·58 智能系统学报 第2卷 small strain adaptive elasticity [J ]Journal of Elasticity, [15]FRIEDENBERG Z B,ZEMSKYL M,POLLIS R P,et 1976(6):337.352. al.The response of nomtraumatized bone to direct cur- [4]COWIN S C,NACHL IN GER RR.Bone remodeling III: rent [J].J Bone Jt Surg,1974,56A:1023-1030. Uniqueness and stability in adaptive elasticity theory [J]. [16]LAVINE L S,LUSTRIN I,SHAMOS M H,et al. Journal of Elasticity,1978,8:285-295. The influence of electric current on bone regeneration in [5]G ELSVIK A.Bone remodeling and piezoelectricity-I vivo [J ]Acta Orthop Scand,1971,42:305-314. [J].Journal of Biomechanics,1973(6):69-77. (17]BRIGHTON C T,FRIEDENBERG Z B,ZEMSKY L [6]G ELSVIK A.Bone remodeling and piezoelectricity-II M,et al.Direct-current stimulation of nonunion and [J ]Journal of Biomechanics,1973(6):187-197. congenital pseudarthrosis:Exploration of its clinical [7]MARTIN R B,BURR BB.A hypothetical mechanism for application [J].J Bone Jt Surg,1975,57A:368-377. simulation of osteonal remodeling by fatigue damage [J]. [18]SHARRARD WJ.SUTELIFFE ML,ROBSON MJ, Journal of Biomechanics,1982,15:37-147. et al.The treatment of fibrous nonunion of fracture by [8]BEAUPREA G S,ORR T E,CARTER D R.An ap- pulsing electromagnetic stimulation [J].J Bone Jt proach for time-dependent bone modeling and remode- Surg,1982,64B:189.193. ling:theoretical development [J ]Journal of Orthopaedic [19]QIN Q H,YE J Q.Thermoelectroelastic solutions for Research,1990(8):651.661. internal bone remodeling under axial and transverse [9]BEAUPREA GS,ORR T E,CARTER D R.An ap- loads [J ]International Journal of Solids and Struc- proach for time-dependent bone modeling and remode- tures,2004,41:2447-60. ling:application:a preliminary remodeling simulation [20]QIN Q H,QU C Y,YEJ Q.Thermoelectro-elastic so- [J ]Journal of Orthopaedic Research,1990,8:662- lutions for surface bone remodeling under axial and 670. transverse loads [J ]Biomaterials,2005,26:6798- [10]BESSETT C A,VALDES M G,HERNANDEZ E. 6810. Modification of fracture repair with selected pulsing e- [21]QU C Y,QIN Q H.Evolution of bone structure under lectromagnetic fields [J].Journal of Bone and Joint axial and transverse loads [J ]Structural Engineering Surgery-American Volume,1982,64:888-895 and Mechanics,2005,24(1):19.29. [11]MCL EOD KJ,RUBIN C T.The effect of low-frequen- [22]COWIN S C,VAN BUSKIRK W C.Internal bone re- cy electrical field on osteogenesis [J ]Journal of Bone modeling induced by a medullary pin [J].Journal of Bi- and Joint Surgery -American Volume,1992,74:920- omechanics,1978,11:269.75. 929. 作者简介： [12]GIORDANO N,BATTISTI E.Effect of electromag- netic fields on bone mineral density and biochemical 曲传咏，男，1980年生，博士研究生， markers of bone turnover in osteoporosis:a single 主要研究方向为生物力学 blind,randomized pilot study [J].Current Therapeutic Email:qu chuanyong @hotmail. Research,2001,62:187.193. com. [13]KORENSTEIN R,SOMI EN D,FISCHL ER H,et al. Capacitative pulsed electric stimulation of bone cells. Induction of cyclic-AMP and DNA synthesis [J ]Bio- 秦庆华，男，1958年生，教授，博士生 chem Biophys Acta,1984.803:302-307. 导师，主要研究方向为智能生物材料力 [14 ]LUBEN R A,CAIN C D,CHEN M C Y,et al.Effects 学、计算力学，主持各类课题9项，其中 of electromagnetic stimuli on bone and bone cells in 获省部级奖项2项，发表论文120余 vitro:Inhibition of responses to parathyroid hormone 篇，其中被SCI EV ISTP收录70余篇 by low-energy low-frequency fields [J ]Proc Natl E mail qhqin @tju.edu.cn. Acad Sci,1982,79:4180.4184. 1994-2008 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.netsmall strain adaptive elasticity [J ]. Journal of Elasticity , 1976 (6) : 337 - 352. [4 ]COWIN S C , NACHL IN GER R R. Bone remodeling III: Uniqueness and stability in adaptive elasticity theory [J ]. Journal of Elasticity , 1978 ,8 : 285 - 295. [5 ] GJ ELSVIK A. Bone remodeling and piezoelectricity —Ⅰ [J ]. Journal of Biomechanics , 1973 (6) : 69 - 77. [6 ] GJ ELSVIK A. Bone remodeling and piezoelectricity —Ⅱ [J ]. Journal of Biomechanics , 1973 (6) : 187 - 197. [7 ] MARTIN R B , BURR B B. A hypothetical mechanism for simulation of osteonal remodeling by fatigue damage [J ]. Journal of Biomechanics , 1982 ,15 : 37 - 147. [8 ]BEAU PREA^ G S , ORR T E , CARTER D R. An ap2 proach for time2dependent bone modeling and remode2 ling : theoretical development [J ]. Journal of Orthopaedic Research ,1990 (8) :651 - 661. [9 ]BEAU PREA^ G S , ORR T E , CARTER D R. An ap2 proach for time2dependent bone modeling and remode2 ling : application : a preliminary remodeling simulation [J ]. Journal of Orthopaedic Research , 1990 , 8 : 662 - 670. [ 10 ] BESSETT C A , VALDES M G, HERNANDEZ E. Modification of fracture repair with selected pulsing e2 lectromagnetic fields [J ]. Journal of Bone and Joint Surgery —American Volume , 1982 ,64 : 888 - 895. [11 ]MCL EOD KJ , RUBIN C T. The effect of low2frequen2 cy electrical field on osteogenesis [J ]. Journal of Bone and Joint Surgery —American Volume , 1992 ,74 : 920 - 929. [12 ] GIORDANO N , BA TTISTI E. Effect of electromag2 netic fields on bone mineral density and biochemical markers of bone turnover in osteoporosis: a single2 blind , randomized pilot study [J ]. Current Therapeutic Research , 2001 ,62 : 187 - 193. [13 ] KORENSTEIN R , SOMJ EN D , FISCHL ER H , et al. Capacitative pulsed electric stimulation of bone cells. Induction of cyclic2AMP and DNA synthesis [J ]. Bio2 chem Biophys Acta , 1984 ,803 :302 - 307. [14 ]LUBEN R A , CAIN C D , CHEN M C Y , et al. Effects of electromagnetic stimuli on bone and bone cells in vitro : Inhibition of responses to parathyroid hormone by low2energy low2frequency fields [ J ]. Proc Natl Acad Sci , 1982 ,79 :4180 - 4184. [15 ]FRIEDENBERG Z B , ZEMSKY L M , POLL IS R P , et al. The response of non2traumatized bone to direct cur2 rent [J ]. J Bone Jt Surg , 1974 ,56A :1023 - 1030. [16 ]LAVIN E L S , LUSTRIN I , SHAMOS M H , et al. The influence of electric current on bone regeneration in vivo [J ]. Acta Orthop Scand , 1971 ,42 :305 - 314. [17 ]BRIGH TON C T , FRIEDENBERG Z B , ZEMSKY L M , et al. Direct2current stimulation of nonunion and congenital pseudarthrosis: Exploration of its clinical application [J ]. J Bone Jt Surg , 1975 ,57A :368 - 377. [18 ]SHARRARD W J , SU TEL IFFE M L , ROBSON M J , et al. The treatment of fibrous nonunion of fracture by pulsing electromagnetic stimulation [J ]. J Bone Jt Surg , 1982 ,64B :189 - 193. [19 ]QIN Q H , YE J Q. Thermoelectroelastic solutions for internal bone remodeling under axial and transverse loads [J ]. International Journal of Solids and Struc2 tures , 2004 ,41 : 2447 - 60. [ 20 ]QIN Q H , QU C Y , YE J Q. Thermoelectro2elastic so2 lutions for surface bone remodeling under axial and transverse loads [J ]. Biomaterials , 2005 ,26 : 6798 - 6810. [21 ]QU C Y , QIN Q H. Evolution of bone structure under axial and transverse loads [J ]. Structural Engineering and Mechanics , 2005 , 24 (1) : 19 - 29. [22 ]COWIN S C , VAN BUSKIR K W C. Internal bone re2 modeling induced by a medullary pin [J ]. Journal of Bi2 omechanics , 1978 ,11 :269 - 75. 作者简介 : 曲传咏 ,男 ,1980 年生 ,博士研究生 , 主要研究方向为生物力学. E2mail : qu _ chuanyong @ hotmail. com. 秦庆华 ,男 ,1958 年生 ,教授 ,博士生 导师 ,主要研究方向为智能生物材料力 学、计算力学 ,主持各类课题 9项 ,其中 获省部级奖项 2 项 ,发表论文120 余 篇 ,其中被 SCI/ EI/ ISTP 收录 70余篇. 85 · E2mail :qhqin @tju. edu. cn. · 智 能 系 统 学 报 第 2 卷