Reduced Order Modeling of Neurons: Capturing the internal dynamics without pruning the spines

Steve Cox
Dept. of Computational & Applied Mathematics (CAAM)
Rice University
Houston, Texas, USA


Abstract:

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. An empirical interpolation method is then used similarly to construct a basis of snapshots for the nonlinear ion channel kinetics. 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.