We analyze the wave speed of the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model that was previously created and applied to simulate the growth and spread of glioblastoma (GBM), a particularly aggressive primary brain tumor. We extend the PIHNA model by allowing for different hypoxic and normoxic cell migration rates and study the impact of these differences on the wave-speed dynamics. Through this analysis, we find key variables that drive the outward growth of the simulated GBM. We find a minimum tumor wave-speed for the model; this depends on the migration and proliferation rates of the normoxic cells and is achieved under certain conditions on the migration rates of the normoxic and hypoxic cells. If the hypoxic cell migration rate is greater than the normoxic cell migration rate above a threshold, the wave speed increases above the predicted minimum. This increase in wave speed is explored through an eigenvalue and eigenvector analysis of the linearized PIHNA model, which yields an expression for this threshold. The PIHNA model suggests that an inherently faster-diffusing hypoxic cell population can drive the outward growth of a GBM as a whole, and that this effect is more prominent for faster-proliferating tumors that recover relatively slowly from a hypoxic phenotype. The findings presented here act as a first step in enabling patient-specific calibration of the PIHNA model.

中文翻译：

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由于增强的缺氧诱导迁移导致胶质母细胞瘤生长速率的速度切换

我们分析了增殖侵袭缺氧坏死血管生成 (PIHNA) 模型的波速，该模型之前创建并应用于模拟胶质母细胞瘤 (GBM)（一种特别具有侵袭性的原发性脑肿瘤）的生长和扩散。我们通过允许不同的缺氧和常氧细胞迁移率来扩展 PIHNA 模型，并研究这些差异对波速动力学的影响。通过这种分析，我们找到了驱动模拟 GBM 向外增长的关键变量。我们找到模型的最小肿瘤波速；这取决于常氧细胞的迁移和增殖速度，并且在一定条件下通过常氧细胞和缺氧细胞的迁移速度实现。如果缺氧细胞迁移率大于阈值以上的常氧细胞迁移率，波速增加到预测的最小值以上。这种波速的增加是通过线性化 PIHNA 模型的特征值和特征向量分析来探索的，它产生了这个阈值的表达式。PIHNA 模型表明，固有的扩散速度较快的缺氧细胞群可以推动 GBM 整体向外生长，并且这种效应对于从缺氧表型中恢复相对较慢的快速增殖肿瘤更为突出。此处介绍的研究结果是实现 PIHNA 模型特定于患者的校准的第一步。PIHNA 模型表明，固有的扩散速度较快的缺氧细胞群可以推动 GBM 整体向外生长，并且这种效应对于从缺氧表型中恢复相对较慢的快速增殖肿瘤更为突出。此处介绍的研究结果是实现 PIHNA 模型特定于患者的校准的第一步。PIHNA 模型表明，固有的扩散速度较快的缺氧细胞群可以推动 GBM 整体向外生长，并且这种效应对于从缺氧表型中恢复相对较慢的快速增殖肿瘤更为突出。此处介绍的研究结果是实现 PIHNA 模型特定于患者的校准的第一步。