SU‐E‐T‐07: Estimation of Effective Field Size with Leaf‐Based Algorithm

Purpose: Demonstrate a geometric algorithm for calculating equivalent squares of multileaf collimator defined fields. Methods: Equivalent square (Q) can be modeled as the product of a field's size (square root of area) and a function of its shape, f(E), where f(E)=1 for squares and f(E)<1 for elongated or eccentric shapes. It follows from Sterling's approximation that f(E) = (2*S^0.5)/(S+1) for rectangles with aspect ratio S. By Day's approximation, f(E)=1.8/pi^ 0.5 for circles. For MLC‐defined fields, effective width can be modeled as the average separation between opposing leaf‐tips, where leaf position is weighted both by leaf thickness and by inverse‐square distance of the leaf tip from central axis. Inverse‐square weighting is heuristic, based on the observation that scatter‐air‐ratio is concave with radius. A ratio by area yields effective length and Sterling's approximation yields equivalent square. This algorithm was benchmarked against both Sterling and Day using square, circular, and rectangular fields. Ratios of phantom dose in blocked versus open fields were also used to determine Q through iterative comparison to clinical Sp and TMR tables. Results: The leaf‐based algorithm produced f(E) values of approximately one, greater than one, and less than one where these were expected. It also produced good agreement with benchmarks, with a maximum difference of 3%. In heavily blocked fields, the agreement between the leaf‐based algorithm and the benchmark was superior to the agreement between the benchmark and the measurement. Conclusion: The separation of size from shape is a useful construct in evaluating the equivalent squares of MLC defined fields. The leaf‐based algorithm is a promising technique for calculating equivalent square that produces results consistent with classic benchmarks and accuracies consistent with the limitations of the underlying equivalent square model.