Comparison of the Batho, ETAR and Monte Carlo dose calculation methods in CT based patient models

This paper shows the contribution that Monte Carlo methods make in regard to dose distribution calculations in CT based patient models and the role it plays as a gold standard to evaluate other dose calculation algorithms. The EGS4 based BEAM code was used to construct a generic 8 MV accelerator to obtain a series of x-ray field sources. These were used in the EGS4 based DOSXYZ code to generate beam data in a mathematical water phantom to set up a beam model in a commercial treatment planning system (TPS), CADPLAN V.2.7.9. Dose distributions were calculated with the Batho and ETAR inhomogeneity correction algorithms in head/sinus, lung, and prostate patient models for 2 x 2, 5 x 5, and 10 X 10 cm2 open x-ray beams. Corresponding dose distributions were calculated with DOSXYZ that were used as a benchmark. The dose comparisons are expressed in terms of 2D isodose distributions, percentage depth dose data, and dose difference volume histograms (DDVH's). Results indicated that the Batho and ETAR methods contained inaccuracies of 20%-70% in the maxillary sinus region in the head model. Large lung inhomogeneities irradiated with small fields gave rise to absorbed dose deviations of 10%-20%. It is shown for a 10 x 10 cm2 field that DOSXYZ models lateral scatter in lung that is not present in the Batho and ETAR methods. The ETAR and Batho methods are accurate within 3% in a prostate model. We showed how the performance of these inhomogeneity correction methods can be understood in realistic patient models using validated Monte Carlo codes such as BEAM and DOSXYZ.     

楔形野剂量计算中的误差分析和修正

目的研究楔形野剂量计算中的误差,并探讨解决方法.材料与方法在10MV和6MVX线条件下,用NEFarmer25710.6cc指形电离室和三维水箱在水模中测出平野和楔形野的各种参数,并用二种方法计算剂量,结果与实侧值比较.结果实测数据显示Pdd和Scp在平野和楔形野情况下存在差异.楔形因子因此随深度而变化,变化程度受射线能量、楔形板规格影响.与实测值比较,用传统方法计算楔形野剂量的结果存在误差,误差大小与能量、野面积、深度有关.6MVX线、15×15野、20cm深度处的计算误差可达11%.而用改进的方法进行计算,可将误差控制在1%以内.结论由于忽略了Pdd等物理参数在楔形野条件下的变化,用传统方法计算楔形野剂量存在误差.为保证临床剂量计算的准确性,应在计算公式中加入修正因子.     

Practical application of the differential Batho method for inhomogeneity correction on kerma in a photon beam

The Batho equation gives a satisfactory method to correct the dose for points in the electronic equilibrium region for a uniform slab of inhomogeneity in a photon beam. In spite of the many investigations, we believe no simple and adequate method has been found for routine clinical dose calculations which require dose correction of a small-volume inhomogeneity in an arbitrary location. In the present report, we combine the values of the two calculation types of the differential Batho method, which we have developed previously, to give a new calculated value for the scatter perturbation due to an annulus of inhomogeneity. The coefficients in the combination, which we derived from a detailed analysis of the scatter perturbation, are simple geometrical ratios. The new calculated values are in good agreement with measured values. We believe this application of the differential Batho method can provide a practical and accurate method of correcting for inhomogeneities of any size and shape in clinical dose calculations.     

Calculation of dose in off-central axis planes using off-axis ratios

Accuracy of dose calculation for regular fields in off-central axis planes was investigated on a RAD-8 treatment planning computer for 4- and 10-MV x-ray beams produced by Varian Clinac -4 and Clinac -18 linear accelerators. These calculations, which are based on central axis depth dose and off-axis ratios in the principal planes, can be in error by as much as 25%-30% at locations well within the irradiated volume for the 4-MV x-ray beam. These large errors for the Clinac -4 beam result from the falloff in dose beyond the peak dose along a diagonal of a large field at distances greater than 14 cm from the central axis due to the lead flattening filter. The profile data stored in the computer along the principal planes cannot be used to calculate the dose accurately in such a situation. Computed doses for the 10-MV x-ray beam agreed with the measured doses within 4%-6% at all locations.     

基于循环对抗生成网络的胸部锥形束CT校正及剂量计算准确性

目的:采用循环对抗生成网络算法建立胸部锥形束CT（CBCT）校正模型,探讨该模型用于提升CBCT质量的可行性,评估校正的CBCT（CCBCT）用于剂量计算的准确性。方法:选择食管癌或肺癌患者已配准的CBCT和定位CT 70例,随机选取其中60例作为训练集,用来训练循环对抗生成网络,生成CBCT的校正模型。剩余10例作为测试集,对CBCT、CCBCT和定位CT之间的CT值平均绝对误差、峰值信噪比、归一化互相关进行统计学分析。将原调强计划（CT Plan）移植到CCBCT上,生成CCBCT Plan,以CT Plan剂量分布为参考,对CCBCT Plan进行三维剂量γ分析。结果:CBCT经校正后散射伪影显著减少,CT值平均绝对误差降低了52.74[%±]6.47%,峰值信噪比和归一化互相关分别提高了7.95[%±]3.56%和1.68[%±]3.38%,差异均有统计学意义（t=18.47、-7.31、-6.77, P[<]0.05）。在2 mm/2%、2 mm/1%和1 mm/1%条件下,CCBCT Plan三维剂量平均γ通过率分别为99.16[%±]0.34%、98.01[%±]0.72%、93.95[%±]1.62%。结论:基于循环对抗生成网络构建的CBCT影像校正模型用于提升CBCT影像质量是可行的,经校正的胸部CBCT可用于放疗剂量计算,为CBCT用于自适应放疗剂量计算奠定基础。     

Improved scatter correction using adaptive scatter kernel superposition

Accurate scatter correction is required to produce high-quality reconstructions of x-ray cone-beam computed tomography (CBCT) scans. This paper describes new scatter kernel superposition (SKS) algorithms for deconvolving scatter from projection data. The algorithms are designed to improve upon the conventional approach whose accuracy is limited by the use of symmetric kernels that characterize the scatter properties of uniform slabs. To model scatter transport in more realistic objects, nonstationary kernels, whose shapes adapt to local thickness variations in the projection data, are proposed. Two methods are introduced: (1) adaptive scatter kernel superposition (ASKS) requiring spatial domain convolutions and (2) fast adaptive scatter kernel superposition (fASKS) where, through a linearity approximation, convolution is efficiently performed in Fourier space. The conventional SKS algorithm, ASKS, and fASKS, were tested with Monte Carlo simulations and with phantom data acquired on a table-top CBCT system matching the Varian On-Board Imager (OBI). All three models accounted for scatter point-spread broadening due to object thickening, object edge effects, detector scatter properties and an anti-scatter grid. Hounsfield unit (HU) errors in reconstructions of a large pelvis phantom with a measured maximum scatter-to-primary ratio over 200% were reduced from -90 ± 58 HU (mean ± standard deviation) with no scatter correction to 53 ± 82 HU with SKS, to 19 ± 25 HU with fASKS and to 13 ± 21 HU with ASKS. HU accuracies and measured contrast were similarly improved in reconstructions of a body-sized elliptical Catphan phantom. The results show that the adaptive SKS methods offer significant advantages over the conventional scatter deconvolution technique.     

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.     

10-MV x-ray primary and scatter dose calculation using convolutions

Three-dimensional (3-D) forward and backward primary dose spread functions in water were developed for 10-MV x rays. Three-dimensional forward and backward primary dose spread functions in a heterogeneous medium were constructed from the ones in water using the density scaling theorem. Each of the forward and backward primary dose components were calculated using a method of convolving the primary water collision kerma distribution with the forward or backward primary dose spread function. Scatter dose was separated into forward and backward components. Each scatter dose component was calculated using a differential scatter method, a kind of convolution method, where the primary water collision kerma distribution was convolved with a differential scatter-maximum ratio or differential backscatter factor equation. From the dose calculation and measurement results obtained for water phantoms containing a cork or aluminum slab, it was found that the 3-D forward and backward primary dose functions were effective especially in regions where there was a loss of longitudinal and/or lateral electronic equilibrium.     

Electron dose calculation using multiple-scattering theory: thin planar inhomogeneities

In this article in our series on electron dose calculation using multiple-scattering theory, we apply the Fermi-Eyges theory to the problem of a thin planar inhomogeneity present in an otherwise-layered medium. We derive expressions for the distribution function P and the location distribution L (which multiplied by the restricted mass collision stopping power is the dose directly deposited by the primary electrons) for various types of incident beams: a completely arbitrary distribution, a Gaussian point source, a pencil beam, an isotropic point source, and a broad parallel beam. We show how divergent-beam dose distributions can be determined from parallel-beam calculations, through use of equivalent configurations dependent upon the depth of dose calculation. Also, we indicate how this work can be applied to the design of wedges (or "compensators") for beam shaping to provide desired dose distributions or to match juxtaposed radiation fields. Explicit formulas for thin plates are then worked out, and we examine the appearance of hot and cold spots distal to the edge of a localized inhomogeneity, for thin half-slabs and for narrow strips. Finally, considering the case of a thin straight wedge-shaped inhomogeneity, we theoretically discover the phenomenon of a "focused hot spot" without an accompanying cold spot, and suggest the design of a "multiple-scattering lens".     

Electron dose calculation using multiple-scattering theory: second-order multiple-scattering theory

This article is part of a series on the calculation of electron dose using multiple-scattering theory. It presents systematically the second-order multiple-scattering theory which is a generalization of the (first-order) Fermi-Eyges theory, outlining its derivation and giving explicit formulas for its defining functions. The predictions of the Fermi-Eyges theory and of the second-order theory are compared with modified Monte Carlo calculations, demonstrating the increased accuracy of the latter multiple-scattering theory. We derive and compare broad-beam angular distributions for the two theories, and note the effect of large-angle scattering upon dose profiles. Finally, we present the second-order theory in Fourier-transformed space, which is appropriate to a high-speed dose-calculation algorithm using the fast Fourier transform (FFT) technique.     

Analysis of tissue-maximum ratio/scatter-maximum ratio model relative to the prediction of tissue-maximum ratio in asymmetrically collimated fields

The tissue-maximum ratio/scatter-maximum ratio model has been examined as an empirical model capable of predicting the variation in tissue-maximum ratio observed in fields shifted off-axis by independent collimators. This model has been assessed for its sensitivity to the necessary extrapolation of percentage depth dose data and phantom-scatter factors to zero field size and to large field sizes. This model was found to yield good results for both 6- and 24-MV x rays and to be relatively insensitive to the assumptions made regarding unmeasurable beam parameters.     

Three-dimensional electron dose calculation using an improved hybrid pencil beam model

An improved hybrid-pencil beam model (HPBM) for electron-beam three-dimensional dose calculation has been studied. The model is based on the fact that away from the edges of a large field, the electron distribution function exactly equals that for an infinitely wide electron beam. In the present model, we use the bipartition model to calculate the longitudinal part of the pencil-beam distribution function, and Fermi-Eyges multiple-scattering theory to calculate its transverse part. In order to describe the electron beam characteristics accurately, we introduce a new parameter, which is extracted from measured profile data near the surface of a water phantom, to correct the transverse distribution determined by the Fermi-Eyges theory. Furthermore, we introduce an effective energy spectrum to describe the effect on the collimated electron beam of the accelerator head. The dose distributions calculated with the improved HPBM were compared with the experimental data, and the agreement was within 1% in most of cases. This preliminary study has demonstrated the potential for use of the model in the clinical therapy.     

Electron dose calculation using multiple-scattering theory: localized inhomogeneities--a new theory

In this fourth article in a series on the calculation of electron dose using multiple-scattering theory, we deal with localized inhomogeneities by solving the Fermi equation for scattering power which is an arbitrary function of position. In fact, we go further, by solving the second-order multiple-scattering equation which supersedes the (first-order) Fermi equation, again for scattering power which is an arbitrary function of position. Thus, we are no longer restricted to a horizontally layered medium, as is the case with the Fermi-Eyges theory. Our general solution is in the form of a perturbation series which evidently converges rapidly enough that only its first two or three terms need be taken for accurate dose calculation. Regarding the energy directly deposited by the primary electrons, the formulas developed in this article give very good agreement with Monte Carlo calculations for the thick half-slab configuration, as will be seen in the next article in this series. Moreover, our first-rank, second-order formulas, when expressed in Fourier-transformed space, are simple enough to be implemented in a treatment planning system providing full three-dimensional electron dose calculation for arbitrary configurations of inhomogeneities.     

用CUDA实现放射治疗中剂量的快速计算

剂量计算是放射治疗计划系统的关键技术之一,它既要有较高的计算精度又要有较快的计算速度。有限笔束(FSPB)算法是目前放射治疗计划系统大多采用的光子线剂量计算算法,其计算速度尚不能达到实时治疗计划程度。本文采用图形处理器(GPU),对FSPB算法中最耗时的部分实现了基于GPU并行化计算,与基于中央处理器(CPU)的计算相比,在中低端GPU(Geforce GT320)上,剂量计算速度提高可达25~35倍,在较高端GPU(TeslaC1060)上计算速度提高可达55~100倍,计算效率完全可用于实时治疗计划中的剂量计算。     

Study of the IMRT interplay effect using a 4DCT Monte Carlo dose calculation

Respiratory motion may lead to dose errors when treating thoracic and abdominal tumours with radiotherapy. The interplay between complex multileaf collimator patterns and patient respiratory motion could result in unintuitive dose changes. We have developed a treatment reconstruction simulation computer code that accounts for interplay effects by combining multileaf collimator controller log files, respiratory trace log files, 4DCT images and a Monte Carlo dose calculator. Two three-dimensional (3D) IMRT step-and-shoot plans, a concave target and integrated boost were delivered to a 1D rigid motion phantom. Three sets of experiments were performed with 100%, 50% and 25% duty cycle gating. The log files were collected, and five simulation types were performed on each data set: continuous isocentre shift, discrete isocentre shift, 4DCT, 4DCT delivery average and 4DCT plan average. Analysis was performed using 3D gamma analysis with passing criteria of 2%, 2 mm. The simulation framework was able to demonstrate that a single fraction of the integrated boost plan was more sensitive to interplay effects than the concave target. Gating was shown to reduce the interplay effects. We have developed a 4DCT Monte Carlo simulation method that accounts for IMRT interplay effects with respiratory motion by utilizing delivery log files.     

Accurate convolution/superposition for multi-resolution dose calculation using cumulative tabulated kernels

Convolution/superposition (C/S) is regarded as the standard dose calculation method in most modern radiotherapy treatment planning systems. Different implementations of C/S could result in significantly different dose distributions. This paper addresses two major implementation issues associated with collapsed cone C/S: one is how to utilize the tabulated kernels instead of analytical parametrizations and the other is how to deal with voxel size effects. Three methods that utilize the tabulated kernels are presented in this paper. These methods differ in the effective kernels used: the differential kernel (DK), the cumulative kernel (CK) or the cumulative-cumulative kernel (CCK). They result in slightly different computation times but significantly different voxel size effects. Both simulated and real multi-resolution dose calculations are presented. For simulation tests, we use arbitrary kernels and various voxel sizes with a homogeneous phantom, and assume forward energy transportation only. Simulations with voxel size up to 1 cm show that the CCK algorithm has errors within 0.1% of the maximum gold standard dose. Real dose calculations use a heterogeneous slab phantom, both the 'broad' (5 x 5 cm2) and the 'narrow' (1.2 x 1.2 cm2) tomotherapy beams. Various voxel sizes (0.5 mm, 1 mm, 2 mm, 4 mm and 8 mm) are used for dose calculations. The results show that all three algorithms have negligible difference (0.1%) for the dose calculation in the fine resolution (0.5 mm voxels). But differences become significant when the voxel size increases. As for the DK or CK algorithm in the broad (narrow) beam dose calculation, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 10% (7%) of the maximum dose. As for the broad (narrow) beam dose calculation using the CCK algorithm, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 1% of the maximum dose. Among all three methods, the CCK algorithm is demonstrated to be the most accurate one for multi-resolution dose calculations.     

Magnetic fields with photon beams: dose calculation using electron multiple-scattering theory

Strong transverse magnetic fields can produce large dose enhancements and reductions in localized regions of a patient under irradiation by a photon beam. We have developed a new equation of motion for the transport of charged particles in an arbitrary magnetic field, incorporating both energy loss and multiple scattering. Key to modeling the latter process is a new concept, that of "typical scattered particles." The formulas which we have arrived at are particularly applicable to the transport of, and deposition of energy by, Compton electrons and pair-production electrons and positrons generated within a medium by a photon beam, and we have shown qualitatively how large dose enhancements and reductions can occur. A companion article examines this dose modification effect through systematic Monte Carlo simulations.     

Electron dose calculation using multiple-scattering theory. A. Gaussian multiple-scattering theory

This article is the first in a series on the calculation of electron dose using multiple-scattering theory. In it we develop a unified theory, which we term Gaussian multiple-scattering theory, starting from a number of contributions already in the literature: the Fermi-Eyges multiple-scattering theory, the Yang path length distribution, the second-order multiple-scattering theory of Jette [Med. Phys. 12, 178 (1985)], and the diffusion theory of Bethe et al. [Proc. Am. Philos. Soc. 78, 573 (1938)]. After examining in detail the ramifications and limitations of Gaussian multiple-scattering theory, we derive basic formulas generalizing the Fermi-Eyges theory, for use in subsequent articles. We also find explicit, accurate expressions for incorporating the scattering power into the theory.     

The influence of beam model differences in the comparison of dose calculation algorithms for lung cancer treatment planning

In this study, we show that beam model differences play an important role in the comparison of does calculated with various algorithms for lung cancer treatment planning. These differences may impact the accurate correlation of dose with clinical outcome. To accomplish this, we modified the beam model penumbral parameters in an equivalent path length (EPL) algorithm and subsequently compared the EPL doses with those generated with Monte Carlo (MC). A single AP beam was used for beam fitting. Two different beam models were generated for EPL calculations: (1) initial beam model (init_fit) and (2) optimized beam model (best_fit) , with parameters optimized to produce the best agreement with MC calculated profiles at several depths in a water phantom. For the 6 MV, AP beam, EPL(init_fit) calculations were on average within 2%/2 mm (1.4 mm max.) agreement with MC; the agreement for EPL(best_fit) was 2%/1.0 mm (1.3 mm max.) for EPL(best_fit). Treatment planning was performed using a realistic lung phantom using 6 and 15 MV photons. In all homogeneous phantom plans, EPL(best_fit) calculations were in better agreement with MC. In the heterogeneous 6 MV plan, differences between EPL(best_fit and init_fit) and MC were significant for the tumour. The EPL(init_fit), unlike the EPL(best_fit) calculation, showed large differences in the lung relative to MC. For the 15 MV heterogeneous plan, clinically important differences were found between EPL(best_fit or init_fit) and MC for tumour and lung, suggesting that the algorithmic difference in inhomogeneous cases, differences between EPL(best_fit) and MC for lung tissues were smaller compared to those between EPL(init_fit) and MC. Although the extent to which beam model differences impact the dose comparisons will be dependent upon beam parameters (orientation, field size and energy), and the size and location of the tumour, this study shows that failing to correctly account for beam model differences will lead to biased comparisons between dose algorithms. This may ultimately hinder our ability to accurately correlate dose with clinical outcome.