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Implementation of Cascade Gamma and Positron Range Corrections for I-124 Small Animal PET S. Harzmann, F. Braun, A. Zakhnini, W. A. Weber, U. Pietrzyk, Member, IEEE, and M. Mix
Abstract—Small animal Positron Emission Tomography (PET) should provide accurate quantification of regional radiotracer concentrations and high spatial resolution. This is challenging for nonpure positron emitters with high positron endpoint energies, such as I-124: On the one hand the cascade gammas emitted from this isotope can produce coincidence events with the 511 keV annihilation photons leading to quantification errors. On the other hand the long range of the high energy positron degrades spatial resolution. This paper presents the implementation of a comprehensive correction technique for both of these effects. The established corrections include a modified sinogram-based tail-fitting approach to correct for scatter, random and cascade gamma coincidences and a compensation for resolution degradation effects during the image reconstruction. Resolution losses were compensated for by an iterative algorithm which incorporates a convolution kernel derived from line source measurements for the microPET Focus 120 system. The entire processing chain for these corrections was implemented, whereas previous work has only addressed parts of this process. Monte Carlo simulations with GATE [1] and measurements of mice with the microPET Focus 120 show that the proposed method reduces absolute quantification errors on average to 2.6% compared to 15.6% for the ordinary Maximum Likelihood Expectation Maximization algorithm. Furthermore resolution was improved in the order of 11-29% depending on the number of convolution iterations. In summary, a comprehensive, fast and robust algorithm for the correction of small animal PET studies with I-124 was developed which improves quantitative accuracy and spatial resolution. Index Terms—Cascade gamma coincidences, image resolution, Monte Carlo simulations, non-pure positron emitter, positron emission tomography (PET), positron range. Manuscript received July 15, 2013; revised October 24, 2013; accepted November 26, 2013. Date of publication January 29, 2014; date of current version February 06, 2014. This work was supported by the Federal Ministry of Education and Research Germany (BMBF), Molecular Imaging - MoBiTech, contract number: 13N10455 and the German Federal Ministry of Economics and Technology, contract numbers: 02E10176 and 02E10971 . S. Harzmann is with the Department of Nuclear Medicine, Medical Center University of Freiburg, Freiburg, Germany and also with the Faculty of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, Germany (e-mail:
[email protected]). F. Braun and M. Mix are with the Department of Nuclear Medicine, Medical Center - University of Freiburg, Freiburg, Germany (e-mail:
[email protected]). A. Zakhnini is with the Institute of Resource Ecology, Helmholtz Center Dresden-Rossendorf, Research Site Leipzig, Leipzig, Germany. W. A. Weber is with the Memorial Sloan-Kettering Cancer Center, New York, NY 10065 USA. U. Pietrzyk is with the Faculty of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal, Germany and also with the Institute of Neuroscience and Medicine, Forschungszentrum Jülich GmbH, Jülich, Germany. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNS.2013.2293914
I. INTRODUCTION
S
MALL animal Positron Emission Tomography (PET) offers the possibility to monitor animals in vivo with a higher quantification accuracy and spatial resolution compared to human PET imaging. Conventionally used isotopes have relatively short half-lives (F-18: 109.8 min, C-11: 20.4 min) limiting long-term studies and synthesis procedures [2]. The non-pure positron emitter I-124 offers benefits in terms of a longer half life of 4.2 days which allows the tracing of slow biochemical processes and the sequential dosimetry of the same animal. Several disadvantages arise from the complex decay scheme of I-124. Besides a low positron abundance of only about 23%, cascade gammas are emitted in conjunction with the positron decay. The energies of the dominant photons fall into the default energy window of commercially available small animal PET scanners with abundances of 63% for the 602.7 keV and 10% for the 722.8 keV gamma line [3]. These photons can cause coincidences with one 511 keV annihilation photon or with each other (cascade gamma coincidences). This leads to an increase in background for the reconstructed images due to the lack of spatial correlation of the cascade gamma coincidences to the point of positron annihilation similar to the effect caused by random coincidences. Furthermore I-124 has high positron endpoint energies of 1.5 MeV (12%) and 2.1 MeV (11%) [3] leading to long mean positron ranges in water of mm compared to 0.5 mm for F-18 [4]. This degrades the image quality of the reconstructed images and results in a blurring effect. Monte Carlo simulations have been used before to quantify and remove cascade gamma coincidences for non-pure positron emitters [5]–[8]. In [5] an analysis framework within GATE was developed which allows the separation of the spurious coincidences. For Br-76, scatter and cascade gammas for centered and off-center phantoms were quantified and removed [6]. Several correction methods include a subtraction of the cascade gamma background in the sinograms by a uniform value [9] or by a linear fit between the endpoints of the projection tails [10]. In [11] the cascade gammas distribution was modeled by convolving the true activity distribution with a spatially variant attenuation-dependent kernel in sinogram space and then subtracting this component before reconstruction. Resolution degradation effects at clinical and preclinical PET scanners were determined by line source [12] and catheter [13] measurements. To correct for resolution losses due to high positron energy emitters, resolution recovery has been implemented in
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Fig. 1. Images and corresponding simulations in GATE of the physical phantoms. (a) Image Quality Phantom (photo) (b) Image Quality Phantom in GATE. (c) Attenuation Phantom (photo). (d) Attenuation Phantom in GATE. (e) Resolution Phantom (photo). (f) Resolution Phantom in GATE with [mm] of the five different segments (top left).
various different manners. In [14], the measured projection data was divided by a positron range function in Fourier space to remove blurring. Other correction methods implemented the range correction through a convolution in image space. In [15]–[17] positron range was modeled for homogeneous and inhomogeneous materials and included in the forward projection system matrix. Another approach was to convolve the estimated activity distribution with a range kernel before projection [18]–[21]. In the past, these aspects of I-124 were treated and corrected separately with no or less focus on a large number of small animal PET scans. Thus we mainly concentrate our corrections on time-efficiency and completeness. The novel approach of our work presented here, focuses on the implementation of a complete procedure dedicated to preclinical routine in order to correct and quantify the before-mentioned issues attributed to I-124. This paper is based on previously presented work [22]. Our corrections are especially intended to be applied on a broad basis during preclinical imaging for small animal scans. All measured results were underlined by corresponding GATE simulations. Measurements and simulations alike were compared with the reference isotope F-18 and with the negative ion F-18 Tetrafluoroborat (F-18 TFB) for the small animal in vivo scans. First simulations and measurements were accomplished to adjust the blurring effect and the effect of cascade gamma coincidences. To increase quantification, the sinograms were pre-corrected for scatter, cascade gammas and randoms by a practical edge-finding algorithm. Resolution losses were recovered by applying a convolution operation before the projection step. Besides phantom measurements and GATE Monte Carlo simulations, the corrections were also applied to 20 in vivo small animal scans. II. MATERIALS AND METHODS
Emission Tomography (GATE) version 6.1 [1] were calculated for this scanner. GATE enables access to different kinds of information levels (hits, singles, coincidences) which are not all accessible for real PET scanners. For instance detailed information about particle interactions (like the energy, time, position and parent particle identification number) can be extracted from the hits. In concordance with the measurements, an energy window of 350-650 keV and a timing window of 6 ns were chosen for the simulated digitizer module. A mean energy blurring of 20% was extracted from crystal energy calibration measurements. The system was simulated with a non-paralyzable deadtime (110.4 ns) for the components of detection of single events. For the coincidence sorter a non-paralyzable deadtime of 42.79 ns was used. In case of a non-paralyzable deadtime, only the first arriving signal is processed within the given deadtime, following signals will be discarded. After the integration time, the detector is again ready to accept the first arriving signal. Pile-up was simulated with a signal formation time of 100 ns on the detector block [23], [24]. B. Radionuclides I-124 was used to investigate the effects of isotopes with cascade gamma coincidences and positron range degradation effects simultaneously. To assess the blurring effect from high positron energy isotopes solely, Ga-68 was chosen. Ga-68 is an almost pure positron emitter (89%) with no cascade gammas in the default energy window of commercially available PET scanners. The maximum positron energy of 1.9 MeV and the mean range in water of 3.1 mm [4] is comparable to those values for I-124. F-18 was selected as a reference isotope to compare both effects to a pure and low energy -emitter. For the comparison of F-18 and I-124 in animal studies, F-18 TFB was used. Like the negative ion I-124, TFB radiolabelled with F-18 is transported by the human sodium iodide symporter (hNIS) [25], [26].
A. PET Scanner and Simulations in GATE
C. Physical Phantoms
Measurements were performed with the small animal PET scanner Concorde microPET Focus 120. The lutetium oxyorthosilicate (LSO) crystals have a size of mm and are arranged in crystal arrays. Each detector block is coupled via optical fibers to a position-sensitive photomultiplier tube and repeated 4 times axially and 24 times radially. Including the crystal pitch this results into an axial extent of 7.6 cm and a detector ring diameter of 14.7 cm. In addition Monte Carlo simulations with the Geant4 Application for
In order to verify the implemented cascade gamma and positron range corrections on a broader basis, measurements and corresponding GATE simulations were performed for all phantom geometries explained below and shown in Fig. 1. For Table III the same activity concentrations and acquisition time intervals were used for the measurements and simulations. 1) Image Quality Phantom: The purpose of this phantom is to imitate the imaging of a small rodent which besides “hot” lesions has also uniform “hot” and “cold” parts [27]. The Image
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Quality Phantom (QRM, Möhrendorf, Germany) according to the NEMA NU 4-2008 standard possesses two different parts (Fig. 1(b)): A hot water-filled background area (diameter mm) with two cold cylindrical inserts (water and air, mm, length l mm) and a cold area made of polymethylmethacrylate (PMMA) with five hot water-filled cylindrical inserts with different diameters (1, 2, 3, 4 and 5 mm) and each having a length of 20 mm. The background and the cylindrical inserts were filled with a radioactive source solution containing F-18 FDG and I-124 with purified water (ultrafiltration). 2) Attenuation Phantom: To test the corrections for larger objects where attenuation comes more into play, a self-made attenuation phantom according to the IEC 61675-1 standard [28] was constructed and manufactured by QRM, Möhrendorf, Germany (Fig. 1(c), 1(d)). The Attenuation Phantom has the same geometrical characteristics as the one for human applications downscaled by a factor of five to fit for small animal imaging purposes: Three cold interchangeable cylindrical inserts (here: Teflon, water and air, mm, mm) are surrounded by a hot water-filled area ( mm, mm) filled with I-124 and purified water (ultrafiltration). 3) Resolution Phantom: The Animal PET Resolution Phantom 100/57 (BS Industrieelektronik & Medizintechnik, Lübbecke, Germany) consists of a PMMA phantom body ( mm) with five different segments which can be filled separately (Fig. 1(e)). The diameters d of each bore hole of the particular segment range from 1 to 3 mm in steps of 0.5 mm (Fig. 1(f)). The center-to-center distances between neighboring rods are as follows: For segment 1 ( mm): 4 mm, segment 2( mm): 5 mm, segment 3 ( mm): 6 mm, segment 4( mm): 8 mm and for segment 5 ( mm): 9 mm. The height of the fillable bore holes of 88 mm allows coverage of a large axial Field of View (FOV).
for the I-124 imaged animals. As the absolute uptake is unknown in contrast to the activity concentration for the physical phantoms, the following substitute variables are introduced. Signal to Noise Ratios (SNR) for the background (BG) were calculated according to:
D. Animal Studies One intention of this work was to test the implemented corrections especially on real small animal PET data. The animal scans were taken from different studies all having different tumor uptakes. In total 20 I-124 mice PET scans were selected. As the scanning protocol was changed according to radiation protection and animal care issues (lower injected volume), the activity was reduced for the later 2nd group. Therefore there was one animal group with a mean injected activity of MBq (weight: g) and the other one with a lower mean activity of MBq (weight: g). Additionally 11 out of the 20 mice were also imaged with F-18 TFB (injected activity: MBq, weight: g). Thus for 11 animals a direct comparison between I-124 and F-18 for the same individual uptake behavior was possible. Each I-124 (F-18 TFB) animal scan was acquired in list mode with a total scan duration of 45 (15) minutes and a summed frame over the whole time period was used for the corrections later. The xenografts were implanted subcutaneously at the shoulder. Not all animals were kept fasted, so the uptake in the stomach differed. Therefore the only constant comparable criteria on a statistical base was the uptake behavior in the thyroid
(1) The background was defined by a 3D region of interest over at least 250 voxels. The ROI was placed in a homogeneous volume away from high activity structures. For the mouse studies, this 3D ROI was placed in the lower part of the abdomen between the stomach and the bladder. The Maximum Contrast (MaxC) and the Contrast-to-Noise Ratio (CNR) for the thryoid were calculated as follows: thyroid
(2)
and thyroid
(3)
with max(thyroid) as the maximum value in the thyroid, as the standard deviation and as the mean value of the background. E. Mouse Voxel Phantom The realistic digital mouse whole body phantom (MOBY, [31]) is a voxel-based animal model which allows the generation of 3D emission and attenuation image data. Different organs can be individually selected at any user-defined resolution. These generated mouse anatomy data sets can be used as phantom and source inputs for GATE simulations. The physical anatomy and the activity distribution of the MOBY phantom were selected to correspond to the realistic animal studies from II-D. As current studies use lower activities similar to the second reference group from this section, an activity of 2.62 MBq was used for the MOBY phantom. To simulate a standardized tumor, a spherical lesion with mm was added to the MOBY mouse phantom near the left shoulder (Fig. 2). For the phantom geometry in GATE, seven different organs were distinguished besides the background material (“body”) and the tumor lesion tissue (“muscle”): Thryoid, bladder, intestine air, stomach, lung air, bones (skull, spine) and rib. The total size of the phantom was voxels and three different pixel sizes (0.32/ 0.354/ 0.40 mm) were chosen to simulate a mouse with three different weights (19/ 25/ 36 g). F. Workflow Fig. 3 shows the established processing chain from the quantification of the different coincidence types in GATE (Section II-F1) until the final reconstruction of the pre-corrected sinograms (Section II-F3). It allows the usage of the same reconstruction packages for both the measured and simulated sinograms: Both data sets can be either reconstructed with the
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Fig. 2. Simulated MOBY Mouse Voxel Phantom with one lesion at the left shoulder. (a)/(b): 2D coronal views with ROVER [29]. (c) 3D rendering of a fused PET-CT image with OsiriX [30].
Fig. 3. Processing chain for quantification, correction and image reconstruction for I-124 measured and simulated data.
scanner implemented microPET software, with an MLEM algorithm or with a Positron Range corrected MLEM (PR-MLEM). Thus it was possible to investigate the impact of the cascade gamma coincidences on a sinogram- and image-based basis and to calculate correction factors for quantification. In the following sections each step of the workflow is explained in more detail. 1) Simulation of Cascade Gamma Coincidences: In GATE all coincidences involving at least one cascade gamma were separated from the coincidences between the two 511 keV annihilation photons with a script written in ROOT [32]. The separation was accomplished by additionally using the information of each particle interaction (“hit”) along with the coincidences. From the hits it is possible to extract information about the track and type of the parent particle which caused the coincidence. The “cascade gamma” coincidences can be a coincidence between a 511 keV annihilation photon and a cascade gamma as well as
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coincidences between two cascade gammas. Thus in our analysis framework the cascade gamma coincidences include also scattered coincidences with at least one prompt cascade gamma involved. “Trues”, “randoms” and “scatter” are denoted as coincidences between the two 511 keV annihilation photons. Except for the randoms, the true and scattered coincidences originate from the same positron decay. These four different types of GATE simulated coincidences of interest were rebinned into sinograms by a script from [33] which was adapted for the microPET scanner. Simulations with activity concentrations from 2.62 to 20.53 MBq were calculated for the above-mentioned phantoms and for the three different sized MOBY voxel phantoms. For this analysis, reduced total counts of were simulated as no image reconstruction was performed. The GATE simulations and corresponding measurements in this study were all performed for a central position in the FOV with no radial offset. 2) Sinogram-Based Corrections: The implemented correction method aims to correct for scatter, random and cascade gamma coincidences simultaneously. Therefore prompt coincidence sinograms without randoms subtraction are used as input data. The sinograms have a size of (span of 3 and ring difference of 47) with a transaxial bin size of 0.815 mm and an axial bin size of 0.796 mm. The sinogram-based corrections are carried out in two steps with a script written in MATLAB [34] similar to the tail-fitting procedure described in [35] and the Gaussian scatter correction in [36]. This method uses the counts outside the object’s boundaries (“tails”) to estimate the scatter within the object. This is accomplished by fitting a Gaussian-shaped function to the tails. In our implementation the background is first estimated for each of the 144 profile lines in every sinogram by the mean value of 15 bins outside the object’s borders. Then this background is uniformly subtracted by this constant value for the whole profile line in order to correct for random and cascade gamma coincidences. The second step of the correction procedure involves the scatter correction which depends mainly on the density of the material and its geometrical extents. Scatter scaling factors (SSF) from GATE simulated sinograms were calculated as the integral fraction of the scattered to the total sinogram profile line within the object’s borders for each line in all sinograms of direct slices (segment zero). The SSFs are based on GATE simulations of the physical phantoms used in this study and on three equivalent MOBY mouse voxel phantom versions with different volumes (19/ 25/ 36 g) which approximate realistic small animal scans. The factors serve as template values and are used to scale the counts of each measured sinogram profile line. Then a Gaussian-shaped function is fit to the scaled profile line to approximate the scatter component within the subject’s boundaries. For the fit the knowledge of the exact phantom or animal boundary is essential if the subject being investigated is not exactly centered or especially for an animal having an irregular shape. In the usual case of low count statistics, several profile lines have to be averaged for the Gaussian-shaped fit. For these sinograms the summation cannot be carried out in a simple manner but has to take into account the potential shift of every profile line. Therefore first every sinogram is smoothed by a median filter and binarized by the mean of the central 15
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kernel depends on the isotope specific positron range and the possible artifact-free image reconstruction. The chosen set-up for the measurement of the kernel is explained in more detail in Section II-H. G. Normalization, Attenuation and Calibration Factor
Fig. 4. Sinogram of the Image Quality Phantom measured at the microPET (20.7 MBq, 60 min). Left: Original sinogram. Right: Shifted sinogram after a fit for every bin with and as the offset to the central bin.
sinogram bins. A sinusoidal fit is applied to every sinogram bin to calculate a transformation matrix for the shift of every profile line in relation to the central bin of the sinogram (Fig. 4). After the shift, every 12 profiles are averaged and a threshold of 20% of the maximum value is applied to determine the subject’s edges. These pixel coordinates are transformed back onto the original not shifted data set and the scatter correction fits can be applied to the unshifted original data set. 3) Positron-Range Corrected Image Reconstruction: One method to correct for positron range degradation effects is to convolve the estimated activity concentration in each voxel with a kernel before the projection [18]–[21]: backprojector (4)
projector with
For the microPET Focus 120 differences in detector efficiencies are corrected for by a component-based normalization method [38]. The normalization factors are stored in sinogram format from a scan with a Ge-68 cylinder phantom (Eckert & Ziegler, Valencia, CA, USA). The inverse of these factors is backprojected with STIR and used as the sensitivity image in (4). All crystals in the GATE simulations had the same efficiencies. Thus the normalization procedure for the simulated sinograms reduces to a pure geometrically-based component. The calibration factor for quantification was determined from a scan and a GATE simulation of a 20 ml Injekt syringe (B. Braun, Melsungen, Germany) for F-18 and I-124 respectively. Following the scaling method results for the mouse-sized syringe phantom discussed in [39], the reconstructions include a compensation for attenuation for objects which have comparable extents and are placed in a similar position. The scaling method assumes that attenuation in a small animal can be approximated by a homogenous cylindrical object. This assumption is made due to the small differences in densities in such a small animal. A single global scale factor is then used for the reconstructed image. In [39] the quantification accuracy with the scaling method for a mouse-sized phantom ( mm) was compared to the true activity concentration. As the syringe’s volume and diameter of 20.3 mm correspond approximately to the extents of the small rodents scanned, the calibration factors derived from the 20 ml syringe scans encompass an attenuation correction for equally sized and placed objects. The calibration factor for I-124 was determined after all scatter, random and cascade gamma corrections were applied. H. Determination of Resolution Degradation Effect
(5) where is the measured binned data and is the system matrix. The implemented Positron Range corrected Maximum Likelihood Expectation Maximization algorithm (PR-MLEM) utilizes the Ray Tracing projectors from STIR [37]. For each iteration the normalized log-likelihood function is calculated with the complete convergence criteria according to:
(6) The sinograms were corrected for randoms, cascade gammas and scatter as described in II-F2. Then these corrected sinograms were reconstructed using the PR-MLEM and the MLEM algorithm as a reference. The aim of the implemented PR-MLEM algorithm was to recover the resolution obtained with F-18. The choice of the
In order to determine the kernel for the positron-range corrected MLEM algorithm experimentally, a custom-made set-up was developed (Fig. 5). The set-up is fixed tightly to the animal bed of the microPET scanner and therefore ensures an exact and reproducible positioning of the glass capillary without an inclination. The line source has an inner diameter of 0.28 mm and was filled with I-124 and Ga-68 separately. Additionally F-18 was used to approximate the intrinsic resolution. Due to the high positron energies, the line sources were surrounded by a Plexiglas cylinder with a diameter of 25.3 mm. The set-up was moved tangentially across the field of view (FOV) from - to mm in steps of 5 mm. The measurements were repeated for different axial offsets: 0, and off the FOV and a total of 600 measurement positions for I-124 (Ga-68: 176, F-18: 137) were acquired. The images were reconstructed by the scanner implemented 3D Filtered Backprojection (3D FBP) algorithm with no additional filter applied at an image pixel size of mm . The Full Width at Half Maximum (FWHM) was determined according to the NEMA NU 4-2008 standard [27]: One-dimensional profiles were formed in parallel and orthogonal to the profile line across the peak of the
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Fig. 5. (a) Set-up for line source measurements. In position 1 the radial and tangential resolutions are measured. From position 2 the axial component is determined. (b) 3D FBP of a line source filled with I-124 demonstrating its long positron range.
image volume and summed within FWHM. The maximum value for the FWHM calculation was determined by a parabolic fit through the peak value and its two neighboring pixels. The FWHM was then calculated by linear interpolation between the two pixels which are adjacent to 50% of the maximum value. I. Image Analysis For quantification purposes, regions of interest were drawn in the uniform background area and analyzed using the ROVER software [29]. The limited number of data points in a simple profile plot complicates the calculation of resolution. To increase the amount of data points, the blurred edges of a cylindrical or spherical source are summed in polar coordinate form with the origin of the coordinate system being in the center of the source [40]. Then a function is fitted to this data. Resolution was determined according to this procedure, which is included in ROVER, for the cylindrical inserts with the largest diameter (Image Quality: 5 mm and Resolution Phantom: 3 mm).
Fig. 6. Summed projection lines for all sinograms belonging to segment 0 of a GATE simulation of the Resolution Phantom. All prompt coincidences (black) have to be corrected for randoms (R), cascade gammas (C) and scattered (S) coincidences to obtain the true coincidences solely from the two 511 keV annihilation photons (blue): (a) Prompts + all coincidences which have to be corrected. (b) cascade gammas + randoms component. (c) Total scatter contribution to prompt coincidences after subtracting the randoms and cascade gammas. (d) True coincidences solely caused by the two unscattered annihilation photons (without randoms and scatter).
TABLE I GATE SIMULATED SINOGRAMS SEPARATED ACCORDING COINCIDENCE TYPES FOR I-124
TO
DIFFERENT
III. RESULTS A. Simulation of Cascade Gammas and Scatter in GATE Summed sinogram profiles for a GATE simulation of the Resolution Phantom with I-124 are shown in Fig. 6. The Resolution Phantom was chosen here as an example as it is the one with the largest diameter and thus has the highest amount of scatter and attenuation. The total component which has to be subtracted (green profile in Fig. 6(a)) to obtain the true unscattered coincidences (Trues) coming solely from the two annihilation photons (Fig. 6(d)) is comprised of two parts: The fairly uniform part coming from the cascade gammas (C) together with the randoms (R) and the scatter (S) component. 1) Cascade Gammas and Randoms: Centered objects exhibit a nearly homogenous background elevation due to the cascade gamma and random coincidences (green profile in Fig. 6(b)) with only a slight reduction of counts in the center of the phantom due to attenuation. The green profile in Fig. 6(a) shows that all the activity found outside the object’s borders does not contribute to the true coincidences. Inside the phantom borders, this component is also fairly uniform and can be approximately assessed from the edges of the profile lines outside these borders for centered small animal sized phantoms. To
Activity A [MBq]; Total simulated counts TC [ ]; Scatter S [%]; Cascade Gammas C [%]; Randoms R [%]; Trues T [%]
perform the uniform background subtraction, a sufficient count statistics is necessary. Table I shows the contribution of the different coincidence types on a sinogram basis. Depending on the scatter contribution and the activity applied, and therefore the generated randoms, between 28% and 42% of all prompt coincidences have to be uniformly subtracted. 2) Scatter: As it is also the case for pure positron emitters, an additional inhomogenous scatter component exists within the phantom borders (green profile in Fig. 6(c)). A median scatter scaling factor SSF is used to scale the counts for each profile line within the phantom boundaries. For this simplified scatter correction method described in more detail in Section II-F2, quantifaction accuracy is increased on average to about 3% and the scatter contribution tends more to be underestimated. The higher the subject’s weight is, the more accurate the corrections are. Larger objects with dimensions comparable to the Resolution
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TABLE II CALCULATED MEAN RESOLUTION VALUES (FWHM) WITH STANDARD DEVIATION FOR THE LINE SOURCE MEASUREMENTS WITH DIFFERENT RADIAL OFFSETS
averaged FWHM from offsets -
to
mm
Resolution Phantom, the scatter can be estimated with an accuracy of 0.2% with this simplified method, while for the MOBY phantom (19 g) the accuracy is 2.7%. B. Resolution Measurements Radial, tangential and axial resolution profiles measured with fillable line sources are plotted versus the radial offset in Fig. 7 for three different isotopes. There exists a constant offset between the F-18 and I-124 profiles, while the shape for the I-124 and Ga-68 curves is almost the same. Mean resolution values (FWHM) were calculated at the center of the scanner (offset 0 mm) and at a radial offset of mm in Table II. Additionally for the FOV of interest of our imaged small animals, the resolutions for radial offsets between - and mm were averaged. From these mean resolution values in all three spatial dimensions another equivalent mean resolution was determined. The standard deviation of this value indicates, besides the uncertainty of the measurement position, the fluctuation across the FOV from - to mm for the three different isotopes: F-18: mm, I-124: mm and Ga-68: mm. Assuming that the intrinsic resolution of the scanner FWHM can be measured with F-18, the additional blurring effect FWHM which is due to I-124 FWHM , can be calculated as follows (similar to [41]):
FWHM
Fig. 7. Spatial resolution measurements with glass capillaries filled with I-124, F-18 and Ga-68. The FWHM was calculated according to the NEMA NU 4-2008 standard in all three spatial dimensions. The vertical bars indicate the FOV of interest for our scanned small animals. Error bars are shown per measurement position and are sometimes smaller than the symbols used for plotting.
Phantom possess a stronger Gaussian-shaped scatter distribution than small objects which have a flatter scatter shape. For the
FWHM
FWHM
(7)
This results in an FWHM of mm or, for the equivalent Gaussian, in a standard deviation of mm. Therefore the convolution kernel for the PR-MLEM algorithm was chosen to be a Gaussian with mm which corresponds to the size of one image pixel. This approach assumes that the resultant resolution is composed of a convolution of two Gaussians representing the intrinsic and the resolution loss due to the high positron energy isotope respectively. A comparable method was suggested in [42] where the system resolution was also derived from F-18 line source measurements, but deconvolved with an exponential positron range function which is dependent on the maximum energy and the distance from the source. This intrinsic resolution kernel was then convolved with isotope-dependent kernels calculated from this positron range function, whereas we used the measured resolution with I-124. C. Log-Likelihood Function After 75 iterations the implemented algorithm is nearly converged as the gradient of the log-likelihood is negligible small . In the following, 75 iterations were calculated as
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to with solely the randoms and cascade gammas corrections (w/ CGR). E. Resolution
Fig. 8. Log-likelihood function for the MLEM and PR-MLEM algorithm with 10 and 25 convolution iterations (iter.). Iterations 10-75 are only shown to emphasize the effect by the PR-MLEM algorithm.
this is a good trade-off between convergence and reconstruction time. For the PR-MLEM algorithm, the convolution operation was applied to the last 25 iterations (PR-MLEM, 25 iter.). Less iterations with convolution after the projection step were also used. Then the PR-MLEM was truncated after 60 iterations to have 10 convolution iterations (PR-MLEM, 10 iter.). Fig. 8 shows the effect of the convolution operations for the convergence of the log-likelihood. If some iterations with convolution are followed by iterations without convolution, the algorithm needs 5-6 iterations to reach the plateau again (PR-MLEM 51-60 iter. in Fig. 8). In the following the convolution iterations are applied at the end of the algorithm to preserve the deblurring effect. This increases the log-likelihood until it reaches a plateau again (PR-MLEM, 51-75 iter. in Fig. 8). D. Absolute Quantification Table III summarizes measured and GATE simulated activity concentrations for the Image Quality and the Attenuation Phantom. For the measured Attenuation Phantom, the three cold inserts (water, Teflon, air) were analyzed too and an accurate material-dependent attenuation correction was applied here. The relative activity concentrations given in the last part of Table III are obtained from ROIs placed over the non-radioactive inserts in relation to the phantom’s central part filled with I-124. The residual relative background activity in the inserts is between 6 to 9%. Additionally activity concentrations for the background, stomach and tumor of the GATE simulation with the MOBY mouse voxel phantom are shown. The different corrections were applied in increasing order from left to right. Without the application of any corrections, the activity concentration is overestimated by for the measurements together with the GATE simulations. Applying only the sinogram corrections (cascade gammas, randoms and scatter), the quantification improved to . The effect of the additional convolution operation is negligible small with a contribution of . Especially for larger objects scatter correction cannot be neglected. Neglecting the additional scatter correction for the measured and GATE simulated physical phantoms resulted in an absolute quantifaction accuracy of (w/ CGR). For the organs of the MOBY mouse voxel phantom, scatter correction is less important with an quantifaction accuracy of (w/ CGR S) compared
Table IV summarizes calculated image resolutions (FWHM) from measurements and GATE simulations with the Image Quality and Resolution Phantom. Applying more convolution iterations results in an increase of resolution recovery: For 10 iterations, the mean improvement for the measured (simulated) data is 12.5% (16.7%) and for 25 iterations 20.6% (23.7%). Applying the convolution operation to all 75 iterations increases the recovered resolution further to mm (for the 3 mm bore hole of the Resolution Phantom). But the image resolution comparable to that of F-18 cannot be achieved with this kernel size and without the production of any image artifacts. The more convolution iterations are applied, the lower the Signal to Noise Ratio is: For 10 convolution iterations, the SNR for the measured (simulated) Image Quality Phantom is 13.0 (5.7) and for 25 convolved iterations the SNR reduces to a value of 10.7 (4.5). For the uncorrected MLEM, the SNR is the highest: 15.7 (7.7). Fig. 9 compares reconstructions with and without the implemented corrections for I-124 with F-18. For both GATE simulated and measured data sets, the I-124 background is significantly reduced for the PR-MLEM algorithm including the sinogram-based corrections and comparable to that of F-18. Visually also the resolution and contrast is enhanced compared to the ordinary MLEM for I-124. F. Animal Studies Fig. 10 and 11 show the effect of applying the sinogram corrections and the PR-MLEM algorithm on the GATE simulated MOBY mouse voxel phantom version and on the real mice PET data. Especially the air-filled compartments in the lung and intestine become more visible and the blurring is diminished for both PR-MLEM reconstructions (Fig. 10(b),10(c)). The irregular uptake in the tumor on the right shoulder of the mouse is not clearly visible for the ordinary MLEM algorithm (Fig. 10(e)). Applying convolution iterations, the inhomogenous uptake becomes more evident (Fig. 10(f), 10(g)). Both PR-MLEM reconstructed images are comparable to the MLEM reconstruction with F-18 TFB (Fig. 10(h)) without the production of any image artifacts. When 25 convolution iterations instead of 10 are carried out, the resolution increases but also the noise in the reconstructed image. The same holds for mouse scans with a more heterogeneous uptake behavior and a higher injected activity (Fig. 11): Hot structures become more visible with only slight shifts in the activity distribution (stomach). Analyzing a total of 20 mice imaged with I-124, the CNR of the thyroid was lower for the original MLEM ( ) compared to the PR-MLEM. For 10 convolution iterations, the CNR was almost the same as for 25 iterations: compared to . The maximum contrast of the thyroid for the uncorrected MLEM was , while for the PR-MLEM with 10 convolution iterations it was . Applying 25 convolution iterations increases the maximum contrast further to . The reverse is the case for the SNR of the background. The less convolution iterations are applied, the better the SNR (10 iterations: and 25 iterations: ).
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TABLE III QUANTIFICATION OF I-124 GATE SIMULATIONS (TOP) AND MEASUREMENTS (BOTTOM) FOR PR-MLEM (25 CONVOLUTION ITERATIONS) AND MLEM (WITH AND WITHOUT SINOGRAM CORRECTIONS CORR) WITH DIFFERENCE TO SIMULATED/ APPLIED ACTIVITY. CGR-CORR: CASCADE GAMMAS + RANDOMS CORRECTIONS, CGR S-CORR: CASCADE GAMMAS + RANDOMS + SCATTER CORRECTIONS. SD: STANDARD DEVIATION OF THE RELATIVE ACTIVITY CONCENTRATION
resolution adapted values
For the uncorrected MLEM algorithm, the SNR of the background is the highest: . IV. DISCUSSION A. Quantification of Cascade Gammas and Scatter The results of the GATE simulations indicate that the effect of the cascade gammas is limited to a fairly homogeneous background elevation for centered small animal sized objects. Single photons coming from random and cascade gamma coincidences have no angular dependency as it is the case for the two 511 keV annihilation photons. Thus they carry no information about the true activity distribution. The assumption of a uniform background elevation due to cascade gammas from I-124 is in concordance with previously published work [43]–[45]. For objects with larger diameters, like the Resolution Phantom with a diameter of 57 mm, attenuation of the prompt gamma coincidences is more important and a minor dip can be observed in the center. These results are in concordance with the ones in [6] where the cascade distribution for Br-76 was found to be uniform for centered objects with diameters less than 10 cm. As the size of all our scanned animals and phantoms was well below that, the randoms together with the cascade gammas can be effectively corrected for by a uniform subtraction. This first order approximation produced also sufficient quantitative results comparable to F-18 for other isotopes with spurious coincidences [9], [10]. In [9] subtraction of a uniform background from the Y-86 sinogram profile line rendered profiles very similar to F-18. The authors stated that reconstructing these subtracted sinograms resulted in images which are comparable to F-18 concerning the
values in the inserts of an attenuation phantom. This phantom is similar to our attenuation phantom but upscaled for human imaging purposes. In [10] a slightly modified approach to cascade gamma removal of Br-76 scans was suggested which includes a linear fit between the outermost bins at the projection tails. Subtracting this background estimate improved correction accuracy comparable to F-18. The residual activity concentration in the cold structures of our attenuation phantom indicates, that our implemented corrections underestimate scatter and randoms in regions with no activity uptake. In the interpretation of the higher values for our microPET than the reported values in [43] for a human PET scanner, it has to be taken into account, that the image reconstruction differs too. While [43] used filtered backprojection, our approach was based on MLEM with the known limitation of slow convergence in cold regions. Sufficient count statistics have to be acquired in order to perform these corrections as, depending on the activity and the geometrical extents, between 28 and 42% of all counts in the sinograms have to be subtracted for usual phantoms and mouse scans. A similar analysis framework to separate the spurious coincidences with the aid of the hits information was developed for GATE simulations in [5]. The sinogram profiles shown in this work for an I-124 simulation of a thorax phantom also demonstrate the high amount of cascade gamma and scattered coincidences. Among other things, the amount and shape of the scatter component depends on the dimensions, density and composition of the material. While the scatter contribution for the larger physical phantoms cannot be neglected (between 9-16%) it is less important for real small animal scans (5%). For the MOBY mouse voxel phantom, the shape of the scatter is also
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Fig. 10. Coronal views of the MOBY phantom (2.62 MBq) simulated in GATE (a-d) and a mouse measured at the microPET (e-h) with I-124 (left 3, 1.0 MBq) and F-18/ F-18 TFB (right, 3.1 MBq). Images were thresholded to the same maximum (SUV of 7.8).
Fig. 9. Transaxial views of measurements (microPET) and GATE simulations of the Image Quality and Resolution Phantom with I-124 and F-18 reconstructed with MLEM and PR-MLEM (25 convolution iterations). Images were thresholded to have a similar gray level to compare the individual uptakes.
TABLE IV IMAGE RESOLUTION OF GATE PHANTOM SIMULATIONS AND MEASUREMENTS FOR MLEM (I-124 AND F-18) AND PR-MLEM (I-124)
Fig. 11. Coronal views of a mouse measured with I-124 (8.0 MBq). Images were thresholded to the same maximum (SUV of 3.2). (a) MLEM, I-124 (b) PR-MLEM, 10 iter., I-124 (c) PR-MLEM, 25 iter., I-124.
flatter compared to the physical phantoms which exhibit more Gaussian-shaped scatter distributions. B. PR-MLEM Resolution can be improved when convolving the estimated image with a kernel before the projection. This kernel was derived from line source measurements with F-18 and I-124 and applied for the last 10 or 25 convolution iterations during
MLEM reconstruction. For complex physical phantoms resolution improvements of around 20% are possible without the production of any image artifacts which are similar to the “salt-and-pepper” effect. The more iterations are calculated, the noisier the final image is and the stronger this effect becomes. For a single isolated line source a resolution enhancement of 46% was achieved. This demonstrates the limitations of the correction technique. Depending on the heterogeneity of the activity distribution and on the count statistics, only a few convolution iterations can be applied to avoid image artifacts. Also the more convolution iterations are applied, the lower the SNR is. The noise behavior of convolution-based algorithms, especially for higher number of iterations retrospectively for an increase in resolution recovery, was documented well in literature before [17], [46]. Additionally the higher the number of convolution iterations, the higher the maximum contrast increases. Hot structures obtain more activity while cold regions
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lose it. This can lead to shifts in activity distributions for the reconstructed images. Care must been taken to avoid these image artifacts and to choose the right amount of convolution iterations.
discretization of the kernels due to the detector size of the ring scanner. For this resolution the exact range kernel and the approximation by a Gaussian only differ significantly in the central pixel out of a total 21. For our implemented convolution-based method, this small difference in kernel shape has no impact.
C. Kernel Measurements For our implemented PR-MLEM algorithm, the necessary kernel was determined from line source measurements with F-18 and I-124 to adjust the image degradation effect similar as previously done for a clinical PET scanner [12]. Comparative GATE simulations with point and line sources and additional measurements with a Na-22 point source showed that the calculated resolution value from line source measurements is slightly worse compared to the resolution determined from point sources. The main intention of our work was the artifact-free implementation of a complete correction scheme for non-pure and high positron energy isotopes where the completeness and the practical implementation into preclinical routine work was the main focus. Therefore we chose the glass capillary measurements as it simplified the experimental procedure and different isotopes could be measured under the same circumstances with the same set-up which would have been more difficult for point source measurements. The low mean standard deviation per line source position (Fig. 7) for a total of 913 single measurements shows the reproducibility of the obtained results. For the two high positron energy isotopes, I-124 and Ga-68, similar results were obtained and their FWHM is about 70% larger compared to F-18. From the difference between F-18 and I-124, we determined one mean shift-invariant resolution kernel for our relatively small FOV of interest (- to mm). Utilizing only one kernel size instead of a shift-variant kernel results in an error of 2.6% for the radial (tangential: 6.2%, axial: 6.5%) direction for the central position of the FOV. At a radial offset of mm the errors are as follows: radially: 9.7%, tangentially: 5.2% and axially: 1.0%. For our purposes we assumed these deviations to be negligible. This is in concordance with other findings where it was stated that one shift-invariant kernel produces sufficient resolution recovery results for small animal PET imaging [16] and where there was only little improvement coming from an inhomogeneous model [17]. It is well-known that the positron range is an isotope-dependent function with an irregular shape which is not necessarily Gaussian [47]. As also shown in [13] we noticed a longer tail for the high positron energy isotopes I-124 and Ga-68 resulting in a larger Full Width at Tenth Maximum compared to the pure positron emitter F-18. In order to test our simplification of the positron range being approximated by a Gaussian-shaped function, we performed point source simulations in GATE for different materials and with the before-mentioned isotopes. Three-dimensional convolution kernels for the water-equivalent phantom simulations were formed from the one-dimensional positron range histograms and tested with our implemented PR-MLEM algorithm. Subsequent comparisons of the two different kernels for different numbers of convolution iterations showed that the results are nearly equivalent as far as absolute quantification, resolution improvement and artifact-free image reconstruction are concerned. The reason should be the
V. CONCLUSION With the aid of GATE, it was possible to implement a complete practical correction technique for the non-pure and high energy positron emitter I-124. Our approach is applied to small animal imaging where low activities and small object dimensions are used. These result in low randoms, scatter and attenuation which is in contrast to human PET imaging. The proposed method was verified by several GATE Monte Carlo simulations with phantoms and measurements at the microPET Focus 120 and could be successfully transferred to real small animal PET data. It was possible to improve the average quantitative accuracy to approximately 3% and the resolution for I-124 by approximately 20%. Our future work will focus on the verification of the proposed kernel model including the analysis of its effects on the PR-MLEM algorithm and on the verifaction of the proposed simplified scatter correction method especially for small animals. REFERENCES [1] S. Jan, D. Benoit, E. Becheva, T. Carlier, F. Cassol, P. Descourt, T. Frisson, L. Grevillot, L. Guigues, L. Maigne, C. Morel, Y. Perrot, N. Rehfeld, D. Sarrut, D. Schaart, S. Stute, U. Pietrzyk, D. Visvikis, N. Zahra, and I. Buvat, “A major enhancement of the GATE simulation platform enabling modelling of CT and radiotherapy,” Phys. Med. Biol., vol. 56, pp. 881–901, 2011. [2] L. Koehler, K. Gagnon, S. McQuarrie, and F. Wuest, “Iodine-124: A promising positron emitter for organic PET chemistry,” Molecules, vol. 15, pp. 2686–2718, 2010. [3] Nuclear Decay data in the MIRD Format [Online]. Available: http:// www.nndc.bnl.gov/mird/ [4] H. de Jong, L. Perk, G. Visser, R. Boellaard, G. van Dongen, and A. , Lammertsma, “High resolution PET imaging characteristics of and compared to ,” in Proc. IEEE Nucl. Sci. Symp. Conf. Record, 2005, pp. 1624–1627. [5] J. Beenhouwer, S. Staelens, S. Vandenberghe, J. Verhaeghe, R. Van Holen, E. Rault, and I. Lemahieu, “Physics process level discrimination of detections for GATE: Assessment of contamination in SPECT and spurious activity in PET,” Med. Phys., vol. 36, no. 4, pp. 1053–1060, 2009. [6] R. Laforest and X. Liu, “Cascade removal and microPET imaging with ,” Phys. Med. Biol., vol. 54, 2009. [7] X. Zhu and G. El Fakhri, “Monte Carlo modeling of cascade gamma PET imaging: Preliminary results,” Phys. Med. Biol., vol. rays in 54, pp. 4181–4193, 2009. [8] S. Vandenberghe, “Three-dimensional positron emission tomography and ,” Nucl. Med. Commun., vol. 27, pp. imaging with 237–245, 2006. [9] K. S. Pentlow, R. D. Finn, S. M. Larson, Y. E. Erdi, B. J. Beattie, and J. L. Humm, “Quantitative imaging of Yttrium-86 with PET: The occurrence and correction of anomalous apparent activity in high density regions,” Clin. Positron Imaging, vol. 3, no. 3, pp. 85–90, 2000. [10] M. Lubberink, H. Schneider, M. Bergström, and H. Lundqvist, “Quantitative imaging and correction for cascade gamma radiation of with 2D and 3D PET,” Phys. Med. Biol., vol. 47, pp. 3519–3534, 2002. [11] B. J. Beattie, R. D. Finn, D. J. Rowland, and K. S. Pentlow, “Quantitative imaging of bromine-76 and yttrium-86 with PET: A method for the removal of spurious activity introduced by cascade gamma rays,” Med. Phys., vol. 30, no. 9, pp. 2410–2423, Sep. 2003. [12] D. E. González Trotter, R. M. Manjeshwar, M. Doss, C. Shaller, M. K. Robinson, R. Tandon, G. P. Adams, and L. P. Adler, “Quantitation activity distributions using a clinical PET/CT of Small-Animal scanner,” J. Nucl. Med., vol. 45, no. 4, pp. 1237–1244, Jul. 2004.
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