A toolbox for intensity modulated radiation therapy optimization

We have designed a toolbox that provides an environment for testing radiotherapy optimization techniques, objective functions, and constraints. A set of three-dimensional (3D) pencil beam dose distributions have been computed for a cylindrical phantom. The 6 MV pencil beams were computed using a superposition-based dose engine commissioned for an Elekta SL20 linear accelerator. Due to the cylindrical symmetry of the phantom, the pencil beam dose distributions for any arbitrary beam angle can be determined by simply rotating the pencil beam data sets. Thus, the full accuracy is maintained without the need for additional dose calculations or large data storage requirements. In addition to the pencil beam data sets, tools are included for (1) rotating the pencil beams, (2) calculating the beam's eye view, (3) drawing structures, (4) writing the pencil beam dose data out to the optimizer, and (5) visualizing the optimized results. The pencil beam data sets and the corresponding tools are available for download at http://medschool.umaryland.edu/departments/radiationoncology/pencilbeam/. With this toolbox, researchers will have the ability to rapidly test new optimization techniques and formulations for intensity modulated radiation therapy and 3D conformal radiotherapy.     

Beam orientation optimization for intensity-modulated radiation therapy using mixed integer programming

The purpose of this study is to extend an algorithm proposed for beam orientation optimization in classical conformal radiotherapy to intensity-modulated radiation therapy (IMRT) and to evaluate the algorithm's performance in IMRT scenarios. In addition, the effect of the candidate pool of beam orientations, in terms of beam orientation resolution and starting orientation, on the optimized beam configuration, plan quality and optimization time is also explored. The algorithm is based on the technique of mixed integer linear programming in which binary and positive float variables are employed to represent candidates for beam orientation and beamlet weights in beam intensity maps. Both beam orientations and beam intensity maps are simultaneously optimized in the algorithm with a deterministic method. Several different clinical cases were used to test the algorithm and the results show that both target coverage and critical structures sparing were significantly improved for the plans with optimized beam orientations compared to those with equi-spaced beam orientations. The calculation time was less than an hour for the cases with 36 binary variables on a PC with a Pentium IV 2.66 GHz processor. It is also found that decreasing beam orientation resolution to 10 degrees greatly reduced the size of the candidate pool of beam orientations without significant influence on the optimized beam configuration and plan quality, while selecting different starting orientations had large influence. Our study demonstrates that the algorithm can be applied to IMRT scenarios, and better beam orientation configurations can be obtained using this algorithm. Furthermore, the optimization efficiency can be greatly increased through proper selection of beam orientation resolution and starting beam orientation while guaranteeing the optimized beam configurations and plan quality.     

Beam configurations for 3D tomographic intensity modulated radiation therapy

We extend the theory of three-dimensional (3D) tomographic intensity modulated radiation therapy (IMRT). The geometry consists of two-dimensional modulated beams on a sphere centred in the tumour. The theory provides an efficient algorithm for computing beam modulation patterns that approximately 'reconstruct' the prescribed dose function. In this paper optimum beam numbers are estimated from dose function spherical harmonics using the 3D projection-slice theorem. An extension to three dimensions of the 'Bow Tie' criterion for beam numbers is derived. The effects of insufficient beam front sampling and beam numbers are characterized with a configuration-dependent matrix. Factors that independently increase beam numbers, such as tumour size and shape, are related to the spherical harmonic content in the dose function. Examples of tomographic IMRT reconstruction with a 3D concave tumour are given.     

Robust optimization for intensity modulated radiation therapy treatment planning under uncertainty

The recent development of intensity modulated radiation therapy (IMRT) allows the dose distribution to be tailored to match the tumour's shape and position, avoiding damage to healthy tissue to a greater extent than previously possible. Traditional treatment plans assume that the target structure remains in a fixed location throughout treatment. However, many studies have shown that because of organ motion, inconsistencies in patient positioning over the weeks of treatment, etc, the tumour location is not stationary. We present a probabilistic model for the IMRT inverse problem and show that it is identical to using robust optimization techniques, under certain assumptions. For a sample prostate case, our computational results show that this method is computationally feasible and promising-compared to traditional methods, our model has the potential to find treatment plans that are more adept at sparing healthy tissue while maintaining the prescribed dose to the target.     

A set cover approach to fast beam orientation optimization in intensity modulated radiation therapy for total marrow irradiation

The beam orientation optimization (BOO) problem in intensity modulated radiation therapy (IMRT) treatment planning is a nonlinear problem, and existing methods to obtain solutions to the BOO problem are time consuming due to the complex nature of the objective function and size of the solution space. These issues become even more difficult in total marrow irradiation (TMI), where many more beams must be used to cover a vastly larger treatment area than typical site-specific treatments (e.g., head-and-neck, prostate, etc). These complications result in excessively long computation times to develop IMRT treatment plans for TMI, so we attempt to develop methods that drastically reduce treatment planning time. We transform the BOO problem into the classical set cover problem (SCP) and use existing methods to solve SCP to obtain beam solutions. Although SCP is NP-Hard, our methods obtain beam solutions that result in quality treatments in minutes. We compare our approach to an integer programming solver for the SCP to illustrate the speed advantage of our approach.     

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.     

Beam delivery sequencing for intensity modulated proton therapy

Methods of beam fluence sequencing for intensity modulated proton therapy (IMPT) using the beam scanning technique are presented. Proton beam weight maps optimized by the treatment planning system (TPS) for a discrete set of regularly spaced narrow pencil beams were interpolated, using convolution with various kernel functions, to simulate continuous beam scanning on a raster pattern. Expected dose distributions at the proton Bragg peak range were then calculated and compared to those planned by the TPS, to evaluate the discrepancy due to the differences between the treatment planning and delivery approaches. An iteratively optimized adjustment was applied to the simulated continuous beam fluence profiles to reduce such discrepancy. Calculation showed that by accounting for the specifics of the scanning method, the planned dose distribution on the target may be reproduced to within 0.5% of the maximum target dose, given the pencil beam spacing smaller or equal to the beam sigma is used for treatment planning. For the beam weight maps generated using a spot spacing larger than sigma, a substantial reduction in the calculated dose discrepancy may be attained by applying an iterative adjustment of fluence profiles obtained by interpolating over artificially expanded set of beam spots.     

Reshapable physical modulator for intensity modulated radiation therapy

A new method of generating beam intensity modulation filters for intensity modulated radiation therapy (IMRT) is presented. The modulator was based on a reshapable material, which is not compressible but can be deformed under pressure. A two-dimensional (2D) piston array was used to repeatedly shape the attenuating material. The material is a mixture of tungsten powder and a silicon-based binder. The linear attenuation coefficient of the material was measured to be 0.409 cm(-1) for a 6 MV x-ray beam. The maximum thickness of the physical modulator is 10.2 cm, allowing a transmission of 1.5%. A 16 x 16 square piston array was used to generate a depth pattern in the deformable attenuating material. Each piston has a cross section of 6.37 x 6.37 mm2. The modulator was placed 65 cm from the radiation source of the linear accelerator in the position of the shielding tray. At this position, each piston projects to a 1.0 x 1.0 cm2 area at the isocenter, giving a treatment field of 16 x 16 cm2. The percent depth dose curve and output factor measurement show a slight beam hardening and a 1%-4% increase in scatter fraction when 2.2-4.4 cm uniform thickness filters are in the beam. The surface dose was decreased with the filter in the beam. Ion chamber and verification films were used to verify the entrance dose. The measured absolute and relative doses were compared with the calculated dose. The agreement of measurements and calculations is within 3%. In order to verify the spatial modulation of dose, 1-D dose profiles were obtained using dose calculations. Calculated and measured profiles were compared. The 20%-80% penumbra of the modulator was measured to be 5.5-10 mm. The results show that a physical modulator formed using a 16 x 16 piston array and a deformable attenuation material can provide intensity modulation for IMRT comparable with those provided by currently available commercial MLC techniques.     

Motion effects in (intensity modulated) radiation therapy: a review

During a course of fractionated radiation therapy and between the fractions the tissues of the human body may move relative to some reference location in which the radiation therapy was planned. This has been known for over a century and simple 'coping mechanisms' (margins) have been used to approximately compensate. Since the introduction of highly accurate conformal radiation therapy and intensity-modulated radiation therapy (IMRT) attention has focused strongly in the last few years on understanding and compensating more appropriately for these motions. Thus, unlike most of the reviews in this special 50th anniversary issue which look back over decades of development, this one looks back at most within just the past decade and reviews the current situation. There is still much more work to be done and many of the techniques reviewed are themselves not yet implemented widely in the clinic.     

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.     

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.     

Film dosimetry for intensity modulated radiation therapy: dosimetric evaluation

X-ray film has been used for the dosimetry of intensity modulated radiation therapy (IMRT). However, the over-response of the film to low-energy photons is a significant problem in photon beam dosimetry, especially in regions outside penumbra. In IMRT, the radiation field consists of multiple small fields and their outside-penumbra regions; thus, the film dosimetry, for it involves the source of over-response in its radiation field. In this study we aim to verify and possibly improve film dosimetry for IMRT. Two types of modulated beams were constructed by combining five to seven different static radiation fields using 6 MV x rays. For verifying film dosimetry, x-ray films and an ion chamber were used to measure dose profiles at various depths in a phantom. The film setups include both parallel and perpendicular arrangements against the beam incident direction. In addition, to reduce an over-response, we placed 0.01 in. (0.25 mm) thick lead filters on both sides of the film. Compared with ion-chamber measurement, measured dose profiles showed the film over-response at outside-penumbra and low-dose regions. The error increased with depths and approached 15% as a maximum for the field size of 15 cm x 15 cm at 10 cm depth. The use of filters reduced the error down to 3%. In this study we demonstrated that film dosimetry for IMRT involves sources of error due to its over-response to low-energy photons, with the error most transparent in the low-dose region. The use of filters could enhance the accuracy in film dosimetry for IMRT. In this regard, the use of an optimal filter condition is recommended.     

A topographic leaf-sequencing algorithm for delivering intensity modulated radiation therapy

Topographic treatment is a radiation therapy delivery technique for fixed-gantry (nonrotational) treatments on a helical tomotherapy system. The intensity-modulated fields are created by moving the treatment couch relative to a fan-beam positioned at fixed gantry angles. The delivered dose distribution is controlled by moving multileaf collimator (MLC) leaves into and out of the fan beam. The purpose of this work was to develop a leaf-sequencing algorithm for creating topographic MLC sequences. Topographic delivery was modeled using the analogy of a water faucet moving over a collection of bottles. The flow rate per unit length of the water from the faucet represented the photon fluence per unit length along the width of the fan beam, the collection of bottles represented the pixels in the treatment planning fluence map, and the volume of water collected in each bottle represented the delivered fluence. The radiation fluence per unit length delivered to the target at a given position is given by the convolution of the intensity distribution per unit length over the width of the beam and the time per unit distance along the direction of travel that an MLC leaf is open. The MLC opening times for the desired dose profiles were determined using a technique based on deconvolution using a genetic algorithm. The MLC opening times were expanded in terms of a Fourier series, and a genetic algorithm was used to find the best expansion coefficients for a given dose distribution. A series of wedge shapes (15, 30, 45, and 60 deg) and "dose well" test fluence maps were created to test the algorithm's ability to generate topographic leaf sequences. The accuracy of the leaf-sequencing algorithm was measured on a helical tomotherapy system using radiographic film placed at depth in water equivalent material. The measured dose profiles were compared with the desired dose distributions. The agreement was within +/- 2% or 2 mm distance-to-agreement (DTA) in the high dose gradient regions for all test cases. The central axis measured dose was between 3.6% and 4.2% higher than the expected dose for the wedge cases. For the "dose well" test cases, the calculated and measured doses agreed to within +/- 0.5% at the peak and within +/- 1.6% in the "dose well." The topographic leaf-sequencing algorithm produced deliverable dose distributions that agreed well with the calculated dose distributions. This delivery technique could be used for treatment of whole intact breast. However, additional work is needed to further improve the algorithm in order to get better agreement between the calculated, deliverable, and measured dose distributions.     

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.     

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.     

A simplified intensity modulated radiation therapy technique for the breast

A simplified intensity modulated radiation therapy (sIMRT) technique for the breast is presented. The technique aims to produce a uniform dose distribution in the entire breast volume. Using the standard tangential beam arrangement, we first determine for each pencil beam the midpoint of the segment that intersects the treatment volume. The dose to the midpoint from the open field is then calculated. The intensity of the pencil beam is determined as proportional to the inverse of the open field dose. With this intensity modulated beam, the dose delivered to the midpoint of each pencil beam segment that intersects the treatment volume is now equalized. The dose distribution in the entire treatment volume is nearly as uniform as can be achieved under the given beam arrangement. Fifteen left breast patients were planned with the sIMRT technique. For comparison, the same group of patients was also planned with the standard wedged pair technique and the full-fledged volume-based IMRT (vIMRT) technique. Both the sIMRT and the vIMRT techniques achieved more homogeneous dose in the treatment volume than the standard plan. Doses to the heart, the ipsilateral lung, and the contralateral breast were also reduced. The planning time and the treatment time for the sIMRT technique were comparable to that of the standard technique, and significantly less than that required by the vIMRT technique. The sIMRT technique is practical for large-scale implementation in a busy clinic without requiring significant increase of resources.     

Treatment planning considerations of reshapeable automatic intensity modulator for intensity modulated radiation therapy

As compared with multi-leaf collimator based intensity modulated radiation therapy (IMRT) techniques, physical modulators have the major advantage of temporally invariant intensity map delivery which makes it more flexible with monitor unit rate, simpler resolution of interrupted treatment and easier implementation and use with respiratory gating. However, traditional physical modulator techniques require long fabrication time and operator intervention during treatments. It has been previously proposed [Xu et al., Med. Phys. 29, 2222-2229 (2002)] that a reshapeable automatic intensity modulator (RAIM) can automatically produce physical modulators by molding a deformable high x-ray attenuation material using a matrix of computer-controlled pistons. RAIM can potentially eliminate the limitations of traditional physical modulators. The present study addresses the treatment planning considerations of RAIM for IMRT. In this study, a 3D treatment-planning system (PLUNC) was modified to include the capability of providing treatment planning using RAIM. Two clinically representative cases were studied: nasopharyngeal and prostate tumors. First, the RAIM system with two different spatial resolutions at isocenter, 1 x 1 cm2 and 0.5 x 0.5 cm2, were evaluated. The treatment planning results of RAIM were then compared with other IMRT techniques such as smooth modulator with ideal (100%-2%) and limited (100%-13%) intensity modulation ranges, segmental multi-leaf collimator (SMLC) with ten intensity levels, 1 cm leaf width and 0.5 cm step size and serial tomotherapy using the Peacock system. Bringing the spatial resolution of RAIM down to 0.5 x 0.5 cm2 did not show improvement due to the effect of penumbra. The RAIM system with 1 x 1 cm2 proved slightly inferior as compared to the ideal smooth physical modulator but better than the SMLC technique and the smooth modulator with limited modulation range. When compared to serial tomotherapy, RAIM is only inferior in brain stem sparing for the nasopharynx case. Furthermore, the RAIM system with 1 x 1 cm2 resolution required significantly lower monitor units as compared to the other IMRT techniques for the two cases studied.