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Transient FEM Calculation of the Spatial Heat Distribution in Hard Dental Tissue During and After IR Laser Ablation Günter Uhrig, Dirk Meyer, and Hans-Jochen Foth Dept. of Physics, University of Kaíserslautern, Germany

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Contents Motivation Basics of model calculations Results –single Pulse –low number of pulses –large number of pulses –influence of repetition rate Conclusion

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cw versus pulsed mode operation Dentin, CO 2 laser, 10.6 m 2 Watt, Super Pulse 20 Watt cw

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CO 2 Laser 20 W, cw, no cooling

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Laser System CO 2 laser, Sharplan 40C Pulse width in super pulse mode Correlation: Repetition rate to selected mean power

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Thermal damage Important: Combination of temperature rise and time Temperature [°C] Time [s] Tissue damage No tissue damage

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Experimental problems to measure the temperature T(x,y,z,t) at a point (x,y,z) inside the tissue for various times t Artefacts due to heat capacity and absorption of the thermocouples Only the surface is recorded

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Experimental Set-Up for the Determination of Laser Induced Heat

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Motivation for Model Calculation Laser induced heat deposition on surface or bottom of a crater Three-dimensional, transient calculation Surface temperature T S (x,y,z,t) Measurement of T S by IR Camera Inside temperature T inside (x,y,z,t) Good agreement ensures that calculation of T inside is correct

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Principles of FEM Calculation FEM = Finite Element Method Generate Grid Points Equation for heat conduction with = density c = heat capacity T = temperature t = time = heat conductivity Q = heat source = Laplace operator Finite Elements With K = matrix of constant heat conduction coefficients C = matrix of constant heat capacity coefficients P = vector of time dependent heat flow

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Gauß profil and Beer‘s law

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Geometric Shape

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Analytical Model Calculation

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Solution

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Results: 1Laser induced heat during the laser pulse interaction We can ignore heat conduction during the laser pulse

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2Temperature distribution after one pulse

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Temperature and temperature gradient along the symmetry axis z

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Temperature gradient in the z-x-plane

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What does these numbers mean ? Values were calculated using the thermodynamical values of dentin Density 2.03 g/cm 3 Specific Heat c1.17 J/(g·K) Heat Conduction 0.4 10 -3 W/(mm·K) Thermal Extension a11.9 10 -6 1/°C Elasticity Module E12,900 N/mm 2 Energy flow through the surface was 0.4 MW/cm 2 at a spot of 0.1mm radius Maximum of temperature slope dT/dz = - 16,400 °C/mm in a depth 60 m beneath the surface Mechanical stress up to ~ 1000 N/cm 2 = 10 MPa Maximum stress in dentin up to 20 MPa* * Private communication R. Hibst

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3Low number of pulses Temperature evolution between two pulses 7 ms 12 ms 19 ms

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Temperature after various pulses After 1st pulseAfter 2nd After 3rd After 4th

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Temperature development at crater center

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Temperature rise in the center of the crater Absolute value is not gauged

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4Large number of pulses

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Result of the movie After 10 Pulses: Temperature evolution between pulses is repeated Temperature distribution is moved into the tissue We reached dynamical confinement Computer program is o.k.

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5Influence of repetition rate Results of Finite Element Calculation Compared to Analytical Approximation Temperatures at the points p 1 to p 3 Tissue is removed by laser pulses; z = 40 m Point p 1

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Results of Finite Element Calculation Compared to Analytical Approximation Point p 3 Point p 2 FEM: Three dimensional24 hours Analytical:one spatial point2 minutes

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Which amount of heat is removed by the proceeding pulse?

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Propagation of isotherms

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Ablation depth versus repetition rate 1086.713.32040 time between pulses [ms]

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First laser pulse tissue ablated volume heat front Energy loss High ablation efficiency due to preheated tissue Next laser pulse

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Speciality in Plexiglas Propagation of the isotherm of 160 °C (melting point)

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CO 2 laser on Plexiglas, the influence of heat is visible by the thickness of the melting zone

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Superposition of Crater 1 and 2

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Conclusion cw laser mode gives deep thermal damage In pulse mode, low repetition rates are not automatically the best version, since high repetition rates giveless thermal stress higher efficiency for ablation This model was worked out by FEM and analytical model calculations and checked by experiments

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