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Superellipse: A Novel Approach for the Dosimetric Definition of (small) Field Sizes

I Mendez*, B Casar, Institute of Oncology Ljubljana, Ljubljana, SI,


(Sunday, 7/12/2020)   [Eastern Time (GMT-4)]

Room: AAPM ePoster Library

Field size dimensions are commonly defined by the full width half maximum (FWHM) of the lateral dose profiles; the 50% (half maximum) isodose delimits the field size. Fields that are nominally square have, in fact, rounded corners, which turn small fields into near-elliptic shapes. All these shapes, as well as rectangular and cone field sizes, can be fitted by superellipses, a family of curves that encompass ellipses and rectangles. The objectives of this work were: to analyze the suitability of superellipses to fit 50% isodose curves of square fields accurately, to examine the advantages and disadvantages of determining field sizes with superellipses, and to propose a general and realistic definition of equivalent field area based on the dosimetric shape.

Square fields with nominal side lengths of 0.5, 0.8, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, and 10.0 cm, were irradiated with an Elekta Versa HD (Elekta AB, Stockholm, Sweden) using 6 and 10 MV with and without flattening filters. Field size dimensions were measured according to the Cranmer-Sargison et al. and the superellipse approaches by employing radiochromic films and a research version of

For both approaches, the goodness of fit of the 50% isodoses, as well as the differences in the values of equivalent field areas and equivalent square small field sizes, were calculated. Their dependence on the side length was analyzed.

Superellipses define geometric square fields more accurately than dosimetric square fields, especially for small fields.
Superellipses require 2D detectors and more sophisticated computations. However, they use the whole 50% isodose and provide more accurate field dimensions. Furthermore, cone and rectangular fields are handled uniformly.
Equivalent field areas for cones and rectangular fields can be directly obtained from the formula of the area of a superellipse.

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