Advanced Physics for Brachytherapy 2018

The MC method …

The Central Limit Theorem : the sum of a large number of identical, independent random variables is approximately normally distributed.

So, if I want to calculate an unknown quantity, m, and k is a random variable of expectation value E(k)=m and variance Var(k)=b 2 . If k 1 , k 2 , …, k N are N RANDOMLY selected values of k,

is normally distributed with E( )=Nm and V ( )=Nb 2

then:

or equivalently:

or:

So, if I want to estimate the photon fluence (or any related quantity ) at point r, I can average the contribution of N photon tracks RANDOMLY sampled from the probability distribution of all possible tracks