Semi‐empirical model for depth dose distributions of megavoltage x‐ray beams

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Abstract
The dose distribution due to absorption of photon energy fluence in a homogeneous water phantom irradiated by megavoltage X-ray beams was analyzed with a semiempirical model. The method generalizes an analytical formalism for the scattering component of dose within a water phantom which was recently developed for monoenergetic photon beams. Contributions to dose via Compton interaction and pair creation form the essential structure of the secondary component formula. The central-axis percent depth dose and off-central-axis ratios can be determined for beams of different sizes, used at any value of source to surface distance. The input includes the values of linear attenuation and energy-absorption coefficients in water at energies between 10 keV and the equivalent energy of the beam. Predicted values of the central-axis percent depth dose and the off-central-axis ratios are compared with the measurements for 2, 4, 6, 8, 10, 14, 20, 35, 45 and 70 MVp X-ray beams. For the central-axis percent depth dose, agreement is within 3% for fields of sizes between 5 .times. 5 and 20 .times. 20 cm2, and 5% for larger fields with beams of MVp up to 20. For higher energy beams, comparison was made only for the 10 .times. 10 cm2 fields and the discrepancies were within 3%. For the off-central-axis ratios, agreement between the predicted and measured values is within 5% over the umbra region but worsens in the penumbra region and geometrical shadow. This formalism requires large computer storage for generating data for all realistic beams irradiating normal-size phantoms.

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