Simulations of thermal processes in tooth proceeding during cold pulp vitality testing

Transcription

1 a o Boegeeg ad Boeas ol. 8 No Ogal pape DOI: 0.577/BB Sulaos o eal poesses oo poeedg dug old pulp valy esg MIUSZ CIESIELSKI * BOHDN MOCHNCKI JOSŁW SIEDLECKI 3 Isue o Copue ad Ioao Sees Cęsoowa Uvesy o eology Cęsoowa Polad. Hge Sool o Laou Saey Maagee Kaowe Polad. 3 Isue o Maeas Cęsoowa Uvesy o eology Cęsoowa Polad. Pupose: s pape deals w e aeaal odelg o e eal poesses oug e oo dug a vey e oa a ew seods w a vey old lqud o a pa o e oo ow. I s way oe a sulae a ea ase oo poeedg dug a deal dagos es pulp valy esg. e pa o apd ae eal ages ag o e oo a ause ooae. Meods: e aeaal odel: a syse o paal deeal equaos w al-ouday odos e axallysyeal pole ad e ueal soluos usg e ool volue eod s dsussed. esuls: Sulao esuls o e kes o e epeaue ages sde e oo ae peseed. e exaple o e ool volue es usg e ooo polygos well desg e sape o a ola oo s gve. Colusos: e sulao esuls e epeaue dsuo e oo a ay oe o e sulao e ad e kes o epeaue vaao a e pos o e oo doa osdeed a elp dess e seleo o a appopae eod o eae. Key wods: o-ea ase aeaal odelg eal poesses oo ssue deal pulp esg. Ioduo Deal pulp esg also kow as a valy es o a sesly esg ] ] 7] 8] s a vesgao a povdes poa dagos oao o e deal la. e oo s oposed o ee layes: eael del ad e pulp. e oue laye e eael s ade o ad ysal ad s e os oga oe. e de les us ude e eael ad s e a suue o e oo avg popees as a oe-lke susae. e dee osss o osop lud-lled aels alled dee uules. I e ddle o e oo s e pulp. e ealy pulp s e val ssue ossg o ueous lood vessels eves ad ells u e pulp e auaed oo s o eessaly evaed. ee ae wo geeal ypes o pulp esg ] 7]: a eal es old ad ea ad a eleal oe. I s pape oly old eal es s osdeed. I s es a egea.e. dloodluooeae eyl lode a 50 C s spayed o a sall oo pelle ad appled o e oo ow. s es auses oao o e deal lud w e deal uules. e apd low o lud ese uules esuls o e ydodya oes ag o e eve es. s a ause a sap sesao pa e ealy evaed pulp o e oo w akes a ew seods ae e eoval o old sulus ]. e esea peseed s pape s elaed o e opuaos o epeaue dsuo e ola oo. e a o s pape s e aeaal odelg o e eal poesses oug e oo ssues eael de pulp eg oa w old lqud a oseed oo pelle. Dee oa es w e old lqud ae aalyed. e geoey o e oo s eaed ee as a axally- * Coespodg auo: Maus Ceselsk Isue o Copue ad Ioao Sees Cęsoowa Uvesy o eology ul. Dąowskego Cęsoowa Polad. el: e-al: aus.eselsk@s.p.pl eeved: Novee 8 04 eped o pulao: Sepee s 06

2 34 M. CIESIELSKI e al. syeal doa. e dealed kowledge o eal poesses oug e oo doa wll allow opao o dagoss ad eae saeges o lal applaos. ee s a eed o sudy e eal eavo o oo ad s e a a o s esea. e ea ase e oo doa was osdeed e.g. wok 8] u e aeaal odel s ased o e Foue equao. I woks 5] 9] sulaos wee osdeed a elaed o dee ypes o deal llgs a oo w was oa w a old lqud. e esea pape 0] deals w e eal sulao e D ask o dee oelaed w lud low e deal uule. I sould e poed ou a e pulp s a val ssue ad e odels ased o e Pees equao oag es w e lood peuso ad eaols sould e appled. Deals oeg e oea ase odels a e oud aog oes 4] 0] ] 4]. I s evde a e aalyal soluo o e pole osdeed s possle ad e ueal eods sould e used. I s pape e ool volue eod CM 3] 6] usg e ooo essellao 6] ode o osu e geoeal es oveg e oo doa s appled. e oe o e ueal eod s o adeal. e CM paula usg e ooo essellao osues a vey eeve ool o a appoxae soluo o ouday-al poles oeed w e aeaal odels o ea ase poesses. e dee sapes o ool volues allow us o eosu e eal sape o e D oe o e ase o e oogeeous ad eeogeeous doa. e doa dseao a e loally oeaed o exaple lose o e exeal ouday. e sape o ooo polygos oes us e possly o oe ad exa eodg eegy alaes oulao. ey osue e ase o osuo o e al syse o lea equaos oespodg o e aso o e o e +.. Maeals ad eods.. Maeaal odel e oo doa eaed as e axally syeal oe s sow Fg.. e doa osss o e ollowg su-doas: e eael e de ad e pulp 3. e oue suae lg e doa oudaes ad s eal oa w evoe a. ddoally a so peod o e e ouday s sueed o e vey old lqud. e ouday 0 epeses oa w e gu. Fg.. Suue o a ypal ola oo soue: p:// ad e oo doa osdeed logudal seo e epeaue eld e doa osdeed s desed y e ollowg syse o equaos Q pe Q e ] 3 wee dex dees e paula su-doas e eael e de 3 e pulp C] s e epeaue ] s] deoe spaal oodaes ad e J/ 3 C] W/ C] ae e volue spe ea ad e eal oduvy espevely. e Laplae opeao e yldal axsyeal oodaes syse s gve as ]. I equao e es Q pe ad Q e W/ 3 ] ae e apaes o volue eal ea soues oeed w e lood peuso ad eaols espevely. ssug a e pulp s ed y a lage ue o uoly spaed apllay lood vessels ad e lood vessels ae o pese e del ad eael oe as

3 Sulaos o eal poesses oo poeedg dug old pulp valy esg 35 Q 0 G 3 pe ] wee G 3 s e lood peuso ae e pulp 3 lood/s 3 ssue] s e lood volue spe ea ad s e lood epeaue. e eaol ea soue Q e 3 e pulp su-doa a e eaed as a osa value o a epeaue-depede uo 0] ad sulaeously Q e = Q e = 0 o e eael ad del su-doas ave ee assued. Equao s suppleeed y e oudayal odos. Fo = 0 e al odo s kow O e oa suaes ewee oo sudoas e ouy odos ae assued k l k l : k l k l k l { 3} 5 wee / s a oal devave. O e exeal suaes o e su-doas e Dle o e suaes 0 ad ad e o o e suae o e oo ow ad ouday odos ae gve { 0 }: ssue 3 6 a : a a ] : a a a ] o 0 ] oa ] lq a lq ] o oa ] 7 8 wee a lq W/ C] ae e oveve ea ase oees ad a a a lq C] ae e epeaues o e a o lud espevely. I e aeaal odel e ollowg splaos ae assued: e epeaue o e lud gows aodg o a gve uo ad e ea ase oees ae eaed as e osa values depede o seveal aos lud veloy suae geoey aue o oo e.. e s a oe o sulao e a w e oa o e oseed oo pelle w old lqud akes plae. e oa s e oa e o e pelle w e oo ow ad s e al e o sulao. I e e eval 0 ] e pae as a ope ou ad eag s auses oolg o e oo w espe o e al epeaue eoe sag a dagos es. O e ouday e o-lux ouday odo s gve : Cool volue eod e sage o ueal odelg e ool volue eod CM usg e ooo essellao as ee used. sla veso o CM o e D ask was dsussed deal y Ceselsk ad Moak 3] 6]. I s pape e ool volues ae e sape o gs. So e doa aalyed e logudal seo o e oo s dvded o N volues e seo o e g-saped elee oespods o e sape o e ooo polygo. I Fg. e exaple o e ool volue es N = 835 ad e seleed ool volue ae peseed. e CM algo allows oe o d e ase epeaue eld a e se o odes oespodg o e eal pos o e ool volues wle e odal epeaues ae oud o e ass o eegy alaes o e suessve C. I Fg. 3 e oss-seo o ool volue C w e eal ode p = s peseed. s oss-seo s a o-egula -sded polygo a e sae e s e ue o adae ool volues C o =... oag e odes p. Susp daes e dex ue o e adae C. e dsae ewee odes p ad p s deoed y weeas e aea o oa suae ee e suae oaed y oao o e polygo sde aoud e axs ewee wo adae C ad C s equal o ad e volue o g-saped C s deoed y. I e polygo suae s oveed y e ousde ouday o su-doas e e vual egoug ode p les ousde e doa osdeed ad e opuaoal algo

4 36 M. CIESIELSKI e al. e dex epeses e dex ag o e ouday ee 0 o. C C C Q pe Q dd ]dd e ]dd. 0 pplyg e dvegee eoe o e volue C ouded y e suae = oe oas C C Q pe Q dd ]dd e ]dd. e ueal appoxao o e le-ad sde o equao a e aeped e o Fg.. e ool volue es e seo o e oo ad seleed g-saped ool volue C dd Fg. 3. Cool volue C wee s a egal ea o eal apay ad s value s appoxaed y e volue spe ea oespodg o e epeaue expl see. e soue e equao o e pulp su-doa 3 s eaed a sla way I s assued o ea ool volue C a e eal apaes ad e apaes o eal ea soues ae oeaed a e odes epeseg elees wle e eal essaes ae oeaed o e seos og e odes. e eegy alaes oespodg o e ea exage ewee e aalyed ool volue C ad adog ool volues esul o e egao o eegy equao w espe o e ad volue C. Le us osde e eval o e =. e C Q Q pe pe Q Q e e dd ] G3 Qe ]. 3 e e deeg ea oduo ewee C ad s egouoods C a e we o e expl see e o

5 Sulaos o eal poesses oo poeedg dug old pulp valy esg 37. ] d ] d d ] d ]d 4 I e ase we s plaed ewee C ad eal C e s appoxaed as ollows ] 5 wee s e ao ea eal oduvy ewee odes p ad p deed as 6 ad / s e eal essae. I s a pa o e ouday o e oe o e ouday odos 7 o 8 s used ad s ase e ollowg oula s appled a 7 wee a { a a a lq } ad { a lq } sould e seleed espevely. Oe a see a e deoao e aove oula oespods o e eal essae elaed o e o ouday odo. I s a pa o e ouday 0 o e e Dle ouday odo 6 s used ad e oula deeg s o e o. ssue 8 I e ase we odes w e axs = 0 e..e. equvale o 0 ssue 9 e sage o ueal opuaos e plae o a lage value.e. 0 0 a e assged. I ode o esue e uao o oaos o e ouday oulas 7 8 ad 9 w e geeal oula 5 oe a use e ollowg values } ad { lq a ssue ssue a lq a a 0 depede o e appopae ouday odos. e eegy alae we e expl o leads o e equao Q G e ] 3 o. 3 e Q G e al odo 4 s pleeed as 0 = =... N. I ode o esue e saly odo o expl see e oee elaed w us e posve 0 3 G 3 o all ool volues C = N. Hee allows oe o deee e al e sep G 3. 4

6 38 M. CIESIELSKI e al. 3. esuls wo ueal sulaos o eal poesses poeedg e oo doa ave ee exeued. I Fg. e sape ad desos o e doa osdeed ad e ool volue es ae peseed. e ollowg eopysal paaees o e oo layes ave ee assued 9]: = 750 = 70 3 = 400 J/kg K = 900 = 00 3 = 000 kg/ 3 = 0.9 = = 0.59 W/ K. e al epeaue s = 36.6 C e epeaue o e ae lud s lq a = C ad e ea ase oee s lq = 000 W/ C wle paaees o e a ae e ollowg a a = 5 C ad a = 5 W/ C. I sulaos wo oa es oa = s ad oa = 4 s e e ls = 60 s = 90 s ad e ssue epeaue ssue = 36.6 C ave ee assued. Fg. 5. epeaue dsuo e oo su-doas a e 60 + oa s] Fg. 6. epeaue dsuo e oo su-doas a e 75 s Fg. 4. epeaue dsuo e oo su-doas a e 60 s I Fgs. 4 5 ad 6 e soes e oo sudoas o es 60 s 60 s + oa ad 75 s ae sow espevely. e kes o epeaue vaao a seleed pos B ad C loaed ea e oudaes o oo su-doas see Fg. ae peseed Fg. 7. Fgue 8 sows e e devaves o epeaue a pos B ad C. e ool volues epeseed y e eal odes B ad C ae plaed e de ad e pulp su-doas espevely. Fg. 7. e kes o epeaue vaao a seleed pos see Fg.

7 Sulaos o eal poesses oo poeedg dug old pulp valy esg 39 Fg. 8. e e devaves a pos B ad C see Fg. 4. Dsusso Fs o all e auos assued a e epeaue o e oo a e al oe o e oespods o e aveage ody epeaue 36.6 C. Nex o ue e pae as s ou ope wle e des pepaes o peo a dagos es. s e e oo s ooled y e poess o eag peod eag ou o ool a ad wa a exalao. e sage o ueal odelg e ea splao s odued aely a osa aveage epeaue e oal avy o a peod o ue s assued. e aou o ea dsspaed y e oo a s e depeds o aog oes e equey ad esy o eag e geoey o e ou e ae epeaue ad ae udy e. I s a oplex poess ad e ea exage a e sage o alulaos was esseally spled y e assupo o e osa ea ase oee oug e o ouday odo. O e ass o e epeaue eld sow Fg. 4 oe a see a as a esul o oolg e axu epeaue dop o e ow suae equals aou 3 K. e epeaue eld Fg. 4 oespods o e sae wee a apd oolg o e oo ude e luee o a exeal ao egs. e pole o apd oolg e odeled ask as also ee spled y e use o e d kd o ouday odo e o odo ad e adopo o e suoudg edu epeaue e o o uoal depedee wle e ea ase oee s assued o e a osa value. e ouse o e uo lq a depeds o ay aos u sould e a easg uo eause e soaked swa e oseed oo pelle s eaed y e wae oo e ou. Fgues 5 ad 6 sow e epeaue elds oaed o dee oa es ewee e oola ad oo wle Fg. 7 e epeaue soes a seleed pos ae peseed. I a e see a e epeaue deees o e ow suae e peod o wo aalyed oa es dug apd oolg ae sall. I oas e deees ae oe oeale e e layes o e oo espeally e aeas lose o e ouday ewee e eael ad de po B. alyg e kes o epeaue ages oe a olude a e eduo o epeaue sde e oo akes plae eve ae e oo oa w a oo swa. e epeaue dop e de laye a po B see Fg. 8 s oeale eve a ew seods ae e de lqud oolg ad e axu value eaes alos 3 K/s. I e pulp laye a po C e epeaue dop s salle up o 0.5 K/s ad akes a log peod o e. e apd dop epeaue e de laye auses a age pessue o e deal lud w e aels ad s oao aodg o oe eoy o pa sesao so a ovee o e lud a ause ao o e eve es. I e daaged dead oo ee ae o ave eve es ad e pa sould o e el. So a we dd o d ay sla esuls o o expeeal ad aeaal odels e leaue a a e used o aalyse ad opae w ou ueal sulao esuls. Fo a expeeal po o vew e use o e val oo e vvo vesgao s ae possle o eal easos. e wdely used eod o sudy e eal eavou o ua oo vo s ased o eoouples u a e eally allegg o e sudy due o e sall se ad oplex geoeal suue o e ologal oo. ese expeeal esuls ay oa easuee eos ad e ause s e.g. low spaal esoluo ad oa easuee. Fo a val oo e suggval pa o e oo s suouded y e evoeal ssues w lood vessels. Seveal woks wee elaed o e expees w ee. I wok 0] e epla o a axsye odel o oo o expeeal puposes as ee used ode o sulae e eal poesses oug wle dkg o lquds. Jakuek e al. 9]

8 40 M. CIESIELSKI e al. ave ee odelled ad sulaed e poess o poopolyeao ad elaed o e ages epeaue dug lg-ug o deal esoaos. I pape ] e auos peseed e expeeal esuls also vo as e eld epeaue dsuo o e suae o a oss-seo o a ua ola oo sled logudally o wo alves. e oo was eaed y ulag o wae ad ooled dow y a ad a e sae e e aed aea egseed e oo suae epeaue. Oe a oe a su expeeal appoaes e esea aed ou e laoaoes do o ully oespod w e ologal ealy. e a a o expeeal sudes s o all was o deee e eopysal paaees o paula layes o a oo ad e paaees o odos ag o e oo w a e used sulaos peoed o e ass o aeaal odels. I sould e eoed a e way o odellg o e ea ase pole poeedg dug pulp valy esg so a as o appeaed e kow woks. 5. Colusos vey oo pole dsussed aade woks s oo sesvy o vaous exeal sulaos. e odel peseed a povde oao elaed o e epeaue eld e oo ad e kes o e epeaue ages e vaous oo su-doas ad e sulao esuls a asss dess e seleo o a appopae eod o dagoss ad eae. Fo exaple dely ae e opleo o eeg e epeaue a po eases wle a pos B ad C oues o deease. s esuls o e edued epeaue o e eael su-doa. So e oolg ee lass loge a e eal oa w e oola. I oe wods a sudde dop o epeaue a pos plag pulp ad de su-doas a ause sap pa e oo lasg eve a ew seods ae opleo o eeg. e esuls o ueal sulaos dsussed ee oe e seleed oo geoey u e algo peseed a e used o e dee paaees oug e aeaal odel ad ay geoeal sape o e oo. I s pape e possles o e CM applao o a ueal soluo o e oea ase ae sow. e ool volue eses usg e ooo polygos auaely epodue e geoey o e oo e assupo a D axally-syeal appoxao s aepale s a esseal advaage o e eod poposed. I e uue esea s plaed oeed w e elaoao o e ueal algo ased o e ool volue eod w e eopysal paaees o oo su-doas wll e eaed as e eval ues 5] 7]. s esuls o e a a e ologal ssue popees ae depede o e dvdual aaess su as gede age e. ddoally e expeeal esea usg e eal agg eques wll e ealed. Su a sudy wll allow oe a leas o oseve e ouse o ase epeaue eld o e suae o e oo ow. eeees ] CHEN E. BBO P.. Deal Pulp esg: evew I. J. De ] CHONG B.S. Hay s Edodos Clal Pae 6 ed. Cull Lvgsoe 00. 3] CIESIELSKI M. MOCHNCKI B. pplao o e Cool olue Meod usg e ooo polygos o ueal odelg o o-ea ase poesses J. eoe. ppl. Me. 04 ol ] CIESIELSKI M. MOCHNCKI B. Nueal sulao o e eag poess e doa o ssue sulaed y poeve log J. ppl. Ma. Copu. Me. 04 ol ] DE EE J.H.P. SPIEINGS H..M. PLSSCHE.J.M. Sulao Model o ase eal alyss o esoed ee J. De. es. 983 ol ] DOMNSKI Z. CIESIELSKI M. MOCHNCKI B. pplao o Cool olue Meod usg e ooo essellao Nueal Modellg o Soldao Poess :]. Kosusky ed. Cue ees Egeeg See 009 IP Co. Po. 00 ol ] GOPIKISHN. PDEEP G. ENKESHBBU N. ssesse o pulp valy: a evew I. J. Paeda. De. 009 ol ] JFZDEH H. BBO P.. evew o pulp sesly ess. Pa I: Geeal oao ad eal ess I. Edod. J. 00 ol ] JKUBINEK M.B. O NEILL C. FELIX C. PICE.B. WHIE M.. epeaue exusos a e pulp-de uo dug e ug o lg-avaed deal esoaos De. Mae. 008 ol ] LIN M. XU F. LU.J. BI B.F. evew o ea ase ua oo Expeeal aaeao ad aeaal odelg De. Mae. 00 ol ] LIN M. LIU Q.D. XU F. BI B.F. LU.J. I vo vesgao o ea ase ua oo 4 I. Co. dv. Exp. Me Sgapoe 009. ] MJCHZK E. pplao o dee vaas o e BEM ueal odelg o oea ase poles Mol. Cell. Boe. 03 ol ] MJCHZK E. MOCHNCKI B. DZIEWOŃSKI M. JSIŃSKI M. Nueal odelg o ypeea ad ypoea po-

9 Sulaos o eal poesses oo poeedg dug old pulp valy esg 4 esses Copuaoal Maeals See PS -3. Book Sees: dv. Mae. es 0 ol ] MOCHNCKI B. MJCHZK E. Sesvy o e sk ssue o e avy o exeal ea soues Cop. Model. Eg. S. 003 ol ] MOCHNCKI B. PISECK BELKHY. Nueal odelg o sk ssue eag usg e eval e deee eod Mol. Cell. Boe. 03 ol ] OKBE. BOOS B. SUGIH K. CHIU S.N. Spaal essellaos: Coeps ad pplaos o ooo Dagas d ed. Wley ] PISECK BELKHY. Ieval ouday elee eod o D ase duso pole usg e deed eval ae Eg. al. Boud. Ele. 0 ol ] PEISKON M. ŻMUD S. YKOWSKI J. PNS. PEISKON M. I vo vesgaos o e ea ase peoea ua oo a Boeg. Boe. 003 ol ] SIEDLECKI J. CIESIELSKI M. Sulaos o eal poesses a esoed oo J. ppl. Ma. Copu. Me. 03 ol ] SPIEINGS.. PEES M.C. BOSMN F. PLSSCHE.J. eao o eoeal odelg o ea assso ee y vvo expees J. De. es. 987 ol