In this paper, we have developed a multi-scale, lattice-free, agent based model of avascular tumour growth in epithelial tissue. The model integrates different events to identify the underlying diversity within intracellular, cellular, and extracellular layer dynamics. The model considers every cell as an agent. A cellular agent may proliferate, spawns two identical daughter agents, or it may be transformed into other phenotypes during its life time depending on its internal proteins′ activity as well as its external microenvironment. In this context, a simplified age-structured cell cycle model is adopted from the existing literature. The model considers that the intracellular events are regulated by p27 gene expression. In this model, p27 protein controls the overall tumour growth dynamics. Moreover, p27 is controlled by the external oxygen and nutrients that are modelled with the reaction-diffusion equations. The model also considers several biophysical forces which directly effect on the tumour growth dynamics.

This modelling framework offers biologically realistic outcomes and also covers important criteria of the hallmarks of cancer which include oxygen and nutrient consumptions, micro-environmental heterogeneity, tumour cell proliferation by avoiding growth suppressor signals, replication of tumour cells at an abnormally faster rate, and resistance of apoptosis. The avascular tumour growth model is validated with immunohistochemistry and histopathology data. The outcome of the proposed model is very close to the range of the patient data, which concludes that the model is capable enough to mimic these complex biophysical phenomena.

在本文中，我们开发了一种多尺度、无格子、基于代理的上皮组织中无血管肿瘤生长模型。该模型整合了不同的事件，以识别细胞内、细胞和细胞外层动力学中的潜在多样性。该模型将每个单元格视为一个代理。细胞因子可能会增殖，产生两个相同的子代因子，或者在其生命周期内根据其内部蛋白质的活性和外部微环境转化为其他表型。在这种情况下，从现有文献中采用了简化的年龄结构细胞周期模型。该模型认为细胞内事件受 p27 基因表达的调控。在这个模型中，p27 蛋白控制着整体的肿瘤生长动态。而且，p27 受外部氧气和营养物质的控制，这些氧气和营养物质以反应扩散方程为模型。该模型还考虑了直接影响肿瘤生长动力学的几种生物物理力。

该建模框架提供了生物学上现实的结果，还涵盖了癌症标志的重要标准，包括氧气和营养消耗、微环境异质性、通过避免生长抑制信号的肿瘤细胞增殖、肿瘤细胞以异常更快的速度复制和抵抗的凋亡。无血管肿瘤生长模型通过免疫组织化学和组织病理学数据进行验证。所提出模型的结果非常接近患者数据的范围，由此得出结论，该模型足以模拟这些复杂的生物物理现象。