  Data assimilation, defined as the fusion of data with preexisting knowledge,
is particularly suited to elucidating underlying phenomena from
noisy/insufficient observations. Although this approach has been widely used in
diverse fields, only recently have efforts been directed to problems in
neuroscience, using mainly intracranial data and thus limiting its
applicability to invasive measurements involving electrode implants. Here we
intend to apply data assimilation to non-invasive electroencephalography (EEG)
measurements to infer brain states and their characteristics. For this purpose,
we use Kalman filtering to combine synthetic EEG data with a coupled
neural-mass model together with Ary's model of the head, which projects
intracranial signals onto the scalp. Our results show that using several
extracranial electrodes allows to successfully estimate the state and
parameters of the neural masses and their interactions, whereas one single
electrode provides only a very partial and insufficient view of the system. The
superiority of using multiple extracranial electrodes over using only one, be
it intra- or extracranial, is shown over a wide variety of dynamical
behaviours. Our results show potential towards future clinical applications of
the method.
