Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic.To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate () represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (kp) deals with cell line specific factors to promote growth. The KH,KN describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models.Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of and lower kp, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate () and vary greatly in kp, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth.However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.异种移植瘤（Xenografts）作为简化的癌症动物模型，与临床肿瘤相比在脉管系统与间质结构上存在显著差异，这使得基于数学模型开展临床结局预测的工作颇具挑战性。本研究旨在进一步阐明动物模型与临床病例在肿瘤进展及生理学特征层面的差异。 为达成这一目标，我们提出了一款基于肿瘤病理生理学的数学模型，其中以作为内分泌递送替代标志物的氧气为核心研究重点。该氧驱动模型（Oxygen-Driven Model, ODM）借助氧气扩散方程，对肿瘤生长、缺氧及坏死进程进行描述。该模型涵盖两项关键生理参数：其一为表观氧摄取率（Apparent Oxygen Uptake Rate），该参数反映了细胞增殖所需的表观氧消耗量；细胞所需表观氧量越高，氧运输过程的变异程度也就越高，其数值差异来源于脉管系统、间质结构及肿瘤形态学特征。其二为增殖速率（Proliferating Rate, kp），该参数与细胞系特异性生长促进因子相关。KH、KN则用于表征缺氧与坏死的转化过程。 在回顾性分析存档数据的过程中，我们纳入了38株异种移植细胞系及5株患者来源类异种移植模型的纵向肿瘤体积数据集。通过对参数空间的探索，我们可将参数划分为两组：第一组细胞系的表观氧摄取率分布范围较广且kp值较低，提示此类肿瘤灌注较差且生长缓慢；第二组细胞系的表观氧摄取率数值较为集中，而kp值差异显著，我们据此认为此类肿瘤的氧运输水平相近，但肿瘤内在生长异质性更高。 不过，当在类外植体动物模型中进行验证时，该模型存在一定局限性——这类模型复杂的肿瘤-间质形态特征无法在当前版本的模型中得到体现。将间质结构纳入氧驱动模型后，将有助于解释这些差异，我们已提供了相关示例。该模型简洁且通用性强，适用于临床前实验设计，可在保证预测可靠性的前提下进行修改与优化。