| graphical scheme based on the diagrammatic calculus outlined by Abbott, Farhi and Gutmann (1991) for constructing the Green's function for dendritic cable equations is developed and implemented here. The program implementing this scheme is general, flexible and useful in a wide range of applications. It can be used to evaluate the Green's functions for arbitrary dendritic structures of any length and diameter for each branch, any number of terminals and junctions, and both sealed and killed terminals to any desired accuracy. No special restrictions on the lengths or the diameters of branches are imposed.;The general behaviors of the graphical scheme such as the number of trips as a function of the number of steps, the convergence, and the short time approximations are analyzed and compared with computer simulations. Neurons with very complex structures are studied as example applications of the scheme. The effectiveness of the source current depends mainly on its distance from the soma. The potential distribution over the dendritic tree decays with time due to current leakage through the membrane. It is also flattened due to current reflection at sealed terminals. Killed terminals accelerate the decay of the potential distribution over the dendritic tree. The effect of boundary conditions is localized to nearby branches. The shortest trips make a good approximation to the Green's function at short time (t... |
