Biomedical Engineering Reference
In-Depth Information
make them equal to the average distance between the cluster centers and the training pat-
terns. This can be mathematically given by
1
M
j
x
j
(
x
p
-
w
1
j
)
2
2
j
(5.5)
where
j
is the set of training patterns grouped with cluster center
w
1
j
, and
M
j
is the num-
ber of training patterns assigned to the group
j
.
The adaptation of the weights in the output layer occurs only when the parameters of
the basis function (
w
1
j
,
j
) have been determined. The nodes in the output layer are com-
puted using a LMSs learning algorithm that utilizes error correction. The training data for
this process is a set of input-output pairs (
x
p
,
d
) where is
d
is the desired output given
x
p
.
Based on the previously determined basis function parameters the output of the
i
th
node,
the node output, is calculated using Eqs. (5.3) and (5.4). Typically, the weight adaptation
for the feed forward weights of the
i
th
node in layer 2 is
w
2
i
(
new
)
w
2
i
(
old
)
(
y
1
d
i
)
u
1
j
(5.6)
where
is the learning rate which determines the step size for changing the value of the
weight after each iteration.
5.3.1.2 Multivariate Calibration Surface for a bR Photocell
Among the numerous biomaterials being investigated for engineering applications, bacte-
riorhodopsin (bR) has received a great deal of attention as a “smart material” for accom-
plishing a variety of complex functions. bR is a retinal protein found in the cell membrane
of
Halobacterium salinarum
. Absorption of light by the retinal chromophore of bR causes a
photoinduced isomerization, followed by a complex photochemical cycle through several
spectrally distinct intermediate states. During the photocycle, bR pumps a proton from the
cytoplasmic side to the extracellular side of the cell membrane, resulting in a charge dis-
placement and an electrochemical potential across the membrane. This proton gradient is
used by the bacterium to generate energy by the synthesis of ATP from ADP.
A simple bR-based photocell was recently constructed by placing a thin film of bR
between two indium tin oxide (ITO) electrodes as shown in Figure 5.4. The purple mem-
brane (PM) that contained the bR molecules was isolated from strains 14 of
Halobacterium
halobium
according to the method described in Wang et al. (45). The PMs were orientated and
electrophoretically deposited onto the ITO electrode that was connected to ground. The
cytoplasmic side of the bR membrane was attached to the ITO conductive surface; the extra-
cellular side of the bR membrane was contacted with the second ITO electrode that was the
input of the measurement circuit. A polyester thin film was used as the spacer separating the
two ITO electrodes. The diameter of the active area of the photocell is about 5 mm.
The signal generated by the bR photocell corresponds to the charge displacement inside
the protein and can be detected as a photovoltage across the membrane or a photocurrent
through the membrane. The photovoltage generated by the dried bR film can be modeled
as an equivalent RC circuit (45,46) as shown in Figure 5.5. The experimental results reveal
that both wavelength and intensity of the incident light influence the amplitude of the sig-
nal. Under illumination of a laser light with a fixed wavelength, the photocell signal as
shown in Figure 5.6 is approximately linear except near the saturating intensities. The sat-
uration of light intensity is related to the physical properties of the bR photocell such as
thickness, area, and optical density of the bR film. This property was studied by using a
tunable argon or krypton laser system with five selectable wavelengths ranging from 476
