A comparison of coordinate systems for use in determining a radiotherapy delineation margin for whole breast

Cartesian co-ordinates, traditionally used for radiotherapy margins, calculated at 6 points, may not adequately represent changes in inter-observer contour variation as necessary to define a delineation margin. As a first step, this study compared the standard deviation (SD) in contour delineation using Polar and Cartesian co-ordinates for whole breast. Whole breast Clinical Target Volumes (CTV) were delineated by eight observers for 9 patients. The SD of contour position was determined for Polar co-ordinates at 1 degree increments for 5 slices and averaged across all patients. The mean centre of mass (COM) was used as the origin for the right breast, for the left the COM was shifted 1cm superiorly to avoid clipping. The SD was determined for Cartesian co-ordinates for medial-lateral and anterior-posterior positions.At slice Z=0cm considering Polar co-ordinates, the SD peaked medially reaching 3.55cm at 15 degrees for the right breast, and 1.44 cm at 171 degrees for the left. The SD of the remaining slices maintained a similar distribution, with variation in the peak occurring within 10 degrees of the Z=0cm positions. by comparison, for Cartesian co-ordinates at slice Z=0cm, the largest SD in the medial-lateral and anterior-posterior directions was 0.54/0.57cm and 1.03/0.67 cm respectively for right/left breasts. The SD for inter-observer variation for whole breast varies with anatomical position. The maximum SD determined with Polar co-ordinates was greater than with Cartesian co-ordinates. A delineation margin may thus need to vary with angle over the entire structure and Cartesian co-ordinates may not be the best approach for margin determination for whole breast.