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Günter Uhrig, Dirk Meyer, and Hans-Jochen Foth Dept. of Physics, University of Kaíserslautern,

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. Contents. Motivation Basics of model calculations Results

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Günter Uhrig, Dirk Meyer, and Hans-Jochen Foth Dept. of Physics, University of Kaíserslautern,

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  1. 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

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

  3. cw versus pulsed mode operation Dentin,CO2 laser, 10.6 mm2 Watt, Super Pulse 20 Watt cw

  4. CO2 Laser 20 W, cw, no cooling

  5. Laser SystemCO2 laser, Sharplan 40C Pulse width in super pulse mode Correlation: Repetition rate to selected mean power

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

  7. Experimental problemsto 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

  8. Experimental Set-Up for the Determination of Laser Induced Heat

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

  10. Generate Grid Points Principles of FEM Calculation FEM = Finite Element Method Equation for heat conduction with r = density c = heat capacity T = temperature t = time l = heat conductivity Q = heat source D = 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

  11. Gauß profil and Beer‘s law

  12. Geometric Shape

  13. Analytical Model Calculation

  14. Solution

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

  16. 2 Temperature distribution after one pulse

  17. Temperature and temperature gradient along the symmetry axis z

  18. Temperature gradient in the z-x-plane

  19. Values were calculated using the thermodynamical values of dentin Density r 2.03 g/cm3 Specific Heat c 1.17 J/(g·K) Heat Conduction l 0.4 10-3 W/(mm·K) Thermal Extension a 11.9 10-6 1/°C Elasticity Module E 12,900 N/mm2 Energy flow through the surface was 0.4 MW/cm2 at aspot of 0.1mm radius Maximum of temperature slope dT/dz = - 16,400 °C/mm in a depth 60 mm beneath the surface Mechanical stress up to ~ 1000 N/cm2 = 10 MPa Maximum stress in dentin up to 20 MPa* * Private communication R. Hibst What does these numbers mean ?

  20. 3 Low number of pulses Temperature evolution between two pulses 7 ms 19 ms 12 ms

  21. Temperature after various pulses After 3rd After 1st pulse After 2nd After 4th

  22. Temperature development at crater center

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

  24. 4 Large number of pulses

  25. 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.

  26. 5 Influence of repetition rate Results of Finite Element Calculation Compared to Analytical Approximation • Temperatures at the points p1 to p3 Tissue is removed by laser pulses; Dz = 40 mm Point p1

  27. Results of Finite ElementCalculation Compared to Analytical Approximation Point p3 Point p2 FEM: Three dimensional 24 hours Analytical: one spatial point 2 minutes

  28. Which amount of heat is removed by the proceeding pulse?

  29. Propagation of isotherms

  30. Ablation depth versus repetition rate 40 20 13.3 10 8 6.7 time between pulses [ms]

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

  32. Speciality in PlexiglasPropagation of the isotherm of 160 °C (melting point)

  33. CO2 laser on Plexiglas, the influence of heat is visible by the thickness of the melting zone

  34. Superposition of Crater 1 and 2

  35. Conclusion • cw laser mode gives deep thermal damage • In pulse mode, low repetition rates are not automatically the best version, since high repetition rates give less 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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