Biomedical Engineering Reference
In-Depth Information
x
axis and
y
axis. The three rows of plots from top to bottom display respectively the reconstructed
position, the velocity, and the acceleration. In each subplot, the red line indicates the desired signal,
the blue line indicates the expectation estimation, and green line indicates the MLE estimation.
The Monte Carlo approach offers the best reconstruction for the position and the velocity. How-
ever, it should be remembered that the reconstructions of the kinematic states will vary among the
realizations. The statistical information of correlation coefficients between the desired signal and
the estimations for 20 times Monte Carlo runs is given in Table
6.3
.
The reconstructed kinematics estimated from the expectation of the joint posterior density
performed better than the one from the noise MLE. The position shows the best results as 0.8161
for
x
and 0.8730 for
y
than other two kinematic variables. This result may be because velocity and
acceleration are derived as differential variables, where the noise in the estimation might be magni-
fied. Another interesting phenomenon is that the
y
kinematics is reconstructed always better than
x
, which was the same situation in previous approaches.
To compare the performance with another generative model, Kalman filter algorithm was
applied on the same data [
24
] to predict the hand positions from the binned neural spiking rate.
Compared to the approach shown here, the Kalman filter simply assumes both the kinematic dy-
namic system model and tuning function are linearly related and the posterior density is Gaussian
distributed. The average correlation coefficients for reconstructed position and
y
are 0.62
±
0.26
and 0.82
±
0.11, respectively, with sliding window for 40 samples prediction, which is 4 sec long.
Because we have different sampling frequency (100 Hz for kinematics rather than 10 Hz), here the
average correlation coefficients are calculated with 50% overlapping window. The average correla-
tions for positions
x
and
y
are 0.8401
±
0.0738 and 0.8945
±
0.0477, respectively, which is better
than the Kalman filter results.
6.5 SUMMaRy
Although spike trains are very telling of neuronal processing, they are also very removed from the
time and macroscopic scales of behavior. Therefore, the spike train methodology begs an answer to
the question of how to optimally bridge the time scale of spikes events (milliseconds) with the time
scale of behavior (seconds). Most often, the relatively rudimentary method of binning is used, but
much of the resolution of the representation is lost, suggesting that better, model-based methodolo-
gies need to be developed.
The fundamental problem in spike-based BMI modeling is how to find more effective ways
to work directly with spikes for modeling that overcome the difficulties of the conventional ap-
proaches. Here we have shown how a Monte Carlo sequential estimation framework could be used
as a probabilistic approach to reconstruct the kinematics directly from the multichannel neural spike
