On the use of pseudo-spectral method in model reduction and simulation of active dendrites

Most of dendrites in the central nervous system are now known to have active channels. These active dendrites play important roles not only in signal summation but also in computation. For the simulation of these important active dendrites, the compartment model based on the finite volume or finite difference discretization was mainly adopted. In this paper, we employ the Chebychev pseudo-spectral method well developed in computational physics, and demonstrate that it can achieve a higher precision with the same number of equations than the compartment model. Moreover, it is also shown that the Chebychev pseudo-spectral method converges faster to attain a given precision. Hence, for the simulations of active dendrites, the Chebychev pseudo-spectral method can be an attractive alternative to the compartment model since it leads to a low order model with higher precision or converges faster for a given precision.