Thermal Effects of Laser osteotomy on Bone: Mathematical Computation Using Maple

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1 Short Communiction Therml Effects of Lser osteotomy on Bone: Mthemticl Computtion Ug Mple Asghr Gholmi, Molood Brdrn Ghhfrokhi,, Mrjn Erhimi 3, Mild Brdrn Ghhfrokhi 4,5 Deprtment of Electricl nd Computer Engineering, Isfhn University of Technology, Isfhn, Irn, Medicl Student s Reserch Center, School of Medicine, Isfhn University of Medicl Sciences, Isfhn, Irn, 3 Deprtment of Physics, Khorsgn (Isfhn) Brnch, Islmic Azd University, Isfhn, Irn, 4 Deprtment of Medicl Physics nd Medicl Engineering, School of Medicine, Isfhn University of Medicl Sciences, Isfhn, Irn, 5 Deprtment of Medicl Rdition Engineering, Fculty of Advnced Sciences nd Technologies, Isfhn University, Isfhn, Irn Sumission: 6 3 Accepted: ABSTRACT In recent yers, interest in medicl ppliction of lsers especilly s surgicl lterntive is considerly increg due to their distinct dvntges such s non contct intervention, cteriostsis, less trumtiztion, miniml invsiveness, decresed leeding nd less het dmge. The present study imed to evlute the temperture chnges nd the consequent relesed therml stress in corticl one cused y n Erium:yttrium luminum grnet (Er:YAG) lser (Fideliss 3A, Foton Inc., Deggingen, Germny) during osteotomy, ug mthemticl computtion y mens of Mple softwre, version 9.5 (Mplesoft, division of Wterloo Mple Inc., Cnd). The results otined here were compred with the experimentl mesurements ug Er:YAG lser in the osteotomy clinics. A one sl with thickness of mm ws simulted in Mple softwre. Then, n Er:YAG lser emitting μs pulses t wvelength of 94 nm were modeled. Two different clinicl settings of the Er:YAG lser with mj nd 4 mj energies, oth with μs exposure nd 5 μs silence were studied. To investigte the temperture distriution in the corticl one, the time dependent het conduction equtions were defined nd solved in the Mple softwre. Finlly, y defining the het distriution function in the Mple, therml stress in the one ws investigted. Results of the computtions showed tht, on the one irrdited re (center of the one surfce) the mximum temperture rise ws.8 C nd.6 C, for mj nd 4 mj Er:YAG lser exposure, respectively. The temperture rise reched to its minimum t rdil distnces of. cm from the point of irrdited re for mj lser while it ws.5 cm for 4 mj lser. For mj lser the mximum derived rdil (s rr ), xil (s zz ) nd zimuthlly (s ) stress components were.,.6 nd.8 MP, respectively. While, for 4 mj lser the mximum derived s rr, s zz nd s stress components were.39,.3 nd.6 MP, respectively. These results confirm tht use of μs Er:YAG lser pulses with 5 μs silence t nd 4 mj energies minimizes therml tissue dmge for the lser osteotomies, without continued wter cooling (irrigtion) on the exposed re. Key words: Erium:yttrium luminum grnet lser, lser osteotomy, Mple softwre INTRODUCTION In recent yers, interest in medicl ppliction of lsers especilly s surgicl lterntive is considerly increg. [] Considering distinct disdvntges of the urrs nd sws such s extensive het deposition, rodening of cuts, mechnicl trumtiztion, the deposition of metl shvings nd cteril contmintion, lsers offer severl significnt dvntges. Compred with other conventionl surgicl procedures the lser distinct dvntges in surgery re non contct intervention, cteriostsis, less trumtiztion, miniml invsiveness, decresed leeding nd less het dmge. [] The first serious ttempts on ug lsers to replce the urr is reported y Horch et l. who hve extensively studied the potentil use of lsers for osteotomy procedures. [3,4] It hs een stted tht, excessive het is the mjor source of dmge in ony tissues during one osteotomy. [5] Eriksson nd Alrektsson descried the criticl temperture of 47 C for one. Moreover, they lso noted tht temperture elevtion etween 44 C nd 47 C my lredy led to tissue necrosis. [6,7] It should e noted tht, het nd necrosis hve directly proportionl reltionship [6,8] nd incresed res of necrosis result in tissue rekdown nd impirment of wound heling. [7,8] If the zone of necrotic one exceeds certin limit, the ody is no longer le to esily remove the devitlized tissues. In this regrd, investigtors hve shown tht reduction of het, shortens heling periods nd llows fster integrtion of osteosynthesis. [9] Address for correspondence: Dr. Mild Brdrn Ghhfrokhi, Deprtment of Medicl Physics nd Medicl Engineering, Isfhn University of Medicl Sciences, Isfhn , Irn. E mil: mrdrn@edc.mui.c.ir 6 Vol 3 Issue 4 Oct-Dec 3

2 Gholmi, et l.: Therml effects of Er:YAG lser osteotomy on one However, sfety nd the efficcy of the lser depend on pplied lser prmeters s well s on the tissue chrcteristics. [] Erium:yttrium luminum grnet (Er:YAG) lser re widely used for osteotomy procedures. The Er:YAG lser, with the wvelength of.94 μm, hs demonstrted promig results with one tissue due to mximum coincides with wter sorption in the one. [] Mjorn et l. found tht, het diffusion for Er:YAG lser t short pulse length (5 3 μs) is negligile. [,] Moreover, clinicl trils studying lser drilling in dentine with Er:YAG lser light t pulse length of μs did lredy confirm the tissue preserving the chrcter of the lser prmeters. [3] To void temperture rise in hrd tissue structures, the pulse durtion hs to e set close to the therml relxtion time of the tissue respective of ltion thresholds. [] It cn e ssumed tht the therml relxtion time for one is est estimted t rnge etween μs nd 8 μs. The im of this study ws to evlute the temperture chnges nd the consequent relesed therml stress in corticl one slices cused y n Er:YAG lser during osteotomy, ug mthemticl computtion y mens of Mple softwre, version 9.5 (Mplesoft, division of Wterloo Mple Inc., Cnd). The results otined here were compred with the experimentl mesurements ug Er:YAG lser in the osteotomy clinics. [] According to the est of our knowledge, the use of such computtion with methodology descried here on lser systems for clinicl pplictions on humn one hs not een reported so fr. The use of computtionl methods for the study of ntomicl orgns cn yield informtion tht is difficult or impossile to otin experimentlly. Therefore, t this study computtionl method ws used to ssess the chnges in temperture during lser osteotomy. MATERIALS AND METHODS Study method ws in ccordnce with the experimentl work on the mesurements of temperture chnges in corticl one slices during osteotomy procedure. [] A one sl with thickness of mm ws simulted ug Mple softwre. Tle gives the thermo mechnicl chrcteristics of the corticl one for the clcultions. Then, n Er:YAG lser (Fideliss 3A, Foton Inc., Deggingen, Germny) emitting μs pulses t wvelength of 94 nm ws modeled. The lser ws considered with uilt in 65 nm nd mw trget em. At the point of Tle : Thermo-mechnicl chrcteristics of the corticl one Prmeter Vlue Young s modulus (E) (GP) [4] 4.8 Poison rtio ( ) [5]. Density (kg/m 3 ) [5] 9 Therml expnsion (mm/ C) [6] 7.5±3.9 6 Therml contrction (mm/ C) [6] 7.±5. 6 Therml conductivity (W/mK) [7].54 Specific het (J/kg K) [] 6 incidence of the lser em, the dimeter of the irrdited re ws set to e pproximtely. mm. At this work different clinicl settings of the Er:YAG lser with mj nd 4 mj energies, oth with μs exposure nd 5 μs silence were studied. Wter cooling ws neglected from this study. However, for clinicl pplictions, one cn clculte the wter flow rte ug results of the temperture chnges nd the consequent relesed therml stress in the one slice. To investigte the temperture distriution in the corticl one, the time dependent het conduction equtions were defined nd solved in the Mple softwre. The eqution of the het distriution function cn e clculted s follows: [] T( z, t)= m= ( ( ) ) l mlπ cos mπ e Q + l l + m π K m l π z + l cos mπ e l l + m π Q + K cos nπ Q K nπ K + n π ρ c n= l ( ( ) ) n= 4 π mc ρ t r 4 ω ρ m l z Qe + K K z e e n= ( ) nπ Q K ( ) 4 nπ K + n π ρ c Qe nπ z 4 π + π ρ ( ) n K n c nπ n t n c t π cos πρ e r 4 4 ω p () Vol 3 Issue 4 Oct-Dec 3 63

3 Gholmi, et l.: Therml effects of Er:YAG lser osteotomy on one Finlly, y defining the het distriution function in the Mple, therml stress in the one ws investigted ug elow equtions. [8] σ rr ro T E = rtdr v r r r rtdr r σ = T E θθ T + + v rtdr r r σ zz T E = T + v r r r rtdr rtdr Where s rr, s zz nd s re the rdil, xil nd zimuthlly stress components respectively, E is the young s modulus; n is the Poisson rtio nd T is therml expnsion coefficient. RESULTS Results of the computtions showed tht, on the one irrdited re the mximum temperture rise ws.8 C () (3) (4) nd.6 C, for mj nd 4 mj Er:YAG lser exposure, respectively. The temperture rise reched to its minimum t rdil distnces of. cm from the point of irrdited re for mj lsers, while it ws.5 cm for 4 mj lsers. Figure shows the distriution of temperture rise on the corticl one surfce for oth mj nd 4 mj Er:YAG lser t different rdii from the irrdited re. Considering the one depth from the irrdited re, for mj lser the temperture rise reched to its minimum vlue t.5 mm. While, for 4 mj lser the mentioned depth ws.8 mm, significntly higher thn mj lser. Figure gives the distriution of temperture rise on the corticl one irrdited re for mj nd 4 mj Er:YAG lser t the one irrdited re to depth of.5 mm from the irrdited re. Figure 3 illustrtes the one temperture rise following n μs pulse of the mj nd 4 mj Er:YAG lser t different rdii nd depths from the irrdited re. Figure : Distriution of temperture rise on the corticl one irrdited re for, () mj nd, () 4 mj Erium:yttrium luminum grnet lser t different rdii from the irrdited re Figure : Distriution of temperture rise on the corticl one irrdited re for, () mj nd, () 4 mj Erium:yttrium luminum grnet lser t different depths from the irrdited re 64 Vol 3 Issue 4 Oct-Dec 3

4 Gholmi, et l.: Therml effects of Er:YAG lser osteotomy on one Considering the consequent derived therml stress due to lser exposure, it ws found tht for mj lser the mximum derived rdil (srr), xil (szz) nd zimuthlly (s ) stress components were.,.6 nd.8 MP, respectively. While, for 4 mj lser the mximum derived srr, szz nd s stress components were.39,.3 nd.6 MP, respectively. Figures 4 nd 5 show the derived srr, szz nd s stress components for nd 4 mj lser, respectively, t different depths nd rdii from the exposed re. DISCUSSION In this study, the temperture chnges nd the consequent relesed therml stress in corticl one slices cused y n Er:YAG lser during osteotomy ws evluted ug Figure 3: Bone temperture rise following n μs pulse of the mj nd 4 mj Erium: yttrium luminum grnet lser t different rdii, () nd depths, () from the irrdited re c Figure 4: Derived () srr, () szz, nd (c) s stress components for mj lser t different depths nd rdii from the exposed re (minus vlue refers to one contrction) c Figure 5: Derived () srr, () szz nd (c) s stress components for 4 mj lser t different depths nd rdii from the exposed re (minus vlue refers to one contrction) Vol 3 Issue 4 Oct-Dec 3 65

5 Gholmi, et l.: Therml effects of Er:YAG lser osteotomy on one Mple mthemticl computtion. The nlysis ws performed sed on the previous work on the experimentl mesurements of temperture chnges in corticl one slices during osteotomy procedure. [] The results showed tht, for μs pulse of 4 mj Er:YAG lser, the temperture rise t the exposed re is.6 C [Figure ]. This ws in good greement with the mesured vlue of. C ug digitl thermometer plced on the one during Er:YAG lser osteotomy t sme settings. However, for mj lser, the discrepncy etween the computed nd mesured vlue ws reltively higher (up to. C). The discrepncy ws minly due to uncertinties in the experimentl mesurements nd lso the used thermo mechnicl chrcteristics in the simultions. Since thermo mechnicl chrcteristics of the corticl one is relted to ge nd diseses, mteril uncertinty might cuse considerle effect on the simulted model. [9] As cn e seen from Figures 4 nd 5, derived consequent therml stress ws less thn.4 MP for μs pulse, significntly elow thn the one yield stress of MP. However, it should e noted tht for continues exposure or pulse durtion of > μs the derived vlue reches lrger vlue. Generlly, the stress ehvior of one is relted to the mechnicl properties of the minerl phse, the spect rtio of the minerl pltelets nd the mechnicl properties of the orgnic mtrix. [9] Gerold Eyrich, mesured the temperture rise nd potentil therml dmge to tissue during ltion of one ug n Er:YAG lser, equipped with wter cooling spry. The results of his work reveled the men temperture rise of. C on the one irrdited re. While, in this work, het conduction eqution ws solved for the similr one slice dimensions nd the temperture rise t the exposed re ws clculted to e.6 C [Figure ], which ws in good greement with Gerold Eyrich mesurements. [] Recently, Elhi nd Frsi, simulted the temperture distriution in dentin under pulse Er:YAG lser rdition. In ccordnce to our work, they hve solved het conduction eqution nd consequently they hve otined the temperture distriution in dentin. Bsed on their results, on the dentin irrdited re the mximum temperture rise ws 3.7 C, for 3 mj Er:YAG lser exposure, which hve very good consistency with the experiment. It should e noted tht, compred with our work, the min differences ws the defined thermo mechnicl chrcteristics of the corticl one nd dentin for the clcultions. [] Lee et l. presented new therml model for one drilling with pplictions to orthopedic surgery. Their new model comined unique het lnce eqution for the system of the drill it nd the chip strem, n ordinry het diffusion eqution for the one nd het genertion t the drill tip, rig from the cutting process nd friction. In ccordnce to our results, they found tht, the mximum temperture 66 rise depends strongly on the osteotomy rdius nd depth [Figure 3 nd ]. [] At this study, different comintions of power were considered to evlute the temperture chnges nd consequent therml stress. However, it is lso extremely difficult to determine precise vlue, due to the individul difference etween one smples, e.g., mturity of one, degree of minerliztion, distriution of one components (collgen), density of one, orienttion of lyers nd etc., For simplicity, only n verge vlue of the thermo mechnicl properties of one ws introduced, tking into ccount for the nlysis. These results could e used s guideline in numerous clinicl pplictions in one osteotomy, especilly in designing wter coolnt, i.e., wter flow rte. However, the fesiility of the method depends on ccurte geometry construction, precise oundry condition definition nd suitle thermo mechnicl chrcteriztion. [] As stted erlier, to prevent therml dmge to djcent tissue lyers, the rise in one tissue temperture my not exceed 47 C, nor persist for durtion longer thn min on 44 C. [,] Results of this study confirm tht, use of μs Er:YAG lser pulses with 5 μs silence, without continued wter cooling on the exposed re, minimizes therml tissue dmge for the lser osteotomies. In this work, simple model hs een considered wherein the viscoelstic nture, hierrchicl orgniztion nd locl vritions in minerl content of one tissue hve not een tken into ccount. Moreover, the orienttion of the minerl nd orgnic hs not een considered. We hve ssumed tht the minerl nd orgnic re isotropic. We hve lso neglected the complicted shpe, orienttion nd distriution of the micro porosity. CONCLUSION In this pper, therml effects nd the consequent relesed therml stress in corticl one slices cused y n Er:YAG lser during osteotomy ws evluted ug mthemticl computtions. These results confirm tht use of μs Er:YAG lser pulses with 5 μs silence t nd 4 mj energies minimizes therml tissue dmge, without continued wter cooling on the exposed re. The results otined were compred with the experimentl mesurements nd good greement ws found. REFERENCES. Lee J, Rin Y, Ozdognlr OB. A new therml model for one drilling with pplictions to orthopedic surgery. Med Eng Phys ;33: Eyrich GK. Lser osteotomy induced chnges in one. Med Lser Appl 5;:5 36. Vol 3 Issue 4 Oct-Dec 3

6 Gholmi, et l.: Therml effects of Er:YAG lser osteotomy on one 3. Horch HH. Zum ktuellen Stnd der Lser osteotomie. Orthopdie 984;3:5. 4. Horch HH, McCord RC, Keiditsch E. Histologicl nd long term results following lser osteotomy. In: Kpln, I. (editor). Lser Surgery II. Jeruslem Acd Press; Li S, Chien S, Brånemrk PI. Het shock induced necrosis nd poptosis in osteolsts. J Orthop Res 999;7: Eriksson AR, Alrektsson T. Temperture threshold levels for het induced one tissue injury: A vitl microscopic study in the rit. J Prosthet Dent 983;5: Eriksson RA, Alrektsson T. The effect of het on one regenertion: An experimentl study in the rit ug the one growth chmer. J Orl Mxillofc Surg 984;4: Lundskog J. Het nd one tissue. An experimentl investigtion of the therml properties of one nd threshold levels for therml injury. Scnd J Plst Reconstr Surg 97;9: Eriksson RA, Adell R. Tempertures during drilling for the plcement of implnts ug the osseointegrtion technique. J Orl Mxillofc Surg 986;44:4 7.. Elhi P, Frsi B. The nlyticl clcultion of the temperture distriution in dentin under pulse Er:YAG lser rdition. Eur Phys J Appl Phys ;5:7.. Zhn H, Jungnickel V, Ertl T, Schmid S, Muller G. Bone surgery with Er:YAG lser. Lsermedizin 997;3:3 3.. Mjorn B, Sustercic D, Lukc M, Skleric U, Funduk N. Het diffusion nd deris screening in Er:YAG lser ltion of hrd iologicl tissues. Appl Phys B 998;66: Nir PN, Bltensperger MM, Luder HU, Eyrich GK. Pulpl response to Er:YAG lser drilling of dentine in helthy humn third molrs. Lsers Surg Med 3;3: Rho JY, Ashmn RB, Turner CH. Young s modulus of treculr nd corticl one mteril: Ultrsonic nd microtensile mesurements. J Biomech 993;6: Dechow PC, Wng Q, Peterson J. Edentultion lters mteril properties of corticl one in the humn crniofcil skeleton: Functionl implictions for crniofcil structure in primte evolution. Ant Rec (Hooken) ;93: Rnu HS. The therml properties of humn corticl one: An in vitro study. Eng Med 987;6: Dvidson SR, Jmes DF. Mesurement of therml conductivity of ovine corticl one. Med Eng Phys ;: Hung YS, Tsi HL, Chng FL. Thermo optic effects ffecting the high pump power end pumped solid stte lsers: Modeling nd nlysis. Opt Commun 7;73: Koth SP, Guzelsu N. Tensile ehvior of corticl one: Dependence of orgnic mtrix mteril properties on one minerl content. J Biomech 7;4: Bermn AT, Reid JS, Ynicko DR Jr, Sih GC, Zimmermn MR. Thermlly induced one necrosis in rits. Reltion to implnt filure in humns. Clin Orthop Relt Res 984;86: Kruse LS, Co CM, Rpley JW, Killoy WJ, Spencer P. Lser irrdition of one. I. An in vitro study concerning the effects of the CO lser on orl mucos nd sujcent one. J Periodontol 997;68:87 8. How to cite this rticle: Gholmi A, Brdrn Ghhfrokhi M, Erhimi M, Mild Brdrn Ghhfrokhi M. Therml Effects of Lser osteotomy on Bone: Mthemticl Computtion Ug Mple. J Med Sign Sens ;3: Source of Support: Nil, Conflict of Interest: None declred Vol 3 Issue 4 Oct-Dec 3 67

7 Gholmi, et l.: Therml effects of Er:YAG lser osteotomy on one BiogrphIES Asghr Gholmi received his B.Sc. nd M. Sc. degrees in Electronics Engineering from Isfhn University of Technology, Isfhn, Irn, in 993 nd 996, respectively, nd Ph.D. degree in Electricl Engineering from Ecole Supérieure d Electricité (Supélec), Frnce, in 3. He ws wrded post-doctorl fellowship y Supélec University in 7. As post-doctorl fellow he worked on the Modeling, Simultion nd Chrcteriztion of Next-Genertion Multimode Fiers. He hs pulished severl reserch ppers in this re. He is currently Assistnt Professor t the Deprtment of Electricl nd Computer Engineering, Isfhn University of Technology, Isfhn, Irn. E-mil: Gholmi@cc.iut.c.ir Molood Brdrn Ghhfrokhi is currently M.Sc. student of Electronics Engineering t the Deprtment of Electricl nd Computer Engineering, Isfhn University of Technology, Isfhn, Irn. Her reserch interests include Medicl Applictions of Lsers nd Rdiofrequency Rdition. She hs pulished severl reserch ppers in these res. E-mil: M.rdrn@ec.iut.c.ir Mrjn Erhimi received the B.Sc. degree in Atomic Physics from Islmic Azd University, Shhrez (Isfhn) Brnch, Isfhn nd M.Sc. degree in Lser Physics from Shirz Pym-e-Noor University, Shirz, Irn. Her reserch interests include Medicl Applictions of Lsers nd Biomedicl Engineering. E-mil: Mrjn_erhimi@yhoo.com Mild Brdrn Ghhfrokhi ws orn in Isfhn, Irn, in 983. He received the B.Sc. degree in Mechnicl Engineering nd M.Sc. degree in Medicl Rdition Engineering from Shirz University, Shirz, Irn. He is currently Ph.D. student of Medicl Physics t Isfhn University of Medicl Sciences, Isfhn, Irn. His reserch interests include iomechnicl Finite Element Modeling, Monte Crlo simultion, 4D rdiotherpy, rdition shielding design nd mnufcturing nd nonionizing rdition. E-mil: Mild_gh@yhoo.com 68 Vol 3 Issue 4 Oct-Dec 3