ESWL结石模型中的弹性波数值模拟
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摘要
体外冲击波碎石技术(Extracorporeal shock wave lithotripsy)是20世纪人体结石去除技术的革命性进展,因其无创伤的非侵入式疗法能够大大减轻病人的痛苦而被誉为与MRI,CT并列的三大医疗技术之一。
本文首先回顾了ESWL技术的发展及现状,简单说明了该技术中存在的目前尚未明确的问题,着重论述了人体结石受冲击波直接作用导致破坏的机理。为了能够明确冲击脉冲在结石中的传播情况并对此进行数值模拟,本文之后介绍了用于弹性波计算的特征线方法及差分法的基本理论,构造了基于特征线算法的显式差分格式。在此基础上,利用FORTRAN 95编制计算程序,对三种不同材料的一维弹性固体中的弹性波传播进行了数值模拟,并利用Origin pro7.5后处理软件对计算结果进行了可视化处理。
数值计算结果表明,特征线法能够很好的计算模拟冲击脉冲或阶跃载荷在一维弹性固体中的传播。对于末端固定位移边界条件及应力自由位移边界的两种情形下的数值模拟结果显示弹性波在结石末端的反相与同相反射非常明显。对于这部分,ESWL中常用的正压峰值为30MPa左右,负压峰值10MPa左右的冲击脉冲在结石末端反射之后叠加的拉应力可达到很高的数值,这样不断的作用足以使结石碎裂。
ESWL(Extracorporeal shock wave lithotripsy),which is highly praised as one of the three most important medical treatment technologies as MRI ,CT。Developed over twenty years ago,ESWL is a innovation revolution for kidney stone removal.It’s non-invasive treatment method can greatly lighten the pain of the patients.
The paper review the development and status of ESWL at first,also it simply explains many problems which are not definite in this field.The focus are all on the fracture mechanism of kidney stones with shock wave’s direct impact.In order to definite the propagation of shock waves in the kidney stones,the paper introduce the fundmental theory of Characteristic Curve Method and Finite Difference Method. The author then constructs the Explicit Difference Scheme based on Characteristic Curve Method.Programming with Fortran95,the author solve the algebraic equations and obtains the numerical solutions of propagation of elastic waves.In this work the author simulates the propagation of 1-dimension elastic waves in three materials with different boundary conditions.The numerical results are dealt with Origin pro7.5.
The numerical values appear that that Characteristic Curve Method is able to perfectly simulate the propagation of elastic waves with step load on the boundary of the solid materials.All the analysis demonstrate that the tensile stress due to the reflection of the pulse with a step compressive front with pressure of the order of 30MPa decaying to a negative pressure of 10MPa at the end of the stone is go up to a higher value,with continuous impact which is enough to destroy the stones in human body.
本文首先回顾了ESWL技术的发展及现状,简单说明了该技术中存在的目前尚未明确的问题,着重论述了人体结石受冲击波直接作用导致破坏的机理。为了能够明确冲击脉冲在结石中的传播情况并对此进行数值模拟,本文之后介绍了用于弹性波计算的特征线方法及差分法的基本理论,构造了基于特征线算法的显式差分格式。在此基础上,利用FORTRAN 95编制计算程序,对三种不同材料的一维弹性固体中的弹性波传播进行了数值模拟,并利用Origin pro7.5后处理软件对计算结果进行了可视化处理。
数值计算结果表明,特征线法能够很好的计算模拟冲击脉冲或阶跃载荷在一维弹性固体中的传播。对于末端固定位移边界条件及应力自由位移边界的两种情形下的数值模拟结果显示弹性波在结石末端的反相与同相反射非常明显。对于这部分,ESWL中常用的正压峰值为30MPa左右,负压峰值10MPa左右的冲击脉冲在结石末端反射之后叠加的拉应力可达到很高的数值,这样不断的作用足以使结石碎裂。
ESWL(Extracorporeal shock wave lithotripsy),which is highly praised as one of the three most important medical treatment technologies as MRI ,CT。Developed over twenty years ago,ESWL is a innovation revolution for kidney stone removal.It’s non-invasive treatment method can greatly lighten the pain of the patients.
The paper review the development and status of ESWL at first,also it simply explains many problems which are not definite in this field.The focus are all on the fracture mechanism of kidney stones with shock wave’s direct impact.In order to definite the propagation of shock waves in the kidney stones,the paper introduce the fundmental theory of Characteristic Curve Method and Finite Difference Method. The author then constructs the Explicit Difference Scheme based on Characteristic Curve Method.Programming with Fortran95,the author solve the algebraic equations and obtains the numerical solutions of propagation of elastic waves.In this work the author simulates the propagation of 1-dimension elastic waves in three materials with different boundary conditions.The numerical results are dealt with Origin pro7.5.
The numerical values appear that that Characteristic Curve Method is able to perfectly simulate the propagation of elastic waves with step load on the boundary of the solid materials.All the analysis demonstrate that the tensile stress due to the reflection of the pulse with a step compressive front with pressure of the order of 30MPa decaying to a negative pressure of 10MPa at the end of the stone is go up to a higher value,with continuous impact which is enough to destroy the stones in human body.
引文
[1] 孙西钊.医用冲击波[M].中国科学技术出版社,2006.
[2] Delius M, G. Heine, and W. Brendel, A mechanism of gallstone destruction by extracorporeal shock waves[J]. Naturwissenschaften 1988,75:200-201
[3] Chaussy C., Brendel W., and Schmiedt E..Extracorporeally induced destruction of kidney stones by shock waves[J]. Lancet 1980,2(12)65-127
[4] Lokhandwalla M., and Sturtevant B.Fracture mechanics model of stone comminution in ESWLand implications for tissue damage[J] Phys. Med. Biol. 2000,45(7):23-40
[5] Eisenmenger W.The mechanisms of stone fragmentation in ESWL[J]. Ultrasound Med. Biol. 2001,27:683-693
[6] Vakil N., Gracewski S. M., and Everbach E. C..Relationship of model stone properties to fragmentation mechanisms during lithotripsy[J]. Lithotripsy & Stone Disease,1991,3(4):304-310
[7] Ebrahimi F and Wang F.Fracture behaviour of urinary stones under compression[J] J. Biomed. Mater. Res.1989,23(5):07–21
[8] Cohen NP,Whitfield HN.Mechanical testing of urinary calculi.World.J Urol.1993,11(1):13-8.
[9] Petr, V.Experimental and Numerical studies of shock wave propagation in a geomedium [Dissertation].Thesis, Colorado School of Mines, Golden, Colorado. 2001
[10] Kolsky H., and Sheaman, A. C. Investigation of fractures produced by transient waves[J].Research,1949,2(3):84-90
[11] Barclay,D.W..Shock calculations for axially symmetric shear wave propagation in a hyperelastic incompressible solid[J].International Journal of Non-Linear Mechanics,2004,3(9):101-121
[12] Y.K. Wu, H. Hao, Y.X. Zhou & K. Chong. Propagation characteristics of blast-induced shock waves in a jointed rock mass[J]. Soil Dynamics and Earthquake Engineering,1998,17:407–412
[13] Songlin Zhu,Frankin H.Cocks,Glenn M.Preminger and Pei Zhong. The role of stress waves and cavitation in stone comminution in shock wave lithotripsy[J]. Ultrasound in Med. & Biol., Vol. 2002,28(5):661–671
[14] Zhong P, Chuong CJ. Propagation of shock waves in elastic solids caused by the impact of cavitation microjets: Part I. Theoretical formulation[J]. J. Acoust.Soc.Am.,1993,94:19–28
[15] Zhong P, Chuong CJ. Preminger GM. Propagation of shock waves in elastic solids caused by the impact of cavitation microjets: Part II.Application to extracorporeal shock wavelithotripsy[J]. J .Acoust . Soc. Am,1993b,94:29–36
[16] Xi XF, Zhong P. Dynamic photoelastic study of the transient stress field in solids during shock wave lithotripsy[J]. J. Acoust. Soc. Am,2001,109:1226–1239
[17] Xi XF, Zhong P. Improvement of stone fragmentation during shock wave lithotripsy using a combined EH/PEAA shock wave generator—In vitro experiments[J].Ultrasound Med Biol 2000,6:457–467
[18] Brace WF, Bombolakis EG. A note on brittle crack growth in compression[J]. J. Geophysics Res,1963,68:3709–3713
[19] Chuong CJ, Zhong P, Preminger GM. A comparison of stone damage caused by different modes of shock wave generation[J]. J.Urol,1992,148:200–205
[20] Dahake G., Gracewski S.M.. Finite difference predictions of P-SV wave propagation inside submerged solids. I. Liquid-solid interface conditions[J]. J Acoust.. Soc. Am., 1997,102(2):125–2137
[21] Dahake G., Gracewski S.M.. Finite difference predictions of P-SV wave propagation inside submerged solids. II. Effect of geometry. J Acoust. Soc. Am. ,1997,102(2)138–214
[22] Delius M., Heine G., Brendel W.. A mechanism of gallstone destruction by extracorporeal shock waves[J]. Naturwissenschaften 1988,75:200–201
[23] Gracewski S.M., Dahake G., Ding Z., Burns S.J., Everbach EC. Internal stress wave measure-ments in solids subjected to lithotripter pulses[J]..J Acoust Soc Am 1993,94:652–661.
[24] Howard D., Sturtevant B. In vitro study of the mechanical effects of shock-wave lithotripsy[J]. Ultrasound Med Biol 1997,23:1107–1122
[25] Johrde L.G., Cocks F.H.. Fracture strength studies of renal calculi[J]. J Mat Sci Lett 1985,4:1264-1265
[26] Khan S.R., Hackett R.L., Finlayson B.. Morphology of urinary stone particles resulting from ESWL treatment[J]. J Urol 1986,13(6):1367–1372
[27] Mueller S.C., Wilbert D., Thueroff J.W., Alken P.. Extracorporeal shock wave lithotripsy of ureteral stones: Clinical experience and experimental findings[J]. J Urol 1986,135:831–834
[28] Sass W., Braunlich W.M., Dreyer HP, et al. The mechanisms of stone disintegration by shock waves[J], Ultrasound Med Biol 1991;7(3):239–243
[29] Sutor D.J.. The nature of urinary stones. In: Finlayson B. Hench IL,Smith LH, eds. Urolithiasis: Physical aspects. Washington, DC:National Academy of Sciences, 1972:43–63
[30] Whelan J.P., Finlayson B.. An experimental model for the systematic investigation of stone fracture by extracorporeal shock wave lithotripsy[J].J. Urol 1988,140:395–400
[31] Rinehart J. S., and Pearson,. Behavior of metals under impulsive loads[J], J. Appl. Mech,1954,29:439
[32] Barenblatt G. I.. The mathematical theory of equilibrium cracks in brittle fracture[J]. Adv. Appl. Mech. 1962, 7:55-129
[33] Brace W. F. and Bombolakis E. G.. A note on brittle crack growth in compression[J]. J. Geophys. Res. 1963,68(37):09–13
[34] Chaussy C.H. and Fuchs G.J.. Current state and future developments of non-invasive treatment of human urinary stones with ESWL[J].J. Endourol. 1989,141: 782–934
[35] Chuong C. J., Zhong P.and Preminger M.. Acoustic and mechanical properties of renal calculi: implications in SWL[J] J. Endourol. 1993,7:437–445
[36] Cohen N. P. and Whitfield H.N.. Mechanical testing of urinary calculi[J]. World J. Urology 1993,11:13-18
[37] Camacho G.T. and Ortiz M. Computational modelling of impact damage in brittle materials[J]. Int. J. Solids Structures 1996,20(2):899–938
[38] Muller M.. Comparison of Dornier lithotripters: measurement of shockwave fields and fragmentation effectiveness[J]. Biomed. Tech. 1990,35(2):50–62
[39] Nemat-Nasser S. and Deng H.. Strain-rate effect on brittle failure in compression Acta Metall. Mater. 1994,42(10):13–24
[40] Pittomvils G., Vanduersen H., Wevers M., Lafaut J.P., De Ridder D., De Meester P., Boving R., Baert L.. The influence of internal stone structure on the fracture behavior of urinary calculi [J].Ultrasound Med Biol 1994,20:803– 810.
[41] Sylven E.T., Agarwal S., Briant C.L., Cleveland R.O.. High strainrate testing of kidney stones[J]. J Mater Sci Mater Med 2004,15:613–617.
[42] Crum L.A.. Cavitation microjets as a contributory mechanism for renal calculi disintegration in ESWL[J]. J Urol 1988,140:158.
[43] Dreyer T., Riedlinger R.E., Steiger E.. Experiments on the relation of shock wave parameters to stone disintegration. 135th ASA Conference Proceedings 1998:2811–2812.
[44] Heimbach D., Munver R., Zhong P., Jacobs J, Hesse A, Muller SC,Preminger GM. Acoustic and mechanical properties of artificial stones in comparison to natural kidney stones[J]. J Urol 20001,64:537-544.
[45] Parr NJ, Pye SD, Ritchie AWS, Tolley DA. Mechanisms responsible for diminished fragmentation of ureteral calculi: An experimental and clinical study[J]. J Urol 1992,184:1079–1083.
[46] Renner C, Rassweiler J.Treatment of renal stones by extracorporal shock wave lithotripsy[J]. Nephron 1999,81:71– 81.
[47] Sass W, Braunlich M, Dreyer HP, Matura E, Folberth W, Priesmeyer HG, Seifert J. The mechanisms of stone disintegration by shock waves[J]. Ultrasound Med Biol 1991,17:239 –243.
[48] 王礼立.应力波基础[M].国防工业出版社,2005.
[49] 陈景秋.王宗笠.多维双曲波问题的双特征方法[M],重庆大学出版社,2001
[50] 杨大地.数值分析[M].科学出版社,2006
[51] 李太宝.计算声学[M].科学出版社,2005
[52] 丁启财.固体中的非线性波[M]. 中国友谊出版公司,1985
[53] 杨贵通.张善元.弹性动力学[M] 中国铁道出版社
[2] Delius M, G. Heine, and W. Brendel, A mechanism of gallstone destruction by extracorporeal shock waves[J]. Naturwissenschaften 1988,75:200-201
[3] Chaussy C., Brendel W., and Schmiedt E..Extracorporeally induced destruction of kidney stones by shock waves[J]. Lancet 1980,2(12)65-127
[4] Lokhandwalla M., and Sturtevant B.Fracture mechanics model of stone comminution in ESWLand implications for tissue damage[J] Phys. Med. Biol. 2000,45(7):23-40
[5] Eisenmenger W.The mechanisms of stone fragmentation in ESWL[J]. Ultrasound Med. Biol. 2001,27:683-693
[6] Vakil N., Gracewski S. M., and Everbach E. C..Relationship of model stone properties to fragmentation mechanisms during lithotripsy[J]. Lithotripsy & Stone Disease,1991,3(4):304-310
[7] Ebrahimi F and Wang F.Fracture behaviour of urinary stones under compression[J] J. Biomed. Mater. Res.1989,23(5):07–21
[8] Cohen NP,Whitfield HN.Mechanical testing of urinary calculi.World.J Urol.1993,11(1):13-8.
[9] Petr, V.Experimental and Numerical studies of shock wave propagation in a geomedium [Dissertation].Thesis, Colorado School of Mines, Golden, Colorado. 2001
[10] Kolsky H., and Sheaman, A. C. Investigation of fractures produced by transient waves[J].Research,1949,2(3):84-90
[11] Barclay,D.W..Shock calculations for axially symmetric shear wave propagation in a hyperelastic incompressible solid[J].International Journal of Non-Linear Mechanics,2004,3(9):101-121
[12] Y.K. Wu, H. Hao, Y.X. Zhou & K. Chong. Propagation characteristics of blast-induced shock waves in a jointed rock mass[J]. Soil Dynamics and Earthquake Engineering,1998,17:407–412
[13] Songlin Zhu,Frankin H.Cocks,Glenn M.Preminger and Pei Zhong. The role of stress waves and cavitation in stone comminution in shock wave lithotripsy[J]. Ultrasound in Med. & Biol., Vol. 2002,28(5):661–671
[14] Zhong P, Chuong CJ. Propagation of shock waves in elastic solids caused by the impact of cavitation microjets: Part I. Theoretical formulation[J]. J. Acoust.Soc.Am.,1993,94:19–28
[15] Zhong P, Chuong CJ. Preminger GM. Propagation of shock waves in elastic solids caused by the impact of cavitation microjets: Part II.Application to extracorporeal shock wavelithotripsy[J]. J .Acoust . Soc. Am,1993b,94:29–36
[16] Xi XF, Zhong P. Dynamic photoelastic study of the transient stress field in solids during shock wave lithotripsy[J]. J. Acoust. Soc. Am,2001,109:1226–1239
[17] Xi XF, Zhong P. Improvement of stone fragmentation during shock wave lithotripsy using a combined EH/PEAA shock wave generator—In vitro experiments[J].Ultrasound Med Biol 2000,6:457–467
[18] Brace WF, Bombolakis EG. A note on brittle crack growth in compression[J]. J. Geophysics Res,1963,68:3709–3713
[19] Chuong CJ, Zhong P, Preminger GM. A comparison of stone damage caused by different modes of shock wave generation[J]. J.Urol,1992,148:200–205
[20] Dahake G., Gracewski S.M.. Finite difference predictions of P-SV wave propagation inside submerged solids. I. Liquid-solid interface conditions[J]. J Acoust.. Soc. Am., 1997,102(2):125–2137
[21] Dahake G., Gracewski S.M.. Finite difference predictions of P-SV wave propagation inside submerged solids. II. Effect of geometry. J Acoust. Soc. Am. ,1997,102(2)138–214
[22] Delius M., Heine G., Brendel W.. A mechanism of gallstone destruction by extracorporeal shock waves[J]. Naturwissenschaften 1988,75:200–201
[23] Gracewski S.M., Dahake G., Ding Z., Burns S.J., Everbach EC. Internal stress wave measure-ments in solids subjected to lithotripter pulses[J]..J Acoust Soc Am 1993,94:652–661.
[24] Howard D., Sturtevant B. In vitro study of the mechanical effects of shock-wave lithotripsy[J]. Ultrasound Med Biol 1997,23:1107–1122
[25] Johrde L.G., Cocks F.H.. Fracture strength studies of renal calculi[J]. J Mat Sci Lett 1985,4:1264-1265
[26] Khan S.R., Hackett R.L., Finlayson B.. Morphology of urinary stone particles resulting from ESWL treatment[J]. J Urol 1986,13(6):1367–1372
[27] Mueller S.C., Wilbert D., Thueroff J.W., Alken P.. Extracorporeal shock wave lithotripsy of ureteral stones: Clinical experience and experimental findings[J]. J Urol 1986,135:831–834
[28] Sass W., Braunlich W.M., Dreyer HP, et al. The mechanisms of stone disintegration by shock waves[J], Ultrasound Med Biol 1991;7(3):239–243
[29] Sutor D.J.. The nature of urinary stones. In: Finlayson B. Hench IL,Smith LH, eds. Urolithiasis: Physical aspects. Washington, DC:National Academy of Sciences, 1972:43–63
[30] Whelan J.P., Finlayson B.. An experimental model for the systematic investigation of stone fracture by extracorporeal shock wave lithotripsy[J].J. Urol 1988,140:395–400
[31] Rinehart J. S., and Pearson,. Behavior of metals under impulsive loads[J], J. Appl. Mech,1954,29:439
[32] Barenblatt G. I.. The mathematical theory of equilibrium cracks in brittle fracture[J]. Adv. Appl. Mech. 1962, 7:55-129
[33] Brace W. F. and Bombolakis E. G.. A note on brittle crack growth in compression[J]. J. Geophys. Res. 1963,68(37):09–13
[34] Chaussy C.H. and Fuchs G.J.. Current state and future developments of non-invasive treatment of human urinary stones with ESWL[J].J. Endourol. 1989,141: 782–934
[35] Chuong C. J., Zhong P.and Preminger M.. Acoustic and mechanical properties of renal calculi: implications in SWL[J] J. Endourol. 1993,7:437–445
[36] Cohen N. P. and Whitfield H.N.. Mechanical testing of urinary calculi[J]. World J. Urology 1993,11:13-18
[37] Camacho G.T. and Ortiz M. Computational modelling of impact damage in brittle materials[J]. Int. J. Solids Structures 1996,20(2):899–938
[38] Muller M.. Comparison of Dornier lithotripters: measurement of shockwave fields and fragmentation effectiveness[J]. Biomed. Tech. 1990,35(2):50–62
[39] Nemat-Nasser S. and Deng H.. Strain-rate effect on brittle failure in compression Acta Metall. Mater. 1994,42(10):13–24
[40] Pittomvils G., Vanduersen H., Wevers M., Lafaut J.P., De Ridder D., De Meester P., Boving R., Baert L.. The influence of internal stone structure on the fracture behavior of urinary calculi [J].Ultrasound Med Biol 1994,20:803– 810.
[41] Sylven E.T., Agarwal S., Briant C.L., Cleveland R.O.. High strainrate testing of kidney stones[J]. J Mater Sci Mater Med 2004,15:613–617.
[42] Crum L.A.. Cavitation microjets as a contributory mechanism for renal calculi disintegration in ESWL[J]. J Urol 1988,140:158.
[43] Dreyer T., Riedlinger R.E., Steiger E.. Experiments on the relation of shock wave parameters to stone disintegration. 135th ASA Conference Proceedings 1998:2811–2812.
[44] Heimbach D., Munver R., Zhong P., Jacobs J, Hesse A, Muller SC,Preminger GM. Acoustic and mechanical properties of artificial stones in comparison to natural kidney stones[J]. J Urol 20001,64:537-544.
[45] Parr NJ, Pye SD, Ritchie AWS, Tolley DA. Mechanisms responsible for diminished fragmentation of ureteral calculi: An experimental and clinical study[J]. J Urol 1992,184:1079–1083.
[46] Renner C, Rassweiler J.Treatment of renal stones by extracorporal shock wave lithotripsy[J]. Nephron 1999,81:71– 81.
[47] Sass W, Braunlich M, Dreyer HP, Matura E, Folberth W, Priesmeyer HG, Seifert J. The mechanisms of stone disintegration by shock waves[J]. Ultrasound Med Biol 1991,17:239 –243.
[48] 王礼立.应力波基础[M].国防工业出版社,2005.
[49] 陈景秋.王宗笠.多维双曲波问题的双特征方法[M],重庆大学出版社,2001
[50] 杨大地.数值分析[M].科学出版社,2006
[51] 李太宝.计算声学[M].科学出版社,2005
[52] 丁启财.固体中的非线性波[M]. 中国友谊出版公司,1985
[53] 杨贵通.张善元.弹性动力学[M] 中国铁道出版社