## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Philosophy to be presented with due permission of the Department
of Electrical and Communications Engineering for public
examination and debate in Auditorium E at Helsinki University of Technology (Espoo, Finland) on the
11^{th} of January, 2008, at 12 noon.

Overview in PDF format (ISBN 978-951-22-9143-4) [366 KB]

Dissertation is also available in print (ISBN 978-951-22-9142-7)

Magnetoencephalography (MEG) enables noninvasive measurements of cerebral activity with excellent temporal resolution, but localising the neural currents generating the extracranial magnetic fields admits no unique solution. By imposing some mathematical constraints on the currents, reasonable solutions to this electromagnetic inverse problem can be obtained.

In this work, we adopt the statistical formulation of the inverse problem in which the constraints are encoded as Bayesian prior probabilities. The prior is combined with a statistical MEG observation model via Bayes' theorem to yield the posterior probability of the unknown parameters, that is the currents, given the MEG data and modeling assumptions. Apart from the currents, the prior probability density may contain further parameters which are subject to uncertainty. These parameters are not related directly to the MEG observations and are called second-level parameters or hyperparameters, giving the model a hierarchical structure.

The thesis considers hierarchical generalisations of the classical Minimum-Norm and Minimum-Current Estimates (MNE and MCE). The MNE and MCE are distributed source reconstruction methods from which the former is known to produce spatially diffuse distributions and the latter more focal. The here studied extensions of the MNE and MCE prior structures allow more general and flexible modeling of distributed sources with properties in between MNE and MCE.

The first two studies included in this thesis involve more theoretical Bayesian analyses on the properties of the hierarchical distributed source models and the resulting inverse estimates. The latter two studies focus on validation of the models with empirical MEG data, practical analyses and interpretation of the inverse estimates.

This thesis consists of an overview and of the following 4 publications:

- Auranen, T., Nummenmaa, A., Hämäläinen, M. S., Jääskeläinen, I. P., Lampinen,
J., Vehtari, A., and Sams, M. (2005). Bayesian analysis of the neuromagnetic
inverse problem with ℓ
^{p}-norm priors. NeuroImage, 26 (3): 870-884. © 2005 Elsevier Science. By permission. - Nummenmaa, A., Auranen, T., Hämäläinen, M. S., Jääskeläinen, I. P., Lampinen, J., Sams, M., and Vehtari, A. (2007). Hierarchical Bayesian estimates of distributed MEG sources: theoretical aspects and comparison of variational and MCMC methods. NeuroImage, 35 (2): 669-685. © 2007 Elsevier Science. By permission.
- Nummenmaa, A., Auranen, T., Hämäläinen, M. S., Jääskeläinen, I. P., Sams, M., Vehtari, A., and Lampinen, J. (2007). Automatic relevance determination based hierarchical Bayesian MEG inversion in practice. NeuroImage, 37 (3): 876-889. © 2007 Elsevier Science. By permission.
- Nummenmaa, A., Auranen, T., Vanni, S., Hämäläinen, M. S., Jääskeläinen, I. P., Lampinen, J., Vehtari, A., and Sams, M. (2007). Sparse MEG inverse solutions via hierarchical Bayesian modeling: evaluation with a parallel fMRI study. Helsinki University of Technology, Laboratory of Computational Engineering Publications, Report B65, ISBN 978-951-22-9141-0. © 2007 by authors.

**Keywords:**
magnetoencephalography, inverse problem, Bayesian analysis

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© 2008 Helsinki University of Technology

Last update 2011-05-26