# Modeling geometrical uncertainties for radiotherapy plan optimization without margins

Modeling geometrical uncertainties for radiotherapy plan optimization without margins

Author Contributor Faculty Department Date2015-01-06

AbstractRadiotherapy is one of the methods used to treat cancer. One common approach for radiotherapy is exposing the patient to external beams of high-energy X-ray photons. Using the intensity-modulated radiation therapy (IMRT) technique, the fluence (radiation energy per unit area) of the radiation beams can be modulated to optimally shape the 3D high-dose volume to the tumor shape. The term radiotherapy will henceforward refer to this technique. Before radiotherapy can be administered, a treatment plan must be generated to accomplish high tumor-dose and maximum sparing of surrounding healthy tissues. This planning is usually based on a computer-tomography (CT) scan showing the tumor and healthy organs-of-interest, called the planning CT scan. The treatment itself is normally given in several fractions over several days (e.g. about 40 for prostate cancer), where for each fraction a proportional part of the dose is given. Due to movements and deformations, the geometrical positions of the organs in the body at the time of the treatment sessions might not be the same as in the planning CT scan. These geometrical uncertainties can make radiation beams miss the target (the tumor site, usually called the clinical target volume, CTV), making the actually delivered dose in the CTV less than what is prescribed. So, eradication of the tumor may fail. To prevent this, the irradiated area is usually enlarged with a margin, following a margin recipe. Although using a margin recipe can prevent underdosage in the CTV, unfortunately it can also potentially harm the healthy organs-at-risk (OAR) around the CTV. The larger the margin, the higher the probability of damaging the OAR. The aim of this thesis is to develop a method to calculate the optimized fluence profiles of the radiation beams, while taking into account the geometrical uncertainties. The irradiated area will also be enlarged as with the margin-recipe, but now more locally adapted to the movements and deformations of the organs, sparing the OAR as much as possible, while delivering a high enough dose to the CTV. In this thesis, the movements and deformations are first modeled for a whole patient population. Then a useful method is described with which in this uncertain geometry the expected radiation dose and its corresponding variance can be calculated. Finally the corresponding radiation plan is optimized. The first step is to model the movements and deformations of the organs. For this, a method called principal component analysis (PCA) has been used, which extracts the dominant modes of movements of the voxels (the volume discretization units) of the organs, as well as estimating their probabilities. Unfortunately PCA can usually not be done directly to a new patient because there is generally just one CT scan (or at most a few) available for this patient, which gives not enough data on movements and deformations. Therefore in this thesis a scheme for combining the movement data for the organs of interest from a population of patients has been developed, and tested for a prostate cancer site. PCA has then been applied to the resulting database, and it turns out that the dominant modes have plausible physical explanations. Further verification has been obtained by carrying out an error analysis, which shows that the dominant modes are also shared by prostates which are not included in the database. The movements and deformations have been used to calculate the expected value (mean) and the variance of the dose. To do this, an integration over the probability space is needed, which is computationally expensive. If the mean and the variance of the dose are going to be used in the objective functions and constraints of the fluence optimization, they have to be calculated for every optimization iteration. To shift the burden of probability integrations away from the optimization iterations, dynamic dose deposition matrices have been developed. Multiplication of these matrices with the fluence profile vectors gives the expected value and variance of the voxel doses. The dynamic dose deposition matrices also help to calculate the derivatives of the expected value and the variance of the dose with respect to the fluencies. These derivatives are usually needed in optimizers, such as Erasmus-iCycle (an optimization suite developed in Erasmus MC Cancer Institute in Rotterdam, The Netherlands), which is used in this thesis. Numerical derivations without dynamic dose deposition matrices, for example using the Monte Carlo method, are computationally expensive, especially since the derivatives must be calculated for each optimization iteration as well. Once the dynamic dose deposition matrices are calculated, inclusion of the expected value and the variance of the doses in the fluence optimization algorithm (called here dynamic optimization) is computationally as costly as the usual fluence optimization (called static optimization). In this thesis, dynamic optimization is done by substituting the dose (in static optimization) with the expected value of the dose in the objective functions and constraints. The variance is included in the form of the average of the voxel variances. The preprocessing effort to calculate the average of the variances is much less than to calculate the variances at every voxel separately. In Erasmus-iCycle, the formulation of the optimization criteria is done using a wish-list. There the objective functions (costlets) are ranked according to their priorities, and each costlet has its own goal. For example for a prostate CTV, a costlet for dynamic optimization can be to maximize the mean dose (expected dose), with the goal of 78 Gy. In the wish-list, some hard constraints are also prescribed, e.g. the minimum mean dose in the prostate CTV can be 74.1 Gy (95% of 78 Gy). Using an optimization method called 2p?c, the costlets are optimized with respect to the constraints in two steps, so that a Pareto-optimal solution is obtained, where no improvement of a costlet can be made without deteriorating the others. To evaluate the results of the fluence optimization, a new evaluation tool called dose probability volume histogram (DPVH) is introduced in this thesis to complement the conventional dose volume histogram (DVH). While in dynamic optimization the DVH depicts the volume percentage of the organ that receives a certain expected dose, the DPVH shows the probability that the delivered dose in the organ actually fulfills the optimization criteria. Dynamic optimization using the dynamic deposition matrices has been tested for a simple cubic geometry and a prostate case. The results show that the margin-recipe solution prescribes a larger irradiated area for the same DVH in the CTV compared to dynamic optimization using expected values of the doses. Consequently using expected doses in the dynamic optimization damages the OAR less than the margin-recipe solution. Adding costlets on the average value of the variances improves the DVH and DPVH for the CTV. Unfortunately our results are not yet conclusive for the OAR in this case. It has further been shown though, that the local movements are even more taken into account, when the variances are included.

Subjectradiotherapy

geometrical uncertainties

population-based model

principal component analysis

treatment-plan optimization

9789461087898

Part of collectionInstitutional Repository

Document typedoctoral thesis

Rights(c) 2015 Budiarto, E.