithm. We tested this new method in two datasets where spikes were simultaneously recorded using a multi-electrode array in the primary motor cortex of two monkeys. It was found that this method significantly improves the model-fitting over the classical GLM, for hidden dimensions varying from 1 to 4. This method also provides more accurate decoding of hand state (reducing the mean square error by up to 29% in some cases), while retaining real-time computational efficiency. These improvements on representation and decoding over the classical GLM model suggest that this new approach could contribute as a useful tool to motor cortical decoding and prosthetic applications.

Figure 1

Upper two panels: True hand trajectory, x- and y-position, for one example trial in the study. Bottom panel: A raster plot of spike trains of 5 simultaneously-recorded neurons during the same example trial. We plot the hand trajectory as one-dimensional plots to help show the temporal correspondence between the hand trajectory and the spike trains.

Figure 2

CIFs in the GLMHS-IS and GLM with IPP spike trains in one example trial. Upper plot: The thick black line denotes the CIF for the 50th neuron from Dataset 1 under the GLMHS-IS IPP Model with d = 4 with 95% confidence intervals (thin gray lines). The dashed black line denotes the CIF of the classical GLM. Here we see that the CIF for the GLMHS-IS model can capture more of the dynamics of the spike train when compared to the classical GLM. Lower plot: the original spike train.

Figure 3

A. A comparison of the NLLRs for the GLMHS-IS models in the testing part of Dataset 1 when the spike train is modeled as an inhomogeneous Poisson process (solid line with stars) and when modeled as a non-Poisson process (dashed line with circles). The model is a classical GLM if the hidden dimension d = 0. We notice that the NLLR increases as d increases in both IPP and NPP cases. Also, we see the NLLR for the NPP case is higher than that for the IPP case. B. Same as A but for Dataset 2.

Figure 4

A. A comparison of the NLLRs for the GLMHS-DS models in the testing part of Dataset 1 when the spike train is modeled as an IPP (solid lines with stars) and when modeled as an NPP (dashed lines with circles). The model is a classical GLM if the hidden dimension d = 0. We observe that the NLLR increases with respect to d in both IPP and NPP cases. Also, we see the NLLR for the NPP case is higher than for the IPP case. B. Same as A but for Dataset 2.

Figure 5

A. True hand trajectory (dashed red), x- and y-position, of an example trial from dataset 1, and its reconstruction (solid blue) and 95% confidence region (thin solid blue) using the GLMHS-IS with d = 4 under the IPP case. The reconstruction by the classical GLM (solid green) is also shown here. B. Same as A except from another trial in dataset 2 in the NPP case with d = 1 in the model. In both cases, we see that the reconstructions from the GLMHS models perform well, and they are close to those from the classical GLM models.

Figure 6

Log-likelihoods of the GLM (dashed line with stars) and the GLMHS-IS with d = 1 under the IPP case (solid line with circles) in dataset 2 where the kinematic order varies from 1 to 6. We see that the separation between the GLM and GLMHS is fairly constant for all kinematic orders.