The authors study an integral inverse problem arising in the biology of the olfactory system. The transduction of an odor into an electrical signal is accomplished by a depolarising influx of ions through cyclic-nucleotide-gated (CNG for short) channels on the cilium membrane. The inverse problem studied in this paper consists in finding the spatial distribution of the CNG channels from the measured transduce electrical signals. The Mellin transform allows us to write an explicit formula for its solution. Proving observability and continuity inequalities is then a question of estimating the Mellin transform of the kernel of this integral equation on vertical lines. New estimates using arguments in the spirit of the stationary phase method are proven and a numerical scheme is proposed to reconstruct the density of CNG channels from modeled current representing experimental data, for an approximated model. For the original model an identifiability and a non observability (in some weighted L2 spaces) results are proven.
Accepté le :
DOI : 10.1051/m2an/2017062
@article{M2AN_2018__52_5_2083_0,
author = {Bourgeron, Thibault and Conca, Carlos and Lecaros, Rodrigo},
title = {Determining the distribution of ion channels from experimental data},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2083--2107},
publisher = {EDP-Sciences},
volume = {52},
number = {5},
year = {2018},
doi = {10.1051/m2an/2017062},
zbl = {1411.92040},
mrnumber = {3900702},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017062/}
}
TY - JOUR AU - Bourgeron, Thibault AU - Conca, Carlos AU - Lecaros, Rodrigo TI - Determining the distribution of ion channels from experimental data JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 2083 EP - 2107 VL - 52 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017062/ DO - 10.1051/m2an/2017062 LA - en ID - M2AN_2018__52_5_2083_0 ER -
%0 Journal Article %A Bourgeron, Thibault %A Conca, Carlos %A Lecaros, Rodrigo %T Determining the distribution of ion channels from experimental data %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 2083-2107 %V 52 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017062/ %R 10.1051/m2an/2017062 %G en %F M2AN_2018__52_5_2083_0
Bourgeron, Thibault; Conca, Carlos; Lecaros, Rodrigo. Determining the distribution of ion channels from experimental data. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 5, pp. 2083-2107. doi : 10.1051/m2an/2017062. http://www.numdam.org/articles/10.1051/m2an/2017062/
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