Biomedical Engineering Reference
In-Depth Information
C H A P T E R 3
Input-output BMI Models
additional Contributors: Sung-Phil Kim, yadunandana Rao, and
deniz Erdogmus
The BMI experimental paradigm lends itself to statistical signal processing methodologies used to
derive optimal models from data. Indeed, in the BMI setting, the researcher has available synchro-
nously both the input to the BMI (neuronal activity − spike trains) as well as the desired response
(kinematics of movement). The problem can be then framed in terms of “decoding,” by which spike
occurrences of individual neurons are translated into intended movement. In terms of modeling,
the aim is to find a functional relationship between neural activity and the kinematic variables of
position, velocity, acceleration, and force. Here, we will describe how to translate the BMI decod-
ing problem into a system identification framework, where a parametric linear or nonlinear system
can be trained directly from the collected data to achieve outputs close to the kinematics as in
Figure
3.1
. Model building has been extensively studied in control theory and signal processing so
there are a wealth of methods that can be utilized [
1
].
Because the data are collected by multielectrode arrays, and each electrode can potentially
sense several neurons, spike sorting is commonly utilized to identify individual neurons. Provided
that the spike features have been accurately extracted, the neuronal spike firings become the decod-
ing model input. Because the desired responses are continuous amplitude signals with unknown
structure, we will treat them as random processes. As for the neural data, this chapter will deal with
spike rate coding in short windows of 100 msec (called binned data), and a stochastic model for
the data will also be assumed. This problem can therefore be framed as system identification with
stochastic processes, which is a very well developed area in optimal signal processing and controls
[
2
]. However, its application to BMI is not without problems for the following reasons:
1.
There is a huge difference in the time scale of spike trains (msec) and that of behavior (sec)
that the model has to bridge. Binning the spikes firing of each neuron over an appropriate
time window (50 ~ 100 msec) has been widely used to smooth the spike trains and provide
a time scale closer to behavior. It also implements a simple method for time to amplitude
conversion of the neural modulation.
