Are dose calculations during dose optimization in brachytherapy necessary?

We consider the problem of anatomy based dose optimization in brachytherapy. A calculation method for some objective functions and their derivatives is proposed which significantly reduces the number of required operations. The optimization in some cases, ignoring a preprocessing step, is independent of the number of sampling points. The idea is that some of the objectives and their derivatives used for dose optimization do not require the explicit calculation of dose values. Dose optimization with the new modified computation method for the objectives and derivatives is, depending on the number of sampling points, up to 100 times faster than the conventional method with dose calculation.

Global convergence analysis of fast multiobjective gradient-based dose optimization algorithms for high-dose-rate brachytherapy.

We consider the problem of the global convergence of gradient-based optimization algorithms for interstitial high-dose-rate (HDR) brachytherapy dose optimization using variance-based objectives. Possible local minima could lead to only sub-optimal solutions. We perform a configuration space analysis using a representative set of the entire non-dominated solution space. A set of three prostate implants is used in this study. We compare the results obtained by conjugate gradient algorithms, two variable metric algorithms and fast-simulated annealing. For the variable metric algorithm BFGS from numerical recipes, large fluctuations are observed. The limited memory L-BFGS algorithm and the conjugate gradient algorithm FRPR are globally convergent. Local minima or degenerate states are not observed. We study the possibility of obtaining a representative set of non-dominated solutions using optimal solution rearrangement and a warm start mechanism. For the surface and volume dose variance and their derivatives, a method is proposed which significantly reduces the number of required operations. The optimization time, ignoring a preprocessing step, is independent of the number of sampling points in the planning target volume. Multiobjective dose optimization in HDR brachytherapy using L-BFGS and a new modified computation method for the objectives and derivatives has been accelerated, depending on the number of sampling points, by a factor in the range 10-100.

A hybrid evolutionary algorithm for multi-objective anatomy-based dose optimization in high-dose-rate brachytherapy.

Multiple objectives must be considered in anatomy-based dose optimization for high-dose-rate brachytherapy and a large number of parameters must be optimized to satisfy often competing objectives. For objectives expressed solely in terms of dose variances, deterministic gradient-based algorithms can be applied and a weighted sum approach is able to produce a representative set of non-dominated solutions. As the number of objectives increases, or non-convex objectives are used, local minima can be present and deterministic or stochastic algorithms such as simulated annealing either cannot be used or are not efficient. In this case we employ a modified hybrid version of the multi-objective optimization algorithm NSGA-II. This, in combination with the deterministic optimization algorithm, produces a representative sample of the Pareto set. This algorithm can be used with any kind of objectives, including non-convex, and does not require artificial importance factors. A representation of the trade-off surface can be obtained with more than 1000 non-dominated solutions in 2-5 min. An analysis of the solutions provides information on the possibilities available using these objectives. Simple decision making tools allow the selection of a solution that provides a best fit for the clinical goals. We show an example with a prostate implant and compare results obtained by variance and dose-volume histogram (DVH) based objectives.

Multiobjective anatomy-based dose optimization for HDR-brachytherapy with constraint free deterministic algorithms.

In high dose rate (HDR) brachytherapy, conventional dose optimization algorithms consider multiple objectives in the form of an aggregate function that transforms the multiobjective problem into a single-objective problem. As a result, there is a loss of information on the available alternative possible solutions. This method assumes that the treatment planner exactly understands the correlation between competing objectives and knows the physical constraints. This knowledge is provided by the Pareto trade-off set obtained by single-objective optimization algorithms with a repeated optimization with different importance vectors. A mapping technique avoids non-feasible solutions with negative dwell weights and allows the use of constraint free gradient-based deterministic algorithms. We compare various such algorithms and methods which could improve their performance. This finally allows us to generate a large number of solutions in a few minutes. We use objectives expressed in terms of dose variances obtained from a few hundred sampling points in the planning target volume (PTV) and in organs at risk (OAR). We compare two- to four-dimensional Pareto fronts obtained with the deterministic algorithms and with a fast-simulated annealing algorithm. For PTV-based objectives, due to the convex objective functions, the obtained solutions are global optimal. If OARs are included, then the solutions found are also global optimal, although local minima may be present as suggested.

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.

A multiobjective gradient-based dose optimization algorithm for external beam conformal radiotherapy.

A multiobjective gradient-based algorithm has been developed for the purpose of dose distribution optimization in external beam conformal radiotherapy. This algorithm is based on the concept of gathering the values of all objectives into a single value. The weighting factors of the composite objective values are varied in different steps, allowing the reconstruction of the trade-off surfaces (three or more objectives) or curves (two objectives) which define the boundary between the feasible and non-feasible domain regions. The analysis of these curves allows the decision-maker to select the solution that best fits the clinical goals. In contrast to all the other algorithms, our method provides not a single solution but a sample of solutions representing all possible clinical importance factors (weights) for the objectives used. The application of this algorithm to two test cases shows that a correct selection for the importance factors to multiply the individual objectives in the global objective value is not trivial and that the location and shape of the boundary region between the feasible and non-feasible solution regions are case dependent. Provided that the individual objective functions are analytically differentiable and that the number of objectives is the range of two to three, the computation times are acceptable for clinical use. Furthermore, the optimization for a unique combination of importance factors within the aggregate objective function is performed in less than 1 min.

A new algorithm for autoreconstruction of catheters in computed tomography-based brachytherapy treatment planning.

This paper describes innovative software for automatic reconstruction, which we term autoreconstruction, of plastic and metallic brachytherapy catheters using computed tomography (CT) data. No such automatic facility has previously existed in any treatment planning software. The patient data consists of a set of post-implantation CT images with the catheters in situ in their final positions. This new software solves those difficulties which arise when the catheters are intersecting or when loop techniques are used. With the software algorithms, catheter reconstruction time is significantly reduced and accuracy is also improved when compared with that achieved using the classical manual method of CT-slice-by-CT-slice reconstruction.

Autoactivation of source dwell positions for HDR brachytherapy treatment planning.

The most accurate classical dose optimization algorithms in HDR brachytherapy strongly depend on an appropriate selection of source dwell positions which fulfill user-defined geometrical boundary conditions which are relative to patient anatomy. Most anatomical situations, such as for prostate and head and neck tumors, are complex and can require geometries with 5-15 catheters with 48 possible dwell positions per catheter depending on the tumor volume. The manual selection of dwell positions using visual checks by trial and error is very time consuming. This can only be improved by the use of a technique which automatically recognizes and selects the optimum dwell positions for each catheter. We have developed an algorithm, termed an autoactivation algorithm, which improves implant planning by providing a facility for the necessary automatic recognition of HDR source dwell positions.

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.

Dose-volume histograms computation comparisons using conventional methods and optimized fast Fourier transforms algorithms for brachytherapy.

In anatomy based optimization procedures for large volume implants the calculation of dose-volume histograms (DVH) accounts for the major part of the time involved and can be as long as a few hours. This time is proportional to the number of seeds or source dwell positions required for the implant. A procedure for the calculation of brachytherapy seed dose distribution calculation employing fast Fourier transforms (FFT) and the convolution theorem has been described by others and was supposed to significantly improve the speed of the dose distribution computation. Using new significantly improved FFT algorithms and various other optimization techniques we have compared the calculated differential and integral DVHs in high dose rate (HDR) brachytherapy with a single stepping source using actual clinical implants. This is so that we could assess the efficiency and accuracy of the FFT method with that of conventional methods. Our results showed that the FFT based method of calculating DVHs in brachytherapy is comparable in speed with conventional dose calculation methods, but only for implants with more than 287 sources. It is therefore of limited practical use even for large implants. This result is in direct opposition to the claim by other authors.

CT imaging based digitally reconstructed radiographs and their application in brachytherapy.

The aim of our study was to develop an algorithm to simulate the digitally reconstructed radiograph (DRR) calculation process for different beam qualities (photon energies) in the range 50 keV to 12 MeV. This was achieved using volumetric anatomical data for the patient obtained from three-dimensional diagnostic CT images. These DRR images can be used in three-dimensional treatment planning for external beam radiotherapy as well as for brachytherapy in the same way as conventional radiographic films. The advantages of using such DRRs in modern 3D brachytherapy treatment planning are shown. A number of tools are described, illustrating that the application of DRRs in brachytherapy is very useful.

Generation of uniformly distributed dose points for anatomy-based three-dimensional dose optimization methods in brachytherapy.

We have studied the accuracy of statistical parameters of dose distributions in brachytherapy using actual clinical implants. These include the mean, minimum and maximum dose values and the variance of the dose distribution inside the PTV (planning target volume), and on the surface of the PTV. These properties have been studied as a function of the number of uniformly distributed sampling points. These parameters, or the variants of these parameters, are used directly or indirectly in optimization procedures or for a description of the dose distribution. The accurate determination of these parameters depends on the sampling point distribution from which they have been obtained. Some optimization methods ignore catheters and critical structures surrounded by the PTV or alternatively consider as surface dose points only those on the contour lines of the PTV. D(min) and D(max) are extreme dose values which are either on the PTV surface or within the PTV. They must be avoided for specification and optimization purposes in brachytherapy. Using D(mean) and the variance of D which we have shown to be stable parameters, achieves a more reliable description of the dose distribution on the PTV surface and within the PTV volume than does D(min) and D(max). Generation of dose points on the real surface of the PTV is obligatory and the consideration of catheter volumes results in a realistic description of anatomical dose distributions.

Catheter autoreconstruction in computed tomography based brachytherapy treatment planning.

The aim of this study is to develop an automatic reconstruction of brachytherapy catheters using CT (computed tomography) data. Previously no such automatic facility has existed in any treatment planning software. To achieve this facility we have developed tools for the automatic reconstruction (which we term autoreconstruction) of plastic and metallic catheters. These algorithms overcome a number of difficulties which arise when a large number of catheters are present. These include situations with intersecting catheters and with loop techniques. The time required for the catheter reconstruction process using our autoreconstruction method is significantly reduced. The accuracy of our autoreconstruction is at least as high as the classical manual slice-by-slice method.

Anatomy-based three-dimensional dose optimization in brachytherapy using multiobjective genetic algorithms.

In conventional dose optimization algorithms, in brachytherapy, multiple objectives are expressed in terms of an aggregating function which combines individual objective values into a single utility value, making the problem single objective, prior to optimization. A multiobjective genetic algorithm (MOGA) was developed for dose optimization based on an a posteriori approach, leaving the decision-making process to a planner and offering a representative trade-off surface of the various objectives. The MOGA provides a flexible search engine which provides the maximum of information for a decision maker. Tests performed with various treatment plans in brachytherapy have shown that MOGA gives solutions which are superior to those of traditional dose optimization algorithms. Objectives were proposed in terms of the COIN distribution and differential volume histograms, taking into account patient anatomy in the optimization process.