to build detailed models. With the advent of multi-core workstations and high-
performance computing clusters, these tools have been augmented with parallel capa-
bilities (Migliore et al., 2006), permitting ever more realistic simulations. Data acqui-
sition techniques have correspondingly improved along with computing power so that
dendritic structure need not be done via manual tracing, a tedious and error-prone
process, but rather by automated processes using advanced microscopy techniques
and state of the art image processing software (Losavio et al., 2008). Together, the
advances in computational and experimental tools have led the field of neuroscience
to a point where an almost arbitrary level of detail can be achieved, provided one can
wait long enough for the simulation to finish.
1.3 Model Reduction in Computational Neuroscience
In the midst of these rapid increases in model complexity, a fundamental question
remains: is such detail necessary to accurately model neuronal behavior? Guided by
the maxim of “minimal modeling”, researchers continually sought qualitative accuracy
in models of much smaller dimension than their full-scale counterparts. Arguably
the greatest success was achieved by Traub and Miles (TM) in their 19-compartment
reduction of a pyramidal cell (Traub and Miles, 1991), which was even further reduced
by Pinsky and Rinzel (PR) to a 2-compartment model (Pinsky and Rinzel, 1994).
Though the TM and PR models generate similar outputs to the full-blown pyramidal
cell model, they are developed ad hoc (instead of algorithmically) and the inputs and