Modeling neuronal magnetic fields
Our first investigation of magnetic fields was through the analysis of magnetoencephalogram (MEG) signals in human subjects . By comparing simultaneously recorded EEG and MEG recordings in awake subjects, we characterized the spectral structure of both signals. While EEG scales between 1/f and 1/f2 over the scalp, we found that MEG signals scale with a significantly lower exponent, from 1/f0.5 to 1/f at low frequencies . We calculated maps of the scaling exponent across the brain surface, and found that the scaling exponent of MEG displayed a coherent structure across the surface of the brain. The difference of scaling between EEG and MEG signals constitute an evidence that the system cannot be considered as resistive (see details in ).
Motivated by the importance of the magnetic field for brain activity measurements, we investigated models of neuronal magnetic fields, and how they are generated by dendritic cables . We formulated a generalized cable model in which the extracellular magnetic field can be calculated by an iterative procedure, at any position and any degree of accuracy. One of the finding of this theoretical model is that the extracellular magnetic field will be influenced by the nature of the extracellular medium. This is because the nature of the medium will influence the current sources, in particular the axial currents in neurons, which mostly generate the magnetic field. This predicts that the nature of the medium should affect the frequency scaling of the neuronal magnetic signals.
More recently, we collaborated with several research groups in France, Germany and Portugal, in a European project called Magnetrodes, which was aimed at providing local-scale measurements of biological magnetic fields, which are so far not available. The magnetrode consists of a magnetic sensor based on the giant-magnetoresistance (GMR) effect, which is mounted on a needle, and is aimed to be the magnetic equivalent of an electrode. The goal is to record magnetic fields of small population of cells, such as in brain slices or in muscle fibers. We published this year the first experimental measurements of local-scale magnetic fields in living tissue using a magnetrode . This collaborative effort combines the design and fabrication of the magnetrode, the measurements of biological magnetic fields, and the biophysical modeling of such magnetic fields. The measurements and models were made on muscle fibers, which generate strong magnetic fields easily recordable and that are straightforward to be modeled. The further testing of the magnetrode in brain slices and in vivo is currently under way.
 Dehghani, N, Bedard, C., Cash, S.S., Halgren, E. and Destexhe, A. Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media. J. Computational Neurosci. 29: 405-421, 2010 (see abstract).
 Bedard, C. and Destexhe, A. Generalized cable formalism to calculate the magnetic field of single neurons and neuronal populations. Phys. Rev. E 90: 042723, 2014 (see abstract)
 Barbieri, F., Trauchessec, V.. Caruso, L., Trejo Rosillo, J., Telenczuk, B., Paul, E., Bal, T., Destexhe, A., Fermon, C., Pannetier-Lecoeur, M. and Ouanounou, G. Local recording of biological magnetic fields using Giant Magneto Resistance-based micro-probes. Nature Scientific Reports 6: 39330, 2016 (see abstract)
Department of Integrative and Computational Neuroscience (ICN),