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Unformatted text preview: Propagation in dendrites takes time and spreads potentials generated remotely. Equivalentcircuit models for action potentials are RC circuits with many conductances. r m c m r L Δ x 2a Cable models use radii ( e.g. , a = 2 μ m), specific membrane resistances ( e.g. , r m = 1 M Ω ⋅ mm 2 ) and capacitances ( e.g. , c m = 10 nF ⋅ mm2 ), and intracellular resistivities ( e.g. , r L = 1 k Ω ⋅ mm). Cable Equation: τ m ∂ v ∂ t = λ 2 ∂ 2 v ∂ x 2 − v + r m i e With typical values (see Slide 5): τ m = r m c m = 10 ms λ = ar m 2 r L = 1 mm Three Examples of Solutions of the Cable Equation: 1.Infinite, SteadyState Cable with Current Injection at the Middle… The potential falls with distance from the injection point, since current escapes at various points of the neural cable. ? Cable Equation: τ m ∂ v ∂ t = λ 2 ∂ 2 v ∂ x 2 − v + r m i e With typical values in previous slides: τ m = r m c m = 10 ms λ = ar m 2 r L = 1 mm τ m ∂ v ∂ t = λ 2 ∂ 2 v ∂ x 2 − v + r m i e Cable Equation: τ m ∂ v ∂ t = λ 2 ∂ 2 v ∂ x 2 − v + r m i e Outside the injection point and at steady state: 0 Three Examples of...
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This note was uploaded on 06/08/2009 for the course BME 575L taught by Professor Grzywacz during the Spring '09 term at USC.
 Spring '09
 Grzywacz

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