Dual energy CT for attenuation correction with PET/CT

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1 Dual energy CT for attenuation correction with PET/CT Ting Xia Department of Bioengineering, University of Washington, Seattle, Washington Adam M. Alessio Department of Radiology, University of Washington, Seattle, Washington Paul E. Kinahan a) Departments of Radiology and Bioengineering, University of Washington, Seattle, Washington (Received 8 May 2012; revised 15 October 2013; accepted for publication 15 October 2013; published 4 December 2013) Purpose: The authors evaluate the energy dependent noise and bias properties of monoenergetic images synthesized from dual-energy CT (DECT) acquisitions. These monoenergetic images can be used to estimate attenuation coefficients at energies suitable for positron emission tomography (PET) and single-photon emission computed tomography (SPECT) imaging. This is becoming more relevant with the increased use of quantitative imaging by PET/CT and SPECT/CT scanners. There are, however, potential variations in the noise and bias of synthesized monoenergetic images as a function of energy. Methods: The authors used analytic approximations and simulations to estimate the noise and bias of synthesized monoenergetic images of water-filled cylinders with different shapes and the NURBSbased cardiac-torso (NCAT) phantom from 40 to 520 kev, the range of SPECT and PET energies. The dual-kvp spectra were based on the GE Lightspeed VCT scanner at 80 and 140 kvp with added filtration of 0.5 mm Cu. The authors evaluated strategies of noise suppression with sinogram smoothing and dose minimization with reduction of tube currents at the two kvp settings. The authors compared the impact of DECT-based attenuation correction with single-kvp CT-based attenuation correction on PET quantitation for the NCAT phantom for soft tissue and high-z materials of bone and iodine contrast enhancement. Results: Both analytic calculations and simulations displayed the expected minimum noise value for asynthesizedmonoenergeticimageatanenergybetweenthemeanenergiesofthetwospectra.in addition the authors found that the normalized coefficient of variation in the synthesized attenuation map increased with energy but reached a plateau near 160 kev, and then remained constant with increasing energy up to 511 kev and beyond. The bias was minimal, as the linear attenuation coefficients of the synthesized monoenergetic images were within 2.4% of the known true values across the entire energy range. Compared with no sinogram smoothing, sinogram smoothing can dramatically reduce noise in the DECT-derived attenuation map. Through appropriate selection of tube currents for high and low kvp scans, DECT can deliver roughly the same amount of radiation dose as that of asinglekvpctscan,butcouldbeusedforpetattenuationcorrectionwithreducedbiasincontrast agent regions by a factor of 2.6 and slightly reduced RMSE for the total image. Conclusions: When DECT is used for attenuation correction at higher energies, there is a noise amplification that is dependent on the energy of the synthesized monoenergetic image of linear attenuation coefficients. Sinogram smoothing reduces the noise amplification in DECT-derived attenuation maps without increasing bias. With an appropriate selection of CT techniques, a DECT scan with the same radiation dose as a single CT scan can result in a PET image with improved quantitative accuracy American Association of Physicists in Medicine. [ Key words: dual energy CT, PET/CT, attenuation correction, noise and bias 1. INTRODUCTION Quantitative imaging by positron emission tomography (PET) and single-photon emission computed tomography (SPECT) is receiving increased attention for clinical applications. 1 5 In quantitative PET and SPECT, correction for the effect of photon attenuation is of paramount importance. 6 The x- ray computed tomography (CT) component in a PET/CT or SPECT/CT system not only provides precise anatomical localization of regions identified on the tracer uptake images, but is also used for attenuation correction of the PET or SPECT emission data At the energies of x-ray CT, attenuation is due to Compton scatter and photoelectric absorption, while at SPECT energies, and particularly PET energies, Compton scatter is the dominant process for biological materials. A list of energies of interest are given in Table I, and Fig. 1 plots the mass attenuation coefficients of common materials over the energy ranges relevant to PET/CT and SPECT/CT imaging Med. Phys. 41 (1), January /2014/41(1)/012501/11/$ Am. Assoc. Phys. Med

2 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT TABLE I. Photon energies of common isotopes used in PET/CT and SPECT/CT Imaging. Mode Isotope Energy (kev) PET All (i.e. F-18, C-11, N-13, etc.) 511 SPECT Xe SPECT Tc-99m 140 SPECT I SPECT Ga , 93, 300 SPECT In , 245 CT-based attenuation correction offers several benefits over transmission scanning with an isotope at or near the energy of the nuclear tracer isotope. 9 CT scans are substantially faster than lengthy nuclear transmission scans and can provide attenuation correction factors that are orders of magnitude lower in noise. Moreover, CT scans contain no bias from the emission contamination present in postinjection imaging. 9 CT attenuation correction factors are, however, susceptible to bias due to the need to transform the polyenergetic CT image to attenuation correction factors at the nuclear isotope energy, typically either at 140 or 511 kev. Three potential solutions are employed for transforming attenuation maps from CT energies to SPECT and PET energies: 9 segmentation, linear scaling, and multilinear scaling. Segmentation methods can be used to separate the CT image into regions corresponding to different tissue types, which then are replaced with appropriate attenuation coefficients at the appropriate energy. This method has a potential source of error due to tissue misclassification and the assumption of uniform attenuation throughout a region. 11 Asecondmethoduseslinearscalingof the entire CT image with the ratio of attenuation coefficients of water (representing soft tissues) at the photon energies of CT and the target energy, offering a simple solution for the transformation. 7 For bone, however, linear scaling is a poor approximation, since the photoelectric absorption to Compton scatter ratio changes differently for bone compared to soft tissue across the range of energies of interest. 7 Finally, the most common method for transforming to SPECT or PET energies is Multilinear/Hybrid Scaling In these methods, different scaling factors (for water and air and for water and bone, respectively) are used to calculate the attenuation values for CT numbers H for which 1000 < H < 0, and for H > 0. In practice, the multilinear scaling method and other hybrid methods have been shown to give reasonable results for low-z biological materials. However, high-z materials, such as contrast agents, can introduce significant 9, bias. Dual energy (It is more accurate to use the term dualkvp CT, since each CT acquisition is polyenergetic, not monoenergetic. However, the term dual-energy CT is already in wide use.) CT (DECT) is an accepted method to estimate material properties using either photoelectric and Compton components 17 or physical basis materials such as plastic and aluminum. 18 DECT has been proposed to remove the bias from the CT attenuation correction for SPECT (Refs. 19 and 20)andPET. 9, 20 AchallengewiththeuseofDECTisthe significant noise amplification due to the poorly conditioned inverse problem of estimating the component sinograms, 21 leading to excessive noise amplification. It has already been shown in the literature that the noise amplification is energy dependent in the diagnostic CT energy range, 17, 22, 23 but the noise and bias at SPECT or PET energies are largely unknown. Another potential drawback of dual energy is the additional patient radiation dose required to acquire two separate energies and/or to reduce noise. To address these issues with DECT-based attenuation correction we have previously investigated alternate methods using iterative CT reconstruction 24 and image-based strategies. 25 In this study, we aim to (1) evaluate the energy dependent noise properties of monoenergetic images synthesized from dual-energy CT in the energy range appropriate for nuclear imaging ( kev) and (2) minimize noise and radiation dose in DECT-based attenuation correction. FIG. 1. Mass attenuation coefficient as a function of energy for different materials. 2. MATERIALS AND METHODS We used three approaches to study the noise and bias properties of using DECT for PET attenuation correction as a function of energy: analytical approximations to directly calculate sinogram noise, simulations of cylindrical water phantoms to measure sinogram noise, and simulations of cylindrical water phantoms and the NCAT phantom to measure noise and bias in the reconstructed PET images. In Sec. 2.A,wedescribe the theoretical prediction that uses an approximate analytical method. In Sec. 2.B, we outline the simulation tools. In Sec. 2.C, wemeasuretheenergydependentnoiseofthe DECT derived monoenergetic sinograms and corresponding reconstructed images for two different size water phantoms. Asimplenoisesuppressionanddoseminimizationstrategyis proposed in Sec. 2.D. In Sec. 2.E, we evaluate the impact of DECT-based attenuation correction on PET image quantitation with the NCAT phantom.

3 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT A. Theoretical prediction We first used analytic approximations to estimate the variance of the synthesized monoenergetic sinogram. This approach was based on the work of Doost-Hoseini and others, 18, 22, 23 where the variance of an entry in the monoenergetic sinogram is approximated by 2 (f a (E m )k 2b f b (E m )k 2a ) 2 σ1 σm 2 = I1 2 + (f a (E m )k 1b f b (E m )k 1a ) 2 σ 2 2 I2 2, (1) (k 1a k 2b k 1b k 2a ) 2 where I 1 and I 2 are entries in the measured signals for the two kvp scans, σ 2 1 and σ 2 2 are the variances for the two kvp scans, f a (E) and f b (E) are attenuation coefficients of the basis materials at energy E, E m is the target energy, k ia = (1 / I i )( I i / A a )isthevariationofmeasuredsignalintensity with basis material, and A a is the line integral through the basis material a. Itwasshownthatσ m reached its minimum at an optimum target energy E opt,whichwasafunction of object thickness. 23 We used Eq. (1) to estimate the energydependent coefficient of variation (COV) for an object at the monoenergetic target energy Em as COV Em = σ m µ m, (2) where σ m is the noise of the object and µ m is the linear attenuation coefficient of the object at energy E m.wecalculated the normalized COV Em for the target energy E m ranging from 10 to 525 kev with 1 kev increments, where the normalized COV Em was the COV Em divided by the minimum value of COV at the optimal energy. We note that the derivation of Eq. (1) used a first order Taylor approximation and assumed monoenergetic x-rays, 23 thus not accounting for beam-hardening effects. In order to confirm this analytic relationship, we used polyenergetic simulations to estimate the noise of the synthesized monoenergetic data, σ m,overthesameenergyrangeof10 525keV. 2.B. Simulation tools 2.B.1. CT and PET simulators We used the Computer Assisted Tomography SIMulator (CATSIM) for simulation of the x-ray CT imaging. 26 It includes a Monte Carlo-based simulation package called CATDOSE for estimation of the CT radiation dose. Both CATSIM and CATDOSE have been validated relative to GE Lightspeed Volumetric Computed Tomography (Lightspeed VCT, General Electric Medical Systems, Waukesha, WI) measurements for a series of test objects. 26 The CT simulation models the effects of the x-ray source focal spot, polychromatic tube spectra, beam conditioning, bowtie filter, and beam hardening. Although fully described in Ref. 26,we provide a brief summary here of the properties modeled by CAT- SIM. CT raw data y i at sinogram index, i, are formed from the combination of a quantum noise process p i and electronic noise process z i,i.e.,y i = p i + z i,followingmethods described by De Man et al., 27 similar to the methods described by others. 28, 29 The quantum noise is modeled as [ ] p i = E k x ik f C, (3) k where E refers to photon energy, k is the energy bin index, f C is a factor to convert from kev to the number of electrons, and x ik is a Poisson random process with mean λ ik, x ik P(λ ik ), where λ ik = η N ik ( 1 S exp ) l iso µ ok + y ik (4) s o and η is the detector quantum efficiency (fraction of photons absorbed), N ik is the number of photons arriving at the detector without attenuation for energy bin k, s is the tube-ofresponse subsampling index for the total of S subsamples (where the tube-of-response between the source and detector is subsampled to better model the finite beam width), l iso is the intersection length between the line with index is and the object element with index o, µ ok is the linear attenuation coefficient of object at o at energy k, andy ik is the estimated scatter at sinogram index i with energy index k. The electronic noise z i is modeled as a Gaussian random process, z i N(d,σ 2 e ), where d is the dark current, and σ e is the standard deviation of the electronic noise. The PET images were simulated using a simplified version of ASIM, 30 which included the physical effects of attenuation, background noise, and photon counting. The noisy prompt coincidences p follow a Poisson pseudorandom process with mean m, ( p P (m)), defined as m = α t t + α b b, (5) where t represents the true coincidences, b is the background noise including scattered and random coincidences, and α t and α b are global scale factors for true coincidences and background noise. 2.B.2. Test objects Three test phantoms were simulated. The first was a 10 cm diameter and 10 cm long water cylinder. The second was a uniform cm elliptical water cylinder, with a 10 cm axial dimension. The third was derived from the NURBS-based cardiac-torso (NCAT) phantom. 31, 32 The NCAT phantom had three regions with focal FDG uptake: A 1.6-cm-diameter bone lesion, a 3-cm-diameter contrast enhanced liver lesion, and a

4 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT cm-diameter soft tissue lesion. In terms of mass percentage, the iodine contrast is 1% in blood, and equivalent to 10.6 mg/ml in our simulation. The PET activity distribution was set to tracer uptake ratios of (background: liver: lung: lesion) = (1:3:0.5:6). The parameters α t and α b in Eq. (5) were chosen to match total typical clinical counts ( )inthe sinogram with a scatter fraction of 30%. The two water phantoms allowed evaluation of energy dependent noise and bias in the DECT derived attenuation map for uniform soft tissues. The rotational symmetry of the first 10 cm diameter water cylinder allowed evaluation of variance in the central projection bin of the synthesized monoenergetic sinograms, which assumed that noise is uncorrelated across view angles. The second elliptical water phantom invoked slightly more realistic beam hardening effects and allowed evaluation of energy dependent noise and bias in the DECT derived attenuation maps. The elliptical phantom was also used for dose estimation and optimization in a torsolike object. The NCAT phantom was used for a more realistic study of the quantitative accuracy of the estimated PET tracer uptake with selected combinations of DECT acquisition parameters for comparison to single-kvp CT-based attenuation correction with similar radiation dose levels. 2.B.3. Dual-energy basis material decomposition We used the basis material decomposition (BMD) technique, 18, 33 with basis materials of aluminum and plastic (polyethylene). For calibration we followed the procedure of Chuang et al. 33 and defined polyethylene (Pl, ρ = 0.93 g/cm 3 ) and aluminum (Al, ρ = 2.72 g/cm 3 )stepwedgephantoms. 34 The calibration and measurement procedures were as follows: Calibration: 1. Define step wedges made of aluminum and plastic for calibration (Al: 0 8 steps, 4 mm/step; Plastic: 0 17 steps, 12.5 mm/step). 2. Generate sinograms from high and low kvp scans for the step wedges. 3. Calculate In(I 0 /I) foreachcombinationofaluminum and plastic steps. 4. Generate calibration coefficients {d i }, {e j } for each material: A α = d 0 + d 1 T H + d 2 T L + d 3 T H T L + d 4 T 2 H + d 5T 2 L + d 6 (T H T L ) 2 + d 7 T 3 H + d 8T 3 L, (6) A β = e 0 + e 1 T H + e 2 T L + e 3 T H T L + e 4 T 2 H + e 5T 2 L + e 6 (T H T L ) 2 e 7 T 3 H + e 8T 3 L, (7) where A α and A β correspond to the thicknesses of the two materials, with units of cm, and T H = In(I 0 /I) H and T L = In(I 0 /I) L are for the high (H) and low (L) kvp scans. Measurement: 5. Generate high and low kvp sinogram data for the test object at the given settings (mas). 6. Using the generated coefficients {d i }, {e j }, obtain basis material sinograms of A α and A β for the test object according to Eqs. (6) and (7). 7. Obtain the basis material attenuation sinograms at desired energy E, usingknownattenuationvaluesversus E for each material: µ α (E) ds = A α µ α (E), (8) µ β (E) ds = A β µ β (E). (9) 8. Sum the attenuation sinograms of each material to obtain the total attenuation sinogram of the test object at the desired energy E. µ test (E) ds = µ α (E) ds + µ β (E) ds. (10) 9. Reconstruct attenuation maps at desired energy E. 2.C. Evaluation of energy-dependent noise and bias In this subsection, we evaluated energy-dependent noise and bias on the dual energy CT derived monoenergetic sinograms and corresponding reconstructed attenuation maps using simple cylindrical and elliptical water phantoms. We simulated CT step-and-shoot mode with a gantry rotation time of 0.5 s. The dual-energy spectra were based on the GE Lightspeed VCT scanner at 80 and 140 kvp, with added 0.5 mm copper filtration following the bowtie filter. Multiple x-ray tube currents were simulated at [64, 91, 110, 128, 181, 256, 362, 512, 724, and 1024] ma for each kvp scan. Synthesized monoenergetic data and images were formed at [50, 60, 70, 80, 90, 100, 140, 171, 185, 245, and 511] kev covering the range of photon energies for SPECT and PET imaging listed in Table I. TheCTsinogramwas888channels 984 views. Default ideal kernel filter and water-only beam hardening correction in CATSIM package were applied. The CT slice thickness was mm, comparable with the PET slice thickness (for studies in Sec. 2.E). All DECT-derived attenuation maps were reconstructed to the size of pixels using filtered back projection (FBP) over a 50 cm field of view (FOV) to match PET image dimensions. We estimated the COV according to Eq. (2) in the sinogram for the 10 cm diameter cylinder by estimating the mean attenuation and the standard deviation for the central sinogram bin across view angles. We also estimated the COV in the image domain using Eq. (2) as follows: For the 10 cm diameter water cylinder, a centered 2D region of interest (ROI) with diameter of 6 cm was used for analysis. For the cm elliptical water cylinder, a total of 18 nonoverlapping 2D ROIs, each with radius of 2 cm, were drawn on the cross-section of the phantom as shown in Fig. 2.TheaveragedmeanandCOVfor all ROIs were calculated. The bias was calculated as the difference between the average of the mean pixel value over all ROIs and the true attenuation value of water.

5 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT E. Comparison of PET attenuation correction with dual- and single kvp-derived attenuation map To study the impact of DECT-based attenuation correction on PET quantitation, we used the NCAT phantom with iodinebased contrast agent to compare both DECT and single kvp CT attenuation corrected PET images. FIG. 2. Elliptical cylindrical phantom with cm cross-section, 18 2D ROIs each with radius of 2 cm were drawn for evaluation. 2.D. DECT noise suppression and dose minimization for attenuation correction We then evaluated the effects of noise suppression and dose minimization on the DECT derived attenuation data, again using the elliptical water cylinder. To further reduce DECT noise, the high and low kvp CT sinograms of the elliptical water cylinder acquired with the tube current of 64, 91, 110, 128, 181, 256, 362, 512, 724, and 1024 ma for each kvp scan were filtered by 2D 5 5 boxcar smoothing, followed by an adaptive trimmed mean filter (ATM) before logarithmic conversion. Then, with basis material decomposition method and image reconstruction similar to the procedure performed in Sec. 2.C, we generated the sinogram smoothed DECT-derived attenuation map for each synthesized energy of 50, 60, 70, 80, 90, 100, 140, 171, 185, 245, and 511 kev. For each synthesized energy, we evaluated the COV in the reconstructed attenuation map as a function of tube currents for high and low kvp scans. With the simulation package CATDOSE, we estimated the total radiation dose for each combination of tube currents at high and low kvp scans for the cm elliptical water cylinder. Comparing the dose distribution and COV distribution as a function of tube currents for the two kvp CT scans, we were able to estimate the parameters for the DECT acquisition for attenuation correction with the minimum radiation dose. This was equivalent to estimating the parameters for the DECT acquisition for attenuation correction with the minimum COV for the given radiation dose. For comparison, a single kvp CT scan of the cm elliptical water cylinder was obtained. The CT technique was selected to be comparable to clinical low dose CTAC protocol 38 with a tube voltage of 120 kvp, tube current of 100 ma, and gantry rotation time of 0.5 s. The spectra were conditioned with a bowtie only. The slice thickness was the same as the DECT images. Radiation dose was estimated through CATDOSE. 2.E.1. Single kvp CT-based PET attenuation correction Acquisitions of NCAT phantom were simulated with CAT- SIM, which uses analytic projectors for a step-and-shoot acquisition with CT tube voltage of 120 kvp (with a bowtie filter but no other filtration), tube current of 100 ma, and gantry rotation time of 0.5 s. The CT slice thickness was mm, comparable with the PET slice thickness. The CT sinogram was 888 channels 984 views. Default ideal kernel filter and water-only beam hardening correction in CATSIM package were applied. The CT image was reconstructed to image matrix, using filtered back projection (FBP) over a50cmfieldofview(fov)tomatchpetimagedimensions. Then a modified version of the bilinear transformation method that relates the CT number to the attenuation coefficient at 511 kev was used to generate the attenuation map for PET. 9, 39 In the modified method, the slopes for the transformation line of the soft-tissue and bone were estimated with the best fit using the known true values. With the generated attenuation map, both noise-free and noisy attenuation corrected PET images were reconstructed using weighted OSEM (16 subsets, 14 iterations) on pixel matrix over a 50 cm FOV. 2.E.2. DECT-based PET attenuation correction The data flow of DECT-based PET attenuation correction process is shown in Fig. 3. TheCTtubecurrentsforthe140 and 80 kvp scans were selected based on the optimal estimation result of Sec. 2.D for the elliptical water cylinder, with added 0.5 mm copper filtration following the bowtie filter. This combination yielded the same radiation dose as that of 120 kvp 50 mas single-kvp scan. The CT sinograms for the high and low kvp scans were then smoothed with a 2D 5 5boxcarfollowedbytheadaptive trimmed mean filter (ATM) before logarithmic conversion for noise suppression. With basis material decomposition method, the synthesized attenuation map at 511 kev was reconstructed with FBP to pixels over the 50 cm FOV. The DECT-derived attenuation map was used for PET attenuation correction. Both noise-free and noisy attenuation corrected PET images were reconstructed using weighted OSEM (16 subsets, 14 iterations) on a pixel matrix over a 50 cm FOV. 2.E.3. Image analysis and comparison The difference images between the true attenuation map and the single-kvp or DECT derived attenuation map, and

6 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT FIG. 3. Data flow for evaluating use of DECT for PET attenuation correction. the corresponding noise-free and noisy PET image were compared for the NCAT phantom. For each of the single-kvp and DECT derived attenuation map, six 2D ROIs were drawn on the attenuation map in locations of interest. Six corresponding ROIs were also drawn on the reconstructed noise-free and noisy PET images for analysis. The total root-mean-square errors (RMSE) within the spatial extent of the object of the attenuation and attenuation corrected PET images for the NCAT phantom were also calculated. A horizontal profile through the center of the noisefree PET images containing the lesions with contrast and in bone was drawn for comparative analysis. estimated as A pl = T H T L T H T L TH T L T H 2 T L TH T L 3, (11) A Al = T H T L T H T L TH T L T H 2 T L TH T L 3. (12) 3. RESULTS 3.A. Theoretical prediction The theoretical prediction [Eq. (1)] for the central sinogram bin for the 10 cm diameter water cylinder is shown as one of the curves in Fig. 4,wheretheCOVisnormalizedtoa minimum value of 1. It can be observed from Fig. 4 that with increasing energy the normalized coefficient of variation first decreases to reach its expected minimum value at an energy point between the mean energies of the high and low transmitted spectra. Then the COV increases until it plateaus near 160 kev, at a level of approximately three times the minimum relative COV, and then remains almost constant with increasing energy. 3.C. Evaluation of energy-dependent noise and bias The normalized COV for the central bin of the synthesized attenuation sinogram as a function of energy for the 10 cm 3.B. Dual-energy basis material decomposition Before the added copper filter (Cu, Z = 64, 0.5 mm), the mean energy of the 80 and 140 kvp spectra were 42.7 and 59.7 kev, respectively. After the added filter, the mean energy of the 80 and 140 kvp spectra were 57.1 and 77.0 kev, respectively. The coefficients {d i }, {e j } describing the relationships between aluminum and polyethylene thickness and the highand low-kvp log-transformed projections for the central bin without sinogram smoothing [Eqs. (6) and (7)] were FIG. 4. Normalized noise vs synthesized energy of monoenergetic attenuation data. The trend of decreasing linear attenuation coefficient of water with increased energy is also shown in the plot (the vertical axis at right side). Dual energy CT was acquired at 80 kvp with 256 ma and 140 kvp with 110 ma. Further details are given in the text.

7 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT diameter water cylinder is shown in Fig. 4 and agrees closely with the theoretical prediction. The normalized COV for the reconstructed attenuation map of the 10 cm diameter water cylinder as a function of energy is also shown for comparison. In this case the trend is similar to the theoretical prediction and sinogram domain simulations, but the exact amplification factor was slightly lower. Also shown in Fig. 4 is the normalized COV for the reconstructed attenuation map for the elliptical water cylinder. It can be seen that the image domain normalized COV curves for the elliptical and 10 cm circular water phantoms are similar if no sinogram smoothing is applied. For all the combinations of tube currents for high and low kvp scans, the percentage bias for both phantoms as a function of synthesized energy were very small, less than 2.4% for diagnostic CT energy range, and 0.4% for SPECT and PET energies. 3.D. DECT noise suppression and dose minimization for attenuation correction The total radiation dose (mgy) to the cm diameter water phantom as a function of tube currents of the high and low kvp scans are shown in Fig. 5. Asexpected,with increasing tube currents, the radiation dose increased. Figure 6 shows the averaged COV (unitless) of the 18 2D ROIs in the reconstructed attenuation map with sinogram smoothing as a function of tube currents for high and low kvp scans for the elliptical water phantom. The values acquired with DECT tube currents corresponding to give the same radiation dose as that of a single kvp scan of 120 kvp, 50 mas (1.63 mgy) are also highlighted. It can be observed that, in general, COV vs tube currents in Fig. 6 has an inverse rela- FIG. 6. Isocontour plot of coefficient of variation of DECT-derived attenuation map of elliptical water cylinder at 511 kev (PET photon energy) acquired with different CT tube currents at high and low kvps, respectively. The values obtained with DECT that have the same radiation dose as that of a single CT scan of 120 kvp, 50 mas are shown with the solid curve copied from Fig. 5. tionship with that of dose vs tube currents in Fig. 5. Based on Fig. 6, onecanestimatetheoptimalcombinationofthetube currents that gave the same radiation dose as a single kvp CT scan, but generate an attenuation map at 511 kev (PET photon energy) with the minimum COV, which are 110 ma (55 mas) for the 140 kvp scan and 256 ma for the 80 kvp scan. Note that the dual energy simulation included more spectral filtration (+0.5 mm Cu) than the single energy study. At the optimal tube current combination, the image domain normalized COV vs synthesized energy for the elliptical water cylinder with sinogram smoothing is also shown in Fig. 4 for comparison, which shows a reduction in noise at higher photon energies. The trend of normalized COV vs energy for sinogram smoothing case is the same as that without sinogram smoothing case, but the noise amplification factor is reduced from 2.4 to 1.9 at SPECT and PET photon energies. FIG. 5. Isocontourplotoftheradiationdose(mGy)toa20 30 cm diameter water phantom acquired as a function of mas for high vs low energy (kvp) scans. The tube current levels that result in the same radiation dose as a low-dose single CT scan (120 kvp, 50 mas, 1.63 mgy) are shown as a solid curve. 3.E. Comparison of PET attenuation correction with DECT and single kvp-derived attenuation map Both DECT and single kvp derived attenuation maps were generated with roughly comparable radiation doses. At fixed optimal tube currents for high and low kvp CT scans, Fig. 7 shows the comparison of attenuation maps of the NCAT phantom derived from DECT or single-kvp scans. Table II lists the bias in each ROI and the total object RMSE for the two attenuation maps. Both PET attenuation maps have bias in the contrast agent region, 5.4% for the DECT-derived attenuation map compared to 11.0% in the single-kvp-based map. The total normalized RMSE for the object support region in the attenuation map is 2.6% with single-kvp-based estimation and to 1.9% with DECT method.

8 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT FIG. 7. Comparison of attenuation maps at 511 kev. The corresponding reconstructed PET images are shown in Fig. 8. The first row of Fig. 8 shows (from left to right) the reconstructed noise-free PET image with perfect attenuation correction, the noisy PET image attenuation corrected with the DECT method, and the one attenuation corrected with single-kvp method. The second row of Fig. 8 shows the difference image between the reconstructed PET images and the noise-free truth. The ROIs and profile for comparison are also illustrated in Fig. 8. TheROIquantitationresults are compared in Table III. Figure9 shows the comparison of profiles in the reconstructed noise-free PET images attenuation corrected with DECT and single-kvp derived methods. It can be clearly observed that the PET image attenuation corrected with DECT method slightly reduced RMSE for the total image and reduced the bias in contrast agent by a factor of DISCUSSION Standard methods of CT-based attenuation correction for SPECT and PET have been shown to work well for low density biological objects. 9, 16 In cases where there is PET or SPECT tracer uptake in bone or other confounding high- Zmaterials(e.g.,contrastagent,implants)moreaccurate methods such as dual-energy CT-based attenuation correction may provide significantly more accurate images. 19, 25 DECT is known to be problematic because of the noise amplification and the additional patient radiation dose required to perform two scans and to reduce noise. To analyze the properties of DECT-based attenuation correction we focused on the noise and bias of synthesized monoenergetic attenuation maps FIG. 8. Comparison of PET images using DECT and single-kvp CT-based AC methods. as a function of the synthesized energy and source currents. Then we studied DECT noise suppression and dose minimization for attenuation correction. Finally, we used the NCAT phantom with iodine contrast to compare the noise and bias properties in attenuation corrected PET images. There are different strategies for dual energy CT imaging, such as separate dual kvp acquisitions, fast-switching interlaced dual kvp acquistions, simultaneous dual source acquisitions or multienergy detector-based. Our evaluations were based on dual kvp acquisitions. Considering the proposed attenuation correction is based on dual-energy synthesized attenuation maps (as shown in Fig. 3), the general methodology could be applied to other dual energy acquisition strategies. We used 0.5 mm Cu as additional flat filters for both high and low kvp scan, since our previous study indicated that this shapes the spectra to be more dose efficient. 38 Although there are advantages for using different filtration for the two sources and a dual-tube scanner, we used the same filtration for both kvp scans as a single-tube CT scanner is more likely to be combined with a SPECT or PET scanner. Figure 4 shows the normalized coefficient of variation vs synthesized energy for water phantoms in the sinogram and image domains. The normalized coefficient of variation (COV) provides relevant information on the energydependent noise level, considering that the linear attenuation coefficient of water is energy dependent. The theoretical prediction was performed in the sinogram domain, and it closely matches the simulation results of the 10 cm diameter water cylinder. It should be noted that this close match is independent of whether COV is normalized or not, and only the central bin is used for simulation of the sinogram COV. The normalized COV vs energy trend could vary among different TABLE II. Comparison of bias and RMSE in the DECT and SCT derived attenuation maps at 511 kev for the NCAT phantom. The RMSE was normalized to the true mean value within the spatial extent of the object. ROI 1 ROI 2 ROI 3 ROI 4 ROI 5 ROI 6 Total Contrast (hot) Soft tissue (hot) Bone (hot) Spine (normal) Background (normal) Lung (normal) Object RMSE DECT bias 5.4% 0.85% 0.69% 0.46% 1.3% 2.5% 1.9% Single-kVp bias 11.0% 2.5% 0.66% 1.5% 2.0% 11.5% 2.6%

9 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT TABLE III. Comparison of noisy PET images with DECT and single kvp-based attenuation correction (AC) with different ROIs in the NCAT phantom (OSEM reconstruction, 16 subsets, 14 iterations). The RMSE was normalized to the true mean value within the spatial extent of the object. ROI 1 ROI 2 ROI 3 ROI 4 ROI 5 ROI 6 Total Contrast (hot) Soft tissue (hot) Bone (hot) Spine (normal) Background (normal) Lung (normal) Object RMSE PET image truth value Bias in PET with DECT AC 6.9% 1.2% 3.3% 0.61% 1.2% 11.7% 21.0% Bias in PET with single-kvp AC 17.8% 5.4% 1.1% 16.7% 4.3% 42.9% 23.3% channels due to the transmitted spectra differences, but the general trend would be similar. The theoretical prediction and sinogram simulation do not agree completely, possibly due to the monoenergetic approximations in the theoretical prediction. Figure 4 also shows that the optimal synthesized energy where the COV reaches its minimum is object dependent. The energy for the minimum point in the curves for the two water phantoms were slightly different, likely due to the beam hardening effects for different thickness of the objects. In general, however, the minimal COV occurs when the energy is between the mean energy of the transmitted spectra. At higher energies, Fig. 4 indicates that the normalized COV increases with increasing energy until it plateaus around 160 kev (i.e., near SPECT energies), and then remains almost constant with increasing energy till up to the PET energy of 511 kev. At the PET energy of 511 kev the normalized COV of the attenuation maps for both water phantoms increased by a factor of approximately 2.4 compared to the minimal COV. Similar results comparing noise properties at 70 and 511 kev were also found by Stenner et al. 40 We then evaluated CT sinogram smoothing as a method to further improve the noise/dose trade-offs. This was motivated by the requirement to smooth the CT image to match the PET resolution for CT-based attenuation correction to avoid artifacts. This smoothing could be performed prior to, during, or after CT image reconstruction. Due to the noise correlations that are introduced, we believe that smoothing should be performed either during or before reconstruction. We have previously evaluated the impact of smoothing the FIG. 9. Profile comparison of the reconstructed noise-free PET images (OSEM reconstruction, 16 subsets, 14 iterations). raw sinogram with simple boxcar filters, both symmetric and non-symmetric, on the attenuation map and attenuation corrected PET images. For the given size of sinogram used in this study (888 channels, 984 views), we found that 5 5boxcar smoothing followed by application of an adaptive trimmed mean filter 35 before logarithmic conversion was a reasonable choice to provide substantial noise reduction while not introducing resolution mismatch artifacts. 37 This is similar to the approach proposed by Colsher et al. 36 Using a 2D 5 5boxcar followed by adaptive trimmed mean filter for sinogram smoothing reduced the noise amplification factor from 2.4 to 1.9. It is possible to use statistically principled DECT reconstruction methods 24 to allow for further improvements in the trade-off between radiation dose and image noise in DECT. It is important to note, however, that the main image quality metric is not CT image noise, but rather the quantitative accuracy of the PET image, which is determined by both noise and bias. For the same 10 cm diameter water cylinder, the maximum normalized COV in the image domain is lower than that in the central bin of the sinogram domain, probably due to noise correlations in image reconstruction, type of image reconstruction and kernel filters used, and bowtie filter effects across the total FOV. Figure 4 only shows one representative tube current combination for high and low kvp scans, and similar results could be obtained for other tube current combinations. As a check, the bias of the linear attenuation coefficients of the synthesized monoenergetic images were within 2.4% of the known true values across the entire energy range for various tube current combinations. Figures 5 and 6 showed the results of radiation dose as a function of tube currents and the tube current settings optimized for DECT-based PET attenuation correction. The dose estimation and parameter optimization were based on the elliptical water phantom. The study on the NCAT phantombased PET quantitation used the optimal parameters suggested from Fig. 6. Thoughitwouldbemorepreciseifthe dose calculation and parameter optimization were based on the NCAT phantom, the estimation was based on the elliptical water phantom as a more readily estimable surrogate. Figures 7 9 showed that with the same CT radiation dose as single energy CT, DECT acquisition parameters can be optimized to generate a more accurate attenuation map (less bias) leading to reduced PET bias in regions containing CT contrast agent and to similar or reduced RMSE for the total PET image. By comparing Tables II and III it can been seen that single-kvp-based attenuation correction leads to an overestimation of attenuation coefficients by 11.0% and

10 Xia, Alessio, and Kinahan: DECT attenuation correction for PET/CT the corresponding PET values by 17.8% in areas with contrast enhancement. With DECT-based attenuation correction, the overestimation of attenuation coefficients was reduced to 5.4% and the corresponding PET values to 6.9% for contrast agent. In practice, the single kvp-based attenuation correction method could be modified to reduce PET bias in iodine contrast. However, it would lead to increased bias for bone. In short, the bilinear method is problematic if both bone and iodine enhanced-regions are required to be quantitatively accurate in PET images. In the estimation of the coefficients for the DECT material basis decomposition formula (equations 6-7 and 11-2), non-zero constant terms have been proposed. 33 However, it is reasonable to assume that A α and A β should be exactly zero when T H and T L are both zero. We evaluated both cases and found that while the error of synthesized attenuation map at 511 kev increased in some regions and decreased in other regions, the overall root-mean-square error remained unchanged. The DECT results here are based on the basis material pair {polyethylene, aluminum}, however there are other potential choices of basis material pairs. 18, 41 The bias for the DECT-based attenuation maps would ideally be zero in Table II. It has been shown, however, that such bias is a function of the choice of basis materials. 41 For example, we repeated the DECT study with a {water, iodine} material pair (data not shown). In this case the bias in contrast agent region of the attenuation map was reduced from 5.4% to 1.6%. However, the bias in the lung region increased from 2.5% to 8.4%. These errors could be due to the strong K-edge of iodine at 33.2 kev in combination with the nonlinear estimation process. The optimal choice of basis material was outside the scope of this study. The findings in this study suggest that there is room for additional CT radiation dose reduction for both single- and dual-kvp-based attenuation correction in PET/CT imaging. We used additional flat Cu filtering to remove low-energy photons and shape the spectrum to be more dose-efficient for dual kvp CT scans, and this additional spectral shaping can be used for single-kvp CT scans as well. 38 With the single and dual- kvp CT protocols in this study, Fig. 8 implies that the noise in the PET scans, not the CT techniques, continues to dominate the noise in the final PET images. The results here agree with our previous study 38 that CT radiation dose could be further reduced by extending the standard techniques for PET/CT imaging with minimal effect on the PET noise and bias. The results presented here are based on simulations using a wide range of parameters to predict the general scanner behaviors for DECT-based PET attenuation correction. Before translation to clinical application, these results need to be confirmed in phantom-based physical experiments and patient studies. 5. CONCLUSION We addressed the energy dependent noise and bias properties for DECT derived attenuation correction for SPECT and PET imaging. Our results showed the expected minimum noise value for a synthesized monoenergetic image at an energy between the mean energies of the two transmitted spectra. In addition it was found that for increasing energy, the coefficient of variation of water reached a plateau near 160 kev, at a level of approximately 2.4 times higher than the minimum coefficient of variation, and then remained constant with increasing energy. The trend of coefficient of variation vs synthesized energy provided confidence in the use of DECT for attenuation correction in PET/CT and SPECT/CT. Analysis of the noise, bias, and radiation dose indicated that there are optimal ranges for the mas of the high and low kvp scans. We provided a solution for noise suppression and dose optimization, and showed that sinogram smoothing could further reduce the noise amplification in DECT-derived attenuation maps. With an appropriate selection of CT techniques, adectscanwiththesameradiationdoseasasinglect scan can result in a PET image with improved quantitative accuracy. ACKNOWLEDGMENTS The authors acknowledge the support of General Electric for the use of CatSim, in particular Dr. Jed Pack, Dr. Bruno De Man and Dr. Paul Fitzgerald, and Mr. Steve Kohlmyer and Mr. Souma Sengupta. The authors also acknowledge many useful discussions with Dr. Jeffrey Fessler and Dr. Paul Segars. 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