[The synthesis of mathematical models of the branched axons and dendrites]

A mathematical apparatus of computer modelling was elaborated reflecting more completely the real morphological and electrophysiological features of axons and dendrites without restrictions and simplifications which were typical of the existing models of these structures. Equivalent electrical circuits of branching axons and dendrites were constructed with in-series and node connections of standard four-terminal networks corresponding to elementary segments with active or passive membrane. Basing on these circuits the equations were obtained describing electrical phenomena in branching neuronal processes. They were generalized for the case of multiple binary branching with arbitrary symmetry and geometry of the branches. A difference scheme common for the whole class of models under consideration was also constructed and an algorithm was elaborated for numerical solution of the obtained system of difference equations. The suggested model allows synthetizing a variety of models of branching axons and dendrites, that promotes the possibilities of model investigation of electrotonus, propagated excitation and their interactions.