Attenuation Correction for Small Animal PET Images: A Comparison of Two Methods

In order to extract quantitative parameters from PET images, several physical effects such as photon attenuation, scatter, and partial volume must be taken into account. The main objectives of this work were the evaluation of photon attenuation in small animals and the implementation of two attenuation correction methods based on X-rays CT and segmentation of emission images. The accuracy of the first method with respect to the beam hardening effect was investigated by using Monte Carlo simulations. Mouse- and rat-sized phantoms were acquired in order to evaluate attenuation correction in terms of counts increment and recovery of uniform activity concentration. Both methods were applied to mice and rat images acquired with several radiotracers such as18F-FDG, 11C-acetate, 68Ga-chloride, and 18F-NaF. The accuracy of the proposed methods was evaluated in heart and tumour tissues using 18F-FDG images and in liver, kidney, and spinal column tissues using 11C-acetate, 68Ga-chloride, and 18F-NaF images, respectively. In vivo results from animal studies show that, except for bone scans, differences between the proposed methods were about 10% in rats and 3% in mice. In conclusion, both methods provide equivalent results; however, the segmentation-based approach has several advantages being less time consuming and simple to implement.


Introduction
Positron emission tomography is a quantitative imaging technique, capable to provide accurate values of radiotracer concentration in each voxel of the reconstructed volume. The knowledge of radiopharmaceutical concentration is important because, combined with adequate mathematical models, it allows to evaluate several physiological parameters of interest, such as perfusion, glucose metabolic rate, and receptors density [1]. In order to obtain an accurate quantification of radiotracer concentration, several physical factors must be taken into account, such as attenuation (AC) [2], scatter [3], and partial volume correction (PVC) [4]. In this work, the attention was focused on attenuation correction for small animal PET images, which is well known to be relevant for human patients [5] but could be also significant for small animals as well. Attenuation correction has been extensively discussed in the literature for human PET and SPECT studies; however, only few papers focus on AC for small animals [6][7][8][9][10][11].
There are several methods to obtain attenuation maps that could be employed to correct PET images for attenuation. They are mainly grouped into two categories: transmission and transmissionless methods.
The first category of methods is based on the acquisition of a transmission image of the subject. The most used approaches are based on (1) transmissive image using, for example, rotating or annular 68 Ga / 68 Ge sources, (2) segmented transmissive image, and (3) X-ray CT image. Transmission scanning can be performed both in coincidence and in single mode.
A quite simple approach consists of using an annular 68 Ga / 68 Ge source surrounding the object and acquiring a transmission image in coincidence mode; however, the resulting image can be very noisy. An alternative approach is to use a rotating rod source; in this case, scatter and random coincidences decrease because only the lines of response (LORs) collinear with the rod source are accepted. The rod source is generally very active, and, thus, the detector near the source exhibits a high dead time causing an important loss of counts [13]. The same problem happens also in the case of single photon source; in order to acquire a good quality transmissive image using a fully 3D scanner, a point source with a very high radioactivity concentration must be used. This problem can be solved with use of collimated, single photon, point sources [14,15]. However, the single mode acquisition method has also several disadvantages: (1) a significant scatter component is included in the transmissive image, and (2) an energy scaling of the attenuation map is needed because of the different photon energy of the transmissive source. For example, 137 Cs emits 662 keV photons. In this case, attenuation maps can be obtained segmenting transmissive images, and the known attenuation coefficients at 511 keV are assigned to each of the segmented regions [16,17]. The last and most used category of transmission methods is based on the acquisition of CT images. Analogously to the method described before, energy scaling of the attenuation coefficients to 511 keV is needed.
Transmission methods are more accurate when estimating attenuation maps because they take into account the inhomogeneities of the object attenuation coefficients. Each of them has also several drawbacks; they are more timeconsuming, as the animal has to be anesthetized for a long time and also receives larger doses of radioactivity compared to transmissionless methods. Transmissive PET images do not suffer from coregistration problems that may introduce artifacts in the attenuation map, but they can be very noisy. In order to reduce the noise in the transmissive PET images, segmentation was introduced, but other problems linked to time and dose still remained.
Transmissionless methods are carried out with manual or automatic delineation of body edges directly on emissive image assuming a uniform distribution of attenuation coefficients inside the object [18,19], or by automatic image segmentation using a fuzzy clustering algorithm [20]. Transmissionless methods are less accurate in delineating the edges and provide a less detailed attenuation map, but they have the advantages of being less time consuming, do not increase the dose to the animal, and allow for noiseless attenuation maps. Moreover, coregistration procedure is not required, and thus the attenuation map are less sensitive to image artifacts.
In this work, two attenuation correction methods are presented: a CT-based method and a transmissionless AC method based on segmentation of PET data. We firstly estimated the magnitude of attenuation effect in small animals using mice and rat phantoms. In order to implement the Xray based method, we calibrated the small animal CT scanner and we obtained a correspondence between CT and 511 keV attenuation coefficients. In order to evaluate the accuracy of the CT-based method with respect to beam-hardening, we performed Monte Carlo simulation for rat-sized objects. As CT scan adds either acquisition time or dose to the animal, we propose a further method based on segmentation of PET images. PET data segmentation may not provide accurate attenuation maps because, depending on the radiotracer used, the body edges are not always well delineated. We acquired images using several radiotracers such as 18 F-FDG, 11 C-acetate, 68 Ga-chloride, and 18 F-NaF and evaluated the accuracy of the PET-based method with respect to CT-AC.

Methods and Materials
2.1. Photon Attenuation. As it is well known, transmission of 511 keV photons crossing matter is expressed by an exponential law formulated as follows: where Φ and Φ 0 are the transmitted and incident photon fluences, is the path of the photon through the object, and ( , ) is the linear attenuation coefficient map. The exponential term, which we refer to as , is the probability that a photon reaches the detector. In PET, events are not detected if at least one of the two annihilation photons is absorbed by the object. In this case, the number of events for each LOR is reduced. The probability that an annihilation event is recorded is given by the product of the probability of each photon reaching the detectors, as expressed by the following equation: where = 1 + 2 , is the projection angle, and is the radial position. As we can see in (2), the probability depends on the total length of the path of the two annihilation photons in the object that in PET is the object thickness along the LOR. The value of is related to the projection angle and the radial position. The equation describing the measured projections is the attenuated Radon transform, formulated as follows: where ( , ) are the projection data at angle and bin , ( , ) is a function representing the original activity concentration image, ( , ) is the attenuation coefficient map, and ( , ) represents the LOR.

Systems Descriptions.
PET images were acquired with the eXplore Vista preclinical PET tomograph (General Electric) [21]. The scanner allows to acquire PET images using three different energy windows (100-700, 250-700, and 400-700 keV). For our purposes, all images were acquired using the 400-700 keV energy window. The scanner detector system consists of 36 detector blocks, arranged in two rings of 11.8 mm diameter. Each block is a 13 × 13 array of 1.45 mm square phoswich crystals: a Lutetium Yttrium Orthosilicate (LYSO) crystal of 7 mm depth optically coupled to an 8 mm depth crystal of Gadolinium Orthosilicate (GSO). This design allows to obtain depth of interaction information [22]. The transverse and axial field of view (FOV) are equal to 6.9 cm and 4.6 cm, respectively. No corrections for randoms and scatter were performed in this study. All the images were  reconstructed using 2D-OSEM algorithm [23] after Fourier rebinning (FORE) [24]. CT images were acquired using the eXplore Locus small animal CT tomography (General Electric). The tube voltage was 80 kV and the current was 450 A. The system is characterized by a fixed anode with a Tungsten target source. The X-ray detector is a CCD array coupled to a Cesium Iodide (CsI) scintillation crystal. The scanner allows to acquire and to reconstruct images with different pixel binning and, thus, with different resolution levels (27-93 m). The transaxial FOV dimension is equal to 8 cm for acquisition at 93 m resolution. The axial FOV is the same for all acquisition protocols, and it is equal to 4.5 cm. For our purposes, all images were acquired using a 93 m resolution. Image reconstruction was performed with the Feldkamp cone beam algorithm [25].

Attenuation Correction Methods.
All the images acquired with the eXplore Vista were attenuation-corrected using the CT and SE methods as described later. The schematic diagrams of CT-AC and SE-AC methods are showed in Figures 1 and 2.

CT-AC Method.
The CT AC method is based on a conversion between HU and the corresponding linear attenuation coefficients at 511 keV. CT images are useful because they provide detailed attenuation coefficients maps. The most important problem when using CT images is the beam hardening effect. In order to investigate the accuracy of the CT AC method, we used PeneloPET, a Monte Carlo code for PET simulations based on PENELOPE [27]. The geometry and composition of both rat-phantoms and eXplore Vista scanner were implemented to match those employed in the real acquisitions. We chose to simulate only the rat-phantom because the beam hardening effect is more important in this case than in mouse-sized objects. The CT-based attenuation corrected image was compared with images simulated without attenuation material. On both images, line profiles and region of interest (ROI) analysis  [26]. CT-AC was implemented using Matlab, and more precisely, PET and the calibrated attenuation map images were forward projected in order to perform attenuation correction according to the attenuated Radon transform (see (3)).
A CT image of each cylinder was acquired and a small (ROI) was drawn on the image in order to calculate the mean value of HU. The attenuation coefficients at 511 keV were plotted with respect to the measured HU, and a quadratic fit to the data was performed.

Segmentation of Emission Image AC Method.
Segmentation of emission image by a global threshold was performed by means of a Matlab code, in order to obtain a 2-level image, corresponding to air and soft tissues. For PET images of phantoms, the contours are always clear, and, thus, the segmentation is quite easy to perform. In animal PET images, the detection of body edges depends on the biodistribution of the radiotracer injected. To assess applicability of the SE method, PET images with different radiotracers were acquired.

Phantom Data.
In order to evaluate the effect of photon attenuation in PET images and the accuracy of the attenuation correction methods described in previous section, several phantoms studies were acquired. Two cylindrical phantoms with different diameters were filled with different concentration of [ 18 F]-fluorodeoxyglucose ( 18 F-FDG) and scanned in both PET and CT modality: (i) a mouse-sized phantom, filled with uniform activity concentration; (ii) a rat-sized phantom, filled with uniform activity concentration; (iii) a rat-sized phantom with a hot sphere inside (sphere to background ratio equal to 4).
Computational and Mathematical Methods in Medicine 5 A syringe of 30 mm diameter filled to 30 cc was used as mouse-sized phantom, while a cylindrical phantom with diameter of 50 mm and length of 80 mm was used as ratsized phantom. The mouse-and rat-sized phantoms were filled with a solution of 18 F-FDG with activity concentrations of about 1 MBq/cc and 0.5 MBq/cc, respectively. Several zeolites soaked with a small amount of 18 F-FDG (about 5 MBq/cc) were fixed around the two phantoms in order to use them as fiducial marks in the coregistration procedure [28]. For each phantom, a 20-minute PET scan and a 6minute CT acquisition were performed. In order to align PET and CT, the two images were coregistered using rigid body transformation implemented in AMIDE [29].
In order to measure the improvement obtained with AC, line profiles and ROI analysis were performed. The recovery values RV for each AC method were calculated with the following equations: where ROI NC , ROI AC-CT , and ROI AC-SE are the mean values in a ROI drawn on the uncorrected image, on the AC-CT, and on the AC-SE image, respectively. In order to evaluate the shape recovery, we calculated also the flatness of the profile (i.e., the relative difference in the number of counts between the edges and the centre of an uniform phantom) with the following formula: where max is the maximum and min is the minimum of the count profile. The rat-sized phantom with a hot sphere was used to simulate a PET image of a hot lesion. The recovery values RV in the sphere for each AC method were evaluated.

Animal Data.
In order to test the attenuation correction methods and particularly the SE-AC on animal images, PET and CT scans of mice and rats were performed using different radiotracers, being all animals studies approved by the Ethical Committee of our institution: (i) 1 rat and 2 mice were injected with 18 F-FDG (an oncological and a cardiac study); (ii) 3 further rats were injected with 18 F-NaF, 11 Cacetate, and 68 Ga-chloride.
All animals were anesthetized with 3%-5% of sevoflurane and 1 l/min of oxygen and were injected intravenously in the tail with activity of about 30 and 50 MBq, respectively. PET acquisitions of 20 minutes were performed after an uptake time depending on the radiotracer. The uptake was of about one hour for 18 F-FDG and 18 F-NaF studies, and about 30 minutes for 68 Ga-chloride acquisitions. The 11 C-acetate images were acquired immediately after the injection. A CT scan of 6 minutes was then performed for each animal after PET acquisition. PET and CT images were coregistered in order to perform AC. The segmentation process was applied on each PET image, and the SE-AC method was tested on animals studied with different radiopharmaceuticals. In order to compare the two methods, CT-AC was performed for each image as well. We analyzed all the images performing profiles across an axial slice of a particular anatomical region related to the radiotracer used and calculating the mean value in the anatomical ROI. Thus, we calculated the recovery values according to (4) and evaluated the segmentation-based AC method on heart, spinal column, liver, and kidneys using 18 F-FDG, 18 F-NaF, 11 C-acetate, and 68 Ga-chloride, respectively.

CT Images Calibration.
In this section the results of CT images calibration are presented. The calibration function ( Figure 3) is given by the following equation: where is the attenuation coefficient at 511 keV, HU is the CT number measured from the image, and the fit coefficients are 1 = −2.05 ⋅ 10 −8 cm −1 , 2 = 9.66 ⋅ 10 −5 cm −1 , and 3 = 0.12 cm −1 . The correlation coefficient 2 was equal to 0.993.

Evaluation of CT-Based Attenuation Map by Monte Carlo
Simulation. In this section, axial slices of real and simulated PET images, before and after CT-AC correction, are shown. More precisely, Figure 4 shows a transaxial slice of original PET and CT-AC images of the rat-sized phantom. Profiles traced across them are shown in Figure 6. They show a count increment of about 40%, and the flatnesses calculated according to (5) for corrected and uncorrected images are about 1% and 22%, respectively. Figure 5 shows an axial slice of simulated PET images with and without attenuation. Profiles traced across the simulated images (see Figure 7) show an increment of counts and a shape recovery. In this case, the flatness of the profile across the uncorrected image is equal to 23%, and the counts increment without attenuation is also of the order of 40%. Then, the simulations predict the same behaviour with regard to attenuation as seen with the CT-AC procedure, thus validating the CT-AC method. Figures 8 and 9 show profiles traced across the center of a transaxial slice of pre-and postcorrected images of the mouse-sized phantom filled with uniform activity concentration. As one can see, there is a significant improvement of image uniformity after AC. In particular, the profiles show the increment of coincidences and shape recovery. Table 2 summarized the counts measured in a ROI at the center of the slice and the flatness of the profile for the original PET, CT-AC, and SE-AC images for both phantom studies.

Phantom Studies.
The values of the RV obtained from (4) show for both mouse-and rat-sized phantoms a significant count recovery. The differences between CT-based and SE-based AC RV are less than 2% and 3% for mouse and rat phantoms, respectively. Profiles traced across the images and flatness values show an improvement between pre-and postcorrected images. In rat-sized phantom, we observe the typical cupping artifact. After AC, the cupping disappears and count recovery is evident. As explained in the previous section, acquisition of a rat phantom including a hot sphere was performed. Figure 10 shows profiles across the hot sphere. The recovery of counts (calculated using (4)) in the hot sphere with respect to the original image for CT-AC, and SE-AC methods is showed in Table 2. The difference between the two methods is about 7%.  radiotracers are presented. Figure 11 shows an example of CT image, segmented PET image, and the overlay between them.  Figure 12 shows the profile across the mouse tumour. The peak on the right side of the profile is relative to the tumour. As one can see, the recovery of counts for both AC images is significant. Table 3 shows counts measured in an ROI inside the tumour. The same analysis was performed on cardiac PET image of a mouse in order to verify the performance of SE-AC method in the quantification of tracer uptake in the myocardium and in the left ventricle. Figure 13 shows the profile traced across the mouse heart. The two peaks in both AC images are well recovered, and, furthermore, they are very similar. More precisely, in Table 4, we show the average Table 2: Average number of counts and recovery value measured on uniformly filled mouse and rat phantom images and in the hot sphere of a rat-sized phantom. For the uniformly filled phantoms, also the flatness is showed.   value of counts in the myocardium and left ventricle for the three images and the relative recovery value for the two AC methods calculated with (4). The differences between RV obtained from the two methods are less than 3%. In order to evaluate the effect of attenuation on cardiac rat images, the same analysis on the myocardium and in the left ventricle was performed on cardiac 18 F-FDG PET image of a rat. Figure 14 illustrates the profiles traced across the rat heart. In Table 5, the mean value of counts on the uncorrected and corrected images and the relative RV are shown. The differences between the SE-AC and CT-AC methods are less than 9%. As discussed in Section 2.3.2, when using 18 F-FDG, it is possible to see clearly the animal edges and, thus, to   perform the segmentation of the PET image to obtain the attenuation map.

Roi counts (cps) RV (%) Flatness
In order to investigate the use of the SE-AC method with other radiopharmaceuticals, we evaluated the performance of the AC methods also on 11 C-acetate, 68 Ga-chloride, and 18 F-NaF images. For each of the these radiopharmaceuticals, a table and line profile plots are shown. Table 6 shows the average value of counts calculated using an ROI drawn inside the rat liver on 11 C-acetate image and the relative RV obtained with the two AC methods. The difference between the two methods is around 11%. Figure 15 shows the profiles  drawn across the rat liver on 11 C-acetate image. The SE-AC method provides good results also for 11 C-acetate images. Figure 16 and Table 7 show the results of the two AC methods for a 68 Ga-chloride image. Note that the profiles traced across the two AC images are very similar; the difference of RV between the two AC methods is approximately 7%. Segmentation of 18 F-NaF image to create the attenuation map is more difficult to obtain. The difference between the RV calculated for both CT-AC and SE-AC methods amounts to  20%. Profiles are shown in Figure 17, and results are shown in Table 8.

Discussion
In order to achieve accurate estimates of radiotracer concentration, corrections for attenuation, scatter, and partial volume effects are necessary. Our main objectives were to assess the importance of attenuation in small animal PET images. On average, our results showed that the count recovery after attenuation correction with respect to uncorrected images is about 20% (40%) for mice (rats) images. Two AC methods were evaluated, namely, a CT-based and a segmentedemission-image-based AC. Similar results were also obtained by El Ali and colleagues [30]. In their work, they evaluated attenuation correction in small animals showing an underestimation of true activity concentration of about 10%-20%. They also showed that PETbased and CT-based methods provide comparable results for attenuation compensation in PET while uniform AC method may be applied only if less accuracy is acceptable.
In our study, we acquired several phantoms, mice, and rats images. We also tested the SE-AC on images acquired using several radiotracers such as 18 F-FDG, 18 F-NaF, 11 Cacetate, and 68 Ga-chloride. In order to implement the CT-AC method, we performed a calibration of GE eXplore Locus CT system to convert CT numbers to attenuation coefficients at 511 keV. Therefore, we were able to create attenuation maps at the correct energy. As the X-ray beam of the CT system employed is polyenergetic, the beam-hardening effect could lead to artifacts influencing the quality of the CT image and consequently the accuracy of the attenuation map. For this reason, we performed Monte Carlo simulation in order to evaluate the difference between CT-AC and MC simulations. The difference between the flatness of true CT-AC PET image and AC simulated image is about 3% showing that beam hardening effects have a negligible influence in CT-AC.
In order to test both AC methods, we acquired several phantoms. A mouse-sized phantom filled with uniform activity concentration was acquired to quantify the importance of attenuation effects and to measure the shape recovery. We acquired also a rat-sized phantom uniformly filled with 18 F-FDG, and we observed a significant improvement in the flatness value. The differences between the SE-AC and CT-AC methods were less than 3% for the count recovery and less than 2% for the flatness value.
In order to quantify the recovery of counts after AC on the myocardium and left ventricle, we acquired both mouse and rat images using 18 F-FDG. Results showed that the SE-AC method leads to difference in count recovery of about 3% and 10% to the CT-AC method for mouse and rat, respectively. We evaluated also the recovery of counts in a mammary tumour in a mouse showing a difference of RV with respect to CT AC method of about 1.5%. The accuracy of the SE-AC method was also evaluated on rat images acquired with 11 C-acetate, 68 Ga-chloride, and 18 F-NaF. The difference between RVCT and RVSE measured in liver on 11 C-acetate image is approximately 11%. The ROI analysis performed on 68 Ga-chloride image on the kidneys leads to a difference of about 7% between CT-AC and CT-AC. ROI analysis on spinal column of 18 F-NaF images showed a difference in RV of about 20%. This slightly higher difference between CT-AC and SE-AC when using 18 F-NaF images is due to more difficulties in contour delineation during the segmentation procedure and also to the error one makes when assigning to bone tissues as seen in 18 F-NaF scans the attenuation coefficient of soft tissues. In vivo studies showed that the RV values obtained by using SE-AC are systematically lower than CT-AC ones, except in tumour mouse study where the RV values are quite similar for both AC methods.

Conclusions
The main goal of the paper was to show that SE-AC provides comparable results with respect to the more complex and time-consuming CT-AC method. We proved this for several radiotracers used in preclinical imaging such as 18 F-FDG, 11 C-acetate, 68 Ga-chloride, and 18 F-NaF. The SE-AC method has, however, some limitations and will probably fail when a very specific tracer is used. In this case, CT-AC method must be applied.
As expected, AC is more important for rat than for mouse images. For all the studies performed on animals, we observe a difference of RV between CT-AC and SE-AC method of less than 10%, except for 18 F-NaF images where the deviation is 20%. In all cases, RV estimated from SE-AC is smaller than the one estimated from CT-AC. Overall, we can conclude that the SE-AC method provides good quantitative estimates of count recovery, comparable to the ones obtained from CT-AC. This is important considering the advantages of the SE-AC: (1) it requires less time with respect to the standard method based on CT images, because the CT image acquisition and, consequently, the coregistration procedure are not needed; (2) it does not add dose to the animal, and this is very important when repeated studies are needed; (3) it can be used also when a small animal CT scanner is not available.

Disclosure
The authors disclose that they have no direct financial relation with any commercial identity mentioned in the paper.