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.     

Some physical factors influencing the accuracy of convolution scatter correction in SPECT

Some important physical factors influencing the accuracy of convolution scatter correction techniques in SPECT are presented. In these techniques scatter correction in the projection relies on filter functions, QF, evaluated by Fourier transforms, from measured scatter functions, Qp, obtained from point spread functions. The spatial resolution has a marginal effect on Qp. Thus a single QF can be used in the scatter correction of SPECT measurements acquired with the low energy high resolution or the low energy general purpose collimators and over a wide range of patient-collimator distances. However, it is necessary to examine the details of the shape of point spread functions during evaluation of Qp. QF is completely described by scatter amplitude AF, slope BF and filter sum SF. SF is obtained by summation of the values of QF occupying a 31 x 31 pixels matrix. Regardless of differences in amplitude and slope, two filter functions are shown to be equivalent in terms of scatter correction ability, whenever their sums are equal. On the basis of filter sum, the observed small influence of ellipticity on QF implies that an average function can be used in scatter correcting SPECT measurements conducted with elliptic objects. SF is shown to increase with a decrease in photon energy and with an increase in window size. Thus, scatter correction by convolution may be severely hampered by photon statistics when SPECT imaging is done with low-energy photons. It is pointless to use unnecessarily large discriminator windows, in the hope of improving photon statistics, since most of the extra events acquired will eventually be subtracted during scatter correction. Regardless of the observed moderate reduction in SF when a lung-equivalent material replaces a portion of a water phantom, further studies are needed to develop a technique that is capable of handling attenuation and scatter corrections simultaneously. Whenever superficial and inner radioactive distributions coexist the observed reduction of SF close to the phantom surface indicates that scatter correction of such distributions has to rely on two distinct filter functions. Corrections based on a surface function produce accurate results in the superficial region, while the central distributions are substantially overestimated. Surface radioactive distributions introduce appreciable errors in the determination of central distributions when corrections are based on central filter function. This function introduces a reduction of about 40% in the measured surface concentration.     

Implementation and quantitative evaluation of analytical methods for attenuation correction in SPECT: a phantom study.

Three differing exact methods of inverting the two-dimensional (2D) exponential Radon transform were implemented and evaluated quantitatively with a phantom study. The phantom had the shape of a pie-chart divided into six cavities, each 480 ml in volume and 10 cm in height, that were symmetrically positioned in a cylinder that was 20 cm in diameter and 10 cm in height. This phantom tests for linearity between true activity concentration and measured activity concentration, and it is denoted as a linearity phantom in the present study. Each cavity contained a different concentration of a homogeneous solution of 99mTc (74, 148, 222, 296, 370 and 444 kBq ml(-1)). Data acquisition was performed with two energy windows: a 20% photopeak energy window set symmetrically over the 140 keV of 99mTc and a secondary 5% energy window set over the 122 keV peak. We optimized a triple-energy window scatter correction method for a gamma camera-collimator system to obtain accurate scatter-corrected projections. A circular ROI 3 cm in diameter was identified over each cavity region, and count density (counts per pixel) was calculated. This value was converted to activity concentration (kBq ml(-1)) using a cross-calibration coefficient between SPECT counts and the gamma well counter. The relation between true activity (x) and measured activity concentration (y) was fitted to a line using the least-squares method. Regression lines were y = 0.63 + 1.0255x (R2 = 0.9987), y = -2.62 + 1.0278x (R2 = 0.9995), and y = 0.092 + 1.0241x (R2 = 0.9989) for the Bellini, Inouye and Metz-Pan methods respectively. In another phantom study using two different types of phantoms, contrast of a cold region in the two was 96% and 101% for all three methods. Combined optimized scatter correction and analytical attenuation correction methods achieve good accuracy in quantification of activity distribution with a uniform attenuating medium.     

Simultaneous compensation for attenuation, scatter and detector response for SPECT reconstruction in three dimensions.

A three-dimensional reconstruction method for simultaneous compensation of attenuation, scatter and distance-dependent detector response for single photon emission computed tomography is described and tested by experimental studies. The method determines the attenuation factors recursively along each projection ray starting at the intersected source voxel closest to the detector. The method substracts the scatter energy window data from the primary energy window data for scatter compensation. The detector response is modelled to be spatially invariant at a constant distance from the detector. The method convolves source distribution with the modelled response function to compensate for the smoothed by use of a non-uniform entropy prior to searching for the maximum a posteriori probability solution. The method was tested using projections acquired from a chest phantom by a three-headed detector system with parallel hole collimators. An improvement was shown in image noise, recognition of object sizes and shapes, and quantification of concentration ratios.     

Calculation and validation of the use of effective attenuation coefficient for attenuation correction in In-111 SPECT

Nuclear medicine tracers using 111In as a radiolabel are increasing in their use, especially in the domain of oncologic imaging. In these applications, it often is critical to have the capability of quantifying radionuclide uptake and being able to relate it to the biological properties of the tumor. However, images from single photon emission computed tomography (SPECT) can be degraded by photon attenuation, photon scattering, and collimator blurring; without compensation for these effects, image quality can be degraded, and accurate and precise quantification is impossible. Although attenuation correction for SPECT is becoming more common, most implementations can only model single energy radionuclides such as 99mTc and 123I. Thus, attenuation correction for 111In is challenging because it emits two photons (171 and 245 keV) at nearly equal rates (90.2% and 94% emission probabilities). In this paper, we present a method of calculating a single "effective" attenuation coefficient for the dual-energy emissions of 111In, and that can be used to correct for photon attenuation in radionuclide images acquired with this radionuclide. Using this methodology, we can derive an effective linear attenuation coefficient Micro(eff) and an effective photon energy E(eff) based on the emission probabilities and linear attenuation coefficients of the 111In photons. This approach allows us to treat the emissions from 111In as a single photon with an effective energy of 210 keV. We obtained emission projection data from a tank filled with a uniform solution of 111In. The projection data were reconstructed using an iterative maximum-likelihood algorithm with no attenuation correction, and with attenuation correction assuming photon energies of 171, 245, and 210 keV (the derived E(eff)). The reconstructed tomographic images demonstrate that the use of no attenuation correction, or correction assuming photon energies of 171 or 245 keV introduces inaccuracies into the reconstructed radioactivity distribution when compared against the effective energy method. In summary, this work provides both a theoretical framework and experimental methodology of attenuation correction for the dual-energy emissions from 111In. Although these results are specific to 111In, the foundation could easily be extended to other multiple-energy isotopes.     

The effect of intrinsic attenuation correction methods on the stationarity of the 3-D modulation transfer function of SPECT.

The application of stationary restoration techniques to SPECT images assumes that the modulation transfer function (MTF) of the imaging system is shift invariant. It was hypothesized that using intrinsic attenuation correction (i.e., methods which explicitly invert the exponential radon transform) would yield a three-dimensional (3-D) MTF which varies less with position within the transverse slices than the combined conjugate view two-dimensional (2-D) MTF varies with depth. Thus the assumption of shift invariance would become less of an approximation for 3-D post- than for 2-D pre-reconstruction restoration filtering. SPECT acquisitions were obtained from point sources located at various positions in three differently shaped, water-filled phantoms. The data were reconstructed with intrinsic attenuation correction, and 3-D MTFs were calculated. Four different intrinsic attenuation correction methods were compared: (1) exponentially weighted backprojection, (2) a modified exponentially weighted backprojection as described by Tanaka et al. [Phys. Med. Biol. 29, 1489-1500 (1984)], (3) a Fourier domain technique as described by Bellini et al. [IEEE Trans. ASSP 27, 213-218 (1979)], and (4) the circular harmonic transform (CHT) method as described by Hawkins et al. [IEEE Trans. Med. Imag. 7, 135-148 (1988)]. The dependence of the 3-D MTF obtained with these methods, on point source location within an attenuator, and on shape of the attenuator, was studied. These 3-D MTFs were compared to: (1) those MTFs obtained with no attenuation correction, and (2) the depth dependence of the arithmetic mean combined conjugate view 2-D MTFs.(ABSTRACT TRUNCATED AT 250 WORDS)     

Removing the interference error between attenuation correction and scatter subtraction in 3D PET imaging.

A method to remove the interference between attenuation correction and scatter subtraction has been developed for the QPET 3D imaging system at Queen's University. Because the detector system has more than 10(10) lines of response, we reconstruct the image by first backprojecting, then filtering. We correct for attenuation at backprojection by weighting each event by the inverse of the attenuation factor calculated by reprojection through an attenuation image. Since the scatter background has not been corrected at backprojection time, this has the side effect that a fraction of the detected scattered events get incorrectly weighted. When a scatter subtraction is subsequently applied, the correction is inaccurate because the scatter distribution has been modified by the attenuation correction procedure. The residual interference error in the reconstructed image is a distorted image of the attenuator. An approximation to this error is obtained by reprojecting through the attenuation image, backprojecting with appropriate weights, then reconstructing. This image is then scaled and multiplied by the calculated scatter distribution to obtain an estimate of the interference error. Both simulations and measurements indicate that for our system, this method provides a reasonable approximation of the interference error in the image.     

A 3D model of non-uniform attenuation and detector response for efficient iterative reconstruction in SPECT

A 3D physical model for iterative reconstruction in SPECT has been developed and applied to experimental data. The model incorporates non-uniform attenuation using reconstructed transmission CT data and distance-dependent detector response based on response function measurements over a range of distances from the detector. The 3D model has been implemented in a computationally efficient manner with practical memory requirements. The features of the model that provide efficiency are described including a new region-dependent reconstruction (RDR) technique. With RDR, filtered backprojection is used to reconstruct areas of the image of minimal clinical importance, and the result is used to supplement the iterative reconstruction of the clinically important areas of the image. The 3D model was incorporated into the maximum likelihood-expectation maximization (ML-EM) reconstruction algorithm and tested in three phantom studies--a point source, a uniform cylinder, and an anthropomorphic thorax--and a patient 9Tc(m) sestamibi study. Reconstructed images with the 3D method exhibited excellent noise and resolution characteristics. With the sestamibi data, the RDR technique produced essentially the conventional ML-EM estimate in the cardiac region with substantial time savings.     

SPECT volume quantitation: influence of spatial resolution, source size and shape, and voxel size

A number of factors influence the accuracy of estimation of source volume with single-photon emission computed tomography (SPECT) imaging. This study investigated the role of a number of factors including system spatial resolution (which includes the influence of low-pass filters applied to suppress noise), source size and shape, and voxel size in determining volume. A rectangular parallelepiped (bar), a right cylinder, and a sphere were mathematically modeled as being imaged with a SPECT system by calculating the three-dimensional (3-D) convolution of them with symmetric Gaussian functions of 20 different full widths at half maximums (FWHM's). The resulting activity profiles were analyzed to determine the location of the edges as a function of the source size relative to the FWHM of the system. The edge definition criteria studied were (1) the location of the 50% count threshold and (2) the maximum in the local gradient. In addition, the threshold which yielded the correct edge location was also determined. A nonstationary computer simulation of SPECT imaging, based on the serial model of the system transfer function, was used to test the predictions of the mathematical model and investigate the influence of (1) voxel size and sampling with a discrete array of voxels; (2) attenuation; (3) scatter; (4) variable spatial resolution; (5) low-pass filtering; and (6) noise. The mathematical model predicted that both the 50% threshold and the maximum in the local gradient methods of estimating edge location would show either an under- or overestimate of source volume depending on both the ratio of source diameter to system FWHM and the source shape.(ABSTRACT TRUNCATED AT 250 WORDS)     

Implementation of a Tc-99m and Ce-139 scanning line source for attenuation correction in SPECT using a dual opposing detector scintillation camera

Image degradation during single photon emission computed tomography (SPECT) due to attenuation and Compton scatter of photons can cause clinical image artifacts and will also result in inaccurate quantitative data. Therefore attenuation correction methods recently received wide interest. Transmission imaging can be performed to obtain the attenuation coefficients of a nonhomogeneous attenuating medium accurately. The aim of this study was firstly to evaluate the imaging characteristics of the scanning line source assembly. The results obtained with Tc-99m and Ce-139 were compared. Secondly the calculated attenuation coefficients were compared with known values from literature, using Tc-99m and Ce-139 as transmission sources. Lastly the method of acquiring simultaneous transmission and emission data was investigated. This study shows that an attenuation coefficient map can be obtained using a scanning line source for transmission imaging with a dual opposing detector camera. The imaging characteristics of Tc-99m and Ce-139 as transmission sources are similar. The resolution obtained with the Ce-139 line source was poorer than that obtained with the Tc-99m line source. A linear relationship was found between CT numbers and attenuation coefficients for transmission images using both Tc-99m and Ce-139 line sources. The attenuation coefficient value for water was underestimated by 1% using the Tc-99m transmission source and underestimated by 10% using Ce-139 as transmission source. This underestimation of attenuation coefficient values was also obtained in the human study. A myocardial perfusion study processed without and with attenuation correction clearly demonstrated the effect of the attenuation correction in the inferior myocardial region. The potential of using a scanning line source as transmission source with a dual opposing detector camera has been demonstrated in this study. The transmission source, Ce-139 was successfully introduced in this investigation for simultaneous acquisition of transmission and emission data.     

Receptive field scatter,topography and map variability in different layers of the hindpaw representation of rat somatosensory cortex

We recorded neurons extracellularly in layers II/III, IV, and V of the hindpaw representation of primary somatosensory cortex in anesthetized rats and studied laminar features of receptive fields (RFs) and representational maps. On average, RFs were smallest in layer IV and largest in layer V; however, for individual penetrations we found substantial deviations from this rule. Within the hindpaw representation, a distinct rostrocaudal gradient of RF size was present in all layers. While layer V RFs were generally largest independent of this gradient, layer IV RFs recorded caudally representing the proximal portions of the paw were larger than layer II/III RFs recorded rostrally representing the digits. The individual scatter of the locations of RFs across laminar groups was in the range of several millimeters, corresponding to about 25% of the average RF diameter. The cutaneous representations of the hindpaw in extragranular layers were confined to the areal extent defined by responsive sites in layer IV. Comparison between RFs determined quantitatively and by handplotting showed a reliable correspondence. Repeated measurements of RFs revealed spontaneous fluctuations of RF size of no more than 5% of the initial condition over an observation period of several hours. The topography and variability of cortical maps of the hindpaw representation were studied with a quantitative interpolation method taking into account the geometric centers of RFs and the corresponding cortical recording sites. On average, the overall topography in terms of preservation of neighborhood relations was present in all layers, although some individual maps showed severe distortions of topography. Factors contributing to map variability were overall position of the representation on the cortical surface, internal topography and spatial extent. Interindividual variability of map layout was always highest in the digit representations. Local topographic orderliness was lowest in layer V, but comparable in layers II/III and IV. Within layer IV, the lowest orderliness was observed in the digit representations. Our data emphasize a substantial variability of RF size, overlap and position across layers and within layers. At the level of representational maps, we found a similar degree of variability that often co-varied across layers, with little evidence for significant layer specificity. Laminar differences are likely to arise from the specific input-output pattern, layer-specific cell types and the connectivity between different layers. Our findings emphasizing similarities in the variability across layers support the notion of tightly coupled columnar interactions between different layers.     

Quantification accuracy and partial volume effect in dependence of the attenuation correction of a state-of-the-art small animal PET scanner

Quantification accuracy and partial volume effect (PVE) of the Siemens Inveon PET scanner were evaluated. The influence of transmission source activities (40 and 160 MBq) on the quantification accuracy and the PVE were determined. Dynamic range, object size and PVE for different sphere sizes, contrast ratios and positions in the field of view (FOV) were evaluated. The acquired data were reconstructed using different algorithms and correction methods. The activity level of the transmission source and the total emission activity in the FOV strongly influenced the attenuation maps. Reconstruction algorithms, correction methods, object size and location within the FOV had a strong influence on the PVE in all configurations. All evaluated parameters potentially influence the quantification accuracy. Hence, all protocols should be kept constant during a study to allow a comparison between different scans.     

Evaluation of the antipyretic effect of psychotropic agents and their influence on the fever-lowering effect of acupuncture

Translated fromByulleten' Eksperimental'noi Biologii i Meditsiny, Vol. 115, N ⁰ 3, pp. 262–264, March, 1993     

Fast implementation of the single scatter simulation algorithm and its use in iterative image reconstruction of PET data

In positron emission tomography (PET), scatter correction is usually performed prior to image reconstruction using a more or less exact model of the scatter processes. These models require estimates of the true activity and object density distributions of the imaged object. The problem is that these estimates are computed from measured data and, therefore, already contain scattered events. The purpose of this work was to overcome this problem by incorporating scatter characteristics directly into the process of iterative image reconstruction. This could be achieved by an optimized implementation of the single scatter simulation (SSS) algorithm, which results in a significant speed-up of the scatter estimation procedure. The scatter simulation was then included in the forward projection step of maximum likelihood image reconstruction. The results demonstrate that this approach leads to a more exact estimation of the scatter component which cannot be obtained by a simple sequential data processing strategy.     

The influence of phantom size on output, peak scatter factor, and percentage depth dose in large-field photon irradiation

Machine outputs, peak scatter factors, and central axis percentage depth dose distributions were measured for various phantom sizes in large radiation fields produced at extended distances by cobalt, 6-MV, and 10-MV photon beams. The results can be applied to practical total body irradiation procedures which usually involve treatment volumes smaller than the actual field sizes in order to provide a uniform total body exposure to radiation. Our study addresses the question of the appropriate phantom dimension to be used in the calibration of photon beams employed in total body irradiations. The measurements show that the machine outputs are only slightly dependent on phantom size; the percentage depth dose distributions, however, are strongly dependent on the phantom size, suggesting that machine data for total body irradiations should be measured in phantoms whose dimensions approximate the patient during the total body irradiation. Peak scatter factors measured in large-field/small-phantom configurations link up well with the published small-field/large-phantom data. The finite patient thickness lowers the dose to points close to the beam exit surface by a few percent, when compared to dose measured at the same depths in infinitely thick phantoms. The surface doses in large radiation fields are essentially independent of phantom cross sections and range from 40% for the 10-MV beam, to 65% for the 6-MV beam and 80% for the cobalt beam.     

Cardiotoxic effects of the antiarrhythmic rhythmidazol and their correction by suphan, befol, and their combinations

The antiarrhythmic rhythmidazol produces a cardiotoxic effect that can be corrected by suphan, befol, and their combinations, as evidenced by normalization of ultrastructural organization of cardiomyocytes and myocardial oxygen consumption by these drugs. Translated fromByulleten' Eksperimental'noi Biologii i Meditsiny, Vol. 124, No. 12, pp. 640–644, December, 1997     

Influence of scatter reduction method and monochromatic beams on image quality and dose in mammography

In mammography, the image contrast and dose delivered to the patient are determined by the x-ray spectrum and the scatter to primary ratio S/P. Thus the quality of the mammographic procedure is highly dependent on the choice of anode and filter material and on the method used to reduce the amount of scattered radiation reaching the detector. Synchrotron radiation is a useful tool to study the effect of beam energy on the optimization of the mammographic process because it delivers a high flux of monochromatic photons. Moreover, because the beam is naturally flat collimated in one direction, a slot can be used instead of a grid for scatter reduction. We have measured the ratio S/P and the transmission factors for grids and slots for monoenergetic synchrotron radiation. In this way the effect of beam energy and scatter rejection method were separated, and their respective importance for image quality and dose analyzed. Our results show that conventional mammographic spectra are not far from optimum and that the use of a slot instead of a grid has an important effect on the optimization of the mammographic process. We propose a simple numerical model to quantify this effect.     

A hybrid scatter correction for 3D PET based on an estimation of the distribution of unscattered coincidences: implementation on the ECAT EXACT HR+

We implemented a hybrid scatter-correction method for 3D PET that combines two scatter-correction methods in a complementary way. The implemented scheme uses a method based on the discrimination of the energy of events (the estimation of trues method (ETM)) and an auxiliary method (the single scatter simulation method (SSSI) or the convolution-subtraction method (CONV)) in an attempt to increase the accuracy of the correction over a wider range of acquisitions. The ETM takes into account the scatter from outside the field-of-view (FOV), which is not estimated with the auxiliary method. On the other hand, the auxiliary method accounts for events that have scattered with small angles, which have an energy that cannot be discriminated from that of unscattered events using the ETM. The ETM uses the data acquired in an upper energy window above the photopeak (550-650 keV) to obtain a noisy estimate of the unscattered events in the standard window (350-650 keV). Our implementation uses the auxiliary method to correct the residual scatter in the upper window. After appropriate scaling, the upper window data are subtracted from the total coincidences acquired in the standard window, resulting in the final scatter estimate, after smoothing. In this work we compare the hybrid method with the corrections used by default in the 2D and 3D modes of the ECAT EXACT HR+ using phantom measurements. Generally, the contrast was better with the hybrid method, although the relative errors of quantification were similar. We conclude that hybrid techniques such as the one implemented in this work can provide an accurate, general-purpose and practical way to correct the scatter in 3D PET, taking into account the scatter from outside the FOV.