Circuit Elements Required for Neural Systems - Brain Theory from a Circuits and Systems Perspective - page 34

Fig. 3.1 Reference pulse, internal voltage relative to outside

cut off, neglecting loss conductance and neglecting the effects of potassium and
other ions, internal voltage would hold at a steady value.
Potassium is also active. The larger potassium ions inside the neuron have their
own effect, moving positive charge away from the interior. This occurs at a lower
rate of charge transfer because potassium ions are larger and move slower at a given
temperature. Once the sodium charging cuts off, the potassium are dominant,
effectively discharging membrane capacitance to below the rest voltage.
Photographs indicate an undershoot of a few tens of millivolts below 70 mV. It

is conjectured that this is necessary in order to snap the molecules within the
membrane into their original locked position and thus put an end to the given pulse.

A Simple Pulse Model

A simple model is useful as an aid to understanding a neural pulse. The charging
current is

v ð t Þ¼ 70mV þ α t

(3.1)

t 1ms :

Time (t) is in milliseconds and 110. Thus at 1 ms the voltage is +40 mV. After

a millisecond the discharging current is modeled as equal to

α ¼

v ð t Þ¼þ 40mV βð t 1 Þ

(3.2)

1ms 2 : 5ms :