Morphologically accurate reduced order modeling of spiking neurons

J Comput Neurosci. 2010 Jun;28(3):477-94. doi: 10.1007/s10827-010-0229-4. Epub 2010 Mar 19.


Accurately simulating neurons with realistic morphological structure and synaptic inputs requires the solution of large systems of nonlinear ordinary differential equations. We apply model reduction techniques to recover the complete nonlinear voltage dynamics of a neuron using a system of much lower dimension. Using a proper orthogonal decomposition, we build a reduced-order system from salient snapshots of the full system output, thus reducing the number of state variables. A discrete empirical interpolation method is then used to reduce the complexity of the nonlinear term to be proportional to the number of reduced variables. Together these two techniques allow for up to two orders of magnitude dimension reduction without sacrificing the spatially-distributed input structure, with an associated order of magnitude speed-up in simulation time. We demonstrate that both nonlinear spiking behavior and subthreshold response of realistic cells are accurately captured by these low-dimensional models.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Action Potentials / physiology*
  • Animals
  • Cell Shape / physiology
  • Central Nervous System / physiology*
  • Computer Simulation*
  • Dendrites / physiology
  • Dendrites / ultrastructure
  • Humans
  • Linear Models*
  • Neurons / cytology
  • Neurons / physiology*
  • Synaptic Transmission / physiology*
  • Time Factors