was generalized in 2005 by Sorensen and DeWeerth to deal with arbitrary numbers of
channel variables as well as to provide an algorithmic, rather than ad hoc, method for
computing the reduced system (Sorensen and DeWeerth, 2006). An important draw-
back of this technique, however, is that it has been developed for single-compartment
models; it’s applicability to non-uniform (i.e., spatially-varying) kinetics, as would be
found in realistic models, has not yet been studied.
Steps toward preserving the nonlinear dynamics for morphologically realistic mod-
els have also been motivated by the need for computational efficiency. Though not
exactly a model reduction scheme, spatial adaptivity is one way to speed-up sim-
ulations without sacrificing nonlinear dynamics. For a CAl pyramidal cell in the
hippocampus, Rempe et al. devised a solution technique in which only areas of the
cell which are “active” need to be updated, whereas areas which are quiet need not
be (Rempe et al., 2008). They were able to achieve an 80% reduction is compu-
tation time for certain problems, but the adaptivity mechanism is dependent upon
the synaptic input pattern (Rempe et al., 2008). As a consequence, simultaneous
multi-branch stimulation, such as that found in realistic cortical cells, will render
this scheme ineffective. While this method did not solve the problem of efficiency
in general, it does underscore an important property that is necessary for a truly
reduced model: it must be able to handle any general input pattern without severe
degradation of computing speed.
Perhaps the closest attempt at incorporating both nonlinear dynamics and mor-