Simulation Experiments for Neural Pulses - Brain Theory from a Circuits and Systems Perspective - page 184

Fig. A.2 Segments of dendrite for modeling purposes

Table A.2 Equations

L 1mm 0.1 cm

¼ ¼

D 1 u 1.0e 4cm

¼ ¼

(D/2) 2

A CS

¼ π

R 1 L/A CS 15.7L/A CS

¼ ρ ¼

A SIDE

¼ π

DL

F/cm 2 C 1 1 μ A SIDE

¼

R LOSS1 1/(0.3e 3 A SIDE )

¼

0. 06725 mA/cm 2

I Na1 A SIDE

¼

0.0304 mA/cm 2 I K A SIDE

¼

Simulation Tools

Simulations are performed with a simple but reliable and transparent circuit analy-
sis program such as Winspice, available inexpensively for download ( http://
winspice.com ; accessed March 4, 2013). The currents in the above list are con-
trolled current sources denoted by G. Triggering at an internal voltage of about

55 mV activates both sodium and potassium currents. The sodium current must
cut off and stay off when internal voltage reaches 40 mV. The potassium current
remains until voltage drops to

90 mV, at which point it also must cut off and stay
off. The electrical circuit of a segment can be modeled as in Fig. A.3 .
Parameters are as in Table A.3 . The current sources depend on internal voltage
v n , as suggested by the simplified neural pulse. The entire segment is referenced to
a rest voltage of

70 mV in series
with the conductive loss resistance R Loss1 . Voltages on the capacitance and current
sources do not matter and are simply tied to a “ground” reference, which means
zero voltage. The suggested code for a subcircuit representing a segment is as
follows.

70 mV. This condition is modeled by placing

.subckt seg1 1 2
vNernst 3 0 70 mV
rNernst 3 1 106MEG
cseg 1 0 31.4p ic ¼70 mV
rseg 1 2 200MEG
xcur 1 0 cur1
.ends