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Two Layer Photon Density Probabilities

Sep 12, 2011 at 6:36 PM


 I have a question about your model. According to papers about two layer, with a short Rho (source-detector separation) you can sample the top layer and with a longer Rho you can sample the bottom one. For the short one I do understand that you are interrogating the top layer with photon migration ( banana ) because the whole thing is in the top layer, but for the long Rho some parts of your banana is in the top layer and major part is in bottom layer. I want to know how you know what is the right portion for bottom out of this second banana.? I have a picture below to clarify my question.

The small banana is only in top region, but the second one is probing both layers. When I have the data for these two layers, how should I separate these two layers. I am sure it is now a simple subtraction because the second banana is probing both layer in contrast to first one which only probing the top layer.


Here is the link for the picture:

Sep 13, 2011 at 12:44 AM

You're absolutely right that the s-d #2 probes both layers. But, the reality is: both s-d separations probe both layers, just to varying degrees. Those "hard" lines in the picture you posted are of course just for visualization...the bananas go "everywhere".

In some cases, with "short enough" s-d separations, one can assume they only detect the top layer. Perhaps, based on this, you could constrain the fit of the long s-d measurement to only fit for the bottom layer.

Still :

1) this doesn't mean that short s-d separation measurements alone guarantee that you can CALCULATE top layer properties well

2) it definitely isn't a simple subtraction to remove unknown bottom-layer properties from a measured signal

There have been publications about inverse models in the frequency domain - have you looked at the early Kienle multi-layer work, Ang Li's mutli-layer paper, or perhaps Tuan Pham/Lars Svaasand (planar photon density waves - not exactly the same geometry, but similar problem...).

The first step in inverse problems is first to understand sensitivity to layer changes (thickness and optical properties) in your particular geometry/use case. Have you done this? What have you found?

Sep 13, 2011 at 12:51 AM

Forgot to add: 

One of your questions was regarding understanding the fraction of photon paths interrogating each layer. The "crude" way to do this is using "Photon Hitting Density" calculations - you'd do a weighted integral of this "banana" function, just as we do in the PHD calculator for homogeneous tissues for the GP-ATK GUI. Best way to do this is to start with one of the analytical models (above) for two layers. The more "refined" way is to do P(V&D) - calculating the "probability of visitation and detection." This is a little more complicated, and is not enabled directly in our Monte Carlo code (yet).

Sep 13, 2011 at 6:37 AM
Edited Sep 13, 2011 at 6:39 AM

I am sorry! I had a TYPO! I meant I am sure it is NOT a simple subtraction! I did read Ang paper! and I am working base on his paper! he just talked about different s-d ( short and long) to probe the phantoms.