Calculation of Analytical Expressions for Measured Percentage Depth Dose Data in Megavoltage Photon Therapy

Background: In external radiation therapy, the percentage depth dose (PDD) is an important factor for estimating patient dose and dose distribution in target volume; therefore, its exact measurement or calculation is important. The aim of this study was to evaluate analytically the dose received by different points in water phantom and to compare it with dosimetry measurement data. Methods: To find the dose distribution throughout the tumor volume, first, the mathematical approach was performed for derivation of percentage depth dose photon beams of 6MV and 18MV Varian accelerator. Second, by dosimetry for different fields in different depths of water phantom, one can parameterize the obtained formula for percentage depth dose. Results: By comparing the mathematical and dosimetry results, the parameters of PDD-expression were computed in terms of the dimension of equivalent square field in different depths. From this formula, one can find the PDD for any fields in different depths, surface skin dose, and depth of build-up region of dose distribution, which are in agreement with empirical results with R2 >0.995, showing a good agreement with the experimental data. Conclusion: So one can measure the surface skin-dose, the depth of build-up region, and their variations in terms of square field size exactly; the measurement of these quantities have some technical problems in radiation dosimetry.