Fast iterative algorithms for three-dimensional inverse treatment planning

Fluence map optimisation for prostate cancer intensity modulated radiotherapy planning using iterative solution method

Here we projected a model-based IMRT treatment plan to produce the optimal radiation dosage by considering that the maximum amount of prescribed dose should be delivered to the target without affecting the surrounding healthy tissues especially the OARs. Fluence mapping is used for inverse planning. This suggested method can generate global minima for IMRT plans with reliable plan quality among diverse treatment planners and to provide better safety for significant parallel OARs in an effective way. The whole methodology is having the capability to handles various objectives and to generate effective treatment procedures as validated with illustrations on the CORT dataset. For the validation of our methodology, we have compared our result with the two other approaches for calculating the objectives based on dose-volume bounds and found that in our methodology dose across the prostate and lymph nodes is maximum and the time required for the convergence is minimum.

A convex optimization approach to radiation treatment planning with dose constraints

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface.

The Scatter Search Based Algorithm for Beam Angle Optimization in Intensity-Modulated Radiation Therapy

This article introduces a new framework for beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) using the Scatter Search Based Algorithm. The potential benefits of plans employing the coplanar optimized beam sets are also examined. In the proposed beam angle selection algorithm, the problem is solved in two steps. Initially, the gantry angles are selected using the Scatter Search Based Algorithm, which is a global optimization method. Then, for each beam configuration, the intensity profile is calculated by the conjugate gradient method to score each beam angle set chosen. A simulated phantom case with obvious optimal beam angles was used to benchmark the validity of the presented algorithm. Two clinical cases (TG-119 phantom and prostate cases) were examined to prepare a dose volume histogram (DVH) and determine the dose distribution to evaluate efficiency of the algorithm. A clinical plan with the optimized beam configuration was compared with an equiangular plan to determine the efficiency of the proposed algorithm. The BAO plans yielded significant improvements in the DVHs and dose distributions compared to the equispaced coplanar beams for each case. The proposed algorithm showed its potential to effectively select the beam direction for IMRT inverse planning at different tumor sites.

Robust fluence map optimization via alternating direction method of multipliers with empirical parameter optimization

For the treatment planning during intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT), beam fluence maps can be first optimized via fluence map optimization (FMO) under the given dose prescriptions and constraints to conformally deliver the radiation dose to the targets while sparing the organs-at-risk, and then segmented into deliverable MLC apertures via leaf or arc sequencing algorithms. This work is to develop an efficient algorithm for FMO based on alternating direction method of multipliers (ADMM). Here we consider FMO with the least-square cost function and non-negative fluence constraints, and its solution algorithm is based on ADMM, which is efficient and simple-to-implement. In addition, an empirical method for optimizing the ADMM parameter is developed to improve the robustness of the ADMM algorithm. The ADMM based FMO solver was benchmarked with the quadratic programming method based on the interior-point (IP) method using the CORT dataset. The comparison results suggested the ADMM solver had a similar plan quality with slightly smaller total objective function value than IP. A simple-to-implement ADMM based FMO solver with empirical parameter optimization is proposed for IMRT or VMAT.

A fast optimization algorithm for multicriteria intensity modulated proton therapy planning

PURPOSE

To describe a fast projection algorithm for optimizing intensity modulated proton therapy (IMPT) plans and to describe and demonstrate the use of this algorithm in multicriteria IMPT planning.

METHODS

The authors develop a projection-based solver for a class of convex optimization problems and apply it to IMPT treatment planning. The speed of the solver permits its use in multicriteria optimization, where several optimizations are performed which span the space of possible treatment plans. The authors describe a plan database generation procedure which is customized to the requirements of the solver. The optimality precision of the solver can be specified by the user.

RESULTS

The authors apply the algorithm to three clinical cases: A pancreas case, an esophagus case, and a tumor along the rib cage case. Detailed analysis of the pancreas case shows that the algorithm is orders of magnitude faster than industry-standard general purpose algorithms (MOSEK'S interior point optimizer, primal simplex optimizer, and dual simplex optimizer). Additionally, the projection solver has almost no memory overhead.

CONCLUSIONS

The speed and guaranteed accuracy of the algorithm make it suitable for use in multicriteria treatment planning, which requires the computation of several diverse treatment plans. Additionally, given the low memory overhead of the algorithm, the method can be extended to include multiple geometric instances and proton range possibilities, for robust optimization.

Sweeping-window arc therapy: an implementation of rotational IMRT with automatic beam-weight calculation

Sweeping-window arc therapy (SWAT) is a variation of intensity-modulated radiation therapy (IMRT) with direct aperture optimization (DAO) that is initialized with a leaf sequence of sweeping windows that move back and forth periodically across the target as the gantry rotates. This initial sequence induces modulation in the dose and is assumed to be near enough to a minimum to allow successful optimization, done with simulated annealing, without requiring excessive leaf speeds. Optimal beam weights are calculated analytically, with easy extension to allow for variable beam weights. In this paper SWAT is tested on a phantom model and clinical prostate case. For the phantom, constant and variable beam weights are used. Although further work (in particular, improving the dose model) is required, the results show SWAT to be a feasible approach to generating deliverable dynamic arc treatments that are optimized.

Towards biologically conformal radiation therapy (BCRT): Selective IMRT dose escalation under the guidance of spatial biology distribution

It is well known that the spatial biology distribution (e.g., clonogen density, radiosensitivity, tumor proliferation rate, functional importance) in most tumors and sensitive structures is heterogeneous. Recent progress in biological imaging is making the mapping of this distribution increasingly possible. The purpose of this work is to establish a theoretical framework to quantitatively incorporate the spatial biology data into intensity modulated radiation therapy (IMRT) inverse planning. In order to implement this, we first derive a general formula for determining the desired dose to each tumor voxel for a known biology distribution of the tumor based on a linear-quadratic model. The desired target dose distribution is then used as the prescription for inverse planning. An objective function with the voxel-dependent prescription is constructed with incorporation of the nonuniform dose prescription. The functional unit density distribution in a sensitive structure is also considered phenomenologically when constructing the objective function. Two cases with different hypothetical biology distributions are used to illustrate the new inverse planning formalism. For comparison, treatments with a few uniform dose prescriptions and a simultaneous integrated boost are also planned. The biological indices, tumor control probability (TCP) and normal tissue complication probability (NTCP), are calculated for both types of plans and the superiority of the proposed technique over the conventional dose escalation scheme is demonstrated. Our calculations revealed that it is technically feasible to produce deliberately nonuniform dose distributions with consideration of biological information. Compared with the conventional dose escalation schemes, the new technique is capable of generating biologically conformal IMRT plans that significantly improve the TCP while reducing or keeping the NTCPs at their current levels. Biologically conformal radiation therapy (BCRT) incorporates patient-specific biological information and provides an outstanding opportunity for us to truly individualize radiation treatment. The proposed formalism lays a technical foundation for BCRT and allows us to maximally exploit the technical capacity of IMRT to more intelligently escalate the radiation dose.

Clinical knowledge-based inverse treatment planning

Clinical IMRT treatment plans are currently made using dose-based optimization algorithms, which do not consider the nonlinear dose-volume effects for tumours and normal structures. The choice of structure specific importance factors represents an additional degree of freedom of the system and makes rigorous optimization intractable. The purpose of this work is to circumvent the two problems by developing a biologically more sensible yet clinically practical inverse planning framework. To implement this, the dose-volume status of a structure was characterized by using the effective volume in the voxel domain. A new objective function was constructed with the incorporation of the volumetric information of the system so that the figure of merit of a given IMRT plan depends not only on the dose deviation from the desired distribution but also the dose-volume status of the involved organs. The conventional importance factor of an organ was written into a product of two components: (i) a generic importance that parametrizes the relative importance of the organs in the ideal situation when the goals for all the organs are met; (ii) a dose-dependent factor that quantifies our level of clinical/dosimetric satisfaction for a given plan. The generic importance can be determined a priori, and in most circumstances, does not need adjustment, whereas the second one, which is responsible for the intractable behaviour of the trade-off seen in conventional inverse planning, was determined automatically. An inverse planning module based on the proposed formalism was implemented and applied to a prostate case and a head-neck case. A comparison with the conventional inverse planning technique indicated that, for the same target dose coverage, the critical structure sparing was substantially improved for both cases. The incorporation of clinical knowledge allows us to obtain better IMRT plans and makes it possible to auto-select the importance factors, greatly facilitating the inverse planning process. The new formalism proposed also reveals the relationship between different inverse planning schemes and gives important insight into the problem of therapeutic plan optimization. In particular, we show that the EUD-based optimization is a special case of the general inverse planning formalism described in this paper.

Re-treatment of a lung tumour using a simple intensity-modulated radiotherapy approach

We present a lung tumour case where, although the proximal spinal cord had already reached its dose tolerance, re-treatment was indicated. Minimization of the cord dose was defined as the main constraint for this case, however additional dose to the heart was considered. A simple (4 field) intensity-modulated radiotherapy (IMRT) treatment which proved superior to the standard conformal plan was developed using the Computerized Medical Systems (CMS) XiO treatment planning system. The IMRT plan was found to be superior to the conventional conformal plan regarding tumour coverage. It provided 100% saturation of the planning target volume (PTV) by the 95% isodose cloud, whereas the latter only provided 77% coverage. A step and shoot delivery using 10 intensity levels was developed and subsequently delivered for this patient. We considered it to be a routine application of IMRT and an important example of how it can offer benefit in individual and appropriate cases where conventional treatment is inadequate.

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

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

Inverse planning in three-dimensional conformal and intensity-modulated radiotherapy of mid-thoracic oesophageal cancer

The aim of this study is to demonstrate the use of inverse planning in three-dimensional conformal radiation therapy (3DCRT) of oesophageal cancer patients and to evaluate its dosimetric results by comparing them with forward planning of 3DCRT and inverse planning of intensity-modulated radiotherapy (IMRT). For each of the 15 oesophageal cancer patients in this study, the forward 3DCRT, inverse 3DCRT and inverse IMRT plans were produced using the FOCUS treatment planning system. The dosimetric results and the planner's time associated with each of the treatment plans were recorded for comparison. The inverse 3DCRT plans showed similar dosimetric results to the forward plans in the planning target volume (PTV) and organs at risk (OARs). However, they were inferior to that of the IMRT plans in terms of tumour control probability and target dose conformity. Furthermore, the inverse 3DCRT plans were less effective in reducing the percentage lung volume receiving a dose below 25 Gy when compared with the IMRT plans. The inverse 3DCRT plans delivered a similar heart dose as in the forward plans, but higher dose than the IMRT plans. The inverse 3DCRT plans significantly reduced the operator's time by 2.5 fold relative to the forward plans. In conclusion, inverse planning for 3DCRT is a reasonable alternative to the forward planning for oesophageal cancer patients with reduction of the operator's time. However, IMRT has the better potential to allow further dose escalation and improvement of tumour control.

Inverse treatment planning with adaptively evolving voxel-dependent penalty scheme

In current inverse planning algorithms it is common to treat all voxels within a target or sensitive structure equally and use structure specific prescriptions and weighting factors as system parameters. In reality, the voxels within a structure are not identical in complying with their dosimetric goals and there exists strong intrastructural competition. Inverse planning objective function should not only balance the competing objectives of different structures but also that of the individual voxels in various structures. In this work we propose to model the intrastructural tradeoff through the modulation of voxel-dependent importance factors and deal with the challenging problem of how to obtain a sensible set of importance factors with a manageable amount of computing. Instead of letting the values of voxel-dependent importance to vary freely during the search process, an adaptive algorithm, in which the importance factors were tied to the local radiation doses through a heuristically constructed relation, was developed. It is shown that the approach is quite general and the EUD-based optimization is a special case of the proposed framework. The new planning tool was applied to study a hypothetical phantom case and a prostate case. Comparison of the results with that obtained using conventional inverse planning technique with structure specific importance factors indicated that the dose distributions from the conventional inverse planning are at best suboptimal and can be significantly improved with the help of the proposed nonuniform penalty scheme.

Incorporating model parameter uncertainty into inverse treatment planning

Radiobiological treatment planning depends not only on the accuracy of the models describing the dose-response relation of different tumors and normal tissues but also on the accuracy of tissue specific radiobiological parameters in these models. Whereas the general formalism remains the same, different sets of model parameters lead to different solutions and thus critically determine the final plan. Here we describe an inverse planning formalism with inclusion of model parameter uncertainties. This is made possible by using a statistical analysis-based frameset developed by our group. In this formalism, the uncertainties of model parameters, such as the parameter a that describes tissue-specific effect in the equivalent uniform dose (EUD) model, are expressed by probability density function and are included in the dose optimization process. We found that the final solution strongly depends on distribution functions of the model parameters. Considering that currently available models for computing biological effects of radiation are simplistic, and the clinical data used to derive the models are sparse and of questionable quality, the proposed technique provides us with an effective tool to minimize the effect caused by the uncertainties in a statistical sense. With the incorporation of the uncertainties, the technique has potential for us to maximally utilize the available radiobiology knowledge for better IMRT treatment.

Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumour as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighbouring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard multileaf collimator (MLC) delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modelled mathematically as a system of linear inequalities. We show that using this method allows us to arrive at a smoother intensity pattern. Including nonlinear terms in the simultaneous projection algorithm to deal with dose-volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and the gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.

Assessment of different IMRT boost delivery methods on target coverage and normal-tissue sparing

PURPOSE

Because of biologic, medical, and sometimes logistic reasons, patients may be treated with 3D conformal therapy or intensity-modulated radiation therapy (IMRT) for the initial treatment volume (PTV(1)) followed by a sequential IMRT boost dose delivered to the boost volume (PTV(2)). In some patients, both PTV(1) and PTV(2) may be simultaneously treated by IMRT (simultaneous integrated boost technique). The purpose of this work was to assess the sequential and simultaneous integrated boost IMRT delivery techniques on target coverage and normal-tissue sparing.

MATERIALS AND METHODS

Fifteen patients with head-and-neck (H&N), lung, and prostate cancer were selected for this comparative study. Each site included 5 patients. In all patients, the target consisted of PTV(1) and PTV(2). The prescription doses to PTV(1) and PTV(2) were 46 Gy and 66 Gy (H&N cases), 45 Gy and 66.6 Gy (lung cases), 50 Gy and 78 Gy (prostate cases), respectively. The critical structures included the following: spinal cord, parotid glands, and brainstem (H&N structures); spinal cord, esophagus, lungs, and heart (lung structures); and bladder, rectum, femurs (prostate structures). For all cases, three IMRT plans were created: (1) 3D conformal therapy to PTV(1) followed by sequential IMRT boost to PTV(2) (sequential-IMRT(1)), (2) IMRT to PTV(1) followed by sequential IMRT boost to PTV(2) (sequential-IMRT(2)), and (3) Simultaneous integrated IMRT boost to both PTV(1) and PTV(2) (SIB-IMRT). The treatment plans were compared in terms of their dose-volume histograms, target volume covered by 100% of the prescription dose (D(100%)), and maximum and mean structure doses (D(max) and D(mean)).

RESULTS

H&N cases: SIB-IMRT produced better sparing of both parotids than sequential-IMRT(1), although sequential-IMRT(2) also provided adequate parotid sparing. On average, the mean cord dose for sequential-IMRT(1) was 29 Gy. The mean cord dose was reduced to approximately 20 Gy with both sequential-IMRT(2) and SIB-IMRT. Prostate cases: The volume of rectum receiving 70 Gy or more (V(>70 Gy)) was reduced to 18.6 Gy with SIB-IMRT from 22.2 Gy with sequential-IMRT(2). SIB-IMRT reduced the mean doses to both bladder and rectum by approximately 10% and approximately 7%, respectively, as compared to sequential-IMRT(2). The mean left and right femur doses with SIB-IMRT were approximately 32% lower than obtained with sequential-IMRT(1). Lung cases: The mean heart dose was reduced by approximately 33% with SIB-IMRT as compared to sequential-IMRT(1). The mean esophagus dose was also reduced by approximately 10% using SIB-IMRT as compared to sequential-IMRT(1). The percentage of the lung volume receiving 20 Gy (V(20 Gy)) was reduced to 26% by SIB-IMRT from 30.6% with sequential-IMRT(1).

CONCLUSIONS

For equal PTV coverage, both sequential-IMRT techniques demonstrated moderately improved sparing of the critical structures. SIB-IMRT, however, markedly reduced doses to the critical structures for most of the cases considered in this study. The conformality of the SIB-IMRT plans was also much superior to that obtained with both sequential-IMRT techniques. The improved conformality gained with SIB-IMRT may suggest that the dose to nontarget tissues will be lower.

Verification of IMRT fields by film dosimetry

In intensity modulated radiation therapy (IMRT) the aim of an accurate conformal dose distribution is obtained through a complex process. This ranges from the calculation of the optimal distribution of fluence by the treatment planning system (TPS), to the dose delivery through a multilamellar collimator (MLC), with several segments per beam in the step and shoot approach. The above-mentioned consideration makes mandatory an accurate dosimetric verification of the IM beams. A high resolution and integrating dosimeter, like the radiographic film, permits one to simultaneously measure the dose in a matrix of points, providing a good means of obtaining dose distributions. The intrinsic limitation of film dosimetry is the sensitivity dependence on the field size and on the measurement depth. However, the introduction of a scattered radiation filter permits the use of a single calibration curve for all field sizes and measurement depths. In this paper the quality control procedure developed for dosimetric verification of IMRT technique is reported. In particular a system of film dosimetry for the verification of a 6 MV photon beam has been implemented, with the introduction of the scattered radiation filter in the clinical practice that permits one to achieve an absolute dose determination with a global uncertainty within 3.4% (1 s.d.). The film has been calibrated to be used both in perpendicular and parallel configurations. The work also includes the characterization of the Elekta MLC. Ionimetric independent detectors have been used to check single point doses. The film dosimetry procedure has been applied to compare the measured absolute dose distributions with the ones calculated by the TPS, both for test and clinical plans. The agreement, quantified by the gamma index that seldom reaches the 1.5 value, is satisfying considering that the comparison is performed between absolute doses.

A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning

We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (> 95%), target homogeneity (< 10% overdosing and < 7% underdosing) and organ sparing using at least one of the two models.

Comparative analysis of intensity modulation inverse planning modules of three commercial treatment planning systems applied to head and neck tumour model

BACKGROUND AND PURPOSE

Three commercial treatment planning modules for intensity modulated radiation therapy (IMRT) Inverse Planning, MDS-Nordion Helax-TMS, Varian Cadplan-Helios, and CMS Focus, were compared in an attempt to determine potential application limits or dosimetric differences among various optimisation algorithms.

MATERIALS AND METHODS

A comparative analysis of intensity modulated dose distributions was conducted at planning level on a group of four patients presenting advanced head and neck cancers. In the study, we analysed primarily the static 'step and shoot' multileaf implementation of modulation realisation with some investigation, on the Cadplan-Helios implementation of the 'sliding window', the Varian dynamic approach to IMRT delivery. The whole study was carried out using the inverse planning tools implemented by vendors fully optimising each plan to obtain the best dosimetry given some general plan objectives. To achieve adequate target coverage, optimisation was carried out on Helax-TMS and CMS Focus adding extra margins of 5 or 6mm to the planning target volume (PTV). Beam arrangements were set with five and nine equally spaced fields. The study was conducted with two complexity levels. At the first level, dose-volume constraints were applied only to the target volume and to the spinal cord, while parotid glands were added at the second level. The relative values of dose distributions and dose-volume histograms were compared, together with an estimate of the biological implications in terms of Equivalent Uniform Dose to the target. In the Cadplan-Helios system also the dosimetric implications of the number of intensity levels selected for the discretisation of the fluence matrix were investigated.

RESULTS

With the application of common planning strategies and the proper consideration of treatment planning system (TPS) specific features (e.g. the PTV margin problem), no substantial differences among the three algorithms were demonstrated at the first level for PTV and spinal cord. At the second level of the study differences were outlined for Helax-TMS, where sub-optimal results were obtained with the 5-field geometry. Mainly due to the differences in optimisation volumes, Cadplan-Helios presented significant better sparing of healthy tissue around the PTV, in terms of mean dose to healthy tissue and Irradiated Volume at 50% dose level. Finally, to achieve dosimetrically acceptable and stable results on target, a minimum of eight intensity levels should be applied for the multileaf collimator (MLC) segmentation, giving an average of 1.5 segments per field and per intensity level.

CONCLUSIONS

Results obtained for the three IMRT TPS show in first instance that the optimisation algorithms analysed, as well as the conversion from computed fluences to multileaf sequences implemented in the planning systems can produce substantially equivalent dose plans (for target coverage and organs at risk sparing) if planning is performed with common strategies and once a strong understanding of each system feature is achieved. Secondly, a limited number of dose levels (about eight) is adequate at planning level.

An optimization algorithm for intensity modulated radiotherapy--the simulated dynamics with dose-volume constraints

We have developed a new method for optimization in intensity modulated radiation therapy (IMRT) that makes use of simulated dynamics in a classical system of interacting particles. An analogy is drawn between intensity profile optimization in IMRT and relaxation to the equilibrium configuration in a dynamic system. The intensities of beamlets are equivalent to the positions of the virtual particles. The potential energy of the system is defined by the objective function, which determines the equations of motion for the virtual particles. In this paper, we present the implementation of dose constraints and dose-volume constraints. Our strategy is to optimize the dose to the planned target volume (PTV) while keeping all constraints to the organs at risk (OARs) satisfied rigorously. A simple quadratic objective function is used that only includes terms for PTV voxels. By this approach, no additional parameters other than that for prescribing desired dose and constraints, such as importance factors, are needed. The hard constraints that require non-negative beamlet intensities and that the dose at any voxel in an OAR cannot exceed a maximum tolerance, are implemented as semi-transmittable potential barriers of infinite height. Dose-volume constraints are handled by placing hard constraints on partial volumes. Handling of the clinically applied constraints was tested using phantoms and clinical cases. Our results show that the dose-volume histogram (DVH) type of plan prescription can be fulfilled with satisfactory PTV coverage. In addition to the convenience of implementation, our method can achieve a high computational efficiency with the understanding of the dynamic behavior of the system.

Technical considerations in the application of intensity-modulated radiotherapy as a concomitant integrated boost for locally-advanced cervix cancer

The technical aspects of IMRT applied to cervix cancer are discussed in this paper, as well as issues related to tumor delineation, target volume definitions, inverse planning, and IMRT delivery. A theoretical example illustrating how IMRT can accurately mimic dose distributions obtained using conventional planning plus HDR brachytherapy is also shown. The notion of clinical optimization parameters is introduced to account for the radiation delivery variables, which affect the overall treatment time. This is especially relevant to the possible introduction of intrafractional movement and resulting inaccuracy, as well as facility efficiency.

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.

Application of constrained least-squares techniques to IMRT treatment planning

PURPOSE

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

METHODS AND MATERIALS

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

RESULTS

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

CONCLUSIONS

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

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

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

Beyond bixels: generalizing the optimization parameters for intensity modulated radiation therapy

Intensity modulated radiation therapy (IMRT) treatment planning systems optimize fluence distributions by subdividing the fluence distribution into rectangular bixels. The algorithms typically optimize the fluence intensity directly, often leading to fluence distributions with sharp discontinuities. These discontinuities may yield difficulties in delivery of the fluence distribution, leading to inaccurate dose delivery. We have developed a method for decoupling the bixel intensities from the optimization parameters; either by introducing optimization control points from which the bixel intensities are interpolated or by parametrizing the fluence distribution using basis functions. In either case, the number of optimization search parameters is reduced from the direct bixel optimization method. To illustrate the concept, the technique is applied to two-dimensional idealized head and neck treatment plans. The interpolation algorithms investigated were nearest-neighbor, linear and cubic spline, and radial basis functions serve as the basis function test. The interpolation and basis function optimization techniques were compared against the direct bixel calculation. The number of optimization parameters were significantly reduced relative to the bixel optimization, and this was evident in the reduction of computation time of as much as 58% from the full bixel optimization. The dose distributions obtained using the reduced optimization parameter sets were very similar to the full bixel optimization when examined by dose distributions, statistics, and dose-volume histograms. To evaluate the sensitivity of the fluence calculations to spatial misalignment caused either by delivery errors or patient motion, the doses were recomputed with a 1 mm shift in each beam and compared to the unshifted distributions. Except for the nearest-neighbor algorithm, the reduced optimization parameter dose distributions were generally less sensitive to spatial shifts than the bixel optimization. These results indicate that significant reductions in optimization parameter sets can be accomplished with a negligible reduction in dose distribution quality. The decreased parameters can result in a reduced optimization time, or can be used to allow an improved and consequently more computation-intensive dose calculation for more accurate dose calculations during the optimization process. The basis functions may be generalized to model the accelerator motion for direct computation of the accelerator motion sequence, removing the need for developing an independent leaf sequence step.

Minimizing delivery time and monitor units in static IMRT by leaf-sequencing

Intensity-modulated radiation therapy (IMRT) requires the determination of the appropriate multileaf collimator settings to deliver an intensity map. The purpose of this work was to attempt to reduce the number of segments required for IMRT delivery and the number of monitor units required to deliver an intensity map. An intensity map may be written as a matrix. Leaf sequencing was formulated as a problem of decomposing the matrix into a series of sub-matrices. Sets of random intensity matrices were created and the segmentations produced by applying different algorithms were compared. The number of segments, important if verification and record (VR) overhead is significant, and beam on times were examined. It is shown that reducing the value of the matrix entries by the maximum amount at each stage results in the smallest number of steps. Reducing the 2-norm (sum of the squares) of the matrix entries by the maximum amount at each step results in the smallest beam on time. Three new algorithms are introduced, two of which produce results that are superior to those generated by the algorithms of other researchers. The resulting methods can be expanded upon to include tongue and groove effects and leaf inter-digitization. With square random matrices of the order 15, the reduction in beam time and segmentation is up to 30-40%. Compared to previous algorithms, those presented here have demonstrated a reduction in the beam on time required to deliver an intensity map by 30-40%. Similarly, the number of segments needed to deliver an intensity map is also reduced.

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.

[Improvement of dose distribution of esophageal irradiation using the field-within-a-field technique]

The wide radiation field for mediastinal dose distribution should be inhomogeneous with the usual simple opposed beam irradiation. The purpose of this study was to improve the dose distribution of the mediastinum using a conventional planning system with a dose-volume histogram (DVH) and the field-in-field technique. Three-dimensional (3D) dose distribution is obtained in bilateral opposed-field irradiation. An overdose area obtained from the 3D dose distribution is defined and reprojected into the irradiation field. A new reduced field is created by removing the reprojected overdose area. A 3D dose distribution is again obtained and compared with the results from first one. Procedures were repeated until each of the target volumes was within +/-5% of the prescribed dose and the irradiation volume within 107% or less of the prescribed dose. From the DVH analysis, our field-within-a-field technique resulted in a more uniform dose distribution within the conventional planning. The field-within-a-field technique involves many parameters, and an inverse planning algorithm is suitable for computation. However, with our method, the forward planning system is adequate for planning, at least in a relatively straightforward planning system such as bilateral opposed fields therapy.

[Dosimetric verification in intensity modulated radiation therapy]

As part of dosimetric verification for IMRT intensity modulated radiation therapy, we examined the selection of a dosimeter in accordance with the purpose of physical measurement and the process of data analysis. Because of the high dose conformation in the target volume and minimum dose in the organs at risk (OAR) in IMRT, dosimetric verification is essential. Because the performance of dosimetric verification in a patient is not allowed, a physical phantom and dosimeter must be used. Dose verification using a physical phantom, from which the beam data optimized for a patient slated for IMRT are transferred, may cause latent error as a result of change in the depth of each beam toward an isocenter. This effect may change the dose distribution and prescription dose. The basic methods of dosimetric verification with physical measurement are point dosimetry, when the reference dose is given at a point by planning software, and volumetric dosimetry, when planning software gives the dose as a volumetric configuration. While the most accurate dosimetry is done using a calibrated ionization chamber, IMRT requires volumetric dosimetry using some kind of portal film or a polymer gel dosimeter, because of the need for dosimetric verification for an irregular dose distribution in IMRT. The importance of indirect dosimetry using these methods is to provide calibration as a dosimeter, absolute dose, and preservation of calibration. In our study, the verification of dose distribution for IMRT using portal film and a RANDO phantom could be performed with an error of less than 2% in all cases. The measurement error for the central dose using a JARP-type ionization chamber and MixDP was less than 3% in all cases except for the case with the maximum error. At the moment, IMRT requires a great deal of effort in the processes of planning, dosimetric verification, and isocenter checking in every fraction to maintain high accuracy. Although the need for a large amount of effort in the service of maintaining accuracy may be reasonable, it could be enough to inhibit the spread of IMRT. It is hoped that an easy method of dosimetric verification that still maintains a high level of accuracy will develop as a result of this great effort.

Optimization of intensity-modulated very high energy (50-250 MeV) electron therapy

This work evaluates the potential of very high energy (50-250 MeV) electron beams for dose conformation and identifies those variables that influence optimized dose distributions for this modality. Intensity-modulated plans for a prostate cancer model were optimized as a function of the importance factors, beam energy and number of energy bins, number of beams, and the beam orientations. A trial-and-error-derived constellation of importance factors for target and sensitive structures to achieve good conformal dose distributions was 500, 50, 10 and I for the target, rectum, bladder and normal tissues respectively. Electron energies greater than 100 MeV were found to be desirable for intensity-modulated very high energy electron therapy (VHEET) of prostate cancer. Plans generated for lower energy beams had relatively poor conformal dose distributions about the target region and delivered high doses to sensitive structures. Fixed angle beam treatments utilizing a large number of fields in the range 9-21 provided acceptable plans. Using more than 21 beams at fixed gantry angles had an insignificant effect on target coverage, but resulted in an increased dose to sensitive structures and an increased normal tissue integral dose. Minor improvements in VHEET plans utilizing a 'small' number (< or =9) of beams may be achieved if, in addition to intensity modulation, energy modulation is implemented using a small number (< or =3) of beam energies separated by 50 to 100 MeV. Rotation therapy provided better target dose homogeneity but unfortunately resulted in increased rectal dose, bladder dose and normal tissue integral dose relative to the 21-field fixed angle treatment plan. Modulation of the beam energy for rotation therapy had no beneficial consequences on the optimized dose distributions. Lastly, selection of beam orientations influenced the optimized treatment plan even when a large number of beams (approximately 15) were employed.

Intensity and energy modulated radiotherapy with proton beams: variables affecting optimal prostate plan

Inverse planning for intensity- and energy-modulated radiotherapy (IEMRT) with proton beams involves the selection of (i) the relative importance factors to control the relative importance of the target and sensitive structures, (ii) an appropriate energy resolution to achieve an acceptable depth modulation, (iii) an appropriate beamlet width to modulate the beam laterally, and (iv) a sufficient number of beams and their orientations. In this article we investigate the influence of these variables on the optimized dose distribution of a simulated prostate cancer IEMRT treatment. Good dose conformation for this prostate case was achieved using a constellation of I factors for the target, rectum, bladder, and normal tissues of 500, 50, 15, and 1, respectively. It was found that for an active beam delivery system, the energy resolution should be selected on the basis of the incident beams' energy spread (sigmaE) and the appropriate energy resolution varied from 1 MeV at sigmaE = 0.0 to 5 MeV at sigmaE= 2.0 MeV. For a passive beam delivery system the value of the appropriate depth resolution for inverse planning may not be critical as long as the value chosen is at least equal to one-half the FWHM of the primary beam Bragg peak. Results indicate that the dose grid element dimension should be equal to or no less than 70% of the beamlet width. For this prostate case, we found that a maximum of three to four beam ports is required since there was no significant advantage to using a larger number of beams. However for a small number (< or = 4) of beams the selection of beam orientations, while having only a minor effect on target coverage, strongly influenced the sensitive structure sparing and normal tissue integral dose.

Pseudo beam's-eye-view as applied to beam orientation selection in intensity-modulated radiation therapy

PURPOSE

To introduce the concept of pseudo beam's-eye-view (pBEV), to establish a framework for computer-assisted beam orientation selection in intensity-modulated radiation therapy (IMRT), and to evaluate the utility of the proposed technique.

METHODS AND MATERIALS

To facilitate the selection of beam orientations for IMRT treatment planning, a scoring of beam direction was introduced. The score function was based on the maximum target dose deliverable by the beam without exceeding the tolerance doses of the critical structures. For the score function calculation, the beam portal at given gantry and couch angles was divided into a grid of beamlets. Each beamlet crossing the target was assigned the maximum intensity that could be used without exceeding the dose tolerances of the organs at risk (OARs) and normal tissue. Thereafter, a score was assigned to the beam according to the target dose delivered. The beams for the treatment were selected among those with the highest scores. In a sense, this technique is similar to the beam's-eye-view approach used in conventional radiation therapy, except that the evaluation by a human is replaced by a score function, and beam modulation is taken into account.

RESULTS

The pBEV technique was tested on two clinical cases: a paraspinal treatment and a nasopharyngeal cancer with both coplanar and noncoplanar beam configurations. The plans generated under the guidance of pBEV for the paraspinal treatment offered superior target dose uniformity and reduced OAR doses. For the nasopharyngeal cancer case, it was also found that the pBEV-selected coplanar and noncoplanar beams significantly improved the target coverage without compromising the sparing of the OARs.

CONCLUSIONS

The pBEV technique developed in this work provides a comprehensive tool for beam orientation selection in IMRT. It is especially valuable for complicated cases, where the target is surrounded by several sensitive structures and where it is difficult to select a set of good beam orientations. The pBEV technique has considerable potential for simplifying the IMRT treatment planning process and for maximizing the technical capacity of IMRT.

Linear algebraic methods applied to intensity modulated radiation therapy

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

Optimization of the step-and-shoot leaf sequence for delivery of intensity modulated radiation therapy using a variable division scheme

To deliver an intensity modulated radiation therapy (IMRT) plan by multileaf collimator (MLC) it is necessary to convert beam profiles, generated from the inverse treatment planning algorithm, into a series of instructions that the MLC control system can execute. An idealized IMRT beam profile can be regarded as a continuously varying two-dimensional function and is usually represented by an intensity map, i.e., a discretized description in space and in intensity of the beam profile. It is common to assume that the intensity map be defined over a regular grid with N steps and equal increments of intensity levels. In reality, this may not be the optimal representation of the beam profile and may introduce unnecessary discrepancies between the intensity pattern delivered and that ideally required. We have implemented an algorithm capable of minimizing the difference between the two patterns on a beam specific basis. In other words, it can produce optimized intensity maps, individually produced to suit the (continuous function) intensity profile they are intended to approximate. This enhancement in conformation is achieved by allowing variable step size and unconstrained intensity levels in the final leaf sequence.

Computer-assisted selection of coplanar beam orientations in intensity-modulated radiation therapy

In intensity-modulated radiation therapy (IMRT), the incident beam orientations are often determined by a trial and error search. The conventional beam's-eye view (BEV) tool becomes less helpful in IMRT because it is frequently required that beams go through organs at risk (OARs) in order to achieve a compromise between the dosimetric objectives of the planning target volume (PTV) and the OARs. In this paper, we report a beam's-eye view dosimetrics (BEVD) technique to assist in the selection of beam orientations in IMRT. In our method, each beam portal is divided into a grid of beamlets. A score function is introduced to measure the 'goodness' of each beamlet at a given gantry angle. The score is determined by the maximum PTV dose deliverable by the beamlet without exceeding the tolerance doses of the OARs and normal tissue located in the path of the beamlet. The overall score of the gantry angle is given by a sum of the scores of all beamlets. For a given patient. the score function is evaluated for each possible beam orientation. The directions with the highest scores are then selected as the candidates for beam placement. This procedure is similar to the BEV approach used in conventional radiation therapy, except that the evaluation by a human is replaced by a score function to take into account the intensity modulation. This technique allows one to select beam orientations without the excessive computing overhead of computer optimization of beam orientation. It also provides useful insight into the problem of selection of beam orientation and is especially valuable for complicated cases where the PTV is surrounded by several sensitive structures and where it is difficult to select a set of 'good' beam orientations. Several two-dimensional (2D) model cases were used to test the proposed technique. The plans obtained using the BEVD-selected beam orientations were compared with the plans obtained using equiangular spaced beams. For all the model cases investigated, the use of BEVD-selected beam orientations improved the dose distributions significantly. These examples indicate that the technique has considerable potential for simplifying the IMRT treatment planning process and allows for better utilization of the technical capacity of IMRT.

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.

Requirements for radiation oncology physics in Australia and New Zealand

This Position Paper reviews the role, standards of practice, education, training and staffing requirements for radiation oncology physics. The role and standard of practice for an expert in radiation oncology physics, as defined by the ACPSEM, are consistent with the IAEA recommendations. International standards of safe practice recommend that this physics expert be authorised by a Regulatory Authority (in consultation with the professional organization). In order to accommodate the international and AHTAC recommendations or any requirements that may be set by a Regulatory Authority, the ACPSEM has defined the criteria for a physicist-in-training, a base level physicist, an advanced level physicist and an expert radiation oncology physicist. The ACPSEM shall compile separate registers for these different radiation oncology physicist categories. What constitutes a satisfactory means of establishing the number of physicists and support physics staff that is required in radiation oncology continues to be debated. The new ACPSEM workforce formula (Formula 2000) yields similar numbers to other international professional body recommendations. The ACPSEM recommends that Australian and New Zealand radiation oncology centres should aim to employ 223 and 46 radiation oncology physics staff respectively. At least 75% of this workforce should be physicists (168 in Australia and 35 in New Zealand). An additional 41 registrar physicist positions (34 in Australia and 7 in New Zealand) should be specifically created for training purposes. These registrar positions cater for the present physicist shortfall, the future expansion of radiation oncology and the expected attrition of radiation oncology physicists in the workforce. Registrar physicists shall undertake suitable tertiary education in medical physics with an organised in-house training program. The rapid advances in the theory and methodology of the new technologies for radiation oncology also require a stringent approach to maintaining a satisfactory standard of practice in radiation oncology physics. Appropriate on-going education of radiation oncology physicists as well as the educating of registrar physicists is essential. Institutional management and the ACPSEM must both play a key role in providing a means for satisfactory staff tuition on the safe and expert use of existing and new radiotherapy equipment.

Comparison of commercially available three-dimensional treatment planning algorithms for monitor unit calculations in the presence of heterogeneities

This study uses an anthropomorphic phantom and its computed tomography (CT) data set to evaluate monitor unit (MU) calculations using the CMS Focus Clarkson, the CMS Focus Multigrid Superposition Model, the CMS Focus FFT Convolution Model, and the ADAC Pinnacle Collapsed Cone Convolution Superposition Algorithms. Using heterogeneity corrections, a treatment plan and corresponding MU calculations were generated for several typical clinical situations. A diode detector, placed in an anthropomorphic phantom, was used to compare the treatment planning algorithms' predicted doses with measured data. Differences between diode measurements and the algorithms' calculations were within reasonable levels of acceptability as recommended by Van Dyk et al. [Int. J. Rad. Onc. Biol. Phys. 26, 261-273 (1993)], except for the CMS Clarkson algorithm, which predicted too few MU for delivery of the intended dose to chest wall fields.

Computer verification of fluence map for intensity modulated radiation therapy

In a treatment planning system for intensity modulated radiation therapy (IMRT), the time sequence of multileaf collimator (MLC) settings are derived from an optimal fluence map as a postoptimization process using a software module called a "leaf sequencer." The dosimetric accuracy of the dynamic delivery depends on the functionality of the module and it is important to verify independently the correctness of the leaf sequences for each field of a patient treatment. This verification is unique to the IMRT treatment and has been done using radiographic film, electronic portal imaging device (EPID) or electronic imaging system (BIS). The measurement tests both the leaf sequencer and the dynamic multileaf collimator (MLC) delivery system, providing a reliable assurance of clinical IMRT treatment. However, this process is labor intensive and time consuming. In this paper, we propose to separate quality assurance (QA) of the leaf sequencer from the dynamic MLC delivery system. We describe a simple computer algorithm for the verification of the leaf sequences. The software reads in the leaf sequences and simulates the motion of the MLC leaves. The generated fluence map is then compared quantitatively with the reference map from the treatment planning system. A set of pre-defined QA indices is introduced to measure the "closeness" between the computed and the reference maps. The approach has been used to validate the CORVUS (NOMOS Co., Sewickley, PA) treatment plans. The results indicate that the proposed approach is robust and suitable to support the complex IMRT QA process.

An optimized forward-planning technique for intensity modulated radiation therapy

Intensity modulated radiation therapy (IMRT) has stirred considerable excitement in the radiation oncology community. Its objective is to make the dose conform to the tumor and spare other organs. Instead of resorting to the rather complex inverse-planning, the technique described here is an extension of the conventional treatment planning technique. The beam orientation and wedge angles are chosen in the conventional rule-based manner. However, within each conformal beam's eye view (BEV) field including margin, a number of sub-field openings are added. The smaller field openings are designed to irradiate the tumor, while sparing the normal tissue of the organs at risk (OARs) that intrude into the target region in the BEV. As the number of intrusions into the target BEV increases, the number of sub-fields for each beam increases. The Cimmino simultaneous projection method was employed to obtain the optimized weighting for each field of each beam. In cases where the dose constraints for the tumor and for the OARs are reasonable, it is possible to obtain a plan with a fairly small number of beams that satisfies the specified dose objectives. This is illustrated for the treatment of prostate cancer, where the rectum creates a concavity in the planning target volume. An advantage of this technique is that the quality assurance for the delivery of these plans does not require extensive special efforts.

Inverse planning incorporating organ motion

Accurate targeting is important in intensity-modulated radiation therapy (IMRT). The positional uncertainties of structures with respect to the external beams arise in part from random organ motion and patient setup errors. While it is important to improve immobilization and reduce the influence of organ motion, the residual effects should be included in the IMRT plan design. Current inverse planning algorithms follow the conventional approach and include uncertainties by assuming population-based margins to the target and sensitive structures. Margin around a structure represents a "hard boundary" and the fact that a structure has a spatial probability distribution has been completely ignored. With increasing understanding of spatial uncertainties of structures and the technical capability of fine-tuning the dose distribution on an individual beamlet level in IMRT, it seems timely and important to fully utilize the information in the planning process. This will reduce the "effective" margins of the structures and facilitate dose escalation. Instead of specifying a "hard margin," we describe an inverse planning algorithm which takes into consideration positional uncertainty in terms of spatial probability distribution. The algorithm was demonstrated by assuming that the random organ motion can be represented by a three-dimensional Gaussian distribution function. Other probability distributions can be dealt with similarly. In particular, the commonly used "hard margin" is a special case of the current approach with a uniform probability distribution within a specified range. The algorithm was applied to plan treatment for a prostate case and a pancreatic case. The results were compared with those obtained by adding a margin to the clinical target volume. Better sparing of the sensitive structures were obtained in both cases using the proposed method for approximately the same target coverage.

Breast-conserving radiation therapy using combined electron and intensity-modulated radiotherapy technique

BACKGROUND AND PURPOSE

To explore the feasibility of a multi-modality breast-conserving radiation therapy treatment technique to reduce high dose to the ipsilateral lung and the heart when compared with the conventional treatment technique using two tangential fields.

MATERIALS AND METHODS

An electron beam with appropriate energy was combined with four intensity modulated photon beams. The direction of the electron beam was chosen to be tilted 10-20 degrees laterally from the anteroposterior direction. Two of the intensity-modulated photon beams had the same gantry angles as the conventional tangential fields, whereas the other two beams were rotated 15-25 degrees toward the anteroposterior directions from the first two photon beams. An iterative algorithm was developed which optimizes the weight of the electron beam as well as the fluence profiles of the photon beams for a given patient. Two breast cancer patients with early-stage breast tumors were planned with the new technique and the results were compared with those from 3D planning using tangential fields as well as 9-field intensity-modulated radiotherapy (IMRT) techniques.

RESULTS

The combined electron and IMRT plans showed better dose conformity to the target with significantly reduced dose to the ipsilateral lung and, in the case of the left-breast patient, reduced dose to the heart, than the tangential field plans. In both the right-sided and left-sided breast plans, the dose to other normal structures was similar to that from conventional plans and was much smaller than that from the 9-field IMRT plans. The optimized electron beam provided between 70 to 80% of the prescribed dose at the depth of maximum dose of the electron beam.

CONCLUSIONS

The combined electron and IMRT technique showed improvement over the conventional treatment technique using tangential fields with reduced dose to the ipsilateral lung and the heart. The customized beam directions of the four IMRT fields also kept the dose to other critical structures to a minimum.

Monte Carlo dose computation for IMRT optimization

A method which combines the accuracy of Monte Carlo dose calculation with a finite size pencil-beam based intensity modulation optimization is presented. The pencil-beam algorithm is employed to compute the fluence element updates for a converging sequence of Monte Carlo dose distributions. The combination is shown to improve results over the pencil-beam based optimization in a lung tumour case and a head and neck case. Inhomogeneity effects like a broader penumbra and dose build-up regions can be compensated for by intensity modulation.

Dosimetric effects of patient displacement and collimator and gantry angle misalignment on intensity modulated radiation therapy

PURPOSE AND OBJECTIVE

The primary goal of this study was to examine systematically the dosimetric effect of small patient movements and linear accelerator angular setting misalignments in the delivery of intensity modulated radiation therapy. We will also provide a method for estimating dosimetric errors for an arbitrary combination of these uncertainties.

MATERIALS AND METHODS

Sites in two patients (lumbar-vertebra and nasopharynx) were studied. Optimized intensity modulated radiation therapy treatment plans were computed for each patient using a commercially available inverse planning system (CORVUS, NOMOS Corporation, Sewickley, PA). The plans used nine coplanar beams. For each patient the dose distributions and relevant dosimetric quantities were calculated, including the maximum, minimum, and average doses in targets and sensitive structures. The corresponding dose volumetric information was recalculated by purposely varying the collimator angle or gantry angle of an incident beam while keeping other beams unchanged. Similar calculations were carried out by varying the couch indices in either horizontal or vertical directions. The intensity maps of all the beams were kept the same as those in the optimized plan. The change of a dosimetric quantity, Q, for a combination of collimator and gantry angle misalignments and patient displacements was estimated using Delta=Sigma(DeltaQ/Deltax(i))Deltax(i). Here DeltaQ is the variation of Q due to Deltax(i), which is the change of the i-th variable (collimator angle, gantry angle, or couch indices), and DeltaQ/Deltax(i) is a quantity equivalent to the partial derivative of the dosimetric quantity Q with respect to x(i).

RESULTS

While the change in dosimetric quantities was case dependent, it was found that the results were much more sensitive to small changes in the couch indices than to changes in the accelerator angular setting. For instance, in the first example in the paper, a 3-mm movement of the couch in the anterior-posterior direction can cause a 38% decrease in the minimum target dose or a 41% increase in the maximum cord dose, whereas a 5 degrees change in the &theta;(1)=20 degrees beam only gave rise to a 1.5% decrease in the target minimum or 5.1% in the cord maximum. The effect of systematic positioning uncertainties of the machine settings was more serious than random uncertainties, which tended to smear out the errors in dose distributions.

CONCLUSIONS

The dose distribution of an intensity modulated radiation therapy (IMRT) plan changes with patient displacement and angular misalignment in a complex way. A method was proposed to estimate dosimetric errors for an arbitrary combination of uncertainties in these quantities. While it is important to eliminate the angular misalignment, it was found that the couch indices (or patient positioning) played a much more important role. Accurate patient set-up and patient immobilization is crucial in order to take advantage fully of the technological advances of IMRT. In practice, a sensitivity check should be useful to foresee potential IMRT treatment complications and a warning should be given if the sensitivity exceeds an empirical value. Quality assurance action levels for a given plan can be established out of the sensitivity calculation.

Beam orientation optimization in intensity-modulated radiation treatment planning

Beam direction optimization is an important problem in radiation therapy. In intensity modulated radiation therapy (IMRT), the difficulty for computer optimization of the beam directions arises from the fact that they are coupled with the intensity profiles of the incident beams. In order to obtain the optimal incident beam directions using iterative or stochastic methods, the beam profiles ought to be optimized after every change of beam configuration. In this paper we report an effective algorithm to optimize gantry angles for IMRT. In our calculation the gantry angles and the beam profiles (beamlet weights) were treated as two separate groups of variables. The gantry angles were sampled according to a simulated annealing algorithm. For each sampled beam configuration, beam profile calculation was done using a fast filtered backprojection (FBP) method. Simulated annealing was also used for beam profile optimization to examine the performance of the FBP for beam orientation optimization. Relative importance factors were incorporated into the objective function to control the relative importance of the target and the sensitive structures. Minimization of the objective function resulted in the best possible beam orientations and beam profiles judged by the given objective function. The algorithm was applied to several model problems and the results showed that the approach has potential for IMRT applications.

Optimization of inverse treatment planning using a fuzzy weight function

A fuzzy approach has been applied to inverse treatment planning optimization in radiation therapy. The proposed inverse-planning algorithm optimizes both the intensity-modulated beam (IMB) and the normal tissue prescription. In the IMB optimization, we developed a fast-monotonic-descent (FMD) method that has the property of fast and monotonic convergence to the minimum for a constrained quadratic objective function. In addition, a fuzzy weight function is employed to express the vague knowledge about the importance of matching the calculated dose to the prescribed dose in the normal tissue. Then, a validity function is established to optimize the normal tissue prescription. The performance of this new fuzzy prescription algorithm has been compared to that based on hard prescription methods for two treatment geometries. The FMD method presented here both provides a full-analytical solution to the optimization of intensity-modulated beams, and guarantees fast and monotonic convergence to the minimum. It has been shown that the fuzzy inverse planning technique is capable of achieving an optimal balance between the objective of matching the calculated dose to the prescribed dose for the target volume and the objective of minimizing the normal tissue dose.

Estimation theory and model parameter selection for therapeutic treatment plan optimization

Treatment optimization is usually formulated as an inverse problem, which starts with a prescribed dose distribution and obtains an optimized solution under the guidance of an objective function. The solution is a compromise between the conflicting requirements of the target and sensitive structures. In this paper, the treatment plan optimization is formulated as an estimation problem of a discrete and possibly nonconvex system. The concept of preference function is introduced. Instead of prescribing a dose to a structure (or a set of voxels), the approach prioritizes the doses with different preference levels and reduces the problem into selecting a solution with a suitable estimator. The preference function provides a foundation for statistical analysis of the system and allows us to apply various techniques developed in statistical analysis to plan optimization. It is shown that an optimization based on a quadratic objective function is a special case of the formalism. A general two-step method for using a computer to determine the values of the model parameters is proposed. The approach provides an efficient way to include prior knowledge into the optimization process. The method is illustrated using a simplified two-pixel system as well as two clinical cases. The generality of the approach, coupled with promising demonstrations, indicates that the method has broad implications for radiotherapy treatment plan optimization.

Matching photon and electron fields with dynamic intensity modulation

A technique was developed to reduce the size and magnitude of the hot and cold spots in the abutting regions of photon and electron fields. The photon and electron fields were set up such that the photon field extended approximately 2 cm into the electron field in the abutting region. The region of the photon beam that overlapped the electron field was modulated using a multileaf collimator, effectively broadening the photon penumbra to make it complimentary to the electron penumbra. The computer calculations were verified using film measurements for abutting a 6 MV photon beam with a 9 MeV electron beam. A uniform dose was achieved at a prespecified depth of 2 cm, and dose uniformity was improved at the specified depth and beyond compared with unmodulated photon beams. A slight increase in dose inhomogeneity was seen at shallower depths. The overall areas of the hot and cold spots were significantly reduced. The technique also reduced the sensitivity of dose homogeneity to setup errors such that the magnitudes of the hot and cold spots were about half of those produced with unmodulated photon beam when an overlap or gap of 4 mm was introduced. The technique was applied to the treatment of a head and neck cancer and a lymphoma involving the right pleura with markedly reduced dose inhomogeneity in the abutting regions.

Optimization of importance factors in inverse planning

Inverse treatment planning starts with a treatment objective and obtains the solution by optimizing an objective function. The clinical objectives are usually multifaceted and potentially incompatible with one another. A set of importance factors is often incorporated in the objective function to parametrize trade-off strategies and to prioritize the dose conformality in different anatomical structures. Whereas the general formalism remains the same, different sets of importance factors characterize plans of obviously different flavour and thus critically determine the final plan. Up to now, the determination of these parameters has been a 'guessing' game based on empirical knowledge because the final dose distribution depends on the parameters in a complex and implicit way. The influence of these parameters is not known until the plan optimization is completed. In order to compromise properly the conflicting requirements of the target and sensitive structures, the parameters are usually adjusted through a trial-and-error process. In this paper, a method to estimate these parameters computationally is proposed and an iterative computer algorithm is described to determine these parameters numerically. The treatment plan selection is done in two steps. First, a set of importance factors are chosen and the corresponding beam parameters (e.g. beam profiles) are optimized under the guidance of a quadratic objective function using an iterative algorithm reported earlier. The 'optimal' plan is then evaluated by an additional scoring function. The importance factors in the objective function are accordingly adjusted to improve the ranking of the plan. For every change in the importance factors, the beam parameters need to be re-optimized. This process continues in an iterative fashion until the scoring function is saturated. The algorithm was applied to two clinical cases and the results demonstrated that it has the potential to improve significantly the existing method of inverse planning. It was noticed that near the final solution the plan became insensitive to small variations of the importance factors.