The Mathematical Model for Predicting the Development of the Tumor Growth Process of Breast Cancer

This paper is devoted to mathematical modelling of breast cancer (BC) progression, including stages and TNM classification. Given the relationship between primary tumour (PT) and metastases (MTS), the problem of discovering the BC process seems to be twofold: first, it is important to describe the whole natural history of BC to understand the process as a whole; second, it is necessary to predict the period of a clinical MTS manifestation. To understand the growth processes of BC at each stage, CoMBreC was proposed as a new research tool in 2017. The CoMBreC model is threefold: CoMPaS (stages I-II), CoM-III (stage III) and CoM-IV (stage IV). A new model rests on an exponential growth model and complementing formulas. For the first time, it allows us to calculate the different growth periods of PT and MTS in patients with/without lymph nodes MTS: 1) the non-visible period for PT; 2) the non-visible period for MTS; and 3) the visible period for MTS. Calculations via CoMBreC correspond to survival data, considering the stage of BC. It may help to improve the prediction accuracy of the BC process using an original mathematical model referred to CoMBreC and corresponding software. Consequently, this study concentrated on 1) calculating the earliest diagnostics period before the manifestation of secondary distant MTS, 2) developing an adequate and precise CoMBreC that reflects the relationship between PT and MTS, and 3) analysing the CoMBreC scope of application. The CoMBreC is implemented as an iOS application as a new predictive tool: 1) it is a solid foundation upon which to develop future studies of BC models; 2) it does not require any expensive diagnostic tests; and 3) it is the first predictor of survival in BC that makes forecasts using only current patient data.