MODELING THE GROWTH OF SOLID TUMORS AND INCORPORATING A METHOD FOR THEIR CLASSIFICATION USING NONLINEAR ELASTICITY THEORY
MODELING THE GROWTH OF SOLID TUMORS AND INCORPORATING A METHOD FOR THEIR CLASSIFICATION USING NONLINEAR ELASTICITY THEORY
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DOI：
10.1007/bf00173886
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发表时间：
1993-05-01
影响因子：
1.9
通讯作者：
SLEEMAN, BD
中科院分区：
文献类型：
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作者：
CHAPLAIN, MAJ;SLEEMAN, BD
在医学上，肿瘤分为两个重要的类别-良性和恶性。一般来说，这两类在增长速度和方式以及随后可能的扩散方面表现出不同的行为。在本文中，我们制定了一个新的方法来肿瘤生长的结果和技术，从非线性弹性理论。本文用膜厚壳理论建立了一个实体肿瘤生长的数学模型。该模型的一个中心特征是通过使用应变-能量函数来表征模型的材料组成，从而允许在模型中明确地对肿瘤的分化程度进行数学描述。条件是在应变能函数的过程中发生的肿瘤的侵袭和转移，被解释为分叉模式的球壳的肿瘤基本上是仿照。我们的结果与实际的实验结果和良性和恶性肿瘤所示的一般行为进行了比较。最后，我们将这些结果与肿瘤表面形态发生的各个方面（特别是实体肿瘤表面的高斯和平均曲率）结合起来，试图产生分期和分级的重要医学过程的数学公式和描述癌症。我们希望，这一办法可以成为实际应用的基础。
Medically, tumours are classified into two important classes - benign and malignant. Generally speaking, the two classes display different behaviour with regard to their rate and manner of growth and subsequent possible spread. In this paper, we formulate a new approach to tumour growth using results and techniques from nonlinear elasticity theory. A mathematical model is given for the growth of a solid tumour using membrane and thick-shell theory. A central feature of the model is the characterisation of the material composition of the model through the use of a strain-energy function, thus permitting a mathematical description of the degree of differentiation of the tumour explicitly in the model. Conditions are given in terms of the strain-energy function for the processes of invasion and metastasis occurring in a tumour, being interpreted as the bifurcation modes of the spherical shell which the tumour is essentially modelled as. Our results are compared with actual experimental results and with the general behaviour shown by benign and malignant tumours. Finally, we use these results in conjunction with aspects of surface morphogenesis of tumours (in particular, the Gaussian and mean curvatures of the surface of a solid tumour) in an attempt to produce a mathematical formulation and description of the important medical processes of staging and grading cancers. We hope that this approach may form the basis of a practical application.