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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/13735

Title: 一步李群估測法於生物細胞組織特性之研究
One-step GPS for the Estimation of the Physical Properties of Bio-tissue
Authors: Chun-Hsien Chen
陳俊憲
Contributors: NTOU:Department of Mechanical and Mechatronic Engineering
國立臺灣海洋大學:機械與機電工程學系
Keywords: 反算問題;熱傳導係數;熱容係數;光學擴散係數;光學吸收係數
Inverse problem;Thermal conductivity coefficient;Thermal capacity coefficient;Optical diffusion coefficient;Optical absorption coefficient
Date: 2006
Issue Date: 2011-06-30T07:26:39Z
Abstract: 本文將以反算問題中的李群估測法(Lie-group Estimation Method, LGEM)應用在生物組織熱傳導方程式以及光學擴散方程式,估測生物細胞組織的熱傳導係數、熱容係數、光學擴散係數及光學吸收係數。   第一部份,我們將生物熱傳導方程式PDE經過空間半離散轉換成 對ODEs,導入初始溫度和最末溫度轉換至增廣閔氏空間,再藉由One-step GPS解出調整因子 ,代入非線性函數,即可求得生物細胞組織的熱傳導係數 以及熱容係數 。 第二部份,我們加入一個新的觀念,將光擴散的ODE方程式乘(1+t)以轉換成PDE,PDE經過半離散轉換成 對ODEs,導入初始溫度和最末溫度轉換至增廣閔氏空間,再藉由One-step GPS解出調整因子,代入非線性函數,即可求得生物細胞組織的光學擴散係數 及光學吸收係數 。
In this paper we are applying the LGEM to estimate the unknown parameters from bio-heat transfer equation and optical propagation equation. It is composed of two parts. First, we discuss PDE of bio-heat transfer equation. The semi-discrete procedure of PDE yields n coupled system of ODEs, and then transform them into the Minkowskian type ODEs. By adding initial and final temperature, we solve adaptive factor by one-step GPS, Substituting the solved adaptive factor into the non-linear equations, we can obtain thermal conductivity and thermal capacity. In the second part, we use a good idea to solve the estimation problem. We will multiply into the ODE of optical propagation equation, such that we have a PDE. The semi-discrete procedure of PDE yields n coupled system of ODEs, and then transform them into the Minkowskian type ODEs. By adding initial and final temperature, we can solve the obtain adaptive factor by one-step GPS, inserting which into the non-linear equation, we can obtain optical diffusion and optical absorption coefficients of tissue.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0M94720054
http://ntour.ntou.edu.tw/ir/handle/987654321/13735
Appears in Collections:[機械與機電工程學系] 博碩士論文

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