Optothermal transfer simulation in laser-irradiated human dentin

Eduardo H. Moriyama; Renato Amaro Zangaro; Paulo Davi de Castro Lobo; Antonio G. J. Balbin Villaverde; Marcos Tadeu Tavares Pacheco; Alex Vitkin

doi:10.1117/1.1560000

1 April 2003 Optothermal transfer simulation in laser-irradiated human dentin

Eduardo H. Moriyama, Renato Amaro Zangaro, Paulo Davi de Castro Lobo, Antonio G. J. Balbin Villaverde, Marcos Tadeu Tavares Pacheco, Alex Vitkin

Author Affiliations +

Journal of Biomedical Optics, Vol. 8, Issue 2, (April 2003). https://doi.org/10.1117/1.1560000

1. Introduction

Laser technology has become an important tool used in several applications in dentistry including hard tissue ablation, oral surgeries, laser therapy, and reduction of dentinal hypersensitivity symptoms. Based on the temperature increase on the surface, Nd:YAG laser (λ=1064 nm) irradiation in dentin causes surface melting that can mechanically block the dentinal tubules.¹ ² ³ ⁴ ⁵ ⁶ The resulting molten layer can avoid the movement of the liquid contained inside the dentinal tubules, which is the largely responsible for the dentin hypersensitivity symptoms.¹ Thus, the major concern during laser irradiation of teeth is the high potential of tissue overheating resulting in high temperatures that can spread in toward the dentin, causing irreversible damage to cells present in the pulp chamber and leading to cell death.

During laser irradiation, the final temperature for any tissue will be dependent mainly on its absorption properties at a determined wavelength.⁷ Thermal damage induced by laser radiation seems to be a tradeoff between thermal and mechanical damage in surrounding tissues,⁸ where the first phenomenon seems to be more evident in dentin, as seen by the morphological effects after Nd:YAG laser irradiation on dentin surface.² ³ ⁴ These optothermal alterations in surface morphology can be enhanced when longer laser pulses containing high energy are used.⁸ Hence, shortening the laser pulse width (τ_p) can reduce damage on dental pulp caused by temperature rise in surface during laser radiation. The use of pulsed laser radiation, as opposed to a continuous one, is advantageous due to: 1. the possibility of achieving precise cutting control and minimize the zone of thermal damage by producing a thermal event that is shorter than the thermal conduction relaxation time (τ_r) of the tissue; See eq. (7) below. 2. the delivery of sufficient energy in each pulse to ablate or modify the tissue, removing hot tissue before heat is transferred to the adjacent structures; and 3. ablation of dense tissue such as bone or tooth by rapid heating and/or plasma formation.⁸

Several studies have shown the effects of laser irradiation on dental pulp, but the results are controversial. Some reports demonstrated no effect on pulp, while others reported different levels of damage. Powell, Whisenant, and Morton⁹ demonstrated that a temperature rise of 6 °C can cause irreversible pulp damage, and temperature rise of 11 °C may cause pulp cell death by apoptosis.¹⁰ It is worth noting that there is some confusion in the literature about thermal effects associated with Nd:YAG laser irradiation on dentin, due to the variety of the laser parameters used.

The use of a Nd:YAG laser to promote dentinal sealing as a dentinal hypersensitivity treatment offers a series of advantages when compared to a CO ₂ laser emitting at 10.6 μm. For instance, dentin irradiation using a CO ₂ laser can produce more extensive cracking lines than a Nd:YAG laser,¹¹ mainly attributed to the carbonization and subsequent contraction of the tissue due to loss of the collagen matrix during laser irradiation¹² and carbonization on the dentin surface. However, some studies have shown that radiation in the range of 9.3 to 9.6 μm is strongly absorbed by dental hydroxyapatite,¹³ thus, less energy might be required to produce surface changes.

This work simulates the temperature distribution in dentine during Nd:YAG laser irradiation of dentine surface using the Crank-Nicolson’s numerical finite difference scheme,¹⁴ and presents a brief discussion of the relevant photothermal mechanisms.

2. Parameters and Methods

2.1.

Laser Parameters

The laser parameters used to calculate the optothermal behavior throughout dentin are described in Table 1. They were selected from our previous studies, where the dentin phase transition threshold was determined by varying the pulse width with a pulse interval of 300 ms. This threshold was achieved using an energy density of 180 J/ cm ² and laser beam diameter of 0.8 mm, corresponding to the total energy density for the eight different irradiation regimes described in Table 1. The morphological changes in the dentin surface resulting from Nd:YAG laser radiation will be described elsewhere.

Table 1

Summary of the sample groups and their irradiation parameters.
Group	Energy per Pulse	Number of Pulses	τ_p	Pulse Interval
Group 1	900 mJ	1	0.9 ms	Single pulse
Group 2	450 mJ	2	0.9 ms	300 ms
Group 3	300 mJ	3	0.9 ms	300 ms
Group 4	150 mJ	6	0.9 ms	300 ms
Group 5	900 mJ	1	90 ms	Single pulse
Group 6	450 mJ	2	90 ms	300 ms
Group 7	300 mJ	3	90 ms	300 ms
Group 8	150 mJ	6	90 ms	300 ms

2.2.

Heat Transport Simulation

The finite difference method is based on the substitution of derivatives in the governing equation, resulting in a set of algebraic equations, which can then be solved if initial boundary conditions are known. Thus, the temperature can be calculated for each point; however, the numerical solution is always an approximate one, which depends on the specific numerical formula, its stability, and convergence. The Crank-Nicolson technique offers an unconditionally convergent solution for the heat conduction equation. In the present study, this method was used to simulate the temperature at the dentin surface and the heat diffusion toward the pulp chamber after Nd:YAG laser radiation using a one-dimensional formulation and constant thermal and optical parameters described by Seka et al.;¹⁵(see Table 2).¹⁶ ¹⁷ Although the radial beam dimension is not much larger than the penetration depth of a Nd:YAG laser, the one-dimensional approximation can be still valid for the sample thickness and the beam spot of interest, used in this simulation.¹⁵

Table 2

Thermal and optical constants of dentin (λ=1054 nm).
Density (ρ)¹⁶	2.1 gcm ⁻³
Specific heat (c)¹⁶	1.17 Jg ⁻¹°C⁻¹,
Thermal conductivity (κ)¹⁶	6.3 × 10⁻³ Wcm ⁻¹°C ⁻¹,
Scattering coefficient (μ_s)¹⁷	260 cm ⁻¹
Absorption coefficient (μ_a)¹⁷	3 cm ⁻¹
Anisotropy parameter¹⁷	0.93

The Crank-Nicolson method is unconditionally stable, even for arbitrarily large time steps. This is advantageous for many applications, because the stability of this scheme means that the errors diminish rather than grow with the time.

The thermal distribution in dentine submitted to laser radiation can be described by the one-dimensional heat conduction equation:¹²

Eq. (1)

ρ c \frac{\partial T (x, t)}{\partial t} = k \frac{\partial^{2} T (x, t)}{\partial x^{2}} + Q (x, t),

where ρ is the mass density (g cm ⁻³), c is the specific heat (J g ⁻¹°C ⁻¹), T is the temperature (°C), t is the time (s), k is the thermal conductivity (W cm ⁻¹°C ⁻¹), x is the coordinate perpendicular to the surface (cm), and Q is the heat source, which can be calculated from the one-dimensional optical diffusion solution:

Eq. (2)

Q (x, t) = μ_{a} I_{o} (t) exp (- μ_{eff} x)

where μ_a is the absorption coefficient (cm ⁻¹), I_o is the incident intensity (W cm ⁻²), and μ_eff is the effective attenuation coefficient defined as:

Eq. (3)

μ_{eff} = {3 μ_{a} [μ_{a} + (1 - g) μ_{s}]}^{1 / 2},

where g is the anisotropy parameter and μ_s is the scattering coefficient (cm ⁻¹).

The spatial differentials are approximated by central difference and the temporal differentials are approximated by backward difference in time as follows¹⁸:

Eq. (4)

{(\frac{\partial^{2} T}{\partial x^{2}})}_{i}^{h + 1} = \frac{T_{i + 1}^{h + 1} - 2 T_{i}^{h + 1} + T_{i - 1}^{h + 1}}{Δ x^{2}},

Eq. (5)

{(\frac{\partial T}{\partial t})}_{i}^{h + 1} = \frac{T_{i}^{h + 1} - T_{i}^{h}}{Δ t},

where i is the space node and h is the time.

The resulting system of tridiagonal finite difference equations can be expressed in a compact matrix form as:

Eq. (6)

(I - \frac{1}{2} ℓ A) T^{h + 1} = (I + \frac{1}{2} ℓ A) T^{h} + Δ tD,

where T is the temperature vector ℓ=Δt/Δx², I is the identity matrix, A is a tridiagonal matrix and D is the boundary conditions.

The system of Eq. (6) can be solved directly by the application of the tridiagonal algorithm.¹⁹ In this study, the compact form was used.

3. Results

The results of the optothermal simulation are shown in Figs. 1 2 3 4. The simulated evolution of temperature at the surface during laser irradiation using 0.9 and 90 ms pulses are presented in Figs. 1 and 2, respectively, where we observe that as the number of pulses increases, the amplitude of the rise of temperature in surface decreases. The highest temperature rise (∼218 °C) was resulted from a single pulse irradiation with τ_p=0.9 ms. For shorter pulses, the differences in final temperature between a single pulse and 2, 3, and 6 pulses are, respectively, 24, 38, and 65 °C. The results show a decrease of thermal confinement levels as laser pulse duration and number of pulses increases. Fractionation of laser radiation results in lower temperatures on the dentin surface and higher internal wall temperatures when compared with a single pulse radiation.

Figure 1

Temporal evolution of the temperature at dentin surface during laser radiation with 1, 2, 3, and 6 pulses (τ_p=0.9 ms).

Figure 2

Temporal evolution of the temperature at dentin surface during laser radiation with 1, 2, 3, and 6 pulses (τ_p=90 ms).

Figure 3

Spatial temperature distribution for 1, 2, 3, and 6 pulses immediately after the end of the last laser pulse (τ_p=0.9 ms).

Figure 4

Spatial temperature distribution for 1, 2, 3, and 6 pulses immediately after the end of the last laser pulse (τ_p=90 ms).

The temperature peak on surface after a single pulse of τ_p=90 ms duration was 191 °C, approximately 27 °C lower when compared to the shorter single pulse.

The highest temperature at the pulp wall (x=1.5 mm) immediately after the end of the last pulse for both laser pulse widths was achieved using six laser pulses. Yet, while higher temperature rises at the dentin surface were observed when 0.9-ms pulses were used, there were minimal differences in the final internal wall temperature. For example the temperature differences at the pulp wall between Group 8 and Group 4 is approximately 1.8 °C. Figures 3 and 4 show the heat distribution inside the samples, from the external surface of the dentine to the internal wall of the pulp chamber (x=1.5 mm). These results represent the depth-dependent temperature calculated immediately after the end of the last pulse.

According to the results, increasing the number of pulses leads to lower temperatures at the dentin surface, while the reverse situation occurs at the pulp region. This can be due to the long pulse intervals, where a sufficient period of time allows losses of energy at the surface and heat diffusion across the dentin.

The results show minimal differences in the final temperature at the internal wall after laser irradiation when the same number of pulses was used. Table 3 shows that shorter pulses result in higher temperatures at the dentin surface.

Table 3

Final temperature immediately after Nd:YAG laser radiation at the surface and at the internal pulp wall.
	T _surface (°C)	T _{Internal Wall} (°C, x=1.5 mm)
Group 1	217.9	27.2
Group 2	195.8	37.8
Group 3	179.5	45.8
Group 4	152.4	63.0
Group 5	191.0	32.2
Group 6	166.3	41.2
Group 7	151.9	49.2
Group 8	129.0	64.8

4. Discussion

The photothermal interaction occurs when the molecule in the tissue absorbs luminous energy and de-excites nonradioactively producing heat. The energy absorbed by the molecule depends on the tissue composition and structure, the laser wavelength, and incident irradiance. As the tissue needs some time to conduct the heat away,²⁰ a crucial aspect in the induction of the thermal effect is the laser pulse duration. Thus, continuous wave lasers promote more evident thermal effects in the tissue when compared to pulsed lasers, even in cases where the same total energy is delivered to the tissue.²¹

Thermal effects in dentin surface result from photothermal interaction between tissue and laser, and occur when energy densities between 1 and 10³ J/ cm ² and exposure time between 1 s and 1 μs are used. According LeCarpentier et al.;,²² pulses with typical duration of 1 ms result in higher thermal confinement than stress confinement inside the sample when compared to shorter laser pulses, yielding higher temperatures at the tissue surface.

According Van Leeween, Jansen, and Motamedi,⁸ the thermal effects depend on laser-tissue interaction time and the resultant temperature from this process. The resultant confinement (stress or thermal) depends on the laser pulse width and the absorption coefficient of the tissue at a determined wavelength. Longer pulses mean longer interaction times between the laser and the tissue, allowing a larger diffusion of heat away from the irradiated site, and resulting in lower temperatures in the surface and higher temperatures in deeper areas. During Nd:YAG laser irradiation on dentin using short pulses (<1 μs), the temperature in the radiated spot decreases during the interval between two subsequent pulses. Thus, the physical and chemical changes due to high temperatures remain confined to a narrow region next to the surface, without much effect on deeper tissues. In general, the shorter the laser pulse, the narrower the affected region.

As seen in the results, the laser irradiation using energy fractionation of the total energy into several laser pulses leads to lower temperatures at the dentin surface; the final temperature depends on the total number of laser pulse interval and the pulse width. However, the results demonstrated that temperature accumulation on the external surface can occur during multiple-pulse irradiation, even if the pulse interval time is long (Figs. 1 and 2). On the other hand, the opposite situation occurs at the dentin internal wall, where the use of more pulses results in higher temperatures in the pulp. This can be explained by the longer pulse intervals that allow energy loss in the surface and, allow the heat diffusion toward the dental pulp.

During Nd:YAG laser irradiation, when the temperature exceeds the threshold for phase change, the ejection of a fraction of material resulting in crater formation can be observed. This ablative effect depends on the energy and duration of the laser pulse and is more evident when the tissue is exposed to long periods of exposure to the laser radiation. Therefore, significant amounts of heat can diffuse out of the area irradiated during the irradiation, reducing the local thermal damage and causing thermal damage to a larger volume of tissue.²³

According to Fried et al.;,¹⁷ at λ=1064 nm human dentine exhibit an absorption coefficient around 3 cm ⁻¹ and a scattering coefficient ranging from 30 to 200 cm ⁻¹. This high variation in dentine μ_s can be explained by the differences in the density of dentin tubules. In the visible and near-infrared spectra, enamel and dentin present low absorption coefficients, thus, scattering can be considered an important parameter for determining the distribution of the energy in dentin.

Thermal effects can be associated with the thermal conduction relaxation time of tissue,²⁰ ²⁴ which is defined as the time required for the peak temperature rise (ΔT peak) in a heated region of tissue to decrease to 37 of the total rise:

Eq. (7)

τ_{r} = \frac{δ^{2}}{N α},

where δ is the penetration depth (cm), N is a geometric factor (N: 4 to 27), and α is the thermal diffusivity of the tissue (cm ² /s).²⁰ If all the light energy is delivered in shorter pulses than the thermal relaxation time (τ_p<τ_r) , only a small portion of the surface will be damaged. In this case, the damage is directly proportional to the amount of energy contained in the laser pulse. However, if the interaction time is much longer than the time of thermal relaxation of the tissue (τ_p>τ_r) , comparatively a more evident thermal effect could be observed on the surface due to the heat dissipation toward the tissue, and consequently deeper structures of tissue can be damaged.

Since dental pulp is highly susceptible to temperature variation, even a slight rise of temperature could cause pulp cell death. Therefore, according to the simulation carried out in this work, the studied parameters are not safe for clinical procedures. However, as seen in the results, shortening the pulse width and increasing the number of pulses could avoid the thermal risk to the pulp due to the high number of pulse intervals, even though higher total energies may be necessary to achieve the needed temperatures to induce dentin melting.

5. Conclusions

Optothermal simulation is important for obtaining safety parameters during laser radiation on dental hard tissue. In this work, we describe the use of a 1-D model to simulate the temperature changes in dental hard tissue during Nd:YAG laser irradiation. According to the results, the parameters studied in this work are not safe for clinical dental treatment protocols due to high temperatures resulting after Nd:YAG laser irradiation around the pulp chamber.

Acknowledgments

This work was financially supported by Fundac¸a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo (FAPESP), Brazil.

REFERENCES

1.

J. M. White , H. E. Goodis , and C. M. Rose , “Nd:YAG pulsed infrared laser for treatment of root surface,” J. Calif. Dent. Assoc. , 19 55 –58 (1991). Google Scholar

2.

L. Miserendino , C. G. Levy , and I. Rizoiu , “Effects of Nd:YAG laser on the permeability of root canal wall dentin,” J. Endod. , 32 83 –87 (1995). Google Scholar

3.

W. H. Lan and H. C. Liu , “Sealing of human dentinal tubules by Nd:YAG laser,” J. Clin. Laser Med. Surg. , 13 329 –333 (1995). Google Scholar

4.

H. C. Liu , C. P. Lin , and W. H. Lan , “Sealing depth of Nd:YAG on human dentinal tubules,” J. Endod. , 23 691 –693 (1997). Google Scholar

5.

A. Ivica , S. Segovic´ , D. Katanec , K. Prskalo , and D. Najizˇar-Fleger , “Scanning electron microscopic study of dentin lased with argon, CO₂, and Nd:YAG laser,” J. Endod. , 24 77 –81 (1998). Google Scholar

6.

K. Yonaga , Y. Kimura , and K. Matsumoto , “Treatment of cervical dentin hypersensitivity by various methods using pulsed Nd:YAG laser,” Lasers Surg. Med. , 17 205 –210 (1999). Google Scholar

7.

J. M. Zuerlein , D. Fried , and J. D. B. Featherstone , “Modeling the modification depth of carbon dioxide laser-treated dental enamel,” Lasers Surg. Med. , 25 335 –47 (1999). Google Scholar

8.

T. G. Van Leeuwen, E. D. Jansen, and M. Motamedi, “Optical-Thermal Response of Laser-Irradiated Tissue,” A. J. Welch and M. Gemert, Eds., pp. 709–763, Plenum Press, New York (1995).

9.

G. Powell , B. Whisenant , and T. Morton , “Carbon dioxide laser oral safety parameters for teeth,” Lasers Surg. Med. , 10 389 –392 (1990). Google Scholar

10.

L. Zach and G. Cohen , “Pulp response to thermal externally applied heat,” Oral Surg., Oral Med., Oral Pathol. , 19 515 –530 (1965). Google Scholar

11.

W. H. Lan , K. W. Chen , J. H. Jeng , C. P. Lin , and Sze-Kwan Lin , “A comparison of the morphological changes after Nd-YAG and CO₂ laser irradiation of dentin surfaces,” J. Endod. , 26 450 –453 (2000). Google Scholar

12.

D. Fried , M. J. Zuerlein , C. Q. Le , and J. D. B. Featherstone , “Thermal and chemical modification of dentin by 9–11 μm CO₂ laser pulses of 5–100 μs duration,” Lasers Surg. Med. , 31 275 –282 (2002). Google Scholar

13.

H. A. Wigdor and J. T. Walsh Jr. , “Histologic analysis of the effect on dental pulp of a 9.6-microm CO₂ laser,” Lasers Surg. Med. , 30 261 –266 (2002). Google Scholar

14.

J. Crank and P. Nicolson , “A practical method for numerical evaluation of solution of partial differential equations of the heat-conduction type,” Proc. Cambridge Philos. Soc. , 43 50 –67 (1947). Google Scholar

15.

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). Google Scholar

16.

M. Braden , “Heat conduction in normal human teeth,” Arch. Oral Biol. , 9 479 –486 (1964). Google Scholar

17.

D. Fried , R. E. Glena , J. D. B. Featherstone , and W. Seka , “Nature of light scattering in dental enamel and dentine at visible and near-infrared wavelengths,” Appl. Opt. , 34 1278 –1285 (1995). Google Scholar

18.

G. D. Smith, “Numerical Solution of Partial Differential Equations Finite Difference Methods,” Oxford Applied Mathematics and Computing Science Series. 2nd ed., pp. 304, Claredon Press, Oxford (1978).

19.

D. U. Von Rosemberg, “Methods for the Numerical Solution of Differential Equations,” American Elsevier Publishing, New York (1969).

20.

R. R. Anderson and J. A. Parrish , “Selective photothermolysis: precise microsurgery by selective absorption of pulsed radiation,” Science , 220 524 –527 (1983). Google Scholar

21.

E. Armon and G. Laufer , “Analysis to determine the beam parameters which yield the most extensive cut with the least secondary damage,” J. Biomech. Eng. , 107 286 –290 (1995). Google Scholar

22.

G. L. LeCarpentier , M. Motamedi , L. P. McMath , S. Rastegar , and A. J. Welch , “Continuous wave laser ablation of tissue: analysis of thermal and mechanical events,” IEEE Trans. Biomed. Eng. , 40 188 –200 (1993). Google Scholar

23.

A. L. McKenzie , “Physics of thermal processes in laser-tissue interaction,” Phys. Med. Biol. , 35 1175 –1209 (1990). Google Scholar

24.

B. Choi and A. J. Welch , “Analysis of thermal relaxation during laser irradiation of tissue,” Lasers Surg. Med. , 29 351 –359 (2001). Google Scholar

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Eduardo H. Moriyama, Renato Amaro Zangaro, Paulo Davi de Castro Lobo, Antonio G. J. Balbin Villaverde, Marcos Tadeu Tavares Pacheco, and Alex Vitkin "Optothermal transfer simulation in laser-irradiated human dentin," Journal of Biomedical Optics 8(2), (1 April 2003). https://doi.org/10.1117/1.1560000

Published: 1 April 2003

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KEYWORDS

Tissues

Pulsed laser operation

Natural surfaces

Nd:YAG lasers

Optical simulations

Laser irradiation

Laser dentistry

1.

Introduction

2.

Parameters and Methods