This thesis develops an approach to determine spatially-varying ionic channel conductances throughout the dendrites of the LGMD neuron from distal transmembrane potential recordings in response to distributed subthreshold current injections. In particular this approach is demonstrated on a straight cable approximation to the LGMD neuron with leak and hyperpolarization-activated h-currents.

Knowledge of the underlying channel conductances can help neuroscientists to characterize, better understand, and predict neuronal behavior---and topographic integration in the LGMD neuron in particular---but it is extremely difficult to measure these conductances directly.

As a consequence, these conductances are commonly estimated by searching for several parameters that lead to simulated responses that are consistent with recorded behavior. In contrast, the approach presented here uses the method of moments to directly recover the underlying conductances, eliminating the need to simulate responses, making this approach both faster and more robust than typical optimization approaches since the solution cannot get trapped in local minima.