Biomedical Engineering Reference
In-Depth Information
the examples of neuronal subset selection for the original data. Figure
4.15b
and c show the ex-
amples for the shifted data and the shuffled data, respectively. The neuronal subsets are presented
along with the corresponding HPs (
z
coordinate) of seven reaching movement examples. It is clear
that very few subsets are selected for the surrogate data. To quantify these subset selection results,
we define a selection rate as the average number of neuronal channels per time instance. From the
experimental results, the selection rates were 0.006 ± 0.006 for the original hand reaching data,
0.001 ± 0.003 for the shifted data, and 9.1 × 10
−4
± 0.004 for the shuffled data, respectively. For 2D
cursor control data, the selection rates were 0.015 ± 0.009 for the original data, and 0.002 ± 0.006
for the shifted data (the selection rate for the shuffled data is considerably lower). Therefore, these
results demonstrate that we can determine the thresholds using the surrogate data with which neu-
ronal subsets selected from the synchronized data is determined to represent real-time correlations
of neuronal activities and kinematics.
We examined if the neuronal subsets showed dependency on the initial condition of the lin-
ear adaptive system. We first define a selection vector as
=
1 2
�
(4.49)
where
s
j
(
n
) = 1 if the
j
th neuronal channel was selected at the
n
th bin, and
s
j
(
n
) = 0 otherwise. We
repeated the neuronal subset selection analysis 100 times for different initial filter weights. Then,
an average of
s
(
n
), denoted as
s
(
n
), over 100 repetitions was computed. If the linear adaptive sys-
tem is robust to initial conditions, the nonzero elements of
s
(
n
) should be close to 1. Hence, we
examined the statistics of those nonzero elements. For 3D food reaching data, the average and
standard deviation were 0.85 and 0.26, respectively. However, if we are only concerned with the
subset selection for movements, the average and standard deviation estimated only during move-
ments were 0.94 and 0.15, respectively. Because we are typically more interested in neuronal subsets
during given movements, the latter result demonstrates that the linear system is reasonably robust
to initial conditions. For 2D cursor control data, the average and standard deviation of the nonzero
elements of
s
(
n
) were 0.91 and 0.19, respectively, which again demonstrates the robustness to ini-
tial conditions.
To find neuronal subsets without separation into each spatial coordinate, we performed the
analysis for individual coordinates and combined the resulting subsets into one. To that end, we per-
formed a Boolean OR operation with
s
(
n
) resulted from every coordinate analysis. This operation
yields a single joint neuronal subset at each time instance. In other words, if a channel is selected for
at least one coordinate of HP, it belongs to the joint subset.
To investigate the temporal variation of neuronal subsets, we tracked the joint subsets over
the entire data. To focus the analysis only on the movement portion of the 3D data, we divided the
entire neuronal subsets into individual segments corresponding to each reaching movement. This
s
( )
n
[ ( ),
s n s n
( ),
,
s
( )]
n
T
M
