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 t...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.展开更多
基金Natural Science Foundation of Beijing Municipality (Grant No. 7192100)。
文摘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.
