Frieboes Hermann B, Zheng Xiaoming, Sun Chung-Ho, Tromberg Bruce, Gatenby Robert, Cristini Vittorio
Department of Biomedical Engineering, University of California-Irvine, Irvine, CA 92697-2715, USA.
Cancer Res. 2006 Feb 1;66(3):1597-604. doi: 10.1158/0008-5472.CAN-05-3166.
The intracellular and extracellular dynamics that govern tumor growth and invasiveness in vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and growth factor concentrations are key variables. In previous work, using a reaction-diffusion mathematical model based on variables that directly describe tumor cell cycle and biology, we formulated the hypothesis that tumor morphology is determined by the competition between heterogeneous cell proliferation caused by spatial diffusion gradients, e.g., of cell nutrients, driving shape instability and invasive tumor morphologies, and stabilizing mechanical forces, e.g., cell-to-cell and cell-to-matrix adhesion. To test this hypothesis, we here obtain variable-based statistics for input to the mathematical model from in vitro human and rat glioblastoma cultures. A linear stability analysis of the model predicts that glioma spheroid morphology is marginally stable. In agreement with this prediction, for a range of variable values, unbounded growth of the tumor mass and invasion of the environment are observed in vitro. The mechanism of invasion is recursive subspheroid component development at the tumor viable rim and separation from the parent spheroid. Results of computer simulations of the mathematical model closely resemble the morphologies and spatial arrangement of tumor cells from the in vitro model. We propose that tumor morphogenesis in vivo may be a function of marginally stable environmental conditions caused by spatial variations in cell nutrients, oxygen, and growth factors, and that controlling these conditions by decreasing spatial gradients could benefit treatment outcomes, whereas current treatment, and especially antiangiogenic therapy, may trigger spatial heterogeneity (e.g., local hypoxia), thus causing invasive instability.
在体内控制肿瘤生长和侵袭性的细胞内和细胞外动力学仍知之甚少。细胞基因型和表型，以及营养物质、氧气和生长因子浓度是关键变量。在之前的工作中，我们使用基于直接描述肿瘤细胞周期和生物学的变量的反应扩散数学模型，提出了一个假设，即肿瘤形态是由空间扩散梯度（例如细胞营养物质的扩散梯度）引起的异质细胞增殖之间的竞争所决定的，这种扩散梯度驱动形状不稳定和侵袭性肿瘤形态，以及稳定的机械力，例如细胞间和细胞与基质的粘附。为了验证这一假设，我们在此从体外培养的人及大鼠胶质母细胞瘤中获取基于变量的统计数据，作为数学模型的输入。该模型的线性稳定性分析预测，胶质瘤球体形态是临界稳定的。与这一预测一致，在一系列变量值范围内，体外观察到肿瘤块的无界生长和对周围环境的侵袭。侵袭机制是在肿瘤存活边缘递归地形成子球体成分，并与母球体分离。数学模型的计算机模拟结果与体外模型中肿瘤细胞的形态和空间排列非常相似。我们提出，体内肿瘤形态发生可能是由细胞营养物质、氧气和生长因子的空间变化所导致的临界稳定环境条件的函数，并且通过降低空间梯度来控制这些条件可能有利于治疗结果，而目前的治疗方法，尤其是抗血管生成疗法，可能会引发空间异质性（例如局部缺氧），从而导致侵袭性不稳定。
