Generalized cable theory for neurons in complex and heterogeneous media

Abstract

Cable theory has been developed over the last decades, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion or capacitive effects, but their impact on cable properties is not known. In this paper, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example in the presence of ionic diffusion, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.

Phys Rev E, in press, 2013 (11 figures)

References in corpus (3)

• Does the 1/f frequency-scaling of brain signals reflect self-organized critical states?
• Macroscopic models of local field potentials and the apparent 1/f noise in brain activity
• A modified cable formalism for modeling neuronal membranes at high frequencies

Cited by in corpus (8)

• The effect of ionic diffusion on extracellular potentials in neural tissue
• Intracellular impedance measurements reveal non-ohmic properties of the extracellular medium around neurons
• Extending integrate-and-fire model neurons to account for the effects of weak electric fields and input filtering mediated by the dendrite
• A framework to reconcile frequency scaling measurements, from intracellular recordings, local-field potentials, up to EEG and MEG signals
• Generalized cable formalism to calculate the magnetic field of single neurons and neuronal populations
• Kramers-Kronig relations and the properties of conductivity and permittivity in heterogeneous media
• Cable equation for general geometry
• Neuronal cable equations derived from the hydrodynamic motion of charged particles