Modeling the efficacy of the extent of surgical resection in the setting of radiation therapy for glioblastoma

Abstract

Standard therapy for glioblastoma (GBM) includes maximal surgical resection and radiation therapy. While it is established that radiation therapy provides the greatest survival benefit of standard treatment modalities, the impact of the extent of surgical resection (EOR) on patient outcome remains highly controversial. While some studies describe no correlation between EOR and patient survival even up to total resection, others propose either qualitative (partial versus subtotal versus complete resection) or quantitative EOR thresholds, below which there is no correlation with survival. This work uses a mathematical model in the form of a reaction-diffusion partial differential equation to simulate tumor growth and treatment with radiation therapy and surgical resection based on tumor-specific rates of diffusion and proliferation. Simulation of 36 tumors across a wide spectrum of diffusion and proliferation rates suggests that while partial or subtotal resections generally do not provide a survival advantage, complete resection significantly improves patient outcomes. Furthermore, our model predicts a tumor-specific quantitative threshold below which EOR has no effect on patient survival and demonstrates that this threshold increases with tumor aggressiveness, particularly with the rate of proliferation. Thus, this model may serve as an aid for determining both when surgical resection is indicated as well as the surgical margins necessary to provide clinically significant improvements in patient survival. In addition, by assigning relative benefits to radiation and surgical resection based on tumor invasiveness and proliferation, this model confirms that (with the exception of the least aggressive tumors) the survival benefit of radiation therapy exceeds that of surgical resection.

Keywords: Extent of resection; glioblastoma; mathematical modeling; radiation therapy; surgical therapy.

Figure 1

The time evolution of the cell density profile as given by the standard reaction–diffusion model of Equation (1), with $c(0,x)=0.8K\ast e^{-0.25x^2}$, K = 10⁵ cells per mm³, D (0.4 mm²/day) and ρ (0.04/day).

Figure 2

Schematic showing cell density versus distance from tumor center, illustrating the use of cell density thresholds to delineate calculated tumor radius on T1 post‐contrast and T2 weighted images.

Figure 3

(a) Cell density profile in space at two time points: just prior to (red curve) and just after radiation therapy (blue curve) for a model tumor (D = 0.2, ρ = 0.02, α = 0.04). It is noted that radiation therapy causes a decrease in the cell density curve. (b) Effect on the cell density profile of a partial (5‐mm) surgical resection, followed by radiation therapy (blue cruve).

Figure 4

(a) T1C radius versus time plots for a model tumor (D = 0.2, ρ = 0.03, α = 0.04). The blue curve represents tumor growth with no therapy; death occurs at 357 days. The red curve represents the changes caused by radiation therapy, with a reduction in radius during therapy, followed by tumor rebound; death now occurs at 422 days. It is noted that the two curves overlap prior to therapy (initial blue segment). (b) Compares radiation therapy alone (blue then red curve) to gross total surgical resection followed by radiation therapy (blue curve); death now occurs at 468 days. It is noted that with surgery followed by radiation therapy, the model tumor disappears on T1 post‐contrast images, with a long lag time (approximately 200 days), followed by tumor recurrence.

Figure 5

Theoretical survival curves for nine patient cohorts in the HH, HL, LH and LL tumor groups. The first curve is without therapy. The second curve represents the improved survival with radiation therapy. Overlapped on this curve are the curves for partial and subtotal resection, showing no added survival benefit. The last curve represents gross total resection followed by radiation therapy, showing an additional benefit for total resection.