A level-set approach for a multi-scale cancer invasion model

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2018-05-19 DOI:10.5206/MASE/11087
T. Carraro, S. Wetterauer, Ana Victoria Ponce Bobadilla, D. Trucu
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引用次数: 1

Abstract

The quest for a deeper understanding of the cancer growth and spread process focuses on the naturally multiscale nature of cancer invasion, which requires an appropriate multiscale modeling and analysis approach. The cross-talk between the dynamics of the cancer cell population on the tissue scale (macroscale) and the proteolytic molecular processes along the tumor border on the cell scale (microscale) plays a particularly important role within the invasion processes, leading to dramatic changes in tumor morphology and influencing the overall pattern of cancer spread. Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new  formulation of this process involving a novel derivation of the macro scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells.
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多尺度肿瘤侵袭模型的水平集方法
为了更深入地了解癌症的生长和扩散过程,重点关注癌症侵袭的自然多尺度性质,这需要适当的多尺度建模和分析方法。在组织尺度(宏观尺度)上癌细胞群体的动态与细胞尺度(微观尺度)上沿肿瘤边界的蛋白水解分子过程之间的串扰在侵袭过程中起着特别重要的作用,导致肿瘤形态的剧烈变化,影响肿瘤扩散的整体格局。基于Trucu等人提出的多尺度移动边界框架(multiscale Model)。Simul 11(1): 309-335),在这项工作中,我们提出了这个过程的新公式,涉及基于微动力学的宏观尺度边界运动规律的新推导,涉及结合水平集方法的输运方程。在基于切割单元的新型有限元宏微观框架中对这一问题进行了数值探讨。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
21 weeks
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