Biomedical Engineering Reference
In-Depth Information
stimuli to the ends of the dendrites would be approximated by a single stimulus. The advantage of this
idea is that computation would become fast and efficient and the actual geometry of the tree would not
matter. It also enabled the analytical solution of attenuation down the dendritic tree. The disadvantage
was that to achieve this collapse of the tree, Rall had to assume a relationship between the radii of all
branches in relation to their main trunk
a
3
/
2
a
3
/
2
a
3
/
2
main
=
branch1
+
branch2
+
... .
(5.1)
This relationship was assumed to apply to
every
branch in the tree. Although Eq. (5.1) appears to be very
restrictive, Rall showed that for many dendritic trees is was a reasonable approximation.
Rall
Figure 5.2:
Rall's equivalent cable.
5.1.2 The Ball and StickModel
Another advantage of the collapsed dendritic tree is that the equivalent cable can be attached to a soma
and axon to create a
ball and stick
model of a neuron. In Fig. 5.3, the dendrites have been collapsed using
the method outlined by Rall and the soma is modeled as single compartment which may be either active
or passive. The axon is in fact not present at all and is simulated by a time delay. As we found in Ch. 4,
once an action potential has fired in the soma, it will propagate down the axon unattenuated to the axon
terminal. So, the delay depends only upon the speed of propagation and length of the axon. All of these
simplifications allow for the behavior of a neuron to solved numerically with a minimum of computing
power.
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$ENDRITES
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'HOD\
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Figure 5.3:
Ball and stick model.
