Below is a draft piece of text that can be used for describing eLORETA in the “Methods” section of a manuscript. Note that references are included below.
Based on the scalp-recorded electric potential distribution, the exact low resolution brain electromagnetic tomography (eLORETA) software (publicly available free academic software at http://www.uzh.ch/keyinst/loreta.htm) was used to compute the cortical three-dimensional distribution of current density. The eLORETA method is a discrete, three-dimensional (3D) distributed, linear, weighted minimum norm inverse solution. The particular weights used in eLORETA endow the tomography with the property of exact localization to test point sources, yielding images of current density with exact localization, albeit with low spatial resolution (i.e. neighboring neuronal sources will be highly correlated). The description of the method together with the proof of its exact zero-error localization property, are described in  and . It is also important to emphasize that eLORETA has no localization bias even in the presence of structured noise. In this sense, eLORETA is an improvement over previously developed tomographies LORETA  and the standardized version sLORETA .
It should be emphasized that the localization properties of any linear 3D inverse solution (i.e. tomography) can always be determined by the localization errors to test point sources. If such a tomography has zero localization error to such point sources located anywhere in the brain, then, except for low spatial resolution, the tomography will localize correctly any arbitrary 3D distribution. This is due to the principles of linearity and superposition. These principles do not apply to non-linear inverse solutions, nor do they apply to schemes that are seemingly linear but are not 3D inverse solutions (e.g. one-at-a-time best fitting dipoles).
The previously developed, related tomography LORETA  has received considerable validation from studies combining LORETA with other more established localization methods, such as functional Magnetic Resonance Imaging (fMRI)  and , structural MRI , Positron Emission Tomography (PET) , , and . Further LORETA validation has been based on accepting as ground truth the localization findings obtained from invasive, implanted depth electrodes, in which case there are several studies in epilepsy , , and  and cognitive ERPs .
In the case of the standardized version sLORETA , it is worth emphasizing that two independent groups,  and , showed that the method has no localization bias in the absence of measurement noise; but in the presence of measurement noise they found that sLORETA has a localization bias. They did not, however, consider the more realistic case where the brain in general is always active, thus producing biological noise. Under these arguably much more realistic conditions (in the presence of both biological and measurement noise), proof was given in  demonstrating that sLORETA has no localization bias.
Furthermore, sLORETA  has recently been validated in several simultaneous EEG/fMRI studies , , and , and in an EEG localization study for epilepsy .
All these results serve also as validation for eLORETA, due to its improved localization properties. It is worth emphasizing that deep structures such as the anterior cingulate cortex , and mesial temporal lobes  can be correctly localized with these methods.
In the current implementation of eLORETA, computations were made in a realistic head model , using the MNI152 template , with the three-dimensional solution space restricted to cortical gray matter, as determined by the probabilistic Talairach atlas . The standard electrode positions on the MNI152 scalp were taken from  and . The intracerebral volume is partitioned in 6239 voxels at 5 mm spatial resolution. Thus, eLORETA images represent the electric activity at each voxel in neuroanatomic Montreal Neurological Institute (MNI) space as the exact magnitude of the estimated current density. Anatomical labels as Brodmann areas are also reported using MNI space, with correction to Talairach space .
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