摘要
Cancer metastasis is a process with multi-step complexity and apparent randomness. In this study, we aimed to establish a stochastic mathematical model to describe the random process of cancer metastasis and predict the drug effect of QAP14 on metastasis in a mouse model. The data of lung metastases on the 22^(nd) day after cancer cell implantation with or without the treatment of QAP14, a new chemical compound, were collected in 4T1 breast cancer BALB/c mice. Based on the exponential growth of the primary tumor and metastatic loci, a joint distribution model of metastasis size and number was developed. Disease progression of metastasis and preclinical efficacy of QAP14 were modeled. Parameters M and m representing maximum and minimum of metastasis volume were 3.24 and 0.0184 mm^(3), respectively. The metastasis growth rate γ and metastasis promotion time ρ were estimated and fixed to be 0.0216 d^(-1) and 7.8 d, respectively. The efficacy of QAP14 acted on metastasis promotion time and metastasis growth rate constant in an exponential term, and the effect parameter Effectρ and Effectγ were 16.6 and 0.327 g/mg, respectively. In the present study, we comprehensively characterized the random process of lung metastasis and efficacy of QAP14 in 4T1 breast cancer mice, which might provide a useful reference for the establishment of a clinical population model of cancer metastasis.
肿瘤转移是一个多步骤的复杂过程,具有明显的随机性。本研究旨在建立一种随机数学模型来描述肿瘤转移的随机过程,预测新化合物QAP14对小鼠肿瘤转移的抑制作用。4T1细胞植入BALB/c小鼠22天后,收集QAP14治疗组与对照组的肺转移数据,基于原发肿瘤和转移灶指数生长的特点和以上数据,建立转移大小和数量的联合分布模型,进而模拟疾病进展和QAP14的临床前药效。参数M和m分别代表转移灶体积的最大值和最小值,估计值分别为3.24和0.0184mm^(3),转移生长速率γ和促转移时间ρ的估计值分别为0.0216/天和7.8天并在药效模型中固定,QAP14对促转移时间和转移生长速率常数的作用以指数的形式加入到模型中,药效参数Effectρ和Effectγ的估计值分别为16.6和0.327g/mg。本研究系统描述了肿瘤转移的疾病进程以及QAP14抑制4T1乳腺癌小鼠肺转移的药效,为临床上建立肿瘤转移的群体模型提供了有价值的参考。
基金
Natural Science Foundation of Beijing Municipality (Grant No. 7192100)。
