Application of boundary perturbations on medical monitoring and imaging techniques
type: Item
instance of: scholarly article
title: Application of boundary perturbations on medical monitoring and imaging techniques
zbMATH Open document ID: 1482.78007
DOI: 10.1007/978-3-030-72563-1_6
author: A. Papargiri
author: Panayiotis Vafeas
author: Michael Doschoris
author: Vassilis Kalantonis
publication date: 2021-09-07T00:00:00Z
review text: The paper aims at providing an analytic overview on the application of boundary perturbations for forward and inverse problems related to Electroencephalography (EEG) and Magnetoencephalography (MEG) predominantly for the spherical geometry, allowing a systematic presentation of the mathematical complexity associated. Extensive use is made of special functions and especially spherical harmonics. The surface of reference has been the homogeneous sphere, leading to solutions with corrections incorporating the deviation from the spherical geometry, included up to the first correction. A major impediment are the constrains, which are brought in by the Neumann condition, leading to the fact that components of either the moment of the dipole or its location or both, remain concealed. Two specific examples are provided for the obtained solutions of both EEG and MEG. For the entire collection see [Zbl 1471.34005].
Mathematics Subject Classification ID: 78A46
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35Q61
Mathematics Subject Classification ID: 92C05
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35R09
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 7392141
zbMATH Keywords: EEG
zbMATH Keywords: MEG
zbMATH Keywords: surface deformations
zbMATH Keywords: perturbation methods
zbMATH Keywords: forward and inverse problem
reviewed by: Dmitry Shepelsky
MaRDI profile type: Publication
full work available at URL: 978-3-030-72563-1 6
OpenAlex ID: W3193687213
cites work: The inverse source problem for Maxwell's equations
cites work: Electro-magneto-encephalography for a three-shell model: dipoles and beyond for the spherical geometry
cites work: On the inverse EEG problem for a 1D current distribution
cites work: Inversion of electroencephalography data for a 2-D current distribution
cites work: On the complementarity of electroencephalography and magnetoencephalography
cites work: The definite non-uniqueness results for deterministic EEG and MEG data
cites work: Q3579593
cites work: Q5182497
cites work: Q3250680
cites work: Error analysis for nonconfocal ellipsoidal systems in the forward problem of electroencephalography
cites work: The Influence of Surface Deformations on the Forward Magnetoencephalographic Problem
cites work: On the resolution of synchronous dipolar excitations via MEG measurements
description: scientific article; zbMATH DE number 7392141