An analytical approach to quantitative reconstruction of non-uniform attenuated brain SPECT

An analytical approach to quantitative brain SPECT (single-photon-emission computed tomography) with non-uniform attenuation is developed. The approach formulates accurately the projection-transform equation as a summation of primary- and scatter-photon contributions. The scatter contribution can be estimated using the multiple-energy-window samples and removed from the primary-energy-window data by subtraction. The approach models the primary contribution as a convolution of the attenuated source and the detector-response kernel at a constant depth from the detector with the central-ray approximation. The attenuated Radon transform of the source can be efficiently deconvolved using the depth-frequency relation. The approach inverts exactly the attenuated Radon transform by Fourier transforms and series expansions. The performance of the analytical approach was studied for both uniform- and non-uniform-attenuation cases, and compared to the conventional FBP (filtered-backprojection) method by computer simulations. A patient brain X-ray image was acquired by a CT (computed-tomography) scanner and converted to the object-specific attenuation map for 140 keV energy. The mathematical Hoffman brain phantom was used to simulate the emission source and was resized such that it was completely surrounded by the skull of the CT attenuation map. The detector-response kernel was obtained from measurements of a point source at several depths in air from a parallel-hole collimator of a SPECT camera. The projection data were simulated from the object-specific attenuating source including the depth-dependent detector response. Quantitative improvement (>5%) in reconstructing the data was demonstrated with the nonuniform attenuation compensation, as compared to the uniform attenuation correction and the conventional FBP reconstruction. The commuting time was less than 5 min on an HP/730 desktop computer for an image array of 1282*32 from 128 projections of 128*32 size.     

A three-dimensional ray-driven attenuation, scatter and geometric response correction technique for SPECT in inhomogeneous media

The qualitative and quantitative accuracy of SPECT images is degraded by physical factors of attenuation, Compton scatter and spatially varying collimator geometric response. This paper presents a 3D ray-tracing technique for modelling attenuation, scatter and geometric response for SPECT imaging in an inhomogeneous attenuating medium. The model is incorporated into a three-dimensional projector-backprojector and used with the maximum-likelihood expectation-maximization algorithm for reconstruction of parallel-beam data. A transmission map is used to define the inhomogeneous attenuating and scattering object being imaged. The attenuation map defines the probability of photon attenuation between the source and the scattering site, the scattering angle at the scattering site and the probability of attenuation of the scattered photon between the scattering site and the detector. The probability of a photon being scattered through a given angle and being detected in the emission energy window is approximated using a Gaussian function. The parameters of this Gaussian function are determined using physical measurements of parallel-beam scatter line spread functions from a non-uniformly attenuating phantom. The 3D ray-tracing scatter projector-backprojector produces the scatter and primary components. Then, a 3D ray-tracing projector-backprojector is used to model the geometric response of the collimator. From Monte Carlo and physical phantom experiments, it is shown that the best results are obtained by simultaneously correcting attenuation, scatter and geometric response, compared with results obtained with only one or two of the three corrections. It is also shown that a 3D scatter model is more accurate than a 2D model. A transmission map is useful for obtaining measurements of attenuation and scatter in SPECT data, which can be used together with a model of the geometric response of the collimator to obtain corrected images with quantitative and diagnostically accurate information.     

Application of discrete data consistency conditions for selecting regularization parameters in PET attenuation map reconstruction

Simultaneous emission and transmission measurement is appealing in PET due to the matching of geometrical conditions between emission and transmission and reduced acquisition time for the study. A potential problem remains: when transmission statistics are low, attenuation correction could be very noisy. Although noise in the attenuation map can be controlled through regularization during statistical reconstruction, the selection of regularization parameters is usually empirical. In this paper, we investigate the use of discrete data consistency conditions (DDCC) to optimally select one or two regularization parameters. The advantages of the method are that the reconstructed attenuation map is consistent with the emission data and that it accounts for particularity in the emission reconstruction algorithm and acquisition geometry. The methodology is validated using a computer-generated whole-body phantom for both emission and transmission, neglecting random events and scattered radiation. MAP-TR was used for attenuation map reconstruction, while 3D OS-EM is used for estimating the emission image. The estimation of regularization parameters depends on the resolution of the emission image controlled by the number of iterations in OS-EM. The computer simulation shows that, on one hand, DDCC regularized attenuation map reduces propagation of the transmission scan noise to the emission image, while on the other hand DDCC prevents excessive attenuation map smoothing that could result in resolution mismatch artefacts between emission and transmission.     

3D RBI-EM reconstruction with spherically-symmetric basis function for SPECT rotating slat collimator

A single photon emission computed tomography (SPECT) rotating slat collimator with strip detector acquires distance-weighted plane integral data, along with the attenuation factor and distance-dependent detector response. In order to image a 3D object, the slat collimator device has first to spin around its axis and then rotate around the object to produce 3D projection measurements. Compared to the slice-by-slice 2D reconstruction for the parallel-hole collimator and line integral data, a more complex 3D reconstruction is needed for the slat collimator and plane integral data. In this paper, we propose a 3D RBI-EM reconstruction algorithm with spherically-symmetric basis function, also called 'blobs', for the slat collimator. It has a closed and spherically symmetric analytical expression for the 3D Radon transform, which makes it easier to compute the plane integral than the voxel. It is completely localized in the spatial domain and nearly band-limited in the frequency domain. Its size and shape can be controlled by several parameters to have desired reconstructed image quality. A mathematical lesion phantom study has demonstrated that the blob reconstruction can achieve better contrast-noise trade-offs than the voxel reconstruction without greatly degrading the image resolution. A real lesion phantom study further confirmed this and showed that a slat collimator with CZT detector has better image quality than the conventional parallel-hole collimator with NaI detector. The improvement might be due to both the slat collimation and the better energy resolution of the CZT detector.     

Hybrid scatter correction applied to quantitative holmium-166 SPECT

Ho-166 is a combined beta-gamma emitter of which the betas can be used therapeutically. From the 81 keV gammas of Ho-166, SPECT images can be obtained, which give opportunities to guide Ho-166 therapy. Accurate reconstruction of Ho-166 images is currently hampered by photopeak-scatter in the patient, down-scatter in the detector, collimator and patient caused by the 1.4 MeV photons and by bremsstrahlung. We developed and validated a method for quantitative SPECT of Ho-166 that involves correction for both types of scatter plus non-uniform attenuation correction using attenuation maps. Photopeak-scatter (S) is compensated for by a rapid 3D Monte Carlo (MC) method that is incorporated in ordered subset (OS) reconstruction of the emission data, together with simultaneous correction for attenuation (A) and detector response (D); this method is referred to as OS-ADS. Additionally, for correction of down-scatter, we use a 14 keV wide energy window centred at 118 keV (OS-ADSS). Due to a limited number of available energy windows, the same 118 keV energy window was used for down-scatter correction of the simultaneously acquired Gd-153 transmission data. Validations were performed using physical phantom experiments carried out on a dual-head SPECT system; Gd-153 transmission line sources were used for acquiring attenuation maps. For quantitative comparison of OS-ADS and OS-ADSS, bottles filled with Ho-166 were placed in both a cylindrical phantom and an anthropomorphic thorax phantom. Both OS-ADS and OS-ADSS were compared with an ordered subset reconstruction without any scatter correction (OS-AD). Underestimations of about 20% in the attenuation map were reduced to a few per cent after down-scatter correction. The average deviation from the true activity contained in the bottles was +72% with OS-AD. Using OS-ADS, this average overestimation was reduced to +28% and with OS-ADSS the deviation was further reduced to 16%. With OS-AD and OS-ADS, these numbers were more sensitive to the choice of volumes of interest than with OS-ADSS. For the reconstructed activity distributions, erroneous background activity found with OS-AD was reduced by a factor of approximately 2 by applying OS-ADS and reduced by a factor of approximately 4 by applying OS-ADSS. The combined attenuation, photopeak-scatter and down-scatter correction framework proposed here greatly enhanced the quantitative accuracy of Ho-166 imaging, which is of the uppermost importance for image-guided therapies. It is expected that the method, with adapted window settings, also can be applied to other isotopes with high energy peaks that contaminate the photopeak data, such as I-131 or In-111.     

Peripheral dose measurements for 6 and 18 MV photon beams on a linear accelerator with multileaf collimator

Peripheral dose (PD) to critical structures outside treatment volume is of clinical importance. The aim of the current study was to estimate PD on a linear accelerator equipped with multileaf collimator (MLC). Dose measurements were carried out using an ionization chamber embedded in a water phantom for 6 and 18 MV photon beams. PD values were acquired for field sizes from 5 x 5 to 20 x 20 cm2 in increments of 5 cm at distances up to 24 cm from the field edge. Dose data were obtained at two collimator orientations where the measurement points are shielded by MLC and jaws. The variation of PD with the source to skin distance (SSD), depth, and lateral displacement of the measurement point was evaluated. To examine the dependence of PD upon the tissue thickness at the entrance point of the beam, scattered dose was measured using thermoluminescent dosemeters placed on three anthropomorphic phantoms simulating 5- and 10-year-old children and an average adult patient. PD from 6 MV photons varied from 0.13% to 6.75% of the central-axis maximum dose depending upon the collimator orientation, extent of irradiated area, and distance from the treatment field. The corresponding dose range from 18 MV x rays was 0.09% to 5.61%. The variation of PD with depth and with lateral displacements up to 80% of the field dimension was very small. The scattered dose from both photon beams increased with the increase of SSD or tissue thickness along beam axis. The presented dosimetric data set allows the estimation of scattered dose outside the primary beam.     

Irregular field calculation on the central beam axis of photon beams using sector-integration

A method is proposed for calculation of irregular field factors on the central beam axis and homogeneous medium for x-ray beams. The irregular field factor is introduced as the ratio of the output of a field with and without blocks on the central beam axis. The algorithm is based on the sector-integration method and the circular field quantities are calculated from in-phantom measurements. These circular field quantities are the output per beam monitor unit for circular fields defined by a hypothetical secondary collimator and reduced to a circular field by blocking. A derivation of the sector-integration equation is given from first principles. As it is shown, the circular field quantities are evaluated from data measured for rectangular, block shaped fields. Such quantities contain all beam components, including photons scattered from the blocks, the block tray, and photons scattered in the phantom. Consequently, the so called primary and secondary beam components are readily incorporated in this approach. Once the circular field quantities have been determined from rectangular field data, the irregular field factors for other geometry can be calculated. Irregular field factors for square, rectangular and circular block-shaped fields were calculated for 6 MV photon beams and compared with measured values. The results agree within 0.7%, even for heavy blocked field cases, i.e., a 40 x 40 cm2 collimator field blocked to a 5 x 5 cm2 field. The method was tested for a particular source to surface distance, depth, phantom composition, and source to block distance. Calculation of irregular field factors in another set up conditions requires the measurement of the appropriate input data.     

Efficient simulation of SPECT down-scatter including photon interactions with crystal and lead

A major image degrading factor in simultaneous Dual Isotope (DI) SPECT or simultaneous Emission-Transmission (ECT-TCT) imaging, is the detection of photons emitted by the higher energy isotope in the energy window used for imaging the lower energy isotope. In Tc-99m/Tl-201 DI-SPECT typically tens of percents of the total detected down-scatter is caused by lead x rays. In Tc-99m/Gd-153 ECT-TCT, a comparable fraction of the down-scatter originates from Tc-99m photons which only partly deposit their energy in the detector crystal (i.e., due to crystal interactions). Efficient simulation methods which model down-scatter can be used to optimize DI-SPECT or ECT-TCT imaging acquisition or reconstruction protocols. In this paper we adapt a previously proposed efficient down-scatter simulation method, to include the interactions of photons with the detector crystal and collimator lead. To this end, point spread function tables including crystal and lead interactions are precalculated. Subsequently, photons are traced through the patient body until their last scatter position, and the precalculated responses are used to project the photons onto the detector plane, while photon attenuation in the patient is taken into account. The approach is evaluated by comparing simulated Tc-99m down-scatter projections with measured projections. Incorporation of photon interaction with crystal and lead leads to significantly improved accuracy of the shape of down-scatter responses, while differences in total counts between simulated and measured projections typically decrease from tens of percents to a couple of percents. Calculating 60 down-scatter projections of an extended distribution on a 64 x 64 x 64 grid takes about three minutes on a PC with two 1.2 GHz processors. We conclude that accurate and efficient simulation of down-scatter is now possible including the major effects of the nonuniform mass density of the patient as well as photon interactions with the crystal and collimator lead.     

Noise, resolution, and sensitivity considerations in the design of a single-slice emission-transmission computed tomographic system

A prototype Emission-Transmission Computed Tomography (ETCT) system is being developed that will acquire single-slice x-ray transmission CT images simultaneously with single photon emission computed tomography (SPECT) images. This system will permit the correlation of anatomical information from x-ray CT with functional information from SPECT images. The patient-specific attenuation map derived from the x-ray CT images can be used to perform attenuation correction of the SPECT images, so that accurate quantitative information can be obtained. The fan-beam scanning geometry and the use of a segmented HPGe detector array impose special constraints on the design of the collimator for the system. Based on a signal detection model, an efficiency-resolution figure of merit (ERFM) as a function of the collimator geometric efficiency, system resolution width, and object diameter is defined. The ERFM is proportional to the square of the detection signal-to-noise ratio. The collimator design parameters can then be optimized by optimizing the ERFM for an anticipated object diameter. The collimator point-spread function, geometric efficiency, and resolution are calculated. The collimator optimized for the detection of a 1-cm object will have a single-slice point source efficiency of 1.2 X 10(-4), and a FWHM of 6.5 mm at the center of the reconstruction circle, at 12 cm from the collimator face. The minimum object contrast which will give a detection SNR of 5 is 74%, for a total accumulated count per slice of 2 X 10(6).     

Single scan parameterization of space-variant point spread functions in image space via a printed array: the impact for two PET/CT scanners

Incorporation of a resolution model during statistical image reconstruction often produces images of improved resolution and signal-to-noise ratio. A novel and practical methodology to rapidly and accurately determine the overall emission and detection blurring component of the system matrix using a printed point source array within a custom-made Perspex phantom is presented. The array was scanned at different positions and orientations within the field of view (FOV) to examine the feasibility of extrapolating the measured point source blurring to other locations in the FOV and the robustness of measurements from a single point source array scan. We measured the spatially-variant image-based blurring on two PET/CT scanners, the B-Hi-Rez and the TruePoint TrueV. These measured spatially-variant kernels and the spatially-invariant kernel at the FOV centre were then incorporated within an ordinary Poisson ordered subset expectation maximization (OP-OSEM) algorithm and compared to the manufacturer's implementation using projection space resolution modelling (RM). Comparisons were based on a point source array, the NEMA IEC image quality phantom, the Cologne resolution phantom and two clinical studies (carbon-11 labelled anti-sense oligonucleotide [(11)C]-ASO and fluorine-18 labelled fluoro-l-thymidine [(18)F]-FLT). Robust and accurate measurements of spatially-variant image blurring were successfully obtained from a single scan. Spatially-variant resolution modelling resulted in notable resolution improvements away from the centre of the FOV. Comparison between spatially-variant image-space methods and the projection-space approach (the first such report, using a range of studies) demonstrated very similar performance with our image-based implementation producing slightly better contrast recovery (CR) for the same level of image roughness (IR). These results demonstrate that image-based resolution modelling within reconstruction is a valid alternative to projection-based modelling, and that, when using the proposed practical methodology, the necessary resolution measurements can be obtained from a single scan. This approach avoids the relatively time-consuming and involved procedures previously proposed in the literature.     

SPECT的数据采集条件对其断层分辨率的影响实验探讨

目的：探讨采集条件的选择对ＳＰＥＣＴ断层分辨率的影响。方法：来用 Ｊａｓｚｃｚａｋ模型。设定不同条件对模型进行 ３６０°采集,并对所采集的４８组原始资料进行重建处理,观察重建图像。结果：配置高能准直器,１２８×１２８矩阵,２００Ｋ以上计数,重建结果可分辨出直径 １１ ｍｍ柱型模型及直径 １２ ｍｍ球形模型,其余采集方式所重建的结果均达不到此分辨效果。讨论;就矩阵大小而言,１２８×１２８矩阵采集分辨能力优于６４×６４矩阵。采集信息量的大小亦是影响分辨率好坏的重要因素之一,采集信息量大,分辨率则高;反之,则分辨率下降。     

Three-dimensional photon detection kernels and their application to SPECT reconstruction.

In single photon emission computed tomography (SPECT), three-dimensional photon detection kernels characterize the probabilities that photons emitted by radio-isotopes in different parts of the source region will be detected at particular projection pixels of the projection images. Monte Carlo modelling is used to study these kernels for the case of parallel hole collimators. The use of vectorized Monte Carlo computer code speeds the modelling computations. The contributions of direct and scattered photons to projection data in a transverse plane from neighbouring planes are significant for the case of uniform activity within a water-filled cylinder. A reconstruction method using the 3D kernels is proposed in which projection measurements in three adjacent planes are used simultaneously to estimate the source activity of the center plane. This multiple slice method accounts for the fact that photons detected in a given transverse plane may have originated in other transverse planes with different activity distributions. The matrix equations for image reconstruction are solved using generalized matrix inverses. The new method shows compensation for 3D photon detection effects when applied to projection data from a numerical simulation and a cardiac phantom experiment. Quantitation for the numerical study is improved compared with results from a single slice reconstruction method.     

Study of the point spread function (PSF) for 123I SPECT imaging using Monte Carlo simulation

The iterative reconstruction algorithms employed in brain single-photon emission computed tomography (SPECT) allow some quantitative parameters of the image to be improved. These algorithms require accurate modelling of the so-called point spread function (PSF). Nowadays, most in vivo neurotransmitter SPECT studies employ pharmaceuticals radiolabelled with 123I. In addition to an intense line at 159 keV, the decay scheme of this radioisotope includes some higher energy gammas which may have a non-negligible contribution to the PSF. The aim of this work is to study this contribution for two low-energy high-resolution collimator configurations, namely, the parallel and the fan beam. The transport of radiation through the material system is simulated with the Monte Carlo code PENELOPE. We have developed a main program that deals with the intricacies associated with tracking photon trajectories through the geometry of the collimator and detection systems. The simulated PSFs are partly validated with a set of experimental measurements that use the 511 keV annihilation photons emitted by a 18F source. Sensitivity and spatial resolution have been studied, showing that a significant fraction of the detection events in the energy window centred at 159 keV (up to approximately 49% for the parallel collimator) are originated by higher energy gamma rays, which contribute to the spatial profile of the PSF mostly outside the 'geometrical' region dominated by the low-energy photons. Therefore, these high-energy counts are to be considered as noise, a fact that should be taken into account when modelling PSFs for reconstruction algorithms. We also show that the fan beam collimator gives higher signal-to-noise ratios than the parallel collimator for all the source positions analysed.     

Artefact reduction in dual-radionuclide subtraction studies

A method is proposed which significantly reduces the artefacts commonly experienced in dual radionuclide subtraction studies. Images of two radionuclides recorded simultaneously differ in resolution, sensitivity and attenuation. Also, one image will include scatter from the second higher-energy radionuclide. As a result severe artefacts are likely to occur when the two images are subtracted. In order to minimise the depth dependence of resolution, attenuation and scatter, the geometric mean of conjugate views was considered. From experimental work with activity placed in a depth of water it was demonstrated that the number and spatial distribution of scattered photons recorded in any energy window could be accurately predicted from the geometric mean image recorded in the photopeak. This prediction was accurate, independent of the depth of the source in water for a range of phantom dimensions. Differences in the instrument sensitivity and resolution at different energies can also be readily compensated for by using geometric mean images, as can differences due to the variation in attenuation. In practice three factors can be experimentally determined for any pair of radionuclides: a scatter ratio, a scatter function and a resolution compensation function. These data are then used to improve the dual-radionuclide subtraction analysis. The ability of the technique to significantly reduce subtraction artefacts has been demonstrated in phantom studies.     

Design and performance of a multi-pinhole collimation device for small animal imaging with clinical SPECT and SPECT-CT scanners

A multi-pinhole collimation device is developed that uses the gamma camera detectors of a clinical SPECT or SPECT-CT scanner to produce high-resolution SPECT images. The device consists of a rotating cylindrical collimator having 22 tungsten pinholes with 0.9 mm diameter apertures and an animal bed inside the collimator that moves linearly to provide helical or ordered-subsets axial sampling. CT images also may be acquired on a SPECT-CT scanner for purposes of image co-registration and SPECT attenuation correction. The device is placed on the patient table of the scanner without attaching to the detectors or scanner gantry. The system geometry is calibrated in-place from point source data and is then used during image reconstruction. The SPECT imaging performance of the device is evaluated with test phantom scans. Spatial resolution from reconstructed point source images is measured to be 0.6 mm full width at half maximum or better. Micro-Derenzo phantom images demonstrate the ability to resolve 0.7 mm diameter rod patterns. The axial slabs of a Micro-Defrise phantom are visualized well. Collimator efficiency exceeds 0.05% at the center of the field of view, and images of a uniform phantom show acceptable uniformity and minimal artifact. The overall simplicity and relatively good imaging performance of the device make it an interesting low-cost alternative to dedicated small animal scanners.     

Analytical cone-beam SPECT reconstruction algorithm with non-uniform attenuation for general non-circular orbit

In single photon emission computed tomography (SPECT), due to the attenuation of gamma photons, the analytical reconstruction is complicated, where attenuation should be compensated to obtain quantitative results. We know that the resolution of SPECT is low. The cone-beam SPECT reconstruction can improve the photon density and spatial resolution of the reconstructed image. In practice, to minimize the effect of distance-dependent resolution variation (DDRV), the detector should be set as close as possible to the patient. Therefore it would be more efficacious for the orbit of the detector to be elliptical or another shape. In this paper, based on the Novikov's reconstruction formula and our Ray-driven Technology, we present an analytical cone-beam SPECT reconstruction algorithm for general non-circular orbit. The simulation results demonstrate the accuracy and robustness of our method.     

Model-based crosstalk compensation for simultaneous 99mTc/123I dual-isotope brain SPECT imaging

In this work, we developed a model-based method to estimate and compensate for the crosstalk contamination in simultaneous 123I and 99mTc dual isotope brain single photo emission computed tomography imaging. The model-based crosstalk compensation (MBCC) includes detailed modeling of photon interactions inside both the object and the detector system. In the method, scatter in the object is modeled using the effective source scatter estimation technique, including contributions from all the photon emissions. The effects of the collimator-detector response, including the penetration and scatter components due to high-energy 123I photons, are modeled using precalculated tables of Monte Carlo simulated point-source response functions obtained from sources in air at various distances from the face of the collimator. The model-based crosstalk estimation method was combined with iterative reconstruction based compensation to reduce contamination due to crosstalk. The MBCC method was evaluated using Monte Carlo simulated and physical phantom experimentally acquired simultaneous dual-isotope data. Results showed that, for both experimental and simulation studies, the model-based method provided crosstalk estimates that were in good agreement with the true crosstalk. Compensation using MBCC improved image contrast and removed the artifacts for both Monte Carlo simulated and experimentally acquired data. The results were in good agreement with images acquired without any crosstalk contamination.     

Head scatter off-axis for megavoltage x rays

Our objective in this study has been to investigate how head scatter varies with the off-axis position in a 6 MV x-ray beam. We define the head-scatter off-axis ratio, HOA, as the ratio of the kerma due to head-scatter photons at the off-axis position x to the kerma from direct primary photons on the central axis. "Direct primary" are those photons that come from the source without interactions in the intervening structures. We determined HOA from measurements with an ionization chamber in a miniphantom. Head-scatter and direct primary photons contribute to a measurement of the ionization per mu Q(x) at the off-axis position x in the open field cx x cy. The ionization per mu QP(x), measured in the same position but with the field collimated to the smallest possible opening (cx x 3 cm), is intended to include only direct primary photons. Head-scatter photons cannot be completely eliminated, and the errors due to remaining head scatter and radiation back-scattered by the movable collimators into the monitor were estimated. For normalization of the final results, ionization due to direct primary photons was also measured on the central axis, QP(0). HOA was derived from these three measurements as HOA(cx,cy,x)=(Q(cx,cy,x) - QP(cx,cy,x))/QP(cx,cy,0). On the central axis (x=y=0), HOA represents the "scatter-to-primary ratio" between head scatter and the direct primary dose. Monte Carlo simulations were made to help with the interpretation and evaluation of the results. HOA could be fitted to a Gaussian model with two components corresponding to sources of widths 1.8 and 14 cm, projected on a plane 5 cm below the x-ray source. The narrow Gaussian component is interpreted as the source of photons scattered in the flattening filter and the primary collimator. The broad component is attributed to photons scattered in the secondary (variable) collimators. Conventional head-scatter models (e.g., a single Gaussian source model) do not fit the measured HOA data for large collimator settings (c>20 cm) or outside beam collimation. The full width at half-maximum (FWHM) of HOA(x) across the field increased with the field width (cx) in the direction of the measurements in a manner consistent with the field of view of the two sources. It was not sensitive to the field measure in the orthogonal direction (cy). Head scatter outside the field also increased with field size, reflecting an increased contribution of photons scattered at large angles. It exceeds the leakage through the collimator 2 cm outside the edge for square fields c>10 cm. Monte Carlo calculations showed considerably less head scatter outside the field than measurements.     

Output factors and dose calculations for blocked x-ray fields

Output factors for blocked fields have been measured in a polystyrene phantom for four collimator field sizes and two blocking schemes using 6-MV x rays. For all measurements the phantom surface was at the calibration source-surface distance (SSD) because, as is shown, the calculation of dose to any point in a phantom at an arbitrary SSD can be expressed in terms of the output factor for the field size at the calibration distance. It is found that output factors are a function of both the surface field size of the blocked field and the collimator field size. Specifically, the output factor for a blocked field is less than that for the collimator field size used but greater than that for an unblocked field of the same surface field size formed by collimator settings only. A method is proposed for utilizing these data to calculate the output factor for any collimator and blocked field size. The validity of the method is checked by using it to calculate dose to a point in a phantom and comparing this to the measured dose.     

Fast hybrid SPECT simulation including efficient septal penetration modelling (SP-PSF)

Single photon emission computed tomography (SPECT) images are degraded by the detection of scattered photons and photons that penetrate the collimator septa. In this paper, a previously proposed Monte Carlo software that employs fast object scatter simulation using convolution-based forced detection (CFD) is extended towards a wide range of medium and high energy isotopes measured using various collimators. To this end, a fast method was developed for incorporating effects of septal penetrating (SP) photons. The SP contributions are obtained by calculating the object attenuation along the path from primary emission to detection followed by sampling a pre-simulated and scalable septal penetration point spread function (SP-PSF). We found that with only a very slight reduction in accuracy, we could accelerate the SP simulation by four orders of magnitude. To achieve this, we combined: (i) coarse sampling of the activity and attenuation distribution; (ii) simulation of the penetration only for a coarse grid of detector pixels followed by interpolation and (iii) neglection of SP-PSF elements below a certain threshold. By inclusion of this SP-PSF-based simulation it became possible to model both primary and septal penetrated photons while only 10% extra computation time was added to the CFD-based Monte Carlo simulator. As a result, a SPECT simulation of a patient-like distribution including SP now takes less than 5 s per projection angle on a dual processor PC. Therefore, the simulator is well-suited as an efficient projector for fully 3D model-based reconstruction or as a fast data-set generator for applications such as image processing optimization or observer studies.