Biomedical Engineering Reference
In-Depth Information
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Figure 3.10:
Demonstration of accommodation of threshold voltage.
3.4 COMPLEX IONICMODELS
While Hodgkin and Huxley created the first physiologically based mathematic model of a neuron, there
were many neuronal phenomenon that it could not reproduce. Below we review some of the ways re-
searchers have extended the Hodgkin-Huxley model.
3.4.1 More Currents
As the electrodes used for the voltage clamp method have become smaller and smaller, and new channel
blocking drugs were found, it became possible to isolate more than the three simple currents of the
Hodgkin-Huxely model.The result has been that more recent models have many more currents included
in
I
ion
. For example, the unspecified leakage current was found to be due to other ions such as
Ca
2
+
,
Mg
2
+
, and
Cl
−
. To include these currents we would simply add them to the parallel conductance
I
ion
term.
I
ion
=
I
Na
+
I
K
+
I
Ca
+
I
Mg
+
I
Cl
.
(3.26)
Here the leakage current has been replaced by
I
Ca
+
I
Cl
. It was also found that
I
K
may in fact be
the summation of many different types of Potassium ion channels.
I
Mg
+
I
ion
=
I
Na
+
I
K
1
+
I
K
2
+
I
K
3
+
I
Ca
+
I
Mg
+
I
Cl
(3.27)
where
I
K
has been split into three different currents. Similarly,
I
Ca
may be decomposed into many
currents. For each current added, there will be new gating variables and new differential equations.
