TAMPERE UNIVERSITY OF TECHNOLOGY Institute of Bioelectromagnetism . Bioelectromagnetism Exercise #2 – Answers. Q1: Characteristic Length and Time Constant.
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TAMPERE UNIVERSITY OF TECHNOLOGY
Institute of Bioelectromagnetism
Bioelectromagnetism
Exercise 2
> ρ = RA / l = ri * A [Ω m]
l
r
R
Bioelectromagnetism
Exercise 2
r
l
r
rm/l
Q1: Characteristic Length and Time Constant  terminologyof the length of the membrane)
d = thickness of the membrane
l = length of the cell
Bioelectromagnetism
Exercise 2
C
Q1: Characteristic Length and Time Constant  terminologyl
d
r
Bioelectromagnetism
Exercise 2
r
x
Q1: Characteristic Length and Time ConstantBioelectromagnetism
Exercise 2
boundary conditions: V’(x=0)=V’, V’(x=)=0
Bioelectromagnetism
Exercise 2
Bioelectromagnetism
Exercise 2
a) What is the strengthduration equation of the cell. How long will it take to reach the stimulus threshold with a 2.5 mA stimulus current. What is the chronaxy of the cell?b) Determine the propagation speed of an action pulse if the cell diameter is 100 µm and coefficient K = 10.47 1/ms in propagation equation
ρ is the intracellular resistivity.
Bioelectromagnetism
Exercise 2
Time
Vm
Q2: StrengthDuration CurveBioelectromagnetism
Exercise 2
Vth= membrane potential, that can generate action impulse
when t=:
== Rheobase
>
Is = 2 * Irh => t = * ln2 = 125 µs
Bioelectromagnetism
Exercise 2
where
K = 10.47 1/ms
d = 100*106 m
ρ = intracellular resistivity
ρ = RA/l =Ri*A
Ri = R/l=8.2*106Ω/cm
ρ = Ri * r2 = 8.2*106Ω/cm * (5000*106cm)2 = 644 Ωcm
Cm = cm/(2r) = 12nF/cm / (2*5000*106cm) = 0.382 µF/cm2
=> 327 cm/s
empirical (eq. 4.33):
Bioelectromagnetism
Exercise 2
Transmembrane current equation
This is eq. 4.10 in the Bioelectromagnetism book
Bioelectromagnetism
Exercise 2
=>
Bioelectromagnetism
Exercise 2
What is the sodium ion conductance GNa (stimulation 56 mV, 2.5 ms)?
Bioelectromagnetism
Exercise 2
I’m = IK (+ICl)
Im = IK + INa (+ICl)
=> INa = Im – I’m
VNa = Vr + 117 mV
Bioelectromagnetism
Exercise 2
Figure 1. Anterior body surface map (BSM).
Bioelectromagnetism
Exercise 2
 inverted?
+

Bioelectromagnetism
Exercise 2