Simulating glioblastoma progression using a novel reaction-diffusion mathematical model

Introduction 

Glioblastoma multiforme (GBM) is the most aggressive primary brain cancer. Mathematical modeling of GBM progression can be an essential tool to predict tumor growth and assist doctors in patient management and prognosis. We evaluated the feasibility and performance the novel ASU-Barrow (ASUB) model, a novel reaction-diffusion model, in a sample of patients treated at Barrow Neurological Institute. 

Methods 

MRI scans of 22 patients with GBM treated and followed at Barrow Neurological Institute were analyzed. Prior to imaging, all patients underwent surgery and chemoradiation. T1-weighted without contrast, T1-weighted with contrast, and FLAIR sequences were manually segmented into contrast-enhancing tumor, necrotic core/resection cavity, and tumor-associated edema (3D Slicer). Native brain geometry was generated automatically (MATLAB with SPM12). GBM progression was simulated between two consecutive scans using the ASUB model. Mean and maximum containment and agreement between segmented and simulated results were analyzed to select the sets of proliferation parameters that produced the best simulation results.  

Results 

A total of 72 simulations from 22 patients were conducted. Average agreement between consecutive scans geometry was 75%. For each simulation, 18 set of proliferation and diffusion parameters were chosen. For all simulations, average mean containment and agreement and average maximum containment and agreement were 0.27, 0.19, 0.52 and 0.34, respectively. Seven sets of parameters that consistently produced good results were identified and used to refine the results, increasing the average mean containment and agreement to 0.40 and 0.26.  

Conclusions 

Due to the heterogeneity of tumor behavior and response to therapy, a mathematical model that can predict tumor growth with relatively high accuracy may be beneficial for patient management and prognosis. The current ASUB model simulates recurrent GBM progression with moderate accuracy in our sample population. With further improvement, this novel method   can be potentially useful to provide possible tumor progression information for patient counseling.