A multiscale numerical method for the heterogeneous cable equation

Several interesting problems in neuroscience are of multiscale type, i.e. possess different temporal and spatial scales that cannot be disregarded. Such characteristics impose severe burden to numerical simulations since the need to resolve small scale features pushes the computational costs to unreasonable levels. Classical numerical methods that do not resolve the small scales suffer from This paper presents an innovative numerical method of multiscale type that ameliorates these maladies. As an example we consider the case of a cable equation modeling heterogeneous dendrites. Our method is not only easy to parallelize, but it is also nodally exact, i.e., it matches the values of the exact solution at every node of the discretization mesh, for a class of problems. To show the validity of our scheme under different physiological regimes, we describe how the model behaves whenever the dendrites are thin or long, or the longitudinal conductance is small. We also consider the case of a large number of synapses and of large or low membrane conductance. & 2011 Elsevier B.V. All rights reserved.