Response classification based on a minimal model of glioblastoma growth is prognostic for clinical outcomes and distinguishes progression from pseudoprogression

Abstract

Glioblastoma multiforme is the most aggressive type of primary brain tumor. Glioblastoma growth dynamics vary widely across patients, making it difficult to accurately gauge their response to treatment. We developed a model-based metric of therapy response called Days Gained that accounts for this heterogeneity. Here, we show in 63 newly diagnosed patients with glioblastoma that Days Gained scores from a simple glioblastoma growth model computed at the time of the first postradiotherapy MRI scan are prognostic for time to tumor recurrence and overall patient survival. After radiation treatment, Days Gained also distinguished patients with pseudoprogression from those with true progression. Because Days Gained scores can be easily computed with routinely available clinical imaging devices, this model offers immediate potential to be used in ongoing prospective studies.

Figure 1

Computing the Days Gained metric of response with models of varying complexity. We use patient-specific simulations of untreated tumor growth to estimate tumor burden on T1Gd MRI imaging at post-treatment time points. 4D-anatomical, 4D-spherical and Linear models simulate GBM growth with decreasing levels of computational complexity. Days Gained scores can be computed from each of the three model types using the simulated T1Gd spherically equivalent radius curve. Top series shows model solutions from a 4D-anatomical UVC for a 53 year-old patient with a left temporal lobe GBM. Bottom plot illustrates concept of Days Gained score as previously published (8).

Figure 2

Linear regression (A, C, E) and Bland-Altman (B, D, F) analyses comparing Days Gained scores computed using the 4D-anatomical, 4D-spherical and Linear model implementations. R² values in A, C and E are the coefficients of determination computed from linear regression analysis; the solid line is the linear regression best fit and the dotted line is unity. Bland-Altman bias, upper limit of agreement (ULA) and lower limit of agreement (LLA) are indicated by dashed lines in B, D and F.

Figure 3

Kaplan-Meier analyses comparing the PFS and OS of patients classified according to Days Gained score. Scores from the minimal “Linear” model discriminated outcomes with a level of significance similar to the other, more detailed, model implementations. Statistics for these analyses are shown in Table 2.

Figure 4

p-values from iterative Kaplan-Meier analyses on PFS and OS. White boxes in the figure correspond to Days Gained thresholds that revealed significant differences (p≤0.05) in the outcomes of higher and lower-scoring patient groups. Figure 3 and Table 2 present the optimal thresholds found for each model implementation.

Figure 5

A: Boxplot of Days Gained scores computed from the minimal model in 36 patients considered to have progression in the first 180 days after radiation. True progressors had significantly lower scores than pseudoprogressors. Negative Days Gained values indicate that post-treatment tumor burden was greater than that predicted by the simulated, untreated tumor. B: ROC curve for detecting pseudoprogression using Days Gained scores. Bi-normal smoothed curve (dashed) overlaid.