Brain decoding involves the determination of a subject’s cognitive state or an associated stimulus from functional neuroimaging data measuring brain activity. In this setting the cognitive state is typically characterized by an element of a finite set, and the neuroimaging data comprise voluminous amounts of spatiotemporal data measuring some aspect of the neural signal. The associated statistical problem is one of classification from high-dimensional data. We explore the use of functional principal component analysis, mutual information networks, and persistent homology for examining the data through exploratory analysis and for constructing features characterizing the neural signal for brain decoding. We review each approach from this perspective, and we incorporate the features into a classifier based on symmetric multinomial logistic regression with elastic net regularization. The approaches are illustrated in an application where the task is to infer from brain activity measured with magnetoencephalography (MEG) the type of video stimulus shown to a subject. / Graduate

Η βέλτιστη γεωμετρική προσομοίωση του εγκεφάλου επιτυγχάνεται με ένα ελλειψοειδές. Η ηλεκτροεγκεφαλογραφία (ΗΕΓ) αφορά τις μετρήσεις του ηλεκτρικού δυναμικού στην επιφάνεια του κρανίου που αναπτύσσεται από νευρωνικά ρεύματα στο εσωτερικό του εγκεφάλου. Στην παρούσα εργασία έχουν παραχθεί οι απαιτούμενες ελλειψοειδείς αρμονικές πέμπτου, έκτου και εβδόμου βαθμού. Στη συνέχεια, χρησιμοποιούμε αυτές τις νέες ελλειψοειδείς αρμονικές συναρτήσεις για να εκφράσουμε το πλήρες αναλυτικό δυναμικό της ΗΕΓ. H δομή της εργασίας είναι: Στο κεφάλαιο 1 περιγράφεται περιληπτικά η φυσιολογία ανάπτυξης δυναμικών στην περιοχή του εγκεφάλου και πως επιτυγχάνεται η μετάδοση αυτών των σημάτων μέσω των νευρώνων. Στο κεφάλαιο 2 περιγράφεται η ελλειψοειδής γεωμετρία καθώς και η μορφή του τελεστή του Laplace στο ελλειψοειδές σύστημα συντεταγμένων. Αναφερόμαστε στην επίλυση της εξίσωσης Lame, στον τρόπο κατασκευής των συναρτήσεων Lame και περιγράφουμε τις αντίστοιχες ελλειψοειδείς αρμονικές. Στο κεφάλαιο 3 καταγράφουμε τις ελλειψοειδείς αρμονικές βαθμού 3. Στα κεφάλαια 4,5,6 και 7 παράγουμε τις ελλειψοειδείς αρμονικές βαθμού 4,5,6 και 7, αντίστοιχα, όπου η εφαρμογή των οποίων στην ΗΕΓ αποτελεί και το θέμα της παρούσας εργασίας. Τέλος στο κεφάλαιο 8 χρησιμοποιούμε τις ελλειψοειδείς αρμονικές που κατασκευάσαμε για να επιτύχουμε την ακριβή συνιστώσα του ηλεκτρικού δυναμικού που ανήκει στον ελλειψοειδή αρμονικό υπόχωρο που γεννούν οι 64 πρώτες αρμονικές συναρτήσεις. / The best geometric simulation of the human brain is achieved by an ellipsoidal system. The Electroencephalography (EEG) concerns the measurements of the electric potential on the surface of the head, which is generated from neuronal current inside the head. In this thesis we have produced the necessary ellipsoidal harmonics of the fifth, sixth and seventh degree. Then, we use these new ellipsoidal harmonic functions to express the full analytical potential of EEG, up to the seventh degree. The present thesis is structured in the following way: In chapter 1 we describe, in short, the physiology which develops the potentials in and outside the brain and how they are transmitted through the neuronal current. In chapter 2 we describe the ellipsoidal geometry as well as the form of the Laplace operator in ellipsoidal coordinates. We consider the solutions of Lame equation, the way Lame constructed them and we describe the corresponding ellipsoidal harmonics. In chapter 3 we report the ellipsoidal harmonics of degree zero through three. In chapters 4, 5, 6 and 7 we develop the ellipsoidal harmonics of degree 4, 5, 6 and 7 respectively. The applications of these functions form the main part of the present master thesis. Finally, in chapter 8 we use all the known ellipsoidal harmonics to express the relative component of the electrical potential. This component belongs to the subspace generated by the first 64 ellipsoidal harmonics.

With MEG, the tiny magnetic fields produced by neuronal currents within the brain can be measured completely non-invasively. But the signals are very small (~100 fT) and often obscured by spontaneous brain activity and external noise. So, a recurrent issue in MEG data analysis is the identification and elimination of this unwanted interference within the recordings. Various strategies exist to meet this purpose. In this thesis, two of these strategies are scrutinized in detail. The first is the commonly used procedure of averaging over trials which is a successfully applied data reduction method in many neurocognitive studies. However, the brain does not always respond identically to repeated stimuli, so averaging can eliminate valuable information. Alternative approaches aiming at single trial analysis are difficult to realize and many of them focus on temporal patterns. Here, a compromise involving random subaveraging of trials and repeated source localization is presented. A simulation study with numerous examples demonstrates the applicability of the new method. As a result, inferences about the generators of single trials can be drawn which allows deeper insight into neuronal processes of the human brain. The second technique examined in this thesis is a preprocessing tool termed Signal Space Separation (SSS). It is widely used for preprocessing of MEG data, including noise reduction by suppression of external interference, as well as movement correction. Here, the mathematical principles of the SSS series expansion and the rules for its application are investigated. The most important mathematical precondition is a source-free sensor space. Using three data sets, the influence of a violation of this convergence criterion on source localization accuracy is demonstrated. The analysis reveals that the SSS method works reliably, even when the convergence criterion is not fully obeyed. This leads to utilizing the SSS method for the transformation of MEG data to virtual sensors on the scalp surface. Having MEG data directly on the individual scalp surface would alleviate sensor space analysis across subjects and comparability with EEG. A comparison study of the transformation results obtained with SSS and those produced by inverse and subsequent forward computation is performed. It shows strong dependence on the relative position of sources and sensors. In addition, the latter approach yields superior results for the intended purpose of data transformation.

The dementias are persistent or progressive disorders affecting more than one cognitive domain that interfere with an individual’s ability to function at work or home, and represent a decline from a previous level of function. In this thesis I consider the neurophysiology of dementia at a number of levels. I investigate the ways in which the connectivity and function of the brain predisposes to the specific focal patterns of neurodegeneration seen in the various dementias. I aim to identify the mesoscopic changes that occur in individuals with neurodegeneration and how these relate to their cognitive difficulties. I show how, by assessing patients in whom there is focal disruption of brain networks and observing the outcomes in comparison to controls, I can gain insight into the mechanisms by which the normal brain makes predictions and processes language. In Chapter 1, I set the scene for the focussed experimental investigations of model diseases by beginning with an introductory, clinically-focussed review that sets out the features, aetiology, management, epidemiology and prognosis of the dementias. This places these model diseases in the context of the broader clinical challenge posed by the dementias. In Chapter 2, I turn to ‘prototypical’ model diseases that represent neurodegenerative tauopathies with predominantly cortical (Alzheimer’s disease, AD) and subcortical (Progressive Supranuclear Palsy, PSP) disease burdens. I investigate the neurophysiological causes and consequences of Tau accumulation by combining graph theoretical analyses of resting state functional MR imaging and in vivo ‘Tau’ PET imaging using the ligand AV-1451. By relating Tau distribution to the functional connectome I provide in vivo evidence consistent with ‘prion-like’ trans-neuronal spread of Tau in AD but not PSP. This provides important validation of disease modification strategies that aim to halt or slow down the progression of AD by sequestration of pathological Tau in the synapse. In contrast, I demonstrate associations consistent with regional vulnerability to Tau accumulation due to metabolic demand and a lack of trophic support in PSP but not AD. With a cross-sectional approach, using Tau burden as a surrogate marker of disease severity, I then go on to show how the changes in functional connectivity that occur as disease progresses account for the contrasting cognitive phenotypes in AD and PSP. In advancing AD, functional connectivity across the whole brain becomes increasingly random and disorganised, accounting for symptomatology across multiple cognitive domains. In advancing PSP, by contrast, disrupted cortico-subcortical and cortico-brainstem interactions meant that information transfer passed through a larger number of cortical nodes, reducing closeness centrality and eigenvector centrality, while increasing weighted degree, clustering, betweenness centrality and local efficiency. Together, this resulted in increasingly modular processing with inter-network communication taking less direct paths, accounting for the bradyphrenia characteristic of the ‘subcortical dementias’. From chapter 3 onwards, I turn to the in-depth study of a model disease called non-fluent variant Primary Progressive Aphasia (nfvPPA). This disease has a clear clinical phenotype of speech apraxia and agrammatism, associated with a focal pattern of mild atrophy in frontal lobes. Importantly, general cognition is usually well preserved until late disease. In chapter 3 itself, I relate an experiment in which patients with nfvPPA and matched controls performed a receptive language task while having their brain activity recorded with magnetoencephalography. I manipulated expectations and sensory detail to explore the role of top-down frontal contributions to predictive processes in speech perception. I demonstrate that frontal neurodegeneration led to inflexible and excessively precise predictions, and that fronto-temporal interactions play a causal role in reconciling prior predictions with degraded sensory signals. The discussion here concentrates on the insights provided by neurodegenerative disease into the normal function of the brain in processing language. Overall, I demonstrate that higher level frontal mechanisms for cognitive and behavioural flexibility make a critical functional contribution to the hierarchical generative models underlying speech perception In chapter 4, I precisely define the sequence processing and statistical learning abilities of patients with nfvPPA in comparison to patients with non-fluent aphasia due to stroke and neurological controls. I do this by exposing participants to a novel, mixed-complexity artificial grammar designed to assess processing of increasingly complex sequencing relationships, and then assessing the degree of implicit rule learning. I demonstrate that agrammatic aphasics of two different aetiologies are not disproportionately impaired on complex sequencing relationships, and that the learning of phonological and non-linguistic sequences occurs independently in health and disease. In chapter 5, I summarise the synergies between the experimental chapters, and explain how I have applied a systems identification framework to a diverse set of experimental methods, with the common goal of defining the physiology of dementia. I then return to the results of chapter 3 with a clinical focus to explain how inflexible predictions can account for subjective speech comprehension difficulties, auditory processing abnormalities and (in synthesis with chapter 4) receptive agrammatism in nfvPPA. Overall, this body of work has contributed to knowledge in several ways. It has achieved its tripartite aims by: 1) Providing in vivo evidence consistent with theoretical models of trans-neuronal Tau spread (chapter 2), and a comprehensive clinical account of the previously poorly-understood receptive symptomatology of nfvPPA (chapter 5), thus demonstrating that systems neuroscience can provide a translational bridge between the molecular biology of dementia and clinical trials of therapies and medications. In this way, I begin to disentangle the network-level causes of neurodegeneration from its consequences. 2) Providing evidence for a causal role for fronto-temporal interactions in language processing (chapter 3), and demonstrating domain separation of statistical learning between linguistic and non-linguistic sequences (chapter 4), thus demonstrating that studies of patients with neurodegenerative disease can further our understanding of normative brain function. 3) Successfully integrating neuropsychology, behavioural psychophysics, functional MRI, structural MRI, magnetoencephalography and computational modelling to provide comprehensive research training, as the platform for a future research programme in the physiology of dementia.

Spielt Ihr Gehirn Ihre letzten Lebenserfahrungen ab, während Sie sich ausruhen? Eine offene Frage in den Neurowissenschaften ist, welche Ereignisse unser Gehirn wiederholt und gibt es eine Korrelation zwischen der Wiederholung und der Dauer des Ereignisses? In dieser Studie habe ich versucht, dieser Frage nachzugehen, indem ich Magnetenzephalographie-Daten aus einem Experiment zum aktiven Hören verwendet habe. Die Magnetenzephalographie (MEG) ist ein nicht-invasives Neuroimaging-Verfahren, das verwendet wird, um die Gehirnaktivität zu untersuchen und die Gehirndynamik bei Wahrnehmungs- und kognitiven Aufgaben insbesondere in den Bereichen Sprache und Hören zu verstehen. Es zeichnet das in unserem Gehirn erzeugte Magnetfeld auf, um die Gehirnaktivität zu erkennen. Ich baue eine Pipeline für maschinelles Lernen, die einen Teil der Experimentdaten verwendet, um die Klangmuster zu lernen und dann das Vorhandensein von Geräuschen im späteren Teil der Aufnahmen vorhersagt, in denen die Teilnehmer untätig sitzen mussten und kein Ton zugeführt wurde. Das Ziel der Untersuchung der Testwiedergabe von gelernten Klangsequenzen in der Nachhörphase. Ich habe ein Klassifikationsschema verwendet, um Muster zu identifizieren, wenn MEG auf verschiedene Tonsequenzen in der Zeit nach der Aufgabe reagiert. Die Studie kam zu dem Schluss, dass die Lautfolgen über dem theoretischen Zufallsniveau identifiziert und unterschieden werden können und bewies damit die Gültigkeit unseres Klassifikators. Darüber hinaus könnte der Klassifikator die Geräuschsequenzen in der Nachhörzeit mit sehr hoher Wahrscheinlichkeit vorhersagen, aber um die Modellergebnisse über die Nachhörzeit zu validieren, sind mehr Beweise erforderlich. / Does your brain replay your recent life experiences while you are resting? An open question in neuroscience is which events does our brain replay and is there any correlation between the replay and duration of the event? In this study I tried to investigate this question by using Magnetoencephalography data from an active listening experiment. Magnetoencephalography (MEG) is a non-invasive neuroimaging technique used to study the brain activity and understand brain dynamics in perception and cognitive tasks particularly in the fields of speech and hearing. It records the magnetic field generated in our brains to detect the brain activity. I build a machine learning pipeline which uses part of the experiment data to learn the sound patterns and then predicts the presence of sound in the later part of the recordings in which the participants were made to sit idle and no sound was fed. The aim of the study of test replay of learned sound sequences in the post listening period. I have used classification scheme to identify patterns if MEG responses to different sound sequences in the post task period. The study concluded that the sound sequences can be identified and distinguished above theoretical chance level and hence proved the validity of our classifier. Further, the classifier could predict the sound sequences in the post-listening period with very high probability but in order to validate the model results on post listening period, more evidence is needed.

This dissertation is comprised of four studies investigating the hypothesis that adults and children who stutter differ from their same-age fluent peers in the neuroanatomy and neurophysiology underlying auditory speech processing. It has been consistently reported that adults who stutter demonstrate unique functional neural activation patterns during speech production, including reduced auditory activation, relative to nonstutterers. The extent to which these functional differences are accompanied by abnormal morphology of the brain in stutterers is unclear. The first study in this dissertation examined the neuroanatomical differences in speech-related cortex between adults who do and do not stutter using magnetic resonance imaging and voxel-based morphometry analyses. Adults who stutter were found to have localized grey matter volume increases in auditory and motor speech related cortex. The second study extended this line of research to children who stutter, who were found to have localized grey matter volume decreases in motor speech related cortex. Together, these studies suggest an abnormal trajectory of regional grey matter development in motor speech cortex of people who stutter. The last two studies investigated the mechanism underlying the repeated findings of reduced auditory activation during speech in people who stutter in more detail. Magnetoencephalography was used to investigate the hypothesis that people who stutter have increased speech induced suppression of early evoked auditory responses. Adults and children who stutter demonstrated typical levels of speech induced suppression relative to fluent peers. However, adults and children who stutter showed differences from peers in the timing of cortical auditory responses. Taken together, the studies demonstrate structural and functional abnormalities in brain regions related to auditory processing and point to the possibility that people who stutter have difficulty forming the neural representations of speech sounds necessary for fluent speech production.

The objective of this study is to test whether human intentions to sustain or cease movements in right and left hands can be decoded reliably from spatially filtered single trial magneto-encephalographic (MEG) signals. This study was performed using motor execution and motor imagery movements to achieve a potential high performance Brain-Computer interface (BCI). Seven healthy volunteers, naïve to BCI technology, participated in this study. Signals were recorded from 275-channel MEG and synthetic aperture magnetometry (SAM) was employed as the spatial filter. The four-class classification for natural movement intentions was performed offline; Genetic Algorithm based Mahalanobis Linear Distance (GA-MLD) and direct-decision tree classifier (DTC) techniques were adopted for the classification through 10-fold cross-validation. Through SAM imaging, strong and distinct event related desynchronisation (ERD) associated with sustaining, and event related synchronisation (ERS) patterns associated with ceasing of hand movements were observed in the beta band (15 - 30 Hz). The right and left hand ERD/ERS patterns were observed on the contralateral hemispheres for motor execution and motor imagery sessions. Virtual channels were selected from these cortical areas of high activity to correspond with the motor tasks as per the paradigm of the study. Through a statistical comparison between SAM-filtered virtual channels from single trial MEG signals and basic MEG sensors, it was found that SAM-filtered virtual channels significantly increased the classification accuracy for motor execution (GA-MLD: 96.51 ± 2.43 %) as well as motor imagery sessions (GA-MLD: 89.69 ± 3.34%). Thus, multiple movement intentions can be reliably detected from SAM-based spatially-filtered single trial MEG signals. MEG signals associated with natural motor behavior may be utilized for a reliable high-performance brain-computer interface (BCI) and may reduce long-term training compared with conventional BCI methods using rhythm control. This may prove tremendously helpful for patients suffering from various movement disorders to improve their quality of life.

Η ηλεκτρομαγνητική δραστηριότητα του εγκεφάλου μελετάται με τη βοήθεια των μη παρεμβατικών μεθόδων της Ήλεκτροεγκεφαλογραφίας και της Μαγνητοεγκεφαλογραφίας. Ειδικότερα, κάθε ηλεκτροχημικά παραγόμενο ρεύμα στο εσωτερικό του εγκεφάλου δημιουργεί ένα ηλεκτρικό και ένα μαγνητικό πεδίο, στο εσωτερικό και στο εξωτερικό του εγκεφάλου αντίστοιχα. Τα πεδία αυτά καταγράφονται στην επιφάνεια και στον εξωτερικό χώρο του κρανίου και δίνουν το Ηλεκτροεγκεφαλόγραφημα (EEG) και το Μαγνητοεγκεφαλόγραφημα (MEG) αντίστοιχα, τα οποία μεταφέρουν πληροφορίες για τη λειτουργία του εγκεφάλου τη χρονική στιγμή της καταγραφής. Η παρούσα διατριβή αφορά στη μαθηματική ανάλυση ευθέων και αντίστροφων προβλημάτων που συνδέονται με τις μεθόδους αυτές με σκοπό τον εντοπισμό και το χαρακτηρισμό της πηγής που παρήγαγε τα μετρούμενα πεδία. Στο Μέρος Ι μελετάται αναλυτικά η δομή και λειτουργία του εγκεφάλου, περιγράφεται το φυσικό πρότυπο που χρησιμοποιούμε και γίνεται αναφορά τόσο στη σφαιρική όσο και στην ελλειψοειδή γεωμετρία που αποτελούν τα γεωμετρικά υπόβαθρα. Στο Μέρος ΙΙ επιλύεται το ευθύ πρόβλημα του Βιοηλεκτρισμού στην περίπτωση του σφαιρικού ομογενούς προτύπου για τον ανθρώπινο εγκέφαλο, όπου η πηγή είναι αυθαίρετη κατανομή ρεύματος. Αποδεικνύεται ό,τι, στο εξωτερικό ηλεκτρικό δυναμικό δεν εμπεριέχεται η συνεισφορά του σωληνοειδούς μέρους της εφαπτομενικής συνιστώσας του ρεύματος και συνεπώς το αντίστοιχο αντίστροφο πρόβλημα είναι μη μοναδικό. Με την απαίτηση το ρεύμα να ελαχιστοποιεί την , το αντίστροφο πρόβλημα επιλύεται μοναδικά και προσδιορίζονται οι συνιστώσες του νευρωνικού ρεύματος από γνωστές μετρήσεις του ηλεκτρικού δυναμικού. Τα κύρια χαρακτηριστικά καθώς και οι περιορισμοί που επιβάλλουν το φυσικό και το γεωμετρικό πρόβλημα αναλύονται λεπτομερώς. Στο Μέρος ΙΙΙ επιλύονται ευθέα προβλήματα του Βιοηλεκτρομαγνητισμού σε ελλειψοειδή γεωμετρία και αντλούμε χρήσιμα συμπεράσματα για την αντιστροφή των προβλημάτων MEG. Συγκεκριμένα υπολογίστηκε η οκταπολική προσέγγιση του μαγνητικού πεδίου που παράγεται στο εξωτερικό του πλέον ρεαλιστικού ομογενούς προτύπου για τον ανθρώπινο εγκέφαλο, που είναι το ελλειψοειδές, συναρτήσει των ελλειψοειδών αρμονικών τρίτου βαθμού. Η βελτίωση αυτή είναι σημαντική καθώς αποδεικνύεται αριθμητικά ότι η μαγνητικά «σιωπηλή» πηγή της τετραπολικής προσέγγισης συνεισφέρει στις μετρήσεις του μαγνητικού πεδίου. Ως εκ τούτου, η νέα αυτή προσέγγιση του μαγνητικού πεδίου παρέχει αρκετές πληροφορίες για την πιθανή αντιστροφή του προβλήματος. Στη συνέχεια επιλύθηκε το ευθύ πρόβλημα του Βιοηλεκτρομαγνητισμού στην περίπτωση που ο εγκεφαλικός ιστός περιλαμβάνει περιοχή υγρού πυρήνα διαφορετικής αγωγιμότητας. Ο πυρήνας αυτός πληρούται από εγκεφαλονωτιαίο υγρό ενώ η πηγή βρίσκεται στον φλοιό του εγκεφαλικού ιστού. Υπολογίζεται το ηλεκτρικό δυναμικό και το μαγνητικό πεδίο στο εξωτερικό του αγωγού και τα αποτελέσματα συγκρίνονται αναλυτικά και αριθμητικά με τα αντίστοιχα αποτελέσματα του ομογενούς προτύπου του εγκέφαλου. Από την σύγκριση αυτή προκύπτει ότι τόσο η ανομοιογένεια εντός του εγκεφαλικού ιστού όσο και η θέση της πηγής υπεισέρχονται με καθοριστικό τρόπο στο μαγνητικό πεδίο του υπό μελέτη προτύπου. / The electromagnetic activity of the human brain is studying via the non invasive methods of Electroencephalography and Magnetoencephalography. It is well known that an electrochemically generated current in the interior of the brain generates an electric and a magnetic field, both in the interior and exterior of the brain. The resulting electric and magnetic fields are measured on the surface and the exterior of the head via the EEG and MEG, respectively. In the present thesis we study direct and inverse EEG and MEG problems in order to identify and characterize the source. In the First Part we describe the morphology and the functionality of the human brain and we state the physical and geometrical models that we use. In the Second Part we solved the direct problem of EEG for the spherical homogeneous model of the brain in the case of a continuously distributed neuronal current. It turns out that the electric potential is independent of the solenoid part of the tangential component of the neuronal current. Consequently, the corresponding inverse problem is not uniquely solvable. Hence, we demand that the current has minimum and in this case we ended up with the complete expansions of the visible part of the current from the knowledge of the electric field. In the Third Part we studied direct problems of MEG in ellipsoidal geometry. In particular we evaluated the octapolic term of the magnetic induction field which it’s produced in the exterior of the ellipsoidal model of the brain-head system. This term provides the highest order terms that can be expressed in closed form. It is shown numerically that the silent source of the quadrupolic term of the magnetic induction field does contribute to the octapolic term. Therefore, the knowledge of the quadrupolic and octapolic terms provides enough data to construct an effective algorithm for inversion. Finally, the direct problem of MEG is presented, in the case where the cerebral tissue is considered as an ellipsoidal conductor and surrounds a fluid ellipsoidal core of different conductivity. The fluid core is occupied by the cerebrospinal fluid and the source lies in the cerebral shell. The electric field in every region and the exterior magnetic induction field are obtained. Furthermore, we compare analytically and numerically the results of the inhomogeneous model with the homogeneous ellipsoidal model. We observed that both the inhomogeniety inside the cerebral tissue and the location of the source appear in the magnetic induction field of the inhomogeneous model. Τhe existence of the fluid core effects the monotonicity of the components of the magnetic field as well as its magnitude.

This dissertation is comprised of four studies investigating the hypothesis that adults and children who stutter differ from their same-age fluent peers in the neuroanatomy and neurophysiology underlying auditory speech processing. It has been consistently reported that adults who stutter demonstrate unique functional neural activation patterns during speech production, including reduced auditory activation, relative to nonstutterers. The extent to which these functional differences are accompanied by abnormal morphology of the brain in stutterers is unclear. The first study in this dissertation examined the neuroanatomical differences in speech-related cortex between adults who do and do not stutter using magnetic resonance imaging and voxel-based morphometry analyses. Adults who stutter were found to have localized grey matter volume increases in auditory and motor speech related cortex. The second study extended this line of research to children who stutter, who were found to have localized grey matter volume decreases in motor speech related cortex. Together, these studies suggest an abnormal trajectory of regional grey matter development in motor speech cortex of people who stutter. The last two studies investigated the mechanism underlying the repeated findings of reduced auditory activation during speech in people who stutter in more detail. Magnetoencephalography was used to investigate the hypothesis that people who stutter have increased speech induced suppression of early evoked auditory responses. Adults and children who stutter demonstrated typical levels of speech induced suppression relative to fluent peers. However, adults and children who stutter showed differences from peers in the timing of cortical auditory responses. Taken together, the studies demonstrate structural and functional abnormalities in brain regions related to auditory processing and point to the possibility that people who stutter have difficulty forming the neural representations of speech sounds necessary for fluent speech production.

Είναι γεγονός ότι τόσο το ευθύ όσο & το αντίστροφο EEG & MEG πρόβλημα έχει αποτελέσει αντικείμενο μελέτης ερευνητών διαφόρων ειδικοτήτων (των Μαθηματικών, της Πληροφορικής, των Φυσικών, των Ηλεκτρολόγων Μηχανικών & φυσικά της Ιατρικής), ήδη από τις δεκαετίες του 1950 & 1960, που αναζητούσαν τρόπους υπολογισμού του ηλεκτρικού & του μαγνητικού πεδίου που παράγουν στο εξωτερικό του εγκεφάλου δεδομένες πηγές που βρίσκονται στο εσωτερικό του (ευθέα προβλήματα EEG - MEG), είτε τρόπους προσδιορισμού των πηγών από μετρήσεις των πεδίων αυτών εξωτερικά του εγκεφάλου (αντίστροφα προβλήματα EEG - MEG). Όλα τα νευρικά σήματα του εγκεφάλου διαδίδονται μέσω μικρών ηλεκτρικών ρευμάτων, τα οποία παράγουν ηλεκτρικό & μαγνητικό πεδίο εντός & εκτός του εγκεφάλου λόγω του συζευγμένου χαρακτήρα του ηλεκτρομαγνητισμού για τα χρονικώς μεταβαλλόμενα φαινόμενα. Τα ηλεκτρικά πεδία & τα μαγνητικά πεδία που παράγονται καταγράφονται από το Ηλεκτροεγκεφαλογράφημα (EEG) & το Μαγνητοεγκεφαλογράφημα (MEG) αντίστοιχα. Στην παρούσα εργασία παρουσιάζουμε τα αποτελέσματα των ερευνών που έχουν καταγραφεί τα τελευταία χρόνια & έχουν δώσει χρήσιμες σχέσεις για το ηλεκτρικό & μαγνητικό πεδίο για τα διάφορα πρότυπα του εγκεφάλου & συγκεκριμένα του σφαιρικού, του σφαιροειδούς & του ελλειψοειδούς προτύπου. Επίσης αναλύεται η αναγωγή προς το σφαιρικό πρότυπο από τα άλλα δύο πρότυπα για να αποδειχθεί ότι τελικά η σφαιρική συμπεριφορά αποκαθίσταται & αναφέρονται ποιες είναι οι σιωπηλές πηγές που δεν συνεισφέρουν στην δημιουργία του μαγνητικού πεδίου στα διάφορα πρότυπα. Τέλος γίνεται αναφορά στο αντίστροφο πρόβλημα του ΗΕΓ που δεν έχει μοναδική λύση & αναφέρουμε πως μπορεί να επιλυθεί αρκεί από τα δεδομένα που έχουμε για το ηλεκτρικό πεδίο να έχει εξαλειφθεί ο θόρυβος με κάποιες μεθόδους που εξηγούνται. Αντικείμενο της εργασίας είναι αρχικά να περιγράψει τη μεθοδολογία για την ανάλυση του ηλεκτρικού πεδίου σε καρτεσιανές συντεταγμένες όσον αφορά το ελλειψοειδές πρότυπο του εγκεφάλου, που είναι & το βέλτιστο δεδομένου ότι ο μέσος εγκέφαλος είναι ελλειψοειδής με άξονες 9, 6.5, 6 cm. Στη συνέχεια δημιουργήσαμε ένα πρόγραμμα σε matlab με σκοπό την καταγραφή των πειραματικών αποτελεσμάτων (που είναι ο προσδιορισμός της πηγής & της θέσης της) & την τρισδιάστατη γραφική παράστασή τους από την παραμετρική ανάλυσή του ηλεκτρικού πεδίου. Στόχος μας ήταν η εύρεση & η σύγκριση των πηγών & των θέσεων που αυτές εντοπίζονται στο εσωτερικό του εγκεφάλου υπό διάφορες συνθήκες που καθορίζονται από την μεταβολή διαφόρων παραμέτρων όπως το πεδίο τιμών των μετρήσεων & των σφαλμάτων τους. / The fact is that both the EEG & MEG problems and the EEG & MEG inverse problems have been studied by researchers of various disciplines (Mathematics, Informatics, Physics, Electrical Engineering & Medicine), since 1950 and 1960, that have been seeking for ways of calculating the electrical and the magnetic field that are produced outside the brain by given sources located within the brain (EEG – MEG problems), or for methods of determining the sources from the measurement of these fields outside the brain (EEG – MEG inverse problems). All the nerve signals of the brain propagate via small electric currents, which produce electric and magnetic fields within and outside the brain due to the coupled nature of electromagnetism for the time-varying phenomena. Electric and magnetic fields, that are generated, are recorded by EEG recording (EEG) & the MEG recording (MEG), respectively. In this work we present the results of surveys in the recent years that have given useful relations for the electric and magnetic field for various models of the brain and in particular the spherical, the spheroid and the ellipsoid model. We also analyzed the reduction in the spherical model from the other two models in order to demonstrate that finally the spherical behavior is restored. Moreover, we listed the silent sources that do not contribute to the creation of the magnetic field in the various models. Finally, we refer to the EEG inverse problem that has not a unique solution and we refer how it can be solved provided that the noise is removed from the data we have - regarding the electric field- with some methods that are explained. The scope of this work is to describe at first the methodology for the analysis of the electric field for the ellipsoid model of the brain (that is the optimal model since the average brain is ellipsoid with axes 9, 6.5, 6 cm) in cartesian coordinates. Then we create a program in matlab in order to record the results, as far as the source and the position of the source are concerned, and their three-dimensional graphics. Our goal is to find and compare the vectors of the sources and the vectors of the positions that these sources are located within the brain, under various conditions determined by changing the various parameters such as the measurement parameters and the errors of the measurement parameters.