血管前球体发育的数学模型和快速转移性生长/肿瘤缓解的灾变理论描述。

Invasion & metastasis Pub Date : 1996-01-01
J A Adam
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引用次数: 0

摘要

在过去的三十年中,提供了肿瘤生长和发展的确定性模型的简要调查。这些模型的演变是从基本的现象学和经验描述开始的,通过依赖时间和不依赖时间的扩散模型(主要在扩散平衡近似内)。这包括对生长抑制剂扩散的研究。讨论了椭球模型在小扰动下的稳定性,以及非线性弹性理论和微分几何在癌症可能的分期和分级中的最新应用。最后,对突变理论进行了探讨,其中认为尖突变(特别是尖突变)可以提供快速的、几乎自发的(i)转移生长或(ii)肿瘤缓解(两者都发生在某些限制性条件下)的定性描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mathematical models of prevascular spheroid development and catastrophe-theoretic description of rapid metastatic growth/tumor remission.

A brief survey is provided of deterministic models of tumor growth and development over the last three decades. The evolution of these models has proceeded from basic phenomenological and empirical descriptions, through both time-dependent and time-independent diffusion models (largely within the diffusive equilibrium approximation). This includes a study of the diffusion of growth inhibitors. The stability of spheroid models to small perturbations is discussed, and also recent applications of nonlinear elasticity theory and differential geometry to possible staging and grading of cancers. Finally, an excursion is made into catastrophe theory, wherein it is suggested that the cusp catastrophe (in particular) may provide a qualitative description of rapid, almost spontaneous (i) growth of metastases, or (ii) tumor remission (both occurring under certain restrictive conditions).

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