Fast voxel and polygon ray-tracing algorithms in intensity modulated radiation therapy treatment planning

We present work on combining three algorithms to improve ray-tracing efficiency in radiation therapy dose computation. The three algorithms include: An improved point-in-polygon algorithm, incremental voxel ray tracing algorithm, and stereographic projection of beamlets for voxel truncation. The point-in-polygon and incremental voxel ray-tracing algorithms have been used in computer graphics and nuclear medicine applications while the stereographic projection algorithm was developed by our group. These algorithms demonstrate significant improvements over the current standard algorithms in peer reviewed literature, i.e., the polygon and voxel ray-tracing algorithms of Siddon for voxel classification (point-in-polygon testing) and dose computation, respectively, and radius testing for voxel truncation. The presented polygon ray-tracing technique was tested on 10 intensity modulated radiation therapy (IMRT) treatment planning cases that required the classification of between 0.58 and 2.0 million voxels on a 2.5 mm isotropic dose grid into 1-4 targets and 5-14 structures represented as extruded polygons (a.k.a. Siddon prisms). Incremental voxel ray tracing and voxel truncation employing virtual stereographic projection was tested on the same IMRT treatment planning cases where voxel dose was required for 230-2400 beamlets using a finite-size pencil-beam algorithm. Between a 100 and 360 fold cpu time improvement over Siddon's method was observed for the polygon ray-tracing algorithm to perform classification of voxels for target and structure membership. Between a 2.6 and 3.1 fold reduction in cpu time over current algorithms was found for the implementation of incremental ray tracing. Additionally, voxel truncation via stereographic projection was observed to be 11-25 times faster than the radial-testing beamlet extent approach and was further improved 1.7-2.0 fold through point-classification using the method of translation over the cross product technique.     

Beam delivery sequencing for intensity modulated proton therapy

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

Robust optimization for intensity modulated radiation therapy treatment planning under uncertainty

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

鲁棒性优化在质子调强放射治疗中的应用

【摘要】质子治疗过程容易受射程偏差、摆位偏差、患者解剖结构改变等不确定因素的影响,质子调强放疗的鲁棒性优化是将这些不确定因素考虑进计划的制定过程中,增加治疗计划鲁棒性的一种方法,在临床中有广泛的应用。鲁棒性优化的方法主要有4种:（1）概率法;（2）最差剂量法;（3）添加约束项;（4）多CT优化。本文综述了这4种方法的原理、优缺点和临床应用情况。同时,还介绍了治疗计划鲁棒性的评估方法。虽然目前剂量体积直方图束是最常用的评估治疗计划鲁棒性的方法,但是,剂量体积直方图束不能反映质子调强放疗计划对解剖结构改变的鲁棒性,因此,还急需建立一个简单易用并能被广泛接受的鲁棒性评估方法,方便质子调强放疗计划的对比和评估。     

Optimization of radiobiological effects in intensity modulated proton therapy

Today, inverse treatment planning for intensity modulated proton therapy (IMPT) usually employs a constant relative biological effectiveness (RBE). In this paper, the potential clinical relevance of RBE variations for scanning techniques in IMPT is investigated, and a new strategy to include the RBE into the inverse planning process is presented. Three-dimensional RBE distributions are calculated based on a phenomenological model that describes the RBE as a function of dose, linear energy transfer (LET) and tissue type in the framework of the linear-quadratic model. This RBE model is integrated into the optimization loop of inverse planning by using a modified version of the standard quadratic objective function, where the physical dose is replaced by the biological effect. This system for "biological optimization" was implemented into a research version of the inverse planning software KonRad and allows the direct optimization of the product of RBE and physical dose. Several treatment plans for a prostate case are presented, which compare the biological with the conventional physical dose optimization for IMPT scanning techniques, in particular distal edge tracking (DET) and the full three-dimensional (3D) modulation of beam spots. Mainly due to their different LET distributions, the RBE effects for these two techniques are quite different: while the RBE distribution was more or less homogeneous in the planning target volume (PTV) for 3D modulation, considerable RBE variations within the PTV were observed for DET. These unfavorable effects could be compensated for by employing the new biological objective function, which led to a more homogeneous distribution of the product of RBE and physical dose in the PTV. The computation time increased by a factor of 2 compared to the optimization of the physical dose. In conclusion, the proposed method allows the simultaneous multifield optimization of the biological effect in a reasonable time, and is therefore well suited for studying the influence of a variable RBE in IMPT as well as for minimizing potentially adverse effects.     

An efficient dose calculation strategy for intensity modulated proton therapy

While intensity-modulated proton therapy (IMPT) has great potential to improve the therapeutic efficacy of radiotherapy, IMPT optimization can be computationally demanding, particularly for large and complex tumors. Here we propose a dose calculation strategy to accelerate IMPT optimization while reducing memory requirements. By using two adjustable threshold parameters, our method separates dose contributions from proton beamlets into major and minor components for each dose voxel. The optimization proceeds with two levels of iterations: in inner iterations, doses are updated in correspondence with changes in beamlet intensities from only the major contributions while keeping the portions from the minor contributions constant; in outer iterations, doses are recalculated exactly by considering both major and minor contributions. Since the number of elements in the influence matrix for major contributions is relatively small, each inner iteration proceeds quickly. Each outer iteration requires a longer computation time, but only a few such iterations are needed. Our study shows that the proposed strategy leads to nearly identical dose distributions as those optimized with the full influence matrix, but reducing computing time by at least a factor of 3 and internal memory requirements by a factor of 10 or more. In addition, we show that the proposed approach could enhance other optimization-related applications such as optimizing beam angles. By using an advanced lung cancer case that would demand large computing resources by conventional optimization approach, we show how our method may potentially help improve IMPT treatment planning in real clinical situations.     

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

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

Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization algorithms

We consider the behaviour of the limited memory L-BFGS algorithm as a representative constraint-free gradient-based algorithm which is used for multiobjective (MO) dose optimization for intensity modulated radiotherapy (IMRT). Using a parameter transformation, the positivity constraint problem of negative beam fluences is entirely eliminated: a feature which to date has not been fully understood by all investigators. We analyse the global convergence properties of L-BFGS by searching for the existence and the influence of possible local minima. With a fast simulated annealing (FSA) algorithm we examine whether the L-BFGS solutions are globally Pareto optimal. The three examples used in our analysis are a brain tumour, a prostate tumour and a test case with a C-shaped PTV. In 1% of the optimizations global convergence is violated. A simple mechanism practically eliminates the influence of this failure and the obtained solutions are globally optimal. A single-objective dose optimization requires less than 4 s for 5400 parameters and 40000 sampling points. The elimination of the problem of negative beam fluences and the high computational speed permit constraint-free gradient-based optimization algorithms to be used for MO dose optimization. In this situation, a representative spectrum of possible solutions is obtained which contains information such as the trade-off between the objectives and range of dose values. Using simple decision making tools the best of all the possible solutions can be chosen. We perform an MO dose optimization for the three examples and compare the spectra of solutions, firstly using recommended critical dose values for the organs at risk and secondly, setting these dose values to zero.     

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

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

A robust algorithm of intensity modulated proton therapy for critical tissue sparing and target coverage

Intensity modulated proton therapy (IMPT) offers the possibility of generating excellent target coverage while sparing the neighbouring organs at risk. However, treatment plans optimized for IMPT may be very sensitive to range and setup uncertainties. We developed a method to deal with these uncertainties in the dose optimization. This method aims at two objectives: one for maintaining the dose coverage within the target, and the other for preventing undesired exposure to organs at risk. The former objective was achieved by the algorithm described in our previous paper to suppress the in-field dose gradient within the target. In this study, the latter objective was achieved by a novel algorithm in which we suppressed pencil beams with high risk to deliver undesired doses to organs at risk under conditions where range and setup uncertainties occur. We defined the risk index that quantifies the likelihood of each pencil beam delivering high doses to organs at risk, and introduced it into the objective function of dose optimizations. In order to test the algorithm's performance, this method was applied to an RTOG benchmark phantom geometry and to a cervical chordoma case. These simulations demonstrated that our method provides IMPT plans that are more robust against range and setup errors compared to conventional IMPT plans. Compared to the conventional IMPT plan, the optimization time for the robust plan increased by a factor of only 3, from 4 to 11 min.     

A pencil beam algorithm for intensity modulated proton therapy derived from Monte Carlo simulations

A pencil beam algorithm as a component of an optimization algorithm for intensity modulated proton therapy (IMPT) is presented. The pencil beam algorithm is tuned to the special accuracy requirements of IMPT, where in heterogeneous geometries both the position and distortion of the Bragg peak and the lateral scatter pose problems which are amplified by the spot weight optimization. Heterogeneity corrections are implemented by a multiple raytracing approach using fluence-weighted sub-spots. In order to derive nuclear interaction corrections, Monte Carlo simulations were performed. The contribution of long ranged products of nuclear interactions is taken into account by a fit to the Monte Carlo results. Energy-dependent stopping power ratios are also implemented. Scatter in optional beam line accessories such as range shifters or ripple filters is taken into account. The collimator can also be included, but without additional scattering. Finally, dose distributions are benchmarked against Monte Carlo simulations, showing 3%/1 mm agreement for simple heterogeneous phantoms. In the case of more complicated phantoms, principal shortcomings of pencil beam algorithms are evident. The influence of these effects on IMPT dose distributions is shown in clinical examples.     

A macropencil beam model: clinical implementation for conformal and intensity modulated radiation therapy

The increasing use of irregularly shaped, off-centre fields in advanced treatment techniques, particularly intensity modulated radiation therapy, has strained the limits of conventional, broad-beam dose calculation algorithms. More recent models, such as kernel-based pencil beams and Monte Carlo methods, are accurate but suffer from the time needed for calculations and from the lack of clearly established methods for determining the parameters needed to match calculations with the particular dosimetric characteristics of an individual machine. This paper presents the implementation of a model that uses an extended source model to calculate the variation of fluence at the patient surface for any arbitrarily shaped field. It uses a macropencil beam model to calculate phantom scatter. Both head scatter and phantom scatter models use exponential functions fit to a series of measurements to determine the model's parameters. The means by which the model can be implemented in a clinical setting using standard dosimetric equipment is presented. Results for two separate machines and three energies are presented. Comparisons with measurements for a set of regular and irregular fields demonstrate the accuracy of the model for conventional, conformal and intensity modulated treatments. For rectangular and irregular fields at depths up to 20 cm, the accuracy was better than < or =1.5%, compared with errors of up to 7.5% with a standard algorithm. For a 20-step intensity modulated field, the accuracy was 3.4% compared with 18% with the conventional algorithm. The advantages of this model for IMRT are discussed.     

Margins for treatment planning of proton therapy

For protons and other charged particles, the effect of set-up errors on the position of isodoses is considerably less in the direction of the incident beam than it is laterally. Therefore, the margins required between the clinical target volume (CTV) and planning target volume (PTV) can be less in the direction of the incident beam than laterally. Margins have been calculated for a typical head plan and a typical prostate plan, for a single field, a parallel opposed and a four-field arrangement of protons, and compared with margins calculated for photons, assuming identical geometrical uncertainties for each modality. In the head plan, where internal motion was assumed negligible, the CTV-PTV margin reduced from approximately 10 mm to 3 mm in the axial direction for the single field and parallel opposed plans. For a prostate plan, where internal motion cannot be ignored, the corresponding reduction in margin was from 11 mm to 7 mm. The planning organ at risk (PRV) margin in the axial direction reduced from 6 mm to 2 mm for the head plan, and from 7 mm to 4 mm for the prostate plan. No reduction was seen on the other axes, or for any axis of the four-field plans. Owing to the shape of proton dose distributions, there are many clinical cases in which good dose distributions can be obtained with one or two fields. When this is done, it is possible to use smaller PTV and PRV margins. This has the potential to convert untreatable cases, in which the PTV and PRV overlap, into cases with a gap between PTV and PRV of adequate size for treatment planning.     

Accounting for range uncertainties in the optimization of intensity modulated proton therapy

Treatment plans optimized for intensity modulated proton therapy (IMPT) may be sensitive to range variations. The dose distribution may deteriorate substantially when the actual range of a pencil beam does not match the assumed range. We present two treatment planning concepts for IMPT which incorporate range uncertainties into the optimization. The first method is a probabilistic approach. The range of a pencil beam is assumed to be a random variable, which makes the delivered dose and the value of the objective function a random variable too. We then propose to optimize the expectation value of the objective function. The second approach is a robust formulation that applies methods developed in the field of robust linear programming. This approach optimizes the worst case dose distribution that may occur, assuming that the ranges of the pencil beams may vary within some interval. Both methods yield treatment plans that are considerably less sensitive to range variations compared to conventional treatment plans optimized without accounting for range uncertainties. In addition, both approaches--although conceptually different--yield very similar results on a qualitative level.     

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.     

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.