Aapo Nummenmaa

Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations

This article considers the application of variational Bayesian methods to joint recursive estimation of the dynamic state and the time-varying measurement noise parameters in linear state space models. The proposed adaptive Kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately. The result is a recursive algorithm, where on each step the state is estimated with Kalman filter and the sufficient statistics of the noise variances are estimated with a fixed-point iteration. The performance of the algorithm is demonstrated with simulated data.

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.

The impact of gradient strength on in vivo diffusion MRI estimates of axon diameter

Diffusion magnetic resonance imaging (MRI) methods for axon diameter mapping benefit from higher maximum gradient strengths than are currently available on commercial human scanners. Using a dedicated high-gradient 3T human MRI scanner with a maximum gradient strength of 300 mT/m, we systematically studied the effect of gradient strength on in vivo axon diameter and density estimates in the human corpus callosum. Pulsed gradient spin echo experiments were performed in a single scan session lasting approximately 2h on each of three human subjects. The data were then divided into subsets with maximum gradient strengths of 77, 145, 212, and 293 mT/m and diffusion times encompassing short (16 and 25 ms) and long (60 and 94 ms) diffusion time regimes. A three-compartment model of intra-axonal diffusion, extra-axonal diffusion, and free diffusion in cerebrospinal fluid was fitted to the data using a Markov chain Monte Carlo approach. For the acquisition parameters, model, and fitting routine used in our study, it was found that higher maximum gradient strengths decreased the mean axon diameter estimates by two to three fold and decreased the uncertainty in axon diameter estimates by more than half across the corpus callosum. The exclusive use of longer diffusion times resulted in axon diameter estimates that were up to two times larger than those obtained with shorter diffusion times. Axon diameter and density maps appeared less noisy and showed improved contrast between different regions of the corpus callosum with higher maximum gradient strength. Known differences in axon diameter and density between the genu, body, and splenium of the corpus callosum were preserved and became more reproducible at higher maximum gradient strengths. Our results suggest that an optimal q-space sampling scheme for estimating in vivo axon diameters should incorporate the highest possible gradient strength. The improvement in axon diameter and density estimates that we demonstrate from increasing maximum gradient strength will inform protocol development and encourage the adoption of higher maximum gradient strengths for use in commercial human scanners.

MGH-USC Human Connectome Project datasets with ultra-high b-value diffusion MRI

The MGH-USC CONNECTOM MRI scanner housed at the Massachusetts General Hospital (MGH) is a major hardware innovation of the Human Connectome Project (HCP). The 3T CONNECTOM scanner is capable of producing a magnetic field gradient of up to 300 mT/m strength for in vivo human brain imaging, which greatly shortens the time spent on diffusion encoding, and decreases the signal loss due to T2 decay. To demonstrate the capability of the novel gradient system, data of healthy adult participants were acquired for this MGH-USC Adult Diffusion Dataset (N=35), minimally preprocessed, and shared through the Laboratory of Neuro Imaging Image Data Archive (LONI IDA) and the WU-Minn Connectome Database (ConnectomeDB). Another purpose of sharing the data is to facilitate methodological studies of diffusion MRI (dMRI) analyses utilizing high diffusion contrast, which perhaps is not easily feasible with standard MR gradient system. In addition, acquisition of the MGH-Harvard-USC Lifespan Dataset is currently underway to include 120 healthy participants ranging from 8 to 90 years old, which will also be shared through LONI IDA and ConnectomeDB. Here we describe the efforts of the MGH-USC HCP consortium in acquiring and sharing the ultra-high b-value diffusion MRI data and provide a report on data preprocessing and access. We conclude with a demonstration of the example data, along with results of standard diffusion analyses, including q-ball Orientation Distribution Function (ODF) reconstruction and tractography.

Comparison of spherical and realistically shaped boundary element head models for transcranial magnetic stimulation navigation

OBJECTIVE MRI-guided real-time transcranial magnetic stimulation (TMS) navigators that apply electromagnetic modeling have improved the utility of TMS. However, their accuracy and speed depends on the assumed volume conductor geometry. Spherical models found in present navigators are computationally fast but may be inaccurate in some areas. Realistically shaped boundary-element models (BEMs) could increase accuracy at a moderate computational cost, but it is unknown which model features have the largest influence on accuracy. Thus, we compared different types of spherical models and BEMs. METHODS Globally and locally fitted spherical models and different BEMs with either one or three compartments and with different skull-to-brain conductivity ratios (1/1-1/80) were compared against a reference BEM. RESULTS The one-compartment BEM at inner skull surface was almost as accurate as the reference BEM. Skull/brain conductivity ratio in the range 1/10-1/80 had only a minor influence. BEMs were superior to spherical models especially in frontal and temporal areas (up to 20mm localization and 40% intensity improvement); in motor cortex all models provided similar results. CONCLUSIONS One-compartment BEMs offer a good balance between accuracy and computational cost. SIGNIFICANCE Realistically shaped BEMs may increase TMS navigation accuracy in several brain areas, such as in prefrontal regions often targeted in clinical applications.

Multimodal functional imaging using fMRI-informed regional EEG/MEG source estimation

We propose a novel method, fMRI-Informed Regional Estimation (FIRE), which utilizes information from fMRI in E/MEG source reconstruction. FIRE takes advantage of the spatial alignment between the neural and the vascular activities, while allowing for substantial differences in their dynamics. Furthermore, with a region-based approach, FIRE estimates the model parameters for each region independently. Hence, it can be efficiently applied on a dense grid of source locations. The optimization procedure at the core of FIRE is related to the re-weighted minimum-norm algorithms. The weights in the proposed approach are computed from both the current source estimates and fMRI data, leading to robust estimates in the presence of silent sources in either fMRI or E/MEG measurements. We employ a Monte Carlo evaluation procedure to compare the proposed method to several other joint E/MEG-fMRI algorithms. Our results show that FIRE provides the best trade-off in estimation accuracy between the spatial and the temporal accuracy. Analysis using human E/MEG-fMRI data reveals that FIRE significantly reduces the ambiguities in source localization present in the minimum-norm estimates, and that it accurately captures activation timing in adjacent functional regions.

Targeting of White Matter Tracts with Transcranial Magnetic Stimulation

BACKGROUND TMS activations of white matter depend not only on the distance from the coil, but also on the orientation of the axons relative to the TMS-induced electric field, and especially on axonal bends that create strong local field gradient maxima. Therefore, tractography contains potentially useful information for TMS targeting. OBJECTIVE/METHODS Here, we utilized 1-mm resolution diffusion and structural T1-weighted MRI to construct large-scale tractography models, and localized TMS white matter activations in motor cortex using electromagnetic forward modeling in a boundary element model (BEM). RESULTS As expected, in sulcal walls, pyramidal cell axonal bends created preferred sites of activation that were not found in gyral crowns. The model agreed with the well-known coil orientation sensitivity of motor cortex, and also suggested unexpected activation distributions emerging from the E-field and tract configurations. We further propose a novel method for computing the optimal coil location and orientation to maximally stimulate a pre-determined axonal bundle. CONCLUSIONS Diffusion MRI tractography with electromagnetic modeling may improve spatial specificity and efficacy of TMS.

Evidence for distinct human auditory cortex regions for sound location versus identity processing

Neurophysiological animal models suggest that anterior auditory cortex (AC) areas process sound-identity information, whereas posterior ACs specialize in sound location processing. In humans, inconsistent neuroimaging results and insufficient causal evidence have challenged the existence of such parallel AC organization. Here we transiently inhibit bilateral anterior or posterior AC areas using MRI-guided paired-pulse transcranial magnetic stimulation (TMS) while subjects listen to Reference/Probe sound pairs and perform either sound location or identity discrimination tasks. The targeting of TMS pulses, delivered 55–145 ms after Probes, is confirmed with individual-level cortical electric-field estimates. Our data show that TMS to posterior AC regions delays reaction times (RT) significantly more during sound location than identity discrimination, whereas TMS to anterior AC regions delays RTs significantly more during sound identity than location discrimination. This double dissociation provides direct causal support for parallel processing of sound identity features in anterior AC and sound location in posterior AC.

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.