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

TL;DR

The paper tackles fast, patient-specific prediction of glioblastoma evolution from MRI data by solving the Fisher–Kolmogorov diffusion–reaction equation with logistic growth on a head-geometry mesh. It combines finite-difference spatial discretization with unconditionally stable exponential time integrators, introducing a fast algorithm to compute the action of the exponential operator via an extended matrix $\mathbf{B}$. In 2D and 3D brain tests on a laptop, the exponential integrator approach achieves up to two orders of magnitude speedups over Crank–Nicolson and outperforms existing exponential-integrator libraries, enabling 100 steps on a $128^3$ grid in under 10 minutes. The results support on-the-fly tumor evolution predictions and pave the way for extensions to drug delivery and data assimilation on high-resolution brain data, with potential impact on real-time clinical decision support. $\hat{D}=p_w D_w + p_g D_g$ and the traveling-wave speed $2\sqrt{\hat{D}\rho}$ provide a link between tissue composition and invasion dynamics.

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.

Figures (10)

• Figure 1: MRI scans of the head of Maciej Paszyński.
• Figure 2: The map of the white and gray matter, cerebral fluid, and the air, on the axial cross-section.
• Figure 3: Comparison of tumor growth starting in two different brain locations. Snapshots illustrate different growth rates in white and gray matter.
• Figure 4: Comparison of tumor growth starting in two different brain locations. Snapshots illustrate different growth rates in white and gray matter.
• Figure 5: White and gray matters in the sagittal and coronal view at the cross-sections of the MRI scan data.