曲折肿瘤血管的形态弹性模型
Morpho-elastic model of the tortuous tumour vessels
摘要：
实体瘤有能力组装自己的血管网络，以优化其对重要营养物质的获取。这些新的毛细血管在形态上不同于正常的生理血管。特别是，它们具有高得多的空间弯曲度，迫使肿瘤周围区域内的血流受损。这是有效递送抗肿瘤药物的主要障碍。这项工作提出了一个形态弹性模型的肿瘤血管。肿瘤毛细血管被认为是一个不断增长的超弹性管，在空间上受到线性弹性环境的约束，代表了间质。我们假设毛细管是一种不可压缩的neo-Hookean材料，其增长模型使用乘法分解的变形梯度。我们研究的毛细管的形态稳定性的方法的增量变形叠加在有限应变，解决相应的增量问题，使用Stroh公式和阻抗矩阵法。不相容的直毛细管的轴向生长被发现控制的曲折形状的分叉的发病。后屈曲形态研究使用混合有限元制定在完全非线性制度。所提出的模型突出了毛细管和周围介质的几何和弹性特性如何同时触发直毛细管的边缘稳定性的损失及其空间曲折度的非线性发展。
英文摘要：
Solid tumours have the ability to assemble their own vascular network for optimizing their access to the vital nutrients. These new capillaries are morphologically different from normal physiological vessels. In particular, they have a much higher spatial tortuosity forcing an impaired flow within the peritumoral area. This is a major obstacle for the efficient delivery of antitumoral drugs. This work proposes a morpho-elastic model of the tumour vessels. A tumour capillary is considered as a growing hyperelastic tube that is spatially constrained by a linear elastic environment, representing the interstitial matter. We assume that the capillary is an incompressible neo-Hookean material, whose growth is modeled using a multiplicative decomposition of the deformation gradient. We study the morphological stability of the capillary by means of the method of incremental deformations superposed on finite strains, solving the corresponding incremental problem using the Stroh formulation and the impedance matrix method. The incompatible axial growth of the straight capillary is found to control the onset of a bifurcation towards a tortuous shape. The post-buckling morphology is studied using a mixed finite element formulation in the fully nonlinear regime. The proposed model highlights how the geometrical and the elastic properties of the capillary and the surrounding medium concur to trigger the loss of marginal stability of the straight capillary and the nonlinear development of its spatial tortuosity.
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