Strategies for Neural Ensemble Data Analysis for Brain–Machine Interface (BMI) Applications

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The advance of BMIs was largely motivated by investigations of velocity encoding in single neurons during stereotypical reaching experiments. However, BMIs are designed to decode neural activity from an ensemble of neurons and direct general reaching movements. Hence, neural data analysis strategies for BMIs are required to: (1) analyze the neural activity from ensemble of neurons, (2) account for the dynamical nature of the neural activity associated with general reaching movements, and (3) explore and exploit other relevant modulating signals.Decoding neural activity can be performed either in a single stage or two stages. Two-stage decoding relies on a preliminary encoding stage to determine how the neurons are tuned to the relevant biological signals. Based on the estimated tuning curves, the neural activity across an ensemble of neurons can be decoded using either a population-vector, maximum likelihood estimation, or Bayesian inference (Pouget et al., 2003). The population-vector approach results in a linear relationship between the spike counts and the estimated biological signal, which can be estimated directly in a single stage using linear regression (Brown et al., 2004). This chapter focuses on single-stage decoding with linear regression, and in particular on two special challenges facing the application of linear regression to neural ensemble decoding during reaching movements (see “Movement Prediction”). First, given the dynamic nature of the decoded signal, it is necessary to include the history of the neural activity, rather than just its current spike count. Second, due to the correlation between the activities of different neurons (see “Ensemble Analysis”) and the activities in different time lags, the resulting regression problem is ill-posed and requires regularization techniques (see “Linear Regression”).Although neural decoding can be performed in a single stage, neural encoding is still important for investigating which signals are encoded in the neural activity. For this purpose, the notion of tuning curves is generalized to characterize how the neural activity represents the spatiotemporal profile of the movement. This analysis quantifies both the spatiotemporal tuning curves and the percent variance of the neural activity that is accounted by the movement profile (see “Neuronal Encoding and Tuning Curves”). For comparison, the percent variance in the neural activity that might be related to general neural modulations is assessed independently under the Poisson assumption (see “Neuronal Modulations”). These two-faced variance analyses provide a viable tool for quantifying the extent to which the neural code is effectively decoded, and the potential contribution of yet undecoded modulating signals.The strategies and algorithms described in this chapter are demonstrated using the neural activity recorded from an ensemble of cortical neurons in different brain areas during a typical target-hitting experiment with pole control as described in Carmena et al., 2003.