Modeling and simulation for three-dimensional signal propagation in passive dendrites

This paper presents a three-dimensional model for neuronal signal processing in passive dendritic branches. The approach is based on Maxwell's equations, in particular, on the equation of continuity for the electric flux. The quantities of interest are the electric potentials in the intra- and extracellular domain as well as the membrane voltage. The model is given by an integral Laplace equation with a source term that models the current through the membrane. We give results based on the numerical solution of the three-dimensional model, and we compare the model with the well known one-dimensional cable equation. One of the features of the new model is that it directly accounts for the possibility to include detailed measured geometry of dendritic branches into a three-dimensional numerical simulation. As a result, we are able to show for the first time that there is a significant impact of the extracellular domain into the solution of neuronal signal propagation in passive dendrites.