Information Technology Reference
In-Depth Information
FIGURE 18. Position of spines in the sea-
urchin after stimulation at the North pole.
Local anatomy and geometry in the neighborhood of a spine is schemati-
cally given in fig. 19 which exaggerates certain proportions for purposes
of clarity. The spine S, centered on pivot P which is attached to a fixed shell
with radius R, can bend in all directions. Muscle fibers M contract when
stimulated by neuron N which will respond to an extension (stretch) of the
integument. If somewhere at the surface a muscle bundle contracts, it causes
the integument to follow, which produces a slight local stretch that is sensed
by the local neuron which, in turn, causes its associated muscle to contract,
and so on. Consider a spine localized at angle f
o
. When bent at angle y from
its radial rest position (y=0) it will shift the integument surface from f
o
to
f. Assume that a stimulus is applied at the North Pole (f
o
= 0), then the shift
Df = f
o
-fat angle f
o
is the result of the summation of differential contrac-
tions -d(Df)/df
o
of intermediate muscles. These, in turn, contract according
to the efferent stimulus of their associated neurons which fire in proportion
to the local perturbation, i.e., the difference between the extension of the
relaxes integument
L
and the stretched integument
H
. Hence, the differen-
tial equation that governs the
local
receptor-effector system is:
()
=-
d
d
o
Df
f
(
)
kL H
,
-
(52)
where the proportionality constant
k
represents the combined transfer
functions for neuron and muscle fiber. From inspection of fig. 19 we have
the simple geometric relations:
Search WWH ::
Custom Search