肿瘤侵袭性生长的多尺度数学模型
A multiscale mathematical model of tumour invasive growth
摘要：
作为癌症的标志之一[30]，癌细胞侵入人体组织是一个复杂的时空多尺度过程，使局部实体瘤转变为全身性、转移性和致命性疾病。该过程探索并利用实体瘤与细胞外基质（ECM）组分和来自周围微环境的其他多种不同细胞类型建立的相互关系。通过分泌各种蛋白水解酶如基质金属蛋白酶（MMP）或尿激酶纤溶酶原激活物（uPA），癌细胞群改变周围ECM组合物的构型并克服物理屏障以最终实现局部癌症扩散到周围组织中。在细胞尺度上，组织尺度肿瘤动力学和蛋白水解酶分子力学之间的积极相互作用强调了生物学上的多尺度入侵特征，并提出了用适当的多尺度方法模拟这一过程的挑战。在本文中，我们提出了一个新的两个规模的移动边界模型的癌症侵袭，探讨组织规模的肿瘤动力学结合尿激酶纤溶酶原激活系统的分子动力学。在[58]中提出的多尺度移动边界方法的基础上，我们在这里提出的建模使我们能够研究由沿着肿瘤侵袭边缘发生的细胞尺度uPA微动力学引起的组织尺度肿瘤形态的变化。我们的计算模拟结果证明了一系列异质动力学，这些动力学在性质上类似于在许多不同类型的癌症中观察到的侵袭性生长模式，例如[33]中讨论的肿瘤浸润性生长模式。
英文摘要：
Known as one of the hallmarks of cancer [30], 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 (MMP) 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 [58], the modelling that we propose here allows us to study the changes in tissue scale tumour morphology caused by the cell-scale uPA micro-dynamics 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 [33].
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