Testing the feasibility of estimating the migration to proliferation rate ratio in glioblastoma from single time-point MRI data

RafaelBravo

University of Texas at Austin

"Testing the feasibility of estimating the migration to proliferation rate ratio in glioblastoma from single time-point MRI data"

Introduction: Glioblastoma tumors with a high migration to proliferation ratio (D/k ratio) are more drug resistant, suggesting 1) that estimating D/k ratios can help predict patient responses, and 2) investigating the cellular mechanisms behind D/k ratios can help understand the mechanisms of drug resistance. Here we quantify the identifiability of D/k ratios using synthetic tumor data. Materials and Methods: We used the standard reaction-diffusion model (i.e. logistic growth and diffusion) initialized with a single cell. Using this model, we grew synthetic tumors, saving the density field for calibration once the tumor had filled 10% of the domain. We fixed proliferation (k, 1/day) and used grid search followed by Levenberg-Marquardt optimization to calibrate the diffusion rate (D, mm2/day) and growth time (t, days) that produced density distributions matching the synthetic data as closely as possible. We quantified the ability of the algorithm to accurately and precisely identify D/k ratios in both the presence and absence of Gaussian noise. Results: Our algorithm finds D/k ratios with very high accuracy: 0.95 +/- 0.72% difference from correct D/k with k fixed at 0.01/day. We found that with 5% noise added the ability to accurately recover D/k ratios improved as its magnitude increased: 9.6 +/- 13.38% when D/k = 10-2 mm2 versus 2.7 +/- 3.65% when D/k = 1 mm2 Future Directions: Ongoing work will establish the minimal data requirements to accurately estimate D/k ratios within 10% of the correct values, and then apply the technique to the brain tumor image segmentation (BRATS) dataset. All BRATS patients have a single segmented pre-treatment MRI (N = 103) which we will use to estimate their D/k ratios. A subset of the BRATS patients also has RNA microarray data available (N = 91). We plan to correlate the patients’ D/k ratios with gene set scores derived from their microarray data to identify cellular mechanisms that potentially underly the D/k ratios.
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