Biomedical Engineering Reference
In-Depth Information
To contend with the problem of selecting delays, the mutual information between the spike
and the delayed linear filter kinematics vector can be computed as a function of the time lag after
a spike arrives. Considering that the response delay ranges from 0 to 500 msec after a neuron fires,
the mutual information is determined as a function of lag according to (
6.20
).
r r
⋅
(
r r
r r
p
(
spike
|
k
(
lag
))
x
∑
∑
I
)
(
lag
)
=
p k
(
⋅
x
(
lag
))
p
(
spike
|
k
⋅
x
(
lag
))
log
(6.20)
r r
2
(
spike
;
k
⋅
x
p
(
spike
)
r r
k
⋅
spike
=
0 1
,
x
where to approximate
p k
x
exactly the same method as the estimation of the non-
linear
f
we discussed in Section
6.4.1
. For all 185 neurons, the mutual information as the function
of time delay was obtained from 10 000 continuous samples of kinematics. The time delay with
most mutual information was assigned as the best time lag for each neuron.
Figure
6.10
shows the mutual information as the function of time delay from 0 to 500 msec
after spikes for five neurons: neurons 72, 77, 80, 99, and 108. The cross on each curve marks the best
time lag, which was 110, 170, 170, 130, and 250 msec, respectively. The average best time delay for
185 neurons is 220 msec and was chosen for the subsequent analysis to simplify the implementation.
(spike |
×
(lag))
6.4.4 Point Process Monte Carlo Sequential Estimation Framework for BMIs
The decoding problem for BMIs is shown in Figure
6.11
. The spike times from multiple neurons
are the multichannel point process observations. The process begins by first windowing the data to
determine if a spike is present or not (assign 1 if there is a spike; otherwise, assign 0). The inter-
val should be chosen to be small enough so that only few intervals have more than one spike, and
therefore still obey largely the Poisson assumption. One must be careful when selecting the kine-
matic state (position, velocity, or acceleration) in decoding because it is still not clear which one the
neuron actually encodes for. The analysis presented here will consider all three kinematic variables.
The velocity is derived as the difference between the current and previous recoded positions, and the
acceleration is estimated by first differences from the velocity. For fine timing resolution, all of the
kinematics are interpolated and time-synchronized with the neural spike trains.
The whole process can be specified in the following steps:
Step 1:
Preprocess and analysis
1.
2.
3.
Generate spike trains from stored spike times.
Synchronize all the kinematics with the spike trains.
Assign the kinematic vector
x
to be reconstructed.
