# Binomial distribution - killing cells with x-rays

## Does the question make sense, and are there any other medical physicists out there?

Poll closed Jun 17, 2006.

2 vote(s)
100.0%

0 vote(s)
0.0%

0 vote(s)
0.0%
4. ### no, I'm not

1 vote(s)
50.0%
1. May 18, 2006

### wendy-medicalphysics

Dear Fellow mathematicians and Physicists,I am doing some MC modelling on tumour growth and radiotherapy treatment modelling and would like to know:

Who out there would agree (or suggest alternatives) to the theroy that the chance of a cell being damaged/hit with radiation (and therefore perhaps dying depending on other parameters) may be described by the bionomial distribution?

Background:
1. Let's say that we have 1000 cells, and k photons will be fired at them
2. Let's also say that a cell will dye if hit 2 or more times (simplistic for now!)
3. I need the number of cells that are hit only 0 or 1 times to be 46% of the total

Can I use the bionomial distribution to work out how may photons that would take (integrating to find the area under the curve to obtain the number of phtotons necessary to achieve point 2.?)

I believe we can think about it as a dice with 1000 number sides.
If we roll the dice k times and take the histogram of the number of times each side came up, then the system is the same as the cell/photon set up...WHAT DO YOU THINK???

Thanks, and write back if you don't understand what I am trying to say

Wendy

2. May 19, 2006

### Gokul43201

Staff Emeritus
Assuming that all photons, with certainty, are absorbed by one of the cells, the above approach seems to me like a reasonable approximation, given the difficulty of incorporating knowledge of the cellular geometry and the radiation source into a model.

I wouldn't call the result a binomial distribution though - perhaps a millenomial distribution ?

3. May 22, 2006

### JierenChen

That would be interesting. And you look at P(X1>=2, X2>=2, X3...)? A very simple and elegant model but I have a feeling it's been superceded. I would look at graphs, random fields, anything with that sort of mapped network type of thingie. Haven't really looked at that kind of stuff in a while so I probably can't help you yet (and I have this ***** of an essay to write.) I suspect what you're looking for is a discrete array of continuous arrays of random numbers. Thus you could model with continuity the cell surface and then model discretely n numbers of cells.

Last edited: May 22, 2006
4. Jun 29, 2006