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\section{Math}   \hspace{20 mm}Each tumor was modeled as a self-avoiding polygon (SAP). A SAP is a closed shape whose perimeter consists of a random walk path which does not visit the same site more than once, also known as a self-avoiding walk (SAW). A SAW of length $N$ in a $2$-dimensional lattice ${\Bbb R}$, starting at point $x$, is defined as a path  \begin{equation}  ω=(ω_0, ω_1, ..., ω_n)  \end{equation}