The name is absent

60

We start in §3.1 with a description of the full model and the solution methods we
employ. In §3.2 we apply the model reduction techniques to simulation data to arrive
at the reduced system. Using this framework, in §3.3 we examine the accuracy of the
reduced system on simplified morphologies and discuss challenges that branched cells
pose. We promptly introduce algorithms to tackle these challenges, and show that
they succeed for simple branched cells. In §3.4-3.5 we show that these techniques
accurately reproduce the spiking dynamics of a broad class of realistic cells. We end
this section with a discussion of applications, improvements, and extensions in §3.6.

3.1 Nonlinear Cable Equation

Using the derivation of the nonlinear cable equation given in §2.3.1 we can proceed
with nonlinear model reduction.

It will be useful to consider not only synaptic input but also direct current in-
jection, for reasons which will become apparent in this section. With the rest state
defined, it is easy to modify (2.17) to use current injection instead of synaptic con-
ductance. If we substitute the rest state Vb(x) for the Vb(x) in the synaptic input
term, then this is equivalent to directly injecting current into the cell, which yields

ɪ S_b

ʃinj,i(ʃ) ŋ ⁼ 2π } √ fl⅛s(f)^(∙E æbs)(^b(ɪ) Ebs)-               (ɜ'ɪ)

'' s=l

If we now partition the cell into N compartments, with C distinct ionic currents

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