Biomedical Engineering Reference
In-Depth Information
5.2 MULTICOMPARTMENTMODELS
It is clear from Fig. 5.1 that not all neurons will follow the assumption of Eq. (5.1). To lift the assump-
tions of the lumped models, we can consider that the dendrites and axons are made up of many small
compartments. The general concept is shown in Fig. 5.4 and is a similar idea to when we derived the
original cable equation using many small patches of membrane. Again, current is passed from one com-
partment to another in one direction only. At a branch, the current is simply split and passed into two
(or more) compartments. Below we will derive equations to describe how this current split is achieved.
Multicompartment models
not only remove the Rall restriction but also allow for many different types of
post-synapses to be incorporated into the model. The post-synapse will be considered in more detail in
Ch. 6. The disadvantage of the multicompartment models is that compared to the Rall model, they must
be solved numerically and required considerable greater computing power. Below we will introduce the
basic elements of how to construct a dendritic tree of any complexity.
Figure 5.4:
Schematic of dendritic compartments.
5.2.1 A Simple Compartment
To begin, we will make a slight change to the definition of a compartment by placing a node at the
center
of each patch as in Fig. 5.5. Each compartment will therefore have a length of 2
dx
and each half resistor
in a compartment will be defined as
dx
·
R
i
πa
2
R
=
.
(5.2)
5.2.2 Change in Fiber Radius
Since the composition of the cytoplasm does not change drastically, the intracellular resistivity (
R
i
,a
material property) does not change.Therefore, the determining factor of the half resistance with a radius,
a
,is
·
dx
R
i
πa
2
=
R(a)
.
(5.3)
