A Novel 2D Probability Density Function Integrating the Rectal Motion and Wall Thickness in Prostate IMRT

This study investigated the variations of rectal motion and wall thickness in prostate intensity-modulated radiotherapy using a novel 2D probability density function. To evaluate the impact of the position, thickness, and deformation of the rectum on the dose distribution in prostate intensity-modulated radiotherapy plans, probability density functions (pdf) of the deformation of rectal cross-section (D_W), rectal dose distribution (R_M), and changes in rectal wall thickness (T_W) were used in the planning optimization.

The problem of approximating the product of a number of Gaussian mixture distributions arises in the number of parameters describing the specific mean value, standard deviation, and weight in every Gaussian. In this work, a pdf model has been developed which specifies the variability of the average rectal wall thickness. The model is based on the histogram of 587 randomly selected patients with prostate cancer.

The average wall thicknesses were determined based on the rectal structure contours drawn on the planning CT image set of the patient. The pdf describing the variability of the rectal wall thickness (pdf_TW) is represented as a three-mode Gaussian mixture of specific (μ_F,σ_F); (μ_PF,σ_PF) and (μ_E,σ_E) and individual weights (w_F, w_PF, and w_E) representing full, partially full, and empty rectal states, respectively.

A 2D Gaussian pdf of rectal motion and rectal thickness (2D pdf_M&TW) function, as a product-mixture model of the pdf of the rectal motion (pdf_M) and the pdf_TW, was developed using published and experimental data, respectively, and presented mathematically. Using correlation values between the functions pdf_M and pdf_TW, the sensitivity of profiles and projections to the 2D pdf_M&TW is numerically demonstrated.