Numerical and experimental evaluation of energy inputs, temperature gradients, and thermal stresses during restorative procedures Wayne S. Brown, PhD Dale O. Christensen, MS B. A. Lloyd, PhD, Salt Lake Cityl
Wet cutting in enamel should be used during re storative procedures. According to evidence re ported here, dry cutting can induce sufficiently high therm al stresses to fracture the enamel. Tempera tures resulting from dry cutting in dentin are high enough to cause b io log ic pulp damage if the cutting is w ithin 1 to 2 mm of the pulp. Cracks induced in the cavity w alls by dry cutting may eventually contribute to m arginal failure. A hand-held syringe directing a small, high-velocity stream of w ater into the cutting region is a more effective cooling technique than an air-water spray.
M odem high-speed dental handpieces are capable o f depositing significant quantities o f energy in the tooth structure while cutting. This can result in excessive tem peratures, w hich may contribute to both biologic and structural dam age to the tooth m aterials. T he dental profession has long been concerned with the potential biologic dam age th at can occur to the tooth pulp tissue from excessive tem pera tu re s .13 Experim ents w ith m onkeys have shown th at a 10 F (5.6 C) intrapulpal tem perature rise resulted in an eventual pulp death rate of 15%, w hereas a 20 F (11.1 C) intrapulpal tem perature rise resulted in a pulp death rate o f 60% .4 Tem perature rise values th at cause irreparable dam age in hum an pulp tissue have not been established con clusively; how ever, it is recom m ended that 2 mm o f dentin be left betw een the pulp tissue and the cavity preparation floor to ensure adequate insu
lation o f the pulp tissue from potentially traum atic therm ogenic operative techniques.3 A lthough biologic dam age to the pulp tissue has received m ajor attention, structural dam age to the tooth enam el during restorative cutting pro ce dures also may be significant.5,6 Such dam age may contribute to breakdow n o f the tooth struc ture at the cavity walls resulting in eventual loss of the restoration or marginal leakage and recurrent caries at the tooth-restoration interface. M any previous studies1-4,714 have m easured tem perature rise in the tooth during the resto ra tion procedure. However^ problem s o f in strum entation, location o f tem perature sensors relative to the bur, variations in tem perature rise with respect to handpiece speed, force applied to handpiece, m ethod o f cooling, duration and fre quency o f cutting, and the inherent problem s of m easuring transient tem peratures from a moving heat source have plagued all o f the investigations. A lthough m uch useful inform ation has been learned, the resulting values for tem perature rise during cutting vary and som etim es conflict. In this study, another approach com bining ex perim ental and num erical analysis techniques is used for determ ining the tim e-dependent tem per ature and therm al-stress distributions in the tooth during cutting. T h e rate of energy deposition into the tooth during cutting, using high-speed dental handpieces (speed 100,000 to 350,000 rpm) was determ ined experim entally as a function o f hand piece type, speed, and force; tooth substrate m a terial; and clinician technique for extracted teeth. JADA, V ol. 96, M arch 1978 ■ 451
From these results, the tem perature and stress distributions in a model o f the tooth undergoing a sim ulated restoration process w ere calculated using num erical finite difference and finite ele m ent com puter codes. T hese calculated tem pera tures and stresses w ere then com pared with ex perim ental observations and analyzed in term s of restorative cutting techniques and equipm ent to provide inform ation necessary to understand and im prove the cutting process.
counter capable of displaying the signals on a rate basis. This arrangem ent perm itted continuous m onitoring and display o f the speed of the hand piece. A M idw est A m erican A ir D rive no. 400 hand piece* and a D entsply International, Inc. Silencer handpiecet w ere used for the cutting tests. Also used w ere S. S. W hite D ental Products In tern a tional 558 L carbide crosscut fissure b u rst and Ransom and Randolph 558-7 diam ond cylindrical burs.§ N ew burs w ere used after about three min utes of test cutting.
E x p e rim e n ta l m eth o d s
Experim ental determ ination o f energy deposition rates during cutting in extracted teeth was made using a calorim eter technique. T he calorim eter and associated apparatus were designed to obtain energy deposition in both m achine- and clinician-operated tests as a function of handpiece speed, type, and air pressure; and applied force, duration, and frequency o f cutting; and tooth sub strate m aterial. D entin and enam el sam ples were prepared and m ounted in the calorim eter from newly extracted third m olars (donors— 20 years of age). T he hand piece and drill w ere m ounted above the calorim e ter with the bur extending into the calorim eter through a m ovable seal. F o r m achine cutting, the calorim eter was m ounted on a m ovable cart, which perm itted application of selected fixed forces betw een the tooth and the cutting bur. F o r clinician cutting tests, the force applied was de pendent on the particular technique. Speed was m easured with a photocell, which detected light pulses produced by passing a beam o f light through a slotted rod protruding from the backside o f the handpiece chuck. Each revolution o f the turbine provided tw o light pulses that the photocell detected and relayed to an electronic
N u m e ric a l tec h n iq u e s
F o r com posite m aterial structures with a geom etry as com plex as a tooth, it is im possible to obtain meaningful solutions for the tem perature and stress distributions by exact analytical m ethods. H ow ever, num erical com puter m od e ls15,16 can be used to obtain approxim ate solu tions to such problem s. F o r this study, twodim ensional, axisym m etric com puter codes w ere obtained from Thiokol Chem ical C orp. in Brigham C ity, U tah. T hese codes were used with appropriate geom etrical m odels of a tooth to cal culate the distribution of tem perature and therm al stress in the m andibular second molar. T he idealized geom etry show n in Figure 1 was devised to represent the tooth. T em perature and stress patterns w ere calcu lated for sim ulated cutting with the use of experi m entally obtained energy deposition rates and m aterial properties o f enamel and dentin taken from the literature. P aram eters analyzed in the num erical solutions included variation o f the en ergy deposition rate, variation of the time of ap plication of the energy (to sim ulate clinical cu t ting), occlusal cuts in enamel and dentin, sim u
TH E A U TH O R S
Dr. Brown is dean of the C olleg e of Engineering, The University of U tah, Salt Lake City, 84112. Dr. Christensen is a m echanical engineer at th e Naval W eapon C enter, China Lake, Calif. Dr. Lloyd is m an ag er of engineering and pro du ction, Xentex Co., Londonderry, NH. Address requests fo r reprints to Dr. Brown. BROW N
4 5 2 ■ JADA, Vol. 96, M arch 1978
CHR ISTENS EN
LLOYD
Fig 1 ■ Finite differ ence tem p erate grid for an idealized m olar (h = c o n ve c tiv e
heat
transfer coefficient).
lated cooling during cutting, and variation o f the m aterial properties o f the tooth enam el.17
Results and discussion ■ E xperim ental studies: Energy deposition rates while cutting enam el and dentin with carbide and diam ond stones using the m achine-operated
M idw est handpiece at a constant air pressure of 30 pounds p er square inch gauge are show n in Figure 2 as a function o f force applied to the handpiece. This data indicates th at the rate of energy deposition varies from about 0.3 to 0.6 calorie/second as the handpiece force varies from 30 to 70 g (1.1 oz to 2.5 oz). T he rate o f energy deposition is about the same for enam el and den tin, with the diam ond stones depositing slightly m ore energy than the carbide crosscut stones. In addition to being dependent on the hand piece force, the energy deposition rate is a func tion o f the handpiece type (air turbine design) and the applied air pressure. F igure 3 show s energy deposition rates in term s of speed of the hand piece while cutting with tw o different handpieces using 558 carbide crosscut burs. T here w ere sig nificant differences in energy deposition rates be tw een the tw o handpieces.
(a )
UJ 0.2------------ 1------------1----------- 1------------i------------1------------1------------1 10
20
30
40
50
60
70
80
FORCE (gm)
(b ) Fig 2 ■ Energy deposition rates vs handpiece fo rc e during m a
Fig 3 ■ Energy de po sition rates versus average speed of hand
chin e cutting in enam el and dentin specim ens.
piece du ring cutting in enam el by dental clinicians.
Brown— C hristensen— Lloyd: TE M P E R A TU R E , T H E R M A L S TR ESS IN R E STO R A TIV E P R O C E D U R E S ■ 453
DENTSPLY-SILENCER HANDPIECE
deposits less energy into the tooth. O bservation o f five clinician cutting techniques indicates th at the highest energy deposition rates w ere experi enced w ith low -attack frequency techniques, heavy applied loads, and handpieces with large torque capabilities operated at high turbine air pressures.
Numerical studies
(O)
(b) F ig 4 ■ Speed of h a n d p ie c e v s tim e d a ta fro m tw o d e n ta l clinicians cuttin g enam el using tw o d iffere n t hand pieces w ith tungstenc arbide 558 burs and constant hand piece air pressure of 30 psig (Q = a v e ra g e energy deposition rate).
Exam ples o f differences in cutting techniques and the resultant average energy deposition rates betw een tw o clinicians using tw o different hand pieces operated at 30 psig air pressure are shown in Figure 4. T he dentist with the lighter touch
T he energy deposition rates determ ined in the experim ental tests w ere used as input to a num eri cal m odel o f a third m olar undergoing an occlusal preparation to obtain tem peratures and therm al stresses generated during various cutting pro ce dures. R esults from this num erical m odel for sim ulated dry cutting in enam el, for one second, using a handpiece th at deposits 0.44 calories per second to the area specified (bur area equal to cavity area), are shown in F igure 5. B ecause the tooth m aterials are good insulators, the heat gen erated during cutting is confined; this results in very high tem peratures im m ediately adjacent to the surface being cut. A plot o f the average calcu lated tem peratures in enamel after one second o f dry cutting is show n in Figure 6 as a function o f distance from the cutting surface for various en ergy deposition rates. It is significant that the tem perature gradient is very steep and that large
H -
F
D
! t I 1 i
i 1 1 1 i
1 1 1 i
i
Fig 5 ■ a) Tem pera ture
distribution
in
m olar after one sec ond o f sim ulated dry cutting in enam el for an energy deposition rate of 0 .44 calorie/ second; b) therm ally induced ho op stress es in m olar after one second of d ry cutting in enam el fo r an en TEMPERATURE CODE (°C) 538 427
316 204 66 43
454 ■ JADA, Vol. 96, M arch 1978
ergy d eposition rate of
STRESS CODE (psi) -70,000 to -40,000 -40,000 to -20,000 -20,000 to -10,000 -10,000 to
-5,000
-5,000 to
0
to
1,000
1.000 to
0
2,000
2.000 to
5,000
0.44
calorie/second
(m odulus of elasticity of enam el 106 psi).
(E )= 6 .7 x
400
—
û 0.44 col/stc O 0 30 col/sec o 0 15 col/sec
0 .5
1 .0 D IS TA N C E
FROM
1.5
2 .0
C U T T IN G
SURFACE,
F ig 6 ■ A v e r a g e te m p e ra tu re v s d is ta n c e fro m s u rfa c e b e in g c u tin enam el w ith o u t c oolan t fo r various energy de po sition rates.
tem perature rises are alm ost com pletely con tained within a 2-mm radius. T he cutting tech nique w as im portant in controlling the tem pera tu re rise as show n by the tem perature p atterns for 0.15, 0.30, and 0.44 calories p er second energy
deposition rates. Figure 7 shows the effect o f the length o f the cutting time interval on the tem pera ture rise experienced at various distances from the surface being cut for an energy deposition rate o f 0.44 calorie/second. N otice how rapidly the enam el tem perature increased within half a mil lim eter from the cutting tool during dry cutting, reaching 136 C (245 F) above the original tooth tem perature within tw o seconds. T he effect o f a cut-and-rest dry cutting tech nique w as investigated over a seven-second inter val, in w hich alternate one-second periods o f cut ting and rest w ere sim ulated in the m odel. R esults after the final cutting period at seven seconds are show n in Figure 7. A lthough this technique re sults in m uch low er tem peratures than a continu ous cut, the overall tem perature rise within a lVi-mm radius is significant. T he large tem perature gradients created in the tooth because of the therm al-insulating properties o f the tooth m aterials result in another potential problem , that o f large therm al stresses in the tooth structure im m ediately adjacent to the cutting sur face. T he therm al stress pattern show n in Figure 5b is plotted in detail in F igure 8 for tw o energy deposition rates and tw o values o f the m odulus of
Fig 7 ■ Effect of length of dry cutting tim e interval on tem p erature
F ig 8 ■ Th erm ally induced hoop stresses vs distance from surface
rise exp erien ced In enam el at various distances aw ay from surface
being cut in enam el a fter one second of dry cutting w ith tw o differ
being cut. Energy deposition ra te = 0 .4 4 calorie/second. Values at
en t values for m odulus of elasticity of enam el (E). (Com pressive
seven seconds are for an interm ittent cutting tech niq ue (alternate
strength values— see references, 18, 20; tensile strength values—
one-second periods o f cutting and rest).
see references 35, 36.)
Brown— C hristensen— Lloyd: TE M P E R A TU R E , TH E R M A L S TR E S S IN R E S TO R A TIV E P R O C E D U R E S ■ 455
Fig 9 ■ B efore and after photo graphs of tooth with Class V resto ration placed by dental clinician on new ly extracted tooth using his standard cutting tech niq ue and no coolant. (Total tim e of preparation was 6 0 seconds with a tungstenc arbide 558 bur.) C racks adjacent to cutting surface are evident and support num erical predictions that, w hen
tooth
is cut dry, therm al
stress levels, can exceed fracture strength of enam el. (Photographs w ere m ade under flu orescent light to enhance fluorescent dye placed on tooth to d etect fracture regions.)
Fig 10 ■ B efore and after photo graphs of a different surface of tooth show n in Figure 9, with a Class V restoration placed by sam e d ental clinician, using sam e cutting tech niq ue and equipm ent at sam e sitting. This preparation, however, was
m ade
with
air-w ater
c oolan t
from
sam e
S ilen cer
handpiece.
spray
DentsplyN otice
ab
sence of alm ost all fracture dam age In tooth m aterial adjacent to cavity walls.
elasticity (a m easure o f the resistance to deform a tion under load). T he stress levels are plotted as a function o f distance from the cutting surface after one second o f dry cutting. N otice that it is possi ble to exceed both the com pressive and tensile strength o f enam el under these conditions.18-21 T herefore, it would be expected that tooth frac tures in the region ju st adjacent to the cutting edge could be experienced during dry cutting. Similar num erical calculations were perform ed for dentin. T he tem perature results w ere similar to those for enam el, but the therm al stress levels w ere much lower. N o critical therm al-stress levels w ere observed for dry cutting in dentin, mainly because dentin is much m ore resilient, that is, it has a significantly low er m odulus of elasticity (1.7-2.4X106 psi). T he tem perature rise in dentin during cutting may be m ore crucial than that in enam el for deep cuts since the pulp tissue may sustain biologic dam age.4 T herefore, dry cutting, even for short time intervals, can be crucial in preparations near the pulp tissue.
C o m p a riso n of n u m e ric a l and e x p e ri m ental studies
Because o f the approxim ations and limitations involved in the num erical modeling technique, 456 ■ JADA, Vol. 96, M arch 1978
experim ental studies w ere conducted to verify the num erical tem perature and stress results pre sented in the previous section. The tem perature results for dry cutting and several coolant m ethods that are presented in detail in reference 22 add considerable support to the validity of the num erical calculations. T he stress calculations w ere verified to consid erable extent by several clinicians cutting C lass V preparations in one setting with and w ithout w ater-coolant on the same tooth using the same equipm ent and cutting technique. Typical before and after results for such tests are shown in Fig ure 9 (dry cutting) and Figure 10 (water-cooled cutting). N ote the fractures within about 1 mm of the cut surface in the dry-cutting condition and the absence o f such fractures in the w et-cutting condi tions. Sim ilar tests were conducted using aircoolant from a hand-held syringe. In all the tests, fractures occurred at the cavity margins when dry cutting o r air-cooled cutting was used. Clinician technique and bur size and type had some effect on the extent of the dam age that occurred, but some fractures w ere created even with short cu t ting time intervals. A lthough a few fractures did occur with the use o f w ater-coolants directed on the cutting interface, they w ere rare and always significantly less than with dry or air-coolant cu t ting. Scanning electron m icroscope m icrographs of
Fig 11 ■ C racks induced during dry cutting in enam el surface adjacent to cut edge. Original m ag nification: left, X1700; right, X3500.
Fig 12 ■ C racks induced during dry cutting in enam el surface adjacent and outward from cut edge. Original m agnification, x 34 0 0 .
the fracture areas adjacent to the cavity wall on the tooth cut dry in Figure 9 are shown in Figures 11 and 12. T he width o f these fractures varies from 0.15 /xm to 0.5 /xm and less than 2 mm in length. Previous studies have shown that these cracks will tend to increase in length and width with time under the changing environm ental con ditions of the m outh.23 Such fractures w eaken the cavity m argins and may contribute significantly to marginal failure both by m echanical loss of tooth structure and carious attack.
S u m m a ry
T he dental equipm ent used in this study deposited energy in the tooth at a rate betw een 0.3 and 0.6 calorie/second during norm al cutting. Energy deposition is about the same w hen cutting enamel or d en tin , and for diam ond or carbide stones o f the sam e diam eter. Clinician techniques varied, as did handpieces, in the rate o f energy deposition during cutting. A low attack frequency with light pressure applied to the bur, and low air pressure to the handpiece turbine, resulted in the low est rate of energy dep osition (and also the lowest rate o f m aterial re moval). A verage clinician cutting techniques de posited about 0.4 calorie/second. T his study showed that the handpiece can be m achine-
calibrated and then m onitored by the speed o f the handpiece to determ ine the energy deposition rate when cutting at a fixed air pressure. This may play a significant part in future clinical studies w here in vivo tem perature patterns or pulp dam age need to be related to cutting technique. N um erical com puter codes, using the m eas ured energy input data, were useful in predicting tem peratures and stresses during cutting. T he num erical results indicated that the tem peratures and stresses developed by all m odes of dry cutting w ere sufficiently high to be detrim ental to the tooth structure. T he greatest potential for damage was within a 1- to 2-mm radius o f the point being cut. W hen the enam el was cut dry or with an aircoolant, therm al stresses induced fractures in the tooth structure extending 1 to 2 mm from the cavity walls. T he use o f w ater-coolant during cut ting elim inates these fractures when the coolant was applied at the cutting interface.
C o n clu sio n s
R esults reported here and in our other articles show that it is desirable to use w et cutting in dental restoration procedures. F urther, it is evi dent that a hand-held syringe directing a small, high-velocity stream o f w ater into the cutting re
B rown— C hristensen— Lloyd: TEM P E R A TU R E , T H E R M A L S TR ESS IN R ES TO R A TIVE P R O C E D U R ES ■ 4 5 7
gion is a m ore effective cooling technique than an air-w ater spray. D ry cutting in enam el can induce sufficiently high therm al stresses to fracture the enam el. T em peratures resulting from dry cutting in dentin are high enough to cause biologic pulp dam age if the cutting is within 1 to 2 mm o f the pulp. C racks induced in the cavity wall by dry cutting m ay eventually contribute to marginal failure.
T h is research was supported by grant DE 027 7 1 -06 from the N ational Institute fo r D ental R esearch, N ational Institutes of Health, B ethesda, M d. Special thanks is given to Con Th ueso n, Gary W at son, and Steven G u nter for their efforts in ob tainin g m uch of the exp erim ental data; to Drs. R. R. Despain, R. C. H asking, Phillip Taylor, B. A. Lloyd, J. E. Hurst, and E. H. W hite, as dental consul tants, and to G arron P. Anderson and Th om as C harlton, com puter consultants from Thiokol C hem ical C orp., fo r use of th e finite d iffere n c e and fin ite elem ent c om puter codes. 'M id w e s t A m erican, 901 W O akton, Des Plaines, III 60018. fD e n ts p ly In ternational, Inc., 500 W C ollege Ave, York, Pa 17404.
6. Kasloff, Z. Enam el cracks caused by rotary instrum ents. J Prosthet D ent 1 4:109 Jan -Feb 1964. 7. Peyton, F.A. T em perature rise in teeth developed by rotating instrum ents. JADA 5 0:629 June 1955. 8. Peyton, F.A. Effectiveness of w ater coolants with rotary cut ting instrum ents. JADA 56:64 M ay 1958. 9. S chuchard, A ., and W atkins, C .E. Therm al and histologic re sponse to high-speed and ultrahigh-speed cutting in tooth stru c ture. JADA 71:1451 D ec 1965. 10. Lisanti, V .F., and Zander, H.A. Th erm al injury to norm al dog teeth: in vivo m easurem ents of pulp tem p erature increases and their effect on th e pulp tissue. J D ent Res 3 1 :548 Aug 1952. 11. B haskar, S .N ., and Lilly, G.E. Intrapulpal tem p erature during cavity preparation. J D ent Res 4 4:644 July-Aug 1965. 12. Alpin, A.W .; C antw ell, K.R.; and M anny, V.R . Effect of c ool ants on te m p era tu re rise resulting from cavity preparation. J Dent Res 38:761 July-Aug 1959. 13. Sorenson, F.M .; C antw ell, K.R.; and A lpin, A.W . Th erm ogenics in cavity preparation using air turbine handpieces: th e relationship of heat transferred to rate of tooth structure rem oval. J Prosthet Dent 1 4:524 M ay-June 1964. 14. Stanley, H .R . T raum atic capacity of high-speed and u l trasonic dental instrum entation. JADA 6 3:750 D ec 1961. 15. Adam s, J.A., and Rogers, D.F. C om puter aided heat tran sfer analysis. N ew Y ork, M cG raw -H ill B ook C o., 1973. 16. Zien kiew icz, O .C. The fin ite elem en t m ethod in engineering science. London, M cG raw -H ill B ook Co., 1971.
t S . S. W h ite D ental Products In ternational, P ennw alt Corp., Th re e Parkw ay, Philadelphia, 19102.
17. C hristensen, D.O. T em perature and stress profiles in teeth during cavity preparation, thesis. University of U tah, M echanical
§ T h e R ansom & R andolph Co., 324 C hestnut St, To ledo, O hio 43604.
Engineering D epartm ent, 1973. 18. Stanford, J.W ., and others. D eterm ination of som e com pres
1. Jarby, D. On tem perature m easurem ents in teeth in vitro and in vivo. O d ont T 66:421, 1958. 2. Langeland, K., and Langeland, L.K. C utting procedures with m inim ized traum a. JADA 76:991 M ay 1968. 3. Stanley, H.R . Pulpal response to dental tech niq ues and m ate rials. Dent Clin North Am 15:115 Jan 1971. 4. Zach, L., and C ohen, G. Pulp response to externally applied heat. Oral Surg 19:515 April 1965. 5. Kasloff, Z.; Sw artz, M.L.; and Phillips, R.W . In vitro m ethod fo r de m onstrating the effects of various cutting instrum ents on tooth structure. J Prosthet D ent 12:1166 N ov-Dee 1962.
4 5 8 ■ JADA, Vol. 96, March 1978
sive properties of hum an enam el and dentin. JADA 57:487 O ct 1958. 19. Craig, R.G.; Peyton, F.A.; and Johnson, D.W. C om pressive properties of enam el, dental cem ents and gold. J D ent 4 0:936 S ept-O ct 1961. 20. B ow en, R .L., and R odriguez, M .S. Tensile strength and m o d ulus of elasticity of tooth structure and several restorative m ate rials. JADA 6 4:378 M arch 1962. 21. M cG inley, M .B ., and others. Tensile strength of enam el. A bstracted, IADR P rogram and Abstracts no. 871 M arch 1972. 22. B row n, W .S ., and others. Therm al aspects of dental restora tive procedures. J D ent Res, in press. 23. B row n, W .S.; Jacobs, H.R.; and Thom pson, R E. Therm al fatigu e in teeth . J D ent Res 51:461 April 1972.
Wet cutting in enamel should be used during re storative procedures. According to evidence re ported here, dry cutting can induce sufficiently high therm al stresses to fracture the enamel. Tempera tures resulting from dry cutting in dentin are high enough to cause b io log ic pulp damage if the cutting is w ithin 1 to 2 mm of the pulp. Cracks induced in the cavity w alls by dry cutting may eventually contribute to m arginal failure. A hand-held syringe directing a small, high-velocity stream of w ater into the cutting region is a more effective cooling technique than an air-water spray.
M odem high-speed dental handpieces are capable o f depositing significant quantities o f energy in the tooth structure while cutting. This can result in excessive tem peratures, w hich may contribute to both biologic and structural dam age to the tooth m aterials. T he dental profession has long been concerned with the potential biologic dam age th at can occur to the tooth pulp tissue from excessive tem pera tu re s .13 Experim ents w ith m onkeys have shown th at a 10 F (5.6 C) intrapulpal tem perature rise resulted in an eventual pulp death rate of 15%, w hereas a 20 F (11.1 C) intrapulpal tem perature rise resulted in a pulp death rate o f 60% .4 Tem perature rise values th at cause irreparable dam age in hum an pulp tissue have not been established con clusively; how ever, it is recom m ended that 2 mm o f dentin be left betw een the pulp tissue and the cavity preparation floor to ensure adequate insu
lation o f the pulp tissue from potentially traum atic therm ogenic operative techniques.3 A lthough biologic dam age to the pulp tissue has received m ajor attention, structural dam age to the tooth enam el during restorative cutting pro ce dures also may be significant.5,6 Such dam age may contribute to breakdow n o f the tooth struc ture at the cavity walls resulting in eventual loss of the restoration or marginal leakage and recurrent caries at the tooth-restoration interface. M any previous studies1-4,714 have m easured tem perature rise in the tooth during the resto ra tion procedure. However^ problem s o f in strum entation, location o f tem perature sensors relative to the bur, variations in tem perature rise with respect to handpiece speed, force applied to handpiece, m ethod o f cooling, duration and fre quency o f cutting, and the inherent problem s of m easuring transient tem peratures from a moving heat source have plagued all o f the investigations. A lthough m uch useful inform ation has been learned, the resulting values for tem perature rise during cutting vary and som etim es conflict. In this study, another approach com bining ex perim ental and num erical analysis techniques is used for determ ining the tim e-dependent tem per ature and therm al-stress distributions in the tooth during cutting. T h e rate of energy deposition into the tooth during cutting, using high-speed dental handpieces (speed 100,000 to 350,000 rpm) was determ ined experim entally as a function o f hand piece type, speed, and force; tooth substrate m a terial; and clinician technique for extracted teeth. JADA, V ol. 96, M arch 1978 ■ 451
From these results, the tem perature and stress distributions in a model o f the tooth undergoing a sim ulated restoration process w ere calculated using num erical finite difference and finite ele m ent com puter codes. T hese calculated tem pera tures and stresses w ere then com pared with ex perim ental observations and analyzed in term s of restorative cutting techniques and equipm ent to provide inform ation necessary to understand and im prove the cutting process.
counter capable of displaying the signals on a rate basis. This arrangem ent perm itted continuous m onitoring and display o f the speed of the hand piece. A M idw est A m erican A ir D rive no. 400 hand piece* and a D entsply International, Inc. Silencer handpiecet w ere used for the cutting tests. Also used w ere S. S. W hite D ental Products In tern a tional 558 L carbide crosscut fissure b u rst and Ransom and Randolph 558-7 diam ond cylindrical burs.§ N ew burs w ere used after about three min utes of test cutting.
E x p e rim e n ta l m eth o d s
Experim ental determ ination o f energy deposition rates during cutting in extracted teeth was made using a calorim eter technique. T he calorim eter and associated apparatus were designed to obtain energy deposition in both m achine- and clinician-operated tests as a function of handpiece speed, type, and air pressure; and applied force, duration, and frequency o f cutting; and tooth sub strate m aterial. D entin and enam el sam ples were prepared and m ounted in the calorim eter from newly extracted third m olars (donors— 20 years of age). T he hand piece and drill w ere m ounted above the calorim e ter with the bur extending into the calorim eter through a m ovable seal. F o r m achine cutting, the calorim eter was m ounted on a m ovable cart, which perm itted application of selected fixed forces betw een the tooth and the cutting bur. F o r clinician cutting tests, the force applied was de pendent on the particular technique. Speed was m easured with a photocell, which detected light pulses produced by passing a beam o f light through a slotted rod protruding from the backside o f the handpiece chuck. Each revolution o f the turbine provided tw o light pulses that the photocell detected and relayed to an electronic
N u m e ric a l tec h n iq u e s
F o r com posite m aterial structures with a geom etry as com plex as a tooth, it is im possible to obtain meaningful solutions for the tem perature and stress distributions by exact analytical m ethods. H ow ever, num erical com puter m od e ls15,16 can be used to obtain approxim ate solu tions to such problem s. F o r this study, twodim ensional, axisym m etric com puter codes w ere obtained from Thiokol Chem ical C orp. in Brigham C ity, U tah. T hese codes were used with appropriate geom etrical m odels of a tooth to cal culate the distribution of tem perature and therm al stress in the m andibular second molar. T he idealized geom etry show n in Figure 1 was devised to represent the tooth. T em perature and stress patterns w ere calcu lated for sim ulated cutting with the use of experi m entally obtained energy deposition rates and m aterial properties o f enamel and dentin taken from the literature. P aram eters analyzed in the num erical solutions included variation o f the en ergy deposition rate, variation of the time of ap plication of the energy (to sim ulate clinical cu t ting), occlusal cuts in enamel and dentin, sim u
TH E A U TH O R S
Dr. Brown is dean of the C olleg e of Engineering, The University of U tah, Salt Lake City, 84112. Dr. Christensen is a m echanical engineer at th e Naval W eapon C enter, China Lake, Calif. Dr. Lloyd is m an ag er of engineering and pro du ction, Xentex Co., Londonderry, NH. Address requests fo r reprints to Dr. Brown. BROW N
4 5 2 ■ JADA, Vol. 96, M arch 1978
CHR ISTENS EN
LLOYD
Fig 1 ■ Finite differ ence tem p erate grid for an idealized m olar (h = c o n ve c tiv e
heat
transfer coefficient).
lated cooling during cutting, and variation o f the m aterial properties o f the tooth enam el.17
Results and discussion ■ E xperim ental studies: Energy deposition rates while cutting enam el and dentin with carbide and diam ond stones using the m achine-operated
M idw est handpiece at a constant air pressure of 30 pounds p er square inch gauge are show n in Figure 2 as a function o f force applied to the handpiece. This data indicates th at the rate of energy deposition varies from about 0.3 to 0.6 calorie/second as the handpiece force varies from 30 to 70 g (1.1 oz to 2.5 oz). T he rate o f energy deposition is about the same for enam el and den tin, with the diam ond stones depositing slightly m ore energy than the carbide crosscut stones. In addition to being dependent on the hand piece force, the energy deposition rate is a func tion o f the handpiece type (air turbine design) and the applied air pressure. F igure 3 show s energy deposition rates in term s of speed of the hand piece while cutting with tw o different handpieces using 558 carbide crosscut burs. T here w ere sig nificant differences in energy deposition rates be tw een the tw o handpieces.
(a )
UJ 0.2------------ 1------------1----------- 1------------i------------1------------1------------1 10
20
30
40
50
60
70
80
FORCE (gm)
(b ) Fig 2 ■ Energy deposition rates vs handpiece fo rc e during m a
Fig 3 ■ Energy de po sition rates versus average speed of hand
chin e cutting in enam el and dentin specim ens.
piece du ring cutting in enam el by dental clinicians.
Brown— C hristensen— Lloyd: TE M P E R A TU R E , T H E R M A L S TR ESS IN R E STO R A TIV E P R O C E D U R E S ■ 453
DENTSPLY-SILENCER HANDPIECE
deposits less energy into the tooth. O bservation o f five clinician cutting techniques indicates th at the highest energy deposition rates w ere experi enced w ith low -attack frequency techniques, heavy applied loads, and handpieces with large torque capabilities operated at high turbine air pressures.
Numerical studies
(O)
(b) F ig 4 ■ Speed of h a n d p ie c e v s tim e d a ta fro m tw o d e n ta l clinicians cuttin g enam el using tw o d iffere n t hand pieces w ith tungstenc arbide 558 burs and constant hand piece air pressure of 30 psig (Q = a v e ra g e energy deposition rate).
Exam ples o f differences in cutting techniques and the resultant average energy deposition rates betw een tw o clinicians using tw o different hand pieces operated at 30 psig air pressure are shown in Figure 4. T he dentist with the lighter touch
T he energy deposition rates determ ined in the experim ental tests w ere used as input to a num eri cal m odel o f a third m olar undergoing an occlusal preparation to obtain tem peratures and therm al stresses generated during various cutting pro ce dures. R esults from this num erical m odel for sim ulated dry cutting in enam el, for one second, using a handpiece th at deposits 0.44 calories per second to the area specified (bur area equal to cavity area), are shown in F igure 5. B ecause the tooth m aterials are good insulators, the heat gen erated during cutting is confined; this results in very high tem peratures im m ediately adjacent to the surface being cut. A plot o f the average calcu lated tem peratures in enamel after one second o f dry cutting is show n in Figure 6 as a function o f distance from the cutting surface for various en ergy deposition rates. It is significant that the tem perature gradient is very steep and that large
H -
F
D
! t I 1 i
i 1 1 1 i
1 1 1 i
i
Fig 5 ■ a) Tem pera ture
distribution
in
m olar after one sec ond o f sim ulated dry cutting in enam el for an energy deposition rate of 0 .44 calorie/ second; b) therm ally induced ho op stress es in m olar after one second of d ry cutting in enam el fo r an en TEMPERATURE CODE (°C) 538 427
316 204 66 43
454 ■ JADA, Vol. 96, M arch 1978
ergy d eposition rate of
STRESS CODE (psi) -70,000 to -40,000 -40,000 to -20,000 -20,000 to -10,000 -10,000 to
-5,000
-5,000 to
0
to
1,000
1.000 to
0
2,000
2.000 to
5,000
0.44
calorie/second
(m odulus of elasticity of enam el 106 psi).
(E )= 6 .7 x
400
—
û 0.44 col/stc O 0 30 col/sec o 0 15 col/sec
0 .5
1 .0 D IS TA N C E
FROM
1.5
2 .0
C U T T IN G
SURFACE,
F ig 6 ■ A v e r a g e te m p e ra tu re v s d is ta n c e fro m s u rfa c e b e in g c u tin enam el w ith o u t c oolan t fo r various energy de po sition rates.
tem perature rises are alm ost com pletely con tained within a 2-mm radius. T he cutting tech nique w as im portant in controlling the tem pera tu re rise as show n by the tem perature p atterns for 0.15, 0.30, and 0.44 calories p er second energy
deposition rates. Figure 7 shows the effect o f the length o f the cutting time interval on the tem pera ture rise experienced at various distances from the surface being cut for an energy deposition rate o f 0.44 calorie/second. N otice how rapidly the enam el tem perature increased within half a mil lim eter from the cutting tool during dry cutting, reaching 136 C (245 F) above the original tooth tem perature within tw o seconds. T he effect o f a cut-and-rest dry cutting tech nique w as investigated over a seven-second inter val, in w hich alternate one-second periods o f cut ting and rest w ere sim ulated in the m odel. R esults after the final cutting period at seven seconds are show n in Figure 7. A lthough this technique re sults in m uch low er tem peratures than a continu ous cut, the overall tem perature rise within a lVi-mm radius is significant. T he large tem perature gradients created in the tooth because of the therm al-insulating properties o f the tooth m aterials result in another potential problem , that o f large therm al stresses in the tooth structure im m ediately adjacent to the cutting sur face. T he therm al stress pattern show n in Figure 5b is plotted in detail in F igure 8 for tw o energy deposition rates and tw o values o f the m odulus of
Fig 7 ■ Effect of length of dry cutting tim e interval on tem p erature
F ig 8 ■ Th erm ally induced hoop stresses vs distance from surface
rise exp erien ced In enam el at various distances aw ay from surface
being cut in enam el a fter one second of dry cutting w ith tw o differ
being cut. Energy deposition ra te = 0 .4 4 calorie/second. Values at
en t values for m odulus of elasticity of enam el (E). (Com pressive
seven seconds are for an interm ittent cutting tech niq ue (alternate
strength values— see references, 18, 20; tensile strength values—
one-second periods o f cutting and rest).
see references 35, 36.)
Brown— C hristensen— Lloyd: TE M P E R A TU R E , TH E R M A L S TR E S S IN R E S TO R A TIV E P R O C E D U R E S ■ 455
Fig 9 ■ B efore and after photo graphs of tooth with Class V resto ration placed by dental clinician on new ly extracted tooth using his standard cutting tech niq ue and no coolant. (Total tim e of preparation was 6 0 seconds with a tungstenc arbide 558 bur.) C racks adjacent to cutting surface are evident and support num erical predictions that, w hen
tooth
is cut dry, therm al
stress levels, can exceed fracture strength of enam el. (Photographs w ere m ade under flu orescent light to enhance fluorescent dye placed on tooth to d etect fracture regions.)
Fig 10 ■ B efore and after photo graphs of a different surface of tooth show n in Figure 9, with a Class V restoration placed by sam e d ental clinician, using sam e cutting tech niq ue and equipm ent at sam e sitting. This preparation, however, was
m ade
with
air-w ater
c oolan t
from
sam e
S ilen cer
handpiece.
spray
DentsplyN otice
ab
sence of alm ost all fracture dam age In tooth m aterial adjacent to cavity walls.
elasticity (a m easure o f the resistance to deform a tion under load). T he stress levels are plotted as a function o f distance from the cutting surface after one second o f dry cutting. N otice that it is possi ble to exceed both the com pressive and tensile strength o f enam el under these conditions.18-21 T herefore, it would be expected that tooth frac tures in the region ju st adjacent to the cutting edge could be experienced during dry cutting. Similar num erical calculations were perform ed for dentin. T he tem perature results w ere similar to those for enam el, but the therm al stress levels w ere much lower. N o critical therm al-stress levels w ere observed for dry cutting in dentin, mainly because dentin is much m ore resilient, that is, it has a significantly low er m odulus of elasticity (1.7-2.4X106 psi). T he tem perature rise in dentin during cutting may be m ore crucial than that in enam el for deep cuts since the pulp tissue may sustain biologic dam age.4 T herefore, dry cutting, even for short time intervals, can be crucial in preparations near the pulp tissue.
C o m p a riso n of n u m e ric a l and e x p e ri m ental studies
Because o f the approxim ations and limitations involved in the num erical modeling technique, 456 ■ JADA, Vol. 96, M arch 1978
experim ental studies w ere conducted to verify the num erical tem perature and stress results pre sented in the previous section. The tem perature results for dry cutting and several coolant m ethods that are presented in detail in reference 22 add considerable support to the validity of the num erical calculations. T he stress calculations w ere verified to consid erable extent by several clinicians cutting C lass V preparations in one setting with and w ithout w ater-coolant on the same tooth using the same equipm ent and cutting technique. Typical before and after results for such tests are shown in Fig ure 9 (dry cutting) and Figure 10 (water-cooled cutting). N ote the fractures within about 1 mm of the cut surface in the dry-cutting condition and the absence o f such fractures in the w et-cutting condi tions. Sim ilar tests were conducted using aircoolant from a hand-held syringe. In all the tests, fractures occurred at the cavity margins when dry cutting o r air-cooled cutting was used. Clinician technique and bur size and type had some effect on the extent of the dam age that occurred, but some fractures w ere created even with short cu t ting time intervals. A lthough a few fractures did occur with the use o f w ater-coolants directed on the cutting interface, they w ere rare and always significantly less than with dry or air-coolant cu t ting. Scanning electron m icroscope m icrographs of
Fig 11 ■ C racks induced during dry cutting in enam el surface adjacent to cut edge. Original m ag nification: left, X1700; right, X3500.
Fig 12 ■ C racks induced during dry cutting in enam el surface adjacent and outward from cut edge. Original m agnification, x 34 0 0 .
the fracture areas adjacent to the cavity wall on the tooth cut dry in Figure 9 are shown in Figures 11 and 12. T he width o f these fractures varies from 0.15 /xm to 0.5 /xm and less than 2 mm in length. Previous studies have shown that these cracks will tend to increase in length and width with time under the changing environm ental con ditions of the m outh.23 Such fractures w eaken the cavity m argins and may contribute significantly to marginal failure both by m echanical loss of tooth structure and carious attack.
S u m m a ry
T he dental equipm ent used in this study deposited energy in the tooth at a rate betw een 0.3 and 0.6 calorie/second during norm al cutting. Energy deposition is about the same w hen cutting enamel or d en tin , and for diam ond or carbide stones o f the sam e diam eter. Clinician techniques varied, as did handpieces, in the rate o f energy deposition during cutting. A low attack frequency with light pressure applied to the bur, and low air pressure to the handpiece turbine, resulted in the low est rate of energy dep osition (and also the lowest rate o f m aterial re moval). A verage clinician cutting techniques de posited about 0.4 calorie/second. T his study showed that the handpiece can be m achine-
calibrated and then m onitored by the speed o f the handpiece to determ ine the energy deposition rate when cutting at a fixed air pressure. This may play a significant part in future clinical studies w here in vivo tem perature patterns or pulp dam age need to be related to cutting technique. N um erical com puter codes, using the m eas ured energy input data, were useful in predicting tem peratures and stresses during cutting. T he num erical results indicated that the tem peratures and stresses developed by all m odes of dry cutting w ere sufficiently high to be detrim ental to the tooth structure. T he greatest potential for damage was within a 1- to 2-mm radius o f the point being cut. W hen the enam el was cut dry or with an aircoolant, therm al stresses induced fractures in the tooth structure extending 1 to 2 mm from the cavity walls. T he use o f w ater-coolant during cut ting elim inates these fractures when the coolant was applied at the cutting interface.
C o n clu sio n s
R esults reported here and in our other articles show that it is desirable to use w et cutting in dental restoration procedures. F urther, it is evi dent that a hand-held syringe directing a small, high-velocity stream o f w ater into the cutting re
B rown— C hristensen— Lloyd: TEM P E R A TU R E , T H E R M A L S TR ESS IN R ES TO R A TIVE P R O C E D U R ES ■ 4 5 7
gion is a m ore effective cooling technique than an air-w ater spray. D ry cutting in enam el can induce sufficiently high therm al stresses to fracture the enam el. T em peratures resulting from dry cutting in dentin are high enough to cause biologic pulp dam age if the cutting is within 1 to 2 mm o f the pulp. C racks induced in the cavity wall by dry cutting m ay eventually contribute to marginal failure.
T h is research was supported by grant DE 027 7 1 -06 from the N ational Institute fo r D ental R esearch, N ational Institutes of Health, B ethesda, M d. Special thanks is given to Con Th ueso n, Gary W at son, and Steven G u nter for their efforts in ob tainin g m uch of the exp erim ental data; to Drs. R. R. Despain, R. C. H asking, Phillip Taylor, B. A. Lloyd, J. E. Hurst, and E. H. W hite, as dental consul tants, and to G arron P. Anderson and Th om as C harlton, com puter consultants from Thiokol C hem ical C orp., fo r use of th e finite d iffere n c e and fin ite elem ent c om puter codes. 'M id w e s t A m erican, 901 W O akton, Des Plaines, III 60018. fD e n ts p ly In ternational, Inc., 500 W C ollege Ave, York, Pa 17404.
6. Kasloff, Z. Enam el cracks caused by rotary instrum ents. J Prosthet D ent 1 4:109 Jan -Feb 1964. 7. Peyton, F.A. T em perature rise in teeth developed by rotating instrum ents. JADA 5 0:629 June 1955. 8. Peyton, F.A. Effectiveness of w ater coolants with rotary cut ting instrum ents. JADA 56:64 M ay 1958. 9. S chuchard, A ., and W atkins, C .E. Therm al and histologic re sponse to high-speed and ultrahigh-speed cutting in tooth stru c ture. JADA 71:1451 D ec 1965. 10. Lisanti, V .F., and Zander, H.A. Th erm al injury to norm al dog teeth: in vivo m easurem ents of pulp tem p erature increases and their effect on th e pulp tissue. J D ent Res 3 1 :548 Aug 1952. 11. B haskar, S .N ., and Lilly, G.E. Intrapulpal tem p erature during cavity preparation. J D ent Res 4 4:644 July-Aug 1965. 12. Alpin, A.W .; C antw ell, K.R.; and M anny, V.R . Effect of c ool ants on te m p era tu re rise resulting from cavity preparation. J Dent Res 38:761 July-Aug 1959. 13. Sorenson, F.M .; C antw ell, K.R.; and A lpin, A.W . Th erm ogenics in cavity preparation using air turbine handpieces: th e relationship of heat transferred to rate of tooth structure rem oval. J Prosthet Dent 1 4:524 M ay-June 1964. 14. Stanley, H .R . T raum atic capacity of high-speed and u l trasonic dental instrum entation. JADA 6 3:750 D ec 1961. 15. Adam s, J.A., and Rogers, D.F. C om puter aided heat tran sfer analysis. N ew Y ork, M cG raw -H ill B ook C o., 1973. 16. Zien kiew icz, O .C. The fin ite elem en t m ethod in engineering science. London, M cG raw -H ill B ook Co., 1971.
t S . S. W h ite D ental Products In ternational, P ennw alt Corp., Th re e Parkw ay, Philadelphia, 19102.
17. C hristensen, D.O. T em perature and stress profiles in teeth during cavity preparation, thesis. University of U tah, M echanical
§ T h e R ansom & R andolph Co., 324 C hestnut St, To ledo, O hio 43604.
Engineering D epartm ent, 1973. 18. Stanford, J.W ., and others. D eterm ination of som e com pres
1. Jarby, D. On tem perature m easurem ents in teeth in vitro and in vivo. O d ont T 66:421, 1958. 2. Langeland, K., and Langeland, L.K. C utting procedures with m inim ized traum a. JADA 76:991 M ay 1968. 3. Stanley, H.R . Pulpal response to dental tech niq ues and m ate rials. Dent Clin North Am 15:115 Jan 1971. 4. Zach, L., and C ohen, G. Pulp response to externally applied heat. Oral Surg 19:515 April 1965. 5. Kasloff, Z.; Sw artz, M.L.; and Phillips, R.W . In vitro m ethod fo r de m onstrating the effects of various cutting instrum ents on tooth structure. J Prosthet D ent 12:1166 N ov-Dee 1962.
4 5 8 ■ JADA, Vol. 96, March 1978
sive properties of hum an enam el and dentin. JADA 57:487 O ct 1958. 19. Craig, R.G.; Peyton, F.A.; and Johnson, D.W. C om pressive properties of enam el, dental cem ents and gold. J D ent 4 0:936 S ept-O ct 1961. 20. B ow en, R .L., and R odriguez, M .S. Tensile strength and m o d ulus of elasticity of tooth structure and several restorative m ate rials. JADA 6 4:378 M arch 1962. 21. M cG inley, M .B ., and others. Tensile strength of enam el. A bstracted, IADR P rogram and Abstracts no. 871 M arch 1972. 22. B row n, W .S ., and others. Therm al aspects of dental restora tive procedures. J D ent Res, in press. 23. B row n, W .S.; Jacobs, H.R.; and Thom pson, R E. Therm al fatigu e in teeth . J D ent Res 51:461 April 1972.
