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说明书+CAD QTZ500 塔式起重机 优化 设计 说明书 CAD

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QTZ500塔式起重机——臂架优化设计【说明书+CAD】,说明书+CAD,QTZ500,塔式起重机,优化,设计,说明书,CAD

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FINISH !退出以前模块/CLEAR !清除系统中所有数据!设置工程的选项/FILNAME,EX1.1 !指定当前工程文件名,所有数据用该文件名保存/UNITS,SI !申明采用国际单位制/TITLE,EX1.1,A BEAM ANALYSIS OF QTZ500!定义标题!进入前处理模块,定义节点/PREP7 !进入前处理器,定义有限元模型/VIEW,1,1,1,3 !指定一号窗口视点（1,1,3）!定义上弦杆一至四节节点N,1,0.948,0.8,0N,2,1.248,0.8,0N,3,1.832,0.8,0N,4,3,0.8,0N,5,4.168,0.8,0N,6,5.336,0.8,0N,7,5.92,0.8,0N,8,6.08,0.8,0N,9,6.664,0.8,0N,10,7.832,0.8,0N,11,9,0.8,0N,12,10.168,0.8,0N,13,11.336,0.8,0N,14,11.92,0.8,0N,15,12.08,0.8,0N,16,12.664,0.8,0N,17,13.832,0.8,0N,18,15,0.8,0N,19,16.168,0.8,0N,20,17.336,0.8,0N,21,17.92,0.8,0N,22,18.08,0.8,0N,23,18.664,0.8,0N,24,19.832,0.8,0N,25,21,0.8,0N,26,22.168,0.8,0N,27,23.336,0.8,0N,28,23.92,0.8,0!定义上弦杆五至九节节点N,29,24.08,0.8,0N,30,24.664,0.8,0N,31,25.832,0.8,0N,32,27,0.8,0N,33,28.168,0.8,0N,34,29.336,0.8,0N,35,29.92,0.8,0N,36,30.08,0.8,0N,37,30.664,0.8,0N,38,31.832,0.8,0N,39,33,0.8,0N,40,34.168,0.8,0N,41,35.336,0.8,0N,42,35.92,0.8,0N,43,36.08,0.8,0N,44,36.664,0.8,0N,45,37.832,0.8,0N,46,39,0.8,0N,47,40.168,0.8,0N,48,41.336,0.8,0N,49,41.92,0.8,0N,50,42.08,0.8,0N,51,42.664,0.8,0N,52,43.832,0.8,0N,53,45,0.8,0N,54,46.168,0.8,0N,55,47.336,0.8,0N,56,47.92,0.8,0N,57,48.08,0.8,0N,58,48.664,0.8,0N,59,49.292,0.8,0!定义前侧下弦杆一至四节节点N,60,0,0,0.5085N,61,0.2,0,0.5085N,62,0.2,0,0.18N,63,1.248,0,0.5085N,64,2.416,0,0.5085N,65,3.584,0,0.5085N,66,4.752,0,0.5085N,67,5.92,0,0.5085N,68,6.08,0,0.5085N,69,7.248,0,0.5085N,70,8.416,0,0.5085N,71,9.584,0,0.5085N,72,10.752,0,0.5085N,73,11.92,0,0.5085N,74,12.08,0,0.5085N,75,13.248,0,0.5085N,76,14.416,0,0.5085N,77,15.584,0,0.5085N,78,16.752,0,0.5085N,79,17.92,0,0.5085N,80,18.08,0,0.5085N,81,19.248,0,0.5085N,82,20.416,0,0.5085N,83,21.584,0,0.5085N,84,22.752,0,0.5085N,85,23.92,0,0.5085!定义前侧下弦杆五至九节节点N,86,24.08,0.0015,0.51N,87,25.248,0.0015,0.51N,88,26.416,0.0015,0.51N,89,27.584,0.0015,0.51N,90,28.752,0.0015,0.51N,91,29.92,0.0015,0.51N,92,30.08,0.0015,0.51N,93,31.248,0.0015,0.51N,94,32.416,0.0015,0.51N,95,33.584,0.0015,0.51N,96,34.752,0.0015,0.51N,97,35.92,0.0015,0.51N,98,36.08,0.0015,0.51N,99,37.248,0.0015,0.51N,100,38.416,0.0015,0.51N,101,39.584,0.0015,0.51N,102,40.752,0.0015,0.51N,103,41.92,0.0015,0.51N,104,42.08,0.0015,0.51N,105,43.248,0.0015,0.51N,106,44.416,0.0015,0.51N,107,45.584,0.0015,0.51N,108,46.752,0.0015,0.51N,109,47.92,0.0015,0.51N,110,48.08,0.0015,0.51N,111,49.248,0.0015,0.51N,112,50,0.0015,0.51N,113,50,0.0015,0.21!定义后侧下弦杆一至四节节点N,114,0,0,-0.5085N,115,0.2,0,-0.5085N,116,0.2,0,-0.18N,117,1.248,0,-0.5085N,118,2.416,0,-0.5085N,119,3.584,0,-0.5085N,120,4.752,0,-0.5085N,121,5.92,0,-0.5085N,122,6.08,0,-0.5085N,123,7.248,0,-0.5085N,124,8.416,0,-0.5085N,125,9.584,0,-0.5085N,126,10.752,0,-0.5085N,127,11.92,0,-0.5085N,128,12.08,0,-0.5085N,129,13.248,0,-0.5085N,130,14.416,0,-0.5085N,131,15.584,0,-0.5085N,132,16.752,0,-0.5085N,133,17.92,0,-0.5085N,134,18.08,0,-0.5085N,135,19.248,0,-0.5085N,136,20.416,0,-0.5085N,137,21.584,0,-0.5085N,138,22.752,0,-0.5085N,139,23.92,0,-0.5085!定义后侧下弦杆五至九节节点N,140,24.08,0.0015,-0.51N,141,25.248,0.0015,-0.51N,142,26.416,0.0015,-0.51N,143,27.584,0.0015,-0.51N,144,28.752,0.0015,-0.51N,145,29.92,0.0015,-0.51N,146,30.08,0.0015,-0.51N,147,31.248,0.0015,-0.51N,148,32.416,0.0015,-0.51N,149,33.584,0.0015,-0.51N,150,34.752,0.0015,-0.51N,151,35.92,0.0015,-0.51N,152,36.08,0.0015,-0.51N,153,37.248,0.0015,-0.51N,154,38.416,0.0015,-0.51N,155,39.584,0.0015,-0.51N,156,40.752,0.0015,-0.51N,157,41.92,0.0015,-0.51N,158,42.08,0.0015,-0.51N,159,43.248,0.0015,-0.51N,160,44.416,0.0015,-0.51N,161,45.584,0.0015,-0.51N,162,46.752,0.0015,-0.51N,163,47.92,0.0015,-0.51N,164,48.08,0.0015,-0.51N,165,49.248,0.0015,-0.51N,166,50,0.0015,-0.51N,167,50,0.0015,-0.21!定义拉杆上端塔尖处节点N,168,0.00,5.988,0.00!定义工况节点N,169,2,0,-0.5085N,170,2,0,0.5085N,171,25,0.0015,-0.51N,172,25,0.0015,0.51N,173,49.75,0.0015,-0.51N,174,49.75,0.0015,0.51!在前处理模块中,定义求解类型、单元类型、材料参数、实常数和各个单元ET,1,BEAM4 !定义第1类单元为三维梁单元ET,2,LINK8 !定义第2类单元为三维杆单元!定义单元材料属性MP,EX,1,210E9 !定义材料的弹性模量为210GPaMP,PRXY,1,0.3 !定义材料的泊松比为0.3MP,DENS,1,7800 !定义材料的密度为7800ACEL,0,9.8,0 !定义沿Y向的重力加速度9.8!定义梁单元实常数R,1,0.0021,0.169E-05,0.169E-05,0.089,0.089!上弦杆一四节实常数R,2,0.0018,0.153E-05,0.153E-05,0.089,0.089!上弦杆五至九节实常数R,3,0.0024,0.228E-05,0.228E-05,0.083,0.083!下弦杆一至四节实常数R,4,0.0015,0.141E-05,0.141E-05,0.080,0.080!下弦杆五至九节实常数R,5,0.254E-03,0.234E-07,0.234E-07,0.030,0.030 !腹杆303实常数!定义杆单元实常数R,6,0.330E-03,0.508E-07,0!腹杆383实常数R,7,0.273E-03,0.290E-07,0!腹杆323实常数R,8,0.254E-03,0.234E-07,0!腹杆303实常数R,9,0.159E-02,0.201E-06,0!吊臂拉杆40实常数!定义臂架上弦杆一至四节TYPE,1REAL,1E,1,2EGEN,28,1,1 !按前面单元的节点连接情况,从单元1开始生成28个单元,每次节点号增加1!定义臂架上弦杆五至九节TYPE,1REAL,2E,29,30EGEN,30,1,29 !按前面单元的节点连接情况,从单元29开始生成30个单元,每次节点号增加1!定义臂架前侧下弦杆一至四节TYPE,1REAL,3E,60,61$E,61,63$E,63,170$E,170,64$E,64,65$E,65,66E,66,67$E,67,68$E,68,69$E,69,70$E,70,71E,71,72$E,72,73$E,73,74$E,74,75$E,75,76E,76,77$E,77,78$E,78,79$E,79,80$E,80,81E,81,82$E,82,83$E,83,84$E,84,85$E,85,86!定义臂架前侧下弦杆五至九节TYPE,1REAL,4E,86,172$E,172,87$E,87,88$E,88,89$E,89,90$E,90,91E,91,92$E,92,93$E,93,94$E,94,95$E,95,96E,96,97$E,97,98$E,98,99$E,99,100$E,100,101E,101,102$E,102,103$E,103,104$E,104,105$E,105,106E,106,107$E,107,108$E,108,109$E,109,110$E,110,111E,111,174$E,174,112!定义臂架后侧下弦杆一至四节TYPE,1REAL,3E,114,115$E,115,117$E,117,169$E,169,118$E,118,119$E,119,120E,120,121$E,121,122$E,122,123$E,123,124$E,124,125E,125,126$E,126,127$E,127,128$E,128,129$E,129,130E,130,131$E,131,132$E,132,133$E,133,134$E,134,135E,135,136$E,136,137$E,137,138$E,138,139$E,139,140!定义臂架后侧下弦杆五至九节TYPE,1REAL,4E,140,171$E,171,141$E,141,142$E,142,143$E,143,144$E,144,145E,145,146$E,146,147$E,147,148$E,148,149$E,149,150E,150,151$E,151,152$E,152,153$E,153,154$E,154,155E,155,156$E,156,157$E,157,158$E,158,159$E,159,160E,160,161$E,161,162$E,162,163$E,163,164$E,164,165E,165,173$E,173,166!定义臂架一至四节侧腹杆TYPE,2REAL,6E,2,61$E,2,63$E,2,115$E,2,117E,3,63$E,3,64$E,3,117$E,3,118E,4,64$E,4,65$E,4,118$E,4,119E,5,65$E,5,66$E,5,119$E,5,120E,6,66$E,6,67$E,6,120$E,6,121E,7,67$E,8,68$E,7,121$E,8,122E,9,68$E,9,69$E,9,122$E,9,123E,10,69$E,10,70$E,10,123$E,10,124E,11,70$E,11,71$E,11,124$E,11,125E,12,71$E,12,72$E,12,125$E,12,126E,13,72$E,13,73$E,13,126$E,13,127E,14,73$E,15,74$E,14,127$E,15,128E,16,74$E,16,75$E,16,128$E,16,129E,17,75$E,17,76$E,17,129$E,17,130E,18,76$E,18,77$E,18,130$E,18,131E,19,77$E,19,78$E,19,131$E,19,132E,20,78$E,20,79$E,20,132$E,20,133E,21,79$E,22,80$E,21,133$E,22,134E,23,80$E,23,81$E,23,134$E,23,135E,24,81$E,24,82$E,24,135$E,24,136E,25,82$E,25,83$E,25,136$E,25,137E,26,83$E,26,84$E,26,137$E,26,138E,27,84$E,27,85$E,27,138$E,27,139E,28,85$E,28,139!定义臂架五至九节侧腹杆TYPE,2REAL,7E,29,86$E,29,140E,30,86$E,30,87$E,30,140$E,30,141E,31,87$E,31,88$E,31,141$E,31,142E,32,88$E,32,89$E,32,142$E,32,143E,33,89$E,33,90$E,33,143$E,33,144E,34,90$E,34,91$E,34,144$E,34,145E,35,91$E,36,92$E,35,145$E,36,146E,37,92$E,37,93$E,37,146$E,37,147E,38,93$E,38,94$E,38,147$E,38,148E,39,94$E,39,95$E,39,148$E,39,149E,40,95$E,40,96$E,40,149$E,40,150E,41,96$E,41,97$E,41,150$E,41,151E,42,97$E,43,98$E,42,151$E,43,152E,44,98$E,44,99$E,44,152$E,44,153E,45,99$E,45,100$E,45,153$E,45,154E,46,100$E,46,101$E,46,154$E,46,155E,47,101$E,47,102$E,47,155$E,47,156E,48,102$E,48,103$E,48,156$E,48,157E,49,103$E,50,104$E,49,157$E,50,158E,51,104$E,51,105$E,51,158$E,51,159E,52,105$E,52,106$E,52,159$E,52,160E,53,106$E,53,107$E,53,160$E,53,161E,54,107$E,54,108$E,54,161$E,54,162E,55,108$E,55,109$E,55,162$E,55,163E,56,109$E,57,110$E,55,163$E,57,164E,58,110$E,58,111$E,58,112$E,58,164E,58,165$E,58,166!定义臂架一至四节底面腹杆TYPE,2REAL,7E,61,115$E,63,117$E,64,118$E,65,119E,66,120$E,67,121$E,68,122$E,69,123E,70,124$E,71,125$E,72,126$E,73,127E,74,128$E,75,129$E,76,130$E,77,131E,78,132$E,79,133$E,80,134$E,81,135E,82,136$E,83,137$E,84,138$E,85,139E,62,63$E,116,117$E,63,118$E,118,65E,65,120$E,120,67$E,68,123$E,123,70E,70,125$E,125,72$E,72,127$E,128,75E,75,130$E,130,77$E,77,132$E,132,79E,80,135$E,135,82$E,82,137$E,137,84E,84,139!定义臂架五至九节底面腹杆TYPE,2REAL,8E,86,140$E,87,141$E,88,142$E,89,143E,90,144$E,91,145$E,92,146$E,93,147E,94,148$E,95,149$E,96,150$E,97,151E,98,152$E,99,153$E,100,154$E,101,155E,102,156$E,103,157$E,104,158$E,105,159E,106,160$E,107,161$E,108,162$E,109,163E,110,164$E,111,165E,140,87$E,87,142$E,142,89$E,89,144$E,144,91E,92,147$E,147,94$E,94,149$E,149,96$E,96,151E,152,99$E,99,154$E,154,101$E,101,156$E,156,103E,104,159$E,159,106$E,106,161$E,161,108$E,108,163E,164,111$E,111,113$E,165,167TYPE,1REAL,5E,112,113$E,113,167$E,167,166!定义臂架拉杆TYPE,2REAL,9E,17,168E,46,168!施加边界条件D,60,UX,0,UY,UZ,ROTX,ROTYD,114,UX,0,UY,UZ,ROTX,ROTYD,168,UX,0,UY,UZ,ROTX,ROTY!施加风载荷SFBEAM,1,1,PRES,26.78SFBEAM,2,1,PRES,26.78SFBEAM,3,1,PRES,26.78SFBEAM,4,1,PRES,26.78SFBEAM,5,1,PRES,26.78SFBEAM,6,1,PRES,26.78SFBEAM,7,1,PRES,26.78SFBEAM,8,1,PRES,26.78SFBEAM,9,1,PRES,26.78SFBEAM,10,1,PRES,26.78SFBEAM,11,1,PRES,26.78SFBEAM,12,1,PRES,26.78SFBEAM,13,1,PRES,26.78SFBEAM,14,1,PRES,26.78SFBEAM,15,1,PRES,26.78SFBEAM,16,1,PRES,26.78SFBEAM,17,1,PRES,26.78SFBEAM,18,1,PRES,26.78SFBEAM,19,1,PRES,26.78SFBEAM,20,1,PRES,26.78SFBEAM,21,1,PRES,26.78SFBEAM,22,1,PRES,26.78SFBEAM,23,1,PRES,26.78SFBEAM,24,1,PRES,26.78SFBEAM,25,1,PRES,26.78SFBEAM,26,1,PRES,26.78SFBEAM,27,1,PRES,26.78SFBEAM,28,1,PRES,26.78SFBEAM,29,1,PRES,26.78SFBEAM,30,1,PRES,26.78SFBEAM,31,1,PRES,26.78SFBEAM,32,1,PRES,26.78SFBEAM,33,1,PRES,26.78SFBEAM,34,1,PRES,26.78SFBEAM,35,1,PRES,26.78SFBEAM,36,1,PRES,26.78SFBEAM,37,1,PRES,26.78SFBEAM,38,1,PRES,26.78SFBEAM,39,1,PRES,26.78SFBEAM,40,1,PRES,26.78SFBEAM,41,1,PRES,26.78SFBEAM,42,1,PRES,26.78SFBEAM,43,1,PRES,26.78SFBEAM,44,1,PRES,26.78SFBEAM,45,1,PRES,26.78SFBEAM,46,1,PRES,26.78SFBEAM,47,1,PRES,26.78SFBEAM,48,1,PRES,26.78SFBEAM,49,1,PRES,26.78SFBEAM,50,1,PRES,26.78SFBEAM,51,1,PRES,26.78SFBEAM,52,1,PRES,26.78SFBEAM,53,1,PRES,26.78SFBEAM,54,1,PRES,26.78SFBEAM,55,1,PRES,26.78SFBEAM,56,1,PRES,26.78SFBEAM,57,1,PRES,26.78SFBEAM,58,1,PRES,26.78SFBEAM,59,1,PRES,26.78SFBEAM,60,1,PRES,26.78SFBEAM,61,1,PRES,26.78SFBEAM,62,1,PRES,26.78SFBEAM,63,1,PRES,26.78SFBEAM,64,1,PRES,26.78SFBEAM,65,1,PRES,26.78SFBEAM,66,1,PRES,26.78SFBEAM,67,1,PRES,26.78SFBEAM,68,1,PRES,26.78SFBEAM,69,1,PRES,26.78SFBEAM,70,1,PRES,26.78SFBEAM,71,1,PRES,26.78SFBEAM,72,1,PRES,26.78SFBEAM,73,1,PRES,26.78SFBEAM,74,1,PRES,26.78SFBEAM,75,1,PRES,26.78SFBEAM,76,1,PRES,26.78SFBEAM,77,1,PRES,26.78SFBEAM,78,1,PRES,26.78SFBEAM,79,1,PRES,26.78SFBEAM,80,1,PRES,26.78SFBEAM,81,1,PRES,26.78SFBEAM,82,1,PRES,26.78SFBEAM,83,1,PRES,26.78SFBEAM,84,1,PRES,26.78SFBEAM,85,1,PRES,26.78SFBEAM,86,1,PRES,26.78SFBEAM,87,1,PRES,26.78SFBEAM,88,1,PRES,26.78SFBEAM,89,1,PRES,26.78SFBEAM,90,1,PRES,26.78SFBEAM,91,1,PRES,26.78SFBEAM,92,1,PRES,26.78SFBEAM,93,1,PRES,26.78SFBEAM,94,1,PRES,26.78SFBEAM,95,1,PRES,26.78SFBEAM,96,1,PRES,26.78SFBEAM,97,1,PRES,26.78SFBEAM,98,1,PRES,26.78SFBEAM,99,1,PRES,26.78SFBEAM,100,1,PRES,26.78SFBEAM,101,1,PRES,26.78SFBEAM,102,1,PRES,26.78SFBEAM,103,1,PRES,26.78SFBEAM,104,1,PRES,26.78SFBEAM,105,1,PRES,26.78SFBEAM,106,1,PRES,26.78SFBEAM,107,1,PRES,26.78SFBEAM,108,1,PRES,26.78SFBEAM,109,1,PRES,26.78SFBEAM,110,1,PRES,26.78SFBEAM,111,1,PRES,26.78SFBEAM,112,1,PRES,26.78!施加50m工况时的集中载荷F,173,FY,-4165F,174,FY,-4165FINISH !退出前处理模块!进入求解模块,定义50m工况时的加载情况,并进入求解/SOLUSOLVE!施加25m工况时的集中载荷F,171,FY,-10633F,172,FY,-10633!进行25m工况时加载情况分析求解SOLVE!施加2m工况时的集中载荷F,169,FY,-19600F,170,FY,-19600!进行2m工况时加载情况分析求解SOLVEFINISH !退出求解模块!进入后处理模块,显示结果/POST1SET,1,1 !读入第1个载荷步的计算结果PLDISP,2 !显示图形变形情况,用虚线表示原模型PRNSOL,U,Y !列表显示节点位移计算结果ETABLE,MFORX,SMISC,1 !建立元素结果表,列出单元轴向力PRETAB !显示单元表中内容SET,2,1 !读入第2个载荷步的计算结果PLDISP,2 !显示图形变形情况,用虚线表示原模型PRNSOL,U,Y !列表显示节点位移计算结果ETABLE,MFORX,SMISC,1 !建立元素结果表,列出单元轴向力PRETAB !显示单元表中内容SET,3,1 !读入第3个载荷步的计算结果PLDISP,2 !显示图形变形情况,用虚线表示原模型PRNSOL,U,Y !列表显示节点位移计算结果ETABLE,MFORX,SMISC,1 !建立元素结果表,列出单元轴向力PRETAB !显示单元表中内容FINISH !退出后处理模块河北建筑工程学院毕业设计（论文）外文资料翻译 系别： 机械工程系 专业： 机械设计制造及其自动化 班级： 机053班 姓名： 张勇杰 学号： 22号 外文出处： European Journal of Radiology 附 件：1、外文原文；2、外文资料翻译译文。指导教师评语：签字： 年 月 日MR imaging at high magnetic fieldsMasaya Takahashia,*, Hidemasa Uematsub, Hiroto HatabuaaDepartment of Radiology, Beth Israel Deaconess Medical Center, Boston, MA 02115, USAbDepartment of Radiology, University of Pennsylvania Medical Center, Philadelphia, PA, USAReceived 12 November 2002; received in revised form 13 November 2002; accepted 14 November 2002AbstractRecently, more investigators have been applying higher magnetic field strengths (3?/4 Tesla) in research and clinical settings.Higher magnetic field strength is expected to afford higher spatial resolution and/or a decrease in the length of total scan time due toits higher signal intensity. Besides MR signal intensity, however, there are several factors which are magnetic field dependent, thusthe same set of imaging parameters at lower magnetic field strengths would provide differences in signal or contrast to noise ratios at3 T or higher. Therefore, an outcome of the combined effect of all these factors should be considered to estimate the change inusefulness at different magnetic fields. The objective of this article is to illustrate the practical scientific applications, focusing on MRimaging, of higher magnetic field strength. First, we will discuss previous literature and our experiments to demonstrate severalchanges that lead to a number of practical applications in MR imaging, e.g. in relaxation times, effects of contrast agent, design ofRF coils, maintaining a safety profile and in switching magnetic field strength. Second, we discuss what will be required to gain themaximum benefit of high magnetic field when the current magnetic field (5/1.5 T) is switched to 3 or 4 T. In addition, we discussMR microscopy, which is one of the anticipated applications of high magnetic field strength to understand the quantitativeestimation of the gain benefit and other considerations to help establish a practically available imaging protocol.# 2002 Elsevier Science Ireland Ltd. All rights reserved.Keywords: Magnetic resonance imaging; Higher magnetic field strength; Contrast agent1. IntroductionThanks to recent technological development, whole-body magnetic resonance (MR) scanners at highermagnetic field strengths (/3 T) have been introducedinto research and clinical settings. In the beginning, oneof the main reasons to install higher fields was its highersensitivity to the blood oxygenation level-dependenteffect for functional MR imaging of the brain 1.Recently, more investigators applied these higher mag-netic field strengths to both research and conventionalclinical settings. The expectation for higher magneticfields in MRI is the improvement in signal-to-noise ratio(SNR) due to higher signal intensity (SI), where themost significant benefit is to decrease the length of timerequired to obtain images. Then, higher spatial resolu-tion may be achievable. One question is how it improvesor practically how beneficial it is when we switch thecurrent magnetic field (5/1.5 T) to 3 or 4 T.Several studies have reported and discussed theadvantages of higher magnetic field in, for example,delineation of various brain lesions 1 or cardiacstructures 2,3. Dougherty et al. 2 reported that theSNR of the anterior myocardium at 4 T was 2.9 timeshigher than that of the same region at 1.5 T. Bernstein etal. demonstrated contrast enhanced imaging at 3 T andconcluded that higher spatial resolution at 3 T couldimprove diagnostic accuracy 4. In addition, if highermagnetic field can provide better image quality, it maybe reasonable to expect a reduction in total injection ofcontrast agent, for example, in MR angiography whichneeds to cover a larger area of the peripheral artery 5or the lung 6,7. However, such speculation would bedifficult to prove as higher magnetic fields change otherimaging aspects besides SNR.Many theoretical and experimental studies have beenemployed to demonstrate the magnetic field dependen-cies. Besides SNR, the magnetic field-dependence is* Corresponding author. Tel.: ?/1-617-667-0198; fax: ?/1-617-667-7021.E-mail address: mtakahas (M. Takahashi).European Journal of Radiology 46 (2003) 45?/52/locate/ejrad0720-048X/02/$ - see front matter # 2002 Elsevier Science Ireland Ltd. All rights reserved.PII: S0720-048X(02)00331-5well-documented in tissue relaxation times 8?/10, aswell as in MR contrast agent effects (e.g. R1, R2 or R2*relaxivities) 11,12. SNR depends upon imaging para-meters, RF coil sensitivity and machine adjustments,such as magnetic field homogeneity, accuracy in excita-tion/refocusing pulse settings, etc. These theoretical andexperimentally proven properties suggest that imagingparameters must be reconfigured for different magneticfields. Unlike relaxation time and MR contrast agenteffects, the benefit to signal intensity at higher magneticfield should be compared under nearly identical experi-mental conditions. Therefore, it is imperative to quan-tify the practical differences in terms of SNR andcontrast-to-noise ratios (CNR) between higher andlower (B/1.5 T) magnetic fields. However, the studiesof direct comparisons between SNRs and CNRs as anoutcome of the combined effect of several magneticfield-dependent parameters at different fields comparedwith the theoretical values are substantially sparse.Hence, it is still unclear how much benefit we can gainin SNR or what we can/should do in switching a currentmagnetic field strength (5/1.5 T in most cases) to ahigher magnetic field. In this article, we consider themagnetic field dependent alterations, e.g. MR signal onthe image, relaxation times, effects of contrast agent,design of RF coil and safety profile. Then, we evaluatethe scientific expectations for MR imaging on a highermagnetic field to quantify the scientific and technicalissues relative to safe human experimentation. Further,the feasibility of MR microscopy, which is one of theexpectations of higher fields, is discussed.2. SI, SNR and CNRThe question of optimum field strength has been asubject of intense controversy for over a decade. Theinterest in higher fields stems from the fact that SNRsincrease with field strength (v), where SI and noise havedifferent magnetic field-dependencies.SI8(number of spins)?(voltage induced by each spin)(1)As shown in Eq. (1), theoretically, the signal intensityfrom a MR experiment is proportional to the square ofthe static magnetic field (v2) since both number ofspins that can be observed and voltage induced by eachspin increase linearly as magnetic field (v) increases.Noise is proportional to the static magnetic field (v),when all noise comes from a sample, resulting in anSNR that is proportional to v in the case. On the otherhand, noise is proportional to one-quarter of v (v1/4)when all noise comes from the RF coil, resulting in anSNR that is proportional to v7/4. Therefore, SNR canbe expected to increase more than 2.7 (?/4/1.5) times at4 than at 1.5 T. If this is true, since the SNR scales as thesquare root of the number of image averages, the timeneeded to obtain the same SNR is reduced by a factor of8.To confirm this theory, we imaged the brain in asubject at both fields. To make our comparison betweenthe magnetic fields as direct as possible, the same sets ofexperiments in the same subjects were conducted at both4 and 1.5 T on the commercially supplied whole-bodyMR scanners (SignaTM, General Electric Systems, Mil-waukee, WI) with the equipped head coils. Fig. 1 showsthe T1-weighted images (top) and T2-weighted images(bottom) obtained in the same level of the brain of thesame subject. Each image was obtained with a conven-tional spin echo sequence with the same imagingparameters at 1.5 and 4 T, respectively. These imagesshowed different tissue contrast between the magneticfields even though the images were acquired with thesame set of imaging parameters. In the quantitativemeasurements of SI, we found that 4 T increased the SIin both white and gray matter (Fig. 1). In addition, thoseenhancement ratios were also different between theimaging parameters (T1-WI and T2-WI). Thus, 4 Tprovides a different tissue contrast compared with 1.5 Tusing the same set of imaging parameters, which mightbe inconsistent with theoretical values.3. Relaxation timesAs discussed above, SNR in biological tissue wasfound to be in approximate proportion to field strength.However, the practically achievable SNR gain may besomewhat less since the above theory assumes that allparameters except the magnetic field are consistent. Onereason for the discrepancy is the increase in T1 relaxa-tion time with increasing field strength. SI is a functionof relaxation time that is, in turn, magnetic field-dependent 3. In theory, T1 value increases in amagnetic field-dependent manner in most biologicaltissues of which the correlation time (tc) of tissue wateris :/10?8s 13, whereas T2 value does not change (Fig.2). Comparisons of relaxation times in humans havebeen published in the literature. Jezzard et al. andDuewell et al. presented a comparison of T1 and T2relaxation times in human subjects between 1.5 and 4 Tin the brain and several peripheral regions 9,10 (Table1). In any tissue, T1 relaxation times are prolonged at ahigher magnetic field, while T2 relaxation times aresomewhat shortening. Those results are consistent withprevious reports (Fig. 2). To confirm this phenomenon,we conducted the same set of phantom experiments atboth 4 and 1.5 T on the same whole-body MR scannerswith head coils 14. Phantoms included different con-centrations of Gd-complex aqueous solution with eachphantom representing tissue with a different T1 relaxa-M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5246tion time. In this study, the trains of spin echo imageswith varied TRs or TEs were obtained with the samecommercial clinical scanners with the head coils de-scribed above. The relaxation times (T1, T2) for allphantoms were determined at both 1.5 and 4 T from thefitting curves. The results in this confirmatory studydemonstrated that any T1 relaxation times were pro-longed (1.10?/1.47 times) at 4 T compared with those at1.5 T, while T2 values were identical or slightlyshortened (Table 2).Further, a standard contrast-enhanced MR angio-graphic sequence (3D spoiled gradient recalled acquisi-tionorSPGR)sequencewiththesameimagingparameters was utilized to confirm changes in SI. PeakSNRs at 4 T increased at least 2.21 times highercompared with those at 1.5 T. Moreover, peak CNRsat 4 T increased at least 1.59 times higher compared withthose at 1.5 T in the range of Gd concentrationsexpected during clinical use. In addition, those enhance-ments of SNR and CNR were a function of a flip anglethat we used. Based on those results, using higherFig. 1. T1- and T2-weighted images of a human subject obtained at 1.5 and 4 Tesla. Each image was acquired with the same set of imagingparameters (TR/TE is indicated in the parentheses), respectively. Note that different magnetic fields provided different image contrast.Fig. 3. Cross-sectional T1-weighted image of a fixed excised spinalcord of the larval sea lamprey. Image was obtained at 9.4 Texperimental machine; resolution was 9?/9 mm resolution. See Ref.27.Fig. 2. Magnetic field dependency in T1 and T2 relaxation times,modified from Ref. 13.M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5247magnetic fields seems to be beneficial in CNRs as well asin SNRs even without optimization of imaging para-meters at each magnetic field.A relationship between the SI of a gradient echosequence, the relaxation time and the optimal flip angle(ao: Ernst angle), can be expressed as follows:SI?b?1 ? exp(?TR=T1) ? exp(?TE=T2?) ? sin a1 ? exp(?TR=T1) ? cos a(2)andcos ao?exp(TR=T1)(3)where b is the scaling factor and a is the flip angle. SI isdetermined by its relaxation times (T1 and T2*) inindividual tissue conditions in any imaging sequence.This implies that the same intensity will not be obtainedwith the same set of imaging parameters due to thealternation of relaxation times at different magneticfield. Since T1 values at higher magnetic field are longerthan those at lower magnetic field, the TR, presumablyas well as the flip angle, should be longer (smaller forflip angle) to optimize the SNR of the same sample atthe higher field. Using longer TR, the advantage in SI ata higher field would be less in unit time. In other words,since the primary limitation imposed by long T1relaxation time at higher magnetic field strength isreflected in the TR, the SNR per unit time is optimizedwith an Ernst angle pulse and the shortest achievablevalue of TR/T1. The necessity of optimization ofimaging parameters was presented in a previous work.Keiper et al. 15 compared the usefulness in thediagnosis of white matter abnormalities in multiplesclerosis patients following the optimization of imagingparameters between 1.5 and 4 T. Their results demon-strated that MR imaging at 4 T (512?/256 matrix) coulddepict smaller lesions that could not be detected at 1.5 T(256?/192 matrix), implying that the higher resolutionat 4 T provides higher accuracy of diagnosis in the samepatients with almost identical total scan time.Although T2 values were substituted for T2* in thephantom study because T2 and T2* values should betheoretically identical in phantoms in each magneticfield 16, it is considered to be different from theconditions in some tissues where the T2* value ismuch shorter than the T2 value in some tissues. Amagnitude of susceptibility (g) is proportional to themagnetic field as shown in the following equation 17:g?Dx2?B0RGz?(4)where Dx is the difference in magnetic susceptibility ofadjoining substances, B0(?/v) is the static magneticfield, R is the cross section radius and Gzis the read-outgradient. However, this effect on T2* depends on T2 intissue since 1/T2* is a function of T2 and T2? (R2*?/R2?/R2?) 18. The shorter T2 and T2* values at ahigher magnetic field may cause a larger decrease in theSNR and CNR than would be expected in some tissue,such as the lung. Previously, we found that the CNRincreased in the central arteries of the lung, but did notincrease in the pulmonary peripheral arteries at 4 T asthe dose of contrast agent increased, ranging from 0.05to 0.2 mmol/kg body weight 19. Therefore, the optimalimaging parameters for the clinical application shouldbe carefully considered, particular when an undesirableT2* effect may be involved.4. Relaxivities of Gd-complexThe R1 relaxivity of MR contrast agent is dependentupon various parameters, such as the type of contrastagent 20, temperature and tissue environment as wellas magnetic field strength 11,12. R1 relaxivity of aparamagnetic contrast agent is higher at lower fieldstrength 11. R2 and R2* values should be theoreticallyidentical in phantoms in each magnetic field 16.In the phantom study described above, the authorsattempted to compare the effects of contrast agent. Foran accurate determination of the efficacy of Gd-complex(R1, R2 and R2*), only some of the relaxation timesTable 1Comparison of T1 and T2 relaxation times in human subject 9,10TissueT1 (s)T2 (ms)1.5 T4 T1.5 T4 TBrainaGray matter0.9?/1.3*1.7277?/9063White matter0.7?/1.1*1.0462 ?/8050Muscleb0.981.833126Fatb0.310.394738Bone marrowb0.290.424742aLezzard et al. 9.bDuewell et al. 10.* From previous literature.Table 2Comparison of T1 and T2 relaxation time in gadolinium doped watersolution at room temperature, modified Ref. 14Gd concentration (mmol/l)T1 (ms)T2 (ms)1.5 T4 T1.5 T4 T025563636164315040.125106715669118620.54195623483511.251912531601602.51231428483567814342At room temperature.M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5248(T1, T2) that could be excellently fitted to the curve (r ?/0.995) were reciprocally plotted against the concentra-tions of Gd at both 4 and 1.5 T. As a result, R1 and R2relaxivity values were determined to be 2.95 and 4.82 (l?/s?1?/mmol?1) at 4 T and 3.89 and 4.67 (l?/s?1?/mmol?1)at 1.5 T, respectively. R1 at 4 T was lower (:/25%) thanR1 at 1.5 T, while the R2 at 4 T was almost that at 1.5 T(Table 3). Hence, we found that R1 relaxivity decreasesas the magnetic field strength increases, while R2relaxivity does not change as much, which is consistentwith previous reports 16.Unlike Gd-complex, R2 and R2* might be consider-ably changed depending upon the type of contrast agent(e.g. super paramagnetic iron oxide: SPIO), applicationroot and/or tissues. This suggested that we should alsoconsider the use of the MR contrast agent, though it isnot clear whether this change is substantially effective incurrent clinical usage at higher magnetic field.5. RF coilThe application of higher magnetic field strengths toMR imaging (particular in whole body imaging) is moredemanding because of the difficulty in building RF coilssince the penetration of radio frequency into the tissuebecomes harder 3,21. It is necessary to understand therelationship between SNR and RF coil, since anincomplete RF coil may sacrifice the advantage inSNR at increased magnetic field strength. RF coilcharacteristics, especially a receive coil, significantlyimpactSNR.SNRincreaseswithdecreasingcoildiameter. Thus, the coil sensitivity of the head coil is:/3-fold higher than that of the body coil. The surfacecoilwithsmallerdiametergainsmoresensitivity,whereas the SNR drops off very rapidly with increasingdepth from the surface. To cover these difficulties, anarray of surface coils must be developed. Reported byWright et al. 22, another idea to increase coil sensitivityand further improve SNR is to reduce coil temperature,thus lowering its resistance and thermal noise voltagesand increasing its Q, while keeping the sample at roomtemperature. The cryogenic SNR gain would be greatestfor coil and sample configurations having QL/QUcloseto 1.6. Safety considerationTheoretical calculations of the interaction of highmagnetic fields with human subjects have been reviewed.To date, no hazardous physical or physiological phe-nomena have been shown. The mechanism consideredincluded orientation of macromolecules and mem-branes, effects on nerve conduction, electrocardiogramsand electroencephalograms, and blood flow.The most current clinical MR imagers at lowermagnetic field (5/1.5 T) equip up to 25 mT/m. If highermagnetic fields are to be used to archive higher spatialresolution, the gradient strength must increase. In thecombination of higher statistic magnetic field andgradients, strength may be an issue in some applicationsdue to limitations in the current FDA guidelines forspecific absorption rate (SAR). SAR is defined asfollow:SAR?sjEj22r?tTR?NPNS(5)where s is conductivity, E is the electric field, r is tissuedensity, t is pulse duration and NPand NSare numberof pulses and image slices, respectively. Since E isproportional to static magnetic field, SAR greatlyincreases at higher magnetic field, which may limit theapplication in number of slices, selection of flip angle,etc. Additionally, RF energy is absorbed more effec-tively at higher frequencies; RF absorption, as expressedby SAR, must be carefully monitored. This could be amajor concern in any application at high field strengthas Bottomley et al. previously suggested 21.7. MR microscopyIn using a higher magnetic field, the investigatorsexpect images with higher spatial resolution to be morebeneficial in research and clinical settings. Recently,transgenic and genetically engineered mouse modelshave been used increasingly and have led to importantadvances in many scientific communities. Thus, therehas been an increased demand to image mice in vivowith a microscopic method. Whereas micro-computedtomography (m-CT) can potentially generate higher-resolution images 23, MR is unique in that it is alsoable to provide detailed information on anatomy andfunction of soft tissues. Many excellent works have beenreported in transgenic mice model genotype to pheno-type 24,25, in which most of the cases were conductedwith an experimental image scanner at a high magneticfield.Besidestransgenicimaging,measurementofapparent diffusion coefficients of water molecules wasTable 3Comparison of relaxivities of gadolinium (Gd)-complex in aqueoussolution, modified Ref. 14Relaxivities1.5 T4 TR13.892.95R24.674.82R2*4.554.67* mmol?1s?1at room temperature.M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5249performed in a single neuron 26. More recently, asingle axon in an excised lamprey spinal cord (Fig. 3)27 was demonstrated and an apparent diffusioncoefficient of the single axon was measured 28.The techniques of very high resolution MR imaginghave been developed largely in the past decade 26. MRmicroscopy has been developed in trabecular boneimaging at the clinical magnetic field strength B/1.5 T.There are at least two reasons for applying MRmicroscopy to bone imaging. First, high signal contrastis raised between bones and surrounding tissue (bonemarrow). Second, a smaller RF coil can be designed forthe wrist or ankle. It is amenable to micromorphometryex vivo and in vivo in laboratory animals and even inhumans 29?/32. The authors have provided new andinteresting information on the use of quantitative in vivoMR microscopy and spectroscopy in conjunction withdigital image processing to evaluate the epiphyseal andmetaphyseal tissues of rabbits treated with dexametha-sone at a 1.5 T clinical scanner 33.One of the difficulties of imaging microarchitecture invivo is achievement of sufficient resolution and SNR toresolve individual structures. The capability for directvisualization will have implications for acquiring suffi-cient image quality in vivo. As we discuss below, thehigher the SNR, the longer the total scan time. How-ever, we need to consider the interface between thedesire for reasonable data acquisition times and ade-quate SNR, in particular in vivo imaging. Here, wediscuss the imaging factors regulating spatial resolutionin considering the protocol for a high resolution imageat high magnetic field.SNR is the most limiting factor to increased spatialresolution in MR imaging, since scan time for a givenSNR scales as the inverse sixth power of the linear voxeldimension 34. SNR is primarily a function of voxelsize, which is determined by the number of samples inthe phase encoding and frequency encoding directions(in-plane resolution), the slice thickness (d) and the fieldof view in both directions, frequency (FOVf) and phase(FOVp) encodings. Hence, decreasing voxel size eitherby decreasing field of view or slice thickness or byincreasing the matrix size, decreases SNR 35. There-fore, any parameter determining voxel volume will alsoaffect SNR, where SNR depends upon FOV quadrati-cally in the same matrix size. The noise averagingprocess of repeated sampling has important implicationson SNR. In theory 35, SNR increases as the squareroot of the number of samples collected. This holds truefor the number of phase encodings (Np), the number offrequency encodings (Nf) as well as the number of signalacquisitionsornumberofexcitations(NEX).The combining factors above can be summarized asfollows:SNR?FOVf? FOVp?ffiffiffiffiffiffiffiffiffiffiffiNEXp? dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNf? Npp(6)Thus, it is true that changing the number of frequencyand phase encodings affects both voxel size and signalaveraging. The net effect is an inverse square rootrelationship between SNR and the product of phaseand frequency encoding. By contrast, SNR scales as thesquare root of the number of excitations. Hence,doubling SNR requires quadrupling of NEX, whichexacts a scan time penalty. Spatial resolution is typicallyexpressed in terms of pixel size that is determined as theratio of FOV divided by the number of phase orfrequency encodings. Hence, we can decide spatialresolution in either of two ways: by manipulating theFOV or the matrix size. Changing slice thickness alsoaffects resolution, albeit in a different way. Increasingslice thickness causes increased partial volume blurring.The effect of pixel size on image is demonstrated in Fig.4. Fig. 4(A) shows a 3D projection image of the distalfemoral epiphysis of a live rabbit obtained at a 1.5 Tclinical scanner with 98?/98?/300 mm3spatial resolu-tion. The total scan time was :/20 min. Fig. 4(B)demonstrates a 3D projection of the small trabecularbone specimen from the proximal tibiae in rats. Loca-tions have been matched to a cube highlighted in Fig.1(A). The imaging was performed on a 9.4 T experi-mental machine with a total scan time of :/55 min toafford 39 mm isotropic voxel. Comparing these twoimages, the reduction in voxel size from 98?/98?/300mm3in vivo conducted at 1.5 T (Fig. 4A) to 39 mm3exvivo at 9.4 T (Fig. 4B) presently entails an approximate50-fold SNR penalty. This could not be recovered fullyby the magnetic statistic field increase from 1.5 to 9.4 Twhen the RF coil insert was the same and had the samesensitivity. This obviously means that the RF power isdissipated beneficially by increasing Q in smaller RFcoils for SNR gain. Basically, RF coil sensitivity (Q-dumpling) is reciprocal in proportion to its diameter21.According to the discussion above, the achievablebenefit in SNR might be a factor of 4 after optimizationof imaging parameters when the magnetic field strengthis changed from 1.5 to 3 or 4 T in clinical situations,where the RF coils have almost the same sensitivitybetween the fields. This contributes to image resolutionincreasing at a factor of up to 4 in the same scan time,e.g. 128?/128 to 256?/256 matrix. In this case, the slicethickness should be kept constant. When we prefer tosave scan time, we can reduce the number of excitationsby half, since SNR is proportional to the square of thetotal scan time. If we want further advances, develop-ment of RF coil, image acquisition, restoration andprocessing techniques should be involved.We estimated the benefits for MR imaging when thecurrent MR scanner with magnetic field strength ofM. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5250B/1.5 T is replaced with a higher field up to 3 or 4 T. Anumber of practical implications in the imaging ofbiological tissues at higher field strength must beconsidered. The gain in SNR from the higher magneticfield strength may be substantially offset by prolongedT1 relaxation times, thus optimization of the imagingparameters is important. Although it was not discussedin this review, higher magnetic field must produce betterfrequency resolution of near degenerated resonancesthat are not resolvable at lower field in magneticresonance spectroscopy. Another motivation for highmagnetic field is the ability to use other nuclei (e.g.23Na,39K), rather than protons, for which sensitivities are notsufficient to be observed at lower magnetic field.Recently, whole-body MR scanners with much highermagnetic fields (8?/10 T) have been developed and somehave been applied in human studies.In conclusion, MR imaging at a higher magnetic fieldstrength (/3 Tesla) will be opening a new arena. Theappropriate optimizations, such as image acquisition,development in RF coil design and image processingalgorithms with adequate safety profiles, would expandthe applications.AcknowledgementsWe would like to thank Dr Shigeru Kiryu at BethIsraelDeaconessMedicalCenter/HarvardMedicalSchool for his assistance in article preparation.References1 Thulborn KR. Clinical rationale for very-high-field (3.0 Tesla)functional magnetic resonance imaging. Top Magn Reson Ima-ging 1999;10:37?/50.2 Dougherty L, Connick TJ, Mizsei G. Cardiac imaging at 4.0Tesla. Magn Reson Med 2001;45:176?/8.3 Noeske R, Seifert F, Rhein KH, Rinneberg H. Human cardiacimaging at 3 T using phased array coils. Magn Reson Med2000;44:978?/82.4 Bernstein MA, Huston J, III, Lin C, Gibbs GF, Felmlee JP. 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