S Morrill

Treatment plan optimization using linear programming.

Linear programming is a versatile mathematical tool for optimizing radiation therapy treatment plans. For planning purposes, dose constraint points, possible treatment beams, and an objective function are defined. Dose constraint points are specified in and about the target volume and normal structures with minimum and maximum dose values assigned to each point. A linear objective function is designed that defines the goal of optimization. A list of potential treatment beams is defined by energy, angle, and wedge selection. Then, linear programming calculates the relative weights of all the potential beams such that the objective function is optimized and doses to all constraint points are within the prescribed limits. Historically, linear programming has been used to improve conventional treatment techniques. It can also be used to create sophisticated, complex treatment plans suitable for delivery by computer-controlled therapy techniques.

MLC quality assurance techniques for IMRT applications

Intensity modulated radiotherapy (IMRT) requires extensive knowledge of multileaf collimator (MLC) leaf positioning accuracy, precision, and long-term reproducibility. We have developed a technique to efficiently measure the absolute position of each MLC leaf, over the range of leaf positions utilized in IMRT, based on dosimetric information. A single radiographic film was exposed to 6 MV x-rays for twelve exposures: one open field with a radio-opaque marker tray present, and eleven fields (1 x 28 cm strips via 1 cm gaps between opposed leaf pairs) separated by 2 cm center to center. The process was repeated while varying direction of leaf travel; each film was digitized using a commercial film dosimetry system. The digital images were manipulated to remove translation and rotation of the film data with respect to the collimator coordinate system by extraction of radiation dose profiles perpendicular to the MLC leaf motion and measuring the center of the x-ray leakage between leaves. Radiation dose profiles in the direction of leaf motion were acquired through the center of each leaf pair (leaves 2-28), which provided leaf position information every 2 cm with 0.2 mm precision. Nine separate leaf reproducibility studies over a 90 day period which evaluated 600 measurement points on each film show 0.3 mm precision for 95% confidence, while hysteresis studies show 0.5 mm precision. Absolute leaf position error measurements demonstrated a radial dependence, with a maximum of 1.5 mm at 16.4 cm from central axis, due to rotational error at calibration. Recalibration of the MLC leaves based utilizing this tool yields absolute leaf position measurements where 91.5% of all leaves/positions were within 0.5 mm, with a mean error of 0.1 mm and a maximum error less than 1.0 mm.

A generic genetic algorithm for generating beam weights

A genetic algorithm for generating beam weights is described. The algorithm improves an objective measure of the dose distribution while respecting dose volume constraints placed on critical structures. The algorithm was used to select beam weights for treatment of abdominal tumors. Weights were selected for up to 36 beams. Dose volume limits were placed on normal organs and a dose inhomogeneity limit was placed on tumor. Volumes were represented as sets of several hundred discrete points. The algorithm searched for the beam weights that would make the minimum tumor dose as high as the constraints would allow. The results were checked using dose volume histograms with standard sized grids. Nineteen trials were created using six patient cases by changing the required field margin or allowed beam position in each case. The sampling of points was sufficiently dense to yield solutions that strictly satisfied the constraints when the prescribed dose was renormalized by a factor of less than 6%. The genetic algorithm supplied solutions in 49 min on average, and in a maximum time of 87 min. The randomized search does not guarantee optimality, but high tumor doses were obtained. An example is shown for which the solution of the genetic algorithm gave a minimum tumor dose 7 Gy higher than the solution given by a simulated annealing algorithm under the same set of constraints. The genetic algorithm can be generalized to admit nonlinear functions of the beam intensities in the objective or in the constraints. These can include tumor control and normal tissue complication probabilities. The genetic algorithm is an attractive procedure for assigning beam weights in multifield plans. It improves the dose distribution while respecting specified rules for tissue tolerance.

Dose-volume considerations with linear programming optimization

A method of incorporating dose-volume considerations within the framework of conventional linear programming is presented. This method is suitable for the optimization of beam weights and angles using a conformal treatment philosophy (i.e., tailoring the high-dose region to the target volume only). Dose-volume constraints are introduced using the concept that volumes of normal tissue nearer the target volume will be allowed higher dose constraints than volumes of normal tissue distal to the target volume. Each involved normal structure is divided into high-dose and low-dose volumes. These two volume partitions are represented by constraint points with either high-dose or low-dose constraints, respectively. Optimized treatment plans for three clinical sites demonstrate that this technique meets or surpasses the original dose-volume constraints for a conformal-type treatment plan using straightforward linear programming in a time frame that is comparable to other linear programming problems.

Comparison of simulated annealing algorithms for conformal therapy treatment planning

PURPOSE The efficiency of four fast simulated annealing algorithms for optimizing conformal radiation therapy treatment plans was studied and the resulting plans were compared with each other and to optimized conventional plans. METHODS AND MATERIALS Four algorithms were selected on the basis of their reported successes in solving other minimization problems: fast simulated annealing with a Cauchy generating function, fast simulated annealing with a Lorentzian generating function, variable step size generalized simulated annealing (VSGSA), and very fast simulated reannealing (VFSR). They were tested on six clinical cases using a multiple beam coplanar conformal treatment technique. Relative beam weights were computed that maximized the minimum tumor dose subject to dose-volume constraints on normal organ doses. Following some initial tuning of the annealing parameters, each algorithm was applied identically to each test case. Optimization tests were run using different random number sequences and different numbers of iterations. RESULTS The VSGSA algorithm consistently produced the best results. Using long run times, it generated plans with the highest minimum tumor dose in five of the six cases. For the short run times, the VSGSA solutions averaged larger minimum tumor doses than those of the other algorithms for all six patients, with increases ranging from 0.4 to 5.9 Gy. For three of the patients, the conformal plan gave a clinically significant increase in the minimum tumor dose over the conventional plan, ranging from 8.2 to 13.0 Gy. In two other cases, there was little difference between the two treatment approaches. For one case, the optimized conventional plan was much better than the conformal plan because the conventional beam arrangement included wedges, which offset the multiple beam advantage of the conformal plans. CONCLUSIONS For equal computing times of both long and short duration, the VSGSA algorithm consistently produced conformal plans that were superior to those produced by the other algorithms. The simple conformal technique used in this study showed a significant potential advantage in the treatment of abdominal tumors. In three of the cases, the conformal plans showed clinically important increases in tumor dose over optimized conventional plans.

VERY FAST SIMULATED REANNEALING IN RADIATION THERAPY TREATMENT PLAN OPTIMIZATION

PURPOSE Very Fast Simulated Reannealing is a relatively new (1989) and sophisticated algorithm for simulated annealing applications. It offers the advantages of annealing methods while requiring shorter execution times. The purpose of this investigation was to adapt Very Fast Simulated Reannealing to conformal treatment planning optimization. METHODS AND MATERIALS We used Very Fast Simulated Reannealing to optimize treatments for three clinical cases with two different cost functions. The first cost function was linear (minimum target dose) with nonlinear dose-volume normal tissue constraints. The second cost function (probability of uncomplicated local control) was a weighted product of normal tissue complication probabilities and the tumor control probability. RESULTS For the cost functions used in this study, the Very Fast Simulated Reannealing algorithm achieved results within 5-10% of the final solution (100,000 iterations) after 1000 iterations and within 3-5% of the final solution after 5000-10000 iterations. These solutions were superior to those produced by a conventional treatment plan based on an analysis of the resulting dose-volume histograms. However, this technique is a stochastic method and results vary in a statistical manner. Successive solutions may differ by up to 10%. CONCLUSION Very Fast Simulated Reannealing, with modifications, is suitable for radiation therapy treatment planning optimization. It produced results within 3-10% of the optimal solution, produced using another optimization algorithm (Mixed Integer Programming), in clinically useful execution times.

MLC dosimetric characteristics for small field and IMRT applications.

The objective of this work was to measure the performance characteristics of a double-focus multileaf collimator (MLC) for intensity modulated radiation therapy (IMRT), specifically the variation in penumbra and leakage for narrow fields as a function of field position over a 20x27 cm space available for segmented MLC IMRT. Measurements were made with 6 MV x rays through a MLC containing 29 leaf pairs (27 pairs of 1 cm width), and EDR2 film at 10 cm depth in solid water at 100 cm SAD. Films were digitized with 0.17 mm resolution and converted to dose. Interleaf and intraleaf transmission were measured along 11 vertical profile locations. Leaf-end transmission was measured along horizontal profiles for each of 9 different leaf abutments, traveling over a 20 cm range. In-plane penumbra measurements were made through a single leaf retracted, for 7 different leaves. Cross-plane penumbra (leaf-end) measurements were made for all 27 leaf pairs, where the 1 cm field width was placed in 11 different off-axis positions (20 cm range). Interleaf leakage (range 1.0%-1.5%), intraleaf transmission (range 0.6%-0.8%), and leaf-end transmission (range 0.8%-2.7%) were consistent for all leaf pairs at a given abutment position. The penumbra for these 1-cm-wide fields was measured to be 0.36 cm+/-0.03 cm for 99% of the measurements. In conclusion, the penumbra and leakage of the double-focus MLC were remarkably consistent for the range of leaf positions studied, producing dosimetric characteristics that are well suited for IMRT segments where opposing leaf pairs are often separated by 10 mm or less.

The influence of dose constraint point placement on optimized radiation therapy treatment planning

To efficiently use linear and quadratic programming for treatment planning optimization on a routine basis, automated methods are needed for placing dose constraint points. We have investigated, for linear programming optimization, the minimum number of constraint points needed to achieve an acceptable approximation to the desired (ideal) solution. Seven different constraint point placement algorithms were evaluated for a given objective function. One of these algorithms was chosen for routine clinical use at our institution. This algorithm places constraint points on the perimeter of the target volume and on the perimeter and in the interior of each normal structure. Additional points are placed on the perimeter of a constant thickness buffer region surrounding the target volume. Excellent optimization results are obtained with 40-70 constraint points per treatment planning slice.

Tissue heterogeneity effects in treatment plan optimization

PURPOSE There is general agreement that tissue density correction factors improve the accuracy of dose calculations. However, there is disagreement over the proper heterogeneity correction algorithm and a lack of clinical experience in using them. Therefore, there has not been widespread implementation of density correction factors into clinical practice. Furthermore, the introduction of optimized conformal therapy leads to new and radically different treatment techniques outside the clinical experience of the physician. It is essential that the effects of tissue density corrections are understood so that these types of treatments can be safely delivered. METHODS AND MATERIALS In this paper, we investigate the effect of tissue density corrections on optimized conformal type treatment planning in the thorax region. Specifically, we study the effects on treatment plans optimized without type treatment planning in the thorax region. Specifically, we study the effects on treatment plans optimized without tissue density corrections, when those corrections are applied to the resulting dose distributions. These effects are compared for two different conformal techniques. RESULTS This study indicates that failure to include tissue density correction factors results in an increased dose of approximately 5-15%. This is consistent with published studies using conventional treatment techniques. Additionally, the high-dose region of the dose distribution expands laterally into the uninvolved lung and other normal structures. The use of dose-volume histograms to compare these distributions demonstrates that treatment plans optimized without tissue density corrections lead to an increased dose to uninvolved normal structures. This increase in dose often violates the constraints used to determine the optimal solution. CONCLUSIONS The neglect of tissue density correction factors can result in a 5-15% increase in the delivered dose. In addition, suboptimal dose distributions are produced. To benefit from the advantages of optimized conformal therapy in the thorax, tissue density correction factors should be used.

Spatially fractionated radiotherapy (GRID) using helical tomotherapy

Spatially fractionated radiotherapy (GRID) was designed to treat large tumors while sparing skin, and it is usually delivered with a linear accelerator using a commercially available block or multileaf collimator (LINAC‐GRID). For deep‐seated (skin to tumor distance (>8 cm)) tumors, it is always a challenge to achieve adequate tumor dose coverage. A novel method to perform GRID treatment using helical tomotherapy (HT‐GRID) was developed at our institution. Our approach allows treating patients by generating a patient‐specific virtual GRID block (software‐generated) and using IMRT technique to optimize the treatment plan. Here, we report our initial clinical experience using HT‐GRID, and dosimetric comparison results between HT‐GRID and LINAC‐GRID. This study evaluates 10 previously treated patients who had deep‐seated bulky tumors with complex geometries. Five of these patients were treated with HT‐GRID and replanned with LINAC‐GRID for comparison. Similarly, five other patients were treated with LINAC‐GRID and replanned with HT‐GRID for comparison. The prescription was set such that the maximum dose to the GTV is 20 Gy in a single fraction. Dosimetric parameters compared included: mean GTV dose (DGTVmean), GTV dose inhomogeneity (valley‐to‐peak dose ratio (VPR)), normal tissue doses (DNmean), and other organs‐at‐risk (OARs) doses. In addition, equivalent uniform doses (EUD) for both GTV and normal tissue were evaluated. In summary, HT‐GRID technique is patient‐specific, and allows adjustment of the GRID pattern to match different tumor sizes and shapes when they are deep‐seated and cannot be adequately treated with LINAC‐GRID. HT‐GRID delivers a higher DGTVmean, EUD, and VPR compared to LINAC‐GRID. HT‐GRID delivers a higher DNmean and lower EUD for normal tissue compared to LINAC‐GRID. HT‐GRID plans also have more options for tumors with complex anatomical relationships between the GTV and the avoidance OARs (abutment or close proximity). PACS numbers: 87.55.D, 87.55.de, 87.55.ne, 87.55.tgSpatially fractionated radiotherapy (GRID) was designed to treat large tumors while sparing skin, and it is usually delivered with a linear accelerator using a commercially available block or multileaf collimator (LINAC-GRID). For deep-seated (skin to tumor distance (>8 cm)) tumors, it is always a challenge to achieve adequate tumor dose coverage. A novel method to perform GRID treatment using helical tomotherapy (HT-GRID) was developed at our institution. Our approach allows treating patients by generating a patient-specific virtual GRID block (software-generated) and using IMRT technique to optimize the treatment plan. Here, we report our initial clinical experience using HT-GRID, and dosimetric comparison results between HT-GRID and LINAC-GRID. This study evaluates 10 previously treated patients who had deep-seated bulky tumors with complex geometries. Five of these patients were treated with HT-GRID and replanned with LINAC-GRID for comparison. Similarly, five other patients were treated with LINAC-GRID and replanned with HT-GRID for comparison. The prescription was set such that the maximum dose to the GTV is 20 Gy in a single fraction. Dosimetric parameters compared included: mean GTV dose (DGTVmean), GTV dose inhomogeneity (valley-to-peak dose ratio (VPR)), normal tissue doses (DNmean), and other organs-at-risk (OARs) doses. In addition, equivalent uniform doses (EUD) for both GTV and normal tissue were evaluated. In summary, HT-GRID technique is patient-specific, and allows adjustment of the GRID pattern to match different tumor sizes and shapes when they are deep-seated and cannot be adequately treated with LINAC-GRID. HT-GRID delivers a higher DGTVmean, EUD, and VPR compared to LINAC-GRID. HT-GRID delivers a higher DNmean and lower EUD for normal tissue compared to LINAC-GRID. HT-GRID plans also have more options for tumors with complex anatomical relationships between the GTV and the avoidance OARs (abutment or close proximity). PACS numbers: 87.55.D, 87.55.de, 87.55.ne, 87.55.tg.