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 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

Validating and improving the correction of ocular artifacts in electro-encephalography

For modern applications of electro-encephalography, including brain computer interfaces and single-trial Event Related Potential detection, it is becoming increasingly important that artifacts are accurately removed from a recorded electro-encephalogram (EEG) without affecting the part of the EEG that reflects cerebral activity. Ocular artifacts are caused by movement of the eyes and the eyelids. They occur frequently in the raw EEG and are often the most prominent artifacts in EEG recordings. Their accurate removal is therefore an important procedure in nearly all electro-encephalographic research. As a result of this, a considerable number of ocular artifact correction methods have been introduced over the past decades. A selection of these methods, which contains some of the most frequently used correction methods, is given in Section 1.5. When two different correction methods are applied to the same raw EEG, this usually results in two different corrected EEGs. A measure for the accuracy of correction should indicate how well each of these corrected EEGs recovers the part of the raw EEG that truly reflects cerebral activity. The fact that this accuracy cannot be determined directly from a raw EEG is intrinsic to the need for artifact removal. If, based on a raw EEG, it would be possible to derive an exact reference on what the corrected EEG should be, then there would not be any need for adequate artifact correction methods. Estimating the accuracy of correction methods is mostly done either by using models to simulate EEGs and artifacts, or by manipulating the experimental data in such a way that the effects of artifacts to the raw EEG can be isolated. In this thesis, modeling of EEG and artifact is used to validate correction methods based on simulated data. A new correction method is introduced which, unlike all existing methods, uses a camera to monitor eye(lid) movements as a basis for ocular artifact correction. The simulated data is used to estimate the accuracy of this new correction method and to compare it against the estimated accuracy of existing correction methods. The results of this comparison suggest that the new method significantly increases correction accuracy compared to the other methods. Next, an experiment is performed, based on which the accuracy of correction can be estimated on raw EEGs. Results on this experimental data comply very well with the results on the simulated data. It is therefore concluded that using a camera during EEG recordings provides valuable extra information that can be used in the process of ocular artifact correction. In Chapter 2, a model is introduced that assists in estimating the accuracy of eye movement artifacts for simulated EEG recordings. This model simulates EEG and eye movement artifacts simultaneously. For this, the model uses a realistic representation of the head, multiple dipoles to model cerebral and ocular electrical activity, and the boundary element method to calculate changes in electrical potential at different positions on the scalp. With the model, it is possible to simulate different data sets as if they are recorded using different electrode configurations. Signal to noise ratios are used to assess the accuracy of these six correction methods for various electrode configurations before and after applying six different correction methods. Results show that out of the six methods, second order blind identification, SOBI, and multiple linear regression, MLR, correct most accurately overall as they achieve the highest rise in signal to noise ratio. The occurrence of ocular artifacts is linked to changes in eyeball orientation. In Chapter 2 an eye tracker is used to record pupil position, which is closely linked to eyeball orientation. The pupil position information is used in the model to simulate eye movements. Recognizing the potential benefit of using an eye tracker not only for simulations, but also for correction, Chapter 3 introduces an eye movement artifact correction method that exploits the pupil position information that is provided by an eye tracker. Other correction methods use the electrooculogram (EOG) and/or the EEG to estimate ocular artifacts. Because both the EEG and the EOG recordings are susceptive to cerebral activity as well as to ocular activity, these other methods are at risk of overcorrecting the raw EEG. Pupil position information provides a reference that is linked to the ocular artifact in the EEG but that cannot be affected by cerebral activity, and as a result the new correction method avoids having to solve traditionally problematic issues like forward/backward propagation and evaluating the accuracy of component extraction. By using both simulated and experimental data, it is determined how pupil position influences the raw EEG and it is found that this relation is linear or quadratic. A Kalman filter is used for tuning of the parameters that specify the relation. On simulated data, the new method performs very well, resulting in an SNR after correction of over 10 dB for various patterns of eye movements. When compared to the three methods that performed best in the evaluation of Chapter 2, only the SOBI method which performed best in that evaluation shows similar results for some of the eye movement patterns. However, a serious limitation of the correction method is its inability to correct blink artifacts. In order to increase the variety of applications for which the new method can be used, the new correction should be improved in a way that enables it to correct the raw EEG for blinking artifacts. Chapter 4 deals with implementing such improvements based on the idea that a more advanced eye-tracker should be able to detect both the pupil position and the eyelid position. The improved eye tracker-based ocular artifact correction method is named EYE. Driven by some practical limitations regarding the eye tracking device currently available to us, an alternative way to estimate eyelid position is suggested, based on an EOG recorded above one eye. The EYE method can be used with both the eye tracker information or with the EOG substitute. On simulated data, accuracy of the EYE method is estimated using the EOGbased eyelid reference. This accuracy is again compared against the six other correction methods. Two different SNR-based measures of accuracy are proposed. One of these quantifies the correction of the entire simulated data set and the other focuses on those segments containing simulated blinking artifacts. After applying EYE, an average SNR of at least 9 dB for both these measures is achieved. This implies that the power of the corrected signal is at least eight times the power of the remaining noise. The simulated data sets contain a wide range of eye movements and blink frequencies. For almost all of these data sets, 16 out of 20, the correction results for EYE are better than for any of the other evaluated correction method. On experimental data, the EYE method appears to adequately correct for ocular artifacts as well. As the detection of eyelid position from the EOG is in principle inferior to the detection of eyelid position with the use of an eye tracker, these results should also be considered as an indicator of even higher accuracies that could be obtained with a more advanced eye tracker. Considering the simplicity of the MLR method, this method also performs remarkably well, which may explain why EOG-based regression is still often used for correction. In Chapter 5, the simulation model of Chapter 2 is put aside and, alternatively, experimentally recorded data is manipulated in a way that correction inaccuracies can be highlighted. Correction accuracies of eight correction methods, including EYE, are estimated based on data that are recorded during stop-signal tasks. In the analysis of these tasks it is essential that ocular artifacts are adequately removed because the task-related ERPs, are located mostly at frontal electrode positions and are low-amplitude. These data are corrected and subsequently evaluated. For the eight methods, the overall ranking of estimated accuracy in Figure 5.3, corresponds very well with the correction accuracy of these methods on simulated data as was found in Chapter 4. In a single-trial correction comparison, results suggest that the EYE corrected EEG, is not susceptible to overcorrection, whereas the other corrected EEGs are