On Consolidated Predictive Model of the Natural History of Breast Cancer: Primary Tumor and Secondary Metastases in Patients with Lymph Nodes Metastases

Abstract

This paper is devoted to mathematical modelling of the progression and stages of breast cancer. The "Consolidated mathematical growth Model of primary tumor (PT) and secondary distant metastases (MTS) in patients with lymph nodes MTS (Stage III)" (CoM-III) is proposed as a new research tool. The CoM-III rests on an exponential tumor growth model and consists of a system of determinate nonlinear and linear equations. The CoM-III describes correctly primary tumor growth (parameter T) and distant metastases growth (parameter M, parameter N). The CoM-III model and predictive software: a) detect different growth periods of primary tumor and distant metastases in patients with lymph nodes MTS; b) make forecast of the period of the distant metastases appearance in patients with lymph nodes MTS; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of breast cancer and facilitate optimisation of diagnostic tests. The CoM-III enables us, for the first time, to predict the it whole natural history of PT and secondary distant MTS growth of patients with/without lymph nodes MTS on each stage relying only on PT sizes.