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A second order asymptotic model for diffusion MRI in permeable media

Bibliographic Details
Title: A second order asymptotic model for diffusion MRI in permeable media
Authors: Marwa Kchaou, Jing-Rebecca Li
Contributors: Sciences, EDP
Source: ESAIM: Mathematical Modelling and Numerical Analysis. 57:1953-1980
Publisher Information: EDP Sciences, 2023.
Publication Year: 2023
Subject Terms: Radiology, Nuclear Medicine and Imaging, Finite element method, Inverse Problems in Mathematical Physics and Imaging, Permeability (electromagnetism), Asymptotic analysis, Structural engineering, higher-order diffusion tensor, [MATH] Mathematics [math], Mechanics, 01 natural sciences, Mathematical analysis, Biochemistry, Diffusion MRI, diffusion MRI, Diffusion, 03 medical and health sciences, 0302 clinical medicine, Differential equation, Engineering, Health Sciences, FOS: Mathematics, Multiscale Methods for Heterogeneous Systems, Homogenization (climate), 0101 mathematics, Anisotropic Water Diffusion, Biology, Mathematical Physics, Homogenization, Ecology, Physics, Membrane, Partial differential equation, Biodiversity, Asymptotic homogenization, Upscaling Techniques, Transverse plane, Chemistry, Diffusion Magnetic Resonance Imaging, Computational Theory and Mathematics, Bloch–Torrey equation, FOS: Biological sciences, Computer Science, Physical Sciences, Medicine, Thermodynamics, Multiscale Methods, Mathematics, Ordinary differential equation
Description: Starting from a reference partial differential equation model of the complex transverse water proton magnetization in a voxel due to diffusion-encoding magnetic field gradient pulses, one can use periodic homogenization theory to establish macroscopic models. A previous work introduced an asymptotic model that accounted for permeable interfaces in the imaging medium. In this paper we formulate a higher order asymptotic model to treat higher values of permeability. We explicitly solved this new asymptotic model to obtain a system of ordinary differential equations that can model the diffusion MRI signal and we present numerical results showing the improved accuracy of the new model in the regime of higher permeability.
Document Type: Article
Other literature type
File Description: application/pdf
ISSN: 2804-7214
2822-7840
DOI: 10.1051/m2an/2023043
DOI: 10.60692/eqjnw-ekv08
DOI: 10.60692/02x6s-df486
Rights: CC BY
Accession Number: edsair.doi.dedup.....80b8b97c54ece9e6f73f2a00cc4af77c
Database: OpenAIRE
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PubType: Academic Journal
PubTypeId: academicJournal
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IllustrationInfo
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  Data: A second order asymptotic model for diffusion MRI in permeable media
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  Data: <searchLink fieldCode="AR" term="%22Marwa+Kchaou%22">Marwa Kchaou</searchLink><br /><searchLink fieldCode="AR" term="%22Jing-Rebecca+Li%22">Jing-Rebecca Li</searchLink>
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  Data: Sciences, EDP
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  Data: <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>. 57:1953-1980
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  Data: EDP Sciences, 2023.
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  Data: 2023
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  Data: <searchLink fieldCode="DE" term="%22Radiology%2C+Nuclear+Medicine+and+Imaging%22">Radiology, Nuclear Medicine and Imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+Problems+in+Mathematical+Physics+and+Imaging%22">Inverse Problems in Mathematical Physics and Imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Permeability+%28electromagnetism%29%22">Permeability (electromagnetism)</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+analysis%22">Asymptotic analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+engineering%22">Structural engineering</searchLink><br /><searchLink fieldCode="DE" term="%22higher-order+diffusion+tensor%22">higher-order diffusion tensor</searchLink><br /><searchLink fieldCode="DE" term="%22[MATH]+Mathematics+[math]%22">[MATH] Mathematics [math]</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanics%22">Mechanics</searchLink><br /><searchLink fieldCode="DE" term="%2201+natural+sciences%22">01 natural sciences</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Biochemistry%22">Biochemistry</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion+MRI%22">Diffusion MRI</searchLink><br /><searchLink fieldCode="DE" term="%22diffusion+MRI%22">diffusion MRI</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion%22">Diffusion</searchLink><br /><searchLink fieldCode="DE" term="%2203+medical+and+health+sciences%22">03 medical and health sciences</searchLink><br /><searchLink fieldCode="DE" term="%220302+clinical+medicine%22">0302 clinical medicine</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equation%22">Differential equation</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering%22">Engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Health+Sciences%22">Health Sciences</searchLink><br /><searchLink fieldCode="DE" term="%22FOS%3A+Mathematics%22">FOS: Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Multiscale+Methods+for+Heterogeneous+Systems%22">Multiscale Methods for Heterogeneous Systems</searchLink><br /><searchLink fieldCode="DE" term="%22Homogenization+%28climate%29%22">Homogenization (climate)</searchLink><br /><searchLink fieldCode="DE" term="%220101+mathematics%22">0101 mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Anisotropic+Water+Diffusion%22">Anisotropic Water Diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Biology%22">Biology</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Physics%22">Mathematical Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Homogenization%22">Homogenization</searchLink><br /><searchLink fieldCode="DE" term="%22Ecology%22">Ecology</searchLink><br /><searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Membrane%22">Membrane</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equation%22">Partial differential equation</searchLink><br /><searchLink fieldCode="DE" term="%22Biodiversity%22">Biodiversity</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+homogenization%22">Asymptotic homogenization</searchLink><br /><searchLink fieldCode="DE" term="%22Upscaling+Techniques%22">Upscaling Techniques</searchLink><br /><searchLink fieldCode="DE" term="%22Transverse+plane%22">Transverse plane</searchLink><br /><searchLink fieldCode="DE" term="%22Chemistry%22">Chemistry</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion+Magnetic+Resonance+Imaging%22">Diffusion Magnetic Resonance Imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+Theory+and+Mathematics%22">Computational Theory and Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Bloch–Torrey+equation%22">Bloch–Torrey equation</searchLink><br /><searchLink fieldCode="DE" term="%22FOS%3A+Biological+sciences%22">FOS: Biological sciences</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Science%22">Computer Science</searchLink><br /><searchLink fieldCode="DE" term="%22Physical+Sciences%22">Physical Sciences</searchLink><br /><searchLink fieldCode="DE" term="%22Medicine%22">Medicine</searchLink><br /><searchLink fieldCode="DE" term="%22Thermodynamics%22">Thermodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Multiscale+Methods%22">Multiscale Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Ordinary+differential+equation%22">Ordinary differential equation</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: Starting from a reference partial differential equation model of the complex transverse water proton magnetization in a voxel due to diffusion-encoding magnetic field gradient pulses, one can use periodic homogenization theory to establish macroscopic models. A previous work introduced an asymptotic model that accounted for permeable interfaces in the imaging medium. In this paper we formulate a higher order asymptotic model to treat higher values of permeability. We explicitly solved this new asymptotic model to obtain a system of ordinary differential equations that can model the diffusion MRI signal and we present numerical results showing the improved accuracy of the new model in the regime of higher permeability.
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  Data: 2804-7214<br />2822-7840
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  Data: 10.1051/m2an/2023043
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  Data: 10.60692/eqjnw-ekv08
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  Data: edsair.doi.dedup.....80b8b97c54ece9e6f73f2a00cc4af77c
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    Identifiers:
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        Value: 10.1051/m2an/2023043
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    PhysicalDescription:
      Pagination:
        PageCount: 28
        StartPage: 1953
    Subjects:
      – SubjectFull: Radiology, Nuclear Medicine and Imaging
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Inverse Problems in Mathematical Physics and Imaging
        Type: general
      – SubjectFull: Permeability (electromagnetism)
        Type: general
      – SubjectFull: Asymptotic analysis
        Type: general
      – SubjectFull: Structural engineering
        Type: general
      – SubjectFull: higher-order diffusion tensor
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      – SubjectFull: [MATH] Mathematics [math]
        Type: general
      – SubjectFull: Mechanics
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        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Biochemistry
        Type: general
      – SubjectFull: Diffusion MRI
        Type: general
      – SubjectFull: diffusion MRI
        Type: general
      – SubjectFull: Diffusion
        Type: general
      – SubjectFull: 03 medical and health sciences
        Type: general
      – SubjectFull: 0302 clinical medicine
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      – SubjectFull: Homogenization (climate)
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      – SubjectFull: 0101 mathematics
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      – SubjectFull: Anisotropic Water Diffusion
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      – SubjectFull: Biology
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      – SubjectFull: Mathematical Physics
        Type: general
      – SubjectFull: Homogenization
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      – SubjectFull: Ecology
        Type: general
      – SubjectFull: Physics
        Type: general
      – SubjectFull: Membrane
        Type: general
      – SubjectFull: Partial differential equation
        Type: general
      – SubjectFull: Biodiversity
        Type: general
      – SubjectFull: Asymptotic homogenization
        Type: general
      – SubjectFull: Upscaling Techniques
        Type: general
      – SubjectFull: Transverse plane
        Type: general
      – SubjectFull: Chemistry
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      – SubjectFull: Diffusion Magnetic Resonance Imaging
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      – SubjectFull: Bloch–Torrey equation
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      – SubjectFull: Medicine
        Type: general
      – SubjectFull: Thermodynamics
        Type: general
      – SubjectFull: Multiscale Methods
        Type: general
      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Ordinary differential equation
        Type: general
    Titles:
      – TitleFull: A second order asymptotic model for diffusion MRI in permeable media
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            NameFull: Marwa Kchaou
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              M: 07
              Type: published
              Y: 2023
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