Patient-specific metrics of invasiveness reveal significant prognostic benefit of resection in a predictable subset of gliomas

Abstract

Object: Malignant gliomas are incurable, primary brain neoplasms noted for their potential to extensively invade brain parenchyma. Current methods of clinical imaging do not elucidate the full extent of brain invasion, making it difficult to predict which, if any, patients are likely to benefit from gross total resection. Our goal was to apply a mathematical modeling approach to estimate the overall tumor invasiveness on a patient-by-patient basis and determine whether gross total resection would improve survival in patients with relatively less invasive gliomas.

Methods: In 243 patients presenting with contrast-enhancing gliomas, estimates of the relative invasiveness of each patient's tumor, in terms of the ratio of net proliferation rate of the glioma cells to their net dispersal rate, were derived by applying a patient-specific mathematical model to routine pretreatment MR imaging. The effect of varying degrees of extent of resection on overall survival was assessed for cohorts of patients grouped by tumor invasiveness.

Results: We demonstrate that patients with more diffuse tumors showed no survival benefit (P = 0.532) from gross total resection over subtotal/biopsy, while those with nodular (less diffuse) tumors showed a significant benefit (P = 0.00142) with a striking median survival benefit of over eight months compared to sub-totally resected tumors in the same cohort (an 80% improvement in survival time for GTR only seen for nodular tumors).

Conclusions: These results suggest that our patient-specific, model-based estimates of tumor invasiveness have clinical utility in surgical decision making. Quantification of relative invasiveness assessed from routinely obtained pre-operative imaging provides a practical predictor of the benefit of gross total resection.

Figure 1. Patient-Specific Simulations of Tumor Cell Distribution and Density for both a Relatively Diffuse and a Relatively Nodular Glioblastoma.

T1Gd and T2 MRIs for two newly diagnosed glioblastoma patients, one relatively diffuse with a low ρ/D (a,c) and one more nodular with a high ρ/D (b,d). A simulation of the diffuse glioma extent predicted by the patient-specific simulation for the diffuse (low ρ/D) patient (e) and the more nodular (high ρ/D) patient (f) is overlayed on the T1Gd MRI with red and blue indicating high and low (but nonzero) glioma cell density, respectively. The effect of GTR is shown as a black region with a white outline and highlights the significant diffuse extent of glioma cells remaining post-GTR. In the more nodular (high ρ/D) case, GTR removes 75% of the pre-treatment glioma cells leaving 8.4e8 cells while in the diffusely invasive (low ρ/D) case, GTR removes only 27% of the pre-treatment glioma cells leaving 4.2e9 cells, an order of magnitude higher than the nodular case. The large number of tumor cells remaining after resection of a diffuse tumor drives recurrence.

Figure 2. ρ/D Assessment.

This figure presents an overview of how the “relative invasiveness,” or ρ/D, is obtained. Tumor volumes are segmented from T1Gd and T2 MRI. The measured volume is approximated with a sphere in order to obtain a radius. The T1Gd and T2 radii are associated with different levels of detection, with T2 at low tumor cell density and T1Gd abnormality associated with high tumor cell density. The relationship between these two radii describes the steepness of the tumor cell profile, or “relative invasiveness.”

Figure 3. Extent of resection necessary to attain significant reduction in glioma cell burden.

A) Simulated predictions of the additional resection volume beyond GTR of the T1Gd abnormality needed to achieve 99% reduction in tumor cell burden, a 2 log kill of tumor cells. The color scale maps to the additional volume (ranging from 10^−1.5 to 10^2.8, corresponding to hemispherectomy of an approximately 1200 cm³ brain volume) outside of the T1Gd abnormality needed to attain desired tumor cell removal. The cutoffs between low and moderate ρ/D (37.2 cm⁻²) and moderate and high ρ/D (135 cm⁻²) are displayed as tick marks on the horizontal axis. These theoretical resection margins necessary to achieve a 2 log kill of tumor cells are visualized for b) a diffuse tumor which requires an extra 237 cc of tissue (green contour) to be removed beyond a conventional GTR of the T1Gd abnormality (pink contour). In contrast, only 25 cc of brain tissue needs to be resected to remove 99% of the glioma cells in the more nodular glioma (c).

Figure 4. Survival Curves for Highly Diffuse (low ρ/D), Moderately Diffuse (mid ρ/D), and Nodular (high ρ/D) for 243 Contrast-enhancing Gliomas.

Comparisons were made between biopsy/subtotal resection (BX/STR) and gross total resection (GTR) in all 243 contrast-enhancing gliomas. A–B) Comparing Bx/STR with GTR in 243 contrast enhancing gliomas at first surgical presentation, there is no significant survival benefit of GTR for highly and moderately diffuse (low and mid ρ/D, p = 0.532, p = 0.445, respectively). C) Patients with the least diffuse and most nodular pattern of growth (high ρ/D) that underwent GTR had a significant survival benefit over patients undergoing Bx or STR (p = 0.00142). Median increase in survival was 227 days (7.5 months) or a 65% improvement over the BX/STR population. When EOR was classified by percent of the T1Gd volume removed, with 76% selected as the cut off, the same selective survival benefit is observed in the nodular cohort (D–F, p = 0.00132). The limits between highly and moderately diffuse, and between moderately diffuse and nodular ρ/D were 0.376 mm⁻² and 1.30 mm⁻², respectively.

Figure 5. Survival Curves for Highly Diffuse (low ρ/D), Moderately Diffuse (mid ρ/D), and Nodular (high ρ/D) for 215 WHO Grade IV glioblastoma multiforme tumors (GBMs) with sufficient imaging.

Comparisons were made between biopsy/subtotal resection (BX/STR) and gross total resection (GTR) in GBMs at first surgical presentation. GTR imparted no significant survival benefit in the highly diffuse (A) and moderately diffuse (B) GBMs. C) GTR imparted a significant survival benefit among patients with nodular GBMs, with a benefit of 239 days (8 months), or a 75% improvement over the Bx/STR group. When EOR was classified by percent of the T1Gd volume removed, with 76% selected as the cut off, the same selective survival benefit is observed in the nodular cohort (D–F, p = 0.0000339). The limits between highly diffuse and moderately diffuse, and between moderately diffuse and nodular ρ/D were 0.439 mm⁻² and 1.36 mm⁻², respectively.

Figure 6. Results of iterative Kaplan-Meier Analysis in each invasiveness cohort.

Number of cells remaining was calculated for each patient, based on their ρ/D and measured residual enhancing disease. Each possible threshold was iterated through to separate the patients into large and small residual tumor cell population cohorts. White boxes correspond to thresholds separating patients into groups with significantly different (p<0.05) survival. White stars indicate tests with no p-value, as the threshold did not separate the patients in the given invasiveness cohort into two groups. Black asterisks indicate tests with p<0.05. Black bins with white x's indicate no the threshold did not separate the patients in the given invasiveness cohort into two groups. For example, for the diffuse case (Figure 3, top row), the black bins with white x's represent the fact that even GTR was unable to achieve a remaining cell burden less than the cutoff (up to approximately 10⁹). Further, amongst the most diffuse gliomas, no threshold for a residual cells following resection was found to be significant of outcome represented visually as the lack of a white bar in the top row. Although less dramatic, the moderate cohort was unable to equate a GTR with <10^8.5 cells remaining represented by the black bars with white x's to the left on middle row of Figure 3. While resection of tumors in the nodular cohort were able to attain residual disease burdens at all levels down to <10⁷ cells.