Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects

An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative to the prediction in {\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.Comment: 21 pages, 9 figures, references and supplementary sections added, accepted for publication in PAS

Outcomes after stereotactic body radiotherapy for lung tumors, with emphasis on comparison of primary lung cancer and metastatic lung tumors

BACKGROUND: The goal of this study was to determine the prognostic factors associated with an improved overall outcome after stereotactic body radiotherapy (SBRT) for primary lung cancer and metastatic lung tumors. METHODS: A total of 229 lung tumors in 201 patients were included in the study. SBRT of 45 Gy in 3 fractions, 48 Gy in 4 fractions, 60 Gy in 8 fractions or 60 Gy in 15 fractions was typically used to treat 172 primary lungs cancer in 164 patients and 57 metastatic lung tumors in 37 patients between January 2001 and December 2011. Prognostic factors for local control (LC) and overall survival (OS) were analyzed using a Cox proportional hazards model. RESULTS: The median biologically effective dose was 105.6 Gy based on alpha/beta = 10 (BED10). The median follow-up period was 41.9 months. The 3-year LC and OS rates were 72.5% and 60.9%, and the 5-year LC and OS rates were 67.8% and 38.1%, respectively. Radiation pneumonitis of grades 2, 3 and 5 occurred in 22 petients, 6 patients and 1 patient, respectively. Multivariate analyses revealed that tumor origin (primary lung cancer or metastatic lung tumor, p < 0.001), tumor diameter (p = 0.005), BED10 (p = 0.029) and date of treatment (p = 0.011) were significant independent predictors for LC and that gender (p = 0.012), tumor origin (p = 0.001) and tumor diameter (p < 0.001) were significant independent predictors for OS. CONCLUSIONS: SBRT resulted in good LC and tolerable treatment-related toxicities. Tumor origin and tumor diameter are significant independent predictors for both overall survival and local control

Prognostic factors for local control of stage I non-small cell lung cancer in stereotactic radiotherapy: a retrospective analysis

Abstract Background The purpose of this study is to investigate the prognostic factors of stereotactic radiotherapy for stage I NSCLC to improve outcomes. Methods Stage I non-small cell lung cancer patients who were treated with stereotactic radiotherapy between 2005 and 2009 at our hospital were enrolled in this study. The primary endpoint was local control rate. Survival estimates were calculated from the completion date of radiotherapy using the Kaplan-Meier method. The prognostic factors including patients’ characteristics and dose-volume histogram parameters were evaluated using Cox’s proportional hazard regression model. Results Eighty patients (81 lesions) treated with 3 dose levels, 48 Gy/4 fractions, 60 Gy/8 fractions and 60 Gy/15 fractions, were enrolled in this study. Median follow-up was 30.4 months (range, 0.3 – 78.5 months). A Cox regression model showed T factor (p = 0.013), biological effective dose calculated from prescribed dose (BED10) (p = 0.048), and minimum dose for PTV (p = 0.013) to be prognostic factors for local control. Three-year overall survival rate and local control rate were 89.9% (T1: 86.8%, T2: 100%) and 89.0% (T1: 97.9%; T2: 64.8%), respectively. When the 3-year local control rates were examined by prescribed doses, they were 100% for the dose per fraction of 48 Gy /4 fractions (105.6 Gy BED10), 82.1% for 60 Gy/8 fractions (105 Gy BED10), and 57.1% for 60 Gy/15 fractions (84 Gy BED10). The median value of the minimum dose for PTV (%) was 89.88 (%), and the 3-year local control rates were 100% in those with the minimum dose for PTV (%) ≥ 89.88% and 79.2% in those with the minimum dose for PTV (%) Conclusions Our results suggest that T factor, BED10, and minimum dose for PTV influence the local control rate. Local control rate can be improved by securing the minimum dose for PTV.</p