Abstract

Algebraic and numerical solutions are presented of the temperature rise in dental tissue due to interaction with ultrashort optical radiation. Results of the studies with femtosecond laser pulses show agreement between theory and experiment. A temperature rise of typically 5 K is found for a 40 millisecond train of 7  nJ, 70 fs laser pulses at a repetition rate of 80  MHz. The peak irradiance in our experimental studies was limited to 3×106W/cm2. Applications include photoacoustic imaging and tomography of dental tissue.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. C. G. A. Hoelen, F. F. de Mul, R. Pongers, and A. Dekker, "Three-dimensional photoacoustic imaging of blood vessels in tissue," Opt. Lett. 23, 648-650 (1998).
    [CrossRef]
  2. C. G. A. Hoelen, R. G. M. Kolkman, M. Letteboer, R. Berendsen, and F. F. M. de Mul, "Photoacoustic tissue scanning," Proc. SPIE 3597, 336-343 (1999).
    [CrossRef]
  3. A. A. Oraevsky, V. A. Andreev, A. A. Karabutov, D. R. Fleming, Z. Gatalica, H. Singh, and R. O. Esenaliev, "Laser opto-acoustic Imaging of the breast: detection of cancer angiogenesis," Proc. SPIE 3597, 352-363 (1999).
    [CrossRef]
  4. X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nature Biotechnol. 21, 803-806 (2003).
    [CrossRef]
  5. P. C. Beard and T. N. Mills, "Characterization of postmortem arterial tissue using time-resolved photoacoustic spectroscopy at 436, 461, and 532 nm," Phys. Med. Biol. 42, 177-198 (1997).
    [CrossRef] [PubMed]
  6. B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, "Femtosecond, picosecond and nanosecond laser ablation of solids," Appl. Phys. A 63, 109-115 (1996).
    [CrossRef]
  7. A. M. Rubenchik, L. B. Da Silva, M. D. Feit, S. M. Lane, R. A. London, M. D. Perry, B. C. Stuart, and J. Neev, "Dental tissue processing with ultrashort-pulse laser," in Lasers in Dentistry II, H. A. Wigdor, J. D. B. Featherstone, J. M. White, and J. Neev, eds., Proc. SPIE 2672, 222-230 (1996).
    [CrossRef]
  8. J. Serbin, T. Bauer, C. Fallnich, A. Kasenbacher, and W. H. Arnold, "Femtosecond lasers as novel tool in dental surgery," Appl. Surf. Sci. 197-198, 737-740 (2002).
    [CrossRef] [PubMed]
  9. M. Frentzen and D. Hamrol, "Kavitätenpräperation mit dem Er:YAG-Laser-eine histologische Studie," Dtsch. Zahnärztl. Z. 55, 114-117 (2000).
    [PubMed]
  10. P. J. Pike, "Photo-acoustic analysis of dental materials and tissue," Ph.D. dissertation (University of Tennessee, Knoxville, TN, 2005).
  11. See, for example, a recent book on thermodynamics by S. R. Turns, Thermodynamics: Concepts & Applications (Cambridge University Press, 2006).
  12. E. G. Gamaly, B. Luther-Davis, and V. T. Tikhonchuk, "Ablation of solids by femtosecond lasers: ablation mechanism and ablation thresholds for metals and dielectrics," Phys. Plasmas 9, 949-957 (2002).
    [CrossRef]
  13. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (McGraw-Hill, 1968).
    [PubMed]
  14. T. Q. Qiu and C. L. Tien, "Size effects on nonequilibrium laser heating of metal films," J. Heat Transfer 115, 842-847 (1993).
    [CrossRef]
  15. A. N. Smith, J. L. Hostetler, and P. M. Norris, "Nonequilibrium heating in metal films: an analytical and numerical analysis," Num. Heat Transfer Part A 35, 859-873 (1999).
    [CrossRef] [PubMed]
  16. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, 1971).
  17. "IMSL PDE/FORTRAN User's Manual," Edition 1.0 (IMSL, Houston, TX) 1986.
  18. A. A. Oraevsky, S. L. Jackues, and F. K. Tittel, "Determination of tissue optical properties by piezoelectric detection of laser-induced stress waves," Proc. SPIE 1882, 86-101 (1993).
    [CrossRef]
  19. E. H. Morriyama, R. A. Zangaro, A. B. Villaverde, and M. T. Pacheco, "Optothermal transfer simulation in laser-irradiated human dentin," J. Biomed. Opt. 8, 298-302 (2003).
    [CrossRef]
  20. W. Seka, D. Fried, J. D. B. Featherstone, and S. F. Borzillary, "Light deposition in dental hard tissue and simulated thermal response," J. Dent. Res. 74, 1086-1092 (1995).
    [CrossRef] [PubMed]
  21. B. Choi and A. J. Welch, "Analysis of thermal relaxation during laser irradiation of tissue," Las. Surg. Med. 29, 351-359 (2001).
    [CrossRef]
  22. F. Hirota and K. Furumoto, "Temperature rise caused by laser (CO2, Nd:YAG, Er:YAG) irradiation of teeth," Intl. Congr. Ser. 1248, 301-304 (2003).
    [CrossRef]
  23. M. H. Smith, R. L. Fork, and S. T. Cole, "Safe delivery of optical power from space," Opt. Express 8, 537-546 (2001).
    [CrossRef] [PubMed]
  24. Thermophysical dental data for enamel and dentin are taken from http://www.lib.umich.edu/dentlib/Dental_tables/toc.html.
  25. Thermal conductivity and specific heat data for porcelain are taken from http://www.engineeringtoolbox.com.

2003

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nature Biotechnol. 21, 803-806 (2003).
[CrossRef]

E. H. Morriyama, R. A. Zangaro, A. B. Villaverde, and M. T. Pacheco, "Optothermal transfer simulation in laser-irradiated human dentin," J. Biomed. Opt. 8, 298-302 (2003).
[CrossRef]

F. Hirota and K. Furumoto, "Temperature rise caused by laser (CO2, Nd:YAG, Er:YAG) irradiation of teeth," Intl. Congr. Ser. 1248, 301-304 (2003).
[CrossRef]

2002

E. G. Gamaly, B. Luther-Davis, and V. T. Tikhonchuk, "Ablation of solids by femtosecond lasers: ablation mechanism and ablation thresholds for metals and dielectrics," Phys. Plasmas 9, 949-957 (2002).
[CrossRef]

J. Serbin, T. Bauer, C. Fallnich, A. Kasenbacher, and W. H. Arnold, "Femtosecond lasers as novel tool in dental surgery," Appl. Surf. Sci. 197-198, 737-740 (2002).
[CrossRef] [PubMed]

2001

B. Choi and A. J. Welch, "Analysis of thermal relaxation during laser irradiation of tissue," Las. Surg. Med. 29, 351-359 (2001).
[CrossRef]

M. H. Smith, R. L. Fork, and S. T. Cole, "Safe delivery of optical power from space," Opt. Express 8, 537-546 (2001).
[CrossRef] [PubMed]

2000

M. Frentzen and D. Hamrol, "Kavitätenpräperation mit dem Er:YAG-Laser-eine histologische Studie," Dtsch. Zahnärztl. Z. 55, 114-117 (2000).
[PubMed]

1999

C. G. A. Hoelen, R. G. M. Kolkman, M. Letteboer, R. Berendsen, and F. F. M. de Mul, "Photoacoustic tissue scanning," Proc. SPIE 3597, 336-343 (1999).
[CrossRef]

A. A. Oraevsky, V. A. Andreev, A. A. Karabutov, D. R. Fleming, Z. Gatalica, H. Singh, and R. O. Esenaliev, "Laser opto-acoustic Imaging of the breast: detection of cancer angiogenesis," Proc. SPIE 3597, 352-363 (1999).
[CrossRef]

A. N. Smith, J. L. Hostetler, and P. M. Norris, "Nonequilibrium heating in metal films: an analytical and numerical analysis," Num. Heat Transfer Part A 35, 859-873 (1999).
[CrossRef] [PubMed]

1998

1997

P. C. Beard and T. N. Mills, "Characterization of postmortem arterial tissue using time-resolved photoacoustic spectroscopy at 436, 461, and 532 nm," Phys. Med. Biol. 42, 177-198 (1997).
[CrossRef] [PubMed]

1996

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, "Femtosecond, picosecond and nanosecond laser ablation of solids," Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

A. M. Rubenchik, L. B. Da Silva, M. D. Feit, S. M. Lane, R. A. London, M. D. Perry, B. C. Stuart, and J. Neev, "Dental tissue processing with ultrashort-pulse laser," in Lasers in Dentistry II, H. A. Wigdor, J. D. B. Featherstone, J. M. White, and J. Neev, eds., Proc. SPIE 2672, 222-230 (1996).
[CrossRef]

1995

W. Seka, D. Fried, J. D. B. Featherstone, and S. F. Borzillary, "Light deposition in dental hard tissue and simulated thermal response," J. Dent. Res. 74, 1086-1092 (1995).
[CrossRef] [PubMed]

1993

A. A. Oraevsky, S. L. Jackues, and F. K. Tittel, "Determination of tissue optical properties by piezoelectric detection of laser-induced stress waves," Proc. SPIE 1882, 86-101 (1993).
[CrossRef]

T. Q. Qiu and C. L. Tien, "Size effects on nonequilibrium laser heating of metal films," J. Heat Transfer 115, 842-847 (1993).
[CrossRef]

Appl. Phys. A

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, "Femtosecond, picosecond and nanosecond laser ablation of solids," Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

Appl. Surf. Sci.

J. Serbin, T. Bauer, C. Fallnich, A. Kasenbacher, and W. H. Arnold, "Femtosecond lasers as novel tool in dental surgery," Appl. Surf. Sci. 197-198, 737-740 (2002).
[CrossRef] [PubMed]

Dtsch. Zahnärztl. Z.

M. Frentzen and D. Hamrol, "Kavitätenpräperation mit dem Er:YAG-Laser-eine histologische Studie," Dtsch. Zahnärztl. Z. 55, 114-117 (2000).
[PubMed]

Intl. Congr. Ser.

F. Hirota and K. Furumoto, "Temperature rise caused by laser (CO2, Nd:YAG, Er:YAG) irradiation of teeth," Intl. Congr. Ser. 1248, 301-304 (2003).
[CrossRef]

J. Biomed. Opt.

E. H. Morriyama, R. A. Zangaro, A. B. Villaverde, and M. T. Pacheco, "Optothermal transfer simulation in laser-irradiated human dentin," J. Biomed. Opt. 8, 298-302 (2003).
[CrossRef]

J. Dent. Res.

W. Seka, D. Fried, J. D. B. Featherstone, and S. F. Borzillary, "Light deposition in dental hard tissue and simulated thermal response," J. Dent. Res. 74, 1086-1092 (1995).
[CrossRef] [PubMed]

J. Heat Transfer

T. Q. Qiu and C. L. Tien, "Size effects on nonequilibrium laser heating of metal films," J. Heat Transfer 115, 842-847 (1993).
[CrossRef]

Las. Surg. Med.

B. Choi and A. J. Welch, "Analysis of thermal relaxation during laser irradiation of tissue," Las. Surg. Med. 29, 351-359 (2001).
[CrossRef]

Nature Biotechnol.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. Wang, "Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain," Nature Biotechnol. 21, 803-806 (2003).
[CrossRef]

Num. Heat Transfer Part A

A. N. Smith, J. L. Hostetler, and P. M. Norris, "Nonequilibrium heating in metal films: an analytical and numerical analysis," Num. Heat Transfer Part A 35, 859-873 (1999).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

P. C. Beard and T. N. Mills, "Characterization of postmortem arterial tissue using time-resolved photoacoustic spectroscopy at 436, 461, and 532 nm," Phys. Med. Biol. 42, 177-198 (1997).
[CrossRef] [PubMed]

Phys. Plasmas

E. G. Gamaly, B. Luther-Davis, and V. T. Tikhonchuk, "Ablation of solids by femtosecond lasers: ablation mechanism and ablation thresholds for metals and dielectrics," Phys. Plasmas 9, 949-957 (2002).
[CrossRef]

Proc. SPIE

A. M. Rubenchik, L. B. Da Silva, M. D. Feit, S. M. Lane, R. A. London, M. D. Perry, B. C. Stuart, and J. Neev, "Dental tissue processing with ultrashort-pulse laser," in Lasers in Dentistry II, H. A. Wigdor, J. D. B. Featherstone, J. M. White, and J. Neev, eds., Proc. SPIE 2672, 222-230 (1996).
[CrossRef]

C. G. A. Hoelen, R. G. M. Kolkman, M. Letteboer, R. Berendsen, and F. F. M. de Mul, "Photoacoustic tissue scanning," Proc. SPIE 3597, 336-343 (1999).
[CrossRef]

A. A. Oraevsky, V. A. Andreev, A. A. Karabutov, D. R. Fleming, Z. Gatalica, H. Singh, and R. O. Esenaliev, "Laser opto-acoustic Imaging of the breast: detection of cancer angiogenesis," Proc. SPIE 3597, 352-363 (1999).
[CrossRef]

A. A. Oraevsky, S. L. Jackues, and F. K. Tittel, "Determination of tissue optical properties by piezoelectric detection of laser-induced stress waves," Proc. SPIE 1882, 86-101 (1993).
[CrossRef]

Other

Thermophysical dental data for enamel and dentin are taken from http://www.lib.umich.edu/dentlib/Dental_tables/toc.html.

Thermal conductivity and specific heat data for porcelain are taken from http://www.engineeringtoolbox.com.

P. J. Pike, "Photo-acoustic analysis of dental materials and tissue," Ph.D. dissertation (University of Tennessee, Knoxville, TN, 2005).

See, for example, a recent book on thermodynamics by S. R. Turns, Thermodynamics: Concepts & Applications (Cambridge University Press, 2006).

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (McGraw-Hill, 1968).
[PubMed]

C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, 1971).

"IMSL PDE/FORTRAN User's Manual," Edition 1.0 (IMSL, Houston, TX) 1986.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(Color online) Computed temperature rise from a single 70 fs pulse.

Fig. 2
Fig. 2

(Color online) Computed temperature rise from a 40 ms pulse train of 70 fs pulses.

Fig. 3
Fig. 3

(Color online) Experimental schematic for temperature measurements.

Fig. 4
Fig. 4

(Color online) Measured temperature after a 8 ms train of 70 fs pulses.

Fig. 5
Fig. 5

(Color online) Measured temperature after a 40 ms train of 70 fs pulses.

Tables (1)

Tables Icon

Table 1 Thermophysical Values for Dental Tissue and Porcelain

Equations (57)

Equations on this page are rendered with MathJax. Learn more.

7   nJ
80   MHz
3 × 10 6 W / cm 2
( 10 14 W / c m 2 )
2 T ( r , t ) a 2 T ( r , t ) t = S ( r , t ) κ ,
T ( r , 0 ) = T 0 ( r ) ,
a 2 = ρ c / κ
[ k g / c m 3 ]
[ J / kg   K ]
[ W / kg   K ]
f ( r , t ) = S / κ
S μ a J
μ a
[ cm 1 ]
[ J / cm 2 ]
T ( r , t ) = 0 t V G ( r , t ; r , t ) f ( r , t ) d τ d V ( r ) a 2 V G ( r , t ; r , 0 ) T 0 ( r ) d V ( r ) .
f ( ξ , τ )
f ( r , t ) = ( 1 R ) κ μ a J   exp [ μ a z ] exp [ 2 ( r ) 2 ω 2 ] δ ( t ) ,
ω ( z ) = ω 0 { 1 + [ λ ( z z 0 ) π ω 0 2 ] 2 } 1 / 2 ,
z 0
ω 0 , λ
G ( r , t ; r , t ) = [ a 2 4 π ( t t ) ] 3 / 2 1 a 2   exp [ a 2 4 | r r | 2 t t ] .
( z = 0 )
T = T 0 + 4 J ( 1 R ) ρ c π τ ( 1 + τ )   exp [ 2 r 2 w 2 ( 1 + τ ) ] ,
τ = 8 t / a 2 ω 2
Δ P = 1 γ β Δ T ,
[ K 1 ]
γ = c p / c v ρ c s 2
[ Pa 1 ]
c v
c p
[ J / g K ]
c s
2 μ K
7   K
1 J / c m 2
1   K
7.3   nJ
820   nm
1   mm
2   mm
3 × 10 6 W / c m 2
0.76 J / c m 2
0.6 J / c m 2
8 μ m
1 J / c m 2
1 J / c m 2
3 J / c m 2
3 × 10 6 W / c m 2
10 2
2   mm
20 μ m
10 4
10 6
10 μ m
10 11 W / c m 2
10 11 W / c m 2

Metrics