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.

中文翻译：

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4T1转移性乳腺癌的疾病进展模型。

癌症转移是各种类型癌症的主要死亡原因。然而，在药理学领域，癌症疾病进展模型集中于以肿瘤体积或重量为目标值的原发性肿瘤的生长，而转移过程则很少提及。我们提出一系列数学模型，从原发性乳腺肿瘤，肺转移和白细胞方面定量描述和预测4T1乳腺癌的疾病进展。将4T1细胞注射入雌性BALB / c小鼠的乳脂垫中，以建立乳腺癌转移的动物模型。测量在不同时间的肺转移的数量和体积。基于以上数据，建立了乳腺癌肺转移的疾病进展模型，并估计了参数值。还模拟了4T1小鼠的白细胞生长和原发性肿瘤生长。建立的模型可以从三个方面描述4T1乳腺癌的肺转移：（1）转移数目的增加；（2）转移量的增长；（3）不同时间点的转移数目大小分布。与基于von Forester方程的现有转移模型相比，我们的模型区分了原发性肿瘤的生长和转移，并获得了4T1小鼠模型的参数值。当前模型通过利用逻辑函数代替先前的幂函数来优化转移数大小分布模型。这项研究对4T1乳腺癌模型的肺转移进展进行了全面描述，