The adjoint method for general EEG and MEG sensor-based lead field equations

Abstract : The inverse source problem in electroencephalography (EEG) and magnetoencephalography (MEG) generally uses a lead field, which relates any source in the brain to its measurements at the sensors. For complex geometries, there is no analytical formula of the lead field. The common approach is to numerically compute the value of the lead field for a finite number of point sources (dipoles). There are several drawbacks: the model of the source space is fixed (a set of dipoles) and the computation can be expensive for as much as 10 000 dipoles. The common idea to bypass these problems is to compute the lead field from a sensor point of view. We show how the adjoint method can be used to derive general EEG and MEG sensorbased lead field equations. Within a simple framework, we provide a complete review of the explicit lead field equations, and we are able to extend these equations to non-point like sensors.
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Supek, Selma and Susac, Ana. Biomag 2010 - 17th International Conference on Biomagnetism, Mar 2010, Dubrovnik, Croatia. Springer, 28, pp.105-108, 2010, IFMBE Proceedings. 〈http://www.springerlink.com/content/m356045q457k2715/fulltext.pdf〉. 〈10.1007/978-3-642-12197-5_20〉
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Théodore Papadopoulo, Sylvain Vallaghé, Maureen Clerc. The adjoint method for general EEG and MEG sensor-based lead field equations. Supek, Selma and Susac, Ana. Biomag 2010 - 17th International Conference on Biomagnetism, Mar 2010, Dubrovnik, Croatia. Springer, 28, pp.105-108, 2010, IFMBE Proceedings. 〈http://www.springerlink.com/content/m356045q457k2715/fulltext.pdf〉. 〈10.1007/978-3-642-12197-5_20〉. 〈inria-00497088〉

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