Three-dimensional heart dose reconstruction to estimate normal tissue complication probability after breast irradiation using portal dosimetry

Irradiation of the heart is one of the major concerns during radiotherapy of breast cancer. Three-dimensional (3D) treatment planning would therefore be useful but cannot always be performed for left-sided breast treatments, because CT data may not be available. However, even if 3D dose calculations are available and an estimate of the normal tissue damage can be made, uncertainties in patient positioning may significantly influence the heart dose during treatment. Therefore, 3D reconstruction of the actual heart dose during breast cancer treatment using electronic imaging portal device (EPID) dosimetry has been investigated. A previously described method to reconstruct the dose in the patient from treatment portal images at the radiological midsurface was used in combination with a simple geometrical model of the irradiated heart volume to enable calculation of dose-volume histograms (DVHs), to independently verify this aspect of the treatment without using 3D data from a planning CT scan. To investigate the accuracy of our method, the DVHs obtained with full 3D treatment planning system (TPS) calculations and those obtained after resampling the TPS dose in the radiological midsurface were compared for fifteen breast cancer patients for whom CT data were available. In addition, EPID dosimetry as well as 3D dose calculations using our TPS, film dosimetry, and ionization chamber measurements were performed in an anthropomorphic phantom. It was found that the dose reconstructed using EPID dosimetry and the dose calculated with the TPS agreed within 1.5% in the lung/heart region. The dose-volume histograms obtained with EPID dosimetry were used to estimate the normal tissue complication probability (NTCP) for late excess cardiac mortality. Although the accuracy of these NTCP calculations might be limited due to the uncertainty in the NTCP model, in combination with our portal dosimetry approach it allows incorporation of the actual heart dose. For the anthropomorphic phantom, and for fifteen patients for whom CT data were available to test our method, the average difference between the NTCP values obtained with our method and those resulting from the dose distributions calculated with the TPS was 0.1% +/- 0.3% (1 SD). Most NTCP values were 1%-2% lower than those obtained using the method described by Hurkmans et al. [Radiother. Oncol. 62, 163-171 (2002)], using the maximum heart distance determined from a simulator image as a single pre-treatment parameter. A similar difference between the two methods was found for twelve patients using in vivo EPID dosimetry; the average NTCP value obtained with EPID dosimetry was 0.9%, whereas an average NTCP value of 2.2% was derived using the method of Hurkmans et al. The results obtained in this study show that EPID dosimetry is well suited for in vivo verification of the heart dose during breast cancer treatment, and can be used to estimate the NTCP for late excess cardiac mortality. To the best of our knowledge, this is the first study using portal dosimetry to calculate a DVH and NTCP of an organ at risk.     

Three-dimensional portal image-based dose reconstruction in a virtual phantom for rapid evaluation of IMRT plans

A new method for rapid evaluation of intensity modulated radiation therapy (IMRT) plans has been developed, using portal images for reconstruction of the dose delivered to a virtual three-dimensional (3D) phantom. This technique can replace an array of less complete but more time-consuming measurements. A reference dose calculation is first created by transferring an IMRT plan to a cylindrical phantom, retaining the treatment gantry angles. The isocenter of the fields is placed on or near the phantom axis. This geometry preserves the relative locations of high and low dose regions and has the required symmetry for the dose reconstruction. An electronic portal image (EPI) is acquired for each field, representing the dose in the midplane of a virtual phantom. The image is convolved with a kernel to correct for the lack of scatter, replicating the effect of the cylindrical phantom surrounding the dose plane. This avoids the need to calculate fluence. Images are calibrated to a reference field that delivers a known dose to the isocenter of this phantom. The 3D dose matrix is reconstructed by attenuation and divergence corrections and summed to create a dose matrix (PI-dose) on the same grid spacing as the reference calculation. Comparison of the two distributions is performed with a gradient-weighted 3D dose difference based on dose and position tolerances. Because of its inherent simplicity, the technique is optimally suited for detecting clinically significant variances from a planned dose distribution, rather than for use in the validation of IMRT algorithms. An analysis of differences between PI-dose and calculation, delta PI, compared to differences between conventional quality assurance (QA) and calculation, delta CQ, was performed retrospectively for 20 clinical IMRT cases. PI-dose differences at the isocenter were in good agreement with ionization chamber differences (mean delta PI = -0.8%, standard deviation sigma = 1.5%, against delta CQ = 0.3%, sigma = 1.0%, respectively). PI-dose plane differences had significantly less variance than film plane differences (sigma = 1.1 and 2.1%, respectively). Twenty-two further cases were evaluated using 3D EPI-dosimetry alone. The mean difference delta over volumes with doses above 80% of the isocenter value was delta = -0.3%, sigma(delta) = 0.7%, and standard deviations of the distributions ranged from 1.0 to 2.0%. Verification time per plan, from initial calculation, delivery, dose reconstruction to evaluation, takes less than 1.5 h and is more than four times faster than conventional QA.     

Midplane dose determination using in vivo dose measurements in combination with portal imaging

The possibility of using portal films in combination with semiconductor in vivo measurements for midplane dose distribution is investigated. A general algorithm, using measured entrance and exit doses and available beam data of the Linac, is proposed to derive the midplane dose for symmetrical inhomogeneities. Experimental verification of the algorithm with phantom measurements is performed for different kinds of inhomogeneities (Al, air and cork) and phantom thicknesses from 13 cm to 30 cm. When using only the entrance dose and the exit dose, provided by the diodes on the beam axis, the algorithm predicts for the different inhomogeneities midplane doses in all cases within 1% of the midplane doses measured with an ionization chamber. When using the portal film in combination with entrance and exit dose measurements to estimate the midplane dose in an off-axis position, the calculated midplane doses are within 3% of the midplane doses measured with an ionization chamber. The midplane doses calculated with the algorithm are compared to the midplane doses obtained with simplified calculation methods, i.e. the arithmetical mean and the geometrical mean of the measured entrance and exit doses. The geometrical mean especially seems to give acceptable results (within 5%) and can as such be used as an easy rule of thumb to estimate roughly the midplane dose. Finally, critical considerations on the validity and the precision of the proposed algorithm are given. The present results confirm the possibility of using the portal film for midplane dose distribution determination at the patient level.     

Dosimetric investigation and portal dose image prediction using an amorphous silicon electronic portal imaging device.

A two step algorithm to predict portal dose images in arbitrary detector systems has been developed recently. The current work provides a validation of this algorithm on a clinically available, amorphous silicon flat panel imager. The high-atomic number, indirect amorphous silicon detector incorporates a gadolinium oxysulfide phosphor scintillating screen to convert deposited radiation energy to optical photons which form the portal image. A water equivalent solid slab phantom and an anthropomorphic phantom were examined at beam energies of 6 and 18 MV and over a range of air gaps (approximately 20-50 cm). In the many examples presented here, portal dose images in the phosphor were predicted to within 5% in low-dose gradient regions, and to within 5 mm (isodose line shift) in high-dose gradient regions. Other basic dosimetric characteristics of the amorphous silicon detector were investigated, such as linearity with dose rate (+/- 0.5%), repeatability (+/- 2%), and response with variations in gantry rotation and source to detector distance. The latter investigation revealed a significant contribution to the image from optical photon spread in the phosphor layer of the detector. This phenomenon is generally known as "glare," and has been characterized and modeled here as a radially symmetric blurring kernel. This kernel is applied to the calculated dose images as a convolution, and is successfully demonstrated to account for the optical photon spread. This work demonstrates the flexibility and accuracy of the two step algorithm for a high-atomic number detector. The algorithm may be applied to improve performance of dosimetric treatment verification applications, such as direct image comparison, backprojected patient dose calculation, and scatter correction in megavoltage computed tomography. The algorithm allows for dosimetric applications of the new, flat panel portal imager technology in the indirect configuration, taking advantage of a greater than tenfold increase in detector sensitivity over a direct configuration.     

A Monte Carlo based three-dimensional dose reconstruction method derived from portal dose images

The verification of intensity-modulated radiation therapy (IMRT) is necessary for adequate quality control of the treatment. Pretreatment verification may trace the possible differences between the planned dose and the actual dose delivered to the patient. To estimate the impact of differences between planned and delivered photon beams, a three-dimensional (3-D) dose verification method has been developed that reconstructs the dose inside a phantom. The pretreatment procedure is based on portal dose images measured with an electronic portal imaging device (EPID) of the separate beams, without the phantom in the beam and a 3-D dose calculation engine based on the Monte Carlo calculation. Measured gray scale portal images are converted into portal dose images. From these images the lateral scattered dose in the EPID is subtracted and the image is converted into energy fluence. Subsequently, a phase-space distribution is sampled from the energy fluence and a 3-D dose calculation in a phantom is started based on a Monte Carlo dose engine. The reconstruction model is compared to film and ionization chamber measurements for various field sizes. The reconstruction algorithm is also tested for an IMRT plan using 10 MV photons delivered to a phantom and measured using films at several depths in the phantom. Depth dose curves for both 6 and 10 MV photons are reconstructed with a maximum error generally smaller than 1% at depths larger than the buildup region, and smaller than 2% for the off-axis profiles, excluding the penumbra region. The absolute dose values are reconstructed to within 1.5% for square field sizes ranging from 5 to 20 cm width. For the IMRT plan, the dose was reconstructed and compared to the dose distribution with film using the gamma evaluation, with a 3% and 3 mm criterion. 99% of the pixels inside the irradiated field had a gamma value smaller than one. The absolute dose at the isocenter agreed to within 1% with the dose measured with an ionization chamber. It can be concluded that our new dose reconstruction algorithm is able to reconstruct the 3-D dose distribution in phantoms with a high accuracy. This result is obtained by combining portal dose images measured prior to treatment with an accurate dose calculation engine.     

Dosimetric verification of x-ray fields with steep dose gradients using an electronic portal imaging device

Regions with steep dose gradients are often encountered in clinical x-ray beams, especially with the growing use of intensity modulated radiotherapy (IMRT). Such regions are present both at field edges and, for IMRT, in the vicinity of the projection of sensitive anatomical structures in the treatment field. Dose measurements in these regions are often difficult and labour intensive, while dose prediction may be inaccurate. A dedicated algorithm developed in our institution for conversion of pixel values, measured with a charged coupled device camera based fluoroscopic electronic portal imaging device (EPID), into absolute absorbed doses at the EPID plane has an accuracy of 1-2% for flat and smoothly modulated fields. However, in the current algorithm there is no mechanism to correct for the (short-range) differences in lateral electron transport between water and the metal plate with the fluorescent layer in the EPID. Moreover, lateral optical photon transport in the fluorescent layer is not taken into account. This results in large deviations (>10%) in the penumbra region of these fields. We have investigated the differences between dose profiles measured in water and with the EPID for small heavily peaked fields. A convolution kernel has been developed to empirically describe these differences. After applying the derived kernel to raw EPID images, a general agreement within 2% was obtained with the water measurements in the central region of the fields, and within 0.03 cm in the penumbra region. These results indicate that the EPID is well suited for accurate dosimetric verification of steep gradient x-ray fields.     

IMRT verification by three-dimensional dose reconstruction from portal beam measurements

A method of reconstructing three-dimensional, in vivo dose distributions delivered by intensity-modulated radiotherapy (IMRT) is presented. A proof-of-principle experiment is described where an inverse-planned IMRT treatment is delivered to an anthropomorphic phantom. The exact position of the phantom at the time of treatment is measured by acquiring megavoltage CT data with the treatment beam and a research prototype, flat-panel, electronic portal imaging device. Immediately following CT imaging, the planned IMRT beams are delivered using the multiple-static field technique. The delivered fluence is sampled using the same detector as for the CT data. The signal measured by the portal imaging device is converted to primary fluence using an iterative phantom-scatter estimation technique. This primary fluence is back-projected through the previously acquired megavoltage CT model of the phantom, with inverse attenuation correction, to yield an input fluence map. The input fluence maps are used to calculate a "reconstructed" dose distribution using the same convolution/superposition algorithm as for the original planning dose calculation. Both relative and absolute dose reconstructions are shown. For the relative measurements, individual beam weights are taken from measurements but the total dose is normalized at the reference point. The absolute dose reconstructions do not use any dosimetric information from the original plan. Planned and reconstructed dose distributions are compared, with the reconstructed relative dose distribution also being compared to film measurements.     

Three-dimensional reconstruction of joint surfaces using a microcomputer

A microcomputer was used to analyse the surface characteristics and geometry of articulating joints. Both hardware configuration and software organisation were described. Data used in this analysis were obtained by sequential resection of entire joints (elbows, metatarsophalangeal joints and knees) secured in an embedding medium. The exposed joint profile after each resection in a bone milling machine was recorded photographically. Each record of freshly cut profile was manually digitised and automatically processed with a desktop microcomputer. The complete structure of these articulating surfaces was reconstructed in three dimensions to be displayed in any desired orientation as a series of parallel, consecutive and uniformly spaced sections. These data have been used to derive information on cartilage thickness, underlying bone structure, orientation and anatomical shape of the joint surfaces. The stored surface geometry may be retrieved at any time for related studies of joint kinematics, joint sizing and prosthetic joint design.     

Beamlet dose distribution compression and reconstruction using wavelets for intensity modulated treatment planning

Intensity modulated radiation therapy (IMRT) treatment planning is often formulated as the optimization of weights of fixed-geometry subfields (beamlets). Efficient optimization techniques can be based on direct storage of the influence matrix relating beamlet weights to dose values. However, direct storage of beamlet dose distributions for IMRT treatment planning can easily exceed several gigabytes, and is therefore often not feasible. We present a method for rapidly calculating full three-dimensional IMRT dose distributions, based on a vector of beamlet weights. The method is based on compressed beamlet dose distributions using fast digital wavelet transforms and so-called hard thresholding. We studied the method with a rectangular beamlet of 0.5 cm x 0.5 cm cross section from a monoenergetic 6 MeV photon point source simulated in homogeneous (water) and heterogeneous (CT-data) phantoms. Dose was calculated using the accurate VMC+ + Monte Carlo engine. The beamlet dose distributions were wavelet transformed and compressed by dropping wavelet coefficients below a given threshold value. Dose is then computed using the remaining wavelets. Selection of the wavelet basis function, decomposition level, and threshold values, for different slice orientations (transverse or parallel to the beam) and varying angles of beamlet incidence are studied. A typical in-slice compression ratio for a plane containing a beamlet was 32:1 using the sym2 wavelet and a threshold of 0.01, with a typical root-mean-square error, for voxels above 50% of the maximum dose, of about 0.04%. The overall compression performance, which includes many planes with little information content, is on the order of 100:1 or greater compared to full matrix storage. Although other methods are available to make the use of stored influence matrix values more feasible in IMRT treatment planning (such as using coarse grids or restricting values to defined volumes of interest) we conclude that wavelet compression facilitates the storage and use of full pencil dose deposition (influence matrix) data in IMRT treatment planning.     

Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging

A new method is described for obtaining a 3-D reconstruction of a bioluminescent light source distribution inside a living animal subject, from multispectral images of the surface light emission acquired on charge-coupled device (CCD) camera. The method uses the 3-D surface topography of the animal, which is obtained from a structured light illumination technique. The forward model of photon transport is based on the diffusion approximation in homogeneous tissue with a local planar boundary approximation for each mesh element, allowing rapid calculation of the forward Green's function kernel. Absorption and scattering properties of tissue are measured a priori as input to the algorithm. By using multispectral images, 3-D reconstructions of luminescent sources can be derived from images acquired from only a single view. As a demonstration, the reconstruction technique is applied to determine the location and brightness of a source embedded in a homogeneous phantom subject in the shape of a mouse. The technique is then evaluated with real mouse models in which calibrated sources are implanted at known locations within living tissue. Finally, reconstructions are demonstrated in a PC3M-luc (prostate tumor line) metastatic tumor model in nude mice.     

Off-axis dose response characteristics of an amorphous silicon electronic portal imaging device

Amorphous silicon (a-Si) electronic portal imaging devices (EPIDs) have typically been calibrated to dose at central axis (CAX). Division of acquired images by the flood-field (FF) image that corrects for pixel sensitivity variation as well as open field energy-dependent off-axis response variation should result in a flat EPID response over the entire matrix for the same field size. While the beam profile can be reintroduced to the image by an additional correction matrix, the CAX EPID response to dose calibration factor is assumed to apply to all pixels in the detector. The aim of this work was to investigate the dose response of the Varian aS500 amorphous silicon detector across the entire detector area. First it was established that the EPID response across the panel became stable (within approximately 0.2%) for MU settings greater than approximately 200 MU. The EPID was then FF calibrated with a high MU setting of approximately 400 for all subsequent experiments. Whole detector images with varying MU settings from 2-500 were then acquired for two dose rates (300 and 600 MU/min) for 6 MV photons for two EPIDs. The FF corrected EPID response was approximately flat or uniform across the detector for greater than 100 MU delivered (within 0.5%). However, the off-axis EPID response was greater than the CAX response for small MU irradiations, giving a raised EPID profile. Up to 5% increase in response at 20 cm off-axis compared to CAX was found for very small MU settings for one EPID, while it was within 2% for the second (newer) EPID. Off-axis response nonuniformities attributed to detector damage were also found for the older EPID. Similar results were obtained with the EPID at 18 MV energy and operating in asynchronous mode (acquisition not synchronized with beam pulses), however the profiles were flatter and more irregular for the small MU irradiations. By moving the detector laterally and repeating the experiments, the increase in response off-axis was found to depend on the pixel position relative to the beam CAX. When the beam was heavily filtered by a phantom the off-axis response variation was reduced markedly to within 0.5% for all MU settings. Independent measurements of off-axis point doses with ion chamber did not show any change in off-axis factor with MUs. Measurements of beam quality (TMR20-10) for MU settings of 2, 5, and 100 at central axis and at 15 cm off-axis could not explain the effect. The response change is unlikely to be significant for clinical IMRT verification with this imaging/acclerator system where MUs are of the order of 100-300, provided the detector does not exhibit radiation damage artifacts.     

Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies

Molecular targeting with exogenous near-infrared excitable fluorescent agents using time-dependent imaging techniques may enable diagnostic imaging of breast cancer and prognostic imaging of sentinel lymph nodes within the breast. However, prior to the administration of unproven contrast agents, phantom studies on clinically relevant volumes are essential to assess the benefits of fluorescence-enhanced optical imaging in humans. Diagnostic 3-D fluorescence-enhanced optical tomography is demonstrated using 0.5 to 1 cm(3) single and multiple targets differentiated from their surroundings by indocyanine green (micromolar) in a breast-shaped phantom (10-cm diameter). Fluorescence measurements of referenced ac intensity and phase shift were acquired in response to point illumination measurement geometry using a homodyned intensified charge-coupled device system modulated at 100 MHz. Bayesian reconstructions show artifact-free 3-D images (3857 unknowns) from 3-D boundary surface measurements (126 to 439). In a reflectance geometry appropriate for prognostic imaging of lymph node involvement, fluorescence measurements were likewise acquired from the surface of a semi-infinite phantom (8x8x8 cm(3)) in response to area illumination (12 cm(2)) by excitation light. Tomographic 3-D reconstructions (24,123 unknowns) were recovered from 2-D boundary surface measurements (3194) using the modified truncated Newton's method. These studies represent the first 3-D tomographic images from physiologically relevant geometries for breast imaging.     

Three-dimensional seed reconstruction for prostate brachytherapy using Hough trajectories

In order to perform intra-operative or post-implant dosimetry in prostate brachytherapy, the 3D coordinates of the implanted radioactive seeds must be determined. Film or fluoroscopy based seed reconstruction techniques use back projection of x-ray data obtained at two or three x-ray positions. These methods, however, do not perform well when some of the seed images are undetected. To overcome this problem we have developed an alternate technique for 3D seed localization using the principle of Hough transform. The Hough method utilizes the fact that, for each seed coordinate in three dimensions, there exists a unique trajectory in Hough feature space. In this paper we present the Hough transform parametric equations to describe the path of the seed projections from one view to the next and a method to reconstruct the 3D seed coordinates. The results of simulation and phantom studies indicate that the Hough trajectory method can accurately determine the 3D seed positions even from an incomplete dataset.     

Three-dimensional cellular-level imaging using full-field optical coherence tomography

An ultrahigh-resolution full-field optical coherence tomography (OCT) system has been developed for cellular-level imaging of biological media. The system is based on a Linnik interference microscope illuminated with a tungsten halogen lamp, associated with a high-resolution CCD camera. En face tomographic images are produced in real time, with the best spatial resolution ever achieved in OCT (0.7 microm x 0.9 microm, axial x transverse). A shot-noise limited detection sensitivity of 80 dB can be reached with an acquisition time per image of 1 s. Images of animal ophthalmic biopsies and vegetal tissues are shown.     

门静脉癌栓与门静脉血栓的多层螺旋CT影像研究

目的 探讨肝硬化合并肝癌、门静脉癌栓患者和肝硬化合并门静脉血栓患者的癌栓与血栓的MSCT影像特点及病变解剖部位的差异。方法 回顾性分析2011年5月—2016年5月北京大学深圳医院和2013年8月—2014年8月广东省海丰县彭湃纪念医院经临床诊断的18例肝硬化合并肝癌、门静脉癌栓患者(癌栓组)和12例肝硬化合并门静脉血栓患者(血栓组)的临床资料。所有患者行MSCT平扫,以及动脉期、门静脉期及延迟期3期增强扫描,并采用多平面重建(MPR)和5 mm厚度最大密度投影(MIP)重建技术对门静脉行3D重建。观察门静脉癌栓和血栓的影像特征、分布情况及侧支循环血管形成情况,比较癌栓和血栓在平扫和增强扫描各时相的密度差异。结果 癌栓组中,CT平扫12例呈低密度并血管增粗,6例呈等密度;CT增强扫描显示动脉期癌栓均呈不均匀强化、15例可见滋养血管影,门静脉期4例呈稍高密度、5例呈等密度、9例呈低密度,延迟期均呈低密度;18例门静脉癌栓均累及门静脉左或/和右支, 仅6例累及门静脉主干。血栓组中,CT平扫3例呈等密度, 3例呈低密度,6例呈稍高密度;CT增强扫描血栓均无强化,门静脉期及延迟期血栓部位无对比剂充盈;12例中,11例门静脉血栓累及门静脉主干,6例血栓延伸至左叶或/和右叶门静脉分支。门静脉癌栓和血栓在CT平扫和增强扫描的延迟期密度的差异均无统计学意义(P值均＞0.05),而增强扫描的动脉期和门静脉期,癌栓密度明显高于血栓,差异均有统计学意义(P值均＜0.05)。癌栓累及门静脉左或/和右支的概率明显高于血栓,而血栓累及门静脉主干的概率明显高于癌栓,差异均有统计学意义(P值均＜0.05)。结论 结合MSCT平扫及3D重建技术,能客观显示肝硬化患者门静脉癌栓与门静脉血栓的影像特点及其累及范围,能为病变诊断提供客观依据,从而指导临床选择合适的治疗方案。     

64层螺旋CT在活体肝门静脉三维重建中的应用

目的:探讨64层螺旋CT应用于正常人体肝门静脉研究的可行性,观察三维重建肝门静脉的一般形态及变异.方法:153例正常受试者经肘正中静脉注射造影剂后,使用64层螺旋CT进行上腹部扫描,图像采集后经容积再现(VR)技术重建肝门静脉.结果:肝门静脉分5型:a型: 83 7%;b型:7 8%;c型:7 8%;d型:无;e型:0 7%.结论:64层螺旋CT可以作为研究活体肝门静脉形态的有效手段,三维重建能更准确、全方位地显示肝门静脉的正常解剖类型和变异.     

Investigation of tilted dose kernels for portal dose prediction in a-Si electronic portal imagers

The effect of beam divergence on dose calculation via Monte Carlo generated dose kernels was investigated in an amorphous silicon electronic portal imaging device (EPID). The flat-panel detector was simulated in EGSnrc with an additional 3.0 cm water buildup. The model included details of the detector's imaging cassette and the front cover upstream of it. To approximate the effect of the EPID's rear housing, a 2.1 cm air gap and 1.0 cm water slab were introduced into the simulation as equivalent backscatter material. Dose kernels were generated with an incident pencil beam of monoenergetic photons of energy 0.1, 2, 6, and 18 MeV. The orientation of the incident pencil beam was varied from 0 degrees to 14 degrees in 2 degrees increments. Dose was scored in the phosphor layer of the detector in both cylindrical (at 0 degrees) and Cartesian (at 0 degrees - 14 micro) geometries. To reduce statistical fluctuations in the Cartesian geometry simulations at large radial distances from the incident pencil beam, the voxels were first averaged bilaterally about the pencil beam and then combined into concentric square rings of voxels. Profiles of the EPID dose kernels displayed increasing asymmetry with increasing angle and energy. A comparison of the superposition (tilted kernels) and convolution (parallel kernels) dose calculation methods via the chi-comparison test (a derivative of the gamma-evaluation) in worst-case-scenario geometries demonstrated an agreement between the two methods within 0.0784 cm (one pixel width) distance-to-agreement and up to a 1.8% dose difference. More clinically typical field sizes and source-to-detector distances were also tested, yielding at most a 1.0% dose difference and the same distance-to-agreement. Therefore, the assumption of parallel dose kernels has less than a 1.8% dosimetric effect in extreme cases and less than a 1.0% dosimetric effect in most clinically relevant situations and should be suitable for most clinical dosimetric applications. The resulting time difference for the parallel kernel assumption versus the tilted kernels was 10.5 s vs 18 h (a factor of approximately 6000), dependent on existing hardware and software details.