Biomedical Engineering Reference
In-Depth Information
the concentration set to zero for all distances greater than
r
(Equation 4.54). The
maximum concentration at the emitting node is 1.0 and the concentration builds up
and decays from this value linearly as defined by Equations (4.55 and 4.56) at a rate
determined by
s
.
e
−
2
d
/
r
×
T
(
t
)
d
<
r
C
(
d
,
t
)=
(4.54)
0
else
H
t
−
t
s
emitting
H
H
t
s
−
t
s
−
H
t
−
t
s
not emitting
T
(
t
)=
(4.55)
0
x
≤
0
H
(
x
)=
x
0
<
x
<
1
(4.56)
1 else
where C(d,t) is the concentration at a distance
d
from the emitting node at time
t
.
t
e
is the time at which emission was last turned on,
t
s
is the time at which emission
was last turned off, and
s
(controlling the slope of the function
T
) is genetically
determined for each node. The total concentration at a node is then determined by
summing the contributions from all other emitting nodes (nodes are not affected by
their own concentration, to avoid runaway positive feedback).
A variant on this diffusion model, based on the cortical plexus diffusion described
earlier in this chapter, involves diffusion of a uniform concentration 'cloud' centred
on some genetically specified site distant from the emitting node. This reflects the
spatial separation of the main plexus and the body of the controlling neurons. The
cloud suddenly turns 'on' or 'off', depending on the state of the controlling neuron,
in keeping with the plexus mode of signalling described earlier.
4.4.3
Modulation
In a typical GasNet model [36], each node in the network can have one of three dis-
crete quantities (zero, medium, maximum) of N possible receptors. Each diffusing-
neurotransmitter/receptor pairing gives rise to a separate modulation to the properties
of the node. The strength of a modulation at node
i
at time
n
,
M
j
, is proportional to
the product of the gas concentration at the node,
C
i
and the relevant receptor quantity,
R
j
as described by Equation 4.57. Each modulation makes some change to one or
more function parameters of the node. All the variables controlling the process are
again set for each node by an evolutionary search algorithm.
M
j
=
ρ
i
C
i
R
j
(4.57)
A number of different receptor linked modulations have been experimented with,
including:
•
Action of receptor 1 : increase gain of node transfer function
•
Action of receptor 2: decrease gain of node transfer function
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