Biomedical Engineering Reference
In-Depth Information
Ito provided the first experimental support for the Marr-Albus model by
showing that conjunctive local stimulation of parallel fibers and climbing fibers
results in a long-lasting depression of parallel fiber-Purkinje cell transmission
(30). The results were obtained from a field potential analysis providing a corre-
sponding significant depression of the
n
2
potential lasting for more than 1 hr.
These experimental data provided the basis for plasticity in the cerebellum.
3.2. Models and Simulations of Selected Cerebellar Functions
With a simple non-adaptive functional model, including adjustable vectors
of weights and nonlinear elements such as thresholds, we were able to simulate
experimentally recorded activity patterns in cerebellar elements of the cat ob-
served during passive movements (37).
The plan of the model is based on three different levels of computation
(Figure 7A). At the receptor level (Figure 7A1), ideal linear receptors are as-
sumed to encode the stimulus G(
t
) function (passive movement) as well as their
first- (
d
G/
dt
) and second-derivative functions (
d
2
G/
dt
2
), either directly (Figure
7A, left column) or reciprocally (Figure 7A, medial column). Specific rectifiers
split positive (pos = positive half-wave rectifier) from negative (neg = negative
half-wave rectifier) velocities or accelerations. At the second,
multiplicative
level
(Figure 7A2), two types of patterns are obtained, one of which, termed the
ON
response, generated by the product of
low
-threshold signals transmitting G(
t
)
and
low
-threshold signals transmitting (
d
G/
dt
) and the other, the
OFF
response,
generated by the product of
high
-threshold signals transmitting G(
t
) and
high
-
threshold inhibiting signals transmitting (
d
G/
dt
). In view of the positive or nega-
tive velocities,
ON
U and
ON
V or
OFF
U and
OFF
V patterns can be obtained for
conceivable synaptic connections (Figure 7A1, third column). Omitting weigh-
ing factors, an
ON
U(
t
) pattern is obtained by
ON
U(
t
) = pos(
d
G/
dt
)
∗
G(
t
),
[1]
and an
OFF
U pattern by
OFF
U(
t
) = neg(
d
G/
dt
)
∗
G(
t
).
[2]
Assuming a linear, ramp-shaped function for G(
t
), its constant positive velocity
pos(
d
G/
dt
) acts as a gate such that only in the presence of the positive velocity
the ramp shape function is transmitted, resulting in an
ON
U pattern. Correspond-
ingly, in
OFF
U patterns the linear, ramp-shaped function G(
t
) is conveyed com-
pletely except during the period when a negative velocity neg(
d
G/
dt
) is present.
At the third,
additive level
(Figure 7A3), the sums of the different
ON
and
OFF
patterns are obtained. Sums of
ON
U and
OFF
V patterns are characteristic for
