Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation

Mathematical and Computer Modelling

Volumn 43, Issue 7-8, 2006, Pages 945-956

  French, Donald A ^a   Flannery, Richard J ^b   Groetsch, Charles W ^a   Krantz, Willam B ^c   Kleene, Steven J ^b  

^a UNIVERSITY OF CINCINNATI   (United States)

^b UNIVERSITY OF CINCINNATI COLLEGE OF MEDICINE   (United States)

^c University of Cincinnati   (United States)

Author keywords

Cilia; Finite differences; Inverse problem; Ion channels; Olfaction

Indexed keywords

FINITE DIFFERENCE METHOD; INVERSE PROBLEMS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; NUMERICAL METHODS;

CILIA; MATHEMATICAL PROBLEM; OLFACTION;

APPROXIMATION THEORY;

EID: 33645017870     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2005.11.010     Document Type: Article

References (19)

1. J. Bell, and G. Craciun A distributed parameter identification problem in neuronal cable theory models Math. Biol. 51 2005 217 246
2. C. Chen, T. Nakamura, and Y. Koutalos Cyclic AMP diffusion coefficient in frog olfactory cilia Biophys. J. 76 1999 2861 2867
3. J. Crank The Mathematics of Diffusion 2nd edition 2001 Oxford University Press Oxford
4. H.W. Engel, M. Hanke, and A. Neubauer Regularization of Inverse Problems 1996 Kluwer Dordrecht
5. C.W. Groetsch The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind 1984 Pitman London
6. J. Keener, and J. Sneyd Mathematical Physiology 1998 Springer New York
7. S.J. Kleene Origin of the chloride current in olfactory transduction Neuron 11 1993 123 132
8. S.J. Kleene, and R.C. Gesteland Transmembrane currents in frog olfactory cilia J. Membr. Biol. 120 1991 75 81
9. S.J. Kleene, and R.C. Gesteland Calcium-activated chloride conductance in frog olfactory cilia J. Neurosci. 11 1991 3624 3629
10. S.J. Kleene, R.C. Gesteland, and S.H. Bryant An electrophysiological survey of frog olfactory cilia J. Exp. Biol. 195 1994 307 328
11. M.V. Klibanov, and T.R. Lucas Numerical solution of a parabolic inverse problem in optical tomography using experimental data SIAM J. Appl. Math. 59 1999 1763 1789
12. H.P. Larsson, S.J. Kleene, and H. Lecar Noise analysis of ion channels in non-space-clamped cables: Estimates of channel parameters in olfactory cilia Biophys. J. 72 1997 1193 1203
13. B. Lindemann Predicted profiles of ion concentrations in olfactory cilia in the steady state Biophys. J. 80 2001 1712 1721
14. M. Luskin, and R. Rannacher On the smoothing property of the Crank-Nicolson scheme Appl. Math. 14 1982/83 117 135
15. K. Matulef, and W.N. Zagotta Cyclic nucleotide-gated ion channels Annu. Rev. Cell Dev. Biol. 19 2003 23 44
16. B.H. Menco Qualitative and quantitative freeze-fracture studies on olfactory and nasal respiratory structures in frog, ox, rat, and dog. I, A general survey Cell Tissue Res. 207 1980 183 209
17. M. Tadi Inverse heat conduction based on boundary measurement Inverse Problems 13 1997 1585 1605
18. M. Tadi, M.V. Klibanov, and W. Cai An inversion method for parabolic equations based on quasireversibility Comput. Math. Appl. 43 2002 927 941
19. R.E. White Finite Element Methods 1985 Springer New York