肿瘤生长和转移中混沌吸引子的理论模型
A Theoretical Model of Chaotic Attractor in Tumor Growth and Metastasis
摘要：
提出了一种新的细胞肿瘤生长和转移的混沌反应扩散模型。该模型是基于多尺度扩散癌症侵袭模型（MDCM），并制定通过引入强非线性耦合到MDCM。新模型表现出时间混沌行为（类似于经典的Lorenz奇异吸引子），但保留了MDCM扩散模型的所有特征。它在数学上描述了癌症发生和转移的过程，以及癌症演变对初始条件和参数的敏感依赖性。在此混沌肿瘤生长模型的基础上，提出了肿瘤发生和转移的一般概念。关键词：反应扩散肿瘤生长模型，混沌吸引子，对初始肿瘤特征的敏感依赖
英文摘要：
This paper proposes a novel chaotic reaction-diffusion model of cellular tumor growth and metastasis. The model is based on the multiscale diffusion cancer-invasion model (MDCM) and formulated by introducing strong nonlinear coupling into the MDCM. The new model exhibits temporal chaotic behavior (which resembles the classical Lorenz strange attractor) and yet retains all the characteristics of the MDCM diffusion model. It mathematically describes both the processes of carcinogenesis and metastasis, as well as the sensitive dependence of cancer evolution on initial conditions and parameters. On the basis of this chaotic tumor-growth model, a generic concept of carcinogenesis and metastasis is formulated. Keywords: reaction-diffusion tumor growth model, chaotic attractor, sensitive dependence on initial tumor characteristics
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