# 臺灣博碩士論文加值系統

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 本文的主旨在於探討高溫微波熱療法中生物體內電能功率與電場的分析，以了解影響體內溫度分佈的各種控制因素。為了模擬實際的加熱微波系統，文中提出了一系列的理論分析，其步驟如下：首先應用Maxwell方程式推導得電磁場能分佈之統御方程式，以及電磁場在穿過不同介質後的變化情形，然後以有限元素法推導出計算各別元素電磁場大小之方程式，得到電磁場在系統內分佈的數值解，以便進行電磁場能分佈之計算最佳化工作，進而提供系統的評估及設計的參考。在利用了此種數值方法得到初步的數據之後，為了確認我們模擬的結果是否正確，我們利用了FEMLAB套裝軟體模擬了已簡化的人體組織情況下的測試案例，以得到此模擬系統之FEMLAB解，再將數值解與此FEMLAB解互相比較，結果顯示我們的數值模式具有不錯的效率且結果也相當具有可行性。
 The study presents the analysis of the power of electric energy and electric field in the organism in the high-temperature microwave hyperthermia, in order to understand the factors that influence the distribution of internal temperature. For the simulation of real heating microwave system , the study presents a series of theory analysis ,and its step is as follows: first use Maxwell equation to derive the governing equation of the system and to derive the equation of EM wave moving through the boundary of different medium ; then use FEM to derive the equation of each element, and get the approximate solution to optimize the result of the system, offering the systematic assessment and reference of the design. After using this Numerical method to get the preliminary data, we utilize the test case under the simple tissue situation of software simulation of FEMLAB in order to confirm whether the result of our simulation is correct ,and get the FEMLAB solution.Finally we compare approximate solution with FEMLAB solution,and the results show that this method have good efficiency and feasibility.
 目 錄中文摘要.....................................................................................................I英文摘要...................................................................................................II誌謝..........................................................................................................III目錄..........................................................................................................IV圖目錄......................................................................................................VI表目錄...................................................................................................VIII第一章 序論..............................................................................................1 1.1 研究動機.....................................................................................1 1.2 文獻回顧.....................................................................................3 1.3 本文架構.....................................................................................6第二章 馬克斯威爾方程式......................................................................7 2.1理論基礎.......................................................................................7 2.2邊界值...........................................................................................9 2.2.1波印亭定理........................................................................9 2.2.2邊界條件..........................................................................10 2.2.3解的唯一性......................................................................11 2.3方程式推導.................................................................................13 2.3.1統御方程式......................................................................13 2.3.2穿越不同介質的電場變化量..........................................14第三章 有限元素分析............................................................................17 3.1理論基礎........................................................................................17 3.1.1 Weighted Residual Method.............................................17 3.1.2 有限元素法....................................................................183.1.3 公式推導........................................................................203.2元素分析........................................................................................23 3.2.1 二十個節點的六面體元素............................................23 3.2.2 數值解法........................................................................26第四章 範例測試....................................................................................30 4.1數值計算.......................................................................................31 4.1.1肺-心臟模擬....................................................................32 4.1.2肌肉-骨骼模擬................................................................35 4.2模擬結果......................................................................................37第五章 結論............................................................................................53參考文獻..................................................................................................54
 1.Song C.W.(1980), ”Physiological factors in hyperthermia, NCI Monograph 61, U.S. Dep. Health and Human Services, pp.169-176; presented at the 3rd Int.Symp.Cancer Therapy by Hyperthermia, Drugs and Radiation,June.2.Gibbs F.A (1984), ”Regional hyperthermia: A clinical appraisal of noninvasive deep-heating methods”, Cancer Res. (suppl.), vol.44, pp.4765s-4770s.3.Strohbehn J.W. and Roemer R.B.(1984), ”A survey of computer simulations of hyperthermia treatments”, IEEE Trans. Biomed. Eng., vol.BME-31,pp.136-149.4.Hagmann M.J., Gandi O.P. and Durney C.H.(1984), ”Numerical caculations of electromagnetic energy deposition for a realistic model of man”, IEEE Trans. Microwave Theory Tech., vol.MTT-27. pp.804-809.5.Hessary M.K. and Chen K.M.(1984), ”EM local heating with HF electric fields”, IEEE Trans. Microwave Theory Tech., vol. MTT-32. pp.569-576.6.Turner P.F.(1984), ”Regional hyperthermia with an annular phased array ”IEEE Trans. Biomed. Eng., vol. 31, pp.106-114.7.Paulsen K.D. , Strohbehn J.W. and Lynch D.R. (1985), ”Comparative theoretical performance for two types of regional hyperthermia system”, Int. J. Radiat. Oncol. Biol. Phys., vol.11, pp1659-1671.8.Sullivan D.M.,Borup D.T. and Gandhi O.P.(1987), ”Use of the finite-difference time-domain method in caculating EM absorption in human tissues” , IEEE Trans.Biomed.Eng. , vol.BME-34, pp148-157.9.Paulsen K.D. , Strohbehn J.W. and Lynch D.R., (1988), ”Theoretical electric field distributions produced by three types of regional hyperthermia devices in a three-dimensional homogeneous model of man”, IEEE Trans. Biomed. Eng., vol.35,pp36-pp45.10.Courant R.(1943), ”Variational methods for the solution of problems of equilibrium and vibrations”Bull. Am. Math. Soc. , Vol.49, pp.1-23.11. Paulsen K.D. , Strohbehn J.W. and Lynch D.R.(1985), ”Finite element solution of Maxwell’s equations for hyperthermia treatment planning”J.Comput.Phys., vol.58, pp.246-269.12. Paulsen K.D. , Strohbehn J.W. and Lynch D.R.(1986), ”Hybrid element method for unbounded electromagnetic problems in hyperthermia”Int.J.Num.Meth.Eng., vol.23, pp.1915-1937.13.Paulsen K.D., Strohbehn J.W. and Lynch D.R.(1988), ”Three-Dimensional Finite, boundary, and hybrid element solution of The Maxwell equations for lossy dielectric media” IEEE Trans. Microwave Theory Tech., vol.36, pp.682-693.14.Thiebaut C. and Lemonnier D.(2000) ”Three dimensional numerical solution of bio-heat transfer equation coupled to Maxwell’s equations in biological tissues during hyperthermia ”Boundary Elment Communications, vol.11 , no.4 , p33-38.15張持忠(1997) 應用電磁學, 全華科技, 台北市.16.Stratton J.A.(1941) Electromagnetic Theory, McGraw-Hill, New york.17.Griffiths D.J.(1999) Introduction to Electrodynamics, Prentice Hall, New Jersey.18.Leon S.J.(1998) Linear Algebra with Applications, Prentice Hall, New Jersey.19.Matthew N.O. and Sadiku (2000) Numerical Techniques in Electromagnetics, CRC, New york.20.BECKER E.B.,Carey G.F. and Oden J.T.(1981) Finite Elements An introduction volume I, Prentice-Hill, London.21.Logan D.L.(2002) A First Course in the Finite Element Method, Brooks/Cole, New york.22.Smith I.V. and Griffiths D.V.(1997) Programming The Finite Element Method , Wiley, New york.23.Gray W.G.(1984) “On normal flow boundary conditions in finite element codes for two-dimensional shallow water flow”, Int.J.Numer.Meth.Fluids, vol.4, pp.99-104.
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