FDTD : Bioheat Equation, Stability Criterion

[somada141]

german bioheat

Hello everyone,

I am back with my favorite topic: FDTD.

In here I will share a piece of knowledge not easily found. Of course this will care only a handful of people so if you're not interested in FDTD and its biomedical applications then you might as well close this post.

I speak of course about the fabled Bioheat Equation (BHE). With it you can calculate the temperature distribution on the human body. However I will not discuss its merits here.

What I will do is attach an excellent paper on using FDTD and the BHE for calculating the temperature distribution on the human head by a mobile phone.

The great thing about this paper (after all this topic has been examined close to 3000 times) is that a stability criterion similar to the EH FDTD time-step criterion (also known as Courant Condition) which lets you calculate the necessary time step for heat transfer applications.

Of course the standard FDTD time step isn't proper for a heat tranfer simulation because:

-> It is incredible small (close to nanoseconds) and would take foerever to do a proper heat tranfer simulation
-> Heat doesn't move with the speed of light

Therefore a new time step is required.

The answer is in this paper.

FDTD Computation of Temperature Rise in the Human Head for Portable Telephones by Jianqing Wang and Osamu Fujiwara

I attach the paper itself here. However since the analysis in the paper is only valid for cubical grids (and because I am feeling generous) I redid the whole analysis for a rectangular grid and post the results in a pdf file here...

I keep contributing and I only want one thing, I want you to call me Adam the FDTD Guru...

Thank you

 

[red5000]

thnks verry interesting

 

[rrumpf]

Here is another interesting FDTD stability problem I came across some time ago. I wanted to better understand how a finite speed of gravity would affect orbital mechanics which is based on the gravity equation. All orbital mechanics assumes the affect of gravity is instantaneous and never discusses this approximation and when it may not be valid. I did find that at the solar system level the effect is negligible, at least over short time periods (centuries). I did find, however, this impacted how galaxies would interact. My step sizes were millenia. I only concluded it was significant here, but never bothered to come up with any conclusions or a stability criterion.

You are the FDTD guru. What say ye?

-Tip

 

[somada141]

I say wow..this is completely beyond me and/or my knowledge in such matters.

I wouldn't know where to start or how to proceed. The only thing I did in this post was to dig up the criterion for the Bioheat equation and generalize the given formula for the generic case...

However I suppose that if you can give me the discretized equations or if you attempt to follow the procedure followed in the doc I attached then you may reach the stability criterion for any equation...Or so I believe...

Still this is way out of my league.

P.S The guru thing was merely a joke. I am still a newbie at FDTD. I am only giving sharing the things regarding this topic that took me a lot of time to come up with and would help others.

 

[rrumpf]

I can't I know what I'm doing either. I just have fun trying!

-Tip