358 research outputs found
Inverse Modeling for MEG/EEG data
We provide an overview of the state-of-the-art for mathematical methods that
are used to reconstruct brain activity from neurophysiological data. After a
brief introduction on the mathematics of the forward problem, we discuss
standard and recently proposed regularization methods, as well as Monte Carlo
techniques for Bayesian inference. We classify the inverse methods based on the
underlying source model, and discuss advantages and disadvantages. Finally we
describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur
State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing
Determining the magnitude and location of neural sources within the brain
that are responsible for generating magnetoencephalography (MEG) signals
measured on the surface of the head is a challenging problem in functional
neuroimaging. The number of potential sources within the brain exceeds by an
order of magnitude the number of recording sites. As a consequence, the
estimates for the magnitude and location of the neural sources will be
ill-conditioned because of the underdetermined nature of the problem. One
well-known technique designed to address this imbalance is the minimum norm
estimator (MNE). This approach imposes an regularization constraint that
serves to stabilize and condition the source parameter estimates. However,
these classes of regularizer are static in time and do not consider the
temporal constraints inherent to the biophysics of the MEG experiment. In this
paper we propose a dynamic state-space model that accounts for both spatial and
temporal correlations within and across candidate intracortical sources. In our
model, the observation model is derived from the steady-state solution to
Maxwell's equations while the latent model representing neural dynamics is
given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Kalman-filter-based EEG source localization
This thesis uses the Kalman filter (KF) to solve the electroencephalographic (EEG) inverse problem to image its neuronal sources. Chapter 1 introduces EEG source localization and the KF and discusses how it can solve the inverse problem. Chapter 2 introduces an EEG inverse solution using a spatially whitened KF (SWKF) to reduce the computational burden. Likelihood maximization is used to fit spatially uniform neural model parameters to simulated and clinical EEGs. The SWKF accurately reconstructs source dynamics. Filter performance is analyzed by computing the innovations’ statistical properties and identifying spatial variations in performance that could be improved by use of spatially varying parameters. Chapter 3 investigates the SWKF via one-dimensional (1D) simulations. Motivated by Chapter 2, two model parameters are given Gaussian spatial profiles to better reflect brain dynamics. Constrained optimization ensures estimated parameters have clear biophysical interpretations. Inverse solutions are also computed using the optimal linear KF. Both filters produce accurate state estimates. Spatially varying parameters are correctly identified from datasets with transient dynamics, but estimates for driven datasets are degraded by the unmodeled drive term. Chapter 4 treats the whole-brain EEG inverse problem and applies features of the 1D simulations to the SWKF of Chapter 2. Spatially varying parameters are used to model spatial variation of the alpha rhythm. The simulated EEG here exhibits wave-like patterns and spatially varying dynamics. As in Chapter 3, optimization constrains model parameters to appropriate ranges. State estimation is again reliable for simulated and clinical EEG, although spatially varying parameters do not improve accuracy and parameter estimation is unreliable, with wave velocity underestimated. Contributing factors are identified and approaches to overcome them are discussed. Chapter 5 summarizes the main findings and outlines future work
Kalman-filter-based EEG source localization
This thesis uses the Kalman filter (KF) to solve the electroencephalographic (EEG) inverse problem to image its neuronal sources. Chapter 1 introduces EEG source localization and the KF and discusses how it can solve the inverse problem. Chapter 2 introduces an EEG inverse solution using a spatially whitened KF (SWKF) to reduce the computational burden. Likelihood maximization is used to fit spatially uniform neural model parameters to simulated and clinical EEGs. The SWKF accurately reconstructs source dynamics. Filter performance is analyzed by computing the innovations’ statistical properties and identifying spatial variations in performance that could be improved by use of spatially varying parameters. Chapter 3 investigates the SWKF via one-dimensional (1D) simulations. Motivated by Chapter 2, two model parameters are given Gaussian spatial profiles to better reflect brain dynamics. Constrained optimization ensures estimated parameters have clear biophysical interpretations. Inverse solutions are also computed using the optimal linear KF. Both filters produce accurate state estimates. Spatially varying parameters are correctly identified from datasets with transient dynamics, but estimates for driven datasets are degraded by the unmodeled drive term. Chapter 4 treats the whole-brain EEG inverse problem and applies features of the 1D simulations to the SWKF of Chapter 2. Spatially varying parameters are used to model spatial variation of the alpha rhythm. The simulated EEG here exhibits wave-like patterns and spatially varying dynamics. As in Chapter 3, optimization constrains model parameters to appropriate ranges. State estimation is again reliable for simulated and clinical EEG, although spatially varying parameters do not improve accuracy and parameter estimation is unreliable, with wave velocity underestimated. Contributing factors are identified and approaches to overcome them are discussed. Chapter 5 summarizes the main findings and outlines future work
Dynamic inverse problem solution using a kalman filter smoother for neuronal activity estimation
En este artículo se presenta un método de estimación de la actividad neuronal sobre el cerebro usando un filtro de Kalman con suavizado, que tiene en cuenta en la solución del problema inverso, la variabilidad dinámica de la serie de tiempo. Este método es aplicado sobre un modelo realista de la cabeza, calculado con elementos finitos de frontera. Se presenta un análisis comparativo entre diferentes métodos de estimación y el método propuesto sobre señales EEG simuladas para diferentes condiciones de relación señal a ruido. La solución del problema inverso se hace utilizando computación de alto desempeño y se presenta una evaluación delcosto computacional para cada método. Como resultado, el filtro de Kalman con suavizado presenta un mejor desempeño en la tarea de estimación comparado con la solución estática regularizada, y la solución dinámica sin suavizado.This article presents an estimation method of neuronal activity into the brain using a Kalman smoother approach that takes into account in the solution of the inverse problem the dynamic variability of the time series. This method is applied over a realistic head model calculated with the boundary element method. A comparative analysis for the dynamic estimation methods is made up from simulated EEG signals for several noise conditions. The solution of the inverse problem is achieved by using high performance computing techniques and an evaluation of the computational cost is performed for each method. As a result, the Kalman smoother approach presents better performance in the estimation task than the regularized static solution, and the direct Kalman filter
Estimation of neuronal activity and brain dynamics using a dual Kalman filter with physiologycal based linear model
In this research article a dynamic estimation of neuronal activity and brain dynamics from electroencephalographic (EEG) signals is presented using a dual Kalman filter. The dynamic model for brain behavior is evaluated using physiological-based linear models. Filter performance is analyzed for simulated and clinical EEG data, over several noise conditions. As a result a better performance on the solution of the dynamic inverse problem is achieved, in case of time varying parameters compared with the system with fixed parameters and the static case. An evaluation of computational load is performed when predicted dynamic cases, estimated using the Kalman filter, are up to ten times faster than the static case
Dynamic inverse problem solution considering non-homogeneous source distribution with frequency spatio temporal constraints applied to brain activity reconstruction
Para reconstruir la actividad cerebral es necesario estimular la ubicación de las fuentes activas del cerebro. El método de localización de fuentes usando electroencefalogramas es usado para esta tarea por su alta resolución temporal. Este método de resolver un problema inverso mal planteado, el cual no tiene una solución única debido al que el números de variables desconocidas es mas grande que el numero de variables conocidas. por lo tanto el método presenta una baja resolución espacial..
Critical comments on EEG sensor space dynamical connectivity analysis
Many different analysis techniques have been developed and applied to EEG
recordings that allow one to investigate how different brain areas interact.
One particular class of methods, based on the linear parametric representation
of multiple interacting time series, is widely used to study causal
connectivity in the brain. However, the results obtained by these methods
should be interpreted with great care. The goal of this paper is to show, both
theoretically and using simulations, that results obtained by applying causal
connectivity measures on the sensor (scalp) time series do not allow
interpretation in terms of interacting brain sources. This is because 1) the
channel locations cannot be seen as an approximation of a source's anatomical
location and 2) spurious connectivity can occur between sensors. Although many
measures of causal connectivity derived from EEG sensor time series are
affected by the latter, here we will focus on the well-known time domain index
of Granger causality (GC) and on the frequency domain directed transfer
function (DTF). Using the state-space framework and designing two simulation
studies we show that mixing effects caused by volume conduction can lead to
spurious connections, detected either by time domain GC or by DTF. Therefore,
GC/DTF causal connectivity measures should be computed at the source level, or
derived within analysis frameworks that model the effects of volume conduction.
Since mixing effects can also occur in the source space, it is advised to
combine source space analysis with connectivity measures that are robust to
mixing
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