Analytical Consideration of Surface Dose and Kerma for Megavoltage Photon Beams in Clinical Radiation Therapy

Background: In radiation therapy, estimation of surface doses is clinically important. This study aimed to obtain an analytical relationship to determine the skin surface dose, kerma and the depth of maximum dose, with energies of 6 and 18 megavoltage (MV). Materials and
Methods: To obtain the dose on the surface of skin, using the relationship between dose and kerma and solving differential equations governing the two quantities, a general relationship of dose changes relative to the depth was obtained. By dosimetry all the standard square fields of 5cm×5cm to 40cm×40cm, an equation similar to response to differential equations of the dose and kerma were fitted on the measurements for any field size and energy. Applying two conditions: a) equality of the area under dose distribution and kerma changes in versus depth in 6 and 18 MV, b) equality of the kerma and dose at x=dmax and using these results, coefficients of the obtained analytical relationship were determined. By putting the depth of zero in the relation, amount of PDD and kerma on the surface of the skin, could be obtained.
Results: Using the MATLAB software, an exponential binomial function with R-Square >0.9953 was determined for any field size and depth in two energy modes 6 and 18MV, the surface PDD and kerma was obtained and both of them increase due to the increase of the field, but they reduce due to increased energy and from the obtained relation, depth of maximum dose can be determined.
Conclusions: Using this analytical formula, one can find the skin surface dose, kerma and thickness of the buildup region.