Probabilistic forward model for electroencephalography source analysis

Abstract

Source localization by electroencephalography (EEG) requires an accurate model of head geometry and tissue conductivity. The estimation of source time courses from EEG or from EEG in conjunction with magnetoencephalography (MEG) requires a forward model consistent with true activity for the best outcome. Although MRI provides an excellent description of soft tissue anatomy, a high resolution model of the skull (the dominant resistive component of the head) requires CT, which is not justified for routine physiological studies. Although a number of techniques have been employed to estimate tissue conductivity, no present techniques provide the noninvasive 3D tomographic mapping of conductivity that would be desirable. We introduce a formalism for probabilistic forward modeling that allows the propagation of uncertainties in model parameters into possible errors in source localization. We consider uncertainties in the conductivity profile of the skull, but the approach is general and can be extended to other kinds of uncertainties in the forward model. We and others have previously suggested the possibility of extracting conductivity of the skull from measured electroencephalography data by simultaneously optimizing over dipole parameters and the conductivity values required by the forward model. Using Cramer-Rao bounds, we demonstrate that this approach does not improve localization results nor does it produce reliable conductivity estimates. We conclude that the conductivity of the skull has to be either accurately measured by an independent technique, or that the uncertainties in the conductivity values should be reflected in uncertainty in the source location estimates.

Data-driven forward model inference for EEG brain imaging

“…There is a broad consensus that forward model uncertainty is an important limiting factor for EEG imaging by source reconstruction [17,24,55,56,57,58,59]. Our results add quantitative evidence to this view, both in terms of the tissue conductivity ratio, which is the main source of uncertainty if the brain topography is correct, and more broadly when both anatomy and conductivities are unknown.…”

Subspace electrode selection methodology for the reduction of the effect of uncertain conductivity values in the EEG dipole localization: a simulation study using a patient-specific head model

“…This was extensively demonstrated in Plis et al (2007). This approach of extracting the conductivity together with the dipole location was also suggested in Lew et al (2007) and Vallaghé et al (2007).…”

“…using Monte Carlo simulations (Chen et al 2010), stochastic Cramér Rao Bound technique (Plis et al 2007) and polynomial chaos decomposition (Gaignaire et al 2010). We can theoretically express this effect on the inverse solution by redefining (5)…”

“…in Haueisen et al (1997), Laarne et al (1999), Gençer and Acar (2004) and Vallaghé and Clerc (2009). The uncertain conductivity values, more specifically the ratio of the skull conductivity to the conductivity values of the soft tissues, have a large influence on the EEG dipole localization accuracy and are the most dominant source of error (Laarne et al 2000, Plis et al 2007, Chen et al 2010. Many values have already been suggested in the literature for the scalp, skull, cerebro-spinal fluid (CSF) and brain: Geddes and Baker (1967) stated that the soft tissue to skull conductivity ratio was 80, Oostendorp et al (2000) 15, Gonçalves et al (2003) 20-50, while Hoekema et al (2003) measured this value to be in the interval 10-40 and Lai et al (2005) as 25.…”

“…Akhtari et al (2010) state that understanding brain electrical conductivity and ways to noninvasively measure them are probably necessary to enhance the ability to localize EEG sources from epilepsy surgery patients. Plis et al (2007) proposed a probabilistic framework for incorporating the uncertain conductivity values in the reconstruction of neural sources. They concluded that the conductivity of the skull has to be either accurately measured by an independent technique, or that the uncertainties in the conductivity values should be reflected in the source localization estimates.…”