Anton Chizhov edited untitled.tex  over 7 years ago

Commit id: 42220245e59fe36315baf8f87c5e6dbd522680f8

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%Modified from PRE2015:  Interpretation of extracellular potentials is unclear  \cite{Buzhaki cite{Buzhaki  et al. 2012}, \cite{Bedard cite{Bedard  et al. 2006}, \cite{Bedard cite{Bedard  and Destexhe 2011}, \cite{Bedard cite{Bedard  and Destexhe 2013}, \cite{Bedard cite{Bedard  and Destexhe 2014} even in the case of synchronous neuronal epileptiform events the relationship  between simultaneously registered extracellular and intracellular  signals is non-trivial \cite{Alvarado-Rojas cite{Alvarado-Rojas  et al. 2015}. Assuming an homogeneous and isotropic extracellular space (but see  \cite{Ranck cite{Ranck  and BeMent 1965}), an extracellular potential is commonly described by the Poisson equation with macroscopically  averaged transmembrane currents as distributed sources  \cite{Nicholson cite{Nicholson  1973}, \cite{Nicholson cite{Nicholson  and Freeman 1975} or by the Laplace equation with the transmembrane currents distributed along  all membrane surfaces \cite{Logothetis cite{Logothetis  2007}, \cite{Linden cite{Linden  et al. 2011}, \cite{Schomburg cite{Schomburg  et al. 2012}, \cite{Gold cite{Gold  et al. 2006}, \cite{Einevoll cite{Einevoll  et al. 2013}, \cite{Ibarz cite{Ibarz  et al. 2010}. If neuronal activity is modeled by multiple compartment neurons, then  calculation of the local field potential (LFP) with the Poisson  equation is straightforward. However, in most cases biophysically detailed mean-field models also  deals with somatic signals of neuronal activity exclusively, and  the question of how to estimate the LFP from these somatic signals  is unclear \cite{Chizhov cite{Chizhov  2014}, \cite{Baladron cite{Baladron  et al. 2012}. A simple formula linking  intracellular parameters of neuronal activity to extracellular  field potential has been derived in \cite{Chizhov cite{Chizhov  et al. 2015}, neglecting ionic dynamics and glial contributions.