Equivalent diameters of elliptical fields.

The equivalent field method is well established as a means of performing dose calculations in rectangular and irregular fields. There is, however, no consensus on the equivalent diameter (D) of elliptical fields, despite their common applications in kilovoltage radiotherapy. Measurements have been performed on 15 elliptical fields and 6 circular fields, comprising all possible combinations of 3 cm, 4 cm, 5 cm, 6 cm, 9 cm and 12 cm diameters, using 150 kV X-rays, with a half-value thickness of 8 mmAl. Equivalent diameters were calculated by a number of methods, including the equal area, ratio of perimeter to area, 2AB/(A+B) and sector integration. The best agreement with measurement was obtained using sector integration, which agreed with measurements within the limits of experimental error. The formula D=2AB/(A+B) was the best of the analytic formulae; at shallow depths it gave predictions of dose within better than 0.5%, whilst at 5 cm deep its greatest error was 1.6%. The equal area formula (D = square root AB) gave the worst predictions, with errors up to 5% at shallow depths, and 9% at a depth of 5 cm.