EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity
The paper is devoted to the analysis of electroencephalography (EEG) in neonates. The goal is to investigate the impact of fontanels on EEG measurements, i.e. on the values of the electric potential on the scalp. In order to answer this clinical issue, a complete mathematical study (modeling, existe...
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| Language: | English |
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AIMS Press
2018-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018041 |
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| author | Hamed Azizollahi Marion Darbas Mohamadou M. Diallo Abdellatif El Badia Stephanie Lohrengel |
| author_facet | Hamed Azizollahi Marion Darbas Mohamadou M. Diallo Abdellatif El Badia Stephanie Lohrengel |
| author_sort | Hamed Azizollahi |
| collection | DOAJ |
| description | The paper is devoted to the analysis of electroencephalography (EEG) in neonates. The goal is to investigate the impact of fontanels on EEG measurements, i.e. on the values of the electric potential on the scalp. In order to answer this clinical issue, a complete mathematical study (modeling, existence and uniqueness result, realistic simulations) is carried out. A model for the forward problem in EEG source localization is proposed. The model is able to take into account the presence and ossification process of fontanels which are characterized by a variable conductivity. From a mathematical point of view, the model consists in solving an elliptic problem with a singular source term in an inhomogeneous medium. A subtraction approach is used to deal with the singularity in the source term, and existence and uniqueness results are proved for the continuous problem. Discretization is performed with 3D Finite Elements of type P1 and error estimates are proved in the energy norm ($H^1$-norm). Numerical simulations for a three-layer spherical model as well as for a realistic neonatal head model including or not the fontanels have been obtained and corroborate the theoretical results. A mathematical tool related to the concept of Gâteau derivatives is introduced which is able to measure the sensitivity of the electric potential with respect to small variations in the fontanel conductivity. This study attests that the presence of fontanels in neonates does have an impact on EEG measurements. |
| format | Article |
| id | doaj-art-e59268dbed064d4cae15e430d38f48c5 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e59268dbed064d4cae15e430d38f48c52025-01-24T02:40:56ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-07-0115490593210.3934/mbe.2018041EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivityHamed Azizollahi0Marion Darbas1Mohamadou M. Diallo2Abdellatif El Badia3Stephanie Lohrengel4GRAMFC INSERM U1105, Department of Medicine, Amiens University Hospital, 80000 Amiens, FranceLaboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80039 Amiens, FranceLaboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80039 Amiens, FranceLaboratoire de Mathématiques Appliquées de Compiègne, Sorbonne Université, Université de Technologie de Compiègne, 60205 Compiègne, FranceLaboratoire de Mathématiques de Reims, EA4535, Université de Reims Champagne-Ardenne, 51687 Reims cedex 2, FranceThe paper is devoted to the analysis of electroencephalography (EEG) in neonates. The goal is to investigate the impact of fontanels on EEG measurements, i.e. on the values of the electric potential on the scalp. In order to answer this clinical issue, a complete mathematical study (modeling, existence and uniqueness result, realistic simulations) is carried out. A model for the forward problem in EEG source localization is proposed. The model is able to take into account the presence and ossification process of fontanels which are characterized by a variable conductivity. From a mathematical point of view, the model consists in solving an elliptic problem with a singular source term in an inhomogeneous medium. A subtraction approach is used to deal with the singularity in the source term, and existence and uniqueness results are proved for the continuous problem. Discretization is performed with 3D Finite Elements of type P1 and error estimates are proved in the energy norm ($H^1$-norm). Numerical simulations for a three-layer spherical model as well as for a realistic neonatal head model including or not the fontanels have been obtained and corroborate the theoretical results. A mathematical tool related to the concept of Gâteau derivatives is introduced which is able to measure the sensitivity of the electric potential with respect to small variations in the fontanel conductivity. This study attests that the presence of fontanels in neonates does have an impact on EEG measurements.https://www.aimspress.com/article/doi/10.3934/mbe.2018041electroencephalography in neonatesdipole sourcesfinite elementssensitivity analysissimulations for realistic head models |
| spellingShingle | Hamed Azizollahi Marion Darbas Mohamadou M. Diallo Abdellatif El Badia Stephanie Lohrengel EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity Mathematical Biosciences and Engineering electroencephalography in neonates dipole sources finite elements sensitivity analysis simulations for realistic head models |
| title | EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity |
| title_full | EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity |
| title_fullStr | EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity |
| title_full_unstemmed | EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity |
| title_short | EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity |
| title_sort | eeg in neonates forward modeling and sensitivity analysis with respect to variations of the conductivity |
| topic | electroencephalography in neonates dipole sources finite elements sensitivity analysis simulations for realistic head models |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018041 |
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