Three-Dimensional Conformal Radiotherapy for Rectal Cancer and the Changes in Cancer Multi-bioma
3D MEDIC和3D SPACE磁共振神经成像在腰骶丛神经根的一致性对比研究
$$Feb.2021Vo . 42$No. 12021年 2月 第 42 卷$ 第 1 期首都医科大学学报Journal of Capital Medical Universi/[doi ： 10. 3969/j. issp. 1006-7795. 2021. 01. 022]・临床研究*3D MEDIC 和3D SPACE 磁共振神经成像在腰骶丛神经根的一 致性对比研究孙峥1!2孔超3鲁世保3陈海％笪宇威％张苗1>2卢洁心（1.首都医科大学宣武医院放射科，北京100053； 2.磁共振成像脑信息学北京市重点实验室，北京100053； 3.首都医科大学宣武医院骨科，北京100053； 4.首都医科大学宣武医院神经内科，北京100053）$摘要】 目的 验证三维多回波数据联合成像(three dimensional multi-echo data imagine combination with selective water excitation , 3D MEDIC WE)和三维快速自旋回波成像(three dimensional sampling peSection with application optimized contrasts byusing d/ferent Uip angle evelu/on , 3D SPACE STIR )序列在腰骶丛神经根成像中的可行性和重复性。
方法 将55例受试者分为腰椎无异常表现的正常对照组(20例)、单纯性腰椎间盘突出症(lumbar d/c hernm/on , LDH )组(20例)和慢性炎性脱髓鞘性多发性神经根神经病症(ch/nw inUamma"/ demyelinating polyradwuloneuropathy , CIBP )组(15例)，分别应用两种腰骶丛神经根成 像，评价图像质量参数信噪比(signal " noise ratio , SNR )、对比噪声比(contrast " noise ratio , CNR )和对比度(contrast ratio , CR )，并验证正常对照组、CBP 组和LDH 组测量神经根直径的一致性。
三维重建及虚拟手术规划在胸腔镜解剖性肺段切除术中的应用
•论著•中国现代医生2020年11月第58卷第32期三维重建及虚拟手术规划在胸腔镜解剖性肺段切除术屮的应用刘海涛王黎彬戚维波银杨帆施谷平张小航赵俊杰马兴杰浙江省嘉兴市第一医院嘉兴学院附属医院心胸外科，浙江嘉兴314000［摘要］目的探讨利用Deepinsinghl软件进行三维重建及虚拟手术规划在胸腔镜解剖性肺段切除术中的应用价值。
方法回顾性分析2018年1~12月我院行胸腔镜解剖性肺段切除术治疗的22例术前疑似早期肺癌患者的临床资料。
术前将胸部增强CT检查的断层二维图像信息以DICOM格式导入Deepinsinghl系统中进行三维重建及虚拟手术规划实施精准肺段切除。
观察指标:①术前三维重建及虚拟手术规划情况;②术中及术后情况。
③随访情况。
结果①术前三维重建及虚拟手术规划情况：22例患者术前均完成三维重建和虚拟手术规划;②术中及术后情况：22例患者均顺利行胸腔镜解剖性肺段切除术，无中转开胸。
22例患者手术时间为(115.05±27.54)min,术中出血量为(78.64±16.14)mL，术后拔管时间为(3.55±1.06)d,术后住院时间为(7.27±2.62)凿遥术后发生肺部感染2例，发生肺动脉栓塞1例，均经保守治疗后痊愈。
术后肿瘤TNM分期为：良性肿瘤1例,0期9例,IA期11例、IB期2例遥三维重建和虚拟手术规划评估肿瘤性质的准确率为95.5%(21/22)遥③随访情况:随访期间所有患者均未发生局部复发、远处转移及死亡情况。
结论应用三维重建及虚拟手术规划能实现精准肺段切除，可提高胸腔镜解剖性肺段切除术的准确性和安全性。
［关键词］肺部肿瘤；三维重建技术;虚拟手术规划技术;肺段切除术［中图分类号］R655.3［文献标识码］A［文章编号］1673-9701(2020)32-0004-04Application of three-dimensional reconstruction and virtual surgical planning in thoracoscopic anatomic lung segment resectionLIU Haitao WANG Libia QI Weibo YANG Fan SHI Guping ZHANG Xiaohang ZHAO Junjie MA XingjieDepartment of Cardiolhoracic Surgery,Jiaxing First Hospital in Zhejiang Province,Affilialed Hospital of Jiaxing University,Jiaxing314000,China［Abstract］Objective To explore the application value of three-dimensional reconstruction and virtual surgical planning using Deepinsinght software in thoracoscopic anatomic lung segment resection.Methods The clinical data of22patients with preoperative suspected early lung cancer who underwent thoracoscopic anatomic lung segment resection in our hospital from January to December2018were retrospectively analyzed.The two-dimensional tomography information of chest enhanced CT examination was imported into Deepinsinght system in DICOM format for3D reconstruction and virtual surgical planning for accurate lung segment resection.The observation index included:①preoperative three-dimensional reconstruction and virtual operation planning;于intraoperative and postoperative conditions;③follow-up situation.Results①Preoperative three-dimensional reconstruction and virtual operation planning:All the22 patients completed3D reconstruction and virtual operation planning before the operation.于Intraoperative and postoperative conditions:All the22patients underwent thoracoscopic anatomic lung segment resection successfully,without conversion to thoracotomy.The operative time of22patients was(115.05±27.54)min,the intraoperative blood loss was(78.64±16.14)mL,the postoperative extubation time was(3.55±1.06)d,and the postoperative hospital stay was(7.27±2.62)d.Postoperative pulmonary infection occurred in2cases and pulmonary embolism in1case,all of which were cured after conservative treatment.Postoperative tumor TNM stage was benign in1case,stage0in9cases,stage IA in11cases, and stage IB in2cases.The accuracy of3D reconstruction and virtual surgical planning in assessing the nature of the tumor was95.5%(21/22).③Follow-up:No local recurrence,distant metastasis,or death occurred during the follow-up period.Conclusion The application of3D reconstruction and virtual surgical planning can achieve accurate lung segment resection and improve the accuracy and safety of thoracoscopic anatomic lung segment resection.［Key words］Lung tumor;Three-dimensional reconstruction technology;Virtual surgical planning technology;Lung segment resection［基金项目］浙江省医药卫生科技计划项目(2018KY796，2018KY800)▲通讯作者4CHINA MODERN DOCTOR Vol.58No.32November2020中国现代医生2020年11月第58卷第32期•论著窑近年来，肺癌的死亡率逐年上升，已居恶性肿瘤死亡之首［1-2］o随着低剂量螺旋CT广泛地应用于普查，早期肺癌越来越多地被发现。
211002142_微结构三维形貌无损检测的双波段显微干涉技术
综合评述2023年第43卷 第1期微结构三维形貌无损检测的双波段显微干涉技术霍霄，高志山*，袁群，郭珍艳，朱丹（南京理工大学 电子工程与光电技术学院，江苏 南京 210094）摘 要：功能型微结构具有调控光场或调控电子导通等功能，一般包含具有规则的几何形状，基于深度和线宽的比值，可以将其区分为高/低深宽比微结构。
目前对微结构的检测，多用有损检测中的扫描电镜（SEM ）剖面成像技术，而产线上迫切需要用于监测与改进制作工艺的无损检测技术。
本文系统总结了作者所在研究团队十余年在微结构三维形貌无损检测方面的低相干显微干涉技术进展，其中白光显微干涉仪用于超光滑表面、台阶、微光学元件、微机械元件等低深宽比微结构的三维形貌检测，近红外显微干涉仪用于硅基高深宽比微结构的三维形貌检测。
文章阐述了两波段显微干涉系统的关键技术与典型样品的检测实例，结果表明：白光显微干涉仪和近红外显微干涉仪是两种高精度的无损检测仪器，前者检测高深宽比小于等于4，后者检测高深宽比大于等于20的微结构三维形貌，数据结果是可信的。
显微干涉无损检测技术获取的三维形貌数据，将有效优化微结构的制造工艺，进一步提升有关器件的性能。
关键词：无损测量；显微干涉法；低相干；三维形貌；微纳器件中图分类号：TB9；TH741；O436.1 文献标识码：A 文章编号：1674-5795（2023）01-0070-11Dual-band microscopic interferometry for nondestructive testing ofthree-dimensional morphology of microstructuresHUO Xiao, GAO Zhishan *, YUAN Qun, GUO Zhenyan, ZHU Dan(Institute of Electronic Engineering and Optoelectronic Technology, Nanjing University of Science andTechnology, Nanjing 210094, China)Abstract: Functional microstructure has the function of regulating light field or electronic conduction, and generally contains regular geometric shapes. Based on the ratio of depth to line width, it can be divided into high/low-aspect-ratio microstructures. At present, the detection of the geometric characteristic parameters of the microstructure is mainly conducted by SEM, which belongs to the destructive detection. The production line urgently needs non-destructive testing technology to monitor and improve its manufactur‑ing process. This article systematically summarizes the progress made by the author's research team in the low-coherence microscopic-interference technology for nondestructive testing of three-dimensional (3D) morphology of microstructures in the past ten years. The white light microscopic interferometer is used to detect the 3D topography of ultra-smooth surfaces, steps, micro optical elements, mi‑cro mechanical elements and other low aspect ratio microstructures. A near-infrared micro interferometer is used to detect the 3D mor‑phology of silicon based high aspect ratio microstructures. In this paper, the key technologies of the two band microscopic interference doi ：10.11823/j.issn.1674-5795.2023.01.06收稿日期：2022-12-24；修回日期：2023-01-10基金项目：国家重点研发计划（2019YFB2005500）；国家自然科学基金（62175107，U1931120）；江苏省六大人才高峰项目（RJFW-019）；中国科学院光学系统先进制造技术重点实验室基金（KLOMT190201）；上海在线检测与控制技术重点实验室基金（ZX2021102）引用格式：霍霄，高志山，袁群，等.微结构三维形貌无损检测的双波段显微干涉技术［J ］. 计测技术，2023，43（1）：70-80.Citation ：HUO X ， GAO Z S ， YUAN Q ， et al. Dual-band microscopic interferometry for nondestructive testingof three-dimensional morphology of microstructures ［J ］. Metrology and measurement technology ， 2023， 43（1）：70-80.··70计测技术综合评述system and the tests of typical samples are described. The results show that white light micro interferometer and near-infrared micro in‑terferometer are two kinds of high-precision nondestructive testing instruments. They can detect the 3D morphology of the microstruc‑tures with aspect ratio ≤4, and ≥20, respectively. The 3D topography data obtained by the microscopic-interference nondestructive test‑ing technology will effectively promote the optimization of the manufacturing process of the microstructure and the further improvementof the performance of related devices.Key words: nondestructive measurement; microscopic interferometry; low coherence; three-dimensional topography; micro-nanodevice0 引言功能微结构器件是一种在深度方向（一维）与横向（二维）同时存在尺度在微米或亚微米量级的纹理组织结构，在空间上一般呈现三维分布。
高分辨率3D-SPACE在老年性前庭神经病诊断中的应用
〔中图分类号〕 Ｒ７６４ 〔文献标识码〕 Ａ 〔文章编号〕 １００５９２０２（２０２１）１４３００００４；ｄｏｉ：１０３９６９／ｊｉｓｓｎ１００５９２０２２０２１１４０２７
全球人口老龄化是目前的重要人口变化趋势， 前庭神经损伤在老年人中高发，６０岁以上有近 ５０％ 表现出某种形式的前庭生理损失。眩晕和失衡是居
ｕｓａｌｂｏｎｅｌｏｓｓ：ａｐｒｏｓｐｅｃｔｉｖｅｓｔｕｄｙ〔Ｊ〕．ＪＢｏｎｅＭｉｎｅｒａｌＲｅｓ，２０１０； １５（１０）：１９６５７３ １３ 白璧辉，谢兴文，李鼎鹏，等 我国近 ５年来骨质疏松症流行病 学研究现状〔Ｊ〕．中国骨质疏松杂志，２０１８；２４（２）：２５３８ １４ ＢｏｓｃｈｉｔｓｃｈＥＰ，ＤｕｒｃｈｓｃｈｌａｇＥ，ＤｉｍａｉＨＰＡｇｅｒｅｌａｔｅｄｐｒｅｖａｌｅｎｃｅｏｆ ｏｓｔｅｏｐｏｒｏｓｉｓａｎｄｆｒａｇｉｌｉｔｙｆｒａｃｔｕｒｅｓ：ｒｅａｌｗｏｒｌｄｄａｔａｆｒｏｍ ａｎａｕｓｔｒｉａｎ
ｍｅｎｏｐａｕｓｅａｎｄｏｓｔｅｏｐｏｒｏｓｉｓｃｌｉｎｉｃ〔Ｊ〕．Ｃｌｉｍａｃｔｅｒｉｃ，２０１７；２０（２）： １５７６３ １５ ＬｉＹ，ＨｕｉＭ，ＣｈａｎｇＸ，ｅｔａｌ．ＢＭＩｒｅｄｕｃｔｉｏｎａｎｄｖｉｔａｍｉｎＤ ｉｎｓｕｆｆｉ ｃｉｅｎｃｙｍｅｄｉａｔｅｄｏｓｔｅｏｐｏｒｏｓｉｓａｎｄｆｒａｇｉｌｉｔｙｆｒａｃｔｕｒｅｓｉｎｐａｔｉｅｎｔｓａｔｎｕ ｔｒｉｔｉｏｎａｌｒｉｓｋ：ａｃｒｏｓｓｓｅｃｔｉｏｎａｌｓｔｕｄｙ〔Ｊ〕．ＥｕｒＪＣｌｉｎＮｕｔｒ，２０１８；７２ （３）：４５５９ １６ Ｋｉｍ ＹＳ，ＨａｎＪＪ，ＬｅｅＪ，ｅｔａｌ．Ｔｈｅｃｏｒｒｅｌａｔｉｏｎｂｅｔｗｅｅｎｂｏｎｅｍｉｎｅｒａｌ ｄｅｎｓｉｔｙ／ｔｒａｂｅｃｕｌａｒｂｏｎｅｓｃｏｒｅａｎｄ ｂｏｄｙｍａｓｓｉｎｄｅｘ，ｈｅｉｇｈｔ，ａｎｄ ｗｅｉｇｈｔ〔Ｊ〕．Ｏｓｔｅｏｐｏｒｏｓ Ｓａｒｃｏｐｅｎｉａ，２０１７；３（２）：Ｓ２４０５５２ ５５１６３００８９９． １７ 刘婷婷，李晓丹，王文志，等 ＢＭＣ／体重指标评价骨质疏松的探 索〔Ｊ〕．中国骨质疏松杂志，２０１７；２３（１０）：１２６１７ １８ Ｒａｄａｋ，Ｔｉｍ ＬＣａｌｏｒｉｃｒｅｓｔｒｉｃｔｉｏｎａｎｄｃａｌｃｉｕｍ′ｓｅｆｆｅｃｔｏｎｂｏｎｅｍｅ ｔａｂｏｌｉｓｍ ａｎｄｂｏｄｙｃｏｍｐｏｓｉｔｉｏｎｉｎｏｖｅｒｗｅｉｇｈｔａｎｄｏｂｅｓｅｐｒｅｍｅｎｏｐａ ｕｓａｌｗｏｍｅｎ〔Ｊ〕．ＮｕｔｒＲｅｖ，２０１０；６２（１２）：４６８８１ １９ ＮａｋａｍｕｒａＹ，ＳｕｚｕｋｉＴ，ＫａｍｉｍｕｒａＭ，ｅｔａｌ．ＶｉｔａｍｉｎＤ ａｎｄｃａｌｃｉｕｍ ａｒｅｒｅｑｕｉｒｅｄａｔｔｈｅｔｉｍｅｏｆｄｅｎｏｓｕｍａｂａｄｍｉｎｉｓｔｒａｔｉｏｎｄｕｒｉｎｇｏｓｔｅｏｐｏ ｒｏｓｉｓｔｒｅａｔｍｅｎｔ〔Ｊ〕．ＢｏｎｅＲｅｓ，２０１７；５（４）：１７０２１ ２０ 罗鹏飞，潘晓群，苏健，等 社区骨质疏松症超声骨密度筛查及 其影响因素分析〔Ｊ〕．中国骨质疏松杂志，２０１７；２３（１１）：１５１２７．
三维带图 焦永昌 一种有效的天线三维辐射方向图计算方法
第23卷 第2期2008年4月电 波 科 学 学 报CH INESE JO URNAL OF RADIO SCIENCEVol.23,N o.2April,2008m E -ma il:ychjiao@x 229文章编号 1005-0388(2008)02-0229-06一种有效的天线三维辐射方向图计算方法*焦永昌m文 园张福顺(西安电子科技大学,天线与微波技术国家重点实验室,陕西西安710071)摘要提出了一种根据已知的天线E 面和H 面方向图计算天线的三维辐射方向图的近似算法。
以全向和定向天线为例,仿真比较了此算法和两种已有算法计算得到的天线三维辐射方向图与理论结果之间的误差。
结果表明,该算法误差较小,可以有效地计算天线的三维辐射方向图。
根据生成的三维辐射方向图,计算了天线的方向性系数,所得结果与理论值吻合良好。
关键词 天线;三维辐射方向图;算法;方向性系数中图分类号 TN820 文献标志码 AAn efficient algorithm for calculating three -dimensionalradiation patterns of antennasJIAO Yong -chang WEN Yuan ZHANG Fu -shun(N ational L abor ator y of A ntennas and M icr ow av e T echnology ,X idian Univer sity ,X i c an S haanx i 710071,China)Abstract This paper presents an approx imatio n alg orithm fo r calculating the thr ee -dim ensional (3D)radiatio n patterns of antennas based on their H -plane and E -plane patterns.By using the proposed algo rithm,the 3D radiation patterns of the omn-i dir ectional antenna and the directional antenna are calculated,and the absolute er -rors o f the obtained results from the theoretical patterns ar e then co mpar ed w ith those prov ided by o ther techniques.T he com parison results indicate that the pro -po sed algo rithm exhibits low appro ximation erro rs,w hich can be used to calculat -ing the 3D r adiation patterns of antennas efficiently.According to the g eneratedthree -dimensional radiatio n patterns,the directivities o f the antennas ar e also calcu -lated,w hich are in g ood agr eement w ith the theo retical values.Key words antenna;thr ee -dimensio nal radiation patterns;algo rithm;dir ectiv ity1 引 言随着现代移动通信网络的发展,基站数目增多,蜂窝网覆盖范围减小,基站到用户的辐射角不能笼统地近似为零度,仅仅了解水平面和垂直面辐射特性已不能满足设计需求,因此需要对天线在全空间的辐射特性进行描述。
肝细胞肝癌放射治疗研究进展
肝细胞肝癌放射治疗研究进展姆尼热·阿卜力米提，谭 遥，伊斯刊达尔·阿布力米提ＡｄｖａｎｃｅｓｉｎｒａｄｉｏｔｈｅｒａｐｙｆｏｒｈｅｐａｔｏｃｅｌｌｕｌａｒｃａｒｃｉｎｏｍａＭｕｎｉｒｅ·Ａｂｕｌｉｍｉｔｉ，ＴＡＮＹａｏ，Ｙｉｓｉｋａｎｄａｅｒ·ＡｂｕｌｉｍｉｔｉＤｅｐａｒｔｍｅｎｔｏｆＴｈｏｒａｃｉｃａｎｄＡｂｄｏｍｉｎａｌＲａｄｉｏｔｈｅｒａｐｙ，ＡｆｆｉｌｉａｔｅｄＴｕｍｏｒＨｏｓｐｉｔａｌｏｆＸｉｎｊｉａｎｇＭｅｄｉｃａｌＵｎｉｖｅｒｓｉｔｙ，ＸｉｎｊｉａｎｇＵｒｕｍｑｉ８３００１１，Ｃｈｉｎａ．【Ａｂｓｔｒａｃｔ】Ｈｅｐａｔｏｃｅｌｌｕｌａｒｃａｒｃｉｎｏｍａ（ＨＣＣ）ｉｓｏｎｅｏｆｔｈｅｌｅａｄｉｎｇｃａｕｓｅｓｏｆｃａｎｃｅｒｄｅａｔｈｗｏｒｌｄｗｉｄｅ．Ｌｉｖｅｒｒｅｓｅｃｔｉｏｎｉｓａｎｉｍｐｏｒｔａｎｔｔｒｅａｔｍｅｎｔｏｐｔｉｏｎ，ｂｕｔｍａｎｙｈｅｐａｔｏｃｅｌｌｕｌａｒｃａｒｃｉｎｏｍａｐａｔｉｅｎｔｓｃａｎｎｏｔｕｎｄｅｒｇｏｐａｒｔｉａｌｈｅｐａｔｅｃｔｏｍｙｏｒｌｉｖｅｒｔｒａｎｓｐｌａｎｔａｔｉｏｎｄｕｅｔｏｔｕｍｏｒｓｔａｇｅｌａｔｅｏｒｃｈｒｏｎｉｃｌｉｖｅｒｄｉｓｅａｓｅａｎｄ／ｏｒｃｉｒｒｈｏｓｉｓ．Ｆｏｒｐａｔｉｅｎｔｓｗｈｏｃａｎｎｏｔｏｒｒｅｆｕｓｅｔｏｓｕｒｇｅｒｙ，ｔｒａｎｓａｒｔｅｒｉａｌｃｈｅｍｏｅｍｂｏｌｉｚａｔｉｏｎ，ｒａｄｉｏｆｒｅｑｕｅｎｃｙａｂｌａｔｉｏｎ，ｒａｄｉｏｔｈｅｒａｐｙ，ｔａｒｇｅｔｅｄｔｈｅｒａｐｙａｎｄｉｍｍｕｎｏｔｈｅｒａｐｙａｒｅｏｐｔｉｏｎａｌ．ＴｈｅｐｒｏｇｒｅｓｓｉｎｔｈｅｄｉａｇｎｏｓｉｓａｎｄｔｒｅａｔｍｅｎｔｏｆＨＣＣａｄｖａｎｃｅｓｉｎｔｈｅｂｉｏｌｏｇｉｃａｌｕｎｄｅｒｓｔａｎｄｉｎｇｏｆｌｉｖｅｒ－ｒａｄｉａｔｉｏｎｔｏｌｅｒａｎｃｅｓａｎｄｒａｄｉｏｔｈｅｒａｐｙｔｅｃｈｎｏｌｏｇｙｈａｖｅｍａｄｅｔｈｅｅｆｆｅｃｔｉｖｅｎｅｓｓａｎｄｓａｆｅｔｙｏｆｒａｄｉｏｔｈｅｒａｐｙｆｏｒＨＣＣｉｍｐｒｏｖｅｄａｎｄｔｈｅｓｕｒｖｉｖａｌａｎｄｐｒｏｇｎｏｓｉｓｏｆＨＣＣｐａｔｉｅｎｔｓａｒｅｉｍｐｒｏｖｉｎｇ．【Ｋｅｙｗｏｒｄｓ】ｈｅｐａｔｏｃｅｌｌｕｌａｒｃａｒｃｉｎｏｍａ，ｒａｄｉｏｔｈｅｒａｐｙ，ｐｏｒｔａｌｖｅｉｎｔｕｍｏｒｔｈｒｏｍｂｕｓＭｏｄｅｒｎＯｎｃｏｌｏｇｙ２０２１，２９（１０）：１８１７－１８２１【指示性摘要】肝细胞肝癌（ｈｅｐａｔｏｃｅｌｌｕｌａｒｃａｒｃｉｎｏｍａ，ＨＣＣ）是世界范围内癌症死亡率较高的肿瘤之一。
磁共振在乳腺癌新辅助治疗疗效评估与预测中的应用进展
磁共振在乳腺癌新辅助治疗疗效评估与预测中的应用进展田力文1，2，王翠艳21 山东大学齐鲁医学院，济南250012；2 山东省立医院医学影像科摘要：新辅助治疗（NAT ）是乳腺癌综合治疗的重要组成部分。
目前，NAT 疗效评估的金标准是组织病理学，但其需要术后标本，存在明显滞后性。
准确评估和预测NAT 疗效对及时改进治疗方案、确定精准的手术计划具有重要价值。
已有多种影像学检查方法被用于乳腺癌NAT 疗效评估与预测，其中磁共振（MR ）检查因其优越的软组织分辨力和多方位、多参数成像特点，成为准确性最高的影像学手段。
传统MR 成像可从肿瘤长径、体积和退缩模式等形态学改变来评估与预测NAT 疗效。
近年来随着MR 功能成像技术不断更新迭代，动态对比增强磁共振成像、扩散加权成像及体素内不相干运动扩散加权成像、酰胺质子转移成像、磁共振波谱成像等MR 功能成像从不同维度实现了对乳腺癌NAT 疗效的早期预测，进一步提高了MR 成像对NAT 疗效的早期预测能力。
关键词：乳腺癌；新辅助治疗；磁共振成像doi ：10.3969/j.issn.1002-266X.2023.13.022中图分类号：R737.9 文献标志码：A 文章编号：1002-266X （2023）13-0087-05世界卫生组织国际癌症研究机构发布的2020年全球最新癌症负担数据显示，乳腺癌已超过肺癌成为全球新发病例最多的恶性肿瘤。
国家癌症中心公布的最新数据显示，2022年我国女性乳腺癌的发基金项目：山东省医学会乳腺疾病科研基金（YXH2020ZX068）。
通信作者：王翠艳（E -mail ： wcyzhang@ ）［9］SHAN S ， ZHU W ， ZHANG G ， et al. Video -urodynamics efficacyof sacral neuromodulation for neurogenic bladder guided by three -dimensional imaging CT and C -arm fluoroscopy ： a single -center prospective study ［J ］. Sci Rep ， 2022，12（1）：16306.［10］王磊，宋奇翔，许成，等.计算机辅助设计3D 打印在骶神经调控术中的应用［J ］.第二军医大学学报，2019，40（11）：1203-1207.［11］ZHANG J ， ZHANG P ， WU L ， et al. Application of an individu⁃alized and reassemblable 3D printing navigation template for accu⁃rate puncture during sacral neuromodulation ［J ］. Neurourol Uro⁃dyn ， 2018，37（8）：2776-2781.［12］BRUNS N ， KRETTEK C. 3D -printing in trauma surgery ： Plan⁃ning ， printing and processing ［J ］. Unfallchirurg ， 2019，122（4）：270-277.［13］GU Y ， LV T ， JIANG C ， et al. Neuromodulation of the pudendalnerve assisted by 3D printed ： A new method of neuromodulation for lower urinary tract dysfunction ［J ］. Front Neurosci ， 2021，15：619672.［14］WANG Q ， GUO W ， LIU Y ， et al. Application of a 3D -printednavigation mold in puncture drainage for brainstem hemorrhage ［J ］. J Surg Res ， 2020，245：99-106.［15］WOO S H ， SUNG M J ， PARK K S ， et al. Three -dimensional -printing technology in hip and pelvic surgery ： Current landscape［J ］. Hip Pelvis ， 2020，32（1）：1-10.［16］CAVALCANTI KUBMAUL A ， GREINER A ， KAMMERLAND⁃ER C ， et al. Biomechanical comparison of minimally invasive treatment options for type C unstable fractures of the pelvic ring［J ］. Orthop Traumatol Surg Res ， 2020，106（1）：127-133.［17］廖正俭，刘宇清，何炳蔚，等.多模态影像融合结合3D 打印技术在大脑镰旁脑膜瘤切除术中的初步应用［J ］.宁夏医学杂志，2020，42（6）：499-501.［18］HU Y ， MODAT M ， GIBSON E ， et al. Weakly -supervised convo⁃lutional neural networks for multimodal image registration ［J ］. Med Image Anal ， 2018，49：1-13.［19］CONDINO S ， CARBONE M ， PIAZZA R ， et al. Perceptual limitsof optical see -through visors for augmented reality guidance of man⁃ual tasks ［J ］. IEEE Trans Biomed Eng ， 2020，67（2）：411-419.［20］SUN R ， ALDUNATE R G ， SOSNOFF J J. The validity of amixed reality -based automated functional mobility assessment ［J ］. Sensors （Basel ）， 2019，19（9）：2183.［21］COOLEN B ， BEEK P J ， GEERSE D J ， et al. Avoiding 3DObstacles in mixed reality ： Does it differ from negotiating real obstacles ［J ］ Sensors （Basel ）， 2020，20（4）：1095.［22］NIAZI A U ， CHIN K J ， JIN R ， et al. Real -time ultrasound -guidedspinal anesthesia using the SonixGPS ultrasound guidance sys⁃tem ： a feasibility study ［J ］. Acta Anaesthesiol Scand ， 2014，58（7）：875-881.［23］WARNAT -HERRESTHAL S ， SCHULTZE H ， SHASTRY K L ，et al. Swarm learning for decentralized and confidential clinical machine learning ［J ］. Nature ， 2021，594（7862）：265-270.［24］PRICE W N 2ND ， COHEN I G. Privacy in the age of medical bigdata ［J ］. Nat Med ， 2019，25（1）：37-43.（收稿日期：2023-02-24）开放科学（资源服务）标识码（OSID ）87病率约为29.05/10万，是女性发病率最高的恶性肿瘤。
Three-dimensional Simulation of Fretting Crack Nucleation and Growth
Three-dimensional simulation of fretting crack nucleation and growthB.J.Carter a ,b ,⇑,E.C.Schenck c ,P.A.Wawrzynek a ,b ,A.R.Ingraffea b ,K.W.Barlow da Fracture Analysis Consultants,Inc.,121Eastern Heights Drive,Ithaca,NY 14850,USAbCornell Fracture Group,Room 643Rhodes Hall,Cornell University,Ithaca,NY 14851,USAc Impact Technologies,LLC,200Canal View Blvd.,Rochester,NY 14623,USAd Naval Air Systems Command,Propulsion and Power Engineering,NAVAIR,22195Elmer Road,Building 106,Patuxent River,MD 20670,USA a r t i c le i nf o Article history:Received 27December 2011Received in revised form 20July 2012Accepted 15August 2012Keywords:Fretting Finite element analyses Crack growthLife predictionMetalsa b s t r a c tFretting nucleation models and three-dimensional finite element analyses are used to com-pute the fretting fatigue life for metallic components.The models predict crack nucleationcycles and location(s).Discrete crack growth simulations provide stress intensity factorhistories,with multiple,non-planar,three-dimensional cracks possible.The histories areinput into crack growth rate model(s)to compute propagation cycles.The sum of frettingnucleation plus propagation cycles is the total life.Experimental fretting data,includingcrack nucleation location and cycles,and crack growth trajectory and propagation cycles,are used to validate the approach.Predictions for a realistic turbine blade/disk are compa-rable to field observations.Ó2012Elsevier Ltd.All rights reserved.1.IntroductionFretting fatigue can be a controlling factor in the life of some aircraft engine components,such as turbine blade/disk assemblies [1,2].Fretting also occurs at threaded joints [3,4],in gears and shafts [5,6],and in wheel/axle assemblies [7]–essentially wherever two parts are in forced-contact and subject to cyclic loading with the occurrence of limited slip be-tween the two parts.The analysis of fretting in turbine engines can be rather complicated due to the loading and temper-ature variations,complex component geometry,anisotropic material properties,residual stress,and non-trivial crack geometry,which might include multiple,interacting/branching,non-planar cracks.Although engine components are de-signed to minimize fretting fatigue [8,9],it often still occurs,leading to possible premature or catastrophic failure due to fret-ting induced discrete crack nucleation and growth.A growing number of technical journal articles are devoted to fretting fatigue,and in particular,to the development and validation of fretting fatigue crack nucleation models [4,6,10–18].Typically,fretting nucleation models are based on exper-imental observations and analytical,semi-analytical or finite element predictions of the contact stress and/or strain near the edge of contact (EOC).These nucleation models generally predict the number of cycles to nucleate a crack,and some also predict the location and orientation of the initial crack.The EOC is typically a region of high stress (and strain)and a common site for fretting crack nucleation.Closed-form solu-tions for the stress in the contact region have been developed for some simple cases,such as sphere-on-flat or cylinder-on-flat geometries [19].Approximate numerical techniques,such as singular integral equations [20,21]or finite element (FE)methods [7,14,22]are used when closed-form solutions are not possible or practical.FE modeling of the contact region re-quires non-linear solution strategies,special elements or constraints on the contact surface,and a sufficiently refined mesh to capture the potentially singular stresses at the EOC.0013-7944/$-see front matter Ó2012Elsevier Ltd.All rights reserved./10.1016/j.engfracmech.2012.08.015⇑Corresponding author at:Fracture Analysis Consultants,Inc.,121Eastern Heights Drive,Ithaca,NY 14850,USA.E-mail address:bjc21@ (B.J.Carter).Various stress-and strain-based fatigue models have been used quite successfully to predict fretting fatigue crack nucle-ation cycles and crack location [11–14];the critical plane versions of these models also predict the initial crack orientation.Lykins et al.[23]evaluated a number of these models using experimental data,and then proposed a new model that uses the critical plane shear stress amplitude [13].This new model has been used successfully to compute the number of cycles to nucleation as well as the location and orientation of the initial crack in experiments.Another model is based on an equivalent stress parameter [12,24];this model does not provide crack orientation,but has been used successfully to predict the crack nucleation location and nucleation cycles.These stress-and strain-based models are often found to be conservative as they under-predict the number of cycles to nucleation.Moreover,they lack a length scale.To account for these issues,averaging over a small distance or volume can be performed [4,25,26];this concept can be related to the nonlinear process zone at a crack front.Borrowing further from frac-ture mechanics,another class of fretting nucleation models,called notch-or crack-analog models [4,15–18,27],have been developed.The various analog models differ primarily in the handling of friction,slip and geometry effects.The analog model developed by Ahmad and Santhosh [16]avoids some of these issues by computing the nucleation parameter under bonded conditions.Fretting crack nucleation generally leads to discrete crack growth.Typically,the crack growth is divided into two stages[18,28];the first stage is inclined growth from the surface near the EOC,driven by shear stress on the contact surface,and the second stage is growth that is roughly perpendicular to the contact surface and dominated by the bulk tensile stress.Studies of fretting crack nucleation and propagation have been performed using analytical and FE techniques [12,29–33].Mostly,these analyses have been limited to two-dimensions (2D)or constrained to simplified three-dimensional (3D)planar,semi-elliptical cracks.A typical crack growth simulation starts from an initial crack;thus,the initial nucleated crack size must be defined.Dur-ing laboratory testing,fretting nucleation cycles are counted until a crack is nucleated,after which crack propagation cycles are counted.The sum of the two represents the total fretting fatigue life of the component.Lykins et al.[13]defined the ini-tial crack size based on typical eddy-current detection limits (760Â380l m),and then computed nucleation and propaga-tion lives by counting striations on fracture surfaces.Golden and Calcaterra [34]define the initial crack to be 25Â125l m,based on fractographic analyses.Navarro et al.[35,36]developed a model that does not require a strict definition of the ini-tial crack size;instead the initial crack size is determined from the combination of the nucleation and propagation rates.By combining the fretting fatigue crack nucleation cycles with discrete crack growth cycles,an analyst can predict the total life of a component that is subject to fretting fatigue.From the authors’perspective,a shortcoming of the above studies has been the simplified fracture mechanics and crack growth analyses that have been performed (either 2D or simplified 3D crack shapes).One exception to this is the work of Pierres et al.[37]who used the extended finite element method (XFEM)to simulate 3D cracking observed during a sphere-on-plate fretting fatigue test.This paper describes a new approach for simulating,in 3D,both fretting nucleation and discrete crack propagation using standard finite element analysis capabilities of ANSYS [38]and FRANC3D [39].The combined software allows an analyst to use one or more of the available fretting nucleation models to predict fretting crack nucleation cycles as well as location and orientation of the initial crack(s).Subsequent discrete 3D crack growth simulations can then be performed to compute stress intensity factor (SIF)histories,which are used to determine crack propagation cycles.Nomenclaturer eq equivalent stress fretting model parameter c critcritical shear stress fretting model parameter C critSmith–Watson–Topper fretting model parameter QRAI’s crack analog fretting model parameter N inumber of load cycles for fretting crack nucleation Pnormal load on fretting test specimen S maxmaximum tangential load on fretting test specimen S minminimum tangential load on fretting test specimen EOCEdge of contact LELeading edge of contact TETrailing edge of contact da /dNCrack growth per cycle K minminimum Mode I stress intensity factor K maxmaximum Mode I stress intensity factor K effeffective Mode I stress intensity factor K ththreshold Mode I stress intensity factor Rratio of K min /K maxSIF stress intensity factor448 B.J.Carter et al./Engineering Fracture Mechanics 96(2012)447–460The fretting nucleation,crack growth,fatigue life models and the software are briefly described in the next section.The software and simulation approach are validated using experimental andfield data obtained from the literature,as described in Section3,while Section4discusses the stochastic nature of this data and the range of numerical predictions provided by the models and the software.2.Fretting fatigue analysis methodology2.1.Analysis softwareFretting fatigue can be simulated using standard FE analysis capabilities.For instance,ANSYS[38]is widely used in indus-try to perform stress analyses of turbine engine components,and includes capabilities for modeling contact between mating parts.The FE analysis provides the displacement,stress,strain and contact information.These results along with the FE mod-el itself are passed along to FRANC3D[39]for fretting and discrete crack analysis.In addition to discrete crack growth capa-bilities,FRANC3D now includes fretting fatigue crack nucleation models,which are used to predict the fretting cycles and the initial crack geometry,specifically the size,location and possibly orientation of the crack(s).2.2.Fretting crack nucleationTo observe and measure fretting fatigue,simple coupon-type testing is often conducted.A typical fretting test consists of a specimen and pads as shown in Fig.1.A constant normal load(P)is applied to the fretting pads,and then the specimen is subjected to a cyclic axial load(S max–S min),which produces shear between the specimen and the pad.Fretting crack nucle-ation occurs after a sufficient number of load cycles.The usual result of such fretting fatigue experiments is a plot,similar to Fig.2,where the number of cycles to crack nucle-ation is plotted against a fretting parameter,f p.The data is typicallyfit to an equation of the form:f p¼aN bi þcN dið1ÞFig.1.Schematic of a typical fretting fatigue experiment.Fig.2.Typical fretting fatigue experimental test data(adapted from[40]).B.J.Carter et al./Engineering Fracture Mechanics96(2012)447–460449The equivalent stress model is defined by:req¼0:5ðD r psuÞwðr maxÞ1Àwð2Þwhere D r psu and r max are functions of the nodal stress components and w is a material dependentfitting parameter.Based on curvefitting of experimental data,the equation,in the form of(1):r eq¼aN bi þcN dið3Þrelates r eq to N i,where coefficients a–d are material dependentfitting parameters.For example,for Ti–6Al–4V,a=52476, b=À0.6471,c=450.85and d=À0.03582[24].The critical plane shear stress amplitude model is defined by:ccrit¼s max=Gð1ÀR sÞmð4Þwhere s max is the maximum shear stress on the critical plane,R s is the shear stress ratio,G is the shear modulus and m is a material dependentfitting parameter.Substituting c crit for r eq in Eq.(3),one can compute N i given the appropriate values for the coefficients a–d.For Ti–6Al–4V,a=6.46,b=À0.686,c=4.65Â10À3and d=1.22Â10À2[40].The critical plane Smith–Watson–Topper model is defined by:C crit¼r maxðD e=2Þ¼ðr2f=EÞð2N iÞ2bþe fð2N iÞbþcð5Þwhere r max is the maximum principal stress and D e represents the normal strain amplitude on the critical plane;this equa-tion is already in the form of Eq.(3).E is the elastic modulus,r f and e f are material strength parameters,and b and c arefitting parameters.For Ti–6Al–4V,r f=376.6MPa,b=1.78Â10À4,c=À0.767and e f=32.4[40].The crack analog model is quite different from the above three models.First,the fretting parameter(Q)is only computed at the nodes along the EOC.Second,the FE analysis must be conducted with bonded contact conditions rather than the stan-dard contact(that allows for slip and requires a coefficient of friction).Q can be related to J II from linear elastic fracture mechanics[16]:Q¼ðJIIE=ð1Àv2ÞÞ1=2ð6Þwhere m is Poisson’s ratio.N i is computed from:log N i¼ðaÀD QÞ=bð7Þwhere a and b are material dependentfitting parameters.D Q=Q maxÀQ min,is determined from the maximum and minimum load cycles.An uncracked FE model along with displacement,stress,strain and contact status results is used to compute fretting nucleation.Contact surfaces are automatically determined from the FE model data and the contact status,and the EOC then is determined from the boundary of the contact surfaces.The analyst can choose one(or more)of the four fretting nucleation models described above to compute N i and the initial crack location(and possibly the initial crack orientation).For every FE node on the contact surface,the nodal displacement vector along with the stress and strain tensors are extracted from the imported analysis results.These results are processed to determine the value of the chosen fretting model parameter and the corresponding N i.Crack nucleation is predicted to occur at the location where N i is the minimum.Note that the N i versus f p curvefit is based on experimental data,where cycles are counted until crack nucleation occurs. This implies that a nucleation crack size is pre-defined,and crack growth simulations can start from this initial crack size.2.3.Fretting crack propagationDiscrete crack propagation starts from the initial fretting crack.A small portion of a FE model can be extracted from a full model and imported into FRANC3D,where crack nucleation and growth is performed.The cracked and remeshed sub-model is recombined with the rest of the model and then analyzed;this means that the solution includes all the relevant boundary conditions and accounts for any load path changes as the crack grows.The process is illustrated in Fig.3using a mini-turbine disk test specimen[41];a small portion of the disk is extracted,cracked,remeshed and then recombined with the full model for analysis.The mesh facets and nodes on the cut-surface are retained to maintain compatibility with the full model.A fretting fatigue analysis is complicated by the contact conditions,multiple load cases,and multiple material regions. Typically,a crack is inserted within or near the edge of original contact surface in one of the regions.The contact surface is automatically redefined after crack insertion and after each step of crack growth because the surface-mesh adjacent to the crack mouth changes.In addition,contact conditions on the crack surface are automatically generated if the analysis re-quires it,which occurs if the minimum load case(S min)is negative and causes crack closure.At each step of crack growth,the cracked local portion is joined with the global portion of the model and a full FE stress analysis is performed.The simulation ultimately produces a series of crack fronts and associated SIFs along the fronts.A SIF history is extracted by following a path that intersects successive crack fronts.This SIF history is required to compute crack propagation cycles as described in the next section.450 B.J.Carter et al./Engineering Fracture Mechanics96(2012)447–4602.4.Fretting fatigue lifeThe fatigue life of a component that is subject to fretting is the sum of the fretting nucleation cycles plus the crack prop-agation cycles.The fretting nucleation cycles are computed from the chosen fretting nucleation model (see Section 2.2).The discrete crack propagation cycles are computed based on the SIF history and a crack growth rate model.Several crack growth rate models are available,including the Paris [42],NASGRO [43]and AFRL [34]ing the selected growth rate model,SIF history and appropriate material dependent data,the propagation cycles are computed and then added to the fret-ting nucleation cycles to determine the total life.3.Fretting fatigue simulation resultsThe analysis approach and software described in Section 2is used to simulate fretting fatigue in both test specimen and actual turbine-engine parts.A typical fretting test specimen is simulated first to validate the fretting nucleation models and the software implementation.A second fretting test specimen,which more closely resembles turbine-engine blade/disk con-nections,is simulated next to validate the fretting nucleation models,the discrete crack growth and the total fatigue life computations.The third model represents actual turbine-engine blade/disk geometry and provides additional validation.3.1.Analysis of dog-bone specimensThe software described in Section 2is used to compute fretting crack nucleation cycles and locations in standard fretting coupon tests of dog-bone specimens with round indenters [13,23].A sketch of the fretting test specimen and pad is shown in Fig.4.The leading EOC (LE)and trailing EOC (TE)are shown to help locate the crack nucleation site(s).A 3D FE model of the fretting specimen and pad is built using ANSYS,taking advantage of symmetry through the spec-imen thickness so that only one fretting pad is modeled.A sample of five of Lykins’fifty test cases are analyzed here;all use the same geometry and the same normal load (P )but with varying S max and S min ,Table 1.The loads are applied using three load cases.First,P is applied (see Fig.1),and then held constant at 1.3kN.Second,S max is applied to the fretting specimen (see Fig.1).The final load case ramps the axial stress down from S max to S min .Q max and Q min values in Table 1are the measured tangential reaction forces on the fretting pad.The fretting specimen and pad are both Ti–6Al–4V;the elastic modulus is 126.1GPa,Poisson’s ratio is 0.34,and the coefficient of friction on the contact surface is set to 0.5.For each test case,Lykins calculated values for the c crit and C crit fretting models.Although Lykins does not provide pre-dicted N i values for each specimen and nucleation model,he does report a ±3N i scatter between experimental and predicted nucleation cycles,for the lower range of N i values.The predicted N i values fall within these bounds,and are similar to Lykins’experimental (exp)results for N i as shown in Tables 2and 3.The last column in Tables 2and 3show the ratio between the predicted and experimental N i values;all values are within ±3N i .Fig.5shows the C crit color contours on the contact surface for specimen #10.A crack nucleation site is predicted at the TE near the free surface of the specimen for both the c crit and C crit models;this matches the location observed in the experi-ments [40].Fig.3.FRANC3D sub-modeling approach [39].3.2.Analysis of dovetail test rigA more advanced fretting fatigue test rig has been designed [34,44],which provides a more realistic comparison to a tur-bine engine blade/disk dovetail contact.A sketch of the fretting test specimen and pads is shown in Fig.6with the lower EOC (LE)labeled to help locate the crack nucleation site(s);the loading grips are not shown.A 3D FE model of this test rig is built using ANSYS taking advantage of symmetry so that only half of the specimen and one fretting pad are modeled.The fretting surface is at a 45°orientation relative to the horizontal and vertical axes.The model isTable 1Applied loading for Lykins’dog-bone specimens [40].Specimen numberS max (MPa)S min (MPa)Q max (kN)Q min (kN)2699.643.90.498À0.3166424.635.20.547À0.44510528.7232.20.191À0.21411686.6455.80.4720.1218410.1273.20.4670.125Fig.4.Sketch of Lykins fretting specimen and pad [40]Table 2G crit nucleation model comparison –experimental versus predicted.Specimen number Lykins (experiment)Predictedc crit Difference (%)N i ratio c crit N i (exp)c crit N i 29.96e À3 2.84e41.01e À2 3.67e4À0.94 1.367.08e À38.27e40.71e À2 1.69e50.29 2.010 6.86e À3 2.36e50.64e À2 3.76e5 6.63 1.6117.37e À3 3.34e50.63e À2 4.93e515.1 1.518 5.27e À3 4.50e70.44e À2>1e917.1–Table 3SWT nucleation model comparison –experimental versus predicted.Specimen number Lykins (experiment)Predicted C crit Difference (%)N i ratio C crit N i (exp)C crit N i2 3.79 2.84e4 3.73 3.07e41.67 1.162.088.27e4 2.04 1.19e51.69 1.410 1.812.36e5 1.77 1.89e52.050.811 1.923.34e5 1.70 2.20e511.30.718 1.06 4.50e70.87>1e917.7–Fig.5.C crit Contour plot for specimen10;maximum value is1.77MPa.Fig.6.Sketch of dovetail fretting test[34,44].Table4Computed fretting nucleation parameters and cycles for dovetail test rig.(MPa)N ic crit0.011 2.71e4C crit 5.17 1.73e4r eq403 1.98e4analyzed using two load steps,representing S max and S min.The fretting specimen and pad are both Ti–6Al–4V;the elastic modulus is126.1GPa,Poisson’s ratio is0.3,and the coefficient of friction on the contact surfaces is set to0.3.Based on the16experiments,Golden and Calcaterra[34]have computed fretting fatigue crack nucleation lives between 5000and50,000cycles.The maximum value of the fretting parameters and the corresponding predicted N i are given in Table4;the nucleation cycles fall within the above range.Fig.7shows the r eq color contours.The LE is the typical site of crack nucleation in the experiments[34].The fretting nucleation models indicate different crack nucleation locations along this EOC.The C crit and r eq models predict crack nucleation near the left end of the LE while the c crit model predicts crack nucleation near the right end.Golden and Calcaterra[34]do not indicate a particular preferred crack nucleation site along the LE from the16tests,but have analyzed a surface elliptical crack at the specimen mid-thickness with a depth of25l m and length of125l m.3.2.1.Crack growth simulation for dovetail test rigA portion of the full ANSYS model was extracted for crack growth analysis,Fig.8.An initial elliptical surface crack with dimensions of0.125Â0.025mm is inserted into the model at mid-specimen thickness at the LE(Fig.9–left panel).This initial crack is propagated for several steps to get an initial SIF history.Then a0.25mm deep edge crack is inserted alongmaximum value is403MPa.Crack nucleation sites are predicted near the leftFig.8.FE model of dovetail fretting test rig with extracted sub-model.surface crack(left panel)and subsequent0.25mm deep edge crack(right panel)inthe entire length of the LE(Fig.9–right panel).This is done to simplify the subsequent crack growth simulation and to speed up the simulation as the ANSYS analysis for each crack growth step was taking up to8h.The initial edge crack is propagated for35steps at which point the crack front has almost reached the top of the specimen.The crack has grown to about12mm in length,as shown in the left panel of Fig.10.The observed surface trace of the crack from one of the tests is shown in the right panel of Fig.10.The observed crack is approximately10mm long and inclined18°from the normal to the contact surface.For the16tests,the observed angles varied from13°to18°[34].The simulated crack is not a planar surface,but the average inclination is about16°,which is in the observed range.The Mode I SIF (K Imax )history is shown in Fig 11.The SIF history is computed along a path through the mid-points of the crack fronts.The Mode I SIF values begin to decrease as the crack front approaches the top of the specimen.The crack growth cycles can be computed using the appropriate Ti–6Al–4V crack growth rate data and the (AFRL)equation [34]:da dN ¼0:0254e B K eff K th P ln K eff K th Q ln K eff K th d ð8Þwhere K eff ¼K max ð1ÀR Þm and R ¼K min =K max K th ,B ,P ,Q ,d and m are material dependent constants.The resulting crack growth cycles are shown in Fig.12.The loading is constant amplitude with R =0.1,and the stress intensity range is above threshold (4.2MPa m 1/2)for this material.The resulting number of discrete propagation cycles is approximately 2.46e5.The predicted number of fretting nucleation cycles ranges from 1.7e4to 2.7e4.Thus the predicted total number of cycles is between 2.63e5and 2.73e5.This is consistent with the observed number of cycles in the experi-ments,which ranged from 1e5to 1e6[34].This crack growth simulation was based on the maximum load.It was assumed that an R of 0.1would be sufficient to keep the crack open at all times and this simplified the numerical modeling effort as crack face contact did not have to be imposed.It was assumed that K Imin /K Imax would reflect this same R value.A more thorough analysis of the fatigue life and variation of K Imin /K Imax with crack length is beyond the scope of this paper.3.3.Analysis of turbine blade/disk dovetailAn ANSYS FE model of a single sector of a turbine blade/disk assembly is shown in Fig.13.The blade and disk material are both Ti–6Al–4V with an elastic modulus of 126.1GPa and Poisson’s ratio equal to 0.3.Loading consists of nodal temperatures and rotation,applied using five load steps.The load steps are defined at 50%,72%,110%,72%and 50%of nominal loading.The model has two sets of contact surfaces (pressure side and suction side)that must be considered during the fretting fatigue analysis.The coefficient of friction is set to 0.5for both contact surfaces.Fretting nucleation parameters are shown in Table 5,using load steps 3and 1as the maximum and minimum,respec-tively.The contour plot for the r eq parameter is shown in Fig.14.The three fretting nucleation models predict different crack panel)and observed (right panel –courtesy of Golden)crack path in dovetail 11.Mode I SIF (K Imax )history for a crack in the dovetail fretting test rigcycles for a crack in the dovetail fretting test rig model using the AFRL crack13.FE model of a single sector blade/disk assembly.Table5Computed fretting nucleation parameters and cycles for the blade/disk dovetail model.(MPa)N ic crit0.015 1.32e4C crit 2.089 5.11e4r eq403 1.98e4nucleation locations,as indicated in Fig.14.The maximum r eq is located near the corner of the pressure side and forward face of the blade on the upper EOC.Relatively high values of r eq also exist midway along the upper EOC on the suction side of the blade.The maximum c crit is located on the suction side of the blade on the upper EOC at the corner of the aft face.The maximum C crit value occurs in the disk rather than the blade,mid-way along the lower EOC on the suction side.3.3.1.Simulated discrete crackingDiscrete crack growth simulations are performed at two locations on the blade,the nucleation sites predicted by the r eq and c crit models.Crack growth from other locations on the blade and disk could be analyzed,but this is beyond the scope of this paper.As shown in Fig.14,the maximum r eq parameter is located on the blade,on the upper EOC,on the pressure side, near the forward face.A penny-shape(radius=0.2mm)surface crack is inserted at this location,Fig.15,and then propa-gated;this location will be referred to as PBU.。
软组织肉瘤的放射治疗
软组织肉瘤的放射治疗许宋锋;余子豪【摘要】软组织肉瘤（soft tissue sarcomas，STS）是起源于结缔组织的软组织恶性肿瘤，具有多种不同类型。
手术是STS主要治疗方法，放疗也是其重要的治疗方式并且是综合治疗早期选择之一。
对STS进行放疗已经超过50年历史，术前和术后放疗对于局部控制都有疗效，只是不良反应不同。
软组织肉瘤放疗技术包括远距离放疗（适形放疗、调强放疗、立体定向放疗等）、近距离放疗（组织间插植放疗、腔内后装放疗、术中放疗等）等。
放疗技术的进步，提高了放疗的精准性和确定性，降低了对病灶周围正常组织的损伤。
本文主要针对STS放疗技术以及适用原则进行综述。
%Soft tissue sarcomas (STS) consist of a heterogeneous group of rare malignancies with mesenchymal origin. Surgical resec-tion is the primary treatment for STS, but radiation therapy (RT) also plays an important role in the treatment. Radiotherapy for STS has advanced significantly over the past 50 years. Both preoperative and postoperative radiotherapies are equivalent in local control but are associated with different toxicity profiles. Boost techniques for STS include brachytherapy, intraoperative radiation therapy (IORT), and external beam. Long-term toxicities of RT to normal tissues have been reduced because of improvements in image guid-ance and intensity-modulated radiotherapy, which significantly increase the precision and delivery of RT. This review discusses RT tech-nologies and their acceptable treatment principles.【期刊名称】《中国肿瘤临床》【年(卷),期】2017(044)001【总页数】5页(P19-23)【关键词】软组织肉瘤;放疗;新辅助放疗;治疗原则【作者】许宋锋;余子豪【作者单位】国家癌症中心，中国医学科学院，北京协和医学院肿瘤医院骨科北京市100021;国家癌症中心，中国医学科学院，北京协和医学院肿瘤医院放疗科北京市100021【正文语种】中文余子豪，教授，主任医师，博士生导师，中国医学科学院肿瘤医院放疗科首席专家。
CT引导下射频消融治疗中晚期非小细胞肺癌的近期疗效观察_刘宝东
中国肺癌杂志2009年7月第12卷第7期Chin J Lung Cancer, July 2009, Vol.12, No.7·临床经验·CT 引导下射频消融治疗中晚期非小细胞肺癌的近期疗效观察刘宝东 支修益 刘磊 胡牧 王若天 许庆生 张毅 苏雷【摘要】 背景与目的 近年来，射频消融术（Radio-Frequency Ablation, RFA ）作为一种新的局部治疗手段运用于肺部肿瘤的治疗，取得了很好的临床效果。
本文探讨CT 引导下射频消融治疗中晚期肺癌的临床价值。
方法 对66例中晚期非小细胞肺癌的68个病灶（其中2例病人各治疗2个病灶）在三维重建CT 引导下进行射频消融治疗，观察近期疗效。
结果 66例病人经CT 引导下射频消融，即刻及1个月复查CT 提示病灶阴影增大，而64个病灶CT 值降低，占94.1%，4个病灶CT 值增加，占5.9%。
1个月复查SPECT 提示T/N 降低至正常值以下的患者占82.4%（56/68）。
治疗后3个月CT 扫描显示在68个肿瘤中，没有肿瘤完全消失（CR ）者，肿瘤缩小者（PR ）73.5%（50/68），肿瘤无变化者（SD ）2.9%（2/68），肿瘤增大者（PD ）8.8%（6/68），6例增大的病灶进行了第2次消融；3个月复查SPECT 提示T/N 降低至正常值以下的患者占79.4%（54/68）。
无严重并发症，无围手术期死亡。
结论 CT 引导下射频消融治疗中晚期非小细胞肺癌安全可行，近期疗效明显。
【关键词】 肺肿瘤；导管消融术；体层摄影术；X 线计算机【中图分类号】 R734.2 DOI:10.3779/j.issn.1009-3419.2009.07.006Evaluation of Three-Dimensional Reconstruction CT in Percutaneous RadiofrequencyAblation (RFA) of the Unresectable Lung Tumor with a Clustered ElectrodeBaodong LIU, Xiuyi ZHI, Lei LIU, Mu HU, Ruotian WANG, Qingsheng XU, Yi ZHANG, Lei SU Department of Thoracic Surgery, Xuanwu Hospital, Capital Medical University, Beijing 100053, ChinaCorresponding author: Baodong LIU, E-mail: ryouhoutou@【Abstract 】 Background and objective Radiofrequency ablation (RFA) of lung tumours has recently received much attention for the promising results achieved. Here, to evaluate the value of three-dimensional reconstruction CT in radiofrequen-cy ablation (RFA) of advanced non-small cell lung cancer. Methods Sixty-six cases of advanced non-small cell lung cancer with 68 lesions (2 patients had 2 lesion treated in one session) were underwent three-dimensional reconstruction CT-giuded percuta-neous RFA therapy. To evaluate short-term therapeutic effect of lung tumors using spiral CT scanning in 1-3 months after RFA to investigate the alterations of tumor size and density pre-and post-procedure, and complications, to observe the short-term cura-tive effect. Results Our experiences have shown an initial increase in lesion size at immediate follow-up CT. The density of 64 lesions was lowered (94.1%) and 4 lesion is increased (5.9%) at immediate and one month follow-up CT. SPECT scan findings that 82.4% (56/68) cases of FDG uptake in tumors after RFA with tumor/non-tumor of lower than 2.5 at one month follow-up. The change in treated lesion size over time, radiologically assessed through measurements of the lesions on axial CT scans in the lung window setting no lesions had complete response, 50 lesions (73.5%) had partial response, 2 lesions with stable disease, 6 lesions showed progressive disease at 3 month follow-up CT. SPECT scan findings that 79.4% (54/68) cases of FDG uptake in tumors after RFA with tumor/non-tumor of lower than 2.5 at 3 month follow-up. Conclusion The percutaneous RFA therapy under the guidance of three-dimensional reconstruction CT scan is safe and effective, with few complications, and can serve as a new method to the treatment of advanced non-small cell lung cancers.【Key words 】 Lung neoplasm; Catheter ablation; Tomography; X-ray computed目前肺癌最有效的治疗手段仍是外科手术，但是由于目前缺乏有效的早期诊断方法，70%以上的的肺癌病人就诊时已属晚期，失去了手术治疗的最佳时机。
三维有限元法分析腰椎不同尺寸关节突成形后相关节段的生物力学特征
5288｜中国组织工程研究｜第25卷｜第33期｜2021年11月三维有限元法分析腰椎不同尺寸关节突成形后相关节段的生物力学特征余 洋1，谢一舟1，石 银1，吴卫东2，顾党伟1，樊效鸿1文题释义：腰椎经皮内镜：与脊柱内窥镜类似，是一个配备有灯光的管子，它从患者身体侧方或者侧后方(可以平可以斜的方式)进入椎间孔，在安全工作三角区实施手术或通过患者后方从椎板间隙进行手术。
在椎间盘纤维环之外操作，在内窥镜直视下可以清楚看到突出的髓核、神经根、硬膜囊和增生的骨组织，然后使用各类抓钳摘除突出组织、镜下去除骨质、射频电极修复破损纤维环。
腰椎经皮内镜手术是同类手术中对患者创伤最小、效果最好的椎间盘突出微创疗法。
三维有限元：利用数学近似的方法对真实物理系统(几何和载荷工况)进行模拟，利用简单而又相互作用的元素(即单元)，就可以用有限数量的未知量去逼近无限未知量的真实系统。
摘要背景：腰椎经皮内镜在全国乃至全世界范围内开展的如火如荼，经椎间孔的侧入路是目前腰椎经皮内镜技术最常用的入路之一，但是对于其术后造成相关节段的生物力学影响鲜有报道。
目的：通过三维有限元法模拟对比不同尺寸(7.5，10，15 mm)的关节突成形并探究其对腰椎相关节段生物力学的影响。
方法：建立L 3-L 5三维有限元模型并验证其有效性。
模拟L 4/5腰椎经皮内镜手术中的关节突成形术，以临床上穿刺针与水平面及冠状面的夹角，以L 5上关节突基底部作为穿刺靶点，根据穿刺路径分别做直径为7.5，10，15 mm 的环锯环切成形，从而获得L 5上关节突基底部不同直径成形的三维有限元模型。
通过对正常模型、7.5，10，15 mm 直径成形有限元模型在6个方向上施加载荷，计算各模型在前屈、后伸、左屈、右屈、左旋、右旋6种状态下操作节段(L 4/5)及邻近节段(L 3/4)椎间盘Von Mises 应力极值和相关节段的活动度情况，并进行相关对比研究，以明确不同尺寸的关节突成形对腰椎生物力学稳定性的影响。
3D Ultrasonic
keyboard
T/R switch MUX variable gain
body array
ADC
display
All digital
Based on the 2D Fourier transform of the transmit and receive radiation patterns.
Based on the theoretical estimations of the 2D Fourier transform of the transmit and receive radiation patterns. The analysis of these estimations allows for the development of the algorithms based on the 3D fast Fourier transform. A theory for developing 3D dynamic focusing algorithms as well as providing results about their mathematical and physical experiments. These algorithms can be efficiently implemented in modern fast signal processing devices.
Advantages
Three-dimensional ultrasound equipment can be one-tenth the cost of CT or MRI machines and does not require specially built facilities for radiation protection.
呼吸门控技术在胸部肿瘤放射治疗中的研究进展
【指示性摘要】随着三维适型、调强、容积旋转等技术的发展，靶区剂量的适型度越来越高。但是由于人体器 官的自身运动及充盈状态的变化，会引起靶区位置的变化。呼吸动度对胸部肿瘤放疗的影响目前是放疗界 研究的热点，临床中控制呼吸 动 度 的 技 术 主 要 为 呼 吸 门 控 技 术，包 括 主 动 呼 吸 门 控 技 术 和 被 动 呼 吸 门 控 技 术，本文将详细介绍目前常用的应用于胸部肿瘤放疗过程中的呼吸控制技术，同时探讨呼吸门控技术的未来 发展方向。 【关键词】呼吸门控；胸部肿瘤；技术；放疗；呼吸动度 【中图分类号】Ｒ７３０．５ 【文献标识码】Ａ ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１６７２－４９９２．２０１９．１２．０４５ 【文章编号】１６７２－４９９２－（２０１９）１２－２２１１－０４
ＣｈｅｎＢｏ１，ＹａｎｇＹｉｐｉｎｇ２
１Ｘｉ＇ａｎＭｅｄｉｃａｌＵｎｉｖｅｒｓｉｔｙ，ＳｈａａｎｘｉＸｉ＇ａｎ７１００２１，Ｃｈｉｎａ；２ＳｈａａｎｘｉＰｒｏｖｉｎｃｉａｌＣａｎｃｅｒＨｏｓｐｉｔａｌ，ＳｈａａｎｘｉＸｉ＇ａｎ７１００６１，Ｃｈｉｎａ． 【Ａｂｓｔｒａｃｔ】Ｗｉｔｈｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｒａｄｉｏｔｈｅｒａｐｙｔｅｃｈｎｏｌｏｇｉｅｓｓｕｃｈａｓｔｈｒｅｅ－ｄｉｍｅｎｓｉｏｎａｌｃｏｎｆｏｒｍａｌｒａｄｉａｔｉｏｎｔｈｅｒａ ｐｙ，ｉｎｔｅｎｓｉｔｙｍｏｄｕｌａｔｅｄｒａｄｉｏｔｈｅｒａｐｙａｎｄｖｏｌｕｍｅｒｏｔａｔｉｏｎ，ｔｈｅａｄａｐｔａｂｉｌｉｔｙｏｆｔａｒｇｅｔｄｏｓｅｓｉｓｇｅｔｔｉｎｇｂｅｔｔｅｒ．Ｈｏｗｅｖｅｒ， ｄｕｅｔｏｔｈｅｍｏｖｅｍｅｎｔａｎｄｆｉｌｌｉｎｇｓｔａｔｅｏｆｈｕｍａｎｏｒｇａｎｓ，ｍｏｖｅｍｅｎｔｉｎｔｈｅｔａｒｇｅｔａｒｅａｍａｙｉｎｃｒｅａｓｅ．Ｔｈｅｅｆｆｅｃｔｏｆｒｅｓｐｉｒａ ｔｏｒｙｍｏｔｉｏｎｏｎｔｈｅｒａｄｉｏｔｈｅｒａｐｙｏｆｔｈｏｒａｃｉｃｔｕｍｏｒｓｉｓｃｕｒｒｅｎｔｌｙａｈｏｔｔｏｐｉｃｉｎｒａｄｉｏｔｈｅｒａｐｙｒｅｓｅａｒｃｈ．Ｔｈｅｔｅｃｈｎｉｑｕｅｓｆｏｒ ｃｏｎｔｒｏｌｌｉｎｇｒｅｓｐｉｒａｔｏｒｙｍｏｔｉｌｉｔｙｉｎｃｌｉｎｉｃａｌｐｒａｃｔｉｃｅａｒｅｒｅｓｐｉｒａｔｏｒｙｇａｔｉｎｇｔｅｃｈｎｉｑｕｅｓ，ｉｎｃｌｕｄｉｎｇａｃｔｉｖｅｒｅｓｐｉｒａｔｏｒｙｇａｔｉｎｇ ａｎｄｐａｓｓｉｖｅｒｅｓｐｉｒａｔｏｒｙｇａｔｉｎｇｔｅｃｈｎｉｑｕｅｓ．Ｔｈｉｓａｒｔｉｃｌｅｉｎｔｒｏｄｕｃｅｄｔｈｅｃｏｍｍｏｎｌｙｕｓｅｄｒｅｓｐｉｒａｔｏｒｙｃｏｎｔｒｏｌｔｅｃｈｎｏｌｏｇｙ ｎｏｗａｄａｙｓ，ａｎｄｄｉｓｃｕｓｓｅｄｔｈｅｆｕｔｕｒｅｄｅｖｅｌｏｐｍｅｎｔｄｉｒｅｃｔｉｏｎｏｆｔｈｅｒｅｓｐｉｒａｔｏｒｙｇａｔｉｎｇｔｅｃｈｎｏｌｏｇｙ． 【Ｋｅｙｗｏｒｄｓ】ｒｅｓｐｉｒａｔｏｒｙｇａｔｉｎｇ，ｔｈｏｒａｃｉｃｎｅｏｐｌａｓｍｓ，ｔｅｃｈｎｉｑｕｅ，ｒａｄｉｏｔｈｅｒａｐｙ，ｂｒｅａｔｈｉｎｇｄｙｎａｍｉｃｓ ＭｏｄｅｒｎＯｎｃｏｌｏｇｙ２０１９，２７（１２）：２２１１－２２１４
胸椎转移瘤3D-CRT与IMRT治疗技术比较
胸椎转移瘤3D-CRT与IMRT治疗技术比较徐敏仙，欧晋,周弘达(湘南学院附属医院肿瘤科，湖南郴州423000)摘要：目的探讨同一靶区三维适形(3D-CRT)与静态调强(IMRT)技术在胸椎转移瘤放射治疗计划的剂量学参数和治疗时间的差异，为临床选择放射治疗方案提供参考。
方法选择20例进行放射治疗的胸椎转移瘤患者，分别设计IMRT计划和3D-CRT计划。
比较靶区和危及器官在两种计划下的剂量学参数以及单次治疗时间。
结果IM-RT计划的靶区剂量学指标适形指数(CI)、均匀指数(HI)、最小剂量(D込)都优于3D-CRT计划(P<0.05)；IMRT计划中危及器官心脏及全肺的平均剂量(。
”锂)、最大剂量(D唤)均优于3D-CRT计划(P<0.05)。
IMRT计划的单次治疗时间为(3.30±0.87)min,3D-CRT的单次治疗时间为(1.20±0.24)min,3D-CRT计划的单次治疗时间短于IMRT计划(P <0.05)。
结论胸椎转移瘤患者放射治疗计划的剂量学参数上IMRT技术优于3D-CRT技术，但是单次治疗时间上长于3D-CRT技术。
对该类患者在这两种放射治疗技术的选择上应综合考虑,个体化治疗。
关键词:胸椎;转移性骨肿瘤;三维适形放射治疗;调强放射治疗;静态中图分类号:R730.5文献标志码:A文章编号:1673-498X(2021)01-0038-04doi：10.16500/ki.l673-498x.2021.01.010乳腺癌、前列腺癌和肺癌等癌症在中、晚期经常会转移到骨组织,并且很大部分会转移到骨盆及脊椎骨⑷。
肿瘤一旦侵犯骨头就会导致骨组织的破坏，甚至还会引起病理性的骨折或者脊髓压迫,从而严重影响患者的生存质量。
据相关报道，放射治疗能够迅速缓解骨转移瘤患者的疼痛，因此临床上发生骨转移的患者多建议采用放射治疗来进行姑息止痛⑵o三维适形(three-dimensional conformal radiation therapy,3D -CRT)和静态调强(intensity modulated radiation therapy,IMRT)这两种放射治疗技术在国内外广为开展,骨转移瘤的治疗基本以这两种方法为主。
Baresch2012
Three-dimensional Acoustic Radiation Force on an Arbitrary Located Elastic SphereDiego BARESCH,Jean-Louis Thomas,R´e gisMarchianoTo cite this version:Diego BARESCH,Jean-Louis Thomas,R´e gis Marchiano.Three-dimensional Acoustic Radia-tion Force on an Arbitrary Located Elastic Sphere.Soci´e t´e Fran¸c aise d’Acoustique.Acoustics 2012,Apr2012,Nantes,France.<hal-00810890>HAL Id:hal-00810890https://hal.archives-ouvertes.fr/hal-00810890Submitted on23Apr2012HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents,whether they are pub-lished or not.The documents may come from teaching and research institutions in France or abroad,or from public or private research centers.L’archive ouverte pluridisciplinaire HAL,est destin´e e au d´e pˆo t et`a la diffusion de documents scientifiques de niveau recherche,publi´e s ou non,´e manant des´e tablissements d’enseignement et de recherche fran¸c ais ou´e trangers,des laboratoires publics ou priv´e s.Three-dimensional Acoustic Radiation Force on anArbitrary Located Elastic SphereD.Baresch a ,J.-L.Thomas a and R.Marchiano baUPMC-INSP (UMR 7588)/IJLRDA(UMR 7190),4,Place Jussieu,Cedex 05-boite courrier840,75252Paris,FrancebUPMC/CNRS,Institut Jean Le Rond D’Alembert -UMR CNRS 7190,Universit´e Pierre etMarie Curie -4place Jussieu,75005Paris,Francediego.baresch@upmc.frProceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, FranceAn analytical model for the radiation forces acting on an elastic sphere placed in an arbitrary acoustic wavefield is proposed.It provides an expression of the axial and transverse forces without any prescription on the sphere’s material,radius or location.To illustrate the capabilities and the generality of the model,we selected a Bessel vortex beam as the incident wavefield.Acoustic vortex refers to a type of beam having an helicoidal wavefront. Such a wavefront is due to a screw type phase singularity,hence the beam has a central dark core of zero amplitude surrounded by a high intensity ring.Wefind that an azimuthal force component appears and is capable of rotating the sphere around the propagation axis.This confirms the transfer of orbital angular momentum from the beam to the sphere.Furthermore,axial forces may turn negative when appropriate parameters are selected and yield a dragging force towards the source of the beam acting as a Tractor Beam.In addition to extending the understanding of the nature of acoustic radiation forces,numerical results provide an impetus for further designing acoustic tweezers for potential applications in particle entrapment and non-contact manipulation.1IntroductionNon-contact manipulation of particles has many current and potential applications[1].Pioneer works established the acceleration and entrapment of particles under radiation pres-sure in light beams[2].Since then accurate particle manipu-lations have been demonstrated with”optical tweezers”ca-pable of handling with precision particles ranging from the nanometric to the micrometric scale[3].Recent research has been concentrated on single-beam particle manipulation in the wavefield of a tightly focused transducer[4,5,6]and is revealing the ability of ultrasonic beams to accomplish similar tasks.Due to the acoustic nature of the beam,the dimensions of the particles of interest and the corresponding forces increase.Acoustic beams also of-fer high penetrability in organic tissues and large impedance contrasts with numerous materials.In this manner,”acoustic tweezers”become advantageous and offer extended applica-tions to optical devices.The precison of optical tweezers comes from complex light interference patterns.In order to trap and then rotate particles,optical vortices were used in early experiments. These light beams are known to carry orbital angular mo-mentum that can be imparted to the particle[7].Further-more,the central dark core of this vortex structure provides an entrapment region where the optic or acoustic intensity is minimum.In acoustics,the analogue vortex beams were syn-thesized with an array of piezoelectric elements in the linear and non-linear regimes[9,10,11].Theoretical investigations of the radiation pressure forces exerted by acoustic beams on spherical particles have only led to the prediction of the axial force when the sphere is on the propagation axis[4,12].When the radius of the sphere is much less than the acoustic wavelength,some effort has been made to evaluate the transverse forces for a sphere displaced from the axis of an acoustic vortex[13].In this paper we present a theoretical model to predict the acoustic radiation forces acting on an elastic sphere in an in-viscidfluid.The choice of the beam is completely arbitrary and no restrictions are made on the sphere’s dimension,ma-terial or location.Since the sphere is allowed to be shifted from the beam axis,our model can predict the axial but also the transverse forces both necessary to completely describe the sphere’s dynamics under acoustic radiation forces.We apply this analysis to the case of a helicoidal Bessel beam capable of exerting axial,radial and azimuthal forces on an elastic sphere.This analysis should be helpful for potential applications that include particle entrapment and manipula-tion with single acoustic beams.2Method2.1Radiation Forces on a sphere in an arbi-trary beamThe forces that allow trapping and manipulation of par-ticles in acoustic beams result from the transfer of pseudo linear and sometimes pseudo-angular momentum from the beam to the particle.The particle alters theflux of momen-tum or angular momentum carried by the beam through scat-tering.The incidentfield is supposed to propagate in an in-viscidfluid.We neglect effects due to thermo-viscosity andthe amplitude of emission is weak enough to discard non-linear effects on the propagation.To evaluate the radiation pressure,the scatteredfield hasto be determined.The natural choice of coordinate systemfor the scattering problem is spherical coordinates(r,θ,ϕ) centered on the sphere(Fig.1).For now,we can write the incidentfield as the superposition of spherical wave func-tionsΦm n,each of which is solution of the Helmholtz equa-tion in spherical coordinates when the harmonic(e−iωt)time convention is adopted:(Δ+k20)Φm n(r,θ,ϕ)=0(1) TheΦm n functions build a natural discrete basis of the prob-lem.Therefore the incident velocity potentialφi can be writ-ten[14]:φi=φ0∞n=0nm=−nA m nΦm n,φi=φ0∞n=0nm=−nA m n j n(k0r)Y m n(θ,ϕ).(2)Whereφ0is the real amplitude,k0is the wavenumber re-lated to the angular frequency and to the phase velocity byk0=ω/c0,Y m n=P m n(cosθ)e imϕare complex spherical har-monics(of degree n and order m)and A m n are the expansioncoefficients for the incidentfield.The incident wave-field being physicallyfinite at the origin,the radial dependency is described by the spherical Bessel function j n(k0r)and the spherical Neumann functions y n(k0r)are discarded due to their singularity at r=0.The P m n functions are the asso-ciated Legendre polynomials.In addition,the scattered velocity potential may be ex-pressed as:φs=φ0∞n=0nm=−nA m n R m n h(1)n(k0r)Y m n(θ,ϕ)(3)Where h(1)n(k0r)=j n(k0r)+iy n(k0r)is the spherical Hankel function of thefirst kind(that respects Sommerfeld’s radi-Proceedings of the Acoustics 2012 Nantes Conference23-27 April 2012, Nantes, Franceation condition when r →∞).As detailed in [15],an ar-bitrarily shaped beam requires a more general approach to the scattering problem in comparison to the case of an inci-dent plane wave.Anyways,it was proved that the scattering coe fficients keep the same expression after applying specific boundary conditions on the surface of the scatterer.We can write :R m n ≡R n =αn +i βn (4)R n are the complex scattering coe fficients for each partialspherical wave and are independent from m .These classic coe fficients are known for a large variety of spheres under plane wave illumination [16,17]and only depend on the ex-citation frequency,the elastic constants of the sphere and the density of the surroundingmedium.Figure 1:Geometry of the radiation force problem.The sphere is illuminated by an acoustic helicoidal Bessel beam.The reference frame (x ,y ,z )and the spherical coordinate system (r ,θ,ϕ)are centered on the elastic sphere.The incidence direction of the Bessel beam is described by thehalf-cone angle β.The radiation force acting on the particle altering the flux of momentum is obtained by integrating the excess of pres-sure p over the oscillating surface of the particle S (t ).It is defined as an averaged quantity,noted . ,over the period T =2π/ωof the incident field oscillations :F=S (t )p dS (5)Again detailed in [15],some alternatives exist to over-come di fficulties owed to integration over a moving bound-ary.The acoustic pressure p is calculated up to the secondorder :p =−ρ0∂φ∂t −ρ0( ∇φ)22+ρ02c 20 ∂φ∂t 2(6)Where φis the superposition of the incident and scatteredfields [φ=(φi +φs )e −i ωt ].Rather fastidious calculations that combine Eqs.(2),(3),(4),(5)and (6)lead to the final ex-pression (7)for the three components of the radiation forcevector Fin the Cartesian basis centered on the sphere. and are the real and imaginary parts respectively and (∗)designs complex conjugation.2.2Incident BeamWe emphasize that the derivation is so far general and expression (7)can be applied to any incident field havinga representation in the spherical basis.However,an impor-tant step consists in computing the spherical decomposition of the incident field to obtain the A m n coe fficients in Eq.(2).They can be obtained numerically using local approxima-tions of the beam in the spherical basis [18].To minimize numerical errors,it is preferable to use analytical solutions of the decomposition.Several wave fields possess analytical expressions for their decomposition coe fficients.A helicoidal Bessel beam is an example of an acoustic vortex.In cylindrical coordinates (ρ,ϕ,z )(Fig.1),the spa-tial part of the complex acoustic velocity potential may be written for a Bessel beam as follows:φ(ρ,ϕ,z )=φ0J m (κρ)e i (m ϕ+k z z )(8)J m is the Bessel function of order m .Sometimes referred to the topological charge [8],m is an integer whose sign defines the handedness of the wavefront rotation and its magnitude determines the pitch of the helix.κand k z are the radial and axial wave numbers respectively,related by the usual disper-sion relation κ2+k 2z=(ω/c 0)2.An exact expression of a Bessel beam in the spherical basis centered on the sphere ex-ists [19]:A m n =in −m(2n +1)(n −m )!(n +m )!P mn(cos β)(9)Where in this case β=arcsin(κ/k 0)has the geometric inter-pretation of a conic angle (between the wavevector k0and the propagation axis in Fig.1)in which the Bessel beam is expanded in terms of partial plane waves [20].On Fig.2we represented the Bessel beam intensity profile in the (x ,y )and (y ,z )planes.They are obtained from the summation in Eq.(2)numerically truncated up to N max =40.As can be seen,this beam has a multi-ringed intensity profile that arises from the radial variation of the Bessel function J m (κρ).As for any sep-arated variable solution of the Helmholtz equation,the beam is invariant along the propagation axis O z .When the sphere is located on the beam axis,the trans-verse forces F x and F y vanish by symmetry.To study ra-dial and sometimes azimuthal forces,the sphere must be dis-placed o ffthe beam axis.In that case,there is no longer ana-lytical expressions for the expansion coe fficients A m n .Fortu-nately,the analytical transformation of spherical wave func-tions are known under translation or rotation of the initial coordinate system [21,22].Thus,from the decomposition of the beam in the initial basis it is possible to calculate the new coe fficients A m n in a rotated or translated basis centered on the sphere.That is equivalent to displacing the sphere.3Results and DiscussionsWe will now present some numerical results for the ra-diation force calculation.The procedure is as follows :first we calculate the scattering coe fficients R n for a given sphere.They are known for a large variety of materials and depend of the radius of the sphere a ,density ρ ,longitudinal wave speed c L and transverse wave speed c T .Then Eq.(7)is ap-plied for di fferent positions of the sphere to obtain the radial,azimuthal and axial forces calculated in a cylindrical refer-ence frame (F ρ,F ϕ,F z ).We have paid attention in using nu-merical values corresponding to typical experimental cases,the incident medium is taken to be water having a density ρ0=1000kg /m 3and the speed of sound is c 0=1500m /s.Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, FranceF x =−0202∞ n =0 |m |<n Q m n(V m n {A m n A m +1∗n +1}− {A m n A m −1∗n +1})D 1n −(V m n {A m n A m +1∗n +1}− {A m n A m −1∗n +1})D 2nF y =−πρ0φ202∞ n =0 |m |<n Q m n−(V m n {A m n A m +1∗n +1}+ {A m n A m −1∗n +1})D 1n −(V m n {A m n A m +1∗n +1}+ {A m n A m −1∗n +1})D 2nF z=−πρ0φ202∞ n =0 |m |<n2(n +m +1)Q m n {A m n A m ∗n +1}D 2n − {A m n A m ∗n +1}D 1n(7)where D 1n =αn +αn +1+2(αn αn +1+βn βn +1),D 2n =βn +1−βn +2(βn +1αn −αn +1βn )And Q m n =2(n +m )!(2n +1)(2n +3)(n −m )!,V m n =(n +m +1)(n +m +2)z/λ−10−50510105510x /λy /λ−505−505Figure 2:Intensity profiles of the incident Bessel Beam in the (y ,z )and (x ,y )planes.Lengths are in units of theacoustic wavelength λThe incident wave has a pressure amplitude P 0=0.1MPa and the driving frequency is f =1MHz.Under these condi-tions,the wavelength is λ=1.5mm.3.1Axial force on spheres in a Bessel BeamFirst we will present examples of the axial force calcula-tion F z .The incident wave field is a Bessel beam having a half-cone angle β=40◦and a topological charge m =1.In Fig.3we show the axial force as a function of the di-mensionless radius a /λof two di fferent spheres.It is clear from the comparison with a rigid sphere (typically the case of aluminum)that when elasticity is taken into account (ny-lon case)the force exhibits intense peaks.Those resonances in the a dependency of the scattering coe fficients R n are as-sociated to weakly damped waves guided by the surface of the sphere [12].The resonance peaks are strongly dependent on the topological charge m and the half-cone angle β(data not shown).In Fig.4,for three di fferent values of the half-cone angle βwe depict theaxial force F z for a polystyrene sphere as aFigure 3:Axial force (Newtons)exerted by a Bessel beam with topological charge m =1on Nylon and Aluminum spheres as a function of the dimensionless radius a .function of its radius,a .It shows that for β=60◦and 70◦there is a region for a where F z <0:0.34λ≤a ≤0.39λand 0.28λ≤a ≤0.32λrespectively.That means that the force is directed towards the source of the beam.In [12]similar calculations had predicted this unexpected negative axial ra-diation force for elastic,rigid and liquid spheres on the axis of Bessel beams.Nevertheless,the potential application that consists in using Bessel beams as Tractor beams relies on both negative axial forces and the transverse stability of the sphere that is stillunexplored.Figure 4:Axial force (Newtons)exerted by a Bessel beam with topological charge m =1on a polystyrene sphere as a function of the dimensionless radius a .Three di fferentvalues of the parameter βare selected.Proceedings of the Acoustics 2012 Nantes Conference23-27 April 2012, Nantes, France3.2Transverse forces on a sphereFigure5shows the radial force Fρas a function of the distance of displacementρfor selected parameters that corre-spond to the negative extrema in the dashed and dotted curves in Fig.4:(a,β)=(0.35λ,60◦)and(a,β)=(0.32λ,70◦).A radial equilibrium position is obtained when both Fρ(ρ)=0 and the slope is negative since for any displacement of the sphere an opposite force appears.Forβ=70◦,we see that the sphere is not trapped in the core of the vortex so it will not be dragged up the propagation axis.The only equilib-rium position in this case is located at a distanceρ=0.48λ. Contrarily,forβ=60◦,we see that the sphere can be trapped and maintained in the central core,meanwhile it is dragged towards the source because of the negative axial force(F z=−21.5nN).Figure6shows that an azimuthal force also appears in the transverse plane.The sphere will start spinning around the beam axis due to the azimuthal forces.This confirms the transfer of pseudo-angular momentum from the beam to the sphere.Figure5:Radial force(Newtons)exerted by a Bessel beam with topological charge m=1on a polystyrene sphere with parametersβ=60◦and a=0,35λ(dashed curve).The dottedcurve is forβ=70◦and a=0.32λ.Both cases correspondtothe negative extrema in Fig.4.Figure6:Azimuthal force(Newtons)same sphere and beamparameters than in Fig.5.As expected,the transverse behavior will also depend on the sphere’s material.In that matter,for a radius a=0.3λand a beam parameterβ=40◦,a polystyrene sphere will be urged away from the beam core(Fig.7)meanwhile the aluminum sphere will strongly be attracted towards the prop-agation axis(Fig.8).This is in agreement with King’s ini-tial work on radiation forces on spheres in a standing plane waves[23].He had predicted that light spheres(in compari-son to the density of the propagation medium)were attracted to pressure anti-nodes and dense spheres to pressure nodes. In fact,the Bessel beam intensity profile(Fig.2)can be un-derstood to have a collection of nodes and anti-nodes in the radial direction.1.5−1−0.500.51 1.51.510.50.511.5Figure7:Transverse stability of a polystyrene sphere(with a=0.3λ)in thefield of a Bessel beam with topological charge m=1.The2D grey-scale represents the beam’sintensity profile.1.5−1−0.500.51 1.51.510.50.511.5Figure8:Transverse stability of an aluminum sphere(with a=0.3λin thefield of a Bessel beam with topologicalcharge m=1.4ConclusionIn this work,we derived an expression for the three di-mensional radiation force on a sphere in an inviscidfluid.To our knowledge,for thefirst time in acoustics it is possible to analyze the axial and transverse stability of an arbitrarily located sphere.There is no restrictions on the sphere’s di-mension or material.Eq.(7)is sufficiently general and can be applied to any incident wavefield that can be expanded in the spherical basis centered on the sphere.We remind that all complications owed to thermo-viscosity were neglectedProceedings of the Acoustics 2012 Nantes Conference23-27 April 2012, Nantes, Francein this work and consequent errors may arise when the ra-dius of the sphere is not much larger than the thickness of the thermal-viscous boundary layer[24].However,for many potential applications these effects are negligible.In order to illustrate our model,we concentrated our ef-forts on calculating the trapping efficiency of incident heli-coidal Bessel beams.It was shown that important peaks in the axial force arise when an elastic nylon sphere was con-sidered.As it was initially observed in[12],for specific high values of theβparameter a surprising reversal of the axial force may lead to beams that can pull the sphere towards the acoustic source.Here we proved that situations with nega-tive F z are not systematically associated to a radial attracting force towards the propagation axis.This last condition is re-quired in order to investigate the potential use of a Bessel beam as a tractor beam.The spheres can rotate around the beam axis due to the transfer of orbital angular momentum through scattering by a the sphere off-axis.We proposed a general model that should be helpful to elaborate acoustic devices for non-contact manipulation of small objects.”Acoustic tweezers”have promising applica-tions in small particle entrapment and manipulation includ-ing in vivo applications.References[1]A.Ashkin,“History of optical trapping and manipula-tion of small-neutral particle,atoms,and molecules”, IEEE Quant.Elec.6,841–856(2000).[2]A.Ashkin,“Acceleration and trapping of particles byradiation pressure”,Phys.Rev.Lett.24,156(1970). [3]D.G.Grier,“A revolution in optical manipulation”,Na-ture424,810–816(2003).[4]X.Chen and R.Apfel,“Radiation force on a sphericalobject in thefield of a focused cylindrical transducer”, J.Acoust.Soc.Am.101,2443–2447(1996).[5]J.Lee,S.Teh,A.Lee,H.H.Kim,C.Lee,and K.K.Shung,“Single beam acoustic trapping”,App.Phys.Lett.95,1–3(2009).[6]J.Lee and K.Shung,“Radiation forces exerted on ar-bitrarily located sphere by acoustic tweezer”,J.Acoust.Soc.Am.120,1084–1094(2006).[7]M.Padgett,S.Barnett,and R.Loudon,“The angularmomentum of light inside a dielectric”,J.Mod.Opt50, 1555–1562(2003).[8]J.-L.Thomas,T.Brunet,and F.Coulouvrat,“General-ization of helicoidal beams for short pulses”,Phys.Rev.E..81,1–14(2010).[9]J.-L.Thomas and R.Marchiano,“Pseudo angular mo-mentum and topological charge conservation for non-linear acoustical vortices”,Phys.Rev.Lett.91,1–4 (2003).[10]J.-L.Thomas and R.Marchiano,“Synthesis and anal-ysis of linear and nonlinear acoustical vortices”,Phys.Rev.E.71,1–11(2005).[11]R.Marchiano and J.-L.Thomas,“Doing arithmeticwith nonlinear acoustic vortices”,Phys.Rev.L.101,1–4(2008).[12]P.Marston,“Radiation force of a helicoidal besselbeam on a sphere”,J.Acoust.Soc.Am.120,3539–3547(2009).[13]S.Kang and C.Yeh,“Potential-well model in acoustictweezers”,IEEE Ultrasonics57,1451–1459(2010). [14]D.Blackstock,Fundamentals of physical acoustics,chapter10(John Wiley&Sons,New York)(2000). [15]D.Baresch,J-L.Thomas,and R.Marchiano,“Three-dimensional acoustic radiation force on an arbitrarilylocated elastic sphere”,J.Acoust.Soc.Am.(SubmittedDecember2012).[16]J.Faran,“Sound scattering by solid cylinders andspheres”,J.Acoust.Soc.Am.23,405–418(1951).[17]P.Epstein and R.Carhart,“The absorption of soundin suspensions and emulsions.i.water fog in air.”,J.Acoust.Soc.Am.25,553–565(1953).[18]G.Gouesbet,J.Lock,and G.Grehan,“Generalizedlorenz mie theories and description of electromagneticarbitrary shaped beams:Localized approximations andlocalized beam models,a review”,J.Quant.Spect.andRad.Transf.112,1–27(2010).[19]J.Stratton,Electromagnetic Theory,chapter6-7(McGraw-Hill,New York)(1941).[20]P.Marston,“Scattering of a bessel beam by a sphere:Ii.helicoidal case and spherical shell example”,J.Acoust.Soc.Am.124,2905–2910(2008).[21]G.Videen,Light Scattering from Microstructures,81–96(Springer,Berlin)(2000).[22]C.H.Choi,C.C.J.Ivanic,M.Gordon,and K.Rueden-berg,“Rapid and stable determination of rotation matri-ces between spherical harmonics by direct recursion”,J.Chem.Phys.111,8825–8831(1987).[23]L.King,“On the acoustic radiation pressure onspheres”,Proc.R.Soc.London147,212–214(1935). [24]S.Danilov and M.Mironov,“Mean force on a smallsphere in a soundfield in a viscousfluid”,J.Acoust.Soc.Am.107,143–153(2000).Proceedings of the Acoustics 2012 Nantes Conference23-27 April 2012, Nantes, France。
具有负折射率的三维超材料
Байду номын сангаас
Experimental Setup for Measuring
• light source: femtosecond synchronously pumped optical parametric oscillator
Applications and Future Research Direction
• applications
– explore a large variety of optical phenomena
– scaling down of photonics and imaging
• future research direction
Frequency (THz)
Theories Analysis
c
Phase advance (deg)
• combined structures • dispersion curve with negative slope
Theories Analysis
Conclusion
• the first 3D NIM at optical frequencies
Three-dimensional Optical Metamaterial with a Negative
Refractive Index
Jason Valentine, Shuang Zhang, Thomas Zentgraf, Erick Ulin-Avila, Dentcho A. Genov, Guy Bartal & Xiang Zhang University of California, Berkeley