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Mathematical Sciences aiming at medical application of light propagation in biomedical tissues and related topics

Research Project

Project/Area Number 16H02155
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKyoto University

Principal Investigator

Iso Yuusuke  京都大学, 情報学研究科, 教授 (70203065)

Co-Investigator(Kenkyū-buntansha) 藤原 宏志  京都大学, 情報学研究科, 准教授 (00362583)
大川 晋平  防衛医科大学校(医学教育部医学科進学課程及び専門課程、動物実験施設、共同利用研究施設、病院並びに防衛, 医用工学, 助教 (20432049)
川越 大輔  京都大学, 情報学研究科, 助教 (30848073)
大石 直也  京都大学, 医学研究科, 特定准教授 (40526878)
木村 正人  金沢大学, 数物科学系, 教授 (70263358)
今井 仁司  同志社大学, 理工学部, 教授 (80203298)
Project Period (FY) 2016-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥44,980,000 (Direct Cost: ¥34,600,000、Indirect Cost: ¥10,380,000)
Fiscal Year 2020: ¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2019: ¥12,350,000 (Direct Cost: ¥9,500,000、Indirect Cost: ¥2,850,000)
Fiscal Year 2018: ¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2017: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Fiscal Year 2016: ¥13,650,000 (Direct Cost: ¥10,500,000、Indirect Cost: ¥3,150,000)
Keywords応用数学 / 数値解析 / 応用解析 / 医用ひかりトモグラフィー / 大規模数値計算 / 逆問題解析 / 光超音波 / 逆問題・非適切問題解析 / 非適切問題解析 / 逆問題 / ひかりトモグラフィ / 数値計算 / 輸送方程式 / 生体医用工学
Outline of Final Research Achievements

The present research program focuses on Diffused Optical Tomography (DOT), and the key idea of the research is dealing with the radiative transport equation (RTE) as the mathematical model of the aimed phenomena. DOT is considered an inverse problem of RTE, and we set the inverse problem to determine the scattering coefficient in the equation by observation of discontinuity of the solution of RTE. We show some mathematical results based on the method of characteristic lines and also numerical ones based on the discontinuous Galerkin method. We also show some new results the concerning photo-acoustic technology and, furthermore, obtain new knowledge on NIRS. We show some interesting numerical results aiming at numerical computation for inverse problems.

Academic Significance and Societal Importance of the Research Achievements

光断層撮影法(Diffused Optical Tomography=DOT)は近赤外光の生体特性を利用する未来の医用技術で、脳科学への寄与も期待できる。この未来技術の基礎理論を数理科学的に確立することが本課題研究の目的である。この問題を輸送方程式の逆問題として扱うことが斬新であり、本課題研究では定常輸送方程式の逆問題解析とその関連研究を展開した。本課題研究の成果のみでDOTが実用化されるわけではないが、方程式の不連続性に対応するデータを逆問題のデータとする問題設定を行い、数学解析と数値解析の両面で新たな知見を得ている。あわせて、近赤外光を利用した未来技術である光超音波技術でも成果を得た。

Report

(6 results)
  • 2021 Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (53 results)

All 2022 2021 2019 2018 2017 2016 Other

All Int'l Joint Research (8 results) Journal Article (17 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 16 results,  Open Access: 5 results) Presentation (26 results) (of which Int'l Joint Research: 19 results,  Invited: 6 results) Funded Workshop (2 results)

  • [Int'l Joint Research] 国立台湾大学/国立成功大学/台湾中央研究院数学研究所(その他の国・地域)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] University of Central Florida(米国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Seoul University/Inha University(韓国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Austrian Academy of Science(オーストラリア)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Karlstad University(スウェーデン)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 国立台湾大学数学系(その他の国・地域 中華民国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] 台湾大学(中華民国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ソウル大学(韓国)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Partial inversion of the 2D attenuated X-ray transform with data on an arc2022

    • Author(s)
      Fujiwara Hiroshi、Sadiq Kamran、Tamasan Alexandru
    • Journal Title

      Inverse Problems & Imaging

      Volume: 16 Issue: 1 Pages: 215-228

    • DOI

      10.3934/ipi.2021047

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] 部分観測による X 線計算機断層撮影法の数値的実現2021

    • Author(s)
      藤原宏志、大石直也、SADIQ, Kamran、TAMASAN, Alexandru
    • Journal Title

      計算数理工学論文集

      Volume: 21 Pages: 37-43

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments2021

    • Author(s)
      Lee Yu-Hsun、Fujiwara Hiroshi
    • Journal Title

      Lecture Notes in Computer Science book series (LNTCS)

      Volume: 12953 Pages: 191-201

    • DOI

      10.1007/978-3-030-86976-2_13

    • ISBN
      9783030869755, 9783030869762
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Numerical regularity map for simple one-dimensional fractional differential equations with Hoelder continuous solutions2021

    • Author(s)
      Mana Kato、Hiroshi Fujiwara and Hitoshi Imai
    • Journal Title

      Adv. Math. Sci. Appl

      Volume: 30 Pages: 499-506

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium2019

    • Author(s)
      Fujiwara Hiroshi、Sadiq Kamran、Tamasan Alexandru
    • Journal Title

      Inverse Problems

      Volume: 36 Issue: 1 Pages: 015005-015005

    • DOI

      10.1088/1361-6420/ab4d98

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Numerical realization of a new generation tomography algorithm based on the Cauchy-type integral formula2019

    • Author(s)
      H. Fujiwara and A. Tamasan
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 28 Pages: 413-424

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Design and implementation of multiple-precision arithmetic environment in MATLAB for reliable numerical computations2019

    • Author(s)
      Fujiwara Hiroshi
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 36 Issue: 3 Pages: 1089-1100

    • DOI

      10.1007/s13160-019-00385-z

    • NAID

      210000182436

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analysis of a projection method for the Stokes problem using an ε-Stokes approach2019

    • Author(s)
      M. Kimura, K. Matsui, A. Muntean, H. Notsu
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 36 Issue: 3 Pages: 959-985

    • DOI

      10.1007/s13160-019-00373-3

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Unidirectional evolution equations of diffusion type2019

    • Author(s)
      G. Akagi and M. Kimura
    • Journal Title

      J. Differential Equations

      Volume: 266 Pages: 1-43

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of finite differential schemes applied to quasi-linear partial differential equation of the normal form2018

    • Author(s)
      N. Higashimori, H. Fujiwara, and Y. Iso
    • Journal Title

      Advances in Difference Equations and Discrete Dynamical Systems. (Springer Proceedings in Mathematics and Statistics)

      Volume: 212 Pages: 113-124

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical experiments on analyticity of solutions to fraction al differential equations2018

    • Author(s)
      H. Fujiwara, N. Higashimori, and H. Imai
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 27 Pages: 169-180

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Gradient Flow Structure of an Extended Maxwell Viscoelastic Model and a Structure-Preserving Finite Element Scheme2018

    • Author(s)
      Kimura Masato、Notsu Hirofumi、Tanaka Yoshimi、Yamamoto Hiroki
    • Journal Title

      Journal of Scientific Computing

      Volume: 78 Issue: 2 Pages: 1111-1131

    • DOI

      10.1007/s10915-018-0799-2

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of Finite Difference Schemes Applied to the Cauchy Problems of Quasi-linear Partial Differential Equations of the Normal Form2018

    • Author(s)
      Higashimori Nobuyuki, Fujiwara Hiroshi, Iso Yuusuke
    • Journal Title

      Advances in Difference Equations and Discrete Dynamical Systems

      Volume: - Pages: 113-124

    • DOI

      10.1007/978-981-10-6409-8_6

    • ISBN
      9789811064081, 9789811064098
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiple-Precision Multiple-Precision Arithmetic Environment in MATLAB and Its Application to Reliable Computation of Fractional Order Derivatives2018

    • Author(s)
      Hiroshi Fujiwara
    • Journal Title

      マス・フォア・インダストリ研究

      Volume: 8 Pages: 83-120

    • Related Report
      2017 Annual Research Report
    • Open Access
  • [Journal Article] Semi-discrete finite difference schemes for the nonlinear Cauchy problems of the normal form2017

    • Author(s)
      Higashimori Nobuyuki, Fujiwara Hiroshi
    • Journal Title

      Proceedings of the Japan Academy, Series A, Mathematical Sciences

      Volume: 93 Issue: 9 Pages: 99-104

    • DOI

      10.3792/pjaa.93.99

    • NAID

      40021392001

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Convergence of a threshold-type algorithm using the signed distance function.2016

    • Author(s)
      木村 正人
    • Journal Title

      Interfaces Free Boundaries

      Volume: Vol.18 Pages: 479-522

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 定常輻射輸送方程式の速度方向区分定数近似の数値解析2016

    • Author(s)
      藤原宏志
    • Journal Title

      計算数理工学論文集

      Volume: 16 Pages: 91-96

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] 特異積分方程式による部分観測でのX線計算機トモグラフィ2022

    • Author(s)
      藤原宏志, K.Sadiq, A.Tamasan
    • Organizer
      日本応用数理学会第18回研究部会連合発表会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 部分観測による X 線計算機断層撮影法の数値的実現2021

    • Author(s)
      藤原宏志,大石直也, SADIQ, Kamran, TAMASAN, Alexandru
    • Organizer
      計算数理工学シンポジウム2021
    • Related Report
      2020 Annual Research Report
  • [Presentation] An Efficient Numerical Scheme for Near-Infrared Light Propagation in Turbid Media2021

    • Author(s)
      H. Fujiwara
    • Organizer
      IUTAM symposium computational methods for large-scale and complex wave problems
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 輸送方程式のソース項同定逆問題による X 線計算機断層撮影の数値的実現2021

    • Author(s)
      藤原宏志
    • Organizer
      第26回計算工学講演会
    • Related Report
      2020 Annual Research Report
  • [Presentation] A proposal of a new numerical algorithm to solve fractional differential equations2018

    • Author(s)
      磯 祐介
    • Organizer
      Japan-Taiwan Joint Workshop on Scientific Computing and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical Computation of the 2D Stationary Radiative Transport Equation on Graded Meshes2018

    • Author(s)
      藤原 宏志
    • Organizer
      Japan-Taiwan Joint Workshop on Scientific Computing and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Accurate numerical computation for one-dimensional fractional differential equations by using spectral collocation methods2018

    • Author(s)
      今井 仁司
    • Organizer
      Japan-Taiwan Joint Workshop on Scientific Computing and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多倍長計算環境exflibの最新計算環境への対応と普及2018

    • Author(s)
      藤原 宏志
    • Organizer
      日本応用数理学会年会2018年度 年会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Gradient flow structure of the Maxwell-Zener model for viscoelasticity2018

    • Author(s)
      木村 正人
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Phase field modeling for crack propagation with irreversibility2018

    • Author(s)
      木村 正人
    • Organizer
      China-Japan Symposium on Defects and Cracks in 2018 CSIAM Annual Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical challenges to the radiative transport equation for near-infrared light propagation in tissue2018

    • Author(s)
      H. Fujiwara
    • Organizer
      Numerical Analysis: Applications to Biomedical Problems and Foundations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Diffused Optical Tomography as an Inverse Problem for the Transport Equation2017

    • Author(s)
      磯 祐介
    • Organizer
      Korea-Japan Joint Workshop on Numerical Analysis and Scientific Computation
    • Place of Presentation
      Jeju National University Unipark, Seoguipo, Jeju,(大韓民国)
    • Year and Date
      2017-02-21
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Semi-discrete numerical scheme of the 2D stationary radiative transport equation on highly-parallel architectures2017

    • Author(s)
      藤原 宏志
    • Organizer
      Korea-Japan Joint Workshop on Numerical Analysis and Scientific Computation
    • Place of Presentation
      Jeju National University Unipark, Seoguipo, Jeju, (大韓民国)
    • Year and Date
      2017-02-21
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical limit and its application to a blow-up problem governed by an ODE system2017

    • Author(s)
      今井 仁司
    • Organizer
      Korea-Japan Joint Workshop on Numerical Analysis and Scientific Computation
    • Place of Presentation
      Jeju National University Unipark, Seoguipo, Jeju, (大韓民国)
    • Year and Date
      2017-02-21
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Generalized hexagonal crystalline motion with facet collision and breaking and application to a snow flake model2017

    • Author(s)
      木村 正人
    • Organizer
      Emerging Developments in Interfaces and Free Boundaries
    • Place of Presentation
      Oberwolfach Research Institute for Mathematics, Germany
    • Year and Date
      2017-01-22
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 生体内の光伝播の数値計算のための定常輻射輸送方程式の上流差分スキームの数値計算2017

    • Author(s)
      藤原宏志
    • Organizer
      日本計算数理工学会(第33回 計算数理工学フォーラム)
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Quantitative simulation of light emitting by optical fibers in the radiative transport equation2017

    • Author(s)
      H. Fujiwara
    • Organizer
      A3 Workshop on Applied Inverse Problems and Related Topics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Direct Numerical Computation of the Stationary Radiative Transport Equation on Modern Parallel Architectures2017

    • Author(s)
      H. Fujiwara, N. Oishi
    • Organizer
      The 16th International Symposium on Distributed Computing and Applications to Business, Engineering and Science
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 光散乱積分の局所化による生体内の光伝播の数理モデルの高速直接計算法2017

    • Author(s)
      藤原 宏志
    • Organizer
      第19回ヒト脳機能マッピング学会
    • Place of Presentation
      京都大学
    • Related Report
      2016 Annual Research Report
  • [Presentation] Finite difference method on a scale of Banach spaces2016

    • Author(s)
      磯 祐介
    • Organizer
      2016 Japan-Taiwan Joint Workshop on Numerical Analysis and Scientif ic Computation
    • Place of Presentation
      Lecture Room 202, Astro-Math Building, National Taiwan University(中華民国)
    • Year and Date
      2016-11-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Semi-discrete upwind finite volume methods for the 2D stationary radiative transport equation by GPGPU2016

    • Author(s)
      藤原 宏志
    • Organizer
      2016 Japan-Taiwan Joint Workshop on Numerical Analysis and Scientif ic Computation
    • Place of Presentation
      Lecture Room 202, Astro-Math Building, National Taiwan University(中華民国)
    • Year and Date
      2016-11-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical limit and its application to a blow-up problem2016

    • Author(s)
      今井 仁司
    • Organizer
      2016 Japan-Taiwan Joint Workshop on Numerical Analysis and Scientif ic Computation
    • Place of Presentation
      Lecture Room 202, Astro-Math Building, National Taiwan University(中華民国)
    • Year and Date
      2016-11-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Unidirectional gradient flow and its application to a crack propagation model2016

    • Author(s)
      木村 正人
    • Organizer
      Variational Models of Fracture
    • Place of Presentation
      Banff International Research Startion, Canada
    • Year and Date
      2016-05-08
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Multiple-precision arithmetic on 64-bit MATLAB based on exflib2016

    • Author(s)
      藤原 宏志
    • Organizer
      Taiwan-Japan Joint Workshop on Inverse Problems 2016
    • Place of Presentation
      Kyoto University(日本)
    • Year and Date
      2016-04-02
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical Computation of the 2D Radiative Transport Equation by Upwind Finite Volume Method2016

    • Author(s)
      藤原 宏志
    • Organizer
      SIAM: East Asian Section Conference 2016
    • Place of Presentation
      University of Macau(中華人民共和国)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Direct computation of the radiative transport equation for near-infrared light propagation in biological tissue2016

    • Author(s)
      藤原 宏志、大石 直也
    • Organizer
      The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Hyatt Regency Orland(アメリカ合衆国)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Funded Workshop] 2021 Japan-Taiwan Joint Online Workshop on Numerical Analysis and Inverse Problems2021

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] Taiwan-Japan Joint Workshop on Inverse Problems in Kanazawa 20172017

    • Related Report
      2017 Annual Research Report

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Published: 2016-04-21   Modified: 2023-01-30  

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