A method for locating regions containing neural activation at a given confidence level from MEG data Page: 3 of 6
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A Method for Locating Regions Containing Neural Activation at a Given
Confidence Level from MEG Data
Schmidt, D.M., George, J.S.
Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico, USA
Introduction
The MEG inverse problem does not have a general, unique solution. Unless restrictive model assumptions
are made, there are generally many more free parameters than measurements and there exist "silent sources"-current
distributions which produce no external magnetic field. By weighting solutions according to how well each fits our
prior notion about what properties good solutions should have, it may be possible to obtain a single current distribution
that "best fits" the data and our expectations. However, in general there will still exist a number of different current
distributions which fit both the data and our prior expectations sufficiently well. For example, a simulated data set
based on a single or several dipoles can generally be fit equally well by a distributed current minimum-norm recon-
struction. In experimental data it is often possible to find a relatively small number of dipoles which both fit the data
and have a norm not much larger than that of the minimum-norm solution. Moreover, the few-dipole solutions often
have currents in different regions than the corresponding minimum-norm solution. Because there exist well-fitting
current distributions which may have current in significantly different locations, it can be misleading to infer locations
of stimulus-correlated neural activity based on a single, best-fitting current distribution. We demonstrate here a method
for inferring the location and number of regions containing neural activation by considering all possible current dis-
tributions within a given model (not just the most likely one) weighted according to how well each fits both the data
and our prior expectations.
Methods
We employ a Bayesian approach which considers a posterior probability distribution, P(j I data), that
assigns each current distribution, j, a relative likelihood based on how well each distribution fits the data and meets
one's prior expectation-explicitly defined by a prior probability distribution, P(j). Specifically, Bayes theorem[1]
states that
P(j I data) oc P(data I j)P(j)
where P(data j .) is the likelihood of the data given the current distribution, j. In some over-determined problems
the information from the data dominates, and the posterior probability distribution is highly peaked. In such cases
inferences from the most likely solution may be reliable. However, with MEG data the posterior distribution is gener-
ally quite broad because of the ill-posed nature of the problem and because there are often more free parameters than
measurements. Most methods widely used or analysis of MEG data infer neural activity based on a single best-fitting
current distribution within the context of a given source model. Implicit model assumptions strongly influence the
nature of the reconstructed current distribution but the consequences of model assumptions are seldom considered. In
our Bayesian approach, model assumptions are made explicit in the form of the prior probability distribution. In ad-
dition, we infer activation from the full posterior distribution, which we believe will yield different and more reliable
estimates than inferences made from a single "most likely" current distribution.
In our model, we assume that there are a small number of compact regions that contain the stimulus-correlated
neural activity. This is appropriate, for example, for stimuli designed to generate a limited, focal evoked response.
What we want to determine is how many of these regions are needed, n, and where they are located, w. Following
Bayes theorem,
P(n, w data) oc P(data n, w)P(n, w)
where P(n, w data) is the posterior probability of the number and location of regions containing activity given the
data, P(n, w) is the prior probability for the number and location of these regions, and P(data n, w) is the likelihood
of the data given a particular number and location of regions. The data, however, do not depend directly on the number
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Schmidt, D. M. & George, J. S. A method for locating regions containing neural activation at a given confidence level from MEG data, article, February 1, 1996; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc672622/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.