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can be found in Cutsuridis and Perantonis [21] and Cutsuridis [18, 19, 20]. As in the
extended model without dopamine (see previous chapter), the GO signal was de-
fined by
2
u
2
G
(
t
)=
G
0
(
t
−
τ
i
)
[
t
−
τ
i
]
/
(
β
+
γ
(
t
−
τ
i
)
)
,
(11.1)
where
G
0
amplifies the
G
0
signal,
i
is the onset time of the
i
th volitional command,
β
is a step function that jumps from 0 to 1 to
initiate movement. The difference vector (DV) with dopamine was described by
and
γ
are free parameters, and
u
[
t
]
dV
i
dt
=
30
(
−
V
i
+
T
i
−
DA
1
A
i
+
DA
1
a
w
(
W
i
(
t
−
τ
)
−
W
j
(
t
−
τ
)))
,
(11.2)
where
T
i
is the target position command,
A
i
is the current limb position command,
a
w
is the gain of the spindle feedback,
W
i
,
j
are the spindle feedback signals from the
antagonist muscles, and DA
1
is the modulatory effect of dopamine on area 4's PPV
inputs to DV cell activity. Dopamine's values ranged from 0 (lesioned) to 1 (nor-
mal). The desired velocity vector (DVV) with dopamine which represented area's 4
reciprocally activated cell activity was defined by
G
+
B
u
DA
4
u
i
=
(
DA
2
V
i
−
DA
3
V
j
+
,
(11.3)
where
i
j
designate opponent neural commands,
B
u
is the baseline activity of
the phasic-MT area 4 cell activity, and DA
2
,DA
3
are the modulatory effects of
dopamine on DV inputs to DVV cell activity and DA
4
is the effect of dopamine
on DVV baseline activity. The reader can notice that parameter DA
1
modulates the
PPV input to area's 5 phasic (DV) cell activity (Equation 11.2), whereas parameters
DA
2
,DA
3
, and DA
4
modulate the DV inputs to DVV and P cell activity (area's 4
reciprocal and bidirectional activities) and to DVV baseline activity (Equations 11.3
and 11.4), respectively. This is, as we explained in a previous section, because DA
afferents are densest in area 4 than they are in area 5. So, the effect of DA depletion
would be stronger in area 4 than in area 5. Also, the DV flexion (
V
i
) cell is mod-
ulated by a different DA parameter DA
2
) from the DV extension (
V
j
) cell (DA
3
).
The latter is supported by the experimental findings of Doudet and colleagues [23]
(for comparison see Figs. 11.4 and 11.5, where the firing intensity of the flexion
cells is affected (reduced) more than the firing intensity of the extension cells). The
co-contractive vector (P) with dopamine which was represented by area's 4 bidirec-
tional neuronal activity was given by
,
G
+
B
P
DA
4
u
i
=
(
DA
2
V
i
−
DA
3
V
j
+
,
(11.4)
whereas the present position vector (PPV) dynamics was defined by
dA
i
dt
=
V
i
]
+
−
V
j
]
+
.
G
[
DA
2
.
G
[
DA
3
.
(11.5)
The renshaw population cell activity with dopamine was modeled by
