Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
The NEURON simulation environment
Neural Computation
The book of GENESIS (2nd ed.): exploring realistic neural models with the GEneral NEural SImulation System
On numerical simulations of integrate-and-fire neural networks
Neural Computation
The NEURON Book
SIAM Journal on Scientific Computing
Extending cable theory to heterogeneous dendrites
Neural Computation
Numerical solution of calcium-mediated dendritic branch model
Journal of Computational and Applied Mathematics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
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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 spurious oscillations and lack of precision. 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.