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.

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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 model's 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.

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 subject's 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.