Cancer metastasis is the main cause of death in various types of cancer. However, in the field of pharmacometrics, cancer disease progression models focus on the growth of primary tumors with tumor volume or weight as target values, while the metastasis process is less mentioned. We propose a series of mathematical models to quantitatively describe and predict the disease progression of 4T1 breast cancer in the aspect of primary breast tumor, lung metastasis and white blood cell. The 4T1 cells were injected into breast fat pad of female BALB/c mice to establish an animal model of breast cancer metastasis. The number and volume of lung metastases at different times were measured. Based on the above data, a disease progression model of breast cancer lung metastasis was established and parameter values were estimated. The white blood cell growth and the primary tumor growth of 4T1 mouse are also modeled. The established models can describe the lung metastasis of 4T1 breast cancer in three aspects: (1) the increase in metastasis number; (2) the growth of metastasis volume; (3) metastasis number-size distribution at different time points. Compared with the prior metastasis models based on von Forester equation, our models distinguished the growth rate of primary tumor and metastasis and got parameter values for 4T1 mouse model. And the current models optimized the metastasis number-size distribution model by utilizing logistic function instead of the prior power function. This study provides a comprehensive description of lung metastasis progression for 4T1 breast cancer model, as well as an alternative disease progression model structure for further pharmacodynamics modeling.
Keywords: 4T1; Breast cancer; Disease progression model; Lung metastasis; Mathematical model.