Biomedical Engineering Reference
In-Depth Information
5ms
0
0
10ms
20ms
40ms
80ms
1
2
4
160ms
6
320ms
12
21
640ms
FIgURE 2.7:
An illustration of the scaled convolution output from the HatWT;
u
j
(
k
) for a given spike
train at a time instance
k
0
. The number in each box denotes the value of
u
j
(
k
0
) for
j
= 0, … , 7.
to not exceed 1 sec because it has been reported that only the past neuronal activity up to 1 sec is cor-
related with the current behavior [
44
]. In the following case examples, we select eight scales of binning
starting at 5 up to 640 msec, with the dyadic scaling of 5, 10, 20, 40, 80, 160, 320, and 640 msec.
With the selected scales, the HatWT is performed on an ensemble of BMI neuronal spike
trains in the following way. We first generate the basic bin count data with a 5-msec nonoverlapping
window for every neuronal channel. Next, the HatWT is applied to the 5-msec bin count data at
each neuronal channel, yielding the convolution output
v
j
(
k
) for
j
= 0, … , 7 following (
2.15
). Each
series
v
j
(
k
) is then multiplied by 2
j
to generate
u
j
(
k
) [in (
2.17
)]. An illustrative example of the gener-
ated
u
j
(
k
) at specific time instance
k
0
is presented in Figure
2.7
.
Note that the sampling rate in
u
j
(
k
) is 200 Hz for any
j
. In terms of the binning process,
u
j
(
k
)
can be interpreted as the bin count data for a given spike train with a 5∙2
j
-msec time window that
slides over time by step of 5 msec. Therefore,
u
j
(
k
) with a larger
j
will add spikes from a longer time
window and will overlap more with the previous bin
u
j
(
k
− 1), which then yields a smoother tem-
poral patterns for larger
j
.
The top panel in Figure
2.8
demonstrates an example of
u
j
(
k
) of a specific neuron for 5-second
period.
u
j
(
k
) for each
j
is normalized to have the maximum value of 1. Darker pixels denote larger
values. The set of
u
j
(
k
) are temporally aligned with the associated hand trajectories plotted in the
bottom panel. To view the correlation of
u
j
(
k
) with the movement for each
j
, the discrete time series
u
j
(
k
) is separately plotted on top of the hand trajectory (the
x
coordinate) in Figure
2.9
[both
u
j
(
k
)
and the hand trajectory are scaled to be in the similar dynamic range for visualization purposes].
This figure is very telling about the difficulties and opportunities of data modeling for BMIs.
It demonstrates that the correlation of
u
j
(
k
) with the hand trajectory increases with larger
j
; in fact,
only the 320- and 640-msec scales have reasonable correlations with the movements. Therefore,
