MATHEMATICAL MODELLING OF AVASCULAR TUMOUR GROWTH BASED ON DIFFUSION OF NUTRIENTS AND ITS VALIDATION
MATHEMATICAL MODELLING OF AVASCULAR TUMOUR GROWTH BASED ON DIFFUSION OF NUTRIENTS AND ITS VALIDATION
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DOI：
10.1002/cjce.20204
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发表时间：
2009-10-01
影响因子：
2.1
通讯作者：
Lakshminarayanan, S.
中科院分区：
文献类型：
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作者：
Kiran, Kanchi Lakshmi;Jayachandran, Devaraj;Lakshminarayanan, S.
本文考虑了无血管肿瘤生长过程中的生理变化，建立了一个以营养物质扩散为基础的数学模型。无血管肿瘤生长涉及三个不同区域的形成，即增殖区、静止区和坏死区。无血管性肿瘤生长所依赖的主要过程是：（i）营养物质从邻近组织通过肿瘤扩散，（ii）肿瘤中细胞对营养物质的消耗速率，以及（iii）细胞凋亡和坏死导致的细胞死亡。在该模型中，我们认为肿瘤是球形的，负责其生长的主要营养物质是氧气和葡萄糖。通过使用开发的模型求解浓度分布，我们能够计算静止区和坏死区以及肿瘤的半径。所提出的模型也验证了使用体外肿瘤生长数据和Gompertzian经验关系参数在文献中。我们的模型也是成功的捕获饱和体积的无血管肿瘤不同的营养浓度在道岔表面。
In this paper, a mathematical model based on the diffusion of nutrients is developed by considering the physiological changes accompanying the growth of avascular tumour. Avascular tumour growth involves the formation of three different zones namely proliferation, quiescent and necrotic zones. The main processes on which avascular tumour growth depends are: (i) diffusion of nutrients through the tumour from the contiguous tissues, (ii) consumption rate of the nutrients by the cells in the tumour, and (iii) cell death by apoptosis and necrosis. In the model, we consider the tumour to be spherical and the principal nutrients responsible for its growth are oxygen and glucose. By solving for the concentration profiles using the model developed, we are able to compute the radii of the quiescent and necrotic zones as well as that of the tumour. The proposed model is also validated using in vitro tumour growth data and Gompertzian empirical relationship parameters available in the literature. Our model is also successful in capturing the saturated volume of the avascular tumour for different nutrient concentrations at the turnout surface.