SU‐GG‐T‐432: Dose‐Volume Histogram Modeling Using the Gaussian Error Function in Radiotherapy

Abstract

Purpose: A mathematical method, containing pair of error and complimentary error functions, is proposed to characterize cumulative dose‐volume histogram (cDVH). The model was illustrated by 5‐beam prostate IMRT plans with shifted clinical target volumes (CTVs) representing the interfraction organ motion. Method and Materials: A phantom including prostate, seminal vesicle, rectum and bladder was created with planning target volume (PTV) 0.5 cm margin from the prostate (CTV). The CTV was shifted 1 cm to the anterior, posterior, left, right, superior and inferior directions. Pinnacle3 TPS was used for IMRT plans with each shifted CTV. The calculated cDVHs for the plans were exported to MATLAB for modeling using the mathematical formula: , where (a1, b1 and c1) and (a2, b2 and c2) are parameters for the error and complimentary error function, respectively. D and V are the dose and volume of the cDVH, respectively. Results: It is found that parameters a1,2, vary with the relative volume of the cDVH. The slope of the cDVH after the curve drop‐off can be adjusted by b1,2, while a variation of c1,2 can change where the cDVH drops off from the normalized volume close to 1. Corresponding cDVHs calculated using the model agree well with those calculated from Pinnacle3. Parameters a1 and b1 are almost constant with variations of a2 and b2. However, parameter c1 is only constant when the CTV displacement is within the PTV, but changes with c2 when the CTV is shifted outside the PTV. It shows that cDVH variation due to parameter c would happen when the margin between the CTV and PTV is underestimated. Conclusion: This error function model for the cDVH provides a new view to study the dose‐volume relationship of a region of interest in radiotherapy.