Biomedical Engineering Reference
In-Depth Information
and the observations are assumed to be discrete. HMM models are the leading technology in speech
recognition because they are able to capture very well the piecewise nonstationary of speech [
20
]. It
turns out that speech production is ultimately a motor function, so HMMs can potentially be also
very useful for motor BMIs. One of the major differences is that there is a well established finite
repertoire of speech atoms called the phonemes, which allow for the use of the HMM framework.
Research into animal motor control is less advanced, but recently there has been interest in studying
complex motor actions as a succession of simpler movements that can be properly called “movemes”
[
21
]. If this research direction meets the expectation, then HMMs would play a more central role in
motor BMIs because the model building problem would be similar to speech recognition.
5.1 PoPUlaTIoN VECToR CodINg
As presented in the Introduction, the population vector algorithm is a physiologically based model
that assumes that a cell's firing rate is a function of the velocity vector associated with the movement
performed by the individual. Population vector coding is based on the use of tuning curves [
22
],
which in principle provide a statistical relationship between neural activity and behavior. The tun-
ing or preferred direction [
2
] of each cell in the ensemble convey the expected value of a probability
density function (PDF) indicating the average firing a cell will exhibit given a particular movement
direction. The PVA model relating the tuning to kinematics is given by (
5.1
)
n
n
x
n
y
n
z
s
(
V
)
=
b
+
b
v
+
b
v
+
b
v
=
B
⋅
V
=
B
V
cos
θ
,
(5.1)
n
0
x
y
z
where the firing rate
s
for neuron
n
is a weighted (
b
n
x,y,z
) sum of the components (
v
x,y,z
) of the
unit velocity vector
V
of the hand plus mean firing rate
b
0
n
. The relationship in (
5.1
) is the inner
product between the velocity vector of the movement and the weight vector for each neuron, that
is, the population vector model considers each neuron independently of the others (see Figure
5.1
).
The inner product (i.e., spiking rate) of this relationship becomes maximum when the weight vec-
tor
B
is collinear with the velocity vector
V
. At this point, the weight vector
B
can be thought as
the neuron's preferred direction for firing because it indicates the direction for which the neuron's
activity will be maximum. The weights
b
n
can be determined by least squares techniques [
1
]. Each
neuron makes a vector contribution
w
in the direction of
P
i
with magnitude given in (
5.2
), where
b
0
is the mean firing rate for neuron
n
. The resulting population vector or movement is given by (
5.3
),
where the reconstructed movement at time
t
is simply the sum of each neuron's preferred direction
weighted by the firing rate.
n
w
(
V
,
t
)
=
V
s
(
)
−
b
,
(5.2)
n
n
0
