Summary
There have been a number of attempts in the last years to localize the generators of brain electromagnetic activity, considering one current dipole as the source model. Single Dipole Localization (SDL) requires the selection of an optimization algorithm (OA). General aspects related with the selection, implementation and evaluation of some of the OA employed for SDL are discussed in this paper. Specifically the performance of two algorithms, those of Hooke-Jeeves and Levenberg-Marquardt, are tested by simulations. Suggestions for including restrictions to the dipole position and comments about some commonly used measures of the goodness of fit are given. Examples of erroneous implementations of these algorithms are also illustrated. A simple graphic rejection criterion, which can be easily used by inexperienced researchers, is introduced and tested in noisy and noise free simulations.
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References
De Munck, J.C., Van Dijk, B.V. and Spelreijse, H. Mathematical dipoles are adequate to describe “realistic” generators of human brain activity. IEEE Trans. Biomed. Eng., 1988, BME35: 960–966.
Denis, J.E. and Schnabel, R.B. Numerical methods for unconstrained optimization and non linear equations, Prentice Halls, Englewood Cliffs, N.J., 1983.
George, J.S., Levis, P.S., Rankin, D.W., Kaplan, L. and Wood, C.C. Anatomical constraint for neuromagnetic source models. In: Abstracts of the 8th International Conference on Biomagnetism, Munster, FRG, 1991.
Golub, G.H. and Preyra, V. The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal, 1973, 10: 413–432.
Hooke, R. and Jeeves, T. A. “Direct search” solution of numerical and statistical problems. J. of the Assn. for Computing Machinery, 1961, 8: 212–229.
Kurike, S., Murose, M. and Takeuchi, F. Locating accuracy of a current source of neuromagnetic response: simulation study for a single current dipole in a spherical conductor. Electroenceph. Clin. Neurophysiol, 1989, 73: 499–506.
Marquardt, D.W., An algorithm for least-squares estimation of non linear parameters. J. Soc. Indust. Appl. Maths., 1963, 11: 431–441.
Walsh, G.R. Methods of Optimization, John Wiley & Sons, New York, 1975.
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The authors are grateful to Roberto D. Pascual Marqui for programming the Hooke-Jeeves algorithm.
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de Peralta Menendez, R.G., Gonzalez Andino, S.L. Single dipole localization: Some numerical aspects and a practical rejection criterion for the fitted parameters. Brain Topogr 6, 277–282 (1994). https://doi.org/10.1007/BF01211173
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DOI: https://doi.org/10.1007/BF01211173