We present an ultra-fast simulator to augment the MRI scan imaging of glioblastoma brain tumors with predictions of future evolution. We consider the glioblastoma tumor growth model based on the Fisher-Kolmogorov diffusion-reaction equation with logistic growth. For the discretization we employ finite differences in space coupled with a time integrator in time employing the routines from [Al-Mohy, et. al. Computing the action of the matrix exponential, with an application to exponential integrators, SIAM Journal on Scientific Computing, 2011] to compute the actions of the exponentials of the linear operator. By combining these methods, we can perform the prediction of the tumor evolution for several months forward within a couple of seconds on a modern laptop. This method does not require HPC supercomputing centers, and it can be performed on the fly using a laptop with Windows 10, Octave simulations, and ParaView visualization. We illustrate our simulations by predicting the tumor growth evolution based on three-dimensional MRI scan data.

翻译：我们提出了一种超快速模拟器，用于通过预测未来演化来增强胶质母细胞瘤的MRI扫描成像。我们考虑基于Fisher-Kolmogorov扩散-反应方程与逻辑增长模型的胶质母细胞瘤生长模型。在离散化方面，我们采用空间有限差分法，并结合使用[Al-Mohy等,《计算矩阵指数作用及其在指数积分器中的应用》, SIAM Journal on Scientific Computing, 2011]中的程序进行时间积分，以计算线性算子指数的作用。通过结合这些方法，我们可在现代笔记本电脑上于数秒内完成对肿瘤未来数月演化的预测。该方法无需高性能计算（HPC）超级计算中心支持，可在配备Windows 10系统、Octave仿真及ParaView可视化工具的便携式计算机上实时执行。我们基于三维MRI扫描数据对肿瘤生长演化进行预测，并以此展示模拟结果。