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Laser heating of tissue / axis symmetric pde problem
Posted Apr 5, 2010, 11:08 a.m. EDT 2 Replies
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Hello!
I'm modelling the heating of tissue with a laser, and based on some papers and discussions I've read, I've been able to model this in 2D with two coefficient form PDE models coupled to a transient heat conduction model.
The first coefficient form PDE is used to model the Arrhenius damage integral which calculates damage = ln(percent damaged cells) = integral of 1/Temperature over time.
The second coefficient form PDE models light transport of the laser in the tissue which I assume is a simple exponential decay into the tissue (absorption dominated, negligible scatter). The light absorbed serves as the heating term for the heat model.
The standard heat conduction model is used for heat diffusion in the tissue.
This all seems to work fine in 2D, except that it really doesn't represent the physical situation, because the 2D symmetry implies that the model extends infinitely in and out of the screen.
What I really want is an axis symmetric model, symmetric around the center of the "cylindrical" laser beam. Now, there is a 2D axis symmetric geometry for the heat conduction model, but none for the coefficient form PDE modes.
I suppose I can model everything in full blown 3D, however, the model is already pretty slow to solve in 2D.
Any advice how how to do this? Please help.
Thanks in advance!
-ilu
I'm modelling the heating of tissue with a laser, and based on some papers and discussions I've read, I've been able to model this in 2D with two coefficient form PDE models coupled to a transient heat conduction model.
The first coefficient form PDE is used to model the Arrhenius damage integral which calculates damage = ln(percent damaged cells) = integral of 1/Temperature over time.
The second coefficient form PDE models light transport of the laser in the tissue which I assume is a simple exponential decay into the tissue (absorption dominated, negligible scatter). The light absorbed serves as the heating term for the heat model.
The standard heat conduction model is used for heat diffusion in the tissue.
This all seems to work fine in 2D, except that it really doesn't represent the physical situation, because the 2D symmetry implies that the model extends infinitely in and out of the screen.
What I really want is an axis symmetric model, symmetric around the center of the "cylindrical" laser beam. Now, there is a 2D axis symmetric geometry for the heat conduction model, but none for the coefficient form PDE modes.
I suppose I can model everything in full blown 3D, however, the model is already pretty slow to solve in 2D.
Any advice how how to do this? Please help.
Thanks in advance!
-ilu
2 Replies Last Post May 2, 2011, 10:28 p.m. EDT
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Posted:
1 decade ago
you should be able to start by deriving your equations in cylindrical coordinates and then implementing them as appropriate by associating cylindrical eqn terms with the terms in the canonical equation forms provided. I recall seeing an example of how to do that in the documentation.
However, from your problem description it sounds like you should be able to use the 2-D axisymmetric conduction model as is. I am not sure why you need to couple it to another PDE. Unless the damage integral is also changing the physical properties it is calculated independently of the actual heat conduction PDE so no trouble there. As for the light absorption, I think you should be able to put it in as an equation that represent an exponentially decaying heat source with z-distance from the surface.
Good luck
Ozgur
However, from your problem description it sounds like you should be able to use the 2-D axisymmetric conduction model as is. I am not sure why you need to couple it to another PDE. Unless the damage integral is also changing the physical properties it is calculated independently of the actual heat conduction PDE so no trouble there. As for the light absorption, I think you should be able to put it in as an equation that represent an exponentially decaying heat source with z-distance from the surface.
Good luck
Ozgur
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Posted:
1 decade ago
I know this maybe an old topic for you. As I am new to Comsol, I have problems to simulate the temperature rising of the plasmonic structure during the laser illumination. Assuming the Electromagnetic wave plus the heat transfer will do the job. According to the suggestion from the Comsol support, one heat source was added using the total power loss of the electromagnetic wave. However, it doesn't work.
Apprecieate any of your suggestions.
Apprecieate any of your suggestions.