Estimating subthreshold tumor on MRI using a 3D-DTI growth model for GBM: An adjunct to radiation therapy planning

Mathematical modeling and serial magnetic resonance imaging (MRI) used to calculate patient-specific rates of tumor diffusion, D, and proliferation, ρ, can be combined to simulate glioblastoma multiforme (GBM) growth. We showed that the proportion and distribution of tumor cells below the MRI threshold are determined by the D/ρ ratio of the tumor. As most radiation fields incorporate a 1‑3 cm margin to account for subthreshold tumor, accurate characterization of subthreshold tumor aids the design of optimal radiation fields. This study compared two models: a standard one‑dimensional (1D) isotropic model and a three‑dimensional (3D) anisotropic model using the advanced imaging method of diffusion tensor imaging (DTI) ‑ with regards to the D/ρ ratio's effect on the proportion and spatial extent of the subthreshold tumor. A validated reaction‑diffusion equation accounting for tumor diffusion and proliferation modeled tumor concentration in time and space. For the isotropic and anisotropic models, nine tumors with different D/ρ ratios were grown to a T1 radius of 1.5 cm. For each tumor, the percent and extent of tumor cells beyond the T2 radius were calculated. For both models, higher D/ρ ratios were correlated with a greater proportion and extent of subthreshold tumor. Anisotropic modeling demonstrated a higher proportion and extent of subthreshold tumor than predicted by the isotropic modeling. Because the quantity and distribution of subthreshold tumor depended on the D/ρ ratio, this ratio should influence radiation field demarcation. Furthermore, the use of DTI data to account for anisotropic tumor growth allows for more refined characterization of the subthreshold tumor based on the patient-specific D/ρ ratio.