A Mathematical Method to Adjust MLC Leaf End Position for Accurate Dose Calculation in Carbon Ion Beam Radiation Therapy Treatment Planning System

Abstract

Introduction. We present a mathematical method to adjust the leaf end position for dose calculation correction in the carbon ion radiation therapy treatment planning system. Methods and Materials. A straggling range algorism of 400 MeV/n carbon ion beam in nine different multileaf collimator (MLC) materials was conducted to calculate the dose 50% point to derive the offset corrections in the carbon ion treatment planning system (ciPlan). The visualized light field edge position in the treatment planning system is denoted as $X_{\text{tang}.\text{p}}$ , and MLC position ( $X_{\text{mlc}.\text{p}}$ ) is defined as the source to leaf end midpoint projection on axis for monitor unit calculation. The virtual source position of energy at 400 MeV/n and straggling range in MLC at different field sizes were used to calculate the dose 50% position on axis. On-axis MLC offset (correction) could then be obtained from the position corresponding to 50% of the central axis dose minus the $X_{\text{mlc}.\text{p}}$ . Results. The exact MLC position in the carbon ion treatment planning system can be used as an offset to do the correction. The offset correction of pure tungsten is the smallest among the others due to its shortest straggling range of carbon ion beam in MLC. The positions of 50% dose of all MLC materials are always located in between $X_{\text{tang}.\text{p}}$ and $X_{\text{mlc}.\text{p}}$ under the largest field of 12 cm by 12 cm. Conclusions. MLC offset should be adjusted carefully at different field sizes in the treatment planning systems especially of its small penumbra characteristic in the carbon ion beam. It is necessary to find out the dose 50% position for adjusting MLC leaf edge on-axis location in the treatment planning system to reduce dose calculation error.