The name is absent

model parameters are not the same as those used in the full model. This disparity
in the input-output map makes it difficult for investigators to directly compare the
results of experiments to those of simulations that employ the reduced models. A
truly reduced model would preserve the input-output relationship of a neuron, but
such models have been rare and of limited utility.

Until recently, the only true morphologically accurate model reduction effort has
been that of Wilfrid Rall. In 1959 he demonstrated that a passive morphology which
satisfies the “3/2” power law and has symmetric synaptic inputs can be collapsed
into an “equivalent cylinder”, thereby drastically reducing the size of the system to
simulate (Rall, 1959). While this was applicable to motoneurons, the assumptions
on the morphology and the inputs precluded the use of this technique in general.
Development of techniques that are applicable to a broader class of neurons has
recently been motivated by a need for efficient computations rather than theoretical
derivations.

Nonlinear ion channel kinetics are expensive to evaluate, but sometimes the ki-
netic variables for different ion channels are similar enough to permit reduction. In
1992, Kepler, Abbott, and Marder introduced the method of “equivalent potentials”
to take advantage of this fact (Kepler et al., 1992). By representing the kinetic vari-
ables as potentials, they were able to identify dependencies between variables and
use these dependencies to reduce the Hodgkin-Huxley model from a four-variable
system to a two-variable system, thus permitting faster simulations. This technique

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