Modeling Gamma Knife Radiosurgical Toxicity for Multiple Brain Metastases

Abstract

Dosing for single fraction radiosurgery has traditionally relied on tumor measurements from a single maximum diameter. Most protocols recommend setting dosing criteria based on assumed risk of radionecrosis roughly correlating with tumor size. However, the risk of radionecrosis after radiosurgery is best modeled by a function of dose and volume treated, with the largest body of evidence supporting the use of brain tissue receiving ≥12 Gy in one fraction (V12, i.e., > 10.9 cm3). Here we show that tumor surface area (SA) and second order dimensions are superior predictors for Gamma Knife radiosurgical toxicity and can be used to estimate V12. A total of 1217 brain metastases from 245 patients treated with a prescribed dose from 13 to 27 Gy in one fraction were retrospectively reviewed. Eight independent modeling parameters were considered; 3 geometric tumor characteristics: SA, volume (V), and largest axial dimension (LAD) and 5 treatment planning variables: prescription dose (Rx), coverage, selectivity, gradient index, and number of shots. Linear regression and power-law formulations were performed to determine which parameters were the most accurate predictors of V12. The power model is dependent on a conceptualized "pseudo surface area" (PSA), defined as the surface area of a sphere with a diameter of LAD of a lesion (PSA = π*LAD2). At the aggregate patient level, the model predicts total brain V12 by summing the V12 values for each singular lesion only by using LAD and Rx as input variables. Tumor SA was the best univariate linear predictor of V12 (adjR2 = 0.770), followed by LAD (adjR2 = 0.755) and V (adjR2 = 0.745). The SA predictive model improves for lesions that have high sphericity > 0.85 (adjR2 = 0.837), with a measure of 1 indicating a perfect sphere. Using bivariable regression analysis, we formulated a single term power model that even more accurately predicts for V12 (V12 = 0.0137 * Rx1.5 * LAD2, adjR2 = 0.906) and is proportional to PSA. At the patient level, this model also accurately predicts for total brain V12 (adjR2 = 0.896) and V12 > 10.9 cm3 (Sensitivity = 99.1%, Specificity = 90.5%). Conceptually, SA univariately predicts for V12 more accurately than other tumor physical dimensions or treatment planning parameters, while the best bivariable power model involves PSA. We provide a preplan model for brain metastases that can help better estimate radionecrosis risk, determine prescription doses given a target V12, and provide safe dose escalation strategies without the use of any planning software.