Toni Auranen

Hierarchical Bayesian estimates of distributed MEG sources: theoretical aspects and comparison of variational and MCMC methods

Magnetoencephalography (MEG) provides millisecond-scale temporal resolution for noninvasive mapping of human brain functions, but the problem of reconstructing the underlying source currents from the extracranial data has no unique solution. Several distributed source estimation methods based on different prior assumptions have been suggested for the resolution of this inverse problem. Recently, a hierarchical Bayesian generalization of the traditional minimum norm estimate (MNE) was proposed, in which the variance of distributed current at each cortical location is considered as a random variable and estimated from the data using the variational Bayesian (VB) framework. Here, we introduce an alternative scheme for performing Bayesian inference in the context of this hierarchical model by using Markov chain Monte Carlo (MCMC) strategies. In principle, the MCMC method is capable of numerically representing the true posterior distribution of the currents whereas the VB approach is inherently approximative. We point out some potential problems related to hyperprior selection in the previous work and study some possible solutions. A hyperprior sensitivity analysis is then performed, and the structure of the posterior distribution as revealed by the MCMC method is investigated. We show that the structure of the true posterior is rather complex with multiple modes corresponding to different possible solutions to the source reconstruction problem. We compare the results from the VB algorithm to those obtained from the MCMC simulation under different hyperparameter settings. The difficulties in using a unimodal variational distribution as a proxy for a truly multimodal distribution are also discussed. Simulated MEG data with realistic sensor and source geometries are used in performing the analyses.

Dynamic retrospective filtering of physiological noise in BOLD fMRI: DRIFTER

In this article we introduce the DRIFTER algorithm, which is a new model based Bayesian method for retrospective elimination of physiological noise from functional magnetic resonance imaging (fMRI) data. In the method, we first estimate the frequency trajectories of the physiological signals with the interacting multiple models (IMM) filter algorithm. The frequency trajectories can be estimated from external reference signals, or if the temporal resolution is high enough, from the fMRI data. The estimated frequency trajectories are then used in a state space model in combination of a Kalman filter (KF) and Rauch-Tung-Striebel (RTS) smoother, which separates the signal into an activation related cleaned signal, physiological noise, and white measurement noise components. Using experimental data, we show that the method outperforms the RETROICOR algorithm if the shape and amplitude of the physiological signals change over time.

Automatic relevance determination based hierarchical Bayesian MEG inversion in practice.

In recent simulation studies, a hierarchical Variational Bayesian (VB) method, which can be seen as a generalisation of the traditional minimum-norm estimate (MNE), was introduced for reconstructing distributed MEG sources. Here, we studied how nonlinearities in the estimation process and hyperparameter selection affect the inverse solutions, the feasibility of a full Bayesian treatment of the hyperparameters, and multimodality of the true posterior, in an empirical dataset wherein a male subject was presented with pure tone and checkerboard reversal stimuli, alone and in combination. An MRI-based cortical surface model was employed. Our results show, with a comparison to the basic MNE, that the hierarchical VB approach yields robust and physiologically plausible estimates of distributed sources underlying MEG measurements, in a rather automated fashion.

Automatic fMRI-guided MEG multidipole localization for visual responses

Previously, we introduced the use of individual cortical location and orientation constraints in the spatiotemporal Bayesian dipole analysis setting proposed by Jun et al. ([2005]; Neuroimage 28:84–98). However, the models performance was limited by slow convergence and multimodality of the numerically estimated posterior distribution. In this paper, we present an intuitive way to exploit functional magnetic resonance imaging (fMRI) data in the Markov chain Monte Carlo sampling ‐based inverse estimation of magnetoencephalographic (MEG) data. We used simulated MEG and fMRI data to show that the convergence and localization accuracy of the method is significantly improved with the help of fMRI‐guided proposal distributions. We further demonstrate, using an identical visual stimulation paradigm in both fMRI and MEG, the usefulness of this type of automated approach when investigating activation patterns with several spatially close and temporally overlapping sources. Theoretically, the MEG inverse estimates are not biased and should yield the same results even without fMRI information, however, in practice the multimodality of the posterior distribution causes problems due to the limited mixing properties of the sampler. On this account, the algorithm acts perhaps more as a stochastic optimizer than enables a full Bayesian posterior analysis. Hum Brain Mapp 2009.

Bayesian inverse analysis of neuromagnetic data using cortically constrained multiple dipoles

A recently introduced Bayesian model for magnetoencephalographic (MEG) data consistently localized multiple simulated dipoles with the help of marginalization of spatiotemporal background noise covariance structure in the analysis [Jun et al., ( 2005 ): Neuroimage 28:84–98]. Here, we elaborated this model to include subjects individual brain surface reconstructions with cortical location and orientation constraints. To enable efficient Markov chain Monte Carlo sampling of the dipole locations, we adopted a parametrization of the source space surfaces with two continuous variables (i.e., spherical angle coordinates). Prior to analysis, we simplified the likelihood by exploiting only a small set of independent measurement combinations obtained by singular value decomposition of the gain matrix, which also makes the sampler significantly faster. We analyzed both realistically simulated and empirical MEG data recorded during simple auditory and visual stimulation. The results show that our model produces reasonable solutions and adequate data fits without much manual interaction. However, the rigid cortical constraints seemed to make the utilized scheme challenging as the sampler did not switch modes of the dipoles efficiently. This is problematic in the presence of evidently highly multimodal posterior distribution, and especially in the relative quantitative comparison of the different modes. To overcome the difficulties with the present model, we propose the use of loose orientation constraints and combined model of prelocalization utilizing the hierarchical minimum‐norm estimate and multiple dipole sampling scheme. Hum Brain Mapp 2007.

Two-Stage Processing of Sounds Explains Behavioral Performance Variations due to Changes in Stimulus Contrast and Selective Attention: An MEG Study

Selectively attending to task-relevant sounds whilst ignoring background noise is one of the most amazing feats performed by the human brain. Here, we studied the underlying neural mechanisms by recording magnetoencephalographic (MEG) responses of 14 healthy human subjects while they performed a near-threshold auditory discrimination task vs. a visual control task of similar difficulty. The auditory stimuli consisted of notch-filtered continuous noise masker sounds, and of 1020-Hz target tones occasionally () replacing 1000-Hz standard tones of 300-ms duration that were embedded at the center of the notches, the widths of which were parametrically varied. As a control for masker effects, tone-evoked responses were additionally recorded without masker sound. Selective attention to tones significantly increased the amplitude of the onset M100 response at 100 ms to the standard tones during presence of the masker sounds especially with notches narrower than the critical band. Further, attention modulated sustained response most clearly at 300–400 ms time range from sound onset, with narrower notches than in case of the M100, thus selectively reducing the masker-induced suppression of the tone-evoked response. Our results show evidence of a multiple-stage filtering mechanism of sensory input in the human auditory cortex: 1) one at early (100 ms) latencies bilaterally in posterior parts of the secondary auditory areas, and 2) adaptive filtering of attended sounds from task-irrelevant background masker at longer latency (300 ms) in more medial auditory cortical regions, predominantly in the left hemisphere, enhancing processing of near-threshold sounds.