Modeling and prediction of set‑up errors in breast cancer image‑guided radiotherapy using the Gaussian mixture model

The aim of the present study was to develop a prediction model for set-up error distribution in breast cancer image-guided radiotherapy (IGRT) using a Gaussian mixture model (GMM). To achieve this, the image-guided set-up errors data of 80 patients with breast cancer were selected, and the GMM was used to develop the set-up errors distribution prediction model. The predicted error center points, covariance and probability were calculated and compared with the planning target volume (PTV) margin formula. A total of 1,200 sets of set-up errors in IGRT for breast cancer were collected. The results of the Gaussian model parameters showed that the set-up errors were mainly in the direction of µ₁-µ₄ center points. All the raw errors in the lateral, longitudinal and vertical directions were -6.30-4.60, -5.40-1.47 and -2.70-1.70 mm, respectively. According to the probability of each center, the set-up error was most likely to shift in the µ₁ direction, reaching 0.53. The set-up errors of the other three centers, µ₂, µ₃ and µ₄, were 0.11, 0.34 and 0.12, respectively. According to the covariance parameters of the GMM, the maximum statistical standard deviation of the set-up errors reached 29.06. In conclusion, the results of the present study demonstrated that the GMM can be used to quantitatively describe and predict the distribution of set-up errors in IGRT for breast cancer, and these findings could be useful as a reference for set-up error control and tumor PTV expansion in breast cancer radiotherapy without routine, daily IGRT.