The effect of interfraction prostate motion on IMRT plans: a dose‐volume histogram analysis using a Gaussian error function model

The Gaussian error function model, containing pairs of error and complementary error functions, was used to carry out cumulative dose-volume histogram (cDVH) analysis on prostate intensity modulated radiation therapy (IMRT) plans with interfraction prostate motion. Cumulative DVHs for clinical target volumes (CTVs) shifted in the anterior-posterior directions based on a 7-beam IMRT plan were calculated and modeled using the Pinnacle3 treatment planning system and a Gaussian error function, respectively. As the parameters in the error function model, namely, a, b and c were related to the shape of the cDVH curve, evaluation of cDVHs corresponding to the prostate motion based on the model parameters becomes possible as demonstrated in this study. It was found that deviations of the cDVH for the CTV were significant, when the CTV-planning target volume (PTV) margin was underestimated in the anterior-posterior directions, particularly in the posterior direction for a patient with relatively small prostate volume (39 cm3). Analysis of the cDVH for the CTV shifting in the anterior-posterior directions using the error function model showed that parameters a1,2, which were related to the maximum relative volume of the cDVH, changed symmetrically when the prostate was shifted in the anterior and posterior directions. This change was more significant for the larger prostate. For parameters b related to the slope of the cDVH, b1,2 changed symmetrically from the isocenter, when the CTV was within the PTV. This was different from parameters c (c1,2 are related to the maximum dose of the cDVH), which did not vary significantly with the prostate motion in the anterior-posterior directions and prostate volume. Using the patient data, this analysis validates the error function model, and further verified the clinical application of this mathematical model on treatment plan evaluations.