早期肿瘤生长模型及其标度律的研究

广西师范大学学报（自然科学版） ›› 2013, Vol. 31 ›› Issue (1): 16-20.

早期肿瘤生长模型及其标度律的研究

蒋重明^1,2, 刘艳辉², 胡林²

1.中山大学物理系,广东广州510275;
2.贵州大学理学院,贵州贵阳550025

收稿日期:2012-12-31 出版日期:2013-03-20 发布日期:2018-11-26
通讯作者: 胡林(1953—),女,贵州贵阳人,贵州大学教授,博士生导师。E-mail:hulin53@sina.com
基金资助:
国家自然科学基金资助项目(11047022,11204045);贵州省社会发展攻关项目(黔科合SY字[2012]3089,黔科合SZ字[2011]3069);贵州省科技基金资助项目(黔科合J字[2010]2141号);贵州大学引进人才基金资助项目(贵大人基合字[2009]001号)

Study of Scaling Law in an Early-stage Tumour Growth Model

JIANG Chong-ming^1,2, LIU Yan-hui², HU Lin²

1.Department of Physics,Sun Yat-Sen University,Guangzhou Guangdong 510275,China;
2.College of Science,Guizhou University,Guiyang Guizhou 550025,China

Received:2012-12-31 Online:2013-03-20 Published:2018-11-26

摘要/Abstract

摘要： 为探究更能准确描述早期肿瘤生长的数学物理模型,探讨几种典型的模型与实际肿瘤生长的差异,以及标度律对肿瘤生长的影响,采用与实体肿瘤生长相似的、结合扩散原理的多细胞肿瘤球体模型(MTS模型)来描述早期肿瘤的生长,引入标度律对MTS模型进行修正,得到与实际数据吻合的单位体积氧气消耗速率函数,进而具体探讨了肿瘤生长中其新陈代谢速率与肿瘤尺寸的关系。结果表明:区别于前人研究肿瘤,对多细胞球体肿瘤的生长引入标度律得到的肿瘤单位体积氧消耗速率Q和半径的关系与实际较一致,说明标度律对肿瘤生长的影响明显,指出肿瘤生长到休眠态时的临界尺寸可视为是氧气消耗速率B和扩散速率I二态竞争的结果,并可由方程B=I得到。

关键词: 早期肿瘤生长, 肿瘤生长模型, MTS模型, 标度律

Abstract: To investigate a better model to describe the tumor growth and to study the effect of scaling law on the growth of tumor,several typical tumor growth models and the differences between the models and the practical tumorgrowth were analyzed in the article.A multicellular tumor spheroids (MTS) modelwhich combines the diffusion theory was used to describe the tumor growth.When thescaling law was introduced,a better oxygen consumption rate in unit volume,Qwas got obtained,and it accords with the experiments well,which means the influence of scalinglaw on the growth of tumor is obvious.The relationship between the metabolic rate and tumor size was also investigated during the tumor growth.The critical size of dormant tumor could be the result of the competition between the diffusionrate and consumption rate of oxygen,and the critical size of tumor can be calculated by the equation B=I.

Key words: early tumor growth, tumor growth model, MTS model, scaling law

中图分类号:

蒋重明, 刘艳辉, 胡林. 早期肿瘤生长模型及其标度律的研究[J]. 广西师范大学学报（自然科学版）, 2013, 31(1): 16-20.

JIANG Chong-ming, LIU Yan-hui, HU Lin. Study of Scaling Law in an Early-stage Tumour Growth Model[J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(1): 16-20.

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