363 research outputs found
Sequential Monte Carlo samplers for semilinear inverse problems and application to magnetoencephalography
We discuss the use of a recent class of sequential Monte Carlo methods for
solving inverse problems characterized by a semi-linear structure, i.e. where
the data depend linearly on a subset of variables and nonlinearly on the
remaining ones. In this type of problems, under proper Gaussian assumptions one
can marginalize the linear variables. This means that the Monte Carlo procedure
needs only to be applied to the nonlinear variables, while the linear ones can
be treated analytically; as a result, the Monte Carlo variance and/or the
computational cost decrease. We use this approach to solve the inverse problem
of magnetoencephalography, with a multi-dipole model for the sources. Here,
data depend nonlinearly on the number of sources and their locations, and
depend linearly on their current vectors. The semi-analytic approach enables us
to estimate the number of dipoles and their location from a whole time-series,
rather than a single time point, while keeping a low computational cost.Comment: 26 pages, 6 figure
Effective connectivity reveals right-hemisphere dominance in audiospatial perception: implications for models of spatial neglect
Detecting the location of salient sounds in the environment rests on the brain's ability to use differences in sounds arriving at both ears. Functional neuroimaging studies in humans indicate that the left and right auditory hemispaces are coded asymmetrically, with a rightward attentional bias that reflects spatial attention in vision. Neuropsychological observations in patients with spatial neglect have led to the formulation of two competing models: the orientation bias and right-hemisphere dominance models. The orientation bias model posits a symmetrical mapping between one side of the sensorium and the contralateral hemisphere, with mutual inhibition of the ipsilateral hemisphere. The right-hemisphere dominance model introduces a functional asymmetry in the brain's coding of space: the left hemisphere represents the right side, whereas the right hemisphere represents both sides of the sensorium. We used Dynamic Causal Modeling of effective connectivity and Bayesian model comparison to adjudicate between these alternative network architectures, based on human electroencephalographic data acquired during an auditory location oddball paradigm. Our results support a hemispheric asymmetry in a frontoparietal network that conforms to the right-hemisphere dominance model.Weshow that, within this frontoparietal network, forward connectivity increases selectively in the hemisphere contralateral to the side of sensory stimulation. We interpret this finding in light of hierarchical predictive coding as a selective increase in attentional gain, which is mediated by feedforward connections that carry precision-weighted prediction errors during perceptual inference. This finding supports the disconnection hypothesis of unilateral neglect and has implications for theories of its etiology
A statistical approach to the inverse problem in magnetoencephalography
Magnetoencephalography (MEG) is an imaging technique used to measure the
magnetic field outside the human head produced by the electrical activity
inside the brain. The MEG inverse problem, identifying the location of the
electrical sources from the magnetic signal measurements, is ill-posed, that
is, there are an infinite number of mathematically correct solutions. Common
source localization methods assume the source does not vary with time and do
not provide estimates of the variability of the fitted model. Here, we
reformulate the MEG inverse problem by considering time-varying locations for
the sources and their electrical moments and we model their time evolution
using a state space model. Based on our predictive model, we investigate the
inverse problem by finding the posterior source distribution given the multiple
channels of observations at each time rather than fitting fixed source
parameters. Our new model is more realistic than common models and allows us to
estimate the variation of the strength, orientation and position. We propose
two new Monte Carlo methods based on sequential importance sampling. Unlike the
usual MCMC sampling scheme, our new methods work in this situation without
needing to tune a high-dimensional transition kernel which has a very high
cost. The dimensionality of the unknown parameters is extremely large and the
size of the data is even larger. We use Parallel Virtual Machine (PVM) to speed
up the computation.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS716 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamic causal modelling for EEG and MEG
Dynamic Causal Modelling (DCM) is an approach first introduced for the analysis of functional magnetic resonance imaging (fMRI) to quantify effective connectivity between brain areas. Recently, this framework has been extended and established in the magneto/encephalography (M/EEG) domain. DCM for M/EEG entails the inversion a full spatiotemporal model of evoked responses, over multiple conditions. This model rests on a biophysical and neurobiological generative model for electrophysiological data. A generative model is a prescription of how data are generated. The inversion of a DCM provides conditional densities on the model parameters and, indeed on the model itself. These densities enable one to answer key questions about the underlying system. A DCM comprises two parts; one part describes the dynamics within and among neuronal sources, and the second describes how source dynamics generate data in the sensors, using the lead-field. The parameters of this spatiotemporal model are estimated using a single (iterative) Bayesian procedure. In this paper, we will motivate and describe the current DCM framework. Two examples show how the approach can be applied to M/EEG experiments
Dynamic filtering of static dipoles in magnetoencephalography
We consider the problem of estimating neural activity from measurements
of the magnetic fields recorded by magnetoencephalography. We exploit
the temporal structure of the problem and model the neural current as a
collection of evolving current dipoles, which appear and disappear, but whose
locations are constant throughout their lifetime. This fully reflects the physiological
interpretation of the model.
In order to conduct inference under this proposed model, it was necessary
to develop an algorithm based around state-of-the-art sequential Monte
Carlo methods employing carefully designed importance distributions. Previous
work employed a bootstrap filter and an artificial dynamic structure
where dipoles performed a random walk in space, yielding nonphysical artefacts
in the reconstructions; such artefacts are not observed when using the
proposed model. The algorithm is validated with simulated data, in which
it provided an average localisation error which is approximately half that of
the bootstrap filter. An application to complex real data derived from a somatosensory
experiment is presented. Assessment of model fit via marginal
likelihood showed a clear preference for the proposed model and the associated
reconstructions show better localisation
Dynamic Decomposition of Spatiotemporal Neural Signals
Neural signals are characterized by rich temporal and spatiotemporal dynamics
that reflect the organization of cortical networks. Theoretical research has
shown how neural networks can operate at different dynamic ranges that
correspond to specific types of information processing. Here we present a data
analysis framework that uses a linearized model of these dynamic states in
order to decompose the measured neural signal into a series of components that
capture both rhythmic and non-rhythmic neural activity. The method is based on
stochastic differential equations and Gaussian process regression. Through
computer simulations and analysis of magnetoencephalographic data, we
demonstrate the efficacy of the method in identifying meaningful modulations of
oscillatory signals corrupted by structured temporal and spatiotemporal noise.
These results suggest that the method is particularly suitable for the analysis
and interpretation of complex temporal and spatiotemporal neural signals
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