Mark Bangert

Shared data for intensity modulated radiation therapy (IMRT) optimization research: the CORT dataset

BackgroundWe provide common datasets (which we call the CORT dataset: common optimization for radiation therapy) that researchers can use when developing and contrasting radiation treatment planning optimization algorithms. The datasets allow researchers to make one-to-one comparisons of algorithms in order to solve various instances of the radiation therapy treatment planning problem in intensity modulated radiation therapy (IMRT), including beam angle optimization, volumetric modulated arc therapy and direct aperture optimization.ResultsWe provide datasets for a prostate case, a liver case, a head and neck case, and a standard IMRT phantom. We provide the dose-influence matrix from a variety of beam/couch angle pairs for each dataset. The dose-influence matrix is the main entity needed to perform optimizations: it contains the dose to each patient voxel from each pencil beam. In addition, the original Digital Imaging and Communications in Medicine (DICOM) computed tomography (CT) scan, as well as the DICOM structure file, are provided for each case.ConclusionsHere we present an open dataset – the first of its kind – to the radiation oncology community, which will allow researchers to compare methods for optimizing radiation dose delivery.

Performance-optimized clinical IMRT planning on modern CPUs.

Intensity modulated treatment plan optimization is a computationally expensive task. The feasibility of advanced applications in intensity modulated radiation therapy as every day treatment planning, frequent re-planning for adaptive radiation therapy and large-scale planning research severely depends on the runtime of the plan optimization implementation. Modern computational systems are built as parallel architectures to yield high performance. The use of GPUs, as one class of parallel systems, has become very popular in the field of medical physics. In contrast we utilize the multi-core central processing unit (CPU), which is the heart of every modern computer and does not have to be purchased additionally. In this work we present an ultra-fast, high precision implementation of the inverse plan optimization problem using a quasi-Newton method on pre-calculated dose influence data sets. We redefined the classical optimization algorithm to achieve a minimal runtime and high scalability on CPUs. Using the proposed methods in this work, a total plan optimization process can be carried out in only a few seconds on a low-cost CPU-based desktop computer at clinical resolution and quality. We have shown that our implementation uses the CPU hardware resources efficiently with runtimes comparable to GPU implementations, at lower costs.

Spherical cluster analysis for beam angle optimization in intensity-modulated radiation therapy treatment planning

An intuitive heuristic to establish beam configurations for intensity-modulated radiation therapy is introduced as an extension of beam ensemble selection strategies applying scalar scoring functions. It is validated by treatment plan comparisons for three intra-cranial, pancreas, and prostate cases each. Based on a patient specific matrix listing the radiological quality of candidate beam directions individually for every target voxel, a set of locally ideal beam angles is generated. The spherical distribution of locally ideal beam angles is characteristic for every treatment site and patient: ideal beam angles typically cluster around distinct orientations. We interpret the cluster centroids, which are identified with a spherical K-means algorithm, as irradiation angles of an intensity-modulated radiation therapy treatment plan. The fluence profiles are subsequently optimized during a conventional inverse planning process. The average computation time for the pre-optimization of a beam ensemble is six minutes on a state-of-the-art work station. The treatment planning study demonstrates the potential benefit of the proposed beam angle optimization strategy. For the three prostate cases under investigation, the standard treatment plans applying nine coplanar equi-spaced beams and treatment plans applying an optimized non-coplanar nine-beam ensemble yield clinically comparable dose distributions. For symmetric patient geometries, the dose distribution formed by nine equi-spaced coplanar beams cannot be improved significantly. For the three pancreas and intra-cranial cases under investigation, the optimized non-coplanar beam ensembles enable better sparing of organs at risk while guaranteeing equivalent target coverage. Beam angle optimization by spherical cluster analysis shows the biggest impact for target volumes located asymmetrically within the patient and close to organs at risk.

Characterizing the combinatorial beam angle selection problem

The beam angle selection (BAS) problem in intensity-modulated radiation therapy is often interpreted as a combinatorial optimization problem, i.e. finding the best combination of η beams in a discrete set of candidate beams. It is well established that the combinatorial BAS problem may be solved efficiently with metaheuristics such as simulated annealing or genetic algorithms. However, the underlying parameters of the optimization process, such as the inclusion of non-coplanar candidate beams, the angular resolution in the space of candidate beams, and the number of evaluated beam ensembles as well as the relative performance of different metaheuristics have not yet been systematically investigated. We study these open questions in a meta-analysis of four strategies for combinatorial optimization in order to provide a reference for future research related to the BAS problem in intensity-modulated radiation therapy treatment planning. We introduce a high-performance inverse planning engine for BAS. It performs a full fluence optimization for ≈3600 treatment plans per hour while handling up to 50 GB of dose influence data (≈1400 candidate beams). For three head and neck patients, we compare the relative performance of a genetic, a cross-entropy, a simulated annealing and a naive iterative algorithm. The selection of ensembles with 5, 7, 9 and 11 beams considering either only coplanar or all feasible candidate beams is studied for an angular resolution of 5°, 10°, 15° and 20° in the space of candidate beams. The impact of different convergence criteria is investigated in comparison to a fixed termination after the evaluation of 10 000 beam ensembles. In total, our simulations comprise a full fluence optimization for about 3000 000 treatment plans. All four combinatorial BAS strategies yield significant improvements of the objective function value and of the corresponding dose distributions compared to standard beam configurations with equi-spaced coplanar beams. The genetic and the cross-entropy algorithms showed faster convergence in the very beginning of the optimization but the simulated annealing algorithm eventually arrived at almost the same objective function values. These three strategies typically yield clinically equivalent treatment plans. The iterative algorithm showed the worst convergence properties. The choice of the termination criterion had a stronger influence on the performance of the simulated annealing algorithm than on the performance of the genetic and the cross-entropy algorithms. We advocate to terminate the optimization process after the evaluation of 1000 beam combinations without objective function decrease. For our simulations, this resulted in an average deviation of the objective function from the reference value after 10 000 evaluated beam ensembles of 0.5% for all metaheuristics. On average, there was only a minor improvement when increasing the angular resolution in the space of candidate beam angles from 20° to 5°. However, we observed significant improvements when considering non-coplanar candidate beams for challenging head and neck cases.

Comparison of beam angle selection strategies for intracranial IMRT.

PURPOSE Various strategies to select beneficial beam ensembles for intensity-modulated radiation therapy (IMRT) have been suggested over the years. These beam angle selection (BAS) strategies are usually evaluated against reference configurations applying equispaced coplanar beams but they are not compared to one another. Here, the authors present a meta analysis of four BAS strategies that incorporates fluence optimization (FO) into BAS by combinatorial optimization (CO) and one BAS strategy that decouples FO from BAS, i.e., spherical cluster analysis (SCA). The underlying parameters of the BAS process are investigated and the dosimetric benefits of the BAS strategies are quantified. METHODS For three intracranial lesions in proximity to organs at risk (OARs) the authors compare treatment plans applying equispaced coplanar beam ensembles with treatment plans using five different BAS strategies, i.e., four CO techniques and SCA, to establish coplanar and noncoplanar beam ensembles. Treatment plans applying 5, 7, 9, and 11 beams are investigated. For the CO strategies the authors perform BAS runs with a 5°, 10°, 15°, and 20° angular resolution, which corresponds to a minimum of 18 coplanar and a maximum of 1400 noncoplanar candidate beams. In total 272 treatment plans with different BAS settings are generated for every patient. The quality of the treatment plans is compared based on the protection of OARs yet integral dose, target homogeneity, and target conformity are also considered. RESULTS It is possible to reduce the average mean and maximum doses in OARs by more than 4 Gy (1 Gy) with optimized noncoplanar (coplanar) beam ensembles found with BAS by CO or SCA. For BAS including FO by CO, the individual algorithm used and the angular resolution in the space of candidate beams does not have a crucial impact on the quality of the resulting treatment plans. All CO algorithms yield similar target conformity and slightly improved target homogeneity in comparison to equispaced coplanar setups. Furthermore, optimized coplanar (noncoplanar) beam ensembles enabled more than a 6% (5%) reduction of the integral dose. For SCA, however, integral dose was increased and target conformity was decreased in comparison to equispaced coplanar setups-especially for a small number of beams. CONCLUSION Both BAS strategies incorporating FO by CO and independent BAS strategies excluding FO provide dose savings in OARs for optimized coplanar and especially noncoplanar beam ensembles; they should not be neglected in the clinic.

Using an Infinite Von Mises-Fisher Mixture Model to Cluster Treatment Beam Directions in External Radiation Therapy

We present a method for fully automated selection of treatment beam ensembles for external radiation therapy. We reformulate the beam angle selection problem as a clustering problem of locally ideal beam orientations distributed on the unit sphere. For this purpose we construct an infinite mixture of von Mises-Fisher distributions, which is suited in general for density estimation from data on the D-dimensional sphere. Using a nonparametric Dirichlet process prior, our model infers probability distributions over both the number of clusters and their parameter values. We describe an efficient Markov chain Monte Carlo inference algorithm for posterior inference from experimental data in this model. The performance of the suggested beam angle selection framework is illustrated for one intra-cranial, pancreas, and prostate case each. The infinite von Mises-Fisher mixture model (iMFMM) creates between 18 and 32 clusters, depending on the patient anatomy. This suggests to use the iMFMM directly for beam ensemble selection in robotic radio surgery, or to generate low-dimensional input for both subsequent optimization of trajectories for arc therapy and beam ensemble selection for conventional radiation therapy.

Analytical probabilistic modeling for radiation therapy treatment planning

This paper introduces the concept of analytical probabilistic modeling (APM) to quantify uncertainties in quality indicators of radiation therapy treatment plans. Assuming Gaussian probability densities over the input parameters of the treatment plan quality indicators, APM enables the calculation of the moments of the induced probability density over the treatment plan quality indicators by analytical integration. This paper focuses on analytical probabilistic dose calculation algorithms and the implications of APM regarding treatment planning. We derive closed-form expressions for the expectation value and the (co)variance of (1) intensity-modulated photon and proton dose distributions based on a pencil beam algorithm and (2) the standard quadratic objective function used in inverse planning. Complex correlation models of high dimensional uncertain input parameters and the different nature of random and systematic uncertainties in fractionated radiation therapy are explicitly incorporated into APM. APM variance calculations on phantom data sets show that the correlation assumptions and the difference of random and systematic uncertainties of the input parameters have a crucial impact on the uncertainty of the resulting dose. The derivations regarding the quadratic objective function show that APM has the potential to enable robust planning at almost the same computational cost like conventional inverse planning after a single probabilistic dose calculation. Beneficial applications of APM in the context of radiation therapy treatment planning are feasible.

Optimization approaches to volumetric modulated arc therapy planning

Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed.

Characterization of a mini-multileaf collimator in a proton beamline

A mini-multileaf collimator (MMLC) was mounted as a field shaping collimator in a proton beamline at the Massachusetts General Hospital. The purpose is to evaluate the devices dosimetric and mechanical properties for the use in a proton beamline. For this evaluation, the authors compared MMLC and brass aperture shaped dose distributions with regard to lateral and depth dose properties. The lateral fall off is generally broader with the MMLC, with difference varying with proton range from 0.2 to 1.2 mm. Central axis depth dose curves did not show a difference in peak-to-entrance ratio, peak width, distal fall off, or range. Two-dimensional dose distributions to investigate the conformity of MMLC shaped doses show that the physical leaf width of approximately 2.5 mm does not have a significant impact. All differences seen in dose distribution shaped by the MMLC versus brass apertures were shown to be clinically insignificant. Measured neutron doses of 0.03-0.13 mSv/Gy for a closed brass beam block (depending on range) are very low compared to the previously published data. Irradiation of the tungsten MMLC, however, produced 1.5-1.8 times more neutrons than brass apertures. Exposure of the staff resulting from activation of the device is below regulatory limits. The measurements established an equivalency between aperture and MMLC shaped dose distributions.

Development of the open‐source dose calculation and optimization toolkit matRad

Purpose We report on the development of the open‐source cross‐platform radiation treatment planning toolkit matRad and its comparison against validated treatment planning systems. The toolkit enables three‐dimensional intensity‐modulated radiation therapy treatment planning for photons, scanned protons and scanned carbon ions. Methods matRad is entirely written in Matlab and is freely available online. It re‐implements well‐established algorithms employing a modular and sequential software design to model the entire treatment planning workflow. It comprises core functionalities to import DICOM data, to calculate and optimize dose as well as a graphical user interface for visualization. matRad dose calculation algorithms (for carbon ions this also includes the computation of the relative biological effect) are compared against dose calculation results originating from clinically approved treatment planning systems. Results We observe three‐dimensional γ‐analysis pass rates ≥ 99.67% for all three radiation modalities utilizing a distance to agreement of 2 mm and a dose difference criterion of 2%. The computational efficiency of matRad is evaluated in a treatment planning study considering three different treatment scenarios for every radiation modality. For photons, we measure total run times of 145 s–1260 s for dose calculation and fluence optimization combined considering 4–72 beam orientations and 2608–13597 beamlets. For charged particles, we measure total run times of 63 s–993 s for dose calculation and fluence optimization combined considering 9963–45574 pencil beams. Using a CT and dose grid resolution of 0.3 cm3 requires a memory consumption of 1.59 GB–9.07 GB and 0.29 GB–17.94 GB for photons and charged particles, respectively. Conclusion The dosimetric accuracy, computational performance and open‐source character of matRad encourages a future application of matRad for both educational and research purposes.