An improved MLC segmentation algorithm and software for step-and-shoot IMRT delivery without tongue-and-groove error

We present an improved multileaf collimator (MLC) segmentation algorithm, denoted by SLS(NOTG) (static leaf sequencing with no tongue-and-groove error), for step-and-shoot intensity-modulated radiation therapy (IMRT) delivery. SLS(NOTG) is an improvement over the MLC segmentation algorithm called SLS that was developed by Luan et al. [Med. Phys. 31(4), 695-707 (2004)], which did not consider tongue-and-groove error corrections. The aims of SLS(NOTG) are (1) shortening the treatment times of IMRT plans by minimizing their numbers of segments and (2) minimizing the tongue-and-groove errors of the computed IMRT plans. The input to SLS(NOTG) is intensity maps (IMs) produced by current planning systems, and its output is (modified) optimized leaf sequences without tongue-and-groove error. Like the previous SLS algorithm [Luan et al., Med. Phys. 31(4), 695-707 (2004)], SLS(NOTG) is also based on graph algorithmic techniques in computer science. It models the MLC segmentation problem as a weighted minimum-cost path problem, where the weight of the path is the number of segments and the cost of the path is the amount of tongue-and-groove error. Our comparisons of SLS(NOTG) with CORVUS indicated that for the same intensity maps, the numbers of segments computed by SLS(NOTG) are up to 50% less than those by CORVUS 5.0 on the Elekta LINAC system. Our clinical verifications have shown that the dose distributions of the SLS(NOTG) plans do not have tongue-and-groove error and match those of the corresponding CORVUS plans, thus confirming the correctness of SLS(NOTG). Comparing with existing segmentation methods, SLS(NOTG) also has two additional advantages: (1) SLS(NOTG) can compute leaf sequences whose tongue-and-groove error is minimized subject to a constraint on the maximum allowed number of segments, which may be desirable in clinical situations where a treatment with the complete correction of tongue-and-groove error takes too much time, and (2) SLS(NOTG) can be used to minimize a more general type of error called the tongue-or-groove error.     

Improved leaf sequencing reduces segments or monitor units needed to deliver IMRT using multileaf collimators.

Leaf sequencing algorithms may use an unnecessary number of monitor units or segments to generate intensity maps for delivery of intensity modulated radiotherapy (IMRT) using multiple static fields. An integer algorithm was devised to generate a sequence with the fewest possible segments when the minimum number of monitor units are used. Special hardware related restrictions on leaf motion can be incorporated. The algorithm was tested using a benchmark map from the literature and clinical examples. Results were compared to sequences given by the routine of Bortfeld that minimizes monitor units by treating each row independently, and the areal or reducing routines that use fewer segments at the price of more monitor units. The Bortfeld algorithm used on average 58% more segments than provided by the integer algorithm with bidirectional motion and 32% more segments than did an integer algorithm admitting only unidirectional sequences. The areal algorithm used 48% more monitor units and the reducing algorithm used 23% more monitor units than did the bidirectional integer algorithm, while the areal and reducing algorithms used 23% more segments than did the integer algorithm. Improved leaf sequencing algorithms can allow more efficient delivery of static field IMRT. The integer algorithm demonstrates the efficiencies possible with an improved routine and opens a new avenue for development.     

A graph-searching method for MLC leaf sequencing under constraints

A new leaf-sequencing algorithm for step-and-shoot IMRT that is based on a graph-searching technique is described. An iterative process guided by a quantitative measure for the complexity of the initial or residual intensity pattern is used to identify the field segments shaped by a multileaf collimator (MLC). Given a user selected number of intensity levels, the algorithm searches deliverable segment candidates considering all intensity levels and two collimator positions separated by 90 degrees. The candidates for each intensity level are obtained as the least number of segments to cover the areas with equal or higher intensity. The shape of a deliverable segment is adjusted by leaving out certain beam elements for later delivery if this results in a simpler residual intensity pattern and the segment is still deliverable. For a MLC design that does not allow leaf interdigitation, it is initially assumed that a single segment cannot cover two disjoined areas. Among all candidates the segment with the greatest reduction of the complexity of the residual intensity distribution is chosen for the current step of iteration. The iterative process generates a set of deliverable segments of simply connected areas. These segments are combined later under specific MLC constraints. Different orders of segment combination are considered for minimizing the beam-on time. The final segments are sequenced to minimize the leaf travel. This algorithm has been tested using randomly generated intensity distributions and clinical cases for the Varian, Siemens, and Elekta MLC systems. The results show that as the number of intensity levels is increased, the numbers of segments and MUs increase only modestly. Using two collimator angles results in decreases in the required number of segments and the number of monitor units that can be as much as 20%.     

Continuous intensity map optimization (CIMO): a novel approach to leaf sequencing in step and shoot IMRT

A new leaf-sequencing approach has been developed that is designed to reduce the number of required beam segments for step-and-shoot intensity modulated radiation therapy (IMRT). This approach to leaf sequencing is called continuous-intensity-map-optimization (CIMO). Using a simulated annealing algorithm, CIMO seeks to minimize differences between the optimized and sequenced intensity maps. Two distinguishing features of the CIMO algorithm are (1) CIMO does not require that each optimized intensity map be clustered into discrete levels and (2) CIMO is not rule-based but rather simultaneously optimizes both the aperture shapes and weights. To test the CIMO algorithm, ten IMRT patient cases were selected (four head-and-neck, two pancreas, two prostate, one brain, and one pelvis). For each case, the optimized intensity maps were extracted from the Pinnacle3 treatment planning system. The CIMO algorithm was applied, and the optimized aperture shapes and weights were loaded back into Pinnacle. A final dose calculation was performed using Pinnacle's convolution/superposition based dose calculation. On average, the CIMO algorithm provided a 54% reduction in the number of beam segments as compared with Pinnacle's leaf sequencer. The plans sequenced using the CIMO algorithm also provided improved target dose uniformity and a reduced discrepancy between the optimized and sequenced intensity maps. For ten clinical intensity maps, comparisons were performed between the CIMO algorithm and the power-of-two reduction algorithm of Xia and Verhey [Med. Phys. 25(8), 1424-1434 (1998)]. When the constraints of a Varian Millennium multileaf collimator were applied, the CIMO algorithm resulted in a 26% reduction in the number of segments. For an Elekta multileaf collimator, the CIMO algorithm resulted in a 67% reduction in the number of segments. An average leaf sequencing time of less than one minute per beam was observed.     

A quality and efficiency analysis of the IMFAST segmentation algorithm in head and neck "step & shoot" IMRT treatments

The performance of segmentation algorithms used in IMFAST for "step & shoot" IMRT treatment delivery is evaluated for three head and neck clinical treatments of different optimization objectives. The segmentation uses the intensity maps generated by the in-house TPS PLANUNC using the index-dose minimization algorithm. The dose optimization objectives include PTV dose uniformity and dose volume histogram-specified critical structure sparing. The optimized continuous intensity maps were truncated into five and ten intensity levels and exported to IMFAST for MLC segments optimization. The MLC segments were imported back to PLUNC for dose optimization quality calculation. The five basic segmentation algorithms included in IMFAST were evaluated alone and in combination with either tongue and groove/match line correction or fluence correction or both. Two criteria were used in the evaluation: treatment efficiency represented by the total number of MLC segments and optimization quality represented by a clinically relevant optimization quality factor. We found that the treatment efficiency depends first on the number of intensity levels used in the intensity map and second the segmentation technique used. The standard optimal segmentation with fluence correction is a consistent good performer for all treatment plans studied. All segmentation techniques evaluated produced treatments with similar dose optimization quality values, especially when ten-level intensity maps are used.     

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 new algorithm for determining collimator angles that favor efficiency in MLC based IMRT delivery

A new algorithm to determine collimator angles that favor delivery efficiency of intensity modulated radiotherapy plans was developed. It was found that the number of segments and monitor units (MUs) were largely reduced with the set of collimator angles determined with the new algorithm without compromising plan quality. The improvement of delivery efficiency using the new algorithm depends on the size and shape of the target(s), the number of modulation levels, and the type of leaf-sequencing algorithm. In a typical prostate case, when a sweeping leaf-sequencer is used for Varian 120 leaf (0.5 x 0.5 cm2 beamlet), 80 leaf (1 x 1 cm2 beamlet) and Elekta 40 leaf (1 x 1 cm2 beamlet), the number of segments was reduced by 42%, 29%, and 5%, respectively. The number of MUs was reduced by 41%, 35%, and 10%. For the Siemens MLC (IMFAST leaf sequencer, 1 x 1 cm2 beamlet) the segment reduction was 32% and the MU reduction was 14%. Comparison of the plans using the new and Brahme algorithms, in terms of target conformity index and dose volume histogram of the organs at risk, showed that the quality of the plans using the new algorithm was uncompromised. Similar results were obtained for a set of head and neck treatment plans.     

Comparison of algorithms for multileaf collimator field segmentation

In the "stop and shoot" method of intensity modulated radiation therapy, it is desirable to use an efficient multileaf collimator (MLC) field segmentation algorithm in the sense that it translates beam intensity maps into the least number of MLC field segments. In this work, we compare the performance of eight different algorithms, including the ones by Bortfeld et al., Galvin et al., Xia and Verhey, the Siemens IMFAST algorithm, and four other algorithms which have not been studied before. We find that the algorithm of Xia and Verhey is most frequently the algorithm that needs the least MLC field segments. However, no single algorithm is the most efficient for all clinical cases or intensity maps. This suggests that it is desirable to have multiple algorithms available in a clinical treatment planning system which will search through all algorithms automatically and find the most efficient delivery sequence for a given treatment. Each intensity map in a treatment could be delivered by a different algorithm, whichever is the most efficient for that map. It is pointed out that when the background intensity level is not zero, it is not always efficient to deliver a segment to bring the background level down to zero.     

A leaf sequencing algorithm to enlarge treatment field length in IMRT

With MLC-based IMRT, the maximum usable field size is often smaller than the maximum field size for conventional treatments. This is due to the constraints of the overtravel distances of MLC leaves and/or jaws. Using a new leaf sequencing algorithm, the usable IMRT field length (perpendicular to the MLC motion) can be mostly made equal to the full length of the MLC field without violating the upper jaw overtravel limit. For any given intensity pattern, a criterion was proposed to assess whether an intensity pattern can be delivered without violation of the jaw position constraints. If the criterion is met, the new algorithm will consider the jaw position constraints during the segmentation for the step and shoot delivery method. The strategy employed by the algorithm is to connect the intensity elements outside the jaw overtravel limits with those inside the jaw overtravel limits. Several methods were used to establish these connections during segmentation by modifying a previously published algorithm (areal algorithm), including changing the intensity level, alternating the leaf-sequencing direction, or limiting the segment field size. The algorithm was tested with 1000 random intensity patterns with dimensions of 21 x 27 cm2, 800 intensity patterns with higher intensity outside the jaw overtravel limit, and three different types of clinical treatment plans that were undeliverable using a segmentation method from a commercial treatment planning system. The new algorithm achieved a success rate of 100% with these test patterns. For the 1,000 random patterns, the new algorithm yields a similar average number of segments of 36.9 +/- 2.9 in comparison to 36.6 +/- 1.3 when using the areal algorithm. For the 800 patterns with higher intensities outside the jaw overtravel limits, the new algorithm results in an increase of 25% in the average number of segments compared to the areal algorithm. However, the areal algorithm fails to create deliverable segments for 90% of these patterns. Using a single isocenter, the new algorithm provides a solution to extend the usable IMRT field length from 21 to 27 cm for IMRT on a commercial linear accelerator using the step and shoot delivery method.     

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

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

Simultaneous minimizing monitor units and number of segments without leaf end abutment for segmental intensity modulated radiation therapy delivery

Leaf end abutment is seldom studied when delivering segmental intensity modulated radiation therapy (IMRT) fields. We developed an efficient leaf sequencing method to eliminate leaf end abutment for segmental IMRT delivery. Our method uses simple matrix and sorting operations to obtain a solution that simultaneously minimizes total monitor units and number of segments without leaf end abutment between segments. We implemented and demonstrated our method for multiple clinical cases. We compared the results of our method with the results from exhaustive search method. We found that our solution without leaf end abutment produced equivalent results to the unconstrained solutions in terms of minimum total monitor units and minimum number of leaf segments. We conclude that the leaf end abutment fields can be avoided without affecting the efficiency of segmental IMRT delivery. The major strength of our method is its simplicity and high computing speed. This potentially provides a useful means for generating segmental IMRT fields that require high spatial resolution or complex intensity distributions.     

Aperture modulated arc therapy

We show that it is possible to translate an intensity modulated radiation therapy (IMRT) treatment plan and deliver it as a single arc. This technique is referred to in this paper as aperture modulation arc therapy (AMAT). During this arc, the MLC leaves do not conform to the projection of the target PTV and the machine output of the accelerator has a constant value. Dose was calculated using the CORVUS 4.0 IMRT system, which uses a pencil beam dose algorithm, and treatments were delivered using a Varian 2100C/D Clinac. Results are presented for a head and neck and a prostate case, showing the equivalence of the IMRT and the translated AMAT delivery. For a prostate AMAT delivery, coronal plane film dose for the IMRT and AMAT deliveries agreed within 7.19 +/- 6.62%. For a meningioma the coronal plane dose distributions were similar to a value of 4.6 +/- 6.62%. Dose to the isocentre was measured as being within 2% of the planned value in both cases.     

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.     

Enhancement of IMRT delivery through MLC rotation

Multileaf collimator (MLC) based intensity modulated radiation therapy (IMRT) techniques are well established but suffer several physical limitations. Dosimetric spatial resolution is limited by the MLC leaf width; interleaf leakage and tongue-and-groove effects degrade dosimetric accuracy and the range of leaf motion limits the maximum deliverable field size. Collimator rotation is used in standard radiation therapy to improve the conformity of the MLC shape to the target volume. Except for opposed orthogonal fields, collimator rotation has not been exploited in IMRT due to the complexity of deriving the MLC leaf configurations for rotated sub-fields. Here we report on a new way that MLC-based IMRT is delivered which incorporates collimator rotation, providing an extra degree of freedom in deriving leaf sequences for a desired fluence map. Specifically, we have developed a series of unique algorithms that are capable of determining rotated MLC segments. These IMRT fields may be delivered statically (with the collimator rotating to a new position in between sub-fields) or dynamically (with the collimator rotating and leaves moving simultaneously during irradiation). This introductory study provides an analysis of the rotating leaf motion calculation algorithms with focus on radiation efficiency, the range of collimator rotation and number of segments. We then evaluate the technique by characterizing the ability of the algorithms to generate rotating leaf sequences for desired fluence maps. Comparisons are also made between our method and conventional sliding window and step-and-shoot techniques. Results show improvements in spatial resolution, reduced interleaf effects and maximum deliverable field size over conventional techniques. Clinical application of these enhancements can be realized immediately with static rotational delivery although improved dosimetric modelling of the MLC will be required for dynamic delivery.     

Minimizing the number of segments in a delivery sequence for intensity-modulated radiation therapy with a multileaf collimator.

This paper proposes a sequencing algorithm for intensity-modulated radiation therapy with a multileaf collimator in the static mode. The algorithm aims to minimize the number of segments in a delivery sequence. For a machine with a long verification and recording overhead time (e.g., 15 s per segment), minimizing the number of segments is equivalent to minimizing the delivery time. The proposed new algorithm is based on checking numerous candidates for a segment and selecting the candidate that results in a residual intensity matrix with the least complexity. When there is more than one candidate resulting in the same complexity, the candidate with the largest size is selected. The complexity of an intensity matrix is measured in the new algorithm in terms of the number of segments in the delivery sequence obtained by using a published algorithm. The beam delivery efficiency of the proposed algorithm and the influence of different published algorithms used to calculate the complexity of an intensity matrix were tested with clinical intensity-modulated beams. The results show that no matter which published algorithm is used to calculate the complexity of an intensity matrix, the sequence generated by the algorithm proposed here is always more efficient than that generated by the published algorithm itself. The results also show that the algorithm used to calculate the complexity of an intensity matrix affects the efficiency of beam delivery. The delivery sequences are frequently most efficient when the algorithm of Bortfeld et al. is used to calculate the complexity of an intensity matrix. Because no single variation is most efficient for all beams tested, we suggest implementing multiple variations of our algorithm.     

Monte Carlo based treatment planning for modulated electron beam radiation therapy

A Monte Carlo based treatment planning system for modulated electron radiation therapy (MERT) is presented. This new variation of intensity modulated radiation therapy (IMRT) utilizes an electron multileaf collimator (eMLC) to deliver non-uniform intensity maps at several electron energies. In this way, conformal dose distributions are delivered to irregular targets located a few centimetres below the surface while sparing deeper-lying normal anatomy. Planning for MERT begins with Monte Carlo generation of electron beamlets. Electrons are transported with proper in-air scattering and the dose is tallied in the phantom for each beamlet. An optimized beamlet plan may be calculated using inverse-planning methods. Step-and-shoot leaf sequences are generated for the intensity maps and dose distributions recalculated using Monte Carlo simulations. Here, scatter and leakage from the leaves are properly accounted for by transporting electrons through the eMLC geometry. The weights for the segments of the plan are re-optimized with the leaf positions fixed and bremsstrahlung leakage and electron scatter doses included. This optimization gives the final optimized plan. It is shown that a significant portion of the calculation time is spent transporting particles in the leaves. However, this is necessary since optimizing segment weights based on a model in which leaf transport is ignored results in an improperly optimized plan with overdosing of target and critical structures. A method of rapidly calculating the bremsstrahlung contribution is presented and shown to be an efficient solution to this problem. A homogeneous model target and a 2D breast plan are presented. The potential use of this tool in clinical planning is discussed.     

DMLC IMRT delivery to targets moving in 2D in Beam's eye view

The goal of this article is to present the algorithm for DMLC leaf control capable of delivering IMRT to tumors that experience motion in two dimensions in the beams eye view (BEV) plane. The generic, two-dimensional (2D) motion of the projection of the rigid target on BEV plane can be divided into two components. The first component describes the motion of the projection of the target along the x axis (parallel to the MLC leaf motions) and the other describes the motion of the target projection on the y axis (perpendicular to the leaf motion direction). First, time optimal leaf trajectories are calculated independently for each leaf pair of the MLC assembly to compensate the x-axis component of the 2D motion of the target on the BEV. These leaf trajectories are then synchronized following the mid time (MT) synchronization procedure. To compensate for the y-axis component of the motion of the target projection on the BEV plane, the procedure of "switching" leaf pair trajectories in the upward (or downward) direction is executed when the target's BEV projection moves upward (or downward) from its equilibrium position along the y axis. When the intensity function is a 2D histogram, the error between the intended and delivered intensity in 2D DMLC IMRT delivery will depend on the shape of the intensity map and on the MLC physical constraint (leaf width and maximum admissible leaf speed). The MT synchronization of leaf trajectories decreases the impact of above constraints on the error in 2D DMLC IMRT intensity map delivery. The proof is provided, that if hardware constraints in the 2D DMLC IMRT delivery strategy are removed, the errors between planned and delivered 2D intensity maps are entirely eliminated. Examples of 2D DMLC IMRT delivery to rigid targets moving along elliptical orbits on BEV planes are calculated and analyzed for 20 clinical fluence maps. The comparisons between the intensity delivered without motion correction, with motion correction along x axis only, and with motion correction for full 2D motion of the target are calculated and quantitatively evaluated. The fluence maps were normalized to 100 MU and the rms difference between the desired and delivered fluence was 12 MU for no motion compensation, 11.18 MU for 1D compensation, and 4.73 MU for 2D motion compensations. The advantage of correcting for full 2D motion of target projected on the BEV plane is demonstrated.     

Automated Gamma Knife dose planning using polygon clipping and adaptive simulated annealing

The Gamma Knife (Elekta Instruments, Inc., Norcross, GA), a neurosurgical, highly focused radiation delivery device, is used to eradicate deep-seated anomalous tissue within the human brain by delivering a lethal dose of radiation to target tissue. This dose is the accumulated result of delivering sequential "shots" of radiation to the target, where each shot is approximately three-dimensional (3-D) Gaussian in shape. The size and intensity of each shot can be adjusted by varying the time of radiation exposure and by using one of four collimator sizes ranging from 4-18 mm. Current dose planning requires that the dose plan be developed manually to cover the target, and only the target, with a desired minimum radiation intensity using a minimum number of shots. This is a laborious and subjective process that typically leads to suboptimal conformal target coverage by the dose. We have previously presented a forward-direct-method, which, using adaptive simulated annealing and Nelder-Mead simplex optimizers, automates the selection and placement of generic Gaussian-based kernels or "shots" to form a simulated dose plan. In order to make the computation of the problem tractable, the algorithm exploits 2-D contouring and polygon clipping and takes a 2 1/2-D approach to defining the problem. In the current paper we present the results of four experiments on two historical clinical datasets, where the generic kernels have been replaced by patient specific kernels calculated by Elekta's Leksell Gamma Plan software. For these experiments the user only selects the maximum number of shots to use and the optimizers are then given the freedom to vary the number of shots as well as the weight, collimator size, and 3-D location of each shot. Highly conformal and competitive dose plans were generated for these two difficult cases.     

Variable depth recursion algorithm for leaf sequencing

The processes of extraction and sweep are basic segmentation steps that are used in leaf sequencing algorithms. A modified version of a commercial leaf sequencer changed the way that the extracts are selected and expanded the search space, but the modification maintained the basic search paradigm of evaluating multiple solutions, each one consisting of up to 12 extracts and a sweep sequence. While it generated the best solutions compared to other published algorithms, it used more computation time. A new, faster algorithm selects one extract at a time but calls itself as an evaluation function a user-specified number of times, after which it uses the bidirectional sweeping window algorithm as the final evaluation function. To achieve a performance comparable to that of the modified commercial leaf sequencer, 2-3 calls were needed, and in all test cases, there were only slight improvements beyond two calls. For the 13 clinical test maps, computation speeds improved by a factor between 12 and 43, depending on the constraints, namely the ability to interdigitate and the avoidance of the tongue-and-groove under dose. The new algorithm was compared to the original and modified versions of the commercial leaf sequencer. It was also compared to other published algorithms for 1400, random, 15 X 15, test maps with 3-16 intensity levels. In every single case the new algorithm provided the best solution.     

Segmentation and leaf sequencing for intensity modulated arc therapy

A common method in generating intensity modulated radiation therapy (IMRT) plans consists of a three step process: an optimized fluence intensity map (IM) for each beam is generated via inverse planning, this IM is then segmented into discrete levels, and finally, the segmented map is translated into a set of MLC apertures via a leaf sequencing algorithm. To date, limited work has been done on this approach as it pertains to intensity modulated arc therapy (IMAT), specifically in regards to the latter two steps. There are two determining factors that separate IMAT segmentation and leaf sequencing from their IMRT equivalents: (1) the intrinsic 3D nature of the intensity maps (standard 2D maps plus the angular component), and (2) that the dynamic multileaf collimator (MLC) constraints be met using a minimum number of arcs. In this work, we illustrate a technique to create an IMAT plan that replicates Tomotherapy deliveries by applying IMAT specific segmentation and leaf-sequencing algorithms to Tomotherapy output sinograms. We propose and compare two alternative segmentation techniques, a clustering method, and a bottom-up segmentation method (BUS). We also introduce a novel IMAT leaf-sequencing algorithm that explicitly takes leaf movement constraints into consideration. These algorithms were tested with 51 angular projections of the output leaf-open sinograms generated on the Hi-ART II treatment planning system (Tomotherapy Inc.). We present two geometric phantoms and 2 clinical scenarios as sample test cases. In each case 12 IMAT plans were created, ranging from 2 to 7 intensity levels. Half were generated using the BUS segmentation and half with the clustering method. We report on the number of arcs produced as well as differences between Tomotherapy output sinograms and segmented IMAT intensity maps. For each case one plan for each segmentation method is chosen for full Monte Carlo dose calculation (NumeriX LLC) and dose volume histograms (DVH) are calculated. In all cases, the BUS method outperformed the clustering, method. We recommend using the BUS algorithm and discuss potential improvements to the clustering algorithms.