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Equivalent diameters of elliptical fields.

G S J Tudor¹, S J Thomas

¹Medical Physics, Addenbrookes NHS Trust, Cambridge CB2 2QQ, UK.

The British Journal of Radiology

|October 28, 2004

Summary

Determining the equivalent diameter for elliptical fields in kilovoltage radiotherapy is crucial. Sector integration best approximates measured doses, outperforming analytic formulas like 2AB/(A+B) and equal area methods.

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Area of Science:

Medical Physics
Radiotherapy Dosimetry

Background:

The equivalent field method is standard for dose calculations in radiotherapy.
Elliptical fields are common in kilovoltage radiotherapy, but a consensus on their equivalent diameter is lacking.

Purpose of the Study:

To evaluate various methods for calculating the equivalent diameter of elliptical fields.
To determine the most accurate method for dose calculations in elliptical fields.

Main Methods:

Measurements were conducted on 15 elliptical and 6 circular fields using 150 kV X-rays.
Equivalent diameters were calculated using methods including equal area, perimeter-to-area ratio, 2AB/(A+B), and sector integration.

Main Results:

Sector integration showed the best agreement with experimental measurements.
The analytic formula D=2AB/(A+B) provided dose predictions within 0.5% at shallow depths and 1.6% at 5 cm depth.
The equal area formula (D = sqrt(AB)) yielded the largest errors, up to 5% at shallow depths and 9% at 5 cm depth.

Conclusions:

Sector integration is the most accurate method for determining equivalent diameter in elliptical fields for kilovoltage radiotherapy.
The D=2AB/(A+B) formula offers a reasonable analytic approximation for dose calculations.

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