扩散光学成像正向问题的求解分析研究 物理学专业VIP免费

摘要扩散光学成像技术被广泛应用于医学领域，它以近红外光作为光源进行探测，光通过组织并经历了吸收和散射作用，最终一部分光离开了组织体，人们通过对前后光学数据的研究对比，就能得到想要的功能信息。这种形式的成像技术与组织体内部的各种参数紧密相连，同时也是十分安全的，不会对组织体造成损伤，与其他的成像技术相比还有便携性、实时性等优势，因此受到了各界的关注，其价值也无法估量。扩散光学成像一般包含正向问题和逆向问题，本文针对其中的正向问题展开研究，用有限元法并根据扩散方程研究了相关的求解方法，在确定了边界条件和组织的光学参数后，针对简化的二维模型，得到了非均匀介质边界上的光学参数。为了验证实验数据的正确性，选择Monte—Carlo即MC方法在相同条件下进行数值模拟，并作了数值的对比。关键词：扩散光学成像，扩散方程，有限元，Monte-Carlo法AbstractDiffuseOpticaltomography（DOT）isusedwidelyinthefieldofmedicine.Itisdetectedbynearinfraredlightasthelightsource.Thelightexperiencesabsorptionandscatteringwhenthroughcelltissue,eventually,partofitwilltransferintodiffusedlightthenleavethebody.Peoplecanobtainthedesirablefunctionalinformationbycomparingthebeforeandafteropticaldata.Thiskindofimagingtechnologyisstronglyconnectedwithvariousparametersinsidethebody.AndDOTisalsoverysafebecauseitwillnotcausedamagetothebody.Comparedwithotherimagingtechniques,ithastheadvantagesofportability,real-timeandsoon.Therefore,ithasbeenwidespreadconcern,anditsvalueisalsoimmeasurable.Diffusionopticalimagingusuallycontainsforwardproblemandinverseproblem.Thispapertargetsattheforwardproblem.Andthefiniteelementmethod(FEM)basedonthediffusionequationisusedtostudytherelatedsolutionmethod.Aftertheboundaryconditionsandopticalparametersofthetissuearedetermined,aimingatthesimplifiedtwo-dimensionalmodel，theopticalparametersontheboundaryofinhomogeneousmediaareobtainedrespectively.Inordertoverifytheexperimentaldata,underthesameconditions，numericalsimulationisongoingbyMC（Monte–Carlo）methodandacomparisonalsohasbeenmade.Keywords:DiffuseOpticaltomography，diffusionequation，FEM，Monte-Carlo目录第一章概述............................................................11.1扩散光学成像的研究意义..............................................11.2实际应用举例........................................................11.2.1脑成像...........................................................11.2.2血氧检测.........................................................21.2.3癌症肿瘤诊断.....................................................21.2.4荧光分子层析成像.................................................21.3论文的结构安排......................................................2第二章扩散光学成像技术的正向问题........................................42.1扩散光..............................................................42.2扩散光学成像........................................................42.3扩散光学成像技术的正向问题..........................................4第三章求解正向问题.....................................................63.1求解方法............................................................63.1.1有限元法.........................................................63.1.2Monte-Carlo法...................................................83.2扩散方程...........................................................103.3边界条件...........................................................113.4实验方案...........................................................123.5实验结果...