Enhanced dynamic wedge factors at off-axis points in asymmetric fields.

Several recent reports have described methods for calculating enhanced dynamic wedge factors (EDWFs). Many of these reports use the monitor-unit (MU) fraction method to predict EDWFs as a function of field size. Although simple in approach, MU fraction methods do not produce accurate EDWFs in large or asymmetric fields. A recently described technique, based on the MU fraction method works well for large and asymmetric fields, but only when the calculation point is in the center of the field. Other existing methods based on beam-segment superposition do not have this limitation. These beam summation methods, however, are difficult to implement in routine clinical MU calculation schemes. In this paper, we present a simple calculation method that estimates EDWFs at off-axis calculation points in both symmetric and asymmetric fields. Our method, which also is based on the MU fraction method, similarly uses empirically determined field-size corrections but also applies wedged-field profiles to estimate EDWFs that are independent of calculation-point location and field symmetry. EDWF measurements for a variety of field sizes and calculation-point locations for both 6- and 18-MV x-ray beams were performed to validate our calculations and those of our ADAC Pinnacle3 Treatment Planning System. The disagreement between the calculated and measured EDWFs over the useful clinical range of field sizes and calculation-point locations was less than 2%. The worst disagreement was 3% and occurred at a point 8.5 cm from the center of an asymmetric 25 (wedged direction)x20 cm2 60 degrees-wedged field. Detailed comparisons of measurements with calculations and wedge factors obtained from the ADAC Pinnacle3 Treatment Planning System will be presented. In addition, the strengths and weaknesses of this calculation method will be discussed.

Modeling scintillation from an aperiodic Kolmogorov phase screen.

We propose a technique for the accurate modeling and simulation of scintillation patterns that are due to Kolmogorov statistics without assuming periodic boundary conditions. We show how the more physically justifiable assumption of smoothness results in a propagation kernel of finite extent. This allows the phase screen dimensions for an accurate simulation to be determined, and truncation can then be used to eliminate the unwanted spectral leakage and diffraction effects usually inherent in the use of finite apertures. A detailed outline of the proposed technique and comparison of simulations with analytic results are presented.

Fast simulation of a kolmogorov phase screen.

A previously presented method for modeling Kolmogorov phase fluctuations over a finite aperture is both formalized and improved on. The method relies on forming an initial low-resolution Kolmogorov phase screen from direct factorization of a covariance. The resolution of the screen is then increased by a randomized interpolation to produce a Kolmogorov phase screen of the desired size. The computational requirement is asymptotically proportional to the number of points in the phase screen.

Analysis of optimal centroid estimation applied to Shack-Hartmann sensing.

The problem of estimating the centroid of an incoherently imaged point with a CCD array is analyzed. An exact analysis is presented that uses the actual short-exposure function at the CCD instead of the traditional Gaussian approximation. The analysis shows that, for Poisson noise, the centroid variance depends on the CCD size and that truncation effects play a significant part in determining the optimum CCD size. The effects of this on a wave-front reconstruction formed by a Shack-Hartmann sensor are described.

Phase retrieval with prior information.

An algorithm for phase retrieval with Bayesian statistics is discussed. It is shown how the statistics of Kolmogorov turbulence can be used to compute the likelihood for a particular phase screen. This likelihood is then added to that of the observed data to produce a functional that is maximized directly by use of conjugate gradient maximization. It is shown that although this can significantly improve the quality of the phase estimate,the issue is complicated by local maxima introduced by the possibility of phase wrapping. The causes of the local maxima are analyzed, and a method that increases the likelihood of convergence to the global maximum is presented.

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.

Biomarker monitoring of a population residing near uranium mining activities.

We investigated whether residents residing near uranium mining operations (target population), who are potentially exposed to toxicants from mining waste, have increased genotoxic effects compared with people residing elsewhere (reference population). Population surveys were conducted, and 24 target and 24 reference residents were selected. The selected subjects and controls were matched on age and gender and they were nonsmokers. Blood samples were collected for laboratory studies. The standard cytogenetic assay was used to determine chromosome aberration frequencies, and the challenge assay was used to investigate DNA repair responses. We found that individuals who resided near uranium mining operations had a higher mean frequency of cells with chromosome aberrations and higher deletion frequency but lower dicentric frequency than the reference group, although the difference was not statistically significant. After cells were challenged by exposure to gamma-rays, the target population had a significantly higher frequency of cells with chromosome aberrations and deletion frequency than the reference group. The latter observation is indicative of abnormal DNA repair response in the target population.

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.

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.

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)

Optimized dynamic rotation with wedges.

Dynamic rotation is a computer-controlled therapy technique utilizing an automated multileaf collimator in which the radiation beam shape changes dynamically as the treatment machine rotates about the patient so that at each instant the beam shape matches the projected shape of the target volume. In simple dynamic rotation, the dose rate remains constant during rotation. For optimized dynamic rotation, the dose rate is varied as a function of gantry angle. Optimum dose rate at each gantry angle is computed by linear programming. Wedges can be included in the optimized dynamic rotation therapy by using additional rotations. Simple and optimized dynamic rotation treatment plans, with and without wedges, for a pancreatic tumor have been compared using optimization cost function values, normal tissue complication probabilities, and positive difference statistic values. For planning purposes, a continuous rotation is approximated by static beams at a number of gantry angles equally spaced about the patient. In theory, the quality of optimized treatment planning solutions should improve as the number of static beams increases. The addition of wedges should further improve dose distributions. For the case studied, no significant improvements were seen for more than 36 beam angles. Open and wedged optimized dynamic rotations were better than simple dynamic rotation, but wedged optimized dynamic rotation showed no definitive improvement over open beam optimized dynamic rotation.

Custom beam profiles in computer-controlled radiation therapy.

A computer-controlled radiation therapy technique is demonstrated which uses multiple concurrent boost fields to modify the beam profile of a conventional treatment beam. A principal field, identical to that of a corresponding conventional treatment plan, delivers the major component of the prescribed dose. Dose increments given from boost fields placed within this principal field compensate for variations in patient anatomy, for variations in target volume shape, and/or for imperfect beam characteristics, such as excessive off-axis dose or inadequate beam wedge angle. This concurrent boost field technique is demonstrated for several treatment sites. It produces significant improvement in uniformity of dose delivered to the target compared to conventional treatment. Implementation of these treatments requires a computer-controlled linear accelerator with independently-movable collimator jaws, an automatic beam set-up procedure, and a patient prescription database. Since all fields are delivered under computer control, concurrent boost technique treatment times are not much longer than those of conventional treatments.

Wave-front reconstruction using a Shack-Hartmann sensor.

An analysis of the problem of wave-front reconstruction from Shack-Hartmann measurements is presented. The wave-front aberration is assumed to result from passage of the wave front through Kolmogorov turbulence. Limitations of using Zernike polynomials as an orthogonal basis for wave-front reconstruction are highlighted, and the advantage of using the Karhunen-Loeve functions for computing the higher-order modes of the wave front is shown.

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.

Treatment planning optimization using constrained simulated annealing.

A variation of simulated annealing optimization called 'constrained simulated annealing' is used with a simple annealing schedule to optimize beam weights and angles in radiation therapy treatment planning. Constrained simulated annealing is demonstrated using two contrasting objective functions which incorporate both biological response and dose-volume considerations. The first objective function maximizes the probability of a complication-free treatment (PCFT) by minimizing the normal tissue complications subject to the constraint that the entire target volume receives a prescribed minimum turmourcidal dose with a specified dose homogeneity. Probabilities of normal tissue complication are based on published normal tissue complication probability functions and computed from dose-volume histograms. The second objective function maximizes the isocentre dose subject to a set of customized normal tissue dose-volume and target volume dose homogeneity constraints (MVDL). Although the PCFT objective function gives consistently lower estimates of normal tissue complication probabilities, the ability to specify individualized dose-volume limits, and therefore the individualized probability of complication, for an individual organ makes the MDVL objective function more useful for treatment planning.

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.

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.

Constrained simulated annealing for optimized radiation therapy treatment planning.

A variation of simulated annealing optimization called 'constrained simulated annealing' is used with a simple annealing schedule to automatically optimize beam weights and beam angles in radiation therapy treatment planning. This optimization technique permits the straightforward utilization of any objective function and any set of dose constraints, even those described by non-analytic functions. Constrained simulated annealing is demonstrated using an objective function which minimizes the probability of normal tissue complications subject to the constraint that the entire target volume receive a tumoricidal dose within specified maximum and minimum limits. Target volume dose constraints are determined by points located on the perimeter of the target volume. Probabilities of normal tissue complications are based on published normal tissue complication probability functions and computed from dose-volume histograms calculated on points spread throughout the normal anatomy.