From Maxwell's equations to the theory of current-source density analysis.
Despite the widespread use of current-source density (CSD) analysis of extracellular potential recordings in the brain, the physical mechanisms responsible for the generation of the signal are still debated. While the extracellular potential is thought to be exclusively generated by the transmembrane currents, recent studies suggest that extracellular diffusive, advective and displacement currents-traditionally neglected-may also contribute considerably toward extracellular potential recordings. Here, we first justify the application of the electro-quasistatic approximation of Maxwell's equations to describe the electromagnetic field of physiological origin. Subsequently, we perform spatial averaging of currents in neural tissue to arrive at the notion of the CSD and derive an equation relating it to the extracellular potential. We show that, in general, the extracellular potential is determined by the CSD of membrane currents as well as the gradients of the putative extracellular diffusion current. The diffusion current can contribute significantly to the extracellular potential at frequencies less than a few Hertz; in which case it must be subtracted to obtain correct CSD estimates. We also show that the advective and displacement currents in the extracellular space are negligible for physiological frequencies while, within cellular membrane, displacement current contributes toward the CSD as a capacitive current. Taken together, these findings elucidate the relationship between electric currents and the extracellular potential in brain tissue and form the necessary foundation for the analysis of extracellular recordings.
Allen Institute for Brain Science, Seattle, WA, 98109, USA.
Sergey L
SL
Gratiy
Faculty of Science and Technology, Norwegian University of Life Sciences, Aas, Norway.
Geir
G
Halnes
Allen Institute for Brain Science, Seattle, WA, 98109, USA.
Daniel
D
Denman
Allen Institute for Brain Science, Seattle, WA, 98109, USA.
Michael J
MJ
Hawrylycz
Allen Institute for Brain Science, Seattle, WA, 98109, USA.
Christof
C
Koch
Faculty of Science and Technology, Norwegian University of Life Sciences, Aas, Norway.|Department of Physics, University of Oslo, Oslo, Norway.
Gaute T
GT
Einevoll
Allen Institute for Brain Science, Seattle, WA, 98109, USA.|Department of Neurology, University of British Columbia, Vancouver, BC, Canada.
Costas A
0000-0002-6793-0611
CA
Anastassiou
D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology*; D004058:Diffusion; D004560:Electricity; D004567:Electrodes, Implanted; D004574:Electromagnetic Fields; D008297:Male; D008564:Membrane Potentials / Q000502:physiology*; D008810:Mice, Inbred C57BL; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D010775:Photic Stimulation; D009435:Synaptic Transmission / Q000502:physiology; D014796:Visual Perception / Q000502:physiology
current transfer; electrical conductivity; electrical stimulation; extracellular recordings; field potentials