The dose delivered by electron beams has a complex dependence on the shape of the field; any field shaping shields, design of collimator systems, and energy of the beam. This complicated dependence is due to multiple scattering of the electron beam as the beam travels from the accelerator head to the patient. The dosimetry of only regular field shapes (circular, square, or rectangular) is well developed. However, most tumors have irregular shapes and their dosimetry is calculated by direct measurement. This is laborious and time consuming. In addition, error can be introduced during measurements. The lateral build up ratio method (LBR), which is based on the Fermi-Eyges multiple scattering theory, calculates the dosimetry of irregular electron beam shapes. The accuracy of this method depends on the function σ _r(r,E) (the mean square radial displacement of the electron beam in the medium) used in the calculation. This research focuses on improving the accuracy of electron dose calculations using lateral build up ratio method by investigating the properties of σ_r(r,E).

The percentage depth dose curves of different circular cutouts were measured using four electron beam energies (6, 9, 12, and 15 MeV), four electron applicator sizes (6×6, 10×10, 14×14, and 20×20 cm), three source-surface distance values (100, 105, 110 cm). The measured percentage depth dose curves were normalized at a depth of 0.05 cm. Using the normalized depth dose, the lateral build up ratio curves were determined. Using the cutout radius and the lateral build up ratio values, σ_r(z,E) were determined. It is shown that the σ value increases linearly with cutout size until the cutout radius reaches the equilibrium range of the electron beam. The σ value of an arbitrary circular cutout was determined from the interpolation of σ versus cutout curve. The corresponding LBR value of the circular cutout was determined using its radius and σ values. The depth dose distribution of an irregular cutout along the axis passing through the cutout is determined by dividing the cutout into many sectors having equal angle and determining their mean radius. The LBR value of each sector was determined. Using these LBR values, depth dose curves of different irregular cutouts were calculated. The calculation was repeated for four electron beam energies. It is shown that taking the cutout size dependence of into account improves the accuracy of the percentage depth dose calculations. The percentage difference between the calculated and the measured percentage depth dose curves was under 2%.