Modelling Biological Neurons in Terms of Electrical Circuits - Advanced Models of Neural Networks - page 24

1.8.4.3 Inward Rectifier

This current appears when the neuron becomes hyperpolarized. The current's
equation has the form

I Kin D g Kin h.V/.V E k /
h.V/ D 1=Œ1 C exp..V V th /=K/

(1.95)

Typical values of the parameters appearing in the above model are V th D85 mV
and K D 5 mV. Considering the existence of a leak current, the steady-state current
becomes

I D g L .V E L / C g Kin h.V/.V E K / (1.96)

Differentiating with respect to V gives

dI
dt

D g L C g Kin h.V/ C g Kin h 0 .V/.V E K /

(1.97)

1.8.5 Voltage Sags

After hyperpolarization of the neuron takes place then an inward current appears
with values between 43 and 0 mV. The current dynamics is [ 16 ]

I h D g h y.V C 43/

dy
dt D .y 1 .V/ y/= y .V/
y 1 .V/ D 1=Œ1 C exp..V V th /=K/
y .V/ D t o sech..V V m /=b/

(1.98)

1.8.6 Currents and Concentration of Ions

The assumption that the concentration of ions in the inner and outer part of the
membrane remains constant is in general acceptable, apart from the case of Ca 2C
ions. The concentration of Ca 2C ions in the inner part of the membrane is very
small (of the order of 10 4 mM) and a small inflow of Ca 2C suffices to change this
concentration significantly. Due to this, cascading reactions in the internal part of
the cell are caused.
Similarly, the concentration of ions K C in the outer part of the membrane is very
small and in case that several neurons fire simultaneously then this concentration
may change.