Cancer results from a complex interplay of different biological, chemical, and physical phenomena that span a wide range of time and length scales. Computational modeling may help to unfold the role of multiple evolving factors that exist and interact in the tumor microenvironment. Understanding these complex multiscale interactions is a crucial step toward predicting cancer growth and in developing effective therapies. We integrate different modeling approaches in a multiscale, avascular, hybrid tumor growth model encompassing tissue, cell, and sub-cell scales. At the tissue level, we consider the dispersion of nutrients and growth factors in the tumor microenvironment, which are modeled through reaction–diffusion equations. At the cell level, we use an agent-based model (ABM) to describe normal and tumor cell dynamics, with normal cells kept in homeostasis and cancer cells differentiated into quiescent, proliferative, migratory, apoptotic, hypoxic, and necrotic states. Cell movement is driven by the balance of a variety of forces according to Newton’s second law, including those related to growth-induced stresses. Phenotypic transitions are defined by specific rule of behaviors that depend on microenvironment stimuli. We integrate in each cell/agent a branch of the epidermal growth factor receptor (EGFR) pathway. This pathway is modeled by a system of coupled nonlinear differential equations involving the mass laws of 20 molecules. The rates of change in the concentration of some key molecules trigger proliferation or migration advantage response. The bridge between cell and tissue scales is built through the reaction and source terms of the partial differential equations. Our hybrid model is built in a modular way, enabling the investigation of the role of different mechanisms at multiple scales on tumor progression. This strategy allows representing both the collective behavior due to cell assembly as well as microscopic intracellular phenomena described by signal transduction pathways. Here, we investigate the impact of some mechanisms associated with sustained proliferation on cancer progression. Speci- fically, we focus on the intracellular proliferation/migration-advantage-response driven by the EGFR pathway and on proliferation inhibition due to accumulation of growth-induced stresses. Simulations demonstrate that the model can adequately describe some complex mechanisms of tumor dynamics, including growth arrest in avascular tumors. Both the sub-cell model and growth-induced stresses give rise to heterogeneity in the tumor expansion and a rich variety of tumor behaviors.

中文翻译：

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肿瘤生长的混合三尺度模型

癌症是由跨越广泛时间和长度尺度的不同生物、化学和物理现象的复杂相互作用引起的。计算建模可能有助于揭示肿瘤微环境中存在并相互作用的多种进化因素的作用。了解这些复杂的多尺度相互作用是预测癌症生长和开发有效疗法的关键一步。我们在包含组织、细胞和亚细胞尺度的多尺度、无血管、混合肿瘤生长模型中集成了不同的建模方法。在组织水平上，我们考虑了营养物质和生长因子在肿瘤微环境中的分散，通过反应-扩散方程建模。在细胞水平，我们使用基于代理的模型 (ABM) 来描述正常和肿瘤细胞动力学，正常细胞保持稳态，癌细胞分化为静止、增殖、迁移、凋亡、缺氧和坏死状态。根据牛顿第二定律，细胞运动是由各种力的平衡驱动的，包括与生长引起的压力有关的力。表型转变由依赖于微环境刺激的特定行为规则定义。我们将表皮生长因子受体 (EGFR) 通路的一个分支整合到每个细胞/试剂中。该路径由涉及 20 个分子的质量定律的耦合非线性微分方程系统建模。一些关键分子浓度的变化率触发增殖或迁移优势反应。细胞和组织尺度之间的桥梁是通过偏微分方程的反应和源项建立的。我们的混合模型以模块化方式构建，能够研究不同机制在多个尺度上对肿瘤进展的作用。该策略允许代表由于细胞组装以及由信号转导途径描述的微观细胞内现象引起的集体行为。在这里，我们研究了一些与持续增殖相关的机制对癌症进展的影响。具体来说，我们专注于由 EGFR 途径驱动的细胞内增殖/迁移优势反应以及由于生长诱导的压力积累引起的增殖抑制。模拟表明，该模型可以充分描述肿瘤动力学的一些复杂机制，包括无血管肿瘤的生长停滞。亚细胞模型和生长诱导的压力都会导致肿瘤扩张的异质性和丰富多样的肿瘤行为。