Comments on "Sampling techniques for the evaluation of treatment plans" [Med. Phys. 20, 151-161 (1993)]

A Fourier analysis of the dose grid resolution required for accurate IMRT fluence map optimization

We present a theoretical and empirical analysis of the errors associated with the spatial discretization of the dose grid employed in optimized intensity modulated radiation therapy (IMRT) treatment plans. An information theory based Fourier analysis of the accuracy of discrete representations of three-dimensional dose distributions is presented. When applied to beamlet-based IMRT dose distributions, the theory produces analytic integrals that can bound worst case aliasing errors that can occur regardless of the location and orientation of the dose grid. The predictions of this theory are compared to empirical results obtained by solving a linear-programming based fluence-map optimization model to global optimality. A reasonable agreement between worst case estimates and the empirical results is attributed to the fact that the optimization takes advantage of aliasing to produce an optimal plan. We predicted and empirically demonstrated that an isotropic dose grid with <2.5 mm spacing is sufficient to prevent dose errors larger than a percent. However, we noted that in practice this resolution is mostly needed in high-dose target regions. Finally, a multiresolution 2-4-6 mm spacing model was developed and empirically tested where these spacings were applied to targets, structures, and tissue, respectively.

A practical approach to inverse planning for high-precision dose escalated conformal prostate radiotherapy

The problem of choosing the best gantry angles and beam weights for dose-escalated conformal prostate treatment planning is formulated using a mixed-integer linear programming approach, to account for tumour dose homogeneity and dose-volume constraints. The formulation allows the number of beams to be restricted and for some of the beams to be compulsory. The present planning algorithm interfaces with and utilizes the three-dimensional planning capabilities of a commercial treatment planning system. A case study is illustrated, which represents a particularly challenging planning problem due to a large planning target volume and an unusually small bladder. Treatment plans with different numbers of beams are generated to compare with each other and with the standard six-field plan. Significant improvement is shown in the reduction of hot regions within the femoral heads and rectal wall, while not unduly compromising homogeneity constraints for the tumour.

Developing a dose-volume histogram computation program for brachytherapy

A dose-volume histogram (DVH) computation program was developed for brachytherapy treatment planning in an attempt to benefit from the DVH's ability to present graphically information on 3D dose distributions. The program is incorporated into a planning system that utilizes a pair of orthogonal radiographs to localize the radiation sources. DVHs are calculated for the volume of tissue enclosed by an isodose surface (e.g. half the value of the reference isodose). The calculation algorithm is based on a non-uniform random sampling that gives a denser point distribution at the centre of the implants. Our program was tested and proved to be fast enough for clinical use and sufficiently accurate (i.e. computation time of 20 s and less than 2% relative error for one point source, for 100,000 calculation points). The accuracy improves when a larger calculation point number is used, but the computation time also increases proportionally. The DVH is presented in the form of a simple graph or table, or as Anderson's 'natural' DVH graph. The cumulative DVH tables can be used to extract a series of indexes characterizing the homogeneity and the dose levels of the distribution in the treatment volume and the surrounding tissues. If a reference plan is available, the DVH results can be assessed relative to the reference plan's DVH.

A method of incorporating organ motion uncertainties into three-dimensional conformal treatment plans

PURPOSE

We describe a method of incorporating organ motion into three-dimensional (3D) conformal treatment plans, which predicts the effect of organ motion on the calculated dose to both the clinical target volume (CTV) and nontarget organs.

METHODS AND MATERIALS

The method is based on measurements of organ motion by means of multiple computed tomography (CT) scans from a group of "reference" patients, in which the data consist of previously drawn contours of the target and nontarget organs. A computer program records the differences in contour position and shape that occur between scans in the reference data, and according to those differences adjusts the contours and dose calculation points of a "study" patient currently being planned, thus simulating organ motion. Dose-volume histograms (DVHs) are accumulated, and the process is repeated over the set of reference patient scans, resulting in a set of treatment plans that are ranked according to a dose-based endpoint. Two plans are selected corresponding to specified lower and upper confidence limits in the endpoint, and the DVHs from these plans are displayed for comparison with the DVHs from the nominal plan in the absence of motion.

RESULTS

As an example of the method's use, it is applied to a 6-field conformal treatment plan for prostate cancer. Confidence limit DVHs of the CTV and rectal wall (in which the plans were ranked by probabilities for tumor control and normal tissue complication, respectively) are presented and compared to those from the nominal plan.

CONCLUSION

The method provides a means of estimating the uncertainty in dose delivered by a treatment plan when organ motion is present. It is generally applicable to any treatment site for which data in the form of multiple CT scans are available, and can be extended to include other treatment uncertainties such as variation in patient positioning.