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.
['Gratiy|Sergey L|SL|', 'Halnes|Geir|G|', 'Denman|Daniel|D|', 'Hawrylycz|Michael J|MJ|', 'Koch|Christof|C|', 'Einevoll|Gaute T|GT|', 'Anastassiou|Costas A|CA|0000-0002-6793-0611']
D000465:Algorithms D000818:Animals D001921:Brain D004058:Diffusion D004560:Electricity D004567:Electrodes, Implanted D004574:Electromagnetic Fields D008297:Male D008564:Membrane Potentials D008810:Mice, Inbred C57BL D008959:Models, Neurological D009474:Neurons D010775:Photic Stimulation D009435:Synaptic Transmission D014796:Visual Perception
extracellular recordings current transfer electrical conductivity electrical stimulation field potentials