Mathematical modelling in neurophysiology: Neuronal geometry in the construction of neuronal models

Tucker, Gayle (2004) Mathematical modelling in neurophysiology: Neuronal geometry in the construction of neuronal models. PhD thesis, University of Glasgow.

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Abstract

The underlying theme of this thesis is that neuronal morphology influences neuronal behaviour. Three distinct but related projects in the application of mathematical models to neurophysiology are presented. The first problem is an investigation into the source of the discrepancy between the observed conduction speed of the propagated action potential in the squid giant axon, and its value predicted on the basis of the Hodgkin-Huxley membrane model. It is shown that measurement error and biological variability cannot explain the discrepancy, nor can the use of a three-dimensional model to represent the squid giant axon. If the propagated action potential achieved the travelling wave speed in the experimental apparatus, as assumed implicitly by Hodgkin and Huxley, then it is suggested that the model of the membrane kinetics requires modification. The second problem involves the generalisation of Rall's equivalent cylinder to the equivalent cable. The equivalent cable is an unbranched structure with electrotonic length equal to the sum of the electrotonic lengths of the segments of the original branched structure, and an associated bijective mapping relating currents on the original branched structure to those on the cable. The equivalent cable is derived analytically and can be applied to any branched dendrite, unlike the Rall equivalent cylinder, which only exists for dendrites satisfying very restrictive morphological constraints. Furthermore, the bijective mapping generated in the construction of the equivalent cable can be used to investigate the role of dendritic morphology in shaping neuronal behaviour. Examples of equivalent cables are given for spinal inter neurons from the dorsal horn of the spinal cord. The third problem develops a new procedure to simulate neuronal morphology from a sample of neurons of the same type. It is conjectured that neurons may be simulated on the basis of the single assumption that they are composed of uniform dendritic sections with joint distribution of diameter and length that is independent of location in a dendritic tree. This assumption, in combination with the kernel density estimation technique, is used to construct samples of simulated interneurons from samples of real interneurons, and the procedure is successful in predicting features of the original samples that are not assumed by the construction process.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Additional Information: Adviser: Jay Rosenberg
Keywords: Neurosciences, Applied mathematics
Date of Award: 2004
Depositing User: Enlighten Team
Unique ID: glathesis:2004-71342
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 10 May 2019 10:49
Last Modified: 10 May 2019 10:49
URI: http://theses.gla.ac.uk/id/eprint/71342

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