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Anton Chizhov edited untitled.tex
over 7 years ago
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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.