Theoretical analysis of radiation field penumbra from a multi leaf collimator

Purpose/Objective: Analysis and measurement of the difference between the light field and the radiation field of the multi leaf collimator (MLC) leaves that are constructed with curved ends. Material and Methods: A Varian MLC with curved leaf ends was installed on a Clinac 2300 C/D. The leaves were 6.13 cm deep (dimension in beam direction) and were located 53.9 cm from the x-ray target. The leaf ends had an 8 cm radius of curvature. A relation was derived using three dimensional geometry predicting the location of the light field edge relative to the geometric projection of the tip of the curved leaf end. This is a nonlinear relationship because the shadow of the leaf is generated by different points along the leaf end surface as the leaf moves across the field. The theoretical edge of the radiation fluence for a point source was taken to be located along the projection of a chord whose length was 1 Half-Value Thickness (HVT). The chords having projection points across the light field edge were computed using an analytical solution. The radiation transmission through the leaf end was then estimated. The HVT used for tungsten alloy, the leaf material, was 0.87 cm and 0.94 cm for the 6 MV and 15 MV photon beams, respectively. The location of the projection of the 1 HVT chord at a distance of 100 cm from x-ray target was also a nonlinear function of the projection of the leaf tip. Results: The displacement of the light field edge relative to the projection of the leaf tip varies from 0 mm when the leaf tip projects to the central axis, to approximately 3.2 mm for a 20 cm half-field width. The light field edge was always displaced into the unblocked area. The displacement of the projection of the 1 HVT chord relative to the projection of the leaf tip varies from 0.3 mm on the central axis to 3.0 mm for a 20 cm half-field width. The projection of 1 HVT chord was deviated from the light field edge by only 0.3 mm which would be slightly increased to 0.4 mm on decreasing of the leaf end radius to 5 cm. Therefore, the light field edge and the point-source radiation fluence edge are displaced from each other by less than 0.5 mm for all leaf positions. However, calculations for a different MLC geometry, an upper-jaw-replacement MLC without secondary collimation, predict a tripling of the displacements. Conclusion: The observed penumbra of 2 mm-4 mm for the MLC leaf end is not due primarily to the shape of the leaf end, but rather is due to other factors such as the extra focal scatter. This explains the observed similarity of the MLC penumbra to focused collimator jaw penumbra. Coincidence of the light field with the radiation field is theoretically predicted (and experimentally observed) throughout the range of motion of the leaves to be within 0.5 mm. The calibration of the leaf position must account for the nonlinear relation between the physical location of the leaf (as determined by an encoder) and the true position of the light and radiation field edges. This investigation was supported in part by PHS grant number CA43840 awarded by the National Cancer Institute