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Constraining Ill-Posed Inverse Problems in Neural Electrophysiology via Biophysically Detailed Forward Simulation

Abstract

Biophysically detailed simulation is an invaluable tool for understanding experimental data when those data do not uniquely determine the underlying state of the system, a situation we refer to as an ill-posed inverse problem. Such problems arise frequently in the study of biological systems with many degrees of freedom. This dissertation presents simulation- based approaches to two ill-posed inverse problems in neural electrophysiology. First, using a large volume of simulated data, we demonstrate that a Convolutional Neural Network can be trained to determine the conductances of various ion channels in a neuron from its somatic membrane potential in response to a current injection. Next, we use a simulation to study the cellular origin of electrical signals recorded at the surface of the brain, and find that they are produced primarily in layers V and VI of the cortex, contrary to the intuition that neurons closer to the electrode should contribute more of the signal. In both cases, simulation is a natural way to incorporate biological constraints to rule out certain a priori plausible solutions. Our results show how the massive throughput, fine-grained control over model parameters, and access to underlying ground-truth details within a simulation can be utilized to overcome the ill-posedness that many biological problems exhibit when stated in physical terms.

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