Peng Lu, Trucu Dumitru, Lin Ping, Thompson Alastair, Chaplain Mark A J
Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK.
Division of Applied and Computational Mathematics, Beijing Computational Science Research Centre, 10 Dongbeiwang West Road, Haidian District, Beijing, 100193, China.
Bull Math Biol. 2017 Mar;79(3):389-429. doi: 10.1007/s11538-016-0237-2. Epub 2017 Feb 16.
Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57-70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309-335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279-1289, 2012).
癌细胞侵袭人体组织是癌症的标志之一（Hanahan和Weinberg，《细胞》，2000年，第100卷，第57 - 70页），这是一个复杂的时空多尺度过程，它能使局部实体瘤转变为一种全身性、转移性和致命性疾病。这个过程探究并利用了实体瘤与细胞外基质（ECM）成分以及周围微环境中其他多种不同细胞类型之间建立的相互关系。通过分泌各种蛋白水解酶，如基质金属蛋白酶或尿激酶型纤溶酶原激活剂（uPA），癌细胞群体改变周围ECM成分的构型，克服物理屏障，最终实现局部癌症向周围组织扩散。组织尺度的肿瘤动力学与细胞尺度所涉及的蛋白水解酶的分子力学之间的积极相互作用，突出了侵袭的生物学多尺度特征，并带来了用适当的多尺度方法对这一过程进行建模的挑战。在本文中，我们提出了一种新的癌症侵袭双尺度移动边界模型，该模型结合尿激酶型纤溶酶原激活系统的分子动力学来探究组织尺度的肿瘤动力学。基于Trucu等人（《多尺度模型与模拟》，2013年，第11卷第1期，第309 - 335页）提出的多尺度移动边界方法，我们在此提出的建模方法使我们能够研究由肿瘤侵袭边缘处发生的细胞尺度uPA微观动力学所引起的组织尺度肿瘤形态变化。我们的计算模拟结果展示了一系列异质动力学，这些动力学在性质上与在许多不同类型癌症中观察到的侵袭性生长模式相似，例如Ito等人（《胃肠病学杂志》，2012年，第47卷，第1279 - 1289页）所讨论的肿瘤浸润性生长模式。
