From Maxwell's equations to the theory of current-source density analysis

Area of Science:

• Neuroscience
• Computational Neuroscience
• Biophysics

Background:

• Current-source density (CSD) analysis is widely used for interpreting extracellular potential recordings in the brain.
• The precise physical mechanisms generating these extracellular potentials, particularly the contribution of non-transmembrane currents, remain under investigation.

Purpose of the Study:

• To elucidate the relationship between various electrical currents and extracellular potentials in brain tissue.
• To determine the contribution of traditionally neglected extracellular currents to recorded potentials.
• To provide a foundational understanding for accurate analysis of extracellular recordings.

Main Methods:

• Justification of the electro-quasistatic approximation of Maxwell's equations for physiological electromagnetic fields.
• Spatial averaging of currents in neural tissue to define CSD.
• Derivation of an equation linking extracellular potential to CSD and extracellular diffusion currents.

Main Results:

• Extracellular potential is influenced by both transmembrane current CSD and gradients of extracellular diffusion currents.
• Extracellular diffusion currents significantly affect potentials at frequencies below a few Hertz.
• Advective and displacement currents are negligible in the extracellular space at physiological frequencies; displacement current acts capacitively within membranes.

Conclusions:

• Extracellular diffusion currents must be accounted for and subtracted for accurate CSD estimation, especially at low frequencies.
• This work clarifies the origins of extracellular potentials, refining the interpretation of electrophysiological data.
• The findings establish a necessary theoretical basis for advanced analysis of brain activity via extracellular recordings.