An investigation into the influence of boundary condition specification in finite difference methods on the behaviour of passive and active neuronal models

Lindsay, K.A., Ogden, J.M. and Rosenberg, J.R. (2002) An investigation into the influence of boundary condition specification in finite difference methods on the behaviour of passive and active neuronal models. Progress in Biophysics and Molecular Biology, 78(1), pp. 3-43. (doi: 10.1016/S0079-6107(02)00004-4)

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Publisher's URL: http://dx.doi.org/10.1016/S0079-6107(02)00004-4

Abstract

Neuronal models provide a major aid to understanding the behaviour of individual neurons and networks of neurons. The solution of the model equations by finite difference methods is widespread because of the inherent simplicity of the technique. Error in the finite difference approach due to spatial and temporal discretisation is shown to be equivalent to a mis-specification of membrane current density. The effect of this mis-specification on the accuracy of the solution to the model equations is shown to depend on the structure of the model and its input, as well as the size of the discretisation intervals themselves. Through a theoretical analysis, illustrated by a number of examples on passive and active dendrites, this article demonstrates that the accuracy with which core current is implemented numerically at segment end-points in elementary models influences the behaviour of the numerical solution of these models, and consequently any physiological conclusions drawn from them.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Rosenberg, Prof Jay and Lindsay, Professor Kenneth
Authors: Lindsay, K.A., Ogden, J.M., and Rosenberg, J.R.
Subjects:R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry
Q Science > QA Mathematics
College/School:College of Medical Veterinary and Life Sciences
Journal Name:Progress in Biophysics and Molecular Biology
ISSN:0079-6107
ISSN (Online):1873-1732
Published Online:25 January 2002

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