Quantifying errors during the source localization process in electroencephalography for confocal systems

Doschoris, Michael; Kariotou, Foteini

doi:10.1093/imamat/hxx043

Cited by 5 publications

(11 citation statements)

References 27 publications

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“…For example, the authors consider in Ref. [37] the frequent case when clinical data of unknown origin are implemented in computational simulations. We mentioned earlier that there exist a plethora of combinations of the product a 1 ,a 2 ,a 3 furnishing the same value for the volume of the brain.…”

Section: Discussionmentioning

confidence: 99%

“…[37] can be considered as rather straightforward, since both ellipsoids under consideration were confocal, that is, members of the same ellipsoidal system enjoying the same foci. In plain words, no member of a confocal family touches another.…”

Section: Discussionmentioning

confidence: 99%

“…In Ref. [38], the authors investigated the effect implied by a deviation of the eccentricities of the ellipsoidal model on the electric potentials registered as the EEG data. In this case, the error reaches high values up to almost 100%.…”

Section: Discussionmentioning

confidence: 99%

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Mathematical Foundation of Electroencephalography

Doschoris¹,

Kariotou²

2017

Electroencephalography

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Electroencephalography (EEG) has evolved over the years to be one of the primary diagnostic technologies providing information concerning the dynamics of spontaneous and stimulated electrical brain activity. The core question of EEG is to acquire the precise location and strength of the sources inside the human brain by knowledge of an electrical potential measured on the scalp. But in what way is the source recovered? Leaving aside the biological mechanisms on the cellular level responsible for the recorded EEG signals, we pay attention to the mathematical aspects of the narrative. Our goal is to provide a brief and concise introduction of the mathematical terminology associated with the modality of EEG. We start from the very beginning, presenting step by step the mathematical formulation behind EEG in a simple and clear manner, keeping the mathematical notation to a minimum. Whilst we serve only the key relations for the described problems, we focus specifically on the limitations of each modelling approach. In this fashion, the reader can appreciate the beauty of the formulas presented and discover every single piece of information encoded within these formulas.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Mathematical Foundation of Electroencephalography

Doschoris¹,

Kariotou²

2017

Electroencephalography

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“…Obviously, analogous relations separating confocal and nonconfocal families do exist. Whereas relation + serves as a definition in order to distinguish the aforementioned families of ellipsoids and has been implemented in the work of Doschoris and Kariotou, 16 here, we employ a separate course of action. Assume that two ellipsoids can be connected by relations of the form…”

Section: The Ellipsoidal System: Confocality Vs Nonconfocalitymentioning

confidence: 99%

“…In the present work, we investigate the effect implied by a deviation of the eccentricities of the ellipsoidal model of the head-brain system on the electric potentials registered as EEG data. In the work of Doschoris and Kariotou, 16 the authors have studied the sensitivity of the forward EEG problem under the assumption that the eccentricities of the ellipsoidal model remain unaltered, ie, the deviation of the ellipsoidal shape is restricted to its size. This is the case when EEG recordings are interpreted as arriving from an average ellipsoidal brain rather than from the subjects' actual head, modeled by its best-fit ellipsoid.…”

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Error analysis for nonconfocal ellipsoidal systems in the forward problem of electroencephalography

Doschoris

Kariotou

2018

Math Methods in App Sciences

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Funding informationEuropean Social Fund Electroencephalography (EEG) remains the utmost important technique recording brain activity. The present investigation examines the sensitivity of analytic algorithms employed in order to evaluate EEG data with respect to different brain template models. These algorithms are based on mathematical models built upon certain geometrical and/or physical assumptions regarding the head-brain shape or the neuronal source. While the ellipsoidal head model provides a realistic approach regarding the interpretation of EEG signals in view of diverse geometries, its eccentricities influence strongly the results. The present study quantifies the deviation of the computed electric potentials when nonconfocal ellipsoids are used to model a homogeneous head conductor. To this end, a correspondence is proposed between points of the different ellipsoids, in view of the Gauss map. The investigation demonstrates that the introduction of nonconfocality imports a highly elevated error rate when EEG recordings are misinterpreted by arriving from different head-brain models, including ellipsoidal vs spherical ones. Moreover, evidence is presented concerning the location of extrema regarding the errors in the upper brain hemisphere, which could lead to a more precise and accurate protocol regarding the placement of sensors. Although the present work refers to the forward EEG problem, its results may be used under other approaches as well. In particular, it provides the error in the solution of an elliptic boundary value problem with transmission conditions under small perturbations of the eccentricities of its ellipsoidal domain. KEYWORDS brain template models, electroencephalography, ellipsoidal coordinate system, error analysis, nonconfocal ellipsoids, nonspherical domains INTRODUCTIONElectroencephalography (EEG) is one of the primary diagnostic technologies providing insight into the large-scale dynamics of spontaneous and stimulated neural electrical activity of the human brain. It allows real-time surveillance of the electric potential distribution on the surface of the head, the analysis of which leads to far-reaching clinical applications such as the evaluation of brain disorders (for a list, see the work of Bickford 1 ).By definition, EEG tracks the outcome of a neurophysiological process, namely, the activation of localized areas inside the brain, making the corresponding inverse problem nonunique. In other words, diverse source configurations are Math Meth Appl Sci. 2018;41:6793-6813.wileyonlinelibrary.com/journal/mma

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On the geometrical perturbation of a three‐shell spherical model in electroencephalography

Papargiri

Kalantonis

Vafeas

et al. 2022

Math Methods in App Sciences

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The forward electroencephalography (EEG) problem is studied in the framework of a multilayered structure, which models the scalp, skull, cerebrospinal fluid, and brain. Both the exterior and all inner boundaries are perturbed spheres so that special localized defects in head-brain imaging are considered in analytic fashion. Linear perturbation analysis is implemented, providing exact expression for the first significant term of the forward EEG solution of the perturbed problem. Comparison with the solution of the corresponding unperturbed spherical problem is included, together with numerical demonstration of the produced errors in special deformation cases. The results suggest that significant errors are caused when large inaccuracies in the headbrain structure in the vicinity of EEG source are not taken into account. Moreover, the suggested procedure provides a mathematical tool for evaluating quantitatively the impact of special deformations in the head representation on the EEG forward analytic solution.

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Quantifying errors during the source localization process in electroencephalography for confocal systems

Cited by 5 publications

References 27 publications

Mathematical Foundation of Electroencephalography

Mathematical Foundation of Electroencephalography

Error analysis for nonconfocal ellipsoidal systems in the forward problem of electroencephalography

On the geometrical perturbation of a three‐shell spherical model in electroencephalography

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