Augmenting MRI scan data with real-time predictions of glioblastoma brain tumor evolution using faster exponential time integrators

Abstract

We present a MATLAB code for exponential integrators method simulating the glioblastoma tumor growth. It employs the Fisher-Kolmogorov diffusion-reaction tumor brain model with logistic growth. The input is the MRI scans of the human head and the initial tumor location. The simulation uses the finite difference formulation in space and the ultra-fast exponential integrators method in time. The output from the code is the input data for ParaView visualization. While there are many brain tumor simulation codes, our method's novelty lies in its implementation using exponential integrators. We propose a new algorithm for the fast computation of exponential integrators. Regarding execution time on a laptop with Win10, using MATLAB, with 11th Gen Intel(R) Core(TM) i5-11500H, 2.92 GHz, and 32 GB of RAM, the algorithm outperforms the state-of-the-art routines from [A. Al-Mohy, N. Higham, Computing the action of the matrix exponential, with an application to exponential integrators. SIAM Journal On Scientific Computing (33) 488-511 (2011)]. We also compare our method with an implicit, unconditionally stable Crank-Nicolson time integration scheme based on the finite difference method. We show that our method is two orders of magnitude faster than the Crank-Nicolson method with finite difference discretization in space on a laptop equipped with MATLAB. The brain tumor two-year future prediction using 128x128x128 computational grid and 100-time steps, built over the MRI scans of the human head, takes less than 10 minutes on the laptop.