Biomedical Engineering Reference
In-Depth Information
to time binned (or continuous) signals; hence, they constrain the time resolution of synchrony.
Moreover, the extension of the analysis of the methods for more than two spike trains is not a trivial
problem. Finally, the algorithms are difficult to apply in online applications or are computationally
complex for large ensembles of neurons. The gravity transform [
96
] successfully tackles some of the
above problems, but it lacks a statistical basis. Most importantly, none of the mentioned measures is
appropriate to analyze transient synchronization because a measure in the time or spike domain is
needed. As one can conclude from the discussion, still more work needs to be done to create a useful
similarity metric for spike trains.
The cross-correlation function in (
2.4
) can be used to quantify synchronized firing among
cells in the ensemble. In this case, small sliding (overlapping) windows of data are defined by
a
(
t
),
which is a matrix-containing
L
-delayed versions of firing patterns from 185 neurons. At each time
tick
t
in the simulation, the cross-correlation between neurons
i
and
j
for all delays
l
is computed.
Because we are interested in picking only the most strongly synchr
on
ized bursting neurons in the
local window, we simply average over the delays in (
2.5
). We define
:
C
as a vector representing how
well correlated the activity of neuron
j
is with the rest of the neuronal ensemble. Next, a single 185
×
1
vector at each time tick
t
is obtained in (
2. 6
) by summing cellular assembly cross-correlations only
within each sampled cortical area, M1 (primary motor), PMd (premotor dorsal), SMA (supplemen-
tary motor associative), and S1 (somatosensory).
é
ë
ê
ù
û
ú
C t
( )
=
E
a
( )
t
a
(
t
-
l
)
ijl
i
j
(2.4)
1
L
å
C t
( )
=
C t
( )
ij
ijl
L
l
=
1
(2.5)
C t
∑
( )
( )
=
C t
j
ij
(2.6)
i
cortex
=
The neural correlation measure in (
2.6
) was then used as a real-time marker of neural activ-
ity corresponding to segments of movements of a hand trajectory. In Figure
2.13
, highly correlated
neuronal activity is shown to be time-varying in synchrony with changes in movement direction as
indicated by the vertical dashed line. Figure
2.13
shows that the correlations contained in the data
are highly variable even for similar movements.
We can immediately see that different neurons present different level of involvement in the
task as measured by correlation. Some participate heavily (hot colors), whereas others basically do
not correlate with the hand motion (blue). But even for the ones that participate heavily, their role
across time is not constant as depicted by the vertical structure of the raster. This is stating that the
time structure of neural firings is nonstationary and heavily dependent upon the task.
