Brachytherapy dose-volume histogram computations using optimized stratified sampling methods.

A stratified sampling method for the efficient repeated computation of dose-volume histograms (DVHs) in brachytherapy is presented as used for anatomy based brachytherapy optimization methods. The aim of the method is to reduce the number of sampling points required for the calculation of DVHs for the body and the PTV. From the DVHs are derived the quantities such as Conformity Index COIN and COIN integrals. This is achieved by using partial uniform distributed sampling points with a density in each region obtained from a survey of the gradients or the variance of the dose distribution in these regions. The shape of the sampling regions is adapted to the patient anatomy and the shape and size of the implant. For the application of this method a single preprocessing step is necessary which requires only a few seconds. Ten clinical implants were used to study the appropriate number of sampling points, given a required accuracy for quantities such as cumulative DVHs, COIN indices and COIN integrals. We found that DVHs of very large tissue volumes surrounding the PTV, and also COIN distributions, can be obtained using a factor of 5-10 times smaller the number of sampling points in comparison with uniform distributed points.

Optimized bounding boxes for three-dimensional treatment planning in brachytherapy.

It is sometimes necessary to determine the optimal value for a direction dependent quantity. Using a search technique based on Powell's quadratic convergent method such an optimal direction can be approximated. The necessary geometric transformations in n-dimensional space are introduced. As an example we consider the approximation of the minimum bounding box of a set of three-dimensional points. Minimum bounding boxes can significantly improve accuracy and efficiency of the calculations in modern brachytherapy treatment planning of the volumes of objects or the dose distribution inside an object. A covariance matrix based approximation method for the minimum bounding box is compared with the results of the search method. The benefits of the use of optimal oriented bounding boxes in brachytherapy treatment planning systems are demonstrated and discussed.