Kenneth P. Camilleri

Review on solving the inverse problem in EEG source analysis

In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided.This paper starts off with a mathematical description of the inverse problem and proceeds to discuss the two main categories of methods which were developed to solve the EEG inverse problem, mainly the non parametric and parametric methods. The main difference between the two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling within these categories are described including minimum norm estimates and their generalizations, LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA FOCUSS (SLF), SSLOFO and ALF for non parametric methods and beamforming techniques, BESA, subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and computational intelligence algorithms for parametric methods. From a review of the performance of these techniques as documented in the literature, one could conclude that in most cases the LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable biophysical and psychological constraints, as done by LAURA has given superior results. The Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF, for different noise levels and different simulated source depths has shown that for single source localization, regularized sLORETA gives the best solution in terms of both localization error and ghost sources. Furthermore the computationally intensive solution given by SLF was not found to give any additional benefits under such simulated conditions.

Review on solving the forward problem in EEG source analysis

BackgroundThe aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.MethodsWhile other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.ResultsIt starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poissons differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poissons equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poissons equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.ConclusionSolving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

Order Estimation of Multivariate ARMA Models

Model order estimation is fundamental in the system identification process. In this paper, we generalize a previous multivariate autoregressive (AR) model order estimation method (J. Lardies and N. Larbi, ¿A new method for model order selection and model parameter estimation in time domain,¿ J. Sound Vibr., vol. 245, no. 2, 2001) to include multivariate autoregressive moving average (ARMA) models and propose a modified model order selection criterion. We discuss the performance analysis of the proposed criterion and show that it has a lower error probability for model order selection when compared to the criterion of G. Liang ¿ARMA model order estimation based on the eigenvalues of the covariance matrix,¿IEEE Trans. Signal Process., vol. 41, no. 10, pp. 3009-03009, Oct. 1993). A Monte-Carlo (MC) analysis of the model order selection performance under different noise variations and randomized model parameters is performed, allowing the MC results to be generalized across model parameter values and various noise levels. Finally we validate the model for both simulated data and real electroencephalographic (EEG) data by spectral fitting, using the model order selected by the proposed technique as compared to that selected by Akaikes Information Criterion (AIC). We demonstrate that with the proposed technique a better fit is obtained.

Thermographic Patterns of the Upper and Lower Limbs: Baseline Data

Objectives. To collect normative baseline data and identify any significant differences between hand and foot thermographic distribution patterns in a healthy adult population. Design. A single-centre, randomized, prospective study. Methods. Thermographic data was acquired using a FLIR camera for the data acquisition of both plantar and dorsal aspects of the feet, volar aspects of the hands, and anterior aspects of the lower limbs under controlled climate conditions. Results. There is general symmetry in skin temperature between the same regions in contralateral limbs, in terms of both magnitude and pattern. There was also minimal intersubject temperature variation with a consistent temperature pattern in toes and fingers. The thumb is the warmest digit with the temperature falling gradually between the 2nd and the 5th fingers. The big toe and the 5th toe are the warmest digits with the 2nd to the 4th toes being cooler. Conclusion. Measurement of skin temperature of the limbs using a thermal camera is feasible and reproducible. Temperature patterns in fingers and toes are consistent with similar temperatures in contralateral limbs in healthy subjects. This study provides the basis for further research to assess the clinical usefulness of thermography in the diagnosis of vascular insufficiency.

Scribbles to vectors: preparation of scribble drawings for CAD interpretation

This paper describes the work carried out on off-line paper based scribbles such that they can be incorporated into a sketch-based interface without forcing designers to change their natural drawing habits. In this work, the scribbled drawings are converted into a vectorial format which can be recognized by a CAD system. This is achieved by using pattern analysis techniques, namely the Gabor filter to simplify the scribbled drawing. Vector line are then extracted from the resulting drawing by means of Kalman filtering.

The analytic common spatial patterns method for EEG-based BCI data

One of the most important stages in a brain-computer interface (BCI) system is that of extracting features that can reliably discriminate data recorded during different user states. A popular technique used for feature extraction in BCIs is the common spatial patterns (CSP) method, which provides a set of spatial filters that optimally discriminate between two classes of data in the least-squares sense. The method also yields a set of spatial patterns that are associated with the most relevant activity for distinguishing between the two classes. The high recognition rates that have been achieved with the method have led to its widespread adoption in the field. Here, a variant of the CSP method that considers EEG data in its complex form is described. By explicitly considering the amplitude and phase information in the data, the analytic CSP (ACSP) technique can provide a more comprehensive picture of the underlying activity, resulting in improved classification accuracies and more informative spatial patterns than the conventional CSP method. In this paper, we elaborate on the theoretical aspects of the ACSP algorithm and demonstrate the advantages of the method through a number of simulations and through tests on EEG data.

Automatic detection of spindles and K-complexes in sleep EEG using switching multiple models

Abstract This work investigates the use of switching linear Gaussian state space models for the segmentation and automatic labelling of Stage 2 sleep EEG data characterised by spindles and K-complexes. The advantage of this approach is that it offers a unified framework of detecting multiple transient events within background EEG data. Specifically for the identification of background EEG, spindles and K-complexes, a true positive rate (false positive rate) of 76.04% (33.47%), 83.49% (47.26%) and 52.02% (7.73%) respectively was obtained on a sample by sample basis. A novel semi-supervised model allocation approach is also proposed, allowing new unknown modes to be learnt in real time.

Complex-Valued Spatial Filters for SSVEP-Based BCIs With Phase Coding

Brain–computer interface (BCI) systems based on steady-state visual evoked potentials (SSVEPs) have gained considerable popularity because of the robustness and high information transfer rate these can provide. Typical SSVEP setups make use of visual targets flashing at different frequencies, where a user’s choice is determined from the SSVEPs elicited by the user gazing at a specific target. The range of stimulus frequencies available for such setups is limited by a variety of factors, including the strength of the evoked potentials as well as user comfort and safety with light stimuli flashing at those frequencies. One way to tackle this limitation is by introducing targets flickering at the same frequency but with different phases. In this paper, we propose the use of the analytic common spatial patterns (ACSPs) method to discriminate between phase coded SSVEP targets, and we demonstrate that the complex-valued spatial filters used for discrimination can exceed the performance of existing techniques. Furthermore, the ACSP method also yields a set of spatial patterns, separable into amplitude and phase components, that provide insight into the underlying brain activity.

The independent components of auditory P300 and CNV evoked potentials derived from single-trial recordings

The back-projected independent components (BICs) of single-trial, auditory P300 and contingent negative variation (CNV) evoked potentials (EPs) were derived using independent component analysis (ICA) and cluster analysis. The method was tested in simulation including a study of the electric dipole equivalents of the signal sources. P300 data were obtained from healthy and Alzheimers disease (AD) subjects. The BICs were of approximately 100 ms duration and approximated positive- and negative-going half-sinusoids. Some positively and negatively peaking BICs constituting the P300 coincided with known peaks in the averaged P300. However, there were trial-to-trial differences in their occurrences, particularly where a positive or a negative BIC could occur with the same latency in different trials, a fact which would be obscured by averaging them. These variations resulted in marked differences in the shapes of the reconstructed, artefact-free, single-trial P300s. The latencies of the BIC associated with the P3b peak differed between healthy and AD subjects (p < 0.01). More reliable evidence than that obtainable from single-trial or averaged P300s is likely to be found by studying the properties of the BICs over a number of trials. For the CNV, BICs corresponding to both the orienting and the expectancy components were found.

Complex-valued spatial filters for task discrimination

The method of common spatial patterns (CSP) has been widely adopted for the discrimination of mental tasks using EEG data. In this paper, some limitations of the standard CSP implementation when considering data where phase relationships play a significant role are highlighted. Furthermore, a variant of the CSP method based on the analytic representation of signals is proposed to make up for these drawbacks. The advantages of the proposed method over the standard CSP implementation are demonstrated using simulated data and tests with real EEG data. Specifically, it is shown that the complex-valued spatial filters and the derived spatial patterns can improve the discrimination process and give a more adequate representation of the tasks being considered, respectively.