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This correspondence provides a new formulation for the pairwise error probability for any coherently demodulated system in arbitrarily correlated Rayleigh fading. The novelty of the result is that the error probability expression can be described as a function of the eigenvalues of a "signal"-only matrix. We also provide the relationship between the pole location of the characteristic function and the resulting error probability. This result allows us to approximate and bound the desired probability. A new simple bound on the pairwise error probability is derived that is better than the standard Chernoff bound and asymptotically tight with the signal-to-noise ratio (SNR) to the true probability. Index Terms--Asymptotic bounds, diversity, pairwise error probability, performance analysis, Rayleigh fading.

Background: Improvements in systemic therapy continue to increase survival for patients with brain metastases. Updated dosimetric models are required to optimize long-term safety of stereotactic radiosurgery (SRS) for this indication. Methods: Patients at a single institution receiving SRS from December 2011 to December 2014 were retrospectively reviewed. Patients with radiographic progression of at least one lesion, and with at least 6 months of follow-up from the start of SRS were included. Grade 3 necrosis was defined as requiring surgical intervention. This data were combined with two additional published datasets to construct logistic models describing necrosis risk as a function of dose and volume. Results: From our institution, 294 brain metastases across 57 patients in 139 treatment plans met inclusion criteria. Primary histologies included non-small cell lung cancer (n = 19), melanoma (n = 13), breast carcinoma (n = 9), renal cell carcinoma (n = 7), and other (n = 9). Median follow-up from SRS of first cranial metastasis was 21.7 months (range: 6.3-56.6) and median overall survival was 25.6 months (range: 6.5-56.6). There were eight cases of Grade 1-2 and two cases of Grade 3 necrosis. As a useful clinical reference point, 20 cc of total brain receiving a single-fraction equivalent dose ≥14 Gy corresponded to 12.1% risk for Grade 1-3 (P < 0.003) and 3.4% risk for Grade 3 necrosis (P < 0.001). Conclusions: These results compare favorably with the QUANTEC brain tolerance estimates for radiosurgery, providing optimism for lower toxicity in the modern era. Additional studies are needed to determine dose tolerance parameters across a broad spectrum of patients. [ABSTRACT FROM AUTHOR]

Purpose: Treatment option of stereotactic radiosurgery versus whole brain radiotherapy for multiple brain metastases (>10) is an ongoing debate. Detailed dosimetric and biological information are presented in this study to investigate the possible clinical outcomes. Materials and Methods: Nine patients with multiple brain metastases (11-25) underwent stereotactic radiosurgery. Whole brain radiotherapy plans are retrospectively designed with the same MR image set and the same structure set for each patient using the standard opposing lateral beams and fractionation (3 Gy × 10). Physical doses and biologically effective doses are calculated for each lesion target and the CNS normal tissues and they are compared between whole brain radiotherapy and stereotactic radiosurgery in the context of clinical efficacy and published toxicities. Results: Tumor biologically effective dose is higher in radiosurgery than in whole brain radiotherapy by factors of 3.2-5.3 in maximum dose and of 2.4-3.1 in mean dose. Biologically effective mean dose in radiosurgery is 1.3-34.3% for normal brain, 0.7-31.6% for brainstem, 0.5-5.7% for chiasm, 0.2-5.7% for optic nerves and 0.6-18.1% for hippocampus of that in whole brain radiotherapy over nine cases presented here. We also presented the dose-volume relationship for normal brain to address the dosimetric concerns in radiosurgery. Conclusions: Dose-volume metrics presented in this study are essential to understanding the safety and efficacy of whole brain radiotherapy and/or radiosurgery for multiple brain metastases. Whole brain radiotherapy has resulted in higher incidence of radiation-related toxicities than radiosurgery. Even for patients with more than 10 brain metastases, the CNS normal tissues receive significantly lower doses in radiosurgery. Mean normal brain dose in SRS is found to correlate with the total volume of lesions rather than the number of lesions treated. [ABSTRACT FROM AUTHOR]

Purpose/Objective: To determine clinically relevant SBRT/stereotactic ablative radiotherapy (SABR) dose tolerance limits for RP based on statistical analysis of outcomes data. Materials and Methods: Eighteen consecutive patients who were treated using volumetric modulated arc therapy (RapidArc) for lung tumors exceeding 80cc were assessed. Clinical outcomes have been published elsewhere, and here we present a normal tissue complication probability (NTCP) analysis. The dose volume histogram (DVH) reduction techniques of total lung V20Gy, V15Gy, V10Gy, V5Gy and mean lung dose (MLD) were each analyzed, as well as ipsilateral lung V5Gy and contralateral lung V5Gy, using the DVH Evaluator software tool. The framework of the Lyman Model was used except that each DVH reduction method was analyzed independently instead of using the power-law relationship for volume dependence. Model parameters were fitted using Maximum Likelihood. Results: RP was reported in 5 patients (CTC Grade 2 in 3, and Grade 3 in 2). Total lung V5Gy and contralateral lung V5Gy were the best predictors of RP (p < 0.0001 for both). For V5Gy, the 10% risk level for Grade 2-3 RP was 27.9% for total lung and 21.8% for contralateral lung. For V20Gy, the 25% risk level is 10.5% of total lung. Conclusions: Analysis of RP endpoints has identified total lung V5Gy and contralateral lung V5Gy as the best predictors of RP following SBRT when delivered with RapidArc. These findings are based on limited clinical data, and longer follow-up in larger patient cohorts is required in order to determine more accurate dose tolerance limits. [ABSTRACT FROM AUTHOR]

PURPOSE AND OBJECTIVES: To estimate effects of tumor growth factor inhibitors on stereotactic body radiation therapy (SBRT) dose tolerance, we reviewed the literature and our patient experience. METHODS: Review of the literature revealed the Barney et al dataset (Int J Radiat Oncol Biol Phys. 2013;87:73–80), which provided SBRT small bowel dose-volume histogram (DVH) data for D5cc, D2cc, Dmax, and other volumes, as well as the corresponding outcomes. Combining their data with ours yielded 175 small bowel contours, 54 managed with inhibitors of vascular endothelial growth factor (VEGF), epidermal growth factor receptor (EGFR), or mammalian target of rapamycin (mTOR) before or after SBRT, from May 2008 through December 2014. No patient in either institution received VEGF, EGFR, or mTOR inhibitors concurrently with SBRT; for our patients, we maintain a 2-week period between SBRT and biologic agents. All doses were first converted to three-fraction equivalent dose using the linear quadratic (LQ) model with alpha/beta = 3 Gy. DVH data were loaded into the DVH Evaluator software (DiversiLabs LLC, Huntingdon Valley, PA), which produced a probit dose-response model to estimate the risk level for each published dose tolerance limit. RESULTS: Seven Common Terminology Criteria for Adverse Events version 4 grade 3–5 gastrointestinal toxicities were associated with VEGF in the published dataset. The probit dose-response model of 175 data points was used to estimate the risk level. In three fractions, the QUANTEC (Quantitative Analysis of Normal Tissue Effects in the the Clinic) Dmax ≤ 30 Gy limit had a 7% risk, and the TG101 Dmax ≤ 25.2 Gy limit had a 3.6% risk. A simple ratio approximated the increased risk from the inhibitors, as 7 of 54 cases with inhibitors and 7 of 175 overall cases had complications; therefore, the increased risk is approximately (7 of 54)/(7 of 175), for a 3.2-fold greater risk. However, none of the patients from our institution who were managed with VEGF, EGFR, or mTOR inhibitors had grade ≥ 3 complications. CONCLUSION: Tumor growth factor inhibitors may cause more toxicity with SBRT than would otherwise be anticipated, although the absence of complications in our patients allows cautious optimism. [ABSTRACT FROM AUTHOR]

PURPOSE AND OBJECTIVES: Mediastinal critical structures, such as the trachea, bronchus, esophagus, and heart, are among the dose-limiting factors for stereotactic body radiation therapy (SBRT) to central lung lesions. The purpose of this study was to characterize the risk of esophagitis for patients treated with SBRT and to develop a statistical dose-response model to assess the equivalent uniform dose (EUD), D10%, D5cc, D1cc, and Dmax dose descriptors of the esophagus for risk of toxicity. METHODS: Toxicity outcomes of a dose-escalation study of 56 CyberKnife patients from 45 Gy to 60 Gy in three to seven fractions at the Erasmus MC - Daniel den Hoed Cancer Center were utilized to create a probit dose-response model for the esophagus in Dose Volume Histogram (DVH) Evaluator software (DiversiLabs LLC, Huntingdon Valley, PA). All analyses were performed in terms of five-fraction equivalent dosing, using the linear quadratic model with alpha/beta = 3 Gy. RESULTS: Five grade 2 esophageal complications were reported (Common Terminology Criteria for Adverse Events version 3.0); four were early effects, and one was a late effect. According to our study, D1cc = 32.9 Gy and Dmax = 43.4 Gy corresponded to a complication probability of 50% for grade 2 toxicity. The Radiation herapy Oncology Group 0813 trial initial Dmax limit of 52.5 Gy in five fractions was associated with > 50% risk of grade 2 toxicity in this series, but no grade ≥ 3 esophageal toxicity occurred. Our estimates of esophageal toxicity are compared with the data in the literature and two other published dose-response models. CONCLUSION: Four articles reported five deaths due to esophageal toxicity; so, our dose escalation began cautiously, and as a result, no grade ≥ 3 esophageal toxicity occurred in our series. Further research needs to be performed to establish more reliable dose limits as longer follow-up and toxicity outcomes are reported in patients treated with SBRT to central lung lesions. [ABSTRACT FROM AUTHOR]

Purpose To quantify rigid and nonrigid motion of liver tumors using reconstructed 3-dimensional (3D) fiducials from stereo imaging during CyberKnife-based stereotactic body radiation therapy (SBRT). Methods and Materials Twenty-three liver patients treated with 3 fractions of SBRT were used in this study. After 2 orthogonal kilovoltage images were taken during treatment, the 3D locations of the fiducials were generated by the CyberKnife system and validated using geometric derivations. A total of 4824 pairs of kilovoltage images from start to end of treatment were analyzed. For rigid motion, the rotational angles and translational shifts were reported by aligning 3D fiducial groups from different image pairs, using least-squares fitting. For nonrigid motion, we quantified interfractional tumor volume variations by using the proportional volume derived from the fiducials, which correlates to the sum of interfiducial distances. The individual fiducial displacements were also reported (1) after rigid corrections and (2) without angle corrections. Results The proportional volume derived by the fiducials demonstrated a volume-increasing trend in the second (101.9% ± 3.6%) and third (101.0 ± 5.9%) fractions among most patients, possibly due to radiation-induced edema. For all patients, the translational shifts in left-right, anteroposterior, and superoinferior directions were 2.1 ± 2.3 mm, 2.9 ± 2.8 mm, and 6.4 ± 5.5 mm, respectively. The greatest translational shifts occurred in the superoinferior direction, likely due to respiratory motion from the diaphragm. The rotational angles in roll, pitch, and yaw were 1.2° ± 1.8°, 1.8° ± 2.4°, and 1.7° ± 2.1°, respectively. The 3D individual fiducial displacements with rigid corrections were 0.2 ± 0.2 mm and increased to 0.5 ± 0.4 mm without rotational corrections. Conclusions Accurate 3D locations of internal fiducials can be reconstructed from stereo imaging during treatment. As an effective surrogate to tumor motion, fiducials provide a close estimation of both rigid and nonrigid motion of liver tumors. The reported displacements could be further utilized for tumor margin definition and motion management in conventional linear accelerator-based liver SBRT. [ABSTRACT FROM AUTHOR]

Purpose: To inform development of procedures for using tumor-treating field arrays (TTFields) during glioblastoma radiation therapy by determining whether the placement and repositioning of arrays affects target volume coverage and cranial skin dose., Methods and Materials: Radiation plans from 10 consecutive patients treated for glioblastoma were copied to a cranial phantom and reoptimized for phantom anatomy. Dose distributions were then recalculated on 3 additional computed tomographic scans of the phantom with the TTFields electrode arrays placed over distinct locations on the phantom scalp to compare planning target volume (PTV) coverage and skin dose with and without TTFields in place in varying positions. Percent depth dose curves were also measured for radiation beams passing through the electrodes and compared with commonly used bolus material., Results: The presence of TTFields arrays decreased PTV V97% and D97% by as much as 1.7% and 2.7%, respectively, for a single array position, but this decrease was mitigated by array repositioning. On averaging the 3 array positions, there was no statistically significant difference in any dosimetric parameter of PTV coverage (V95-97%, D95-97%) across all cases compared with no array. Mean increases in skin D1cc and D20cc of 3.1% were calculated for the cohort. Surface dose for TTFields electrodes was less than that with a 5-mm superflab bolus., Conclusions: Our work demonstrates that placement of TTFields arrays does not significantly affect target volume coverage. We show that repositioning of TTFields arrays, as is required in clinical use, further minimizes any dosimetric changes and eliminates the need for replanning when arrays are moved. A slight, expected bolus effect is observed, but the calculated increases in skin dose are not clinically significant. These data support the development of clinical trials to assess the safety and efficacy of combining concurrent chemoradiotherapy with TTFields therapy for glioblastoma., (© 2019 Published by Elsevier Inc. on behalf of American Society for Radiation Oncology.)

Purpose: Treatment option of stereotactic radiosurgery versus whole brain radiotherapy for multiple brain metastases (>10) is an ongoing debate. Detailed dosimetric and biological information are presented in this study to investigate the possible clinical outcomes.Materials and Methods: Nine patients with multiple brain metastases (11-25) underwent stereotactic radiosurgery. Whole brain radiotherapy plans are retrospectively designed with the same MR image set and the same structure set for each patient using the standard opposing lateral beams and fractionation (3 Gy × 10).Physical doses and biologically effective doses are calculated for each lesion target and the CNS normal tissues and they are compared between whole brain radiotherapy and stereotactic radiosurgery in the context of clinical efficacy and published toxicities., Results: Tumor biologically effective dose is higher in radiosurgery than in whole brain radiotherapy by factors of 3.2-5.3 in maximum dose and of 2.4-3.1 in mean dose. Biologically effective mean dose in radiosurgery is 1.3-34.3% for normal brain, 0.7-31.6% for brainstem, 0.5-5.7% for chiasm, 0.2-5.7% for optic nerves and 0.6-18.1% for hippocampus of that in whole brain radiotherapy over nine cases presented here. We also presented the dose-volume relationship for normal brain to address the dosimetric concerns in radiosurgery., Conclusions: Dose-volume metrics presented in this study are essential to understanding the safety and efficacy of whole brain radiotherapy and/or radiosurgery for multiple brain metastases. Whole brain radiotherapy has resulted in higher incidence of radiation-related toxicities than radiosurgery. Even for patients with more than 10 brain metastases, the CNS normal tissues receive significantly lower doses in radiosurgery. Mean normal brain dose in SRS is found to correlate with the total volume of lesions rather than the number of lesions treated.