Biomedical Engineering Reference
In-Depth Information
Solution: From (10.13),
(
)
10
−
(
)
30
50
e
=
τ
Then
τ
=
19.572 ms
=
R
m
C
m
Hence,
C
m
= 1.957
μ
F or 979 nF/cm
2
Then concentration
=
Exp(979-1,000)/18
=
0.3M
Synapses can be thought of as electrical connections. The main equation for
internal stimulation of the soma or any other compartment where current flow
to other processes or neighbored compartments is prevented has always the same
form: One part of the stimulating current is used to load the capacity
C
m
of the cell
membrane and the other part passes through the ion channels; that is,
d
d
ΔΦ
(10.14)
I
=
C
+
I
stimulus
m
ion
where the ion currents
I
ion
are calculated from appropriate membrane models. The
rate of change of membrane voltage change,
d
ΔΦ
/dt
, follows as:
(
)
I
−
I
d
dt
ΔΦ
stimulus
ion
=
C
m
For multiple ions, one can utilize the Hodgkin-Huxley model, which leads to
the circuit shown in Figure 3.5(c). Since the time of development of Hodgkin and
Huxley model, this model formalism has been applied to a large number of excit-
able cells. This naturally leads to developing methods to estimate the model param-
eters. Using the Nernst equation, one can couple the changes in concentration to
electrical potential.
10.2.3 Other Single Compartmental Systems
As discussed before, concentration difference is the driving force for movement of
molecules and voltage difference is the driving force for electric current. Similarly,
temperature difference is the driving force for heat transfer, and pressure difference
is the driving force for fluid flow. A fluid moves through a conduit due to the pres-
sure difference
(
P
) that overcomes the attrition after the flow (
Q
). A battery or
other power supply develops a “potential difference” that moves electrons around
the circuit to a position of least energy. Thus, a fluid pressure drop (energy per
unit volume) corresponds to a potential difference or voltage drop (energy per unit
charge). Understanding the analogy between electrical, mechanical, and chemical
systems helps in adopting an approach that emphasizes the similarity of modeling
Δ
