Progression analysis of disease applied to breast cancer research
Rachel Jeitziner · 2011
In this paper, we present several applications of a recently developed mathematical field called topological data analysis (TDA). The poster focusses on two dierent methods of TDA : Progression Analysis of Disease and the analysis of Betti numbers. We apply these techniques to a set of microarrays from tissue donated by women undergoing mammoplasty surgery. These are results from breast cancer research; obtained under varying experimental conditions. We find that topological features describe significant structures of the data, insights that could not be gained with standard tools. Abstract In this paper, we present several applications of a recently developed mathematical field called topological data analysis (TDA). The poster focusses on two dierent methods of TDA : Progression Analysis of Disease and the analysis of Betti numbers. We apply these techniques to a set of microarrays from tissue donated by women undergoing mammoplasty surgery. These are results from breast cancer research; obtained under varying experimental conditions. We find that topological features describe significant structures of the data, insights that could not be gained with standard tools. Cancer arises from cells that leave the cell cycle and start to proliferate in an uncontrolled manner. This proliferation could be induced by hormones that are impinging on the breast. Researchers found that receptor activator of nuclear factor B ligand (RANKL) is a protein involved in progesterone induced pro- liferation. To understand what this protein is inducing,we investigate genes that are dierentially expressed, when one stimulates healthy human tissue with RANKL. From the same patient, we stimulate one tissue with RANKL and another one with vehicle (that is a solution in which the RANKL protein is put into suspension). The standard statistical test (a moderatedt-test), highlights only 11 genes whose expression is significantly altered between the two groups. Using instead progression analysis of disease (PAD)(2), with the unstimulated samples as the healthy state model (HSM) (the normal group), we are able to measure the deviation from the HSM for every stimulated sample, implying that we can directly give a qualitative measure of how much a sample is changed upon stimulation with RANKL, where blue means close to the HSM and red means far away.