Mathematical models of cancer growth have become increasingly more accurate both in the space and time domains. However, the limited amount of data typically available has resulted in a larger number of qualitative rather than quantitative studies. In the present study, we provide an integrated experimental-computational framework for the quantification of the morphological characteristics and the mechanistic modelling of cancer progression in 3D environments. The proposed framework allows for the calibration of multiscale, spatiotemporal models of cancer growth using state-of-the-art 3D cell culture data, and their validation based on the resulting experimental morphological patterns using spatial point-pattern analysis techniques. We applied this framework to the study of the development of Triple Negative Breast Cancer cells cultured in Matrigel scaffolds, and validated the hypothesis of chemotactic migration using a multiscale, hybrid Keller-Segel model. The results revealed transient, non-random spatial distributions of cancer cells that consist of clustered, and dispersion patterns. The proposed model was able to describe the general characteristics of the experimental observations and suggests that cancer cells exhibited chemotactic migration and accumulation, as well as random motion during the examined time period of development. The developed framework enabled us to pursue two goals; first, the quantitative description of the morphology of cancer growth in 3D cultures using point-pattern analysis, and second, the relation of tumour morphology with underlying biophysical mechanisms that govern cancer growth and migration.

中文翻译：

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量化 3D 体外环境中癌症进展的形态学和机制：整合实验和多尺度模型

癌症生长的数学模型在空间和时间域都变得越来越准确。然而，通常可获得的有限数据量导致了大量的定性研究而不是定量研究。在本研究中，我们提供了一个集成的实验计算框架，用于量化 3D 环境中的形态特征和癌症进展的机制建模。所提出的框架允许使用最先进的 3D 细胞培养数据校准癌症生长的多尺度时空模型，并使用空间点模式分析技术基于所得的实验形态模式对其进行验证。我们将此框架应用于在 Matrigel 支架中培养的三阴性乳腺癌细胞的发育研究，并使用多尺度混合 Keller-Segel 模型验证了趋化迁移的假设。结果揭示了由聚集和分散模式组成的癌细胞的瞬时、非随机空间分布。所提出的模型能够描述实验观察的一般特征，并表明癌细胞在检查的发育时期表现出趋化性迁移和积累，以及随机运动。开发的框架使我们能够实现两个目标；首先，使用点模式分析对 3D 培养中癌症生长的形态进行定量描述，其次，