# A Bayesian approach to determine the composition of heterogeneous cancer tissue

## Introduction and Background:

Cancer Tissue Heterogeneity is an important consideration in cancer research as it can give insights into the causes and progression of cancer. This necessitates a low cost, scalable algorithm to address the challenge of accurate estimation of the composition of a heterogeneous cancer tissue.

In an accurate, but high cost, optical approach was suggested to determine the compositional breakup of a heterogeneous cancer tissue. In this method, all the cells in the heterogeneous tissue were imaged individually and their red, green and blue fluorescence were measured. Imaging individual cells is a complex method as it requires high resolution imaging followed by complex image processing algorithms. In the proposed algorithm, we aim to develop a mathematical framework to reduce the experimental cost by relying on aggregate observations and minimizing the need for individual cell-by-cell observations. Aggregate observations are the summation of the contribution of individual cells in a heterogeneous tissue. (Figure 1)

Figure 1: Heterogeneous cancer tissue and the attributes

## Proposed Algorithm:

The single cell high resolution data for individual cell lines is used to estimate the mean and variance of the attributes of interest. The algorithm estimates the number of cells of each type using a Bayesian approach assuming a uniform prior on the number of cells. The mean and the variance estimates are the parameters of the posterior distribution of the number of cells. Maximising the posterior distribution isnâ€™t mathematically tractable. To circumvent the problem, we use the Metropolis to generate samples from the posterior and use Kernel Density Estimation to estimate the posterior distribution. We use the maximum aposteriori probability estimate as the estimate of the number of cells.

The details of the paper can be found here.