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MO‐FG‐CAMPUS‐JeP3‐01: A Statistical Model for Analyzing the Rotational Error of Single Iso‐Center Technique
Author(s) -
Chang J
Publication year - 2016
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.4957376
Subject(s) - margin (machine learning) , radiosurgery , standard deviation , random error , nuclear medicine , mathematics , physics , distribution (mathematics) , statistics , radiation therapy , mathematical analysis , computer science , medicine , surgery , machine learning
Purpose: To develop a generalized statistical model that incorporates the treatment uncertainty from the rotational error of single iso‐center technique, and calculate the additional PTV (planning target volume) margin required to compensate for this error. Methods: The random vectors for setup and additional rotation errors in the three‐dimensional (3D) patient coordinate system were assumed to follow the 3D independent normal distribution with zero mean, and standard deviations σx, σy, σz, for setup error and a uniform σR for rotational error. Both random vectors were summed, normalized and transformed to the spherical coordinates to derive the chi distribution with 3 degrees of freedom for the radical distance ρ. PTV margin was determined using the critical value of this distribution for 0.05 significant level so that 95% of the time the treatment target would be covered by ρ. The additional PTV margin required to compensate for the rotational error was calculated as a function of σx, σy, σz and σR. Results: The effect of the rotational error is more pronounced for treatments that requires high accuracy/precision like stereotactic radiosurgery (SRS) or stereotactic body radiotherapy (SBRT). With a uniform 2mm PTV margin (or σx =σy=σz=0.7mm), a σR=0.32mm will decrease the PTV coverage from 95% to 90% of the time, or an additional 0.2mm PTV margin is needed to prevent this loss of coverage. If we choose 0.2 mm as the threshold, any σR>0.3mm will lead to an additional PTV margin that cannot be ignored, and the maximal σR that can be ignored is 0.0064 rad (or 0.37°) for iso‐to‐target distance=5cm, or 0.0032 rad (or 0.18°) for iso‐to‐target distance=10cm. Conclusions: The rotational error cannot be ignored for high‐accuracy/‐precision treatments like SRS/SBRT, particularly when the distance between the iso‐center and target is large.