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.

Computational Methods for Bayesian Estimation of Neuromagnetic Sources

Toni Auranen

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on the 27th of October, 2007, at 12 noon.

Overview in PDF format (ISBN 978-951-22-8954-7)   [3356 KB]
Dissertation is also available in print (ISBN 978-951-22-8953-0)


The electromagnetic inverse problem in human brain research consists of determining underlying source currents in the brain based on measurements outside the head. Solution to the inverse problem is ambiguous, necessitating the use of prior information and modeling assumptions for obtaining reasonable inverse estimates. In this study, we create new and improve existing computational methods for estimating neuromagnetic sources in the human brain.

One straightforward way of incorporating presumptions to this problem is to formulate it in a probabilistic Bayesian manner. Bayesian statistics is largely based on modeling uncertainties associated with parameters constituting the model by representing them with probability distributions. In this work, existing neuroscientific knowledge and information from anatomical and functional magnetic resonance imaging are used as prior assumptions in model implementation.

The neuromagnetic inverse problem is resolved with two different approaches. First, we perform the analysis using distributed source current modeling and infer some arbitrary parameter choices and the source currents from the measurement data by using numerical sampling methods. We apply similar strategies to cortically constrained current dipole localization and suggest using functional magnetic resonance imaging data for guiding the sampling algorithm. The models are tested with simulated and measured data.

The presented methods are rather automatic, yielding plausible and robust inverse estimates of cortical current sources. With the spatiotemporal dipole localization model, the inclusion of functional magnetic resonance imaging data improves performance of the numerical sampling method. However, apparent multimodality of the parameter posterior distribution causes complications especially with empirical data.

We suggest using loose cortical orientation constraints for smoothing down the complicated posterior distribution instead of marginal improvements to the sampling scheme. This might help to overcome the somewhat limited mixing properties of the sampling algorithm and ease the inconvenient multimodality of the posterior distribution.

This thesis consists of an overview and of the following 5 publications:

  1. 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 ℓp-norm priors. NeuroImage, 26 (3): 870-884. © 2005 Elsevier Science. By permission.
  2. 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.
  3. 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.
  4. Auranen, T., Nummenmaa, A., Hämäläinen, M. S., Jääskeläinen, I. P., Lampinen, J., Vehtari, A., and Sams, M. (2007). Bayesian inverse analysis of neuromagnetic data using cortically constrained multiple dipoles. Human Brain Mapping, 28 (10): 979-994.
  5. Auranen, T., Nummenmaa, A., Vanni, S., Vehtari, A., Hämäläinen, M. S., Lampinen, J., and Jääskeläinen, I. P. (2007). Automatic fMRI-guided MEG multidipole localization for visual responses. Helsinki University of Technology, Laboratory of Computational Engineering Publications, Report B63, ISBN 978-951-22-8952-3. Human Brain Mapping, submitted for publication.

Keywords: inverse problem, magnetoencephalography, Markov chain Monte Carlo

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© 2007 Helsinki University of Technology

Last update 2011-05-26