2018/10/13 by Jemy A. Mandujano Valle, Valle, Jemy A. Mandujano, Alexandre L. Madureira +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Neuroscience · #65M32 #92C20 #FOS: Mathematics #Gene Regulatory Network Analysis #Neural Networks and Applications #Neural dynamics and brain function #Numerical Analysis (math.NA) #cs.NA #math.NA #msc:65M32 #msc:92C20
paper · pdf · doi:10.48550/arxiv.1810.05887
openalex publication_date 2018/10/13 · arxiv created 2020/09/26 · arxiv updated 2020/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using neurons of the giant squid. It becomes clear that determining experimentally the conductances of neurons is hard, in particular under the presence of spatial and temporal heterogeneities. Moreover it is reasonable to expect variations between species or even between types of neurons of a same species. Determining conductances from one type of neuron is no guarantee that it works across the board. We tackle the inverse problem of determining, given voltage data, conductances with non-uniform distribution computationally. In the simpler setting of a cable equation, we consider the Landweber iteration, a computational technique used to identify non-uniform spatial and temporal ionic distributions, both in a single branch or in a tree. Here, we propose and (numerically) investigate an iterative scheme that consists in numerically solving two partial differential equations in each step. We provide several numerical results showing that the method is able to capture the correct conductances given information on the voltages, even for noisy data.