Finite element analysis of neuronal electric fields: the effect of   heterogeneous resistivity
  Simulation of extracellular fields is one of the substantial methods used in the area of computational neuroscience. Its most common usage is validation of experimental methods as EEG and extracellular spike recordings or modeling of physiological phenomena which can not be easily determined empirically. Continuous experimental work has been re-raising the importance of polarization effects between neuronal structures to neuronal communication. As this effects relies on very small potential changes, better modeling methods are necessary to quantify the weak electrical fields in the microscopic scale in a more realistic way. An important factor of influence on local field effects in the hippocampal formation is the heterogeneous resistivity of extracellular tissue. The vast majority of modeling studies consider the extracellular space to be homogeneous while experimentally, it has been shown that the stratum pyramidale has two times higher resistivity then other hippocampal layers. Common simulation methods for extracellular electrical fields based on the point source approximation are bound to describe the resistance of the space with a single, linear factor. We propose that models should be based on the space- and time-dependent Maxwell equations in order to account for heterogeneous properties of the extracellular space and specific arrangements of neurons in dense hippocampal layers. To demonstrate the influence of heterogeneous extracellular resistivity and neuronal spatial orientation on modeling results, we combine solutions of classical compartment models with spatiotemporal PDEs solved by the FEM. With the help of these methods, we show that the inclusion of heterogeneous resistivity has a substantial impact on voltages in close proximity to emitting neurons, increasing the extracellular potentials substantially compared to the homogeneous variant. 
Pavol Bauer, Sanja Mikulovic, Stefan Engblom, Katarina E. Le\~ao,   Frank Rattay, Richardson N. Le\~ao
q-bio.NC