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A clear advantage of IRKA is that it handles systems of much larger dimension
than BT. We could not use BT for systems where N > 7000, due to lack of memory,
and even if we could, the computation time would preclude any practical use for such
large systems. IRKA does not suffer from this drawback, which translates into the
ability to compute reduced models of cells with much finer discretizations and to
reduce cells with much more complex dendritic structure.
As an example, we consider neuron n408 (Figure 2.6C), a rat hippocampal cell
from region CAl (Pyapali et al., 1998). We use a 2 μm spatial discretization, yielding
6894 compartments. With a Connor-Stevens ion channel model this gives a total
linear system size of N = 41364. Using IRKA we find that 5 digits of accuracy can
be obtained using a system of dimension к ≈ 15, which is a 2700-fold reduction, or
more than 3 orders of magnitude, in less than a minute (see Figure 2.13). If we use a
finer discretization of h ≈ 0.5 μm, we arrive at a system of size N = 165330. IRKA
produces a 15-dimensional system that is accurate to nearly 5 digits, a monstrous
11000-fold reduction, or 4 orders of magnitude!
2.7 A Quasi-Integrate-and-Fire Model
Quasi-active neuron models cannot spike, but adopting an integrate-and-fire (IAF)
mechanism allows such models to emulate this behavior. Under our assumption that