Self-influenced growth through evolving material inhomogeneities
Self-influenced growth through evolving material inhomogeneities
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DOI：
10.1016/j.ijnonlinmec.2018.08.003
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发表时间：
2018-11-01
影响因子：
3.2
通讯作者：
Grillo, Alfio
中科院分区：
文献类型：
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作者：
Di Stefano, Salvatore;Ramirez-Torres, Ariel;Grillo, Alfio
我们重新制定了无血管肿瘤生长的模型，其中肿瘤组织作为一个双相介质进行研究，具有间质液和固相。生长的描述依赖于两个基本特征：其中之一是由相的组分之间的质量传递给出，这是通过源和汇项考虑的;另一个是固相的变形梯度张量的乘法分解，引入了生长张量，它代表了生长引起的肿瘤结构变化。一般来说，这样的张量是不可积的，并且它可以允许定义具有非平凡曲率的列维-奇维塔联络。此外，它的演变与固相的质量源和质量汇通过一个演变方程联系起来。我们的目标是研究生长张量的不均匀性如何影响生长。为此，我们研究了后者的演变，由两个不同的模型预测。在第一个中，生长张量对肿瘤的物质点的依赖性在演化方程中没有明确考虑。相反，在第二个模型中，生长张量的不均匀性通过将与之相关的曲率引入演化方程来明确解决。我们进行数值模拟，比较这两种模型产生的结果，并评估可能的作用的材料不均匀性的增长。
We reformulate a model of avascular tumour growth in which the tumour tissue is studied as a biphasic medium featuring an interstitial fluid and a solid phase. The description of growth relies on two fundamental features: one of those is given by the mass transfer among the constituents of the phases, which is taken into account through source and sink terms; the other one is the multiplicative decomposition of the deformation gradient tensor of the solid phase, with the introduction of a growth tensor, which represents the growth-induced structural changes of the tumour. In general, such tensor is non-integrable, and it may allow to define a Levi-Civita connection with non-trivial curvature. Moreover, its evolution is related to the source and sink of mass of the solid phase through an evolution equation. Our goal is to study how growth can be influenced by the inhomogeneity of the growth tensor. To this end, we study the evolution of the latter, as predicted by two different models. In the first one, the dependence of the growth tensor on the tumour's material points is not explicitly considered in the evolution equation. In the second model, instead, the inhomogeneity of the growth tensor is resolved explicitly by introducing the curvature associated with it into the evolution equation. We perform numerical simulations to compare the results produced by these two models, and evaluate a possible role of the material inhomogeneities on growth.