Homework_04_solution - BME 402 Homework 4 Due 11am Neural...

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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 myelin-related disease. Homework questions: 1. A uniform cable 5 μ m in diameter has R m =20K cm 2 and R i = 100 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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