The name is absent

12

Chapter 2

Linear Model Reduction

The focus of this chapter is to introduce linear model reduction techniques by
considering a basic neuronal model and then extending it naturally to a realistic
morphology. Using a single-compartment model, I illustrate the important dynamical
features of neurons. This model is then linearized to obtain the quasi-active model in
order to illustrate subthreshold behavior. Once these concepts have been introduced
in this simple framework, I present the general morphologically accurate model and
proceed with linear model reduction. I demonstrate the efficacy of two techniques,
one dense and one iterative, and discuss their application to various investigations of
behavior in large-scale neurons.

2.1 The Isopotential Cell

One of the most basic isopotential models is the leaky integrate-and-fire (IAF)
model, in which the cell can be modeled as a circuit (see Figure 2.1). Following the
material found in my Master’s thesis (Kellems, 2007), using Kirchhoff’s Current Law,
the change in voltage v is given by the ordinary differential equation

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