Mathematical Methods and Software Tools for Prediction of Breast Cancer Developing

This paper is devoted to mathematical modelling of the progression considering stages of breast cancer. Given the relation between PT and MTS, the problem of discovering BC process seems to be twofold: firstly, it is important to describe the whole natural history of BC to understand the process as a whole; secondly, it is necessary to predict the period of a clinical MTS manifestation. In order to understand growth processes of BC on each stage the CoMBreC was proposed as a new research tool. The CoMBreC is threefold: CoMPaS (stages I-II), CoM-III (stage III) and CoM-IV (stage IV). A new model rests on exponential growth model and complementing formulas. For the first time, it allows us to calculate different growth periods of PT and MTS in patients with/without lymph nodes MTS: 1) "non-visible period" for PT; 2) "non-visible period" for MTS; 3) "visible period" for MTS. Calculations via CoMBreC correspond to survival data considering stage of BC. It may help to improve predicting accuracy of BC process using an original mathematical model referred to CoMBreC and corresponding software. Consequently, thesis concentrated on: 1) modelling the whole natural history of PT and MTS in patients with/without lymph nodes MTS; 2) developing adequate and precise CoMBreC that reflects relations between PT and MTS; 3) analysing the CoMBreC scope of application. The CoMBreC was implemented to iOS application as a new predictive tool: 1) is a solid foundation to develop future studies of BC models; 2) does not require any expensive diagnostic tests; 3) is the first predictor of survival in breast cancer that makes forecast using only current patient data.