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Problem: Light transport through biological tissue

Posted 8 years ago

I'm new to Mathematica and while it seems like there should be a way to do this (it is effectively simultaneous equations) I don't know how to input it to Mathematica. I've tried using solve and setting it in a table first but it seems I'm not realizing something or missing something in the documentation about how to play with a few.

The problem represents light passing through tissue. There are two variables in the equation that I need to know, a and b. (if there is a method to input equations/code here can someone point it out to me?)

enter image description here

I(lam), I0(lam) are measured values. I will know these, they are the intensity of the light coming out and going into the volume at wavelength lambda. M(lam) is the absorption of tissue at the wavelength lamda, this I will also know at all lambdas.

d thickness of the tissue, this is a set value.

a and b are what I would like to know. That term represents the light scattering function for the tissue.

What I would like mathematica to do is tell me how many lambda's, or colors of light, do I have to measure at to find what a and b are, and the equation that gives me a and b.

POSTED BY: Alan Riordan
6 Replies
Posted 8 years ago

Thank you to everyone for your help with this!

POSTED BY: Alan Riordan
POSTED BY: Hans Dolhaine
POSTED BY: Hans Dolhaine

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

Please do NOT use images for posting code.

The rules explain how to format your code properly. If you do not format code, it may become corrupted and useless to other members. Please EDIT your posts and make sure code blocks start on a new paragraph and look framed and colored like this.

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

enter image description here

POSTED BY: EDITORIAL BOARD

Hi Alan

Yours problem can be solved if you have 2 equations.

Let's try:

Solve[a + b == c, {a, b}]

(* Solve::svars: Equations may not give solutions for all "solve" variables.*)

Give an error occurs because the number of variables is greater than the number of equations.

If I have 2 equations then:

 Solve[{a + b == c, a == 1}, {a, b}]

 (* {{a -> 1, b -> -1 + c}}*)

is Ok.

Regards,Mariusz.

POSTED BY: Mariusz Iwaniuk

If it's measured data, you probably want one of the *Fit family of function, for example FindFit or NonlinearModelFit. How many values are needed should depend on how noisy the data is, but statistics is not a field I am familiar enough with to give a good answer. The FittedModel returned by NonlinearModelFit will report various measurements of quality; see the docs.

POSTED BY: Michael Rogers
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