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An asymptotic approximation to the cable equation for arbitrary diameter taper

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Asymptotic approximations reveal fundamental properties of voltage flow in tapering dendrites. A Comparison of numerical (blue) and first-order asymptotic (black dashed) methods for determining the steady-state voltage in a quadratically tapering dendritic cable for currents injected at three different sites. B Comparison of numerically-optimised tapering profiles (blue) with those predicted by the asymptotic approximation (black dashed) for dendrites of different electrotonic length.
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Figure 1: Asymptotic approximations reveal fundamental properties of voltage flow in tapering dendrites. A Comparison of numerical (blue) and first-order asymptotic (black dashed) methods for determining the steady-state voltage in a quadratically tapering dendritic cable for currents injected at three different sites. B Comparison of numerically-optimised tapering profiles (blue) with those predicted by the asymptotic approximation (black dashed) for dendrites of different electrotonic length.

Mentions: We have derived an asymptotic approximation to the voltage in dendrites with an arbitrary taper profile using the insight that voltage attenuation is substantially faster than radius change in realistic morphologies (Figure 1A). This result allows faster computation and greater insight than standard approaches using large numbers of cylinders or frusta to numerically compute voltage profiles. In addition, it provides easy generalisations of the standard results of cable theory involving transients and branches.


An asymptotic approximation to the cable equation for arbitrary diameter taper
Asymptotic approximations reveal fundamental properties of voltage flow in tapering dendrites. A Comparison of numerical (blue) and first-order asymptotic (black dashed) methods for determining the steady-state voltage in a quadratically tapering dendritic cable for currents injected at three different sites. B Comparison of numerically-optimised tapering profiles (blue) with those predicted by the asymptotic approximation (black dashed) for dendrites of different electrotonic length.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4697549&req=5

Figure 1: Asymptotic approximations reveal fundamental properties of voltage flow in tapering dendrites. A Comparison of numerical (blue) and first-order asymptotic (black dashed) methods for determining the steady-state voltage in a quadratically tapering dendritic cable for currents injected at three different sites. B Comparison of numerically-optimised tapering profiles (blue) with those predicted by the asymptotic approximation (black dashed) for dendrites of different electrotonic length.
Mentions: We have derived an asymptotic approximation to the voltage in dendrites with an arbitrary taper profile using the insight that voltage attenuation is substantially faster than radius change in realistic morphologies (Figure 1A). This result allows faster computation and greater insight than standard approaches using large numbers of cylinders or frusta to numerically compute voltage profiles. In addition, it provides easy generalisations of the standard results of cable theory involving transients and branches.

View Article: PubMed Central - HTML

No MeSH data available.