Neural decoding of hand motion using a linear state-space model with hidden states

Abstract

The Kalman filter has been proposed as a model to decode neural activity measured from the motor cortex in order to obtain real-time estimates of hand motion in behavioral neurophysiological experiments. However, currently used linear state-space models underlying the Kalman filter do not take into account other behavioral states such as muscular activity or the subject's level of attention, which are often unobservable during experiments but may play important roles in characterizing neural controlled hand movement. To address this issue, we depict these unknown states as one multidimensional hidden state in the linear state-space framework. This new model assumes that the observed neural firing rate is directly related to this hidden state. The dynamics of the hand state are also allowed to impact the dynamics of the hidden state, and vice versa. The parameters in the model can be identified by a conventional expectation-maximization algorithm. Since this model still uses the linear Gaussian framework, hand-state decoding can be performed by the efficient Kalman filter algorithm. Experimental results show that this new model provides a more appropriate representation of the neural data and generates more accurate decoding. Furthermore, we have used recently developed computationally efficient methods by incorporating a priori information of the targets of the reaching movement. Our results show that the hidden-state model with target-conditioning further improves decoding accuracy.

Fig. 1

Graphical model for the hidden-state-included Kalman filter. The neural firing rate, y_k, is directly related to both the hand kinematics, x_k, and the hidden state, n_k. The dynamics of the hand kinematics and hidden state are both Markovian and impact each other over time.

Fig. 2

(A) Eigenvalues of the matrixes (Q₀ − Q₁), (Q₀ − Q₂), and (Q₀ − Q₃) in dataset 1. The eigenvalues are shown in descending order of the magnitude, and only the first 7 of the total 124 values are shown. (B) Eigenvalues of the matrixes (W₀ − W₁), (W₀ − W₂), and (W₀ − W₃) in dataset 1. The eigenvalues are also shown in descending order of the magnitude. (C) and (D) same as (A) and (B) except for dataset 2.

Fig. 3

(A) True hand trajectory (dashed) and reconstruction using the new Kalman filter model with a hidden state (d = 3) of an example trial from dataset 1. Left column: the trajectories in the 2-D working space. Right column: the trajectories by their x and y components. (B) Same as (A) except for an example trial from dataset 2.

Fig. 4

Three components (three rows) of the estimated 3-D hidden state in two test data sets (two columns), where the hidden state is averaged as one value in each test trial.