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

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

Reducing dose calculation time for accurate iterative IMRT planning

A time-consuming component of IMRT optimization is the dose computation required in each iteration for the evaluation of the objective function. Accurate superposition/convolution (SC) and Monte Carlo (MC) dose calculations are currently considered too time-consuming for iterative IMRT dose calculation. Thus, fast, but less accurate algorithms such as pencil beam (PB) algorithms are typically used in most current IMRT systems. This paper describes two hybrid methods that utilize the speed of fast PB algorithms yet achieve the accuracy of optimizing based upon SC algorithms via the application of dose correction matrices. In one method, the ratio method, an infrequently computed voxel-by-voxel dose ratio matrix (R = D(SC)/D(PB)) is applied for each beam to the dose distributions calculated with the PB method during the optimization. That is, D(PB) x R is used for the dose calculation during the optimization. The optimization proceeds until both the IMRT beam intensities and the dose correction ratio matrix converge. In the second method, the correction method, a periodically computed voxel-by-voxel correction matrix for each beam, defined to be the difference between the SC and PB dose computations, is used to correct PB dose distributions. To validate the methods, IMRT treatment plans developed with the hybrid methods are compared with those obtained when the SC algorithm is used for all optimization iterations and with those obtained when PB-based optimization is followed by SC-based optimization. In the 12 patient cases studied, no clinically significant differences exist in the final treatment plans developed with each of the dose computation methodologies. However, the number of time-consuming SC iterations is reduced from 6-32 for pure SC optimization to four or less for the ratio matrix method and five or less for the correction method. Because the PB algorithm is faster at computing dose, this reduces the inverse planning optimization time for our implementation by a factor of 2 to 8 compared with pure SC optimization, without compromising the quality or accuracy of the final treatment plan.     

Feasibility of a fast inverse dose optimization algorithm for IMRT via matrix inversion without negative beamlet intensities

A fast optimization algorithm is very important for inverse planning of intensity modulated radiation therapy (IMRT), and for adaptive radiotherapy of the future. Conventional numerical search algorithms such as the conjugate gradient search, with positive beam weight constraints, generally require numerous iterations and may produce suboptimal dose results due to trapping in local minima. A direct solution of the inverse problem using conventional quadratic objective functions without positive beam constraints is more efficient but will result in unrealistic negative beam weights. We present here a direct solution of the inverse problem that does not yield unphysical negative beam weights. The objective function for the optimization of a large number of beamlets is reformulated such that the optimization problem is reduced to a linear set of equations. The optimal set of intensities is found through a matrix inversion, and negative beamlet intensities are avoided without the need for externally imposed ad-hoc constraints. The method has been demonstrated with a test phantom and a few clinical radiotherapy cases, using primary dose calculations. We achieve highly conformal primary dose distributions with very rapid optimization times. Typical optimization times for a single anatomical slice (two dimensional) (head and neck) using a LAPACK matrix inversion routine in a single processor desktop computer, are: 0.03 s for 500 beamlets; 0.28 s for 1000 beamlets; 3.1 s for 2000 beamlets; and 12 s for 3000 beamlets. Clinical implementation will require the additional time of a one-time precomputation of scattered radiation for all beamlets, but will not impact the optimization speed. In conclusion, the new method provides a fast and robust technique to find a global minimum that yields excellent results for the inverse planning of IMRT.     

A method to improve spatial resolution and smoothness of intensity profiles in IMRT treatment planning

In IMRT optimization, the size of beamlets used for optimizing the beam intensity distributions is a planner-selected parameter. The appropriate setting for the beamlet size is critical to the outcome of IMRT planning. With too small beamlets the dose calculation can be inaccurate, and the resulting intensity profiles can be unnecessarily complex and difficult to generate. Relatively simple intensity profiles can be obtained using large beamlets. However, this may compromise the conformity of the dose distribution. In this paper we present a method, in which multiple beamlet matrices displaced from each other by a shift in MLC leaf travel direction are used instead of the single beamlet matrix per beam in a conventional method, to achieve finer spatial resolution for the intensity distribution than the given beamlet size. Two test cases were used to assess the method by the resultant DVHs and dose distributions and characteristic indices of the intensity profiles. The results show that this method can produce optimized dose distributions that are similar to those produced by the conventional inverse planning method with the benefit of smoother intensity profiles that are easier to deliver with a computer controlled MLC.     

A geometrically based method of step and shoot stereotactic radiosurgery with a miniature multileaf collimator

Conventional methods of inverse planning for intensity-modulated radiotherapy (IMRT) and intensity-modulated radiosurgery (IMRS) are generally based upon optimizing a set of beam fluence profiles according to a set of dose-volume constraints specified by a human planner. This optimization is generally carried out through an iterative approach that relies upon the optimization of a score, driving the plan's ability to satisfy the user-provided constraints. Following optimization of the fluence distribution, the non-trivial problem of converting the fluence distribution into a set of deliverable, intensity-modulated beams must be solved. A novel approach to solving this IMRS total inverse problem is presented in this paper. The proposed method uses a class solution that provides an optimized dose gradient and a method of designing a conformal plan based on an existing geometrically based optimization algorithm. After developing an optimal fluence distribution, the process then arranges the fluence into a set of simple and efficient MLC beam delivery sequences. The algorithm presented here offers several potential advantages for the application of intensity modulation to radiosurgery treatment planning. The geometrically based optimization process' simplicity requires far less human user input and decision making in the specification of dose and dose-volume constraints than do conventional inverse planning algorithms. This simplicity allows the optimization process to be completed much faster than conventional inverse-planning algorithms, literally seconds compared with at least several minutes. Likewise, the fluence conversion step is a simplified process (compared to conventional IMRT planning), which takes advantage of some simplifications uniquely appropriate to the problem at hand (IMRS). The converted, deliverable IMRS beams allow superior conformity and dose gradient relative to conventional IMRS planning or 3DCRT radiosurgery planning. Another benefit is that the number of beam intensity levels is greatly reduced, from hundreds to as few as a half-dozen intensity levels. Finally, since the treatment plan optimization process is based upon proven principles applicable to optimizing radiosurgery (rather than the general problem of optimizing fractionated radiotherapy plans), the plans generated and deliverable with this method of IMRS are potentially superior to those produced by conventional inverse-planning methods of IMRT/IMRS.     

Theoretical considerations of monitor unit calculations for intensity modulated beam treatment planning

A treatment planning system to compute intensity modulated radiotherapy (IMRT) treatments using inverse planning was investigated. The system was designed to optimize the intensity patterns required to treat a specified target volume with specified normal structure constraints. A beam model that uses the convolution of pencil beams was used to compute the dose distributions. A multileaf collimator leaf-setting sequence intended to produce the intensity pattern was computed along with the monitor units required to deliver each of a number of fixed-gantry modulated fields. Computer calculations are commonly verified using an independent manual procedure. It is difficult to calculate treatment delivery monitor units for this variant of IMRT using manual methods. Since manual calculations are not feasible, it is important both to understand and to verify the calculation of treatment monitor units by the planning system algorithm. A formal analysis was made of the dose calculation model and the monitor unit calculation embedded in the algorithm. Experimental verification of the dose delivered by plans computed with the methodology demonstrated an agreement of better than 4% between the dose model and measurements.     

Adaptive diffusion smoothing: a diffusion-based method to reduce IMRT field complexity

Inverse-planned intensity modulated radiation therapy (IMRT) is often able to achieve complex treatment planning goals that are unattainable with forward three-dimensional (3D) conformal planning. However, the common use of IMRT has introduced several new challenges. The potentially high degree of modulation in IMRT beams risks the loss of some advantages of 3D planning, such as excellent target coverage and high delivery efficiency. Previous attempts to reduce beam complexity by smoothing often result in plan degradation because the smoothing algorithm cannot distinguish between areas of desirable and undesirable modulation. The purpose of this work is to introduce and evaluate adaptive diffusion smoothing (ADS), a novel procedure designed to preferentially reduce IMRT beam complexity. In this method, a discrete diffusion equation is used to smooth IMRT beams using diffusion coefficients, automatically defined for each beamlet, that dictate the degree of smoothing allowed for each beamlet. This yields a method that can distinguish between areas of desirable and undesirable modulation. The ADS method has been incorporated into our optimization system as a weighted cost function penalty, with two diffusion coefficient definitions designed to promote: (1) uniform smoothing everywhere or (2) smoothing based on cost function gradients with respect to the plan beamlet intensities. The ADS method (with both coefficient types) has been tested in a phantom and in two clinical examples (prostate and head/neck). Both types of diffusion coefficients produce plans with reduced modulation and minimal dosimetric impact, but the cost function gradient-based coefficients show more potential for reducing beam modulation without affecting dosimetric plan quality. In summary, adaptive diffusion smoothing is a promising tool for ensuring that only the necessary amount of beam modulation is used, promoting more efficient and accurate IMRT planning, QA, and delivery.     

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.     

Improving IMRT delivery efficiency using intensity limits during inverse planning

Inverse planned intensity modulated radiotherapy (IMRT) fields can be highly modulated due to the large number of degrees of freedom involved in the inverse planning process. Additional modulation typically results in a more optimal plan, although the clinical rewards may be small or offset by additional delivery complexity and/or increased dose from transmission and leakage. Increasing modulation decreases delivery efficiency, and may lead to plans that are more sensitive to geometrical uncertainties. The purpose of this work is to assess the use of maximum intensity limits in inverse IMRT planning as a simple way to increase delivery efficiency without significantly affecting plan quality. Nine clinical cases (three each for brain, prostate, and head/neck) were used to evaluate advantages and disadvantages of limiting maximum intensity to increase delivery efficiency. IMRT plans were generated using in-house protocol-based constraints and objectives for the brain and head/neck, and RTOG 9406 dose volume objectives in the prostate. Each case was optimized at a series of maximum intensity ratios (the product of the maximum intensity and the number of beams divided by the prescribed dose to the target volume), and evaluated in terms of clinical metrics, dose-volume histograms, monitor units (MU) required per fraction (SMLC and DMLC delivery), and intensity map variation (a measure of the beam modulation). In each site tested, it was possible to reduce total monitor units by constraining the maximum allowed intensity without compromising the clinical acceptability of the plan. Monitor unit reductions up to 38% were observed for SMLC delivery, while reductions up to 29% were achieved for DMLC delivery. In general, complicated geometries saw a smaller reduction in monitor units for both delivery types, although DMLC delivery required significantly more monitor units in all cases. Constraining the maximum intensity in an inverse IMRT plan is a simple way to improve delivery efficiency without compromising plan objectives.     

Automatic beam angle selection in IMRT planning using genetic algorithm

The selection of suitable beam angles in external beam radiotherapy is at present generally based upon the experience of the human planner. The requirement to automatically select beam angles is particularly highlighted in intensity-modulated radiation therapy (IMRT), in which a smaller number of modulated beams is hoped to be used, in comparison with conformal radiotherapy. It has been proved by many researchers that the selection of suitable beam angles is most valuable for a plan with a small number of beams (< or = 5). In this paper an efficient method is presented to investigate how to improve the dose distributions by selecting suitable coplanar beam angles. In our automatic beam angle selection (ABAS) algorithm, the optimal coplanar beam angles correspond to the lowest objective function value of the dose distributions calculated using the intensity-modulated maps of this group of candidate beams. Due to the complexity of the problem and the large search space involved, the selection of beam angles and the optimization of intensity maps are treated as two separate processes and implemented iteratively. A genetic algorithm (GA) incorporated with an immunity operation is used to select suitable beam angles, and a conjugate gradient (CG) method is used to quickly optimize intensity maps for each selected beam combination based on a dose-based objective function. A pencil-beam-based three-dimensional (3D) full scatter convolution (FSC) algorithm is employed for the dose calculation. Two simulated cases with obvious optimal beam angles are used to verify the validity of the presented technique, and a more complicated case simulating a prostate tumour and two clinical cases are employed to test the efficiency of ABAS. The results show that ABAS is valid and efficient and can improve the dose distributions within a clinically acceptable computation time.     

Incorporating multi-leaf collimator leaf sequencing into iterative IMRT optimization

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

Independent monitor unit calculation for intensity modulated radiotherapy using the MIMiC multileaf collimator

A self-consistent monitor unit (MU) and isocenter point-dose calculation method has been developed that provides an independent verification of the MU for intensity modulated radiotherapy (IMRT) using the MIMiC (Nomos Corporation) multileaf collimator. The method takes into account two unique features of IMRT using the MIMiC: namely the gantry-dynamic arc delivery of intensity modulated photon beams and the slice-by-slice dose delivery for large tumor volumes. The method converts the nonuniform beam intensity planned at discrete gantry angles of 5 degrees or 10 degrees into conventional nonmodulated beam intensity apertures of elemental arc segments of 1 degree. This approach more closely simulates the actual gantry-dynamic arc delivery by MIMiC. Because each elemental arc segment is of uniform intensity, the MU calculation for an IMRT arc is made equivalent to a conventional arc with gantry-angle dependent beam apertures. The dose to the isocenter from each 1 degree elemental arc segment is calculated by using the Clarkson scatter summation technique based on measured tissue-maximum-ratio and output factors, independent of the dose calculation model used in the IMRT planning system. For treatments requiring multiple treatment slices, the MU for the arc at each treatment slice takes into account the MU, leakage and scatter doses from other slices. This is achieved by solving a set of coupled linear equations for the MUs of all involved treatment slices. All input dosimetry data for the independent MU/isocenter point-dose calculation are measured directly. Comparison of the MU and isocenter point dose calculated by the independent program to those calculated by the Corvus planning system and to direct measurements has shown good agreement with relative difference less than +/-3%. The program can be used as an independent initial MU verification for IMRT plans using the MIMiC multileaf collimators.     

Reduction of IMRT beam complexity through the use of beam modulation penalties in the objective function

Inverse planned intensity modulated radiation therapy (IMRT) has become commonplace in treatment centers across the world. Due to the implications of beam complexity on treatment planning, delivery, and quality assurance, several methods have been proposed to reduce the complexity. These methods include beamlet intensity restrictions, smoothing procedures, and direct aperture optimization. Many of these methods typically sacrifice target coverage and/or normal tissue sparing in return for increased beam smoothness and delivery efficiency. In the present work, we penalize beam modulation in the inverse planning cost function to reduce beam complexity and increase delivery efficiency, while maintaining dosimetric quality. Three modulation penalties were tested: two that penalized deviation from Savitzky-Golay filtered versions of the optimized beams, and one that penalized the plan intensity map variation (a measure of overall beam modulation). The modulation penalties were applied at varying weights in a weighted sum objective (or cost) function to investigate their ability to reduce beam complexity while preserving IMRT plan quality. The behavior of the penalties was characterized on a CT phantom, and then clinical optimization comparisons were performed in the brain, prostate, and head/neck. Comparisons were made between (i) plans with a baseline cost function (ii) plans with a baseline cost function employing maximum beamlet intensity limits, and (iii) plans with each of the modulation penalties added to the baseline cost function. Plan analysis was based upon dose-volume histograms, relevant dose metrics, beam modulation, and monitor units required for step and shoot delivery. Each of the techniques yielded improvements over a baseline cost function in terms of MU reduction. In most cases, this was achieved with minimal change to the plan DVHs and metrics. In all cases, an acceptable plan was reached with each of the methods while reducing MU substantially. Each individual method has merit as a tool for reducing IMRT beam complexity and could be easily applied in the clinic to improve overall inverse plan quality. However, the penalty based upon the plan intensity map variation consistently produced the most delivery-efficient plans with the fewest computations.     

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

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

A 2-D diode array and analysis software for verification of intensity modulated radiation therapy delivery

An analysis is made of a two-dimensional array of diodes that can be used for measuring dose generated in a plane by a radiation beam. This measuring device is the MapCHECK Model 1175 (Sun Nuclear, Melbourne, FL). This device has 445 N-type diodes in a 22 x 22 cm2 2-D array with variable spacing. The entire array of diodes is easily calibrated to allow for measurements in absolute dose. For IMRT quality assurance, each beam is measured individually with the beam central axis oriented perpendicular to the plane of diodes. Software is available to do the analytical comparison of measurements versus dose distributions calculated by a treatment planning system. Comparison criteria of percent difference and distance-to-agreement are defined by the operator. Data are presented that show the diode array has linear response when beam fluence changes by over 300-fold, which is typical of the level of modulation in intensity modulated radiation therapy, IMRT, beams. A linear dependence is also shown for a 100-fold change in monitors units delivered. Methods for how this device can be used in the clinic for quality assurance of IMRT fields are described. Measurements of typical IMRT beams that are modulated by compensators and MLCs are presented with comparisons to treatment planning system dose calculations. A time analysis is done for typical IMRT quality assurance measurements. The setup, calibration, and analysis time for the 2-D diode array are on the order of 20 min, depending on numbers of fields. This is significantly less time than required to do similar analysis with radiographic film. The 2-D diode array is ideal for per-plan quality assurance after an IMRT system is fully commissioned.     

Dynamic splitting of large intensity-modulated fields

The aims of this paper are to describe a method of splitting large intensity-modulated fields that cannot be delivered as a single field and to verify the accuracy of our method. Some multi-leaf collimators may be operated in the dynamic mode to deliver intensity-modulated radiation treatments (IMRT) using the 'sliding window' technique. In this technique each pair of leaves sweeps over the treatment field while the beam is on. However, there are limitations on the width of the field that can be treated due to the limited length of the leaves. For instance, the leaf length of the Varian MLC is 14.5 cm. Since each leaf pair must travel from the left boundary to the right boundary of the beam aperture, the maximum width of the field aperture that can be accommodated in one sweep of leaves is also limited to 14.5 cm, in fact to a slightly smaller value. It has been shown that IMRT is more efficient when used to plan and deliver the large and boost fields simultaneously. In such situations, the fields must be large enough to cover simultaneously the volumes of the gross tumour, microscopic disease and electively treated regions. Such field sizes are often larger than 14.5 cm wide. In this paper, we present a dynamic 'feathering' technique to split the large intensity-modulated fields into smaller fields. In this technique, the component beams overlap each other by a small amount, and the intensity in the overlap region gradually decreases for one field component and increases for the other. The sum of intensities remains the same as for the original field. This method eliminates the field matching problems associated with the conventional step 'break' for static fields. The splitting process is integrated into the IMRT treatment procedure and the entire planning process is automated. Comparison of dose distributions calculated and measured in a phantom showed good agreement. Such a method can be applied to the 'step and shoot' technique as well. IMRT fields of widths up to 25 cm can be delivered by splitting only once, which is adequate for most treatments.     

Improved stratification algorithms for step-and-shoot MLC delivery in intensity-modulated radiation therapy

In inverse planning for intensity-modulated radiotherapy (IMRT), the fluence distribution of each treatment beam is usually calculated in an optimization process. The delivery of the resulting treatment plan using multileaf collimators (MLCs) is performed either in the step-and-shoot or sliding window technique. For step-and-shoot delivery, the arbitrary beam fluence distributions have to be transformed into an applicable sequence of subsegments. In a stratification step the complexity of the fluence maps is reduced by assigning each beamlet to discrete intensity values, followed by the sequencing step that generates the subsegments. In this work, we concentrate on the stratification for step-and-shoot delivery. Different concepts of stratification are formally introduced. In addition to already used strategies that minimize the difference between original and stratified beam intensities, we propose an original stratification principle that minimizes the error of the resulting dose distribution. It could be shown that for a comparable total number of subsegments the dose-oriented stratification results in a better approximation of the original, unsequenced plan. The presented algorithm can replace the stratification routine in existing sequencer programs and can also be applied to interpolated plans that are generated in an interactive decision making process of multicriteria inverse planning programs.     

Effect of beamlet step-size on IMRT plan quality

We have studied the degree to which beamlet step-size impacts the quality of intensity modulated radiation therapy (IMRT) treatment plans. Treatment planning for IMRT begins with the application of a grid that divides each beam's-eye-view of the target into a number of smaller beamlets (pencil beams) of radiation. The total dose is computed as a weighted sum of the dose delivered by the individual beamlets. The width of each beamlet is set to match the width of the corresponding leaf of the multileaf collimator (MLC). The length of each beamlet (beamlet step-size) is parallel to the direction of leaf travel. The beamlet step-size represents the minimum stepping distance of the leaves of the MLC and is typically predetermined by the treatment planning system. This selection imposes an artificial constraint because the leaves of the MLC and the jaws can both move continuously. Removing the constraint can potentially improve the IMRT plan quality. In this study, the optimized results were achieved using an aperture-based inverse planning technique called direct aperture optimization (DAO). We have tested the relationship between pencil beam step-size and plan quality using the American College of Radiology's IMRT test case. For this case, a series of IMRT treatment plans were produced using beamlet step-sizes of 1, 2, 5, and 10 mm. Continuous improvements were seen with each reduction in beamlet step size. The maximum dose to the planning target volume (PTV) was reduced from 134.7% to 121.5% and the mean dose to the organ at risk (OAR) was reduced from 38.5% to 28.2% as the beamlet step-size was reduced from 10 to 1 mm. The smaller pencil beam sizes also led to steeper dose gradients at the junction between the target and the critical structure with gradients of 6.0, 7.6, 8.7, and 9.1 dose%/mm achieved for beamlet step sizes of 10, 5, 2, and 1 mm, respectively.     

The effect of dose calculation accuracy on inverse treatment planning

The effect of dose calculation accuracy during inverse treatment planning for intensity modulated radiotherapy (IMRT) was studied in this work. Three dose calculation methods were compared: Monte Carlo, superposition and pencil beam. These algorithms were used to calculate beamlets. which were subsequently used by a simulated annealing algorithm to determine beamlet weights which comprised the optimal solution to the objective function. Three different cases (lung, prostate and head and neck) were investigated and several different objective functions were tested for their effect on inverse treatment planning. It is shown that the use of inaccurate dose calculation introduces two errors in a treatment plan, a systematic error and a convergence error. The systematic error is present because of the inaccuracy of the dose calculation algorithm. The convergence error appears because the optimal intensity distribution for inaccurate beamlets differs from the optimal solution for the accurate beamlets. While the systematic error for superposition was found to be approximately 1% of Dmax in the tumour and slightly larger outside, the error for the pencil beam method is typically approximately 5% of Dmax and is rather insensitive to the given objectives. On the other hand, the convergence error was found to be very sensitive to the objective function, is only slightly correlated to the systematic error and should be determined for each case individually. Our results suggest that because of the large systematic and convergence errors, inverse treatment planning systems based on pencil beam algorithms alone should be upgraded either to superposition or Monte Carlo based dose calculations.