School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA.
Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, 27695, USA.
Sci Rep. 2017 May 31;7(1):2508. doi: 10.1038/s41598-017-02462-0.
Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm to 62 mm, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.
5 只免疫功能正常的 C57BL/6-cBrd/cBrd/Cr（白化 C57BL/6）小鼠被注射了 GL261-luc2 细胞，这是一种具有人类多形性胶质母细胞瘤（GBM）特征的细胞系。这些小鼠在五个不同的时间点使用磁共振（MR）成像，以描述肿瘤的生长和发育。25 天后，尽管小鼠是从同一肿瘤细胞系在精心控制的条件下接种的，但最终肿瘤体积从 12mm 到 62mm 不等。我们提出了一些假设来探索最终肿瘤大小的巨大差异，并使用我们的简单反应扩散模型在三维（3D）有限差分法和二维（2D）水平集法中对其进行了测试。通过最佳拟合程序获得的参数旨在使模拟肿瘤尽可能接近观察到的肿瘤，在详细分析的 3 只小鼠之间变化了一个数量级。这些差异可能反映了肿瘤生长的形态和生物学变异性，以及数学模型的误差，可能是由于肿瘤动力学的过度简化或参数的不可识别性。我们的结果生成了与其他体外和体内实验测量相匹配的参数。此外，我们还计算了波速，与其他大鼠和人类的测量结果相匹配。
