On the visualization of universal degeneracy in the IMRT problem

BACKGROUND: In general, the IMRT optimisation problem possesses many equivalent solutions. This makes it difficult to decide whether a result produced by an IMRT planning algorithm can be further improved, e.g. by adding more beams, or whether it is close to the globally best solution. RESULTS: It is conjectured that the curvature properties of the objective function around any globally optimum dose distribution are universal. This allows an assessment of optimality of dose distributions that are generated by different beam arrangements in a complementary manner to the objective function value alone. A tool to visualize the curvature structure of the objective function is devised. CONCLUSION: In an example case, it is demonstrated how the assessment of the curvature space can indicate the equivalence of rival beam configurations and their proximity to the global optimum

Beam Orientation Optimization for Intensity Modulated Radiation Therapy using Adaptive l1 Minimization

Beam orientation optimization (BOO) is a key component in the process of IMRT treatment planning. It determines to what degree one can achieve a good treatment plan quality in the subsequent plan optimization process. In this paper, we have developed a BOO algorithm via adaptive l_1 minimization. Specifically, we introduce a sparsity energy function term into our model which contains weighting factors for each beam angle adaptively adjusted during the optimization process. Such an energy term favors small number of beam angles. By optimizing a total energy function containing a dosimetric term and the sparsity term, we are able to identify the unimportant beam angles and gradually remove them without largely sacrificing the dosimetric objective. In one typical prostate case, the convergence property of our algorithm, as well as the how the beam angles are selected during the optimization process, is demonstrated. Fluence map optimization (FMO) is then performed based on the optimized beam angles. The resulted plan quality is presented and found to be better than that obtained from unoptimized (equiangular) beam orientations. We have further systematically validated our algorithm in the contexts of 5-9 coplanar beams for 5 prostate cases and 1 head and neck case. For each case, the final FMO objective function value is used to compare the optimized beam orientations and the equiangular ones. It is found that, our BOO algorithm can lead to beam configurations which attain lower FMO objective function values than corresponding equiangular cases, indicating the effectiveness of our BOO algorithm.Comment: 19 pages, 2 tables, and 5 figure

Costlets: A Generalized Approach to Cost Functions for Automated Optimization of IMRT Treatment Plans

We present the creation and use of a generalized cost function methodology based on costlets for automated optimization for conformal and intensity modulated radiotherapy treatment plans. In our approach, cost functions are created by combining clinically relevant “costlets”. Each costlet is created by the user, using an “evaluator” of the plan or dose distribution which is incorporated into a function or “modifier” to create an individual costlet. Dose statistics, dose-volume points, biological model results, non-dosimetric parameters, and any other information can be converted into a costlet. A wide variety of different types of costlets can be used concurrently. Individual costlet changes affect not only the results for that structure, but also all the other structures in the plan (e.g., a change in a normal tissue costlet can have large effects on target volume results as well as the normal tissue). Effective cost functions can be created from combinations of dose-based costlets, dose-volume costlets, biological model costlets, and other parameters. Generalized cost functions based on costlets have been demonstrated, and show potential for allowing input of numerous clinical issues into the optimization process, thereby helping to achieve clinically useful optimized plans. In this paper, we describe and illustrate the use of the costlets in an automated planning system developed and used clinically at the University of Michigan Medical Center. We place particular emphasis on the flexibility of the system, and its ability to discover a variety of plans making various trade-offs between clinical goals of the treatment that may be difficult to meet simultaneously.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47484/1/11081_2005_Article_2066.pd

Respiratory motion models built using MR-derived signals and different amounts of MR image data from multi-slice acquisitions

MR-Linacs provide 2D cine-MR images capturing respiratory motion before and during radiotherapy treatment. Surrogate-driven respiratory motion models can estimate the 3D motion of tumour and organs-at-risk with high spatio-temporal resolution using surrogate signals extracted from 2D cine-MR images. Our motion modelling framework fits the model to unsorted 2D images producing a correspondence model and a motion-compensated super-resolution reconstruction (MCSR). This study investigates the effect of the training data size used to build the respiratory motion models, since long acquisition and processing times limit their application for MR-guided radiotherapy. Four volunteers were scanned on a 1.5T MR scanner with a 3-minute interleaved multi-slice acquisition of 2x2x10mm3 surrogate and motion images, repeated 10 times: sagittal surrogate images from a fixed location, sagittal and coronal motion images covering the thorax. Two surrogate signals were generated by applying principal component analysis to the deformation fields obtained from registering the surrogate images. For each volunteer we built motion models using data from 1, 3, 5, and 10 repetitions, generating a 2x2x2mm3 MCSR. We reconstructed super-resolution images without motion compensation (no-MCSR) to show the improvement obtained with the models. Visual assessment showed plausible estimated respiratory motion with breath-to-breath variations. We computed intensity profiles along the boundary between diaphragm and lung to assess the image quality of the super-resolution reconstructions. We calculated the mean absolute difference (MAD) between the training motion images and the corresponding model-simulated images, averaged over all images and volunteers. The MCSRs presented sharper intensity profiles than no-MCSRs indicating successful motion compensation. MAD increases with the number of repetitions and without motion compensation (for MCSRs/no-MCSRs: 2.10/2.40 with 1 repetition, 2.33/2.56 with 10 repetitions). Computational times to build the models without GPU implementation ranged from ~30 (1 repetition) to ~380 minutes (10 repetitions). Promising results indicated the feasibility of short acquisition and processing times

Evaluation of MRI-derived surrogate signals to model respiratory motion

An MR-Linac can provide motion information of tumour and organs-at-risk before, during, and after beam delivery. However, MR imaging cannot provide real-time high-quality volumetric images which capture breath-to-breath variability of respiratory motion. Surrogate-driven motion models relate the motion of the internal anatomy to surrogate signals, thus can estimate the 3D internal motion from these signals. Internal surrogate signals based on patient anatomy can be extracted from 2D cine-MR images, which can be acquired on an MR-Linac during treatment, to build and drive motion models. In this paper we investigate different MRI-derived surrogate signals, including signals generated by applying principal component analysis to the image intensities, or control point displacements derived from deformable registration of the 2D cine-MR images. We assessed the suitability of the signals to build models that can estimate the motion of the internal anatomy, including sliding motion and breath-to-breath variability. We quantitatively evaluated the models by estimating the 2D motion in sagittal and coronal slices of 8 lung cancer patients, and comparing them to motion measurements obtained from image registration. For sagittal slices, using the first and second principal components on the control point displacements as surrogate signals resulted in the highest model accuracy, with a mean error over patients around 0.80 mm which was lower than the in-plane resolution. For coronal slices, all investigated signals except the skin signal produced mean errors over patients around 1 mm. These results demonstrate that surrogate signals derived from 2D cine-MR images, including those generated by applying principal component analysis to the image intensities or control point displacements, can accurately model the motion of the internal anatomy within a single sagittal or coronal slice. This implies the signals should also be suitable for modelling the 3D respiratory motion of the internal anatomy

Evaluation of MRI-derived surrogate signals to model respiratory motion.

An MR-Linac can provide motion information of tumour and organs-at-risk before, during, and after beam delivery. However, MR imaging cannot provide real-time high-quality volumetric images which capture breath-to-breath variability of respiratory motion. Surrogate-driven motion models relate the motion of the internal anatomy to surrogate signals, thus can estimate the 3D internal motion from these signals. Internal surrogate signals based on patient anatomy can be extracted from 2D cine-MR images, which can be acquired on an MR-Linac during treatment, to build and drive motion models. In this paper we investigate different MRI-derived surrogate signals, including signals generated by applying principal component analysis to the image intensities, or control point displacements derived from deformable registration of the 2D cine-MR images. We assessed the suitability of the signals to build models that can estimate the motion of the internal anatomy, including sliding motion and breath-to-breath variability. We quantitatively evaluated the models by estimating the 2D motion in sagittal and coronal slices of 8 lung cancer patients, and comparing them to motion measurements obtained from image registration. For sagittal slices, using the first and second principal components on the control point displacements as surrogate signals resulted in the highest model accuracy, with a mean error over patients around 0.80 mm which was lower than the in-plane resolution. For coronal slices, all investigated signals except the skin signal produced mean errors over patients around 1 mm. These results demonstrate that surrogate signals derived from 2D cine-MR images, including those generated by applying principal component analysis to the image intensities or control point displacements, can accurately model the motion of the internal anatomy within a single sagittal or coronal slice. This implies the signals should also be suitable for modelling the 3D respiratory motion of the internal anatomy