A Mathematical Model to Predict Diagnostic Periods for Secondary Distant Metastases in Patients with ER/PR/HER2/Ki-67 Subtypes of Breast Cancer

Abstract

Previously, a consolidated mathematical model of primary tumor (PT) growth and secondary distant metastasis (sdMTS) growth in breast cancer (BC) (CoMPaS) was presented. The aim was to detect the diagnostic periods for visible sdMTS via CoMPaS in patients with different subtypes ER/PR/HER2/Ki-67 (Estrogen Receptor/Progesterone Receptor/Human Epidermal growth factor Receptor 2/Ki-67 marker) of breast cancer. CoMPaS is based on an exponential growth model and complementing formulas, and the model corresponds to the tumor-node-metastasis (TNM) staging system and BC subtypes (ER/PR/HER2/Ki-67). The CoMPaS model reflects (1) the subtypes of BC, such as ER/PR/HER2/Ki-67, and (2) the growth processes of the PT and sdMTSs in BC patients without or with lymph node metastases (MTSs) in accordance with the eighth edition American Joint Committee on Cancer prognostic staging system for breast cancer. CoMPaS correctly describes the growth of the PT in the ER/PR/HER2/Ki-67 subtypes of BC patients and helps to calculate the different diagnostic periods, depending on the tumor volume doubling time of sdMTS, when sdMTSs might appear. CoMPaS and the corresponding software tool can help (1) to start the early treatment of small sdMTSs in BC patients with different tumor subtypes (ER/PR/HER2/Ki-67), and (2) to consider the patient almost healthy if sdMTSs do not appear during the different diagnostic periods.