Electroencephalography allows for the recording of neural activity non-invasively by placing a set of electrodes on the scalp. While the fact that electroencephalography is non-invasive has clear advantages for the monitoring of brain activity in humans, it also comes with its limitations.
Neural activity generated by neurons has to propagate through neural tissue, cerebrospinal fluid, skin and bone before reaching the surface electrodes, layers of resistive tissue that alter the original properties of the signal. On top of that, neurons generating the electrical activity are not isolated, but instead, embedded on a complex network of neurons that are constantly active and generating its own electrical activity. All these distortions of the neural signal before it reaches the electrodes placed at the scalp are grouped into the concept of volume conduction effects, technically defined as the distortions an electric (or magnetic) field suffers when it passes through biological tissue towards the measurement sensors. Because of these distortions and diffusions through tissue, scalp sensors can only record brain activity generated at several centimeters below the recording positions. From another prospective, at every position where you put a sensor on the scalp, the recorded brain activity will reflect a weighted sum of the underlying brain sources that span a couple of cm around that position (Makeig et al. 1996).
Despite these distortions, EEG remains as one of the most important approaches to study brain activity. While the volume-conduction effect limits us to an estimated spatial resolution of 5-9cm (Nunez 1981), it keeps a temporal resolution on the scale of ms, one of the highest compared to all other methods available for the study of the nervous system (see Figure 1).
How much can we improve upon these technical limitations? In recent years, there has been remarkable progress in reconstructing the underlying cortical activity from surface electromagnetic data, a set of techniques grouped under the label of source localization or source reconstruction methods (Scherg 1990; Gross et al., 2001; Dale et al. 2000). Intuitively, this technique aims to estimate the spatio-temporal dynamics of currents of the brain that better explain the observed electromagnetic fields through EEG or MEG. In other words, the source localization process consists of calculating, from a set of observed data, what the causal factors that produced them are, what is known as the inverse problem (Figure 2). Note however that, in solving the inverse problem, the number of variables that can be observed (i.e. electrodes we record from) is remarkably small if we compare to the large number of causal factors (i.e. the number of points in the brain where this surface activity could come from, which in practice corresponds to the number of points we would need to create a volume model of a brain). Thus, the inverse problem is, by nature, an ill-posed problem, as we can find more than one solution (brain activity) for an observed scalp voltage.
In order to make this inverse problem well posed, it is necessary to impose additional constraints on the solution. The most common source reconstruction approaches rely on the assumption that sources are temporally uncorrelated, which is particularly appropriate when analyzing the responses sensory stimuli (Mosher et al 1992). Physiological constraints can be introduced by considering that the EEG records signal from populations of neurons localized in the grey matter and are oriented perpendicular to the cortical sheet (Nunez 1981). Knowing the exact shape of the cortical surface through the Magnetic Resonance Imaging (MRI) can further impose anatomical constraints on the head volume conductor model, an approach which is being increasingly used. Constraints on the spatial orientation can also be introduced, especially considering that the non-invasive sensors would record the neural populations that are oriented with a particular angle to the scalp (Miranda et. al 2013). These and other differences would add relative strengths and weaknesses to the different localization methods in terms of accuracy of the approximation, computation time, or spread of the source. For instance, if one expects very few sources, then MAP-estimation may better reflect the true sources while being computationally efficient (Ahlfors et al 1992); if one expects multiple sources with variable spatial extent, then methodologies based on a Sparse-Bayesian Learning may be the most appropriate (Mackay 1992).
While different methods differ on the modeling assumptions, all methods are known to improve spatio-temporal resolution of the EEG, reducing the spatial resolution to 2-4cm (Yao and Dewald 2005; Ding and Lai 2005; Pizzagalli 2007). In the end, the variability in methods to approximate the currents on the brain offer great opportunity to select the most appropriate algorithm for a given experiment.
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