Source identification based on regularization and evolutionary computing in biomagnetism Paolo Di Barba and Maria Evelina Mognaschi Department of Electrical Engineering, University of Pavia, Pavia, Italy Guido Nolte Fraunhofer Institute of Computer Architecture and Software Technology, Berlin, Germany Ryszard Palka Department of Power Systems and Electrical Drives, West Pomeranian University of Technology, Szczecin, Poland, and Antonio Savini Department of Electrical Engineering, University of Pavia, Pavia, Italy Abstract Purpose – The purpose of this paper is to develop a source reconstruction technique, applied to a case study in biomagnetism, using both evolutionary optimization and regularization techniques. Design/methodology/approach – The magnetic field, produced by a current dipole in a spheroidal domain modeling the head, is calculated. Although the model is very simple, the magnetic effect of a brain source is appropriately simulated. In order to solve the source identification problem, the following approaches have been implemented: a single-objective minimization of a residual function, based on an evolutionary algorithm, is applied first; then, the L-curve criterion for regularization is implemented by means of an iterative search. Findings – A variable number of unknown parameters, defining direction and magnitude of the current dipole, have been considered. As a consequence, several optimization problems are solved: a technique based on the use of the lead field matrix identifies the source with the smallest error. Eventually, an iterative procedure based on Tikhonov regularization is proposed. The algorithm is tested with and without noise affecting data. The results showed an accuracy comparable to that obtained independently with the optimization approach. Originality/value –A model problem in inverse biomagnetism, which is both simple and significant, has been formulated and solved. The magnetic source of brain activity is reconstructed in a fast way and with small errors by means of two techniques of field inversion. Keywords Brain, Electromagnetic fields, Optimization techniques Paper type Research paper Introduction All activities of a human being are linked to an electrical activity in a specific area of the brain. Primary sources of these activities are electrolytic currents within the dendrites of the large pyramidal cells of activated neurons in the cortex sheet of the brain. As far as modeling is concerned, these electrolytic currents are generally formulated as a distribution of current sources if the conduction field is the quantity of interest. The formulation of the problem is still an open issue. In fact, it is clear that the The current issue and full text archive of this journal is available at www.emeraldinsight.com/0332-1649.htm COMPEL 29,4 1022 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 29 No. 4, 2010 pp. 1022-1032 q Emerald Group Publishing Limited 0332-1649 DOI 10.1108/03321641011044442