Transient FEM Calculation of the Spatial Heat Distribution in Hard Dental Tissue During and After IR Laser Ablation

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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, CO2
laser, 10.6 mm2 Watt, Super Pulse
20 Watt cw
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CO2 Laser 20 W, cw, no cooling
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Laser SystemCO2 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
Tissue damage
Temperature C
No tissue damage
Time s
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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 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
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Principles of FEM Calculation
FEM Finite Element Method

• Generate Grid Points

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
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Gauß profil and Beers law
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Geometric Shape
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Analytical Model Calculation
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Solution
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Results
1 Laser induced heat during the laser pulse
interaction
We can ignore heat conduction during the laser
pulse
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2 Temperature 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 r 2.03 g/cm3
• Specific Heat c 1.17 J/(gK)
• Heat Conduction l 0.4 10-3 W/(mmK)
• 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
  a spot 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
  

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3 Low number of pulses
Temperature evolution between two pulses
7 ms
19 ms
12 ms
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Temperature after various pulses
After 3rd
After 1st pulse
After 2nd
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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4 Large 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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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
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Results of Finite Element Calculation Compared to
Analytical Approximation
Point p3
Point p2
FEM Three dimensional 24 hours Analytical one
spatial point 2 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
10
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6.7
13.3
20
40
time between pulses ms
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First laser pulse
ablated volume
tissue
Next laser pulse
heat front
High ablation efficiency due to preheated tissue
Energy loss
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Speciality in PlexiglasPropagation of the
isotherm of 160 C (melting point)
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CO2 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 give less thermal stress
• higher efficiency for ablation
• This model was worked out by FEM and analytical
  model calculations and checked by experiments