Υπολογισμος Της Ηλεκτρικης Εγκεφαλικης Δραστηριοτητας Κατα Την Διαρκεια Του Υπνου:εφαρμογη Της Μεθοδου Πεπερασμενων Ογκων Και Των Τεχνητων Νευρωνικων Δικτυων Στις Υπνικες Ατρακτους

Abstract

The reconstruction of the electrical activity of the brain from non-invasive measurements of EEG recordings is an active topic in neurophysiology and consistsof localizing the sources of the brain that produce the electric field, which propagates through the overlying tissues towards the surface of the head. By assuming a volume conductor model of the human head and a source model, it is possible to localize the electric source, by calculating the source parameters (coordinates and strength) that generate electrode potentials which best fit the measured EEG activity. The calculation of the potentials at the scalp electrodes for a given electrical source distribution is referred to as the "forward problem", whereas the estimation of the source parameters that best describe the measured potentials is referred to as the "inverse problem". The inverse problem of the EEG belongs to the category of the "ill-posed" problems, as for a given set of electrode measurements, no unique solutionexists. The present study investigates the accuracy of various algorithms designed in order to provide reliable solution of the inverse problem in the EEG sourcelocalization. The study is focused on specific waveforms, present in the sleep EEG, called spindles.As a first step, the head model was approximated by a set of four concentric spheres with homogeneous conductivity properties. As a concequence, analytical computation of the equations, which connect the scalp potentials and the underlying electrical brain sources, was possible. The sources were simulated by using the model of the (one or two) current dipoles. The solution was estimated by using the Laplace and Poisson equations in a spherical coordinate system and, finally, was expressed as a series expansion of associated Legendre functions. For the estimation of the dipole parameters that generate a field which best fits the potential measurements, an exhaustive algorithm was designed. The position and moment of a dipole (or dipoles)were varied until the squares of differences between the measured data and the forward solutions of the assumed dipoles were minimal.In a second step, a numerical solution has been evaluated, by the use of the FVM. The problem was mathematically formulated into a very large system of linear equations, whose solution consisted on finding the inverse of the system's matrix. As the matrix has a very large condition number, the estimation of a stable and robust PDF created with FinePrint pdfFactory Pro trial version solution becomes more than necessary. For this purpose an algorithm was proposed that estimates a minimum norm - least squares solution of the system, using regularized techniques and iterative CGM. A realistic model of the head geometry wasconstructed from 50 anatomical MRI images and suitably discreetized in an adequate number of voxels, in order to be used for the evaluation of the arithmetic inverseproblem.For evaluating the performance of the proposed algorithms, we have tested them on simulated current sources located at various positions and orientations inside the brain. We particularly studied the influence of the level of noise, which is superimposed on the potential measurements of the simulated field, on the localization accuracy of the inverse methods. The results of the simulations indicatedthat both algorithms could perform the reconstruction of the underlying brain electrical activity accurately, even if the added Gaussian noise rose to a fairly highlevel (SNR=20 dB).The proposed methods were applied to real data retrieved from an all night polysomnographic recording. A total of 21 electrodes were placed according to the 10/20 International System on a healthy female subject. The night sleep record was analysed by an experienced polysomnographer and a time period corresponding to a well-defined spindle was selected. The signals of 21 electrodes were filtered and thedata was used as input to the proposed algorithms. The results revealed that spindle activity is related to the thalamus, the parietal and the central area of the cerebralcortex.In the last part of the dissertation, a spindle detection system based on Multi-Layer Perceptron ANN was designed and evaluated. The scope was to implement a system, which could be used during the preprocessing of the EEG recordings, in order to facilitate and speed up the detection of the time frames to be used as data in the algorithms of the inverse problem. The ANN consisted of 64 input units, a hiddenlayer of 30 units and two output units. The band-pass filtered EEG of the vertex channel was analysed. A suitable set of well-defined spindles was used for training theANN. The performance of the system was evaluated focusing not only on its spindle detection ability but also on its temporal resolution. Following optimum classificationschemes, the sensitivity of the network ranged from 79.2% to 87.5%, while the FP rate ranged from 3.8% to 15.2%. The total inter-spindle interval duration and the total PDF created with FinePrint pdfFactory Pro trial version duration of spindles were calculated with 99% and 92% accuracy, respectively. The results indicate that the present method may also be suitable for investigations of the dynamics between successive inter-spindle intervals, which could provide information on the role of spindles in the sleep process.