Liotta L A, Saidel G M, Kleinerman J
Biometrics. 1976 Sep;32(3):535-50.
A mathematical model is developed to describe the dynamics of the hematogenous metastatic process to the lung from a solid tumor growing in a peripheral body site. The accumulation of tumor cell clumps of various sizes in the pulmonary circulation and the formation of metastatic foci are described by a non-homogeneous, two-dimensional Markov process. An analytical solution is found for the special case of metastases produced by the intravenous injection of tumor cell clumps. The system is decoupled experimentally to determine the time-varying entrance rate of tumor cell clumps into the circulation from a growing fibrosarcoma and the number of metastatic foci produced by the intravenous injection of tumor clumps. Model validation is based on comparisons of model simulations with data for the development of metastatic foci and the probability of cure following tumor excision. The model is used to simulate hypothetical therapy to prevent tumor metastases.
建立了一个数学模型，以描述实体瘤在身体外周部位生长时血行转移至肺部的动力学过程。肺循环中各种大小肿瘤细胞团块的积累以及转移灶的形成由一个非齐次二维马尔可夫过程描述。对于静脉注射肿瘤细胞团块产生转移的特殊情况，找到了一个解析解。通过实验将该系统解耦，以确定肿瘤细胞团块从生长的纤维肉瘤进入循环的时变进入率，以及静脉注射肿瘤团块产生的转移灶数量。模型验证基于模型模拟结果与转移灶发展数据以及肿瘤切除后治愈概率的比较。该模型用于模拟预防肿瘤转移的假设性治疗。
