The damage and healing of bone in the disuse state under mechanical and electromagnetic

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1 Avalable onlne at Proceda Engneerng 1 (211) ICM11 The damage and healng o bone n the dsuse state under mechancal and electromagnetc loadngs Chuan-Yong Qu, a,b Shou-Wen Yu a. * a Department o Engneerng Mechancs, Tsnghua Unversty,Bejn,184,Chna b Department o Mechancs, Tanjng Unversty,Tanjng,372,Chna Abstract The damage behavour o bone tssues has attracted many nterests o scentsts and engneers due to t can repar tsel. Ths renewng process s perormed by bone remodellng. In the present paper, we establsh a mechansm-based damage model to ratonalze the damage evoluton law o bone under smultaneously appled mechancal and electromagnetc elds. An evolutonary law o bone damage and the correspondng modellng methodology are presented to analyze the complcated damage/repar behavour o bone under mult-elds. The model or bone njury under dsuse status s establshed. Then the numercal examples are consdered to very the present theoretcal model and the nluence o those mechancal and non-mechancal actors on the bone damage and healng are smulated based on the new damage model. It s shown by result that compared wth mechancal stmulaton, electromagnetc eld s a knd o more relable method or mprovng dsuse osteopoross wth relatvely small sde eect. 211 Publshed by Elsever td. Open access under CC BY-NC-ND lcense. Selecton and peer-revew under responsblty o ICM11 Keywords: and healng; Bone n dsuse state; mechancal loadng; electro-magnetc loadng 1.Introducton Dsuse s caused by systemc or local bone mass loss or reason o reducton n mechancal orce. Common causes o dsease are: moton ablty s restrcted or has dysuncton; moton system ncludng muscle skeleton s damaged or ll;nerve system s damaged or ll. Dsuse status s requently seen n damage o spnal cord, hemplega, polo and ts sequel, racture, long-term bed rest and space lght. From the vewpont o mechancs, dsuse status s benecal or bone njury, the drvng orce or ormaton o bone njury s obvously reduced because o reducton n external orce load, thus the ormaton speed o bone njury mght be reduced, and the njury extent o bone s reduced. However, rom the vewpont o bology, dsuse status would cause serous problem,.e., osteopoross. Because o exstence o reconstructon uncton o bone, once t s n the dsuse status, ts mechansm o reconstructon would be actvated, as a result, bone mass would be greatly reduced, and that s bone njury n another sense though not n terms o mechancs. The model or bone damage under eect o multple physcal elds that takes nto consderaton the repar eect was prelmnarly establshed n our paper [1,2], some njury behavour o bone under the crcumstance o overload was nvestgated on that bass, and the nluence o multple eld coupled load on the reconstructon behavour o bone njury was approxmately understood. We know rom the Re.[1,2] that there are three nducton actors or reconstructon o bone: overload, dsuse and hormone nluence. Ths paper shall emphatcally pay attenton to the nluence o multple physcal eld load on the bone njury and repar under dsuse status, and establsh the equatons or bone damage and repar under dsuse status. *Correspondng author. Tel: ;FAX; E-mal address: yusw@mal.tsnghua.edu.cn Publshed by Elsever td. Open access under CC BY-NC-ND lcense. Selecton and peer-revew under responsblty o ICM11 do:1.116/j.proeng

2 172 Chuan-Yong Qu and Shou-Wen Yu / Proceda Engneerng 1 (211) Dsuse status o bone and the problems ncurred by dsuse status Osteopoross (DOP) s a knd o secondary osteopoross, and t s the osteopoross caused by systemc bone mneral substance reducton or the reason o restrcton o moton ablty or dysuncton. It can be locally seen, or example, moton mopraga or moton uncton loss o paralyss patent, long-term bed rest, long-term use o plaster mmoblzaton and plate xaton n surgery, etc., can all nduce dsuse osteopoross, t mght also be ncurred by physcal treatment and drug treatment. Actve treatment to prmary dsease shall not be neglected under any crcumstance. Physcal exercse shall be rstly emphaszed n preventon and cure.. Electrcal stmulaton can be adopted or physotherapy, so as to promote the actvty o osteo-blast and nhbt bone absorpton. The eect o pulse electromagnetc eld n bone ormaton and reconstructon o bone has been proved by large quanttes o research over the past 3 years. [4]. Bone metabolsm s aected by pulse electromagnetc eld (PEMF). PEMFs through stmulatng the uncton o osteoblast. It s shown by domestc and oregn research that pulse electromagnetc eld s a knd o non-medcnal method or treatng osteopoross wth relatvely good prospect o applcaton [5] The eect o electromagnetc eld by bophyscal stmulaton shall occur at surace or nteror, such as body trunk and hp bone, etc., bone qualty can be mproved, so as to eectvely prevent and cure the osteopoross caused by dsuse. The eects o the pulse electro=magnetc eld on the bone damage can also be ound n the reerences [6-9]. 3. Establshment o model or bone damage n dsuse status It s shown by the above research that the nluence o dsuse status on bone densty s very great, but ts eect on bone njury s postve. Electromagnetc stmulaton undoubtedly has eect on reconstructon o bone.at present, the research n that aspect s sparse. Thereore, we need to establsh the ollowng model: Frstly, we stll adopt damage quantty D and modulus o elastcty E o bone to relect bone qualty. In act, because o reducton n load under the dsuse status, the mechancal propertes ncludng modulus o elastcty o newly ormed bone would be greatly reduced. The damage quantty D and modulus o elastcty E o bone are dened as ollowng. Some o the ormula can be ound n [1,2] and [4]. E D 1 (1) E E 5 6 ( ( ( ( ( ( (2) where E s related to the porosty p o bone,, and we can get the equaton o damage quantty D and porosty p changng wth tme by the same means as the evoluton law o the porosty and damage: dp QRN R QF N dt dd dd ddh dt dt dt F (3) where the dentons and values o QR and Q F, D and h D can be seen n [1,2]

3 Chuan-Yong Qu and Shou-Wen Yu / Proceda Engneerng 1 (211) dd dt q k R (4) ddh dt k h N F 5) N R F N R(max) R (1 e k D r s 1D s ) 6) N k N (7) Reer to the prevous paper [1,2] or the dentons and values o varables n each o the above expressons. k k c c mn c c c k s c c 1 e max mn n U s stll the relatonshp coecent between bone absorpton and osteogeness, but compared wth the denton n the prevous chapter, n order to research the reconstructon o bone and ts njury under dsuse status, we have addtonally ntroduced an tem,.e., the value when, where s the external load stmulaton actor. q j j e C R C E G H (9) U (8) Then the reducton n external load stmulaton would cause reducton n the number o growth actor contaned n n p 2 bone cell, t s represented as: k c c2 cmn c p. It s hereby set that cmn.11 n ths paper. In the expresson o k under dsuse status at the tme o reconstructon o bone, there s an tem o very specal expresson o the rst term o k, that tem o expresson s related to the porosty o bone, ts ntroducton s to show the nluence o physologcal actor on reconstructon o bone. It s set n ths paper: ater external load ully dsappears, the porosty o bone tssue shall be about p 5%, thus the value range o p s between and p 5% ( p p ). Where n 5 denes the shape o curve. It can be seen that when the bone tssue s n dsuse status, proporton coecent k wll ncrease wth the ncrease n porosty, more osteoblast wll be secreted to generate new bone cell, so as to block urther absorpton o bone tssue. 4. Inluence o dsuse status on bone damage Ater ntroducton o the above hypothess, we can solve reconstructon o bone and the control equaton o reconstructon o bone can be deduced. It can only be consdered to solve by the numercal method. In the solvng process, the ourth-order Runge-Kutta ntegral method s adopted or solvng the above equatons.

4 174 Chuan-Yong Qu and Shou-Wen Yu / Proceda Engneerng 1 (211) For the sake o convenence, we assume that the bone materal s smpled as a cube whose sde length s 1cm. Smlarly, t s supposed that the exerted s j, electrc eld E and magnetc eld H wll return to zero wthn each perod. Reer to [1,2] or the value o parameter used n the model, and the values o quanttes that newly emerge n ths paper have been gven n [1,2]. Several knds o concrete crcumstances are analysed as ollows. 4.1 Inluence o dsuse status on bone damage and bone densty In order to explan the nluence o dsuse status on bone damage and bone densty, three derent models or orce load on bone tssue are selected n ths thess, ncludng P =.18,.16 and.8 KN, and there s no acton o other load except those. The result ater smulaton s shown n Fgure 1 and Fgure 2, among them, Fgure 1 dsplays the nluence o dsuse status on bone njury, and Fgure 2 dsplays the nluence o dsuse status on bone densty kn.12kn.8kn Tme (day) Fg. 1 Dagram o bone damage varable D changng wth tme under acton o derence orce load We can see rom Fgure 1: once bone tssue s n dsuse status, because o reducton n load, the drvng orce or ncrease o njury s also reduced, but reconstructon o bone wll contnue to repar the broken bone cell, thus ts njury varable would be lowered, and that has postve eect on mprovement o bone qualty. Porosty KN.12KN.8KN Tme (day) Fg.2 Dagram or rate o change n bone porosty p changng wth tme under derent orce load

5 Chuan-Yong Qu and Shou-Wen Yu / Proceda Engneerng 1 (211) Fg.dsuse status on bone densty. We can see rom the dagram that wth the decrease n load, bone porosty begns to rse, and bone mass begns to decrease, bone becomes more ragle and bone qualty s reduced, and the adverse eect o dsuse begns to emerge. Fgure 3 shows the change n damage quantty o bone wth derent porosty under the same load eect (P =.6KN) % 15% 5% Tme (day) Fg.3 Dagram o damage varable D o bone wth derent porosty changng wth tme Inluence o varous actors on bone qualty n the rehabltaton process o racture 4.2 Inluence o electromagnetc eld on bone njury behavour under the dsuse status and n the rehabltaton process It was mentoned beore that physotherapy was another method or treatng dsuse osteopoross,.e., the treatment am can be reached by means o electromagnetc stmulaton. Then what s the nluence o electromagnetc eld on bone njury? We shall rstly research the nluence o electromagnetc eld on bone njury behavour under the dsuse status, an electrc eld o 5V/m and 1V/m s respectvely exerted onto the bone tssue under dsuse status, then compare wth that wthout exerton o electrc eld, and the result s shown n Fgure 4 and Fgure E = E = 5 V/m E = 1 V/m Tme (day) Fg. 4 Dagram o bone damage varable D changng wth tme under the dsuse status wth derent electrc eld Fgure 5 shows the eect o electromagnetc eld on the rehabltaton process o dsuse osteopoross. Smlarly, t can be seen rom dagram that n the process o rehabltaton, electromagnetc stmulaton can reduce the njury quantty o bone on the one hand, and qucken the repar speed o bone njury on the other hand. That also explans the mportant actve role that can stll be played by electromagnetc eld n the rehabltaton process o dsuse osteopoross.

6 176 Chuan-Yong Qu and Shou-Wen Yu / Proceda Engneerng 1 (211) No eld Electromagnetc eld Tme (day) Fg. 5 Eect o electromagnetc eld n the rehabltaton process o osteopoross 5. Concluson Based on the theoretcal model establshed n Author s paper [1,2], the model or bone damage under dsuse status s rstly establshed. The nluence o exercse ntensty and restng tme on treatment o dsuse osteopoross was dscussed. The nluence o electromagnetc stmulaton on bone qualty under the dsuse status and the rehabltaton process s calculated. It s shown by result that compared wth mechancal stmulaton, electromagnetc eld s a knd o more relable method or mprovng dsuse osteopoross wth relatvely small sde eect. Acknowledgement: Ths work s supported by Natonal Natural Scence Foundaton o Chna ( No ) and 973 NBRPC (973 Program)27CB Reerences [1] Qu CY, Qn QH, Kang Y. A hypothetcal mechansm o bone remodelng and modelng under electromagnetc loads. Bomaterals, 26; 27(21):45-7. [2] Qu C Y.Yu S W.Feng XQ,Hao ZX. model o bone under mechancal-electrc-magnetc loadng. Proc. o 18 th European conerence on racture,21,august 29-September 3, Dresden, Germany. wll be publshed n Computatonal Materal Scence. [3] Martn RB, Burr DB, Sharky NA. Skeletal Tssue Mechancs, Sprnger, New York, [4] Hazelwood SJ, Martn RB, Rashd MM. A mechanstc model or nternal bone remodelng exhbts derent dynamc responses n dsuse and overload. J Bomech, 21 ;34: [5] Notman MT, Nadelson C. The hormone replacement therapycontro- versy. Arch Woman Health, 22; 5: [6] Rubn CT, Mcleod KJ, anyon E. Preventon o osteopoross by pulsed electromagnetc elds. J Bone Jont Surg AM, 1989;71: [7] Jayanand BJ, ochan R. Eects o low level pulsed rado requency elds on nduced osteopoross n rat bone. Inda J Exp Bol, 23;41: [8] Conzalez-Rola J, Pames JA, Hernandez ER. Inluence o electromagnetc elds on bone mass and growth n developng rats: a morphometrc, denstometrc and hstomorphometrc study. Calc Tssue Int, 1997;6: [9] Garland DE, Adkns RH, Matsuno N N. The eect o pulsed electromagnetc elds on osteopoross at the knee n ndvduals wth spnal cord njury. J Spnal Cord Med, 1999;22(4):