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PubMed1998

A case study comparing the relative benefit of optimizing beam weights, wedge angles, beam orientations and tomotherapy in stereotactic radiotherapy of the brain.

A treatment-planning case study has been performed on a patient with a medium-sized, convex brain tumour. The study involved the application of advanced treatment-plan optimization techniques to improve on the dose distribution of the 'standard plan' used to treat the patient. The standard plan was created according to conventional protocol at the Royal Marsden NHS Trust, and consisted of a three-field (one open and two wedged) non-coplanar arrangement, with field shaping to the beam's-eye view of the planning target volume (PTV). Three optimized treatment plans were created corresponding to (i) the optimization of the beam weights and wedge angles of the standard plan, (ii) the optimization of the beam orientations, beam weights and wedge angles of the standard plan, and (iii) a full fluence tomotherapy optimization of 1 cm wide (at isocentre), 270 degree arcs. (i) and (ii) were created on the VOXELPLAN research 3D treatment-planning system, using in-house developed optimization algorithms, and (iii) was created on the PEACOCK tomotherapy planning system. The downhill-simplex optimization algorithm is used, in conjunction with 'threshold-dose' cost-function terms enabling the algorithm to optimize specific regions of the dose-volume histogram (DVH) curve. The 'beam-cost plot' tool is presented as a visual aid to the selection of beneficial beam directions. The methods and pitfalls in the transfer of plans and patient data between the two planning systems are discussed. Each optimization approach was evaluated, relative to the standard plan, on the basis of DVH and dose statistics in the PTV and organs at risk (OARs). All three optimization approaches were able to improve on the dose distribution of the standard plan. The magnitude of the improvement was greater for the optimized beam-orientation and tomotherapy plans (up to 15% and 30% for the maximum and mean OAR doses). A smaller improvement was observed in the beam-weight and wedge-angle optimized plan (up to 5% and 10% in the maximum and mean OAR doses). In the tomotherapy plan, difficulty was encountered achieving an acceptable homogeneity of dose in the PTV. This was improved by treating the gross tumour volume (GTV) and (PTV - GTV) regions as separate targets in the inverse planning, with the latter region prescribed a slightly higher dose to reduce edge under-dosing. In conclusion, for the medium-sized convex tumour studied, the tomotherapy dose distribution showed a significant improvement on the standard plan, but no significant improvement over a conventional three-field plan where the beam orientations, beam weights and wedge angles had been optimized.

Adenoma↗

PubMed2004

A perspective on atrioventricular delay optimization in patients with a dual chamber pacemaker.

Atrioventricular delay (AVD) is critical in patients with DDD pacemakers (PM). Echo/Doppler evaluation of AVD providing the longest left ventricular filling time (FT) or the highest cardiac output (CO) is used for AVD optimization. Recently myocardial performance index (MPI) has been shown to improve by optimizing AVD. The aim was to compare the CO, FT, MPI derived optimal AVD, and to analyze systolic and diastolic performance at every optimal AVD. Twenty-five patients, 16 men 68 +/- 11 years, ejection fraction >or= 50%, with a DDD PM for third-degree AV block, without other major cardiomyopathies, underwent echo/Doppler AVD optimization. CO, FT, and MPI derived optimal AVDs were identified as the AVDs providing the highest CO, the longest FT, and the minimum MPI, respectively. Isovolumic contraction and relaxation time (ICT, IRT), ejection time (ET), ICT/ET, and IRT/ET ratios were also evaluated at every optimal AVD. CO, FT, and MPI derived optimal AVDs were significantly different (148 +/- 36 ms, 116 +/- 34 ms, and 127 +/- 33 ms, respectively). ICT/ET was similar at CO, FT, and MPI derived optimal AVD (0.22 +/- 0.10, 0.23 +/- 0.11, and 0.21 +/- 0.10, respectively). IRT/ET ratio was similar at FT and MPI derived optimal AVDs (0.34 +/- 0.15 and 0.33 +/- 0.15, respectively) and significantly shorter (P < 0.02) than at CO derived optimal AVD (0.40 +/- 0.15). Different methods indicate different optimal AVDs. However analysis of systolic and diastolic performance shows that different AVDs result in similar systolic or diastolic performance. At MPI optimized AVD, a high CO combined with the most advantageous conditions of both isovolumic contraction and relaxation phases is achieved.

Aged↗

PubMed2002

Incorporating multi-leaf collimator leaf sequencing into iterative IMRT optimization.

Intensity modulated radiation therapy (IMRT) treatment planning typically considers beam optimization and beam delivery as separate tasks. Following optimization, a multi-leaf collimator (MLC) or other beam delivery device is used to generate fluence patterns for patient treatment delivery. Due to limitations and characteristics of the MLC, the deliverable intensity distributions often differ from those produced by the optimizer, leading to differences between the delivered and the optimized doses. Objective function parameters are then adjusted empirically, and the plan is reoptimized to achieve a desired deliverable dose distribution. The resulting plan, though usually acceptable, may not be the best achievable. A method has been developed to incorporate the MLC restrictions into the optimization process. Our in-house IMRT system has been modified to include the calculation of the deliverable intensity into the optimizer. In this process, prior to dose calculation, the MLC leaf sequencer is used to convert intensities to dynamic MLC sequences, from which the deliverable intensities are then determined. All other optimization steps remain the same. To evaluate the effectiveness of deliverable-based optimization, 17 patient cases have been studied. Compared with standard optimization plus conversion to deliverable beams, deliverable-based optimization results show improved isodose coverage and a reduced dose to critical structures. Deliverable-based optimization results are close to the original nondeliverable optimization results, suggesting that IMRT can overcome the MLC limitations by adjusting individual beamlets. The use of deliverable-based optimization may reduce the need for empirical adjustment of objective function parameters and reoptimization of a plan to achieve desired results.

Algorithms↗

PubMed2004

Speed and convergence properties of gradient algorithms for optimization of IMRT.

Gradient algorithms are the most commonly employed search methods in the routine optimization of IMRT plans. It is well known that local minima can exist for dose-volume-based and biology-based objective functions. The purpose of this paper is to compare the relative speed of different gradient algorithms, to investigate the strategies for accelerating the optimization process, to assess the validity of these strategies, and to study the convergence properties of these algorithms for dose-volume and biological objective functions. With these aims in mind, we implemented Newton's, conjugate gradient (CG), and the steepest decent (SD) algorithms for dose-volume- and EUD-based objective functions. Our implementation of Newton's algorithm approximates the second derivative matrix (Hessian) by its diagonal. The standard SD algorithm and the CG algorithm with "line minimization" were also implemented. In addition, we investigated the use of a variation of the CG algorithm, called the "scaled conjugate gradient" (SCG) algorithm. To accelerate the optimization process, we investigated the validity of the use of a "hybrid optimization" strategy, in which approximations to calculated dose distributions are used during most of the iterations. Published studies have indicated that getting trapped in local minima is not a significant problem. To investigate this issue further, we first obtained, by trial and error, and starting with uniform intensity distributions, the parameters of the dose-volume- or EUD-based objective functions which produced IMRT plans that satisfied the clinical requirements. Using the resulting optimized intensity distributions as the initial guess, we investigated the possibility of getting trapped in a local minimum. For most of the results presented, we used a lung cancer case. To illustrate the generality of our methods, the results for a prostate case are also presented. For both dose-volume and EUD based objective functions, Newton's method far outperforms other algorithms in terms of speed. The SCG algorithm, which avoids expensive "line minimization," can speed up the standard CG algorithm by at least a factor of 2. For the same initial conditions, all algorithms converge essentially to the same plan. However, we demonstrate that for any of the algorithms studied, starting with previously optimized intensity distributions as the initial guess but for different objective function parameters, the solution frequently gets trapped in local minima. We found that the initial intensity distribution obtained from IMRT optimization utilizing objective function parameters, which favor a specific anatomic structure, would lead to a local minimum corresponding to that structure. Our results indicate that from among the gradient algorithms tested, Newton's method appears to be the fastest by far. Different gradient algorithms have the same convergence properties for dose-volume- and EUD-based objective functions. The hybrid dose calculation strategy is valid and can significantly accelerate the optimization process. The degree of acceleration achieved depends on the type of optimization problem being addressed (e.g., IMRT optimization, intensity modulated beam configuration optimization, or objective function parameter optimization). Under special conditions, gradient algorithms will get trapped in local minima, and reoptimization, starting with the results of previous optimization, will lead to solutions that are generally not significantly different from the local minimum.

Algorithms↗

PubMed2001

Potential gain from optimizing multigeneration selection on an identified quantitative trait locus.

The potential extra response that can be obtained from the optimal use of a known QTL in selection by optimizing weights in an index of breeding value for the QTL and polygenic EBV was investigated for a range of parameters. Optimal strategies were derived for a deterministic model of simultaneous selection on a QTL and polygenic effects using optimal control theory. Responses over 10 generations to the following selection strategies were compared: 1) standard QTL selection, with QTL weights equal to 1, 2) optimal QTL selection, 3) stepwise single-generation optimal QTL selection, and 4) non-QTL selection based on phenotype. Cumulative discounted response with discount rates of 10 or 30% per generation were evaluated and used as objective for optimal selection strategies. Optimal selection balanced the conflict between short- and long-term responses and gave greater cumulative discounted response than standard QTL selection of up to 20%, but less than 5% for most cases. Discount rate had limited impact. For a QTL with an additive effect of one polygenic standard deviation, cumulative discounted response from optimal QTL selection was less than 5% greater than response for non-QTL selection for most cases. Exceptions were traits with low heritability and recessive QTL at low frequency, for which extra response was up to 55% greater. Stepwise optimal selection resulted in less cumulative discounted response than standard QTL selection for QTL with negative dominance. The benefit of optimal over stepwise optimal selection was limited (less than 4%) for most cases, except for overdominant QTL. These results indicate that optimizing selection on an identified QTL can result in greater responses to selection but that extra responses tend to be limited for the situations studied here of single-stage purebred selection on a single QTL for a trait observed on both sexes.

Animals↗

PubMed2003

Optimal conservation effort for a population in a stochastic environment.

We study the optimal conservation effort for a population in a fluctuating environment. The survivorship of a population is affected by unpredictable environmental fluctuation (noise) and can be improved by conservation effort accompanied by a cost. The optimal effort level is the one that minimizes the total cost, defined as the weighted sum of the population extinction risk and the economic cost of conservation effort. The optimal effort depends on the variance and the probability distribution of the noise, the relative importance of the population's survival vs. the economic cost, the effectiveness of conservation effort, and the time scope over which we optimize. The analysis of dynamic programming illustrates that the choice of extinction risk function greatly affects the optimal effort level. The conservation effort level that is the best solution of a multiple-year optimization may be higher than that for the corresponding single-year optimization, if the population is relatively safe. However, the conservation level for the multiple-year optimization becomes lower than for the single-year optimization if the population is endangered. In a similar manner, the optimal conservation effort level for the problem with a short time scope is either higher or lower than that for the problem with a long time scope, depending on the extinction risk of the population. Next, for each parameter of the model, we define five different sensitivities of extinction probability or of the total cost. We then study the mean increase in the total cost caused by the uncertainty of parameters. To achieve the best conservation result, we need to invest the limited research effort to the parameter with the largest effect to the optimal effort level, rather than to those with large impacts on the extinction probability or on the total cost. The recommended policy should depend critically on the choice of the criterion to optimize, which shows the importance of theoretical study of the relationship in performing proper decision making in conservation practice.

Animals↗

PubMed2000

Treatment-plan optimization for soft-tissue sarcoma brachytherapy using a genetic algorithm.

PURPOSE: To describe a treatment-plan optimization system for temporary implant of soft-tissue sarcomas using a genetic algorithm, and evaluate its potential advantages over manual planning. METHODS AND MATERIALS: A planning system that optimizes the distribution of radioactive seeds needed for adequate coverage of the target in the treatment of soft-tissue sarcomas has been designed and implemented. The treatment-planning procedures include simulation, film digitization, target-volume definition, optimized planning, and plan evaluation. The input to the optimization program consists of seed coordinates reconstructed from isocentric films, prescription points, and a list of available seed activities. The optimization is performed using a genetic algorithm. RESULTS: Case studies are presented, which compare plans generated by computer optimization or by trial and error (manually). As expected, computer-optimized plans are often (but not always) superior to manual plans. This is particularly evident for situations where (unavoidably) catheters are far apart or irregularly spaced, in which case the advantages of optimized planning in terms of tumor coverage can be quite dramatic. When the target volume is well contained, the optimized plan minimizes the dose to normal tissue. Computer-based optimization has the additional advantage of being much faster than manual planning; this is valuable because it often reduces the total time the patient will spend in the hospital before implantation. CONCLUSION: Optimized planning with a genetic algorithm and seeds of different activities significantly improves planning efficiency and generally results in improved plan quality. The utility of this optimization system is not limited to sarcoma implants.

Adult↗

PubMed2001

Role of beam orientation optimization in intensity-modulated radiation therapy.

PURPOSE: To investigate the role of beam orientation optimization in intensity-modulated radiation therapy (IMRT) and to examine the potential benefits of noncoplanar intensity-modulated beams. METHODS AND MATERIALS: A beam orientation optimization algorithm was implemented. For this purpose, system variables were divided into two groups: beam position (gantry and table angles) and beam profile (beamlet weights). Simulated annealing was used for beam orientation optimization and the simultaneous iterative inverse treatment planning algorithm (SIITP) for beam intensity profile optimization. Three clinical cases were studied: a localized prostate cancer, a nasopharyngeal cancer, and a paraspinal tumor. Nine fields were used for all treatments. For each case, 3 types of treatment plan optimization were performed: (1) beam intensity profiles were optimized for 9 equiangular spaced coplanar beams; (2) orientations and intensity profiles were optimized for 9 coplanar beams; (3) orientations and intensity profiles were optimized for 9 noncoplanar beams. RESULTS: For the localized prostate case, all 3 types of optimization described above resulted in dose distributions of a similar quality. For the nasopharynx case, optimized noncoplanar beams provided a significant gain in the gross tumor volume coverage. For the paraspinal case, orientation optimization using noncoplanar beams resulted in better kidney sparing and improved gross tumor volume coverage. CONCLUSION: The sensitivity of an IMRT treatment plan with respect to the selection of beam orientations varies from site to site. For some cases, the choice of beam orientations is important even when the number of beams is as large as 9. Noncoplanar beams provide an additional degree of freedom for IMRT treatment optimization and may allow for notable improvement in the quality of some complicated plans.

Algorithms↗

PubMed2002

Incorporating prior knowledge into beam orientation optimization in IMRT.

PURPOSE: Selection of beam configuration in currently available intensity-modulated radiotherapy (IMRT) treatment planning systems is still based on trial-and-error search. Computer beam orientation optimization has the potential to improve the situation, but its practical implementation is hindered by the excessive computing time associated with the calculation. The purpose of this work is to provide an effective means to speed up the beam orientation optimization by incorporating a priori geometric and dosimetric knowledge of the system and to demonstrate the utility of the new algorithm for beam placement in IMRT. METHODS AND MATERIALS: Beam orientation optimization was performed in two steps. First, the quality of each possible beam orientation was evaluated using beam's-eye-view dosimetrics (BEVD) developed in our previous study. A simulated annealing algorithm was then employed to search for the optimal set of beam orientations, taking into account the BEVD scores of different incident beam directions. During the calculation, sampling of gantry angles was weighted according to the BEVD score computed before the optimization. A beam direction with a higher BEVD score had a higher probability of being included in the trial configuration, and vice versa. The inclusion of the BEVD weighting in the stochastic beam angle sampling process made it possible to avoid spending valuable computing time unnecessarily at "bad" beam angles. An iterative inverse treatment planning algorithm was used for beam intensity profile optimization during the optimization process. The BEVD-guided beam orientation optimization was applied to an IMRT treatment of paraspinal tumor. The advantage of the new optimization algorithm was demonstrated by comparing the calculation with the conventional scheme without the BEVD weighting in the beam sampling. RESULTS: The BEVD tool provided useful guidance for the selection of the potentially good directions for the beams to incident and was used to guide the search for the optimal beam configuration. The BEVD-guided sampling improved both optimization speed and convergence of the calculation. A comparison of several five-field IMRT treatment plans obtained with and without BEVD guidance indicated that the computational efficiency was increased by a factor of approximately 10. CONCLUSION: Incorporation of BEVD information allows for development of a more robust tool for beam orientation optimization in IMRT planning. It enables us to more effectively use the angular degree of freedom in IMRT without paying the excessive computing overhead and brings us one step closer to the goal of automated selection of beam orientations in a clinical environment.

Algorithms↗

PubMed2006

Optimal grids for generalized finite basis and discrete variable representations: definition and method of calculation.

The method of optimal generalized finite basis and discrete variable representations (FBR and DVR) generalizes the standard, Gaussian quadrature grid-classical orthonormal polynomial basis-based FBR/DVR method to general sets of grid points and to general, nondirect product, and/or nonpolynomial bases. Here, it is shown how an optimal set of grid points can be obtained for an optimal generalized FBR/DVR calculation with a given truncated basis. Basis set optimized and potential optimized grids are defined. The optimized grids are shown to minimize a function of grid points derived by relating the optimal generalized FBR of a Hamiltonian operator to a non-Hermitian effective Hamiltonian matrix. Locating the global minimum of this function can be reduced to finding the zeros of a function in the case of one dimensional problems and to solving a system of D nonlinear equations repeatedly in the case of D>1 dimensional problems when there is an equal number of grid points and basis functions. Gaussian quadrature grids are shown to be basis optimized grids. It is demonstrated by a numerical example that an optimal generalized FBR/DVR calculation of the eigenvalues of a Hamiltonian operator with potential optimized grids can have orders of magnitude higher accuracy than a variational calculation employing the same truncated basis. Nevertheless, for numerical integration with the optimal generalized FBR quadrature rule basis optimized grids are the best among grids of the same number of points. The notions of Gaussian quadrature and Gaussian quadrature accuracy are extended to general, multivariable basis functions.

Journal Article↗

PubMed2005

A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning.

Automatic beam angle selection is an important but challenging problem for intensity-modulated radiation therapy (IMRT) planning. Though many efforts have been made, it is still not very satisfactory in clinical IMRT practice because of overextensive computation of the inverse problem. In this paper, a new technique named BASPSO (Beam Angle Selection with a Particle Swarm Optimization algorithm) is presented to improve the efficiency of the beam angle optimization problem. Originally developed as a tool for simulating social behaviour, the particle swarm optimization (PSO) algorithm is a relatively new population-based evolutionary optimization technique first introduced by Kennedy and Eberhart in 1995. In the proposed BASPSO, the beam angles are optimized using PSO by treating each beam configuration as a particle (individual), and the beam intensity maps for each beam configuration are optimized using the conjugate gradient (CG) algorithm. These two optimization processes are implemented iteratively. The performance of each individual is evaluated by a fitness value calculated with a physical objective function. A population of these individuals is evolved by cooperation and competition among the individuals themselves through generations. The optimization results of a simulated case with known optimal beam angles and two clinical cases (a prostate case and a head-and-neck case) show that PSO is valid and efficient and can speed up the beam angle optimization process. Furthermore, the performance comparisons based on the preliminary results indicate that, as a whole, the PSO-based algorithm seems to outperform, or at least compete with, the GA-based algorithm in computation time and robustness. In conclusion, the reported work suggested that the introduced PSO algorithm could act as a new promising solution to the beam angle optimization problem and potentially other optimization problems in IMRT, though further studies need to be investigated.

Algorithms↗

PubMed2006

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Algorithms↗

PubMed1998

Optimization and FROC analysis of rule-based detection schemes using a multiobjective approach.

Computerized detection schemes have the potential of increasing diagnostic accuracy in medical imaging by alerting radiologists to lesions that they initially overlooked. These schemes typically employ multiple parameters such as threshold values or filter weights to arrive at a detection decision. In order for the system to have high performance, the values of these parameters need to be set optimally. Conventional optimization techniques are designed to optimize a scalar objective function. The task of optimizing the performance of a computerized detection scheme, however, is clearly a multiobjective problem: we wish to simultaneously improve the sensitivity and false-positive rate of the system. In this work we investigate a multiobjective approach to optimizing computerized rule-based detection schemes. In a multiobjective optimization, multiple objectives are simultaneously optimized, with the objective now being a vector-valued function. The multiobjective optimization problem admits a set of solutions, known as the Pareto-optimal set, which are equivalent in the absence of any information regarding the preferences of the objectives. The performances of the Pareto-optimal solutions can be interpreted as operating points on an optimal free-response receiver operating characteristic (FROC) curve, greater than or equal to the points on any possible FROC curve for a given dataset and detection scheme. It is demonstrated that generating FROC curves in this manner eliminates several known problems with conventional FROC curve generation techniques for rule-based detection schemes. We employ the multiobjective approach to optimize a rule-based scheme for clustered microcalcification detection that has been developed in our laboratory.

Algorithms↗

PubMed2001

Simultaneous optimization of beam orientations and beam weights in conformal radiotherapy.

A methodology for the concurrent optimization of beam orientations and beam weights in conformal radiotherapy treatment planning has been developed and tested on a cohort of five patients. The algorithm is based on a beam-weight optimization scheme with a downhill simplex optimization engine. The use of random voxels in the dose calculation provides much of the required speed up in the optimization process, and allows the simultaneous optimization of beam orientations and beam weights in a reasonable time. In the implementation of the beam-weight optimization algorithm just 10% of the original patient voxels are used for the dose calculation and cost function evaluation. A fast simulated annealing algorithm controls the optimization of the beam arrangement. The optimization algorithm was able to produce clinically acceptable plans for the five patients in the cohort study. The algorithm equalized the dose to the optic nerves compared to the standard plans and reduced the mean dose to the brain stem by an average of 4.4% (+/- 1.9, 1 SD), p value = 0.007. The dose distribution to the PTV was not compromised by developing beam arrangements via the optimization algorithm. In conclusion, the simultaneous optimization of beam orientations and beam weights has been developed to be routinely used in a realistic time. The results of optimization in a small cohort study show that the optimization can reliably produce clinically acceptable dose distributions and may be able to improve dose distributions compared to those from a human planner.

Algorithms↗

PubMed2002

Direct aperture optimization: a turnkey solution for step-and-shoot IMRT.

IMRT treatment plans for step-and-shoot delivery have traditionally been produced through the optimization of intensity distributions (or maps) for each beam angle. The optimization step is followed by the application of a leaf-sequencing algorithm that translates each intensity map into a set of deliverable aperture shapes. In this article, we introduce an automated planning system in which we bypass the traditional intensity optimization, and instead directly optimize the shapes and the weights of the apertures. We call this approach "direct aperture optimization." This technique allows the user to specify the maximum number of apertures per beam direction, and hence provides significant control over the complexity of the treatment delivery. This is possible because the machine dependent delivery constraints imposed by the MLC are enforced within the aperture optimization algorithm rather than in a separate leaf-sequencing step. The leaf settings and the aperture intensities are optimized simultaneously using a simulated annealing algorithm. We have tested direct aperture optimization on a variety of patient cases using the EGS4/BEAM Monte Carlo package for our dose calculation engine. The results demonstrate that direct aperture optimization can produce highly conformal step-and-shoot treatment plans using only three to five apertures per beam direction. As compared with traditional optimization strategies, our studies demonstrate that direct aperture optimization can result in a significant reduction in both the number of beam segments and the number of monitor units. Direct aperture optimization therefore produces highly efficient treatment deliveries that maintain the full dosimetric benefits of IMRT.

Algorithms↗

PubMed2002

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.

Algorithms↗

PubMed2005

Simultaneous optimization of sequential IMRT plans.

Radiotherapy often comprises two phases, in which irradiation of a volume at risk for microscopic disease is followed by a sequential dose escalation to a smaller volume either at a higher risk for microscopic disease or containing only gross disease. This technique is difficult to implement with intensity modulated radiotherapy, as the tolerance doses of critical structures must be respected over the sum of the two plans. Techniques that include an integrated boost have been proposed to address this problem. However, clinical experience with such techniques is limited, and many clinicians are uncomfortable prescribing nonconventional fractionation schemes. To solve this problem, we developed an optimization technique that simultaneously generates sequential initial and boost IMRT plans. We have developed an optimization tool that uses a commercial treatment planning system (TPS) and a high level programming language for technical computing. The tool uses the TPS to calculate the dose deposition coefficients (DDCs) for optimization. The DDCs were imported into external software and the treatment ports duplicated to create the boost plan. The initial, boost, and tolerance doses were specified and used to construct cost functions. The initial and boost plans were optimized simultaneously using a gradient search technique. Following optimization, the fluence maps were exported to the TPS for dose calculation. Seven patients treated using sequential techniques were selected from our clinical database. The initial and boost plans used to treat these patients were developed independently of each other by dividing the tolerance doses proportionally between the initial and boost plans and then iteratively optimizing the plans until a summation that met the treatment goals was obtained. We used the simultaneous optimization technique to generate plans that met the original planning goals. The coverage of the initial and boost target volumes in the simultaneously optimized plans was equivalent to the independently optimized plans actually used for treatment. Tolerance doses of the critical structures were respected for the plan sum; however, the dose to critical structures for the individual initial and boost plans was different between the simultaneously optimized and the independently optimized plans. In conclusion, we have demonstrated a method for optimization of initial and boost plans that treat volume reductions using the same dose per fraction. The method is efficient, as it avoids the iterative approach necessitated by currently available TPSs, and is generalizable to more than two treatment phases. Comparison with clinical plans developed independently suggests that current manual techniques for planning sequential treatments may be suboptimal.

Algorithms↗

PubMed2006

Introducing robustness in multi-objective optimization.

In optimization studies including multi-objective optimization, the main focus is placed on finding the global optimum or global Pareto-optimal solutions, representing the best possible objective values. However, in practice, users may not always be interested in finding the so-called global best solutions, particularly when these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the robust solutions which are less sensitive to small perturbations in variables. Although robust optimization is dealt with in detail in single-objective evolutionary optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find a robust frontier, instead of the global Pareto-optimal frontier in a problem. The first procedure is a straightforward extension of a technique used for single-objective optimization and the second procedure is a more practical approach enabling a user to set the extent of robustness desired in a problem. To demonstrate the differences between global and robust multi-objective optimization principles and the differences between the two robust optimization procedures suggested here, we develop a number of constrained and unconstrained test problems having two and three objectives and show simulation results using an evolutionary multi-objective optimization (EMO) algorithm. Finally, we also apply both robust optimization methodologies to an engineering design problem.

Algorithms↗