EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity

Hamed Azizollahi; Marion Darbas; Mohamadou M. Diallo; Abdellatif El Badia; Stephanie Lohrengel; Hamed Azizollahi; Marion Darbas; Mohamadou M. Diallo; Abdellatif El Badia; Stephanie Lohrengel

doi:10.3934/mbe.2018041

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 4: 905-932. doi: 10.3934/mbe.2018041

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EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity

1.
GRAMFC INSERM U1105, Department of Medicine, Amiens University Hospital, 80000 Amiens, France
2.
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80039 Amiens, France
3.
Laboratoire de Mathématiques Appliquées de Compiègne, Sorbonne Université, Université de Technologie de Compiègne, 60205 Compiègne, France
4.
Laboratoire de Mathématiques de Reims, EA4535, Université de Reims Champagne-Ardenne, 51687 Reims cedex 2, France

Received: 20 July 2017 Accepted: 13 October 2017 Published: 01 August 2018
MSC : Primary: 92C50, 65N30, 49K40, 35B30; Secondary: 65N12

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.
- Electroencephalography in neonates,
- dipole sources,
- finite elements,
- sensitivity analysis,
- simulations for realistic head models
Citation: 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[J]. Mathematical Biosciences and Engineering, 2018, 15(4): 905-932. doi: 10.3934/mbe.2018041

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Abstract

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.

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