The name is absent

134

Chapter 6

Conclusion

Using the tools in this thesis, models of morphologically accurate spiking cells can
be reduced to systems with significantly fewer variables while maintaining the input-
output properties of the original model. Balanced Truncation (BT) offers a rigorous
theoretical approach to linear model reduction in order to reproduce subthreshold
voltage dynamics, but it is slow and may be computationally intractable for some
systems. An Iterative Rational Krylov Algorithm (IRKA) achieves the same goal,
but it computes the reduced system drastically faster and also makes simulations of
realistic morphologies tractable. Depending on the discretization and the morphology,
the dimension of the system can be reduced by a factor of more than 10000, and the
simulation time can decrease by a factor of nearly 100.

The spiking regime requires a different approach in order to capture the highly
nonlinear voltage response. The Proper Orthogonal Decomposition (POD) reduces
the dimension of the state variables, while a Discrete Empirical Interpolation Method
(DEIM) reduces the complexity of the nonlinear terms that account for ion channel
kinetics. In order for these methods to be accurate for branched cells, I have de-

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