Application of constrained optimization to radiotherapy planning

Variability of Low-Z Inhomogeneity Correction in IMRT/SBRT: A Multi-Institutional Collaborative Study

Dose-calculation algorithms are critical for radiation treatment outcomes that vary among treatment planning systems (TPS). Modern algorithms use sophisticated radiation transport calculation with detailed three-dimensional beam modeling to provide accurate doses, especially in heterogeneous medium and small fields used in IMRT/SBRT. While the dosimetric accuracy in heterogeneous mediums (lung) is qualitatively known, the accuracy is unknown. The aim of this work is to analyze the calculated dose in lung patients and compare the validity of dose-calculation algorithms by measurements in a low-Z phantom for two main classes of algorithms: type A (pencil beam) and type B (collapse cone). The CT scans with volumes (target and organs at risk, OARs) of a lung patient and a phantom build to replicate the human lung data were sent to nine institutions for planning. Doses at different depths and field sizes were measured in the phantom with and without inhomogeneity correction across multiple institutions to understand the impact of clinically used dose algorithms. Wide dosimetric variations were observed in target and OAR coverage in patient plans. The correction factor for collapsed cone algorithms was less than pencil beam algorithms in the small fields used in SBRT. The pencil beam showed ≈70% variations between measured and calculated correction factors for various field sizes and depths. For large field sizes the trends of both types of algorithms were similar. The differences in measured versus calculated dose for type-B algorithms were within ±10%. Significant variations in the target and OARs were observed among various TPS. The results suggest that the pencil beam algorithm does not provide an accurate dose and should not be considered with small fields (IMRT/SBRT). Type-B collapsed-cone algorithms provide better agreement with measurements, but still vary among various systems.

Frontiers in planning optimization for lung SBRT

Emerging data are showing the safety and the efficacy of Stereotactic Body Radiation therapy (SBRT) in lung cancer management. In this context, the very high doses delivered to the Planning Target Volume, make the planning phase essential for achieving high dose levels conformed to the shape of the target in order to have a good prognosis for tumor control and to avoid an overdose in relevant healthy adjacent tissue. In this non-systematic review we analyzed the technological and the physics aspects of SBRT planning for lung cancer. In particular, the aims of the study were: (i) to evaluate prescription strategies (homogeneous or inhomogeneous), (ii) to outline possible geometrical solutions by comparing the dosimetric results (iii) to describe the technological possibilities for a safe and effective treatment, (iv) to present the issues concerning radiobiological planning and the automation of the planning process.

Reduced-order constrained optimization (ROCO): clinical application to head-and-neck IMRT

PURPOSE

The authors present the application of the reduced order constrained optimization (ROCO) method, previously successfully applied to the prostate and lung sites, to the head-and-neck (H&N) site, demonstrating that it can quickly and automatically generate clinically competitive IMRT plans. We provide guidelines for applying ROCO to larynx, oropharynx, and nasopharynx cases, and report the results of a live experiment that demonstrates how an expert planner can save several hours of trial-and-error interaction using the proposed approach.

METHODS

The ROCO method used for H&N IMRT planning consists of three major steps. First, the intensity space of treatment plans is sampled by solving a series of unconstrained optimization problems with a parameter range based on previously treated patient data. Second, the dominant modes in the intensity space are estimated by dimensionality reduction using principal component analysis (PCA). Third, a constrained optimization problem over this basis is quickly solved to find an IMRT plan that meets organ-at-risk (OAR) and target coverage constraints. The quality of the plan is assessed using evaluation tools within Memorial Sloan-Kettering Cancer Center (MSKCC)'s treatment planning system (TPS).

RESULTS

The authors generated ten H&N IMRT plans for previously treated patients using the ROCO method and processed them for deliverability by a dynamic multileaf collimator (DMLC). The authors quantitatively compared the ROCO plans to the previously achieved clinical plans using the TPS tools used at MSKCC, including DVH and isodose contour analysis, and concluded that the ROCO plans would be clinically acceptable. In our current implementation, ROCO H&N plans can be generated using about 1.6 h of offline computation followed by 5-15 min of semiautomatic planning time. Additionally, the authors conducted a live session for a plan designated by MSKCC performed together with an expert H&N planner. A technical assistant set up the first two steps, which were performed without further human interaction, and then collaborated in a virtual meeting with the expert planner to perform the third (constrained optimization) step. The expert planner performed in-depth analysis of the resulting ROCO plan and deemed it to be clinically acceptable and in some aspects superior to the clinical plan. This entire process took 135 min including two constrained optimization runs, in comparison to the estimated 4 h that would have been required using traditional clinical planning tools.

CONCLUSIONS

The H&N site is very challenging for IMRT planning, due to several levels of prescription and a large, variable number (6-20) of OARs that depend on the location of the tumor. ROCO for H&N shows promise in generating clinically acceptable plans both more quickly and with substantially less human interaction.

Multibeam tomotherapy: a new treatment unit devised for multileaf collimation, intensity-modulated radiation therapy

A fully integrated system for treatment planning, application, and verification for automated multileaf collimator (MLC) based, intensity-modulated, image-guided, and adaptive radiation therapy (IMRT, IGRT and ART, respectively) is proposed. Patient comfort, which was the major development goal, will be achieved through a new unit design and short treatment times. Our device for photon beam therapy will consist of a new dual energy linac with five fixed treatment heads positioned evenly along one plane but one electron beam generator only. A minimum of moving parts increases technical reliability and reduces motion times to a minimum. Motion is allowed solely for the MLCs, the robotic patient table, and the small angle gantry rotation of +/- 36 degrees. Besides sophisticated electron beam guidance, this compact setup can be built using existing modules. The flattening-filter-free treatment heads are characterized by reduced beam-on time and contain apertures restricted in one dimension to the area of maximum primary fluence output. In the case of longer targets, this leads to a topographic intensity modulation, thanks to the combination of "step and shoot" MLC delivery and discrete patient couch motion. Owing to the limited number of beam directions, this multislice cone beam serial tomotherapy is referred to as "multibeam tomotherapy." Every patient slice is irradiated by one treatment head at any given moment but for one subfield only. The electron beam is then guided to the next head ready for delivery, while the other heads are preparing their leaves for the next segment. The "Multifocal MLC-positioning" algorithm was programmed to enable treatment planning and optimize treatment time. We developed an overlap strategy for the longitudinally adjacent fields of every beam direction, in doing so minimizing the field match problem and the effects of possible table step errors. Clinical case studies show for the same or better planning target volume coverage, better organ-at-risk sparing, and comparable mean integral dose to the normal tissue a reduction in treatment time by more than 50% to only a few minutes in comparison to high-quality 3-D conformal and IMRT treatments. As a result, it will be possible to incorporate features for better patient positioning and image guidance, while sustaining reasonable overall treatment times at the same time. The virtual multibeam tomotherapy design study TOM'5-CT contains a dedicated electron beam CT (TOM'AGE) and an objective optical topometric patient positioning system (TOPOS). Thanks to the wide gantry bore of 120 cm and slim gantry depths of 70 cm, patients can be treated very comfortably, in all cases tumor-isocentrically, as well as with noncoplanar beam arrangements as in stereotactic radiosurgery with a couch rotation of up to +/- 54 degrees. The TOM'5 treatment unit on which this theoretical concept is based has a stand-alone depth of 40 cm and an outer diameter of 245 cm; the focus-isocenter distance of the heads is 100 cm with a field size of 40 cm x 7 cm and 0.5 cm leaves, which operate perpendicular to the axis of table motion.

A Feasible Application of Constrained Optimization in the IMRT System

The planning of intensity modulated radiation therapy cancer treatment poses an inverse problem and is usually solved by optimization methods. Treatment planning, in a majority of cases, requires restrictions to be imposed on the healthy organs, sensitive to the radiation, which justifies the use of constrained optimization. The application of these techniques in treatment planning usually involves serious complications and limitations due to the huge number of variables appearing in the planning process. This leads to large computation times and memory requirements. In this paper, strategies and algorithmic issues are proposed in order to cope with these limitations. The proposed methods have been applied and tested in real cases of prostate cancer, obtaining satisfactory results regarding computational limitations.

History of tomotherapy

Tomotherapy is the delivery of intensity modulated radiation therapy using rotational delivery of a fan beam in the manner of a CT scanner. In helical tomotherapy the couch and gantry are in continuous motion akin to a helical CT scanner. Helical tomotherapy is inherently capable of acquiring CT images of the patient in treatment position and using this information for image guidance. This review documents technological advancements of the field concentrating on the conceptual beginnings through to its first clinical implementation. The history of helical tomotherapy is also a story of technology migration from academic research to a university-industrial partnership, and finally to commercialization and widespread clinical use.

A comparison of two commercial treatment-planning systems to IMRT

This study compared the clinical functionality of BrainSCAN (BrainLAB) and Helios (Eclipse, Varian) for intensity-modulated radiation therapy (IMRT) treatment planning with the aim of identifying practical and technical issues. The study considered implementation and commissioning, dose optimization, and plan assessment. Both systems were commissioned for the same 6 MV photon beam equipped with a high-resolution multileaf collimator (Varian Millennium 120 leaf). The software was applied to three test plans having identical imaging and contour data. Analysis considered 3D axial dose distributions, dose-volume histograms, and monitor unit calculations. Each system requires somewhat different input data to characterize the beam prior to use, so the same data cannot be used for commissioning. In addition, whereas measured beam data was entered directly into Helios with minimal data processing, the BrainSCAN system required configured beam data to be sent to BrainLAB before clinical use. One key difference with respect to system commissioning was that BrainSCAN required high resolution data, which necessitated the use of detectors with small active volumes. This difference was found to impact on the ability of the systems to accurately calculate dose for highly modulated fields, with BrainSCAN being more successful than Helios. In terms of functionality, the BrainSCAN system uses a dynamically penalized likelihood inverse planning algorithm and calculates four plans at once with various relative weighting of the planning target and organ-at-risk volumes. Helios uses a gradient algorithm that allows the user to make changes to some of the input parameters during optimization. An analysis of the dosimetry output shows that, although the systems are different in many respects, they are each capable of producing substantially equivalent dose plans in terms of target coverage and normal tissue sparing.

Investigation of using a power function as a cost function in inverse planning optimization

The purpose of this paper is to investigate the use of a power function as a cost function in inverse planning optimization. The cost function for each structure is implemented as an exponential power function of the deviation between the resultant dose and prescribed or constrained dose. The total cost function for all structures is a summation of the cost function of every structure. When the exponents of all terms in the cost function are set to 2, the cost function becomes a classical quadratic cost function. An independent optimization module was developed and interfaced with a research treatment planning system from the University of North Carolina for dose calculation and display of results. Three clinical cases were tested for this study with various exponents set for tumor targets and sensitive structures. Treatment plans with these exponent settings were compared, using dose volume histograms. The results of our study demonstrated that using an exponent higher than 2 in the cost function for the target achieved better dose homogeneity than using an exponent of 2. An exponent higher than 2 for serial sensitive structures can effectively reduce the maximum dose. Varying the exponent from 2 to 4 resulted in the most effective changes in dose volume histograms while the change from 4 to 8 is less drastic, indicating a situation of saturation. In conclusion, using a power function with exponent greater than 2 as a cost function can effectively achieve homogeneous dose inside the target and/or minimize maximum dose to the critical structures.

Penalized likelihood fluence optimization with evolutionary components for intensity modulated radiation therapy treatment planning

A novel iterative penalized likelihood algorithm with evolutionary components for the optimization of beamlet fluences for intensity modulated radiation therapy (IMRT) is presented. This algorithm is designed to be flexible in terms of the objective function and automatically escalates dose, as long as the objective function increases and all constraints are met. For this study, the objective function employed was the product of target equivalent uniform dose (EUD) and fraction of target tissue within set homogeneity constraints. The likelihood component of the algorithm iteratively attempts to minimize the mean squared error between a homogeneous dose prescription and the actual target dose distribution. The updated beamlet fluences are then adjusted via a quadratic penalty function that is based on the dose-volume histogram (DVH) constraints of the organs at risk. The evolutionary components were included to prevent the algorithm from converging to a local maximum. The algorithm was applied to a prostate cancer dataset, with especially difficult DVH constraints on bladder, rectum, and femoral heads. Dose distributions were generated for manually selected sets of three-, four-, five-, and seven-field treatment plans. Additionally, a global search was performed to find the optimal orientations for an axial three-beam plan. The results from this optimal orientation set were compared to results for manually selected orientation (gantry angle) sets of 3- (0 degrees, 90 degrees, 270 degrees), 4- (0 degrees, 90 degrees, 180 degrees, 270 degrees), 5- (0 degrees, 50 degrees, 130 degrees, 230 degrees, 310 degrees), and 7- (0 degrees, 40 degrees, 90 degrees, 140 degrees, 230 degrees, 270 degrees, 320 degrees) field axial treatment plans. For all the plans generated, all DVH constraints were met and average optimization computation time was approximately 30 seconds. For the manually selected orientations, the algorithm was successful in providing a relatively homogeneous target dose distribution, while simultaneously satisfying dose-volume limits by diverting dose away from proximal critical structures. The global search for an optimal three-beam orientation set yielded gantry angles of 70 degrees, 170 degrees, and 320 degrees. The EUD for this orientation set was 58 Gy, with 96% of the target within the set upper and lower limits. In comparison, optimized EUDs for the manually selected orientation sets of three, four, five and seven beams were 52.3, 52.6, 56.9, and 61.3 Gy, respectively. The orientation optimized three-beam plan yielded higher EUDs than the manually selected three-, four-, and five-beam plans, but lower EUDs than the seven-beam plan. In conclusion, a novel penalized likelihood algorithm with evolutionary components has successfully been implemented to optimize beamlet fluences for IMRT. Initial results are promising for dose conformity and uniformity of dose to target. When combined with optimal beam orientation selection for prostate cancer treatment planning, the results indicate that plans with a small number of optimized beam orientations achieve results comparable to those with a larger number of conventionally oriented beams.

[Optimization criteria in intensity-modulated radiotherapy]

The present paper provides an overview on the inverse treatment planning for the assessment of intensity-modulated fields. The problem is to find the optimal dose distribution for given attributes of the irradiated tissue. The attributes of the optimal dose distribution are delineated by an objective function. In practice, models are used that evaluate the physical dose distribution, either directly or through their radiobiological effects. In the simplest case, the squared deviation of the achieved dose distribution is minimized to the prescribed dose distribution. For organs structured in parallel, it is common to introduce dose-volume constraints. Another approach is to optimize a value for the probability of complication-free tumor control. The complication probability for normal tissue, in turn, is a rather complex function. However, using the relative seriality, a simple model can be devised with a certain approximation. Other models of "effective dose" are also presented.

Role of advanced 2 and 3-dimensional ultrasound for detecting prostate cancer

PURPOSE

We explored the clinical usefulness of spectrum analysis and neural networks for classifying prostate tissue and identifying prostate cancer in patients undergoing transrectal ultrasound for diagnostic or therapeutic reasons.

MATERIALS AND METHODS

Data on a cohort of 215 patients who underwent transrectal ultrasound guided prostate biopsies at Memorial-Sloan Kettering Cancer Center, New York, New York were included in this study. Radio frequency data necessary for 2 and 3-dimensional (D) computer reconstruction of the prostate were digitally recorded at transrectal ultrasound and prostate biopsy. The data were spectrally processed and 2-D tissue typing images were generated based on a pre-trained neural network classification. We used manually masked 2-D tissue images as building blocks for generating 3-D tissue images and the images were tissue type color coded using custom software. Radio frequency data on the study cohort were analyzed for cancer probability using the data set pre-trained by neural network methods and compared with conventional B-mode imaging. ROC curves were generated for the 2 methods using biopsy results as the gold standard.

RESULTS

The mean area under the ROC curve plus or minus SEM for detecting prostate cancer for the conventional B-mode and neural network methods was 0.66 +/- 0.03 and 0.80 +/- 0.05, respectively. Sensitivity and specificity for detecting prostate cancer by the neural network method were significantly increased compared with conventional B-mode imaging. In addition, the 2 and 3-D prostate images provided excellent visual identification of areas with a higher likelihood of cancer.

CONCLUSIONS

Spectrum analysis could significantly improve the detection and evaluation of prostate cancer. Routine real-time application of spectrum analysis may significantly decrease the number of false-negative biopsies and improve the detection of prostate cancer at transrectal ultrasound guided prostate biopsy. It may also provide improved identification of prostate cancer foci during therapeutic intervention, such as brachytherapy, external beam radiotherapy or cryotherapy. In addition, 2 and 3-D images with prostate cancer foci specifically identified can help surgical planning and may in the distant future be an additional reliable noninvasive method of selecting patients for prostate biopsy.

Application of constrained least-squares techniques to IMRT treatment planning

PURPOSE

The purpose of this work was to apply the method of constrained least-squares to inverse treatment planning and to explore its potential for providing a fast interactive planning environment for intensity-modulated radiation therapy (IMRT).

METHODS AND MATERIALS

The description of the dose inside a patient is a linear matrix transformation of beamlet weights. The constrained least-squares method adds additional matrix operators and produces beamlet weights by a direct linear transformation. These matrix operators contain a priori knowledge about the radiation distribution. The constrained least-squares technique was applied to obtain IMRT plans for prostate and paraspinal cancer patients and compared with the corresponding plans optimized using the CORVUS inverse planning system.

RESULTS

It was demonstrated that a constrained least-squares technique is suitable for IMRT plan optimization with significantly increased computing speed. For the two cases we have tested, the constrained least-squares method was an order of magnitude faster than conventional iterative techniques because of the avoidance of the iterative calculations. We also found that the constrained least-squares method is capable of generating clinically acceptable treatment plans with less trial-and-error adjustments of system variables, and with improved target volume coverage as well as sensitive structure sparing in comparison with that obtained using CORVUS.

CONCLUSIONS

The constrained least-squares method has the advantage that it does not require iterative calculation and thus significantly speeds up the therapeutic plan optimization process. Besides shedding important insight into the inverse planning problem, the technique has strong potential to provide a fast and interactive environment for IMRT treatment planning.

Examination of the effect of increasing the number of radiation beams on a radiation treatment plan

Within the confines of least-squares operations, it is possible to quantify the effect of the addition of treatment fields or beamlets to a treatment plan. Using linear algebra and eigenvalue perturbation theory, the effect of the increase in number of treatments is shown to be equivalent to adding a perturbation operator. The effect of adding additional fields will be negligible if the perturbation operator is small. The correspondence of this approach to an earlier work in beam-orientation optimization is also demonstrated. Results are presented for prostate, spinal and head and neck cases, and the connection to beam-orientation optimization is examined.

Inverse planning algorithms for external beam radiation therapy

Intensity-modulated radiation therapy (IMRT) is a new treatment technique that has the potential to produce superior dose distributions to those of conventional techniques. An important step in IMRT is inverse planning, or optimization. This is a process by which the optimum intensity distribution is determined by minimizing (or maximizing) an objective function. For radiation therapy, the objective function is used to describe the clinical goals, which can be expressed in terms of dose and dose/volume requirements, or in terms of biological indices. There are 2 types of search algorithms, stochastic and deterministic. Typical algorithms that are currently in use are presented. For clinical implementations, other issues are also discussed, such as global minimum vs. local minima, dose uniformity in the target and sparing of normal tissues, smoothing of the intensity profile, and skin flash. To illustrate the advantages of IMRT, clinical examples for the treatment of the prostate, nasopharynx, and breast are presented. IMRT is an emerging technique that has shown encouraging results thus far. However, the technique is still in its infancy and more research and improvements are needed. For example, the effects of treatment uncertainties on the planning and delivery of IMRT requires further study. As with any new technology, IMRT should be used with great caution.

Dose optimization via index-dose gradient minimization

This paper presents an iterative optimization algorithm based on gradient minimization of index dose, defined as the product of physical dose and a numerical index. Acting as a template the index distribution is designed to represent the dosimetry that meets the dose volume histogram-based optimization objectives. The treatment dosimetry is optimized when the uniformity of the index-dose distribution is maximized. Prior to optimization the user can select all or only some of the beams to be intensity modulated. The remaining unmodulated beams can be either open or wedged photon beams, electron beams, or beams of previous treatments. The optimization result and treatment delivery efficiency can often be enhanced by including not only the IM photon beams but also all suitable fixed-beams available on the linac in the treatment plan. In addition, the doses from previous treatments can also be considered in the optimization of current treatment. Five clinical examples with different complexities in optimization objective are presented. The effects of two nonoptimization variables, beam setup and initial beam weights, on the quality of the dose optimization are also presented. The results are analyzed in terms of isodose distribution, dose volume histograms, and a dose optimization quality factor. The optimization algorithm, implemented in our in-house TPS PLanUNC, has been used in clinical application since 1996. The primary advantages of our optimization algorithm include computational efficiency, intensity modulation selection choice, and performance reliability for a wide range of clinical beam setups and optimization objectives.

Optimizing radiation treatment plans for lung cancer using lung perfusion information

PURPOSE

To study the impact of incorporation of lung perfusion information in the optimization of radical radiotherapy (RT) treatment plans for patients with medically inoperable non-small cell lung cancer (NSCLC).

MATERIALS AND METHODS

The treatment plans for a virtual phantom and for five NSCLC patients with typical defects of pre-RT lung perfusion were optimized to minimize geometrically determined parameters as the mean lung dose (MLD), the lung volume receiving more than 20 Gy (V20), and the functional equivalent of the MLD, using perfusion-weighted dose-volume histograms. For the patients the (perfusion-weighted) optimized plans were compared to the clinically applied treatment plans.

RESULTS

The feasibility of perfusion-weighted optimization was demonstrated in the phantom. Using perfusion information resulted in an increase of the weights of those beams that were directed through the hypo-perfused lung regions both for the phantom and for the studied patients. The automatically optimized dose distributions were improved with respect to lung toxicity compared with the clinical treatment plans. For patients with one hypo-perfused hemi-thorax, the estimated gain in post-RT lung perfusion was 6% of the prescribed dose compared to the geometrically optimized plan. For patients with smaller perfusion defects, perfusion-weighted optimization resulted in the same plan as the geometrically optimized plan.

CONCLUSION

Perfusion-weighted optimization resulted in clinically well applicable treatment plans, which cause less radiation damage to functioning lung for patients with large perfusion defects.

[A simple dose-effect model for the optimization of IMRT]

Optimization of percutaneous photon beams with intensity modulation was investigated in terms of the influence of different dose-effect functions for lung tissue on the resulting dose distributions. The fluence profiles were optimized for a cylindrical phantom with a L-shaped target, the spinal cord and lung presenting the critical organs. Concurrent criteria were a minimum dose constraint for the target and a maximum dose constraint for the spinal cord. The dose effect in the lung was minimized using different approaches. All tested approaches were able to control the dose distribution in the lung. The mean dose remained constant, where as the volume of low dose could be changed. Due to the simplicity of functions and parameters, these models are suitable for clinical implementation.

Linear algebraic methods applied to intensity modulated radiation therapy

Methods of linear algebra are applied to the choice of beam weights for intensity modulated radiation therapy (IMRT). It is shown that the physical interpretation of the beam weights, target homogeneity and ratios of deposited energy can be given in terms of matrix equations and quadratic forms. The methodology of fitting using linear algebra as applied to IMRT is examined. Results are compared with IMRT plans that had been prepared using a commercially available IMRT treatment planning system and previously delivered to cancer patients.