A particle track-repeating algorithm for proton beam dose calculation

A particle track-repeating algorithm has been developed for proton beam dose calculation for radiotherapy. Monoenergetic protons with 250 MeV kinetic energy were simulated in an infinite water phantom using the GEANT3 Monte Carlo code. The changes in location, angle and energy for every transport step and the energy deposition along the track were recorded for the primary protons and all secondary particles. When calculating dose for a patient with a realistic proton beam, the pre-generated particle tracks were repeated in the patient geometry consisting of air, soft tissue and bone. The medium and density for each dose scoring voxel in the patient geometry were derived from patient CT data. The starting point, at which a proton track was repeated, was determined according to the incident proton energy. Thus, any protons with kinetic energy less than 250 MeV can be simulated. Based on the direction of the incident proton, the tracks were first rotated and for the subsequent steps, the scattering angles were simply repeated for air and soft tissue but adjusted properly based on the scattering power for bone. The particle step lengths were adjusted based on the density for air and soft tissue and also on the stopping powers for bone while keeping the energy deposition unchanged in each step. The difference in nuclear interactions and secondary particle generation between water and these materials was ignored. The algorithm has been validated by comparing the dose distributions in uniform water and layered heterogeneous phantoms with those calculated using the GEANT3 code for 120, 150, 180 and 250 MeV proton beams. The differences between them were within 2%. The new algorithm was about 13 times faster than the GEANT3 Monte Carlo code for a uniform phantom geometry and over 700 times faster for a heterogeneous phantom geometry.     

A fourier analysis of the dose grid resolution required for accurate IMRT fluence map optimization

We present a theoretical and empirical analysis of the errors associated with the spatial discretization of the dose grid employed in optimized intensity modulated radiation therapy (IMRT) treatment plans. An information theory based Fourier analysis of the accuracy of discrete representations of three-dimensional dose distributions is presented. When applied to beamlet-based IMRT dose distributions, the theory produces analytic integrals that can bound worst case aliasing errors that can occur regardless of the location and orientation of the dose grid. The predictions of this theory are compared to empirical results obtained by solving a linear-programming based fluence-map optimization model to global optimality. A reasonable agreement between worst case estimates and the empirical results is attributed to the fact that the optimization takes advantage of aliasing to produce an optimal plan. We predicted and empirically demonstrated that an isotropic dose grid with <2.5 mm spacing is sufficient to prevent dose errors larger than a percent. However, we noted that in practice this resolution is mostly needed in high-dose target regions. Finally, a multiresolution 2-4-6 mm spacing model was developed and empirically tested where these spacings were applied to targets, structures, and tissue, respectively.     

宫颈癌放疗中计算网格尺寸对物理剂量和生物剂量的影响

目的:定量分析剂量计算网格尺寸（DCGS）对宫颈癌放疗中物理剂量和生物剂量的影响。方法:选取Pinnacle3治疗计划系统中宫颈癌的治疗方案12例,取默认值DCGS=4.0 mm的计算网格,优化调整宫颈癌治疗方案,再改变DCGS（1.0～7.0 mm）,重新计算靶区和危及器官（OAR）的剂量,探讨靶区和OAR的物理剂量和生物剂量随DCGS的变化情况。结果:靶区和OAR的物理剂量随DCGS的变大而减小,在体积剂量直方图上表现出曲线整体向低剂量区平移。除左右股骨头外,靶区的肿瘤控制概率（TCP）和OAR的正常组织并发症概率（NTCP）也随DCGS增大而缓慢降低。PGTVnd的TCP下降率约为0.7%/mm,PTV的TCP下降率约为0.6%/mm,而膀胱和直肠的NTCP下降速度相对较快,膀胱NTCP下降率最大值为15.0%,直肠NTCP下降率最大值为13.5%。结论:宫颈癌放疗中物理剂量和生物剂量随DCGS变大而减少,靶区和OAR的物理剂量在体积剂量直方图上表现出整体向低剂量区平移,这种变化趋势会诱导研究者低估靶区的TCP及OAR的NTCP。     

The influence of the size of the grid used for dose calculation on the accuracy of dose estimation

The standard presentation of a dose distribution as an isodose map is based on interpolation between dose values calculated on a matrix of equally spaced points. We explored the question of how the spacing of the grid used for the dose matrix affects the error due to interpolating the dose at any point. We defined two types of errors: the dose error, which is the difference between the interpolated and true dose at a given point; and the position error, which is the distance between the point of interest and the nearest point which has, in fact, the dose value estimated for the point of interest. We examine the problem using both an analytical beam profile (a Fermi function) and measured 60Co, x-ray and proton beam profiles. Our analysis showed that the interpolation errors are proportional to the curvature of the dose distribution and are relatively high in regions on either side of, but not including, the steepest part of the penumbra. Our results showed how big an interpolation error one should expect for a given size of the calculation grid. The specification of accuracy should be cast in the form of a pair of requirements, one for dose and the other for position. At a given point, only one of the two requirements needs to be satisfied. The position requirement is almost always the less demanding in clinical practice and permits the use of a larger grid spacing than if only a dose requirement is applied.(ABSTRACT TRUNCATED AT 250 WORDS)     

A Monte Carlo dose calculation algorithm for proton therapy

A Monte Carlo (MC) code (VMCpro) for treatment planning in proton beam therapy of cancer is introduced. It is based on ideas of the Voxel Monte Carlo algorithm for photons and electrons and is applicable to human tissue for clinical proton energies. In the present paper the implementation of electromagnetic and nuclear interactions is described. They are modeled by a Class II condensed history algorithm with continuous energy loss, ionization, multiple scattering, range straggling, delta-electron transport, nuclear elastic proton nucleus scattering and inelastic proton nucleus reactions. VMCpro is faster than the general purpose MC codes FLUKA by a factor of 13 and GEANT4 by a factor of 35 for simulations in a phantom with inhomogeneities. For dose calculations in patients the speed improvement is larger, because VMCpro has only a weak dependency on the heterogeneity of the calculation grid. Dose distributions produced with VMCpro are in agreement with GEANT4 results. Integrated or broad beam depth dose curves show maximum deviations not larger than 1% or 0.5 mm in regions with large dose gradients for the examples presented here.     

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy

The goal of this work was to facilitate the clinical use of Monte Carlo proton dose calculation to support routine treatment planning and delivery. The Monte Carlo code Geant4 was used to simulate the treatment head setup, including a time-dependent simulation of modulator wheels (for broad beam modulation) and magnetic field settings (for beam scanning). Any patient-field-specific setup can be modeled according to the treatment control system of the facility. The code was benchmarked against phantom measurements. Using a simulation of the ionization chamber reading in the treatment head allows the Monte Carlo dose to be specified in absolute units (Gy per ionization chamber reading). Next, the capability of reading CT data information was implemented into the Monte Carlo code to model patient anatomy. To allow time-efficient dose calculation, the standard Geant4 tracking algorithm was modified. Finally, a software link of the Monte Carlo dose engine to the patient database and the commercial planning system was established to allow data exchange, thus completing the implementation of the proton Monte Carlo dose calculation engine ('DoC++'). Monte Carlo re-calculated plans are a valuable tool to revisit decisions in the planning process. Identification of clinically significant differences between Monte Carlo and pencil-beam-based dose calculations may also drive improvements of current pencil-beam methods. As an example, four patients (29 fields in total) with tumors in the head and neck regions were analyzed. Differences between the pencil-beam algorithm and Monte Carlo were identified in particular near the end of range, both due to dose degradation and overall differences in range prediction due to bony anatomy in the beam path. Further, the Monte Carlo reports dose-to-tissue as compared to dose-to-water by the planning system. Our implementation is tailored to a specific Monte Carlo code and the treatment planning system XiO (Computerized Medical Systems Inc.). However, this work describes the general challenges and considerations when implementing proton Monte Carlo dose calculation in a clinical environment. The presented solutions can be easily adopted for other planning systems or other Monte Carlo codes.     

A pencil beam model for photon dose calculation.

A method for photon dose calculation in radio therapy planning using pencil beam energy deposition kernels is presented. It is designed to meet the requirements of an algorithm for 3-D treatment planning that is general enough to handle irregularly shaped radiation fields incident on a heterogeneous patient. It is point oriented and thus faster than a full 3-D convolution algorithm and uses the same physical data base to characterize a clinical beam as a full 3-D convolution algorithm. It is shown that photon therapy beams can be characterized with great accuracy from a combination of precalculated Monte Carlo energy deposition kernels and dose distributions measured in a water phantom. The data are used to derive analytical pencil beam kernels that are approximately partitionated into the dose from (i) primary released electrons and positrons, (ii) scattered, bremsstrahlung, and annihilation photons, (iii) contaminating photons, and (iv) charged particles from the collimator head. A semianalytical integration method, based on triangulation of the field, is developed for dose calculation using the analytical kernels. Dose is calculated in units normalized to the incident energy fluence which facilitates output factor calculation. For application in heterogeneous media, a scatter correction factor is derived using monodirectional convolution along the ray path. In homogeneous media results are compared with measurements and in heterogeneous media with Monte Carlo calculations and the Batho method.     

A finite size pencil beam for IMRT dose optimization

Dose optimization for intensity modulated radiotherapy (IMRT) using small field elements (beamlets) requires the computation of a large number of very small, often only virtual fields of typically a few mm to 1 cm in size. The primary requirements for a suitable dose computation algorithm are (1) speed and (2) proper consideration of the penumbra of the fields which are composed of these beamlets. Here, a finite size pencil beam (fsPB) algorithm is proposed which was specifically designed for the purpose of beamlet-based IMRT. The algorithm employs an analytical function for the cross-profiles of the beamlets which is based on the assumption of self-consistency, i.e. the requirement that an arbitrary superposition of abutting beamlets should add up to a homogeneous field. The depth dependence is stored in tables derived from Monte Carlo computed dose distributions. It is demonstrated that the algorithm produces accurately the output factors and cross-profiles of typical multi-leaf-shaped segments. Due to the accurate penumbra model, the dose distribution features physically feasible gradients at any stage of the iterative optimization, which eliminates the problem of large discrepancies in normal tissue dose due to misaligned gradients between optimized and recomputed treatment plans.     

一种基于笔形束核的快速剂量计算方法

针对传统笔形束核剂量算法计算过程复杂、速度较慢的问题,提出一种基于笔形束核的快速剂量计算方法。该方法在球壳坐标系下,利用射束与不同球壳层碰撞后轴线与体素相交情况的相似性,通过对每条射束只计算初始球壳层碰撞点处轴线与体素的相交情况,并将初始球壳层深度与其它球壳层深度的比值作为校正因子得到其他层碰撞点处轴线与体素的相交情况。避免射线追踪法的重复使用,在不影响算法精度的情况下节省大量时间。实验结果表明:在不同射野大小［（3×3）、（5×5）、（10×10） cm2］的水模体中计算深度剂量分布,两种算法的计算精度基本一致,改进算法的计算速度提升约2.7倍。同时当射野面积为（10×10） cm2时,在肺阻块模体和骨阻块模体不同深度的剖面剂量计算中,改进算法与传统算法的计算精度也基本一致,但计算速度提升约2.6倍。     

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.     

Extended collimator model for pencil-beam dose calculation in proton radiotherapy

We have developed a simple collimator model to improve the accuracy of penumbra behaviour in pencil-beam dose calculation for proton radiotherapy. In this model, transmission of particles through a three-dimensionally extended opening of a collimator is calculated in conjunction with phase-space distribution of the particles. Comparison of the dose distributions calculated using the new three-dimensional collimator model and the conventional two-dimensional model to lateral dose profiles experimentally measured with collimated proton beams showed the superiority of the new model over the conventional one.     

Initial beam size study for passive scatter proton therapy. II. Changes in delivered depth dose profiles

In passively scattered proton radiotherapy, a clinically useful treatment beam is produced by spreading a small proton "pencil beam" extracted from the accelerator to create both a uniform dose profile laterally and a uniform spread-out Bragg peak (SOBP) in depth. Lateral spreading and range modulation of the beam are accomplished using specially designed components within the treatment delivery nozzle. The purpose of this study was to determine how changes in the size of the initial proton pencil beam affect the delivery of dose with a passive scatter treatment nozzle. Monte Carlo calculations were used to study changes of the beam's in-air energy distribution at the exit of the nozzle and the central axis depth dose profiles in water resulting from changes in the incident beam size. Our results indicate that the width of the delivered SOBP decreases as the size of the initial beam increases.     

Real-time dose calculation and visualization for the proton therapy of ocular tumours

A new real-time dose calculation and visualization was developed as part of the new 3D treatment planning tool OCTOPUS for proton therapy of ocular tumours within a national research project together with the Hahn-Meitner Institut Berlin. The implementation resolves the common separation between parameter definition, dose calculation and evaluation and allows a direct examination of the expected dose distribution while adjusting the treatment parameters. The new tool allows the therapist to move the desired dose distribution under visual control in 3D to the appropriate place. The visualization of the resulting dose distribution as a 3D surface model, on any 2D slice or on the surface of specified ocular structures is done automatically when adapting parameters during the planning process. In addition, approximate dose volume histograms may be calculated with little extra time. The dose distribution is calculated and visualized in 200 ms with an accuracy of 6% for the 3D isodose surfaces and 8% for other objects. This paper discusses the advantages and limitations of this new approach.     

'A finite size pencil beam for IMRT dose optimization'--a simpler analytical function for the finite size pencil beam kernel

A simple and finite-termed analytical function for the finite size pencil beam kernel was constructed. The dose cross-profile of a semi-infinite field with field edge at x = 0 can be well fitted by the Boltzmann function. The pencil beam cross-profile of width 2x(0) can be obtained as the difference between two semi-infinite fields shifted by 2x(0). If the profile is centred about x = 0, it can derive from P(x + x(0)) - P(x - x(0)). The penumbra influence can be taken by the penumbra tuning factor f. The parameters A(1), A(2), A(3), A(4), f can be obtained by fitting depth-dose curves and cross-profiles for a set of square fields. The two-dimensional dose distribution F(x, y, x(0), y(0), A(1), A(2), A(3), A(4), f(1), f(2)) of a pencil beam of width (2x(0), 2y(0)) is defined by multiplication of two independent one-dimensional profiles.     

Dose calculation models for proton treatment planning using a dynamic beam delivery system: an attempt to include density heterogeneity effects in the analytical dose calculation

The gantry for proton radiotherapy at the Paul Scherrer Institute (PSI) is designed specifically for the spot-scanning technique. Use of this technique to its full potential requires dose calculation algorithms which are capable of precisely simulating each scanned beam individually. Different specialized analytical dose calculations have been developed, which attempt to model the effects of density heterogeneities in the patient's body on the dose. Their accuracy has been evaluated by a comparison with Monte Carlo calculated dose distributions in the case of a simple geometrical density interface parallel to the beam and typical anatomical situations. A specialized ray casting model which takes range dilution effects (broadening of the spectrum of proton ranges) into account has been found to produce results of good accuracy. This algorithm can easily be implemented in the iterative optimization procedure used for the calculation of the optimal contribution of each individual scanned pencil beam. In most cases an elemental pencil beam dose calculation has been found to be most accurate. Due to the long computing time, this model is currently used only after the optimization procedure as an alternative method of calculating the dose.     

A finite size pencil beam algorithm for IMRT dose optimization: density corrections

For beamlet-based IMRT optimization, fast and less accurate dose computation algorithms are frequently used, while more accurate algorithms are needed to recompute the final dose for verification. In order to speed up the optimization process and ensure close proximity between dose in optimization and verification, proper consideration of dose gradients and tissue inhomogeneity effects should be ensured at every stage of the optimization. Due to their speed, pencil beam algorithms are often used for precalculation of beamlet dose distributions in IMRT treatment planning systems. However, accounting for tissue heterogeneities with these models requires the use of approximate rescaling methods. Recently, a finite size pencil beam (fsPB) algorithm, based on a simple and small set of data, was proposed which was specifically designed for the purpose of dose pre-computation in beamlet-based IMRT. The present work describes the incorporation of 3D density corrections, based on Monte Carlo simulations in heterogeneous phantoms, into this method improving the algorithm accuracy in inhomogeneous geometries while keeping its original speed and simplicity of commissioning. The algorithm affords the full accuracy of 3D density corrections at every stage of the optimization, hence providing the means for density related fluence modulation like penumbra shaping at field edges.     

Determining the maximum acceptable work duration for high-intensity work

The aim of this study was to determine the maximum acceptable work duration (MAWD) for high-intensity work. Thirty young individuals participated in this study. Their maximum oxygen uptake ( ) and maximum work rate (MWR) were assessed first. Each subject then performed two cycling tests (60% and 70% MWR) on two separate days. Oxygen uptake and heart rate data were collected throughout the test. The results indicate that the MAWD in the 60% MWR test (18.8 min) was about threefold greater than the MAWD in the 70% MWR test (6.5 min). The MAWD was inversely correlated with the relative workload indices: relative oxygen uptake ( ; r=–0.82, P<0.001) and relative heart rate (RHR; r=–0.79, P<0.001). The was defined as the elevation in oxygen uptake from the resting level as a percentage of the difference between maximum and resting oxygen uptake. The RHR was defined as the elevation in heart rate from the resting level as a percentage of the difference between maximum and restingheart rate. Furthermore, more than 80% of the variations were explained by the exponential decrease regression model for predicting MAWD using the above two variables. The findings of this study can provide useful information for the design of high-intensity jobs. Electronic Publication     

A GPU-based finite-size pencil beam algorithm with 3D-density correction for radiotherapy dose calculation

Targeting at the development of an accurate and efficient dose calculation engine for online adaptive radiotherapy, we have implemented a finite-size pencil beam (FSPB) algorithm with a 3D-density correction method on graphics processing unit (GPU). This new GPU-based dose engine is built on our previously published ultrafast FSPB computational framework (Gu et al 2009 Phys. Med. Biol. 54 6287-97). Dosimetric evaluations against Monte Carlo dose calculations are conducted on ten IMRT treatment plans (five head-and-neck cases and five lung cases). For all cases, there is improvement with the 3D-density correction over the conventional FSPB algorithm and for most cases the improvement is significant. Regarding the efficiency, because of the appropriate arrangement of memory access and the usage of GPU intrinsic functions, the dose calculation for an IMRT plan can be accomplished well within 1 s (except for one case) with this new GPU-based FSPB algorithm. Compared to the previous GPU-based FSPB algorithm without 3D-density correction, this new algorithm, though slightly sacrificing the computational efficiency (～5-15% lower), has significantly improved the dose calculation accuracy, making it more suitable for online IMRT replanning.     

Three-dimensional fourier transformation calculation of the radiation dose received from a60Co source

Conclusion A physical model and software for calculation of three-dimensional distribution of the absorbed dose (kerma) using the Fourier transformation was developed. Approaches to approximate calculation of the point core of scattered photons in tissue-equivalent medium were proposed, and the calculation errors were estimated. The developed method was used for determining the absorbed dose distribution in several typical cases. It was shown that Fourier transformation of 64 × 64 × 64 array took about 0.67 sec. Such a rate is sufficient for practical purposes. Analysis of the calculation results shows that the calculation error is reasonably low in the case of irradiation of a homogeneous medium. The case of heterogeneous media will be considered elsewhere.     

The influence of grid size on accuracy in radiotherapy dose plotting

The recent article by Niemierko and Goitein [Med. Phys. 16, 239-247 (1989)] illustrates well the errors which are occurring in plotting isodose lines. We wish to augment their analysis with similar work done at Cardiff a few years ago; to indicate some practical treatment outcomes they have omitted; to propose even more stringent requirements of the grid size used; and thus to further alert users and software manufacturers to this problem.