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Predictions of tumour morphological stability and evaluation against experimental observations

机译:肿瘤形态稳定性的预测和对实验观察的评价

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摘要

The hallmark of malignant tumours is their spread into neighbouring tissue and metastasis to distant organs, which can lead to life threatening consequences. One of the defining characteristics of aggressive tumours is an unstable morphology, including the formation of invasive fingers and protrusions observed both in vitro and in vivo. In spite of extensive biological, clinical and modelling study and research at physical scales ranging from the molecular to the tissue, the driving dynamics of tumour invasiveness are not completely understood, partly because it is challenging to observe and study cancer as a multi-scale system. Mathematical modelling has been applied to provide further insights into these complex invasive and metastatic behaviours. Modelling a solid tumour as an incompressible fluid, we consider three possible constitutive relations to describe tumour growth, namely Darcy's law, Stokes' law and the combined Darcy–Stokes law. We study the tumour morphological stability described by each model and evaluate the consistency between theoretical model predictions and experimental data from in vitro three-dimensional multicellular tumour spheroids. The analysis reveals that the Stokes model is the most consistent with the experimental observations, and that it predicts our experimental tumour growth is marginally stable. We further show that it is feasible to extract parameter values from a limited set of data and create a self-consistent modelling framework that can be extended to the multi-scale study of cancer.
机译:恶性肿瘤的标志是它们扩散到邻近组织并转移到远处的器官,这可能导致生命危险。侵袭性肿瘤的定义特征之一是形态不稳定,包括在体内和体外均观察到侵袭性手指的形成和突起。尽管在从分子到组织的物理规模上进行了广泛的生物学,临床和模型研究,但肿瘤浸润的驱动动力学尚未完全理解,部分原因是作为多尺度系统观察和研究癌症具有挑战性。已应用数学建模来提供对这些复杂的侵入性和转移性行为的进一步了解。将实体肿瘤建模为不可压缩的流体,我们考虑了三种可能的本构关系来描述肿瘤的生长,即达西定律,斯托克斯定律和达西-斯托克斯组合定律。我们研究每个模型描述的肿瘤形态稳定性,并评估理论模型预测与来自体外三维多细胞肿瘤球体的实验数据之间的一致性。分析表明,斯托克斯模型与实验观察结果最为吻合,并预测我们的实验性肿瘤生长在一定程度上是稳定的。我们进一步表明,从有限的数据集中提取参数值并创建一个自洽的建模框架是可行的,该框架可扩展到癌症的多尺度研究。

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