Abstract
The Proliferation-Invasion (PI) tumor mathematical model provides a rubric to estimate glioblastoma (GBM) growth in terms of patient-specific net proliferation and net invasion rates. The apparent diffusion coefficient (ADC), calculated from diffusion-weighted magnetic resonance imaging (MRI), is believed to be predictive of tumor cellularity and microstructure. Our goal was to investigate how well the PI model-derived invasiveness index (D/ρ) compares to the distribution of ADC values within the tumor. T1Gd and FLAIR images were segmented for twelve patients with contrast-enhancing GBMs. A FLAIR penumbra region of interest (ROI) was created by subtracting the T1Gd and FLAIR ROIs. These ROI’s were then used to mask the co-registered ADC maps. The resulting ADC histogram from the FLAIR ROI was fit using a bimodal Gaussian model. We calculated the percent of ADC voxels classified as being below each peak, within the lower or upper peak, within both peaks, or above the peaks. The PI model relates tumor cell density to tumor cell dispersal (D) and proliferation (ρ) and is parameterized with the T1Gd and FLAIR ROIs. Higher D/ρ tumors are considered more invasive than lower D/ρ tumors. D/ρ was negatively correlated with percent of voxels below the lower peak for both T1Gd and FLAIR ROIs (p<0.001 and p=0.004, respectively) and positively correlated the percent of voxels above the upper peak percent for the T1Gd ROI (p=0.002). Consistent with low D/ρ representing highly cellular (less diffuse) tumors, we observed an increased presence of low ADC, and thus high cellularity, regions within low D/ρ tumors. Analogously, for tumors with a more diffuse phenotype (high D/ρ), we observed an increased presence of high ADC (low cellularity) regions within the tumor. Understanding the relationship between D/ρ and ADC allows us to connect observations on multiparametric imaging and elucidate the tumor biology.
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