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In-Depth Information
In the case of linear methods, a typical formulation consists of sampling neuron
spike-counts at intervals of 50 ms from multiple (15) recording sites. Moreover, the
training stage consists of sampling roughly 1 s of data (20 intervals) and storing this
information into a matrix
R
(
20
×
15
)
while storing the resulting hand position in terms
of
x
)
−
1
R
T
k
and the reconstruction of movement for a history of neural activity
R
is obtained as
u
R
T
R
−
y
coordinates into a vector
k
. Next, the filter is constructed as
f
=(
f
.
2
In addition, there are more sophisticated formulations that take into
account the velocity and acceleration of the movement as well as prior information
about the behavior of neurons in the cortex [82].
Almost all reported BCI methods utilize the same preprocessing stage that con-
sists of spike detection, sorting, and counting over an interval typically in the range
of 50-100 ms. Moreover, correlation methods and principal component analysis
(PCA) with threshold detection are reported as methodologies for the spike detec-
tion [22, 80]. However, Wessberg et al. [155] report using straight linear regression
with no spike detection.
=
×
R
13.9 Neural Network Modeling and the Basal Ganglia
The neurocomputational aspects of Parkinson's disease and DBS have been ex-
amined using neural network models. Aside from their usefulness as classifiers
[129, 98, 67], static neural networks have been used to model the basal ganglia and
the outcome of pallidotomies [60, 58, 104]. In addition, the temporal characteristics
of neurons in these areas and the effects of DBS on neural activity have been inves-
tigated using dynamic, pulsed, or spiking neural networks [56, 57, 53, 17, 43, 44, 70,
149, 54, 8]. The models employed typically include Hodgkin-Huxley formulations
as well as larger networks of simpler integrate-and-fire units [70]. However, there is
a plethora of models that range in complexity and accuracy that may be used to this
end, such as the Noble [112] and Fitzhugh-Nagumo [41] models, as well as many
others [136, 61, 64, 160, 157, 143, 141, 27, 73, 75].
Three general methods of modeling nuclei of the basal ganglia can be found in
the scientific literature. These can be broadly categorized into “functional” models
that are designed to provide insight into the computational function of the basal
ganglia [56, 57, 53, 17, 43, 44, 142, 8], “physiological” models that incorporate more
details of ion transport [70, 149, 54], and “conceptual” models [20, 77, 145, 34, 148]
that provide a description of the synaptic connectivity. Moreover, the physiological
models have been used in simulations of applied deep brain simulation (DBS). In
particular, Grill et al. [54] show that extrinsic high frequency stimulation “masks” or
2
The formulation is included here as it appears in the literature. However, there are some unre-
solved questions. In particular, it would seem that a separate filter would be required for each move-
ment element so that given a history of 20 positions, there are corresponding
x
and
y
-coordinate
vectors
x
and
y
of 20 elements each. In that case, two filters would be derived as
f
x
=(
R
T
R
)
−
1
R
T
x
)
−
1
R
T
y
. Then, given a set of new data
S
in the testing phase, the corresponding hand
positions would be given as
x
new
R
T
R
and
f
y
=(
=
S
×
f
x
and
y
new
=
S
×
f
y
.
