BME 402
Homework 4
Due 11am, 2/21/06
Neural Cables
Be able to derive the cable equation like we did in class using Kirchhoff’s current law.
Know the definition of the space constant
λ
and the input resistance R
in
for an infinite
uniform cable and how these depend on diameter, and know what the steady state voltage
profile looks like in a uniform cable for various boundary conditions (i.e. if the cable
terminates in a fatter or thinner cable or a closed end, or two or more daughter branches).
Know the d
3/2
law for matched input conductances at branch points. Understand why the
speed of voltage propagation in a cable depends more on R
i
than R
m
. Understand why
myelin speeds the propagation of AP’s and why action potentials block when myelin is
disturbed. Be able to briefly discuss at least one myelinrelated disease.
Homework questions:
1. A uniform cable 5
μ
m in diameter has R
m
=20K
Ω
cm
2
and R
i
= 100
Ω
cm with
λ
= sqrt (a R
m
/ 2 R
i
), and R
in
= sqrt(R
m
R
i
/2)/ 2
π
a
3/2
. The cable has a branch point at
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 Spring '06
 Mel
 Ri, Kirchhoff's circuit laws, Complex Plane, diameter, Pole, steady state voltage

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