Isaac I. Rosen

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.

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.

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.

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.

Assessment of a linear accelerator for segmented conformal radiation therapy

Segmented conformal radiation therapy is a new computer-controlled treatment technique under investigation in which the target volume is subdivided into thick transverse segments each of which is then treated individually by rectangular transverse abutting fields. In order to obtain uniform dose at abutments, the machine isocenter remains fixed in the patient and field edges are defined by independently moving focused collimator jaws to give matching geometric divergence. Mechanical variation in jaw and gantry positioning will create some dose variation at field abutments. Film dosimetry was used to study the radiation field positioning accuracy and precision of a commercial linear accelerator. A method of field position calibration was developed using multiple nonabutting fields exposed on the same radiograph. Verification of collimator jaw calibration measurements was performed using multiple abutting fields exposed on a single radiograph. Measurements taken over 5 months of clinical accelerator operation studied the effects of simple jaw motion, simple gantry motion, and combined jaw/gantry motion on jaw position precision and accuracy. The inherent precision and accuracy of radiation field positioning was found to be better than +/- 0.3 mm for both jaws with all types of motions except for the Y2 jaw under combined jaw/gantry motion. When the ability to deliver abutting beams was verified in clinical mode, the average dose variation at abutments was less than 6% at all gantry angles except for one. However, due to accelerator software limitations in clinical mode, the settings for collimator positions could not take advantage of the maximum accuracy of which the hardware is capable.(ABSTRACT TRUNCATED AT 250 WORDS)

Static pion beam treatment planning of deep seated tumors using computerized tomographic scans

Abstract Static negative pion beam treatment of deep seated tumors is in progress at LAMPF. The influence of the physical principles of pions on treatment planning, e.g., an enhanced peak dose, multiple scattering, variations of beam quality, pin beam emittance, and a fixed vertical beam, are discussed. Computerized tomographic (CT) scan data have proven invaluable in providing quantitative information on inhomogeneities within the anatomy. The methods of designing collimation and compensating bolus for tailoring the pion beam to individual patient ports are described. An interim method, using dosimetry measurements in a water phantom and CT scan data to construct patient isodose distribution is outlined. Typical treatment plans for patients with abdominal and head and neck cancers are presented. The method of X-ray simulation in verifying localization of CT-defined tumor volumes is demonstrated for the head and neck.

Improved dose homogeneity in the head and neck using computer-controlled radiation therapy

Computer-controlled radiation therapy techniques are demonstrated which improve dose homogeneity throughout the nasopharynx when compared to conventional treatment techniques. The typical approach using a heavily weighted anterior field and opposed wedged lateral fields results in a dose gradient from 95% to 110% or greater. All three of the computer-controlled techniques investigated improved the dose uniformity to a range from 95% to 105% or less. Multiple overlapping fields are used to compensate for patient anatomy and treatment beam characteristics. Treatment planning and monitor unit calculations are quite time-consuming at this stage of development. Actual treatment time is not unreasonably long and can be improved in future releases of the therapy machine control software.

Uncertainty in dose estimation for gynecological implants

One source of uncertainty in doses computed for intracavitary gynecological applications is the imprecision inherent in localizing the sources and the points of interest on radiographs of the implant and in transferring that data into the treatment planning computer. To quantify the effect of these activities on the accuracy of computed doses, five physicists and two dosimetrists performed computerized dose calculations on five applications chosen randomly from our patient files. For each of these applications, doses were computed at the traditional points A and B and at points in the bladder and rectum. Using identical sets of films, each planner located both the radioactive sources and points of interest, or only the sources, or only the points of interest. Another set of films was used to measure the accuracy of digitizing alone. Planners received no instructions on either the definition or the placement of the points of interest. Overall uncertainties in computed doses to points A and B and bladder were found to be about 7%. Uncertainty in dose to the rectum was on the order of 50%. Analysis of the results showed that about 1% of the error was due to digitization and about 2% to identification of source locations. Among the individual planners, almost all of the dose variation was from differences in placement of the points of interest on the implant radiographs. The results demonstrate the need for standard definitions and locations for points of calculation so that meaningful comparisons can be made among institutions.

Collimator scatter in modeling radiation beam profiles

In computer dose calculations using scatter-air ratio sector summation algorithms, the primary dose from the target to points away from the central axis of a beam is computed using an exponential intensity model of the source and a transmission parameter for the collimator. This model works well inside the beam and near edges but is inaccurate outside the beam at distances of more than 1-2 cm from beam edges. We have modified the standard beam profile model to include a dose contribution representing photon radiation scattered from the collimators. Collimator edges are treated mathematically as line sources and an adjustable parameter is introduced which represents the activity per unit length of the collimator edges. Dose from the collimator edges is assumed to decrease purely geometrically as the inverse of the square of the distance and no modification is made for tissue attenuation. With these assumptions, the total collimator scatter dose to a point is most accurately computed by a line integral over the edges of the beam outline. This modification fits naturally into the standard scatter-air ratio sector summation computer algorithm but adds significantly to dose computation time. Some approximations eliminate the line integration and lead to a collimator scatter term which is proportional to field perimeter and independent of off-axis distance. The modified dose model was tested by comparing measured dose profiles with computed ones using x-ray beams from Philips (6 and 15 MV) and Varian (4 and 6 MV) accelerators. There was significant improvement in fit compared to the standard beam model for points outside the radiation beam.

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.