IMRT delivery to a moving target by dynamic MLC tracking: delivery for targets moving in two dimensions in the beam's eye view

A new modification of the dynamic multileaf collimator (dMLC) delivery technique for intensity-modulated therapy (IMRT) is outlined. This technique enables the tracking of a target moving through rigid-body translations in a 2D trajectory in the beam's eye view. The accuracy of the delivery versus that of deliveries with no tracking and of 1D tracking techniques is quantified with clinically derived intensity-modulated beams (IMBs). Leaf trajectories calculated in the target-reference frame were iteratively synchronized assuming regular target motion. This allowed the leaves defined in the lab-reference frame to simultaneously follow the target motion and to deliver the required IMB without violation of the leaf maximum-velocity constraint. The leaves are synchronized until the gradient of the leaf position at every instant is less than a calculated maximum. The delivered fluence in the target-reference frame was calculated with a simple primary-fluence model. The new 2D tracking technique was compared with the delivered fluence produced by no-tracking deliveries and by 1D tracking deliveries for 33 clinical IMBs. For the clinical IMBs normalized to a maximum fluence of 200 MUs, the rms difference between the desired and the delivered IMB was 15.6 +/- 3.3 MU for the case of a no-tracking delivery, 7.9 +/- 1.6 MU for the case where only the primary component of motion was corrected and 5.1 +/- 1.1 MU for the 2D tracking delivery. The residual error is due to interpolation and sampling effects. The 2D tracking delivery technique requires an increase in the delivery time evaluated as between 0 and 50% of the unsynchronized delivery time for each beam with a mean increase of 13% for the IMBs tested. The 2D tracking dMLC delivery technique allows an optimized IMB to be delivered to moving targets with increased accuracy and with acceptable increases in delivery time. When combined with real-time knowledge of the target motion at delivery time, this technique facilitates improved target conformality relative to no-tracking deliveries and allows PTV margin reduction.     

Comparative efficiency of the multi-leaf collimator and variable-aperture collimator in intensity-modulated radiotherapy

The potential of the variable-aperture collimator (VAC) in intensity-modulated radiation therapy (IMRT) has been evaluated by comparing its performance with that of the multi-leaf collimator (MLC). This comparison used a decomposition algorithm to find the series of collimator segments that would treat a given intensity-modulated beam (IMB). Collimator performance was measured using both the number of segments required to complete the IMB and the monitor-unit efficiency of the treatment. The VAC was modelled with aperture sizes from 4 x 4 cm to 20 x 20 cm, and these apertures were allowed to be located anywhere within the IMB. To enable a direct comparison, a similar scanning MLC was modelled at the same range of aperture sizes. Using both collimators, decompositions were run on 10 x 10 and 20 x 20 random IMBs with integer bixel values ranging from 1 to 10. Clinical IMBs from lung, head and neck, and pelvic patients were taken from a Pinnacle treatment-planning system and tested in the same manner. It was found that for all treatment sites, a small, scanning MLC performs as well or better than an equivalent sized VAC in both number of segments and monitor-unit efficiency, and would be an efficient choice for centres looking for a simple collimator for IMRT.     

Investigating the fundamentals of IMRT decomposition using ten simple collimator models

The fundamentals of IMRT collimation have been studied using ten conceptual collimators. Spanning a range of complexities from the LINAC jaws alone to a full multi-leaf collimator (MLC), these collimators were designed with two abilities in mind: (1) to be able to define arbitrary field shapes, and (2) to be able to irradiate multiple, disconnected regions in a single segment. The collimators were tested by finding decompositions of random and clinical intensity-modulated beams (IMBs), and collimator performance was measured using both the number of segments required to complete the IMB and the monitor-unit efficiency of the treatment. The decompositions were run on 10 x 10 IMBs with integer bixel values randomly between 1 and 10, and clinical IMBs of varying sizes from lung, head and neck, and pelvic patients taken from a Pinnacle treatment-planning system. Results confirmed that although treatment performance improves with increased collimator complexity, it is not solely dependent on the number of segment shapes deliverable by the collimator but instead on how well these shapes lend themselves to IMRT delivery.     

A new concept of multileaf collimator (the shuttling MLC)--an interpreter for high-efficiency IMRT

This paper proposes a radically new concept for a multileaf collimator for a photon linear accelerator for delivering IMRT with high monitor-unit efficiency. The concept is to consider each M (rows) x N (columns) two-dimensional intensity-modulated beam (2D IMB) as a set of N/2 M (rows) x 2 (columns) areas of modulation. Each area is then delivered by a set of M shuttling attenuating elements (called here the shuttling MLC) with a very high monitor-unit efficiency. The elements shuttle between each of the two columns comprising the M x 2 area and the modulation is provided by the variation in dwell time of the elements. The principles of this shuttling multileaf collimator are discussed and examples illustrating its operation are given. The main achievement reported in this paper is the development and robust testing of an interpreter which describes the position-time course of movement of the elements as a function of monitor units. This interpreter fully accounts for leakage transmission through the elements. It completely avoids the across-the-rows tongue-and-groove underdose. A large number of ID and 2D IMBs have been subjected to this interpreter and it is shown that for random patterns of fluence the SMLC is more monitor-unit efficient than the Bortfeld-Boyer technique (the most efficient with a conventional MLC) when the modulation is highly structured.     

Applications of automated simultaneous double fluorescence (SDF). II. HLA class I phenotyping using immunomagnetically separated T lymphocytes

HLA class I phenotyping was performed using T-lymphocyte populations isolated by immunomagnetic beads (IMBs) coated with monoclonal antibodies with specificity for CD2, CD4 or CD8. The results were compared to those obtained using density gradient-separated lymphocytes (PBL). The typing trays were read by the automated simultaneous double-fluorescence (SDF) technique previously established in our laboratory using an Astroscan 2100 system. The aims of the present study were to establish whether the advantages of IMB lymphocyte separation and automated plate reading by SDF were complementary and whether the results obtained by IMB-SDF and PBL-SDF were concordant. Similarity coefficients for paired results obtained by IMB-SDF and PBL-SDF varied between 0.825 using anti-CD8-coated IMBs and 0.914 using anti-CD4-coated IMBs with a consistent excess of stronger results observed with the PBL-SDF technique. The variations observed did not result in incorrect phenotype assignment but would significantly influence a cross-matching test. These results illustrate the feasibility of using IMB-separated lymphocytes for HLA phenotyping by SDF.     

A method of improving the spatial resolution of treatments that involve a multileaf collimator

In this paper we present a novel method of reducing the dosimetric effects of the finite leaf width of a multileaf collimator (MLC) in conformal and intensity modulated radiotherapy (IMRT). This is achieved by decomposing the required high-resolution fluence distribution into two orthogonal components, which are delivered with two leaf sweeps with head-twists differing by 90 degrees. Before the decomposition stage, a filter is applied to the required beam to force it to have a constant gradient in the two delivery directions. The component deliveries were found to be very spiky in nature, resulting in very inefficient delivery with the scanning leaves of our MLC. This method was evaluated using film dosimetry of four idealized beams: a 45 degree edge, a circle, a hemispherical intensity modulated beam (IMB) and a sine-like IMB. The measurements showed that this method had significantly reduced the effects of the 1 cm leaf width of our MLC at the 50% isodose level, but there was significant overdosage at the edge of the field and immediately inside the held edge. This method shows promise but further work is required before it may find clinical utility.     

Intensity-modulated radiation therapy using a variable-aperture collimator

This paper extends some earlier concepts of using a tertiary mask plus jaws for delivering IMRT without a multileaf collimator. The new concept is to sweep a variable-aperture collimator (VAC) across the space of the intensity-modulated beam (IMB) to be delivered and to strip this IMB down into multiple-static-field components, each deliverable with the VAC. The stripping algorithm is described and it is shown, for several designs of VAC, that the mean number of field components and mean number of monitor units is less using the VAC than would be required for a jaws-only (JO) decomposition. The VAC would be simpler to construct than several previously suggested jaws-plus-mask (J+M) combinations. As well as describing a simple VAC for the use with jaws, we propose a design concept of a hybrid VAC. We also show that adding the potential to rotate the simple or hybrid VAC for some components relative to the field to be modulated is advantageous.     

A real-time dynamic-MLC control algorithm for delivering IMRT to targets undergoing 2D rigid motion in the beam's eye view

An MLC control algorithm for delivering intensity modulated radiation therapy (IMRT) to targets that are undergoing two-dimensional (2D) rigid motion in the beam's eye view (BEV) is presented. The goal of this method is to deliver 3D-derived fluence maps over a moving patient anatomy. Target motion measured prior to delivery is first used to design a set of planned dynamic-MLC (DMLC) sliding-window leaf trajectories. During actual delivery, the algorithm relies on real-time feedback to compensate for target motion that does not agree with the motion measured during planning. The methodology is based on an existing one-dimensional (ID) algorithm that uses on-the-fly intensity calculations to appropriately adjust the DMLC leaf trajectories in real-time during exposure delivery [McMahon et al., Med. Phys. 34, 3211-3223 (2007)]. To extend the 1D algorithm's application to 2D target motion, a real-time leaf-pair shifting mechanism has been developed. Target motion that is orthogonal to leaf travel is tracked by appropriately shifting the positions of all MLC leaves. The performance of the tracking algorithm was tested for a single beam of a fractionated IMRT treatment, using a clinically derived intensity profile and a 2D target trajectory based on measured patient data. Comparisons were made between 2D tracking, 1D tracking, and no tracking. The impact of the tracking lag time and the frequency of real-time imaging were investigated. A study of the dependence of the algorithm's performance on the level of agreement between the motion measured during planning and delivery was also included. Results demonstrated that tracking both components of the 2D motion (i.e., parallel and orthogonal to leaf travel) results in delivered fluence profiles that are superior to those that track the component of motion that is parallel to leaf travel alone. Tracking lag time effects may lead to relatively large intensity delivery errors compared to the other sources of error investigated. However, the algorithm presented is robust in the sense that it does not rely on a high level of agreement between the target motion measured during treatment planning and delivery.     

Combining segment generation with direct step-and-shoot optimization in intensity-modulated radiation therapy

A method for generating a sequence of intensity-modulated radiation therapy step-and-shoot plans with increasing number of segments is presented. The objectives are to generate high-quality plans with few, large and regular segments, and to make the planning process more intuitive. The proposed method combines segment generation with direct step-and-shoot optimization, where leaf positions and segment weights are optimized simultaneously. The segment generation is based on a column generation approach. The method is evaluated on a test suite consisting of five head-and-neck cases and five prostate cases, planned for delivery with an Elekta SLi accelerator. The adjustment of segment shapes by direct step-and-shoot optimization improves the plan quality compared to using fixed segment shapes. The improvement in plan quality when adding segments is larger for plans with few segments. Eventually, adding more segments contributes very little to the plan quality, but increases the plan complexity. Thus, the method provides a tool for controlling the number of segments and, indirectly, the delivery time. This can support the planner in finding a sound trade-off between plan quality and treatment complexity.     

A procedural method for modeling the purkinje fibers of the heart

The Purkinje fibers are located in the ventricular walls of the heart, just beneath the endocardium and conduct excitation from the right and left bundle branches to the ventricular myocardium. Recently, anatomists succeeded in photographing the Purkinje fibers of a sheep, which clearly showed the mesh structure of the Purkinje fibers. In this study, we present a technique for modeling the mesh structure of Purkinje fibers semiautomatically using an extended L-system. The L-system is a formal grammar that defines the growth of a fractal structure by generating rules (or rewriting rules) and an initial structure. It was originally formulated to describe the growth of plant cells, and has subsequently been applied for various purposes in computer graphics such as modeling plants, buildings, streets, and ornaments. For our purpose, we extended the growth process of the L-system as follows: 1) each growing branch keeps away from existing branches as much as possible to create a uniform distribution, and 2) when branches collide, we connect the colliding branches to construct a closed mesh structure. We designed a generating rule based on observations of the photograph of Purkinje fibers and manually specified three terminal positions on a three-dimensional (3D) heart model: those of the right bundle branch, the anterior fascicle, and the left posterior fascicle of the left branch. Then, we grew fibers starting from each of the three positions based on the specified generating rule. We achieved to generate 3D models of Purkinje fibers of which physical appearances closely resembled the real photograph. The generation takes a few seconds. Variations of the Purkinje fibers could be constructed easily by modifying the generating rules and parameters.     

A comparison of step-and-shoot leaf sequencing algorithms that eliminate tongue-and-groove effects

The performances of three recently published leaf sequencing algorithms for step-and-shoot intensity-modulated radiation therapy delivery that eliminates tongue-and-groove underdosage are evaluated. Proofs are given to show that the algorithm of Que et al (2004 Phys. Med. Biol. 49 399-405) generates leaf sequences free of tongue-and-groove underdosage and interdigitation. However, the total beam-on times could be up to n times those of the sequences generated by the algorithms of Kamath et al (2004 Phys. Med. Biol. 49 N7-N19), which are optimal in beam-on time for unidirectional leaf movement under the same constraints, where n is the total number of involved leaf pairs. Using 19 clinical fluence matrices and 100000 randomly generated 15 x 15 matrices, the average monitor units and number of segments of the leaf sequences generated using the algorithm of Que et al are about two to four times those generated by the algorithm of Kamath et al.     

The susceptibility of IMRT dose distributions to intrafraction organ motion: an investigation into smoothing filters derived from four dimensional computed tomography data

This study investigated the sensitivity of static planning of intensity-modulated beams (IMBs) to intrafraction deformable organ motion and assessed whether smoothing of the IMBs at the treatment-planning stage can reduce this sensitivity. The study was performed with a 4D computed tomography (CT) data set for an IMRT treatment of a patient with liver cancer. Fluence profiles obtained from inverse-planning calculations on a standard reference CT scan were redelivered on a CT scan from the 4D data set at a different part of the breathing cycle. The use of a nonrigid registration model on the 4D data set additionally enabled detailed analysis of the overall intrafraction motion effects on the IMRT delivery during free breathing. Smoothing filters were then applied to the beam profiles within the optimization process to investigate whether this could reduce the sensitivity of IMBs to intrafraction organ motion. In addition, optimal fluence profiles from calculations on each individual phase of the breathing cycle were averaged to mimic the convolution of a static dose distribution with a motion probability kernel and assess its usefulness. Results from nonrigid registrations of the CT scan data showed a maximum liver motion of 7 mm in superior-inferior direction for this patient. Dose-volume histogram (DVH) comparison indicated a systematic shift when planning treatment on a motion-frozen, standard CT scan but delivering over a full breathing cycle. The ratio of the dose to 50% of the normal liver to 50% of the planning target volume (PTV) changed up to 28% between different phases. Smoothing beam profiles with a median-window filter did not overcome the substantial shift in dose due to a difference in breathing phase between planning and delivery of treatment. Averaging of optimal beam profiles at different phases of the breathing cycle mainly resulted in an increase in dose to the organs at risk (OAR) and did not seem beneficial to compensate for organ motion compared with using a large margin. Additionally, the results emphasized the need for 4D CT scans when aiming to reduce the internal margin (IM). Using only a single planning scan introduces a systematic shift in the dose distribution during delivery. Smoothing beam profiles either based on a single scan or over the different breathing phases was not beneficial for reducing this shift.     

Dosimetric verification of a commercial inverse treatment planning system

A commercial three-dimensional (3D) inverse treatment planning system, Corvus (Nomos Corporation, Sewickley, PA), was recently made available. This paper reports our preliminary results and experience with commissioning this system for clinical implementation. This system uses a simulated annealing inverse planning algorithm to calculate intensity-modulated fields. The intensity-modulated fields are divided into beam profiles that can be delivered by means of a sequence of leaf settings by a multileaf collimator (MLC). The treatments are delivered using a computer-controlled MLC. To test the dose calculation algorithm used by the Corvus software, the dose distributions for single rectangularly shaped fields were compared with water phantom scan data. The dose distributions predicted to be delivered by multiple fields were measured using an ion chamber that could be positioned in a rotatable cylindrical water phantom. Integrated charge collected by the ion chamber was used to check the absolute dose of single- and multifield intensity modulated treatments at various spatial points. The measured and predicted doses were found to agree to within 4% at all measurement points. Another set of measurements used a cubic polystyrene phantom with radiographic film to record the radiation dose distribution. The films were calibrated and scanned to yield two-dimensional isodose distributions. Finally, a beam imaging system (BIS) was used to measure the intensity-modulated x-ray beam patterns in the beam's-eye view. The BIS-measured images were then compared with a theoretical calculation based on the MLC leaf sequence files to verify that the treatment would be executed accurately and without machine faults. Excellent correlation (correlation coefficients > or = 0.96) was found for all cases. Treatment plans generated using intensity-modulated beams appear to be suitable for treatment of irregularly shaped tumours adjacent to critical structures. The results indicated that the system has potential for clinical radiation treatment planning and delivery and may in the future reduce treatment complexity.     

Leaf sequencing algorithms for segmented multileaf collimation

The delivery of intensity-modulated radiation therapy (IMRT) with a multileaf collimator (MLC) requires the conversion of a radiation fluence map into a leaf sequence file that controls the movement of the MLC during radiation delivery. It is imperative that the fluence map delivered using the leaf sequence file is as close as possible to the fluence map generated by the dose optimization algorithm, while satisfying hardware constraints of the delivery system. Optimization of the leaf sequencing algorithm has been the subject of several recent investigations. In this work, we present a systematic study of the optimization of leaf sequencing algorithms for segmental multileaf collimator beam delivery and provide rigorous mathematical proofs of optimized leaf sequence settings in terms of monitor unit (MU) efficiency under most common leaf movement constraints that include minimum leaf separation constraint and leaf interdigitation constraint. Our analytical analysis shows that leaf sequencing based on unidirectional movement of the MLC leaves is as MU efficient as bidirectional movement of the MLC leaves.     

Optimal leaf sequencing with elimination of tongue-and-groove underdosage

The individual leaves of a multileaf collimator (MLC) have a tongue-and-groove or stepped-edge design to minimize leakage radiation between adjacent leaves. This design element has a drawback in that it creates areas of underdosages in intensity-modulated photon beams unless a leaf trajectory is specifically designed such that for any two adjacent leaf pairs, the direct exposure under the tongue-and-groove is equal to the lower of the direct exposures of the leaf pairs. In this work, we present a systematic study of the optimization of a leaf sequencing algorithm for segmental multileaf collimator beam delivery that completely eliminates areas of underdosages due to tongue-and-groove or stepped-edge design of the MLC. Simultaneous elimination of tongue-and-groove effect and leaf interdigitation is also studied. This is an extension of our previous work (Kamath et al 2003a Phys. Med. Biol. 48 307) in which we described a leaf sequencing algorithm that is optimal for monitor unit (MU) efficiency under most common leaf movement constraints that include minimum leaf separation. Compared to our previously published algorithm (without constraints), the new algorithms increase the number of sub-fields by approximately 21% and 25%, respectively, but are optimal in MU efficiency for unidirectional schedules.     

Estimation of a radiation time prolongation factor for intensity-modulated radiotherapy

In general, the deposition of a given target dose requires a longer radiation time for intensity-modulated photon beams (IMBs) than for unmodulated beams. Hence, the routine use of intensity-modulated radiotherapy (IMRT) has repercussions both on the exposure of the patient to scatter and institutional radiation safety. A rule of thumb is presented to assess the maximum prolongation of radiation time for a case class in an idealized setting using static superimposed field segments. The method considers only the degree to which risk structures have to be blocked to meet specified dose restrictions.     

Analysis of stochastic noise in intensity-modulated beams

Inverse planning techniques are known to produce intensity-modulated beams (IMBs) that are highly modulated. They are characterized by the fact that they contain high-frequency modulations that are absent in the profiles that are easier to deliver. For the purpose of this study these clinically unwanted fluctuations are being defined as 'noise'. Although these highly modulated solutions are also optimal solutions, as soon as the profiles are being delivered, they become unfavourable with respect to delivery efficiency and the analysis and verification of treatment. The aim of this work was therefore to understand the origins of the structure and complexity of IMBs. Ultimately, if one can characterize the essential features in optimum beam profiles, it might be possible to control the frequency distribution of IMBs and simplify the IMRT planning and delivery process. The study was based on two common optimization techniques: simulated annealing (SA) and gradient-descent (GD). The assumptions made at the start of this work were that the stochastic noise caused by the SA optimization technique is dominant over other sources of noise and that it could be separated out from the essential modulation after convergence of the cost function by averaging minimum-cost fluence profiles. The results indicate that there are three possible sources of stochastic noise in IMBs, i.e. the optimization technique, the cost function and the definition of convergence of that cost function. In terms of the optimization technique itself, it was confirmed that the gradient-descent technique does not introduce stochastic noise in the IMBs. The SA technique does introduce stochastic noise but averaging of minimum-cost fluence profiles does not result in smoother beam profiles. This originates from the fact that this type of noise is not the dominant factor in the optimization, but rather the curvature of the cost function close to the global minimum. It is shown that the choice of initial temperature in the SA optimization technique is crucial for the convergence of the cost function and the frequency distribution of the fluence profiles. If the initial temperature is too small the stochastic noise will get frozen into the fluence profiles and become the dominant component of noise, resulting in very random-looking and difficult to deliver patterns.     

A method of simulating dynamic multileaf collimators using Monte Carlo techniques for intensity-modulated radiation therapy

A method of modelling the dynamic motion of multileaf collimators (MLCs) for intensity-modulated radiation therapy (IMRT) was developed and implemented into the Monte Carlo simulation. The simulation of the dynamic MLCs (DMLCs) was based on randomizing leaf positions during a simulation so that the number of particle histories being simulated for each possible leaf position was proportional to the monitor units delivered to that position. This approach was incorporated into an EGS4 Monte Carlo program, and was evaluated in simulating the DMLCs for Varian accelerators (Varian Medical Systems, Palo Alto. CA, USA). The MU index of each segment, which was specified in the DMLC-control data, was used to compute the cumulative probability distribution function (CPDF) for the leaf positions. This CPDF was then used to sample the leaf positions during a real-time simulation, which allowed for either the step-shoot or sweeping-leaf motion in the beam delivery. Dose intensity maps for IMRT fields were computed using the above Monte Carlo method, with its accuracy verified by film measurements. The DMLC simulation improved the operational efficiency by eliminating the need to simulate multiple segments individually. More importantly, the dynamic motion of the leaves could be simulated more faithfully by using the above leaf-position sampling technique in the Monte Carlo simulation.     

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.