Elise C Emond
email: elise.emond.16@ucl.ac.uk

Alexandre Bousse

Maria Machado

Joanna Porter

Ashley M Groves

Brian F Hutton

Kris Thielemans

Effect of Attenuation Mismatches in Time of Flight PET Reconstruction

While the pursuit of better time resolution in positron emission tomography (PET) is rapidly evolving, little work has been performed on time of flight (TOF) image quality at high time resolution in the presence of modelling inconsistencies. This works focuses on the effect of using the wrong attenuation map in the system model, causing perturbations in the reconstructed radioactivity image. Previous work has usually considered the effects to be local to the area where there is attenuation mismatch, and has shown that the quantification errors in this area tend to reduce with improved time resolution. This publication shows however that errors in the PET image at a distance from the mismatch increase with time resolution. The errors depend on the reconstruction algorithm used. We quantify the errors in the hypothetical case of perfect time resolution for maximum likelihood reconstructions. In addition, we perform reconstructions on simulated and patient data. In particular, for respiratory-gated reconstructions from a wrong attenuation map, increased errors are observed with improved time resolutions in areas close to the lungs (e.g., from 13.3% in non-TOF to up to 20.9% at 200 ps in the left ventricle).

Introduction

The emergence of the first time of flight (TOF) positron emission tomography (PET) scanners brought a whole new dimension to nuclear imaging, by incorporating within the PET image reconstruction the time information from a coincidence pair to estimate more accurately the localisation of the originating annihilation event. The reconstruction problem is better determined and therefore less ill-posed, accomplishing an overall better image quality and better quantification [START_REF] Conti | Why is TOF PET reconstruction a more robust method in the presence of inconsistent data[END_REF]. Vendors and research teams are now improving the physical characteristics of their scanners in order to get better time resolution [START_REF] Lecoq | Pushing the Limits in Time-of-Flight PET Imaging[END_REF][START_REF] Cates | Evaluation of a TOF-PET detector design that achieves âĽď 100 ps coincidence time resolution[END_REF]. Current PET scanners with TOF capabilities used in clinical settings have TOF resolution between 210 ps [START_REF] Van Sluis | Performance characteristics of the digital biograph vision PET/CT system[END_REF][START_REF] Pan | Performance evaluation of the 5-Ring GE Discovery MI PET/CT system using the national electrical manufacturers association NU 2[END_REF]) and ≈ 550 ps [START_REF] Bettinardi | Physical Performance of the new hybrid PET/CT Discovery-690[END_REF][START_REF] Rausch | Performance evaluation of the Biograph mCT Flow PET/CT system according to the NEMA NU2-2012 standard[END_REF], but sub-100 ps time resolutions are expected in the future. A current initiative is hoping to achieve 10 ps resolution [START_REF] Lecoq | Pushing the Limits in Time-of-Flight PET Imaging[END_REF], The 10 ps Challenge committee 2019), which would possibly allow "reconstruction-less" PET images, as the detected events could be placed directly in the images. However, effects such as photon attenuation and scatter will still have to be taken into account.

Attenuation is defined as the loss of coincidences resulting from the photon interactions occurring within the body of the patient. Whereas photon attenuation is the foundation of X-ray imaging, it represents a major issue in PET where the fraction of photons attenuated in a tissue is proportional to the tissue density and the distance travelled through medium. For large patients, the fraction can be up to 95% and needs to be accounted for [START_REF] Mettler | Essentials of Nuclear Medicine and Nuclear Imaging[END_REF]. In practice, this requires an attenuation map (also referred as µ map). All current scanners are in fact dual modality: they are either combined with a CT gantry (PET/CT) or with a MRI gantry (PET/MR). In this case, the PET attenuation maps are in most cases derived from the coupled modality. A CT acquisition can usually provide quite accurate information to derive the attenuation factors used in the PET image reconstruction, usually via rescaling the CT attenuation values to PET 511 keV photon energy [START_REF] Kinahan | Attenuation correction for a combined 3d pet / ct scanner[END_REF][START_REF] Alessio | PET/CT scanner instrumentation, challenges, and solutions[END_REF]) (although problems exist, e.g., metal artefacts, see Blodgett et al. (2011)). MR-derived attenuation maps are usually less robust [START_REF] Lillington | PET/MRI attenuation estimation in the lung: A review of past, present, and potential techniques[END_REF].

Another common cause of mismatch between the estimated and actual attenuation map is motion [START_REF] Bousse | Maximum-likelihood joint image reconstruction/motion estimation in attenuation-corrected respiratory gated PET/CT using a single attenuation map[END_REF]. Mismatched data are common, especially in case of respiratory motion: errors can be large when no motion correction/gating is used, although intra-gate motion is unavoidable.

The use of "mismatched" attenuation maps in the PET reconstruction can induce large quantification errors in the reconstructed images, as discussed theoretically in [START_REF] Bai | An analytic study of the effects of attenuation on tumor detection in whole-body PET oncology imaging[END_REF], [START_REF] Thielemans | Image-based correction for mismatched attenuation[END_REF], [START_REF] Ahn | Analysis of the effects of errors in attenuation maps on PET quantitation in TOF PET[END_REF] and clinically in [START_REF] Geramifar | Respiratory-induced errors in tumor quantification and delineation in ct attenuation-corrected PET images: Effects of tumor size, tumor location, and respiratory trace: A simulation study using the 4D XCAT phantom[END_REF], [START_REF] Nyflot | Impact of CT attenuation correction method on quantitative respiratory-correlated (4D) PET[END_REF] and [START_REF] Mehranian | Impact of Time-of-Flight PET on Quantification Errors in MR Imaging-Based Attenuation Correction Journal of nuclear medicine : official publication[END_REF].

In the lungs, the attenuation mismatch is not solely due to the "displacement" caused by the compression and dilation, but also to the change of density while doing so. [START_REF] Cuplov | Issues in quantification of registered respiratory gated PET/CT in the lung[END_REF] has shown that up to 17.1% of mass density changes can be observed during respiration. The effect of motion mismatch in the lungs was assessed in [START_REF] Holman | The effect of respiratory induced density variations on non-TOF PET quantitation in the lung[END_REF] specifically for non-TOF reconstructions and demonstrated the importance of the density changes for quantification, additionally to the effect of mis-alignment due to motion displacement. Strategies to mitigate this exist (outside of correcting for motion), such as the use of average CT images for attenuation correction [START_REF] Pan | Attenuation Correction of PET Images with respiration-averaged CT images in PET/CT[END_REF].

In non-TOF reconstruction (i.e., when the time information is not used), when far away from the edges, for an "emission object" that is large enough (for example, in the chest), the effect is mostly local and depends on the size of the perturbation area, as well as the amount of activity in the surrounding areas. This was used to derive approximations to quantify the error in the reconstructed PET image in the area where the mismatch occurs [START_REF] Thielemans | Image-based correction for mismatched attenuation[END_REF][START_REF] Bousse | Evaluation of a direct motion estimation/correction method in respiratory-gated PET/MRI with motion-adjusted attenuation[END_REF]. In [START_REF] Ahn | Analysis of the effects of errors in attenuation maps on PET quantitation in TOF PET[END_REF], the effect of mismatched attenuation maps in TOF reconstruction was also considered as local, which allowed the authors to obtain an approximation of the quantification errors. Under that assumption, if the object size is considered negligible compared to the time resolution, an estimation close to the one found in [START_REF] Thielemans | Image-based correction for mismatched attenuation[END_REF] can be found, now depending on the time resolution instead of the size of the emission object. In both cases, only the local effect of a perturbation in the attenuation map on the emission image was considered in the analysis. This work aims to demonstrate the non-local effect of attenuation mismatches in the reconstructed PET images for high time resolution scanners, with a focus on Maximum Likelihood Expectation Maximisation (MLEM) and Ordered Subset Expectation Maximisation (OSEM) reconstructions. Particular attention will be given to non-local errors in quantification, i.e., in regions where there is no attenuation mismatch.

The paper will first briefly introduce mathematically the reconstruction problem in PET, including a demonstration of the non-local effect and its quantification error for perfect time resolution. Then, it will show the spatial extent of a localised attenuation mismatch in the reconstructed images for different time resolutions. Finally simulations and the reconstruction of patient data will demonstrate the quantification error that can arise from the use of mismatched data. The convergence rates will also be assessed in both cases.

Theory

PET Imaging System

The measured data take the form of a random vector g ∈ N n b , where [g] i is the number of counts at bin i ∈ 1, n b and n b is the number of detection bins. n b depends on the PET system, i.e., n b = n d for non-TOF PET and n b = n d n t for TOF PET, n d and n t denoting the number of detection bins for non-TOF reconstruction and the number of temporal bins, respectively. The imaging system is usually modelled as

p = M λ + n (1)
where p = E[g], λ ∈ R nv + is the unknown emission image, M ∈ R n b ×n b is the imaging system matrix, n is the background term (comprising randoms and scatter), and n v is the number of voxels.

Each entry [M ] i,j = M i,j represents the probability that a pair of unscattered photons emitted in a voxel j is detected at the detection bin i, and incorporates the attenuation. In principle, detector blurring should be modelled after attenuation; however, for simplicity, we will consider the factorisation of M as [START_REF] Leahy | Statistical approaches in quantitative positron emission tomography[END_REF])

M = a(µ)H , ( 2
)
where a(µ) is a n b ×n b diagonal matrix containing the attenuation factors corresponding to µ and H is a system matrix that incorporates a geometrical mapping between the source and the data-each entry [H] i,j = H i,j represents the probability that an emission from voxel j is detected by the detection bin i in the absence of attenuation.

The background term n includes scatter, which in practice can be estimated from the attenuation map [START_REF] Watson | Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine[END_REF][START_REF] Ollinger | Model-based scatter correction for fully 3D PET[END_REF]. In the remainder of this section, we will assume that n = 0, so that (1) becomes p = a(µ)Hλ .

(3)

This can be achieved, for example, by subtracting n from p and zeroing the negative values.

Spatial Extent of Activity Errors due to Local Attenuation Mismatch

We assume the true activity and attenuation images are respectively λ ∈ R nv + and µ ∈ R nv + . Furthermore, we assume that H is full rank with n b ≥ n v such that the mapping H : x → Hx is injective. The transmission system matrix-used to generate the attenuation coefficients-is the discretised line integral operator R ∈ R n d ×nv .

The attenuation coefficient diagonal matrix a(µ) is of size n d n t × n d n t (in non-TOF PET, n t = 1) and for each bin detector pair d ∈ 1, n d and time bin t ∈ 1, n t , the diagonal element at the detection bin

[id = AB]i = (d -1) × n t + ti = (t -1)n t + d is [a(µ)] i,i = exp(-[Rµ] d ) ,
that is to say, in TOF PET, the attenuation coefficients are independent of the time bin.

Let p be an idealised noiseless measurement of the true activity λ with attenuation µ ∈ R nv , i.e., p = a(µ )Hλ .

(4)

In absence of noise, the PET image reconstruction problem becomes find λ such that p = a(µ )Hλ ( 5)

and has a unique solution λ = λ . Now assume that the attenuation map µ used for reconstruction is a perturbed version of µ , i.e., µ = µ + η where η is a small perturbation supported on a small region far from the edges. The reconstruction problem ( 5) is equivalent to solving

a( µ)Hλ = a(µ )Hλ ⇔ Hλ = a(-η)Hλ
Non-TOF PET : Along the lines of [START_REF] Thielemans | Image-based correction for mismatched attenuation[END_REF] and [START_REF] Bousse | Evaluation of a direct motion estimation/correction method in respiratory-gated PET/MRI with motion-adjusted attenuation[END_REF], using a Taylor expansion around Rµ , the problem is approximated in non-TOF PET as:

H(λ -λ ) ≈ diag[Rη]Hλ (6)
where diag [•] is the operator that generates a diagonal matrix from a vector. In non-TOF, the PET system matrix H and transmission matrix R are equal. Furthermore, Rη is sparse and its non-zero entries correspond to the lines of responses i intersecting the support of η. Assuming that Hλ is approximately constant where Rη is nonzero (this is the case, for example, when the perturbation is located far from the body contour), we can further approximate (6) as

R(λ -λ ) ≈ ρRη (7)
where ρ is the mean projected activity along the lines of response intersecting the support of η. Approximation (7) shows that when µ and µ differ from a local perturbation η, then, by injectivity of R, the solution to the approximated reconstruction problem is λ = λ + ρη, which suggests that the error in the reconstructed activity remains localised on the mismatch.

TOF PET : Equation ( 6) can be extended to TOF PET, i.e., for all line of response i intersecting the support of η and for all time bin t,

[H(λ -λ )] i ≈ [Rη] d [Hλ ] i . ( 8
)
Approximation ( 8) implies that for all lines of response i intersecting the mismatch area, the error between the reconstructed activity λ and λ propagates to each time bin t by a factor proportional to [Rη] d , which means the error can no longer be considered local.

The previous equation ( 8) implies that in most cases the system to solve is made of inconsistent equations. For this reason, the solution depends on the cost function used for solving such reconstruction problem.

Maximum-Likelihood Expectation Maximisation in Perfect Time Resolution

In this section we deepen the analysis from Section 2.2 by investigating the effect of the attenuation mismatch from the perspective of MLEM reconstruction. We will consider the highly idealised case of perfect spatial resolution here.

We denote for (i, j) ∈ 1, n b × 1, n v (here i is a TOF bin and n b = n d n t ):

• λ = λ j the activity image reconstructed with the true attenuation map µ , i.e., using M = M i,j = a(µ )H.

• λ = λ j the activity image reconstructed with a wrong attenuation map µ, where

M = M i,j = a( µ)H.
We also define the sets

S j = { i ∈ 1, n b | H i,j = 0 } .
In a hypothetical case of an activity image reconstructed with perfect time resolution as well as perfect spatial resolution, the S j are disjoint, so that

∀i ∈ 1, n b , ∃!j ∈ 1, n v , i ∈ S j . ( 9
)
In other words, [M ] i,j is non-zero if and only if i ∈ S j . Given a system matrix M , which can either be M or M , and the measurement data p = {p i } i∈ 1,n b , the MLEM algorithm (k + 1)-th iteration at a voxel j is

λ (k+1) j = λ (k) j M j n b i=1 M i,j p i nv l=1 M i,l λ (k) l ( 10
)
where

M j = n b i=1 M i,j and λ (k) j
is the value of the activity image at a voxel j and iteration k [START_REF] Dempster | Maximum likelihood from incomplete data via the em algorithm[END_REF][START_REF] Shepp | Maximum likelihood reconstruction in emission tomography[END_REF][START_REF] Lange | Em reconstruction algorithms for emission and transmission tomography[END_REF].

In TOF PET, assuming the temporal resolution is perfect, condition (9) holds and therefore nv l=1 M i,l λ

(k) l = M i,j λ (k) j . Equation (10) simplifies to λ (k+1) j = λ (k) j M j i∈S j M i,j p i M i,j λ (k) j = i∈S j p i i∈S j M i,j (11)
and convergence is achieved after one iteration. Substituting M with M and M successively in (11) leads to

λ j λ j = i∈S j M i,j i∈S j M i,j = i M i,j i M i,j (12)
where the second equation follows from the fact that the S j are disjoint. Therefore, the ratio between the "wrong" and "true" reconstructed images is equal to the ratio of the "true" and "wrong" sensitivity images. The quantification of the non-local effect due to a local error in the attenuation map, from Equation (8) can therefore be quantified easily for MLEM/OSEM in the case of perfect time resolution by the relative error

λ j -λ j λ j = i M i,j i M i,j -1 (13)
The maximum-likelihood (ML) solution being unique in this case, Equation ( 12) and ( 13) are valid for other ML algorithms. It is worth noticing that for small attenuation mismatches and using the same first-order Taylor expansion around µ , (13) resembles an image space version of (8). Similar results for other reconstruction algorithms are shown in the Appendix.

Experiments and Results

In this section we will study the quantification errors in TOF reconstruction due to attenuation mismatch for MLEM/OSEM.

Summary of Simulated and Patient Data

We use four different datasets, either simulated for or acquired on a GE Discovery 690 PET/CT scanner [START_REF] Bettinardi | Physical Performance of the new hybrid PET/CT Discovery-690[END_REF]). The PET reconstructions use two different attenuation maps: the true attenuation map µ and a wrong attenuation map µ.

Simulations

The simulated datasets are the following:

Simulation 1 : A 28.8-cm diameter uniform cylinder (linear attenuation: 0.0916 cm -1 ) is placed at the centre of the FOV. The wrong attenuation map µ is known accurately in the reconstruction except for one small cylinder (diameter = 6 mm) at the centre of the FOV, where the attenuation is overestimated by 15%. This simulation is aimed at studying the impact of a very small attenuation mismatch on the reconstructed activity image. The phantom volumes are shown in Figure 1.

Simulation 2 : An XCAT PET/CT simulation of an FDG oncological pulmonary acquisition at end-inspiration (tumour of 1 cm 3 situated in the lower right lung). Two incorrect input µ maps are assessed:

• Lung density changes only: The incorrect µ map (denoted µ 1 ) is aligned with the structures in the PET data, however the density in the lung is not known accurately (overestimation of 15%). Note that the lung tumour density does not change, as the structure is considered rigid. Such simulation is relevant in motioncompensated image reconstruction (MCIR) or gated reconstruction, when a static µ map is warped to another respiratory gate (for which intra-motion is negligible), but the changes in density are not considered.

• Lung density changes + misalignment: The incorrect µ map (denoted µ 2 ) corresponds to the end-expiration state, therefore both structure alignment and lung density are wrong. The input simulation images are given in Figure 2. Bq/mL 0 0.12 cm -1 Data Generation : The simulations were performed using STIR with TOF [START_REF] Efthimiou | Implementation and validation of time-of-flight PET image reconstruction module for listmode and sinogram projection data in the STIR library[END_REF] in the following order: (i) Forward projection of the true activity image λ to obtain the non-attenuated projection data.

(c) µ 1 (d) | µ 1 -µ | 0 0.12 cm -1 0 1.2 •10 -2 cm -1 (e) µ 2 (f) | µ 2 -µ | 0 0.12 cm -1 0 1.2 •10 -2 cm -1
(ii) Calculation of the attenuation coefficient sinogram a(µ ) from the true attenuation map µ and multiplication by the projection data.

(iii) Reconstruction of the attenuated projection data using either the true attenuation map µ or the incorrect attenuation map µ.

To assess the effect of varying time resolution in the TOF reconstruction, the overall scanner geometry of the GE PET/CT Discovery 690 was used, but the TOF characteristics were altered:

• The maximal number of TOF bins extended to 175 (of width equal 28 ps) instead of the original 55 bins (of width ≈ 89 ps). • The time resolution was modified to test a range of time resolutions, from 70 ps to 550 ps.

Image Reconstruction : For the simulations, the projection data were reconstructed with MLEM (image size: 256 × 256 × 47, voxel size: 2.1306 × 2.1306 × 3.27 mm 3 , no post-filter applied), using a sufficient number of iterations so that the mean difference between the last two iterations was less than 0.1% overall, when the correct attenuation map was used in the reconstruction. The numbers of iterations for the TOF reconstructions, depending therefore on the time resolution, are given in Table 1. 1600 iterations were used in non-TOF reconstructions. For computational reasons, TOF "mashing" was used in this work, therefore combining TOF bins together with only small loss reported for quantification [START_REF] Efthimiou | Implementation and validation of time-of-flight PET image reconstruction module for listmode and sinogram projection data in the STIR library[END_REF].

Patient Data:

A 76-year-old male patient (clinical trial ID: NCT02885961) underwent a static FDG acquisition (injected activity: 170.8 MBq), on a GE Discovery 690 at the Institute of Nuclear Medicine, University College London Hospital (London, UK). Two different CT acquisitions were available: one at end-expiration (CTAC acquisition, multislice helical acquisition at shallow breathing, slice thickness: 3.75 mm, pitch: 1.375, voltage: 120 kVp, current: 40 mA, revolution time: 0.8 s) and one at endinspiration (HRCT, multislice helical acquisition at breathhold, slice thickness: 1.25 mm, pitch: 0.516, voltage: 120 kVp, current: 149 mA, revolution time: 0.6 s). In addition, the listmode data were also (amplitude-) gated into 4 respiratory bins (no cardiac gating) based on the respiratory trace from a Varian RPM system. The end-expiration gated PET data were reconstructed using two µ maps µ and µ, computed from the endexpiration and the end-inspiration CT images, respectively. The alignment between the end-expiration PET data and CT image was visually assessed using non-attenuationcorrected (AC) TOF gated images. The patient data were reconstructed using GE proprietary software in MATLAB (Matlab 2016b), with OSEM using 8 subsets with 200 iterations for non-TOF data and 100 iterations for TOF data. A 2D Gaussian postfilter of FWHM 6 mm and a 1-4-1 weighted z-axis postfilter were applied to the final images (image size: 256 × 256 × 83, voxel size: 2.7344 × 2.7344 × 3.27 mm 3 ).

Measures:

At a given time resolution, we denote λ and λ the reconstructed images at the final reconstruction iteration, using the true attenuation map µ and the incorrect attenuation map µ, respectively. In the following, we will use the relative errors in absolute value defined in a region of interest (ROI) R as

|RE| R = mean R ( λ) -mean R ( λ) mean R ( λ)
where mean R (•) designates the mean value in R.

We also define the relative difference image RD λ (in absolute values) such that

[RD λ ] j∈ 1,nv = λ j -λ j λ j

Results

Simulation 1

We consider five rectangular ROIs (4 × 4 × 45 voxels, the first and last slices are excluded). The first one is placed at the centre of the field of view (FOV), therefore at the centre of the perturbation area. The four other ROIs are off-centre (distance between the centre of the FOV and the ROIs: 12.8 mm, 21.3 mm, 29.8 mm and 55.4 mm respectively). In order to minimise problems related to discretisation, offcentre ROIs measures average values in reconstructed images rotated about the centre of the cylinder (60 rotation angles considered). We computed the relative error within the perturbation area and in the four offcentre ROIs. The plots showing the relative errors with respect to the time resolution are shown in Figure 4, where the relative error at perfect time resolution was predicted by Equation ( 13).

The first subplot is consistent with previous results on TOF, where improved time resolution decreases errors locally in the activity images. The second subplot confirms that the errors propagate globally in the image, in agreement with Equation (8). 13). We used two subplots due to scale differences. time resolution. Similarly as for Simulation 1, the relative errors within the lungs (where the attenuation mismatch is located) decrease with improved time resolution. However, the errors increase in the lung tumour and the descending aorta. The same behaviour was observed for the right and left ventricles, as well as ascending aorta (results not shown). The results show the propagation of the errors outside of the lungs (where the attenuation mismatches lie), in neighbouring regions, as predicted by Formula ( 13). The relative difference images corresponding to different time resolutions are shown in Figure 6.

Simulation 2: Lung

Lung density changes + misalignment:

In Figure 7, the relative difference images in absolute values are shown.

Additionally, the relative errors RE R were quantified in different ROIs R: ascending aorta (AA), descending aorta (DA), left ventricle (LV), right ventricle (RV) and liver. The relative differences |RD| between λ and λ are given in Table 2.

Patient Data

The two input CT images and the relative errors images are shown in Figures 3 and8 5.1% 2.1% 14.0% 8.2% 5.7% 8.6% non-TOF 2.7% 0.5% 13.5% 2.8% 3.6% 5.1% Table 3: Patient data -Relative errors |RE| R in TOF and non-TOF in different ROIs R: ascending aorta (AA), upper descending aorta (U-DA), upper descending aorta (L-DA), left ventricle (LV), right ventricle (RV) and liver. measurements using ITK-SNAP [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability[END_REF]): Ascending Aorta (AA, 1.76 cm 3 ), upper Descending Aorta (U-DA, 1.76 cm 3 ), lower Descending Aorta (L-DA, 1.76 cm 3 ), Left Ventricle (LV, 1.76 cm 3 ), Right Ventricle (RV, 1.54 cm 3 ) and Liver (7.33 cm 3 ).

The relative differences |RE| R in different ROIs R between λ and λ are shown in Table 3.

Discussion

System model inconsistencies in PET reconstruction are a cause of quantification errors. When improving the TOF resolution, local errors in the attenuation map will lead to non-local quantitative errors in the reconstructed activity image. Moreover, the errors in areas away from the attenuation mismatch increase with improved timing resolution.

The errors depend on the optimisation chosen to reconstruct the data. Here we focused on MLEM/OSEM reconstructions, which are the most widely used algorithms in the clinics. We first derived a simple formula for the relative error for perfect time resolution. This formula was confirmed with simulations, by observing the trend for improved time resolution.

Results were first shown for a simple cylindrical simulation, to demonstrate the non-local effect with highly symmetrical structures. They were in agreement with [START_REF] Ahn | Analysis of the effects of errors in attenuation maps on PET quantitation in TOF PET[END_REF] at the centre of the mismatch, however we observed errors in areas outside of the mismatch, as predicted by the theory presented in this paper. The region in closest proximity to the mismatch (12.8 mm off-centre) presented a mixed effect: the corresponding relative error curve (Figure 4) is not monotonic and resembles the curve for the ROI in the region of the mismatch at low time resolution. The study was then extended to XCAT simulations with activity at end-inspiration, first using an aligned µ map with incorrect values in the lung, and then a mismatched end-expiration µ map. As expected, the quantitative errors decreased in the lungs but increased in the neighbouring regions, such as the ventricles and the aorta. Finally patient PET data were gated (end-expiration) and reconstructed using two different µ maps: one close to the PET gate and the second one corresponding to end-inhalation. Both TOF (FWHM: 550 ps) and non-TOF were employed. The differences between the two sets of images were similar to those observed with the second XCAT simulation. While differences in the lung reduced with increased TOF timing resolution, they increased in most neighbouring ROIs, such as the ascending aorta (from 2.7% to 5.1%) or the left ventricles (from 2.8% to 8.2%), similarly to the 12.8 mm off-centre ROI of the cylindrical simulation.

The findings have clinical implications for PET in the thorax. The observed effects are likely to be most important for TOF PET/MR, where existing methods to compute the attenuation map from MR acquisitions are not quantitatively accurate in the thorax, although progress has been made to overcome this issue [START_REF] Lillington | PET/MRI attenuation estimation in the lung: A review of past, present, and potential techniques[END_REF]. It is likely that the problem would be largest in the case where the bones are not inserted in the MR-derived attenuation map used for the reconstruction. Effects due to errors in the attenuation map are also important for PET/CT as perfect alignment between PET and CT is usually impossible (especially in the thorax).

These results also show a possible impact on kinetic modelling. As previously stated, larger errors will be expected in regions commonly used to estimate imagederived input functions, such as the aorta or the left ventricle. From the values in Tables 2 and3, we suggest to use an input function derived from either the ascending aorta or an upper region of the descending aorta. A further complication is that errors due to attenuation mismatch depend on the surrounding activity distribution. This was reported in non-TOF PET [START_REF] Thielemans | Image-based correction for mismatched attenuation[END_REF][START_REF] Holman | The effect of respiratory induced density variations on non-TOF PET quantitation in the lung[END_REF][START_REF] Mérida | Multi-atlas attenuation correction supports full quantification of static and dynamic brain PET data in PET[END_REF] but is also the case with TOF, although this dependency disappears at perfect TOF resolution (see Equation 12). As the activity distribution is globally changing over the duration of the dynamic PET acquisitions, we expect time-dependent errors in presence of an attenuation mismatch on both image-derived input function and reconstructed activity, which would affect estimated kinetic parameters. [START_REF] Kotasidis | Impact of time-of-flight on indirect 3D and direct 4D parametric image reconstruction in the presence of inconsistent dynamic PET data[END_REF] already discussed such errors and found that although the biases were reduced with improved time resolution, they could not completely be resolved.

Furthermore, as shown in Figure 5 the observed effect has consequences for MCIR, where it would therefore be necessary to model the density changes in the lung [START_REF] Cuplov | Issues in quantification of registered respiratory gated PET/CT in the lung[END_REF][START_REF] Emond | Mass Preservation for Respiratory Motion Registration in both PET and CT IEEE[END_REF]) in order to avoid intra-gate inconsistencies.

A possible way to correct the attenuation maps is by using an algorithm such as Maximum-Likelihood reconstruction of Activity and Attenuation (MLAA) [START_REF] Nuyts | Simultaneous maximum a posteriori reconstruction of attenuation and activity distributions from emission sinograms[END_REF]. When TOF information is available, it is possible to determine, from the prompts only, the corrected attenuation sinogram up to a constant [START_REF] Defrise | Time-of-flight PET data determine the attenuation sinogram up to a constant[END_REF]. It becomes therefore possible to compute the entire attenuation sinogram when at least a part of it is known precisely (e.g., when a suitable region of the µ map is known). [START_REF] Rezaei | A Quantitative Evaluation of Joint Activity and Attenuation Reconstruction in TOF-PET[END_REF] has recently demonstrated clinical feasibility of MLAA, when robust calibration and corrections are used. The results in this paper imply that MLAA will become essential at higher TOF timing resolution. The effect observed in this paper also provides an alternative explanation for the fact that MLAA becomes more stable with improved TOF resolution: the non-locality of the error can be a reflection of the inconsistencies between the data and the system model if the wrong attenuation map is used (Equation ( 8)).

This publication only focused on system model inconsistency linked to the attenuation map. The study could be extended to inconsistencies due to incorrect background term within the reconstruction (i.e., including estimation of randoms and scatters). An accurate estimation of the scatter sinogram was indeed shown to be of great importance to obtain quantitative measures in TOF-MLAA [START_REF] Rezaei | A Quantitative Evaluation of Joint Activity and Attenuation Reconstruction in TOF-PET[END_REF].

Conclusion

We have shown that the effect of using an incorrect attenuation map in the reconstruction on the activity image cannot be considered local in TOF reconstructions. The relative errors can be easily quantified for perfect time resolution, which should be very similar to high resolution reconstruction such as 100 ps or better.

In conclusion, even at high time resolution, using an accurate attenuation map within the PET reconstruction is essential to obtain robust quantitative measures. When the attenuation map is not known precisely enough (as is usually the case for lung imaging), the attenuation images would need to be systematically re-estimated, for example via MLAA. This is especially important in future scanners with sub-100 ps time resolution.

Figure 1 :

 1 Figure 1: Simulation 1 -Axial and coronal views of the input images used: (a) true activity, (b) true attenuation and (c) incorrect attenuation.

Figure 2 :

 2 Figure 2: Simulation 2 -Axial and coronal views of the input images used: (a) true activity λ , (b) true attenuation µ , (c) incorrect attenuation µ 1 , (d) absolute difference between µ and µ 1 (e) incorrect attenuation µ 2 and (f) absolute difference between µ and µ 2 .

EndFigure 3 :

 3 Figure 3: Patient Data -(a) Coronal and (b) sagittal view of the end-expiration CT image and (c) coronal and (d) sagittal view of the end-inspiration CT image, used to derive the attenuation maps in this study.

  XCAT Simulation 3.3.1. Lung density changes only: In Figure 5, the relative errors are plotted in different 3×3×3 voxel ROIs (left and right lungs, descending aorta and lung tumour), relative to

Figure 4 :

 4 Figure 4: Simulation 1 -Relative errors versus time resolution at the centre of the cylinder (left) and for three off-centre ROIs (right), from the reconstructions and from Equation (13). We used two subplots due to scale differences.

Figure 5 :

 5 Figure 5: Simulation 2 (Lung density changes only) -Relative errors versus time resolution in different ROIs: left lung, right lung, lung tumour and descending aorta.

Figure 6 :

 6 Figure 6: Simulation 2 (Lung density changes only) -Relative difference images RD λ , in coronal view (a) expected at perfect time resolution and for four reconstructions with different TOF resolution: (b) 70 ps, (c) 200 ps, (d) 550 ps and (e) non-TOF.

Figure 7 :

 7 Figure 7: Simulation 2 (Lung density changes + misalignment) -Relative difference images RD λ , in coronal view (a) expected at perfect time resolution and for four reconstructions with different TOF resolution: (b) 70 ps, (c) 200 ps, (d) 550 ps and (e) non-TOF.

Figure 8 :

 8 Figure 8: Patient data -Relative errors for TOF reconstruction (550 ps) in (a) coronal and (b) sagittal views and for non-TOF reconstruction in (c) coronal and (d) sagittal views.

Table 1 :

 1 Time resolution FWHM simulated and the corresponding number of MLEM iterations used.

	TOF FWHM	70 100 150 200 300 350 400 450 500 550
	MLEM iteration # 80 160 160 240 240 240 240 240 240 240 240

Table 2 :

 2 Simulation 2 (Lung density changes + misalignment) -Relative errors |RE| R for different time resolutions and for non-TOF in different ROIs R: ascending aorta (AA), descending aorta (DA), left ventricle (LV), right ventricle (RV) and liver.

	ROI	AA	DA	LV	RV
	Perfect TOF 12.8% 3.3% 22.9% 25.5%
	70 ps	12% 1.0% 23.0% 26.6%
	200 ps	8.8% 1.7% 20.9% 27.9%
	550 ps	6.5% 4.5% 14.2% 21.8%
	non-TOF	8.3% 5.4% 13.3% 16.6%

, respectively.

Additionally, spherical ROIs were drawn on the end-expiration CT for

Acknowledgments

The authors acknowledge funding support from GlaxoSmithKline (BIDS3000030921) and research support from the National Institute for Health Research, University College London Hospitals Biomedical Research Centre. We would also like to thank Robert Shortman for research governance and administration.

Finally, we would like to thank Michel Defrise (Department of Nuclear Medicine, Vrije Universiteit Brussel, B-1090 Brussels, Belgium) and Johan Nuyts (Department of Nuclear Medicine, Katholieke Universiteit Leuven, Belgium) for the insightful and stimulating discussion.

Appendix: Extension to Other Reconstruction Algorithms

The notations in this appendix follows the one used in Section 2.3. In this appendix, we derive formulas similar to Equation ( 12) for unweighted least-squares reconstructions. When using pre-corrected data, this derivation is equivalent to that of filtered backprojection. The unweighted least-squares solution is obtained by solving

The solutions of ( 14) with M = M and M = M are respectively

where [ • ] T is the transpose matrix operator. For a voxel pair (j, j ) and using (9), we have the following element of M T M :

where δ j,j is the Kronecker delta. Thus, M T M is a diagonal matrix and the solution λ corresponding to a given system matrix M is therefore straightforward (provided that

.

In the noiseless situation p = M λ , then


F Delage

S Béjaoui

S Lemehov

J Somers

W Maschek

Outcomes of the FP-7 project PELGRIMM investigating pelletized and sphere-packed oxide fuels for Minor-Actinides transmutation in a Sodium Fast Reactor

PELGRIMM that stands for "PELlets versus GRanulates: Irradiation, Manufacturing, Modelling", is a 4 years European project started in 2012, that investigates Minor Actinidesbearing fuels, shaped as pellets and beads, for Sodium Fact Reactors. Both Minor-Actinide transmutation options: the MA homogeneous recycle in driver fuels and the MA heterogeneous recycle on UO 2 fuels located in radial core blankets, are under consideration. The objectives of the project are to capitalize on efforts made within the previous European projects: ACSEPT, FAIRFUELS, F-BRIDGE as well as CP-ESFR, and to take a new step in the long range qualification approach regarding fabrication process, irradiation behaviour, performance and safety, for pelletized and sphere-packed shaped Am-bearing fuels. The paper gives an overview of the PELGRIMM outcomes related to: first results on helium and fission gas behaviour in (Am,U)O 2-x fuels irradiated in the separated effect test MARIOS; progress status of the semi-prototypic irradiation MARINE under preparation, that will provide a comparison between sphere-packed and pelletized (U,Am)O 2-x fuel performances; investigations performed to extend Minor Actinide bearing fuel fabrication processes to alternative routes, that are the Weak Acid Resins and micro-wave technologies, in order to limit secondary waste streams; upgrades in calculation codes used to describe conventional fuels behaviour under irradiation, taking into account the specific issues related to MA-bearing fuels and sphere-packed fuels; and finally, progress related to the key issues of core physics, design and safety performance for spherepacked MA-bearing driver fuels.

I. INTRODUCTION

Minor Actinide (MA) incorporation into the fuel is a prerequisite for Gen-IV reactors to bring benefits in the disposal requirements by reducing the MA content in the high level wastes. Since americium displays a strong gamma emission (and curium a high neutron emission), the MA-bearing fuel fabrication process needs shielding, remote handling by robotic arms, simplification as well as implementation of relatively dust-free steps. Moreover the high volatility of some Am compounds has to be managed during fuel fabrication as well as during irradiation stage where Am would be more readily redistributed within the fuel than other actinides. Finally, harmful consequences of additional helium production during fuel irradiation (related to 241 Am transmutation) on fuel swelling, degradation of the thermal properties and high pressurization of the pins have to be prevented.

Based on historical experience and knowledge, oxide fuels have emerged in Europe as the shorter term solution to meet the Gen-IV Sodium Fast Reactors assigned performance and reliability goals and two main MArecycle options are currently under consideration:

x the homogeneous mode, where small quantities (<3%) of MA-oxide are diluted in the (U,Pu)O 2 SFR standard driver fuel, in order to limit the impact of MA addition on SFR core safety parameters (sodium worth void, Doppler effects, delayed neutron fraction) and fuel cycle facilities; x the heterogeneous mode, where MA-oxides are concentrated (contents from 10 to 20%) in UO 2 and MA-bearing sub-assemblies are located in the blanket of the core.

Investigations on both kinds of MA-bearing oxide fuels, started (more or less) recently and experimental knowledge remains mostly limited to laboratory-scale fabrication processes, small amount of characterization and out-of-pile testing, as well as scarce irradiation experiments [START_REF] Delage | Outcomes on oxide fuels developments for Minor Actinides recycling[END_REF].

The project PELGRIMM [START_REF] Delage | Investigation of pelletized and sphere-packed oxide fuels for minor actinide transmutation in sodium fast reactors, within the FP-7 European project PELGRIMM[END_REF] that stands for PELlets versus GRAnulates: Irradiation, Manufacturing and Modelling, aims at investigating a new step in the long term process of the MA-bearing fuel qualification rationale, initiated within the European projects: ACSEPT (2008-2012), F-BRIDGE (2008-2012), CP-ESFR (2008)(2009)(2010)(2011)(2012)(2013) and FAIRFUELS (2009)(2010)(2011)(2012)(2013)(2014)(2015). A total of 12 partners from research laboratories, universities and industries, collaborate to share and leverage their skills, progress and achievements, covering a comprehensive set of investigations, in order to:

x perform the Post-Irradiation Examinations (PIE) on MARIOS and SPHERE pins and fuels, providing the very first results respectively on the helium behaviour in (Am,U)O 2 fuels and a comparison between spherepacked and pelletized (U,Pu,Am)O 2 fuel performances; x take the next step in the (Am,U)O 2 fuel qualification rationale by performing a new irradiation test (MARINE) in HFR; x extend Minor Actinide bearing fuel fabrication processes to alternative routes in order to limit secondary waste streams; x extend the capabilities of existing calculation codes to describe the MA bearing fuel behaviour under irradiation; x accomplish a preliminary design of a sodium cooled fast reactor core with spherepacked (U,Pu,Am)O 2 fuels and perform a preliminary safety assessment.

Finally, PELGRIMM aims at promoting the implication of European students and young researchers too, through: placements of internships in organisations involved in the project, travel grants to young scientists to attend conferences and workshops. This paper gives an overview of the technical outcomes gained within the project.

II. PROGRESS STATUS OF IRRADIATION TESTS

As time required for an irradiation campaign on Ambearing fuels, including the design of the test, the manufacturing and assembly of the components, the implementation in a reactor and the Post-Irradiation Examination program, is longer than the standard duration of an European project (3-4 years), irradiation campaigns have been regularly split in steps that are distributed in projects that follow each other.

The PELGRIMM project hosts the PIE activities for the irradiation tests SPHERE and MARIOS which were designed, manufactured and implemented in HFR within the FP-7 FAIRFUELS project (2009)(2010)(2011)(2012)(2013)(2014)(2015). The design, manufacturing and implementation in HFR of the new irradiation test : MARINE (that stands for MA heterogeneous Recycle semi-INtegral Experiment) is part of the FP-7 PELGRIMM too. (MARINE PIE program will be included in a future European project.) SPHERE [START_REF] Agata | SPHERE: Irradiation of sherepac fuel of UPuO 2-x containing 3% Americium[END_REF] consists of two experimental pins containing an (U,Pu,Am 0.03 )O 2-x fuel, shaped as pellets in one mini-pin and a stack of beads of 2 size fractions (50 & 800µm) in the other mini-pin. Indeed, if MA-bearing fuel pelletized stacks have been preferred so far, the implementation of the spherepacked fuel stacks could lead to a significant simplification of the fabrication process with the elimination of the steps that involve fuel powders (and dust). So, the SPHERE test emerges as a first of a kind since irradiation behaviour of spherepacked and pelletized stacks of an Am-bearing driver type fuel can be compared. The irradiation was performed (within the frame of FAIRFUELS) in HFR up to April 2015, leading to a maximum burnup of ~5at% and a maximum Linear Heat Rate around 300W.cm -1 . Non Destructive Examinations will start soon after a mandatory cooling period of ~3 months.

MARIOS [START_REF] Bejaoui | Americium-Bearing Blanket Separate-effect Experiments: MARIOS and DIAMINO Irradiations[END_REF] is the first separate-effect irradiation performed in HFR (within FAIRFUELS) aiming at studying temperature-and porosity-dependent helium release and fuel swelling for tailored porosity disks of Am 0.85 U 0.15 O 2-x fuels [START_REF] Prieur | Fabrication and characterisation of U 0.85 Am 0.15 O 2-x discs for MARIOS[END_REF], using an astute experimental design that leads to flat temperature profiles in the samples. Thus, four mini-pins, each containing 6 small disks (diameter: 4.5mm and thickness: 1.5mm) of fuels with 2 open-porosity ratios (7.7% and 12.5%), were irradiated during 304 Equivalent Fuel Power Days at constant temperatures that ranged from 980 to 1370°C [START_REF] Agata | The results of the irradiation experiment MARIOS on americium transmutation[END_REF].

Neutron radiography performed after the irradiation has shown an overall good shape of the irradiated disks that has been confirmed for the pin 2 at the dismantling stage completed in HFR hot cells, as most the disks were recovered in 2 fragments of equal size.

Pins puncturing results have shown that helium release was total whatever irradiation temperatures and disk porosity contents. Fission gas releases have displayed temperature dependences regardless porosity ratios (see Figure 1). Finally, unlike axial distributions per disks of the non-volatile fission product 95 Nb, gamma spectrometry results for 137 Cs seems to match (qualitatively) the Fission Gas release rates (see Figures 2 and3), showing that the temperature threshold for Cs release lies near the investigated temperature range.

This very first results on (U,Am)O 2 fuels will be completed in a near future by the Destructive Examination stage to be performed on pins 1 and 3, in the LECA facility at CEA-Cadarache. The semi-integral irradiation test MARINE that is currently under preparation within PELGRIMM for an irradiation start by the end of 2015 for 336 EFPD, is part of the second stage in the long-range qualification approach of (U,Am)O 2 fuels (separated-effect tests like MARIOS belonging to the first step). MARINE is the SPHERE matching piece as it includes 2 mini-pins of pelletized and spherepacked fuel stacks of Am 0.85 U 0.15 O 2-x . Moreover, the MARINE mini-pins are instrumented with pressure transducers follow on-line gaseous release from the fuels during the irradiation.

The synthesis conditions of the fuels are summarized in section III. The design of the experimental device and the irradiation conditions (described in paper 5221 of these proceedings [START_REF] Agata | MARINE: Irradiation of spherepac fuel and pellets of UO 2-x containing 13% Americium[END_REF]) would lead at the end of the irradiation (336 EFPD) to fuel central temperatures of 850 and 990°C for the sphere-packed and pelletized pins respectively. So, outcomes from MARIOS at ~1000°C could directly be used for the interpretation of MARINE PIE results. Moreover, the helium production in MARINE (around 5mg.cm -3 of fuel) would be close to the ~4mg.cm -3 foreseen in recent scenarios [START_REF] Chabert | Technical and economic assessment of different options for Minor Actinide transmutation: the French case[END_REF] for the heterogeneous recycling of Am in sub-assemblies close to the core of an industrial SFR of 3600MWth. Nevertheless, helium production rates in MARINE would not be representative as the MARINE duration would be significantly lower (336EFPD) compared the irradiation time in an industrial reactor (~2000 EFPD).

III. FUEL SYNTHESIS ROUTES INVESTIGATED

Even if powder metallurgy flowsheets, used to supply (U,Pu)O 2 standard fuels at industrial scale, can be used at lab-scale to prepare Am-bearing fuel samples (MARIOS disks for example), dust-free routes and simplified flowsheets, are essential to scale-up the Am-bearing fuel fabrication processes. Several options have been investigated within the project: some are based on sol-gel processes that lead to dense or porous spherical particles of homogeneous compounds as components are mixed in solution; another one consist on the adaptation to oxide fuels of the Weak Acid Resin technology initially implemented in the 1970's for the production of uranium carbide kernels.

Already, within FAIRFUELS, the SPHERE (U,Pu)AmO 2-x beads were prepared by infiltration of porous (U,Pu)O 2 precursor beads (prepared by sol-gel gelation), with americium nitrate solutions. Two sizes of Am-bearing beads (50 and 800µm) were synthesized and heat treated. One batch fraction of small sized beads was then transformed to sintered pellets, which were then loaded in one mini-pin. The other batch fraction of small sized beads and the batch of bigger beads were packed by vibrations in the other mini-pin. For MARINE [START_REF] Agata | MARINE: Irradiation of spherepac fuel and pellets of UO 2-x containing 13% Americium[END_REF] the synthesis procedure was almost similar to SPHERE for the preparation of pellets, using UO 2 as precursor instead of (U,Pu)O 2 . So, UO 2 porous beads were infiltrated by a low acid Am nitrate solution to prevent UO 2 dissolution as much as possible. The resulting granulates were heat treated, pressed and sintered. The dense (95%) and defectfree U 0.87 Am 0.13 O 1.93 pellets (see Figure 4) were then stacked in the MARINE 1 mini-pin. while beads for the small fraction were crushed before sieving. After a sintering steps, granulates were vibropacked to fill in in the second mini-pin and the smeared density is ~60%.

Fig. 6. Large size MARINE beads visual aspect

In parallel, a variant of the internal gelation route described in Figure 6, using for gelation of the drops, a microwave cavity instead of a silicon oil hot bath (that lead to secondary wastes) has been investigated on nonradioactive surrogates [START_REF] Cozzo | Methods of advanced waste conditioning by microwave internal gelatio: set-up development and modelling[END_REF][START_REF] Cabanes-Sempere | Innovative production of nuclear fuel by microwave internal gelation[END_REF]. Promising results have been obtained (Figure 8) and implementation of the devices in glove-boxes started for validation on U-type compounds. Finally, the Weak Acid Resin flowchart has been revisited and adapted (Figure 11) to oxide fuels [START_REF] Picart | Actinide compound microsphere elaboration from organic template: the war process[END_REF][START_REF] Remy | Calcined resin microsphere pelletization (CRMP): A novel process for sintered metallic oxide pellets[END_REF] up to the synthesis of (U,Am)O 2 beads and pellets [START_REF] Remy | Fabrication of uranium-americium mixed oxide pellet from microsphere precursors: application of CRMP process[END_REF]. A batch of 900mg of U 0.90 Am 0.10 O 2-x microspheres was prepared by thermal treatments of ion exchange resins loaded with Am 3+ and UO 2 2+ cations. The degradation of the polymeric skeleton under air followed by reducing heat treatment led to the synthesis of spherical precursors with diameter around 400µm (see Figure 12) and apparent density of 24 % . A solid solution was formed during the reducing heat treatment and ensured a homogeneous distribution of uranium and americium atoms in the solid. Moreover, oxide microspheres were suitable for pressing and a dense pellet (density of 95%) was achieved after dynamic sintering under a reducing atmosphere up to 1800°C. This pellet meets the required specifications for dense pellet envisaged for Am transmutation on an UO 2 support in sodium fast reactors and proves the technical feasibility of this dust-free process. [START_REF] Lassmann | TRANSURANUS: a fuel rod analysis code ready for use[END_REF], SPHERE&SPACON [START_REF] Wallin | The sphere-pac nuclear fuel behaviour modelling at high burnup[END_REF] started within the frame of FP-6 EUROTRANS, FP-7 FAIRFUELS and FP-7 F-BRIDGE to consider some of the specificities for Am-bearing fuels and for spherepacked fuels. The objective of the work within PELGRIMM, is to capitalize on previous investments and to go further in the capabilities of the codes already mentioned plus GERMINAL [START_REF] Bouineau | Toward an improved GERMINAL V2 code to model oxide fuel for sodium fast reactor[END_REF], to describe the behaviour under irradiation of (U,Pu,Am)O 2 and (U,Am)O 2 fuels shaped as pellets or spherepacs. Implementation of new compositions and fuel forms has been made by correction of existing models and correlations for standard fuels when appropriate. Such approach is practical; however, validity of it still shall be tested.

Moreover, the efforts have covered aspects of modeling such as helium production and release under a fast neutron spectrum; plutonium and oxygen redistribution [START_REF] Marcello | Extension of TRANSURANUS plutonium redistribution model for fast reactor performance analysis[END_REF]; melting temperatures [START_REF] Calabrese | Melting temperature of MOX fuel for FBR applications: TRANSURANUS modelling and experimental findings[END_REF]; evolution rate of fuel restructuring, columnar grain growth and central void formation; … For simulation of Helium release, a new model has been developed and the interpretation of some experiments by means of this model enabled to propose a new value for the diffusion coefficient of helium in uranium and uranium-plutonium oxides over a large and representative temperature range, which has been compared to the values in the open literature [START_REF] Talip | Thermal diffusion of Helium in 238Pu-doped UO2[END_REF]. Furthermore, the interpretation of the data by means of the new model allowed to propose a value for the helium bubble diffusion coefficient, as well as for the trapping coefficient associated with intra-granular bubbles.

An assessment and a comparative evaluation of the fuel performance codes and their ability to model the behavior of fuel pins with either sphere-pac or pellets, has been initiated. Experimental data to use are issued from the SPHERE irradiation test for (U,Pu,Am)O 2 and SUPERFACT-1 [START_REF] Prunier | Some specific aspects of homogeneous Am and Np based fuels transmutation through the outcomes of the SUPERFACT experiment in PHENIX fast reactor[END_REF] for (U,MA)O 2 fuel. First calculations with MACROS have shown a good agreement with PIE results for fission gas release, burnup and transmutation behaviour. Disagreements have been pointed out regarding fuel restructuring and central void formation phenomena that have been calculated whereas they are absent. Analysis of input data and models are underway.

V. SIMPLIFIED DESIGN AND SAFETY PERFORMANCE ASSESSMENT OF AN ADVANCED SPHERE-PAC (U,Pu,MA)O 2 SFR CORE

As sphere-packed fuels are foreseen to be good candidates for MA-bearing fuel concepts due to simplification of the fabrication process associated with the production of beads and due to potential good swelling behaviour under irradiation, the PELGRIMM project start linking the investigation of spherepacked fuel synthesis and behaviour under irradiation to problematics of core physics, design and safety performance.

This study is in continuity with the former FP-7 CP-ESFR project which aimed at designing and analyzing a 3600MWth sodium-cooled fast reactor loaded with a standard driver fuel shaped as pellets [START_REF] Fiorini | The collaborative project on European sodium fast reactor: CP-ESFR[END_REF]. The so-called Working Horse (WH) aimed at a reduced sodium void worth, but still relatively high with ~1200 pcm at Beginning Of Life (BOL) and being a major cause for core disruption during an Unprotected Loss Of Flow accident (ULOF). Among the proposed solutions to optimize the core and reduce the positive void worth, the CONF2 core design with a large upper sodium plenum provided a reduced positive void worth [START_REF] Rineiski | ESFR core optimization and uncertainty studies[END_REF]. So, the objective within the FP7-PELGRIMM project is to perform a safety assessment and a comparative evaluation of the CONF2 core loaded with either sphere-packed or pelletized (U,Pu,Am)O 2 driver fuel.

The PELGRIMM investigations started with the design of CONF2 loaded with sphere-packed fuel and the determination of core safety parameters and burn-up behavior. The neutronic analyses were performed with the MCNPX code. Variants of the CONF2 core contain Am fractions from 0 to 4 wt% in the driver fuel. This CONF2 design features a relatively low sodium void worth of ~ 500 pcm at BOL compared to the ~ 1200 pcm of the WH core. Results show the expected worsening of the safety parameters with burn-up and MA content. The Doppler coefficient is decreasing while Na void coefficient is increasing again up to 2100 pcm for EOC3.

The accident simulations are performed with the MAT5DYN code for the accident initiation phase and with the SIMMER-III code for the complete accident scenario. The codes had to be adapted to the specifics of the spherepacked fuel. SIMMER analyses for the CONF2 core with pellet fuel have been performed first, assessing the claimed improvement by introducing the large upper sodium plenum. Results [START_REF] Maschek | Safety analyses for Sodium-Cooled Fast Reactors with Pelletized and Sphere-pac Oxide Fuels within the FP-7 European project PELGRIMM[END_REF] showed that the sodium plenum seems to effectively prevent positive reactivity surges by voiding and subsequent power excursions. The low transient power allows the rewetting of structures and the disruption process remains limited. Differently than in the WH core after a first mild power excursion no recriticality appeared. For sphere-pac fuel under BOL conditions one might discern between BOL 'green fuel' and BOL restructured fuel after some hours of operation. The interest in the 'green fuel' case is because of the low thermal conductivity and consequently possible high fuel centerline temperatures. SIMMER analyses reveal that indeed under these conditions locally centerline temperatures above the melting point are reached. This shows that a starting procedure of the reactor is necessary to achieve a restructured fuel which is in its thermal conditions closer to a pellet fuel of same density. Both for the pellet and sphere-pac core, the plenum effect is active and prevents a scenario with multiple recriticalities. In the CONF2 core with BOL restructured fuel one experiences even a total rewetting of the core in the last phase of the ULOF. These results reveal a new phenomenology not seen before for such large cores. For EOC3 cores the safety parameters are deteriorated and a ULOF in the CONF2 core again ends in whole core melting and core destruction.

No sound experimental data base on transient behavior of sphere-pac fuels exists. The safety analyses therefore represent first scoping studies. Based on the current analyses, the implementation of sphere-pac fuel does not cause any specific design problems for the CP-ESFR. For BOL conditions the ULOF simulation shows a very mild transient for the sphere-pac CONF2 core both with unrestructured and restructured fuel. The first safety analyses also indicate that sphere-pac fuels do not seem to cause any specific safety problems, if introduced in an SFR.

V. CONCLUSIONS

The PELGRIMM project addresses MA-bearing oxide fuels for Generation IV -SFR Systems. Two options, MA homogeneous recycle in driver fuels and heterogeneous recycle in high MA content bearing UO 2 fuels are considered. The project aims at taking a new step in the long term process of the MA-bearing fuel qualification rationale, by investigating a wide range of items: from solid to sphere-packed fuel shape, from fuel fabrication and characterization to behaviour under irradiation; from experiments to modelling and simulation, as well as a spherepacked loaded core physics pre-assessment from normal operating conditions to transients and severe accidents.

The results on helium and Fission Gas behaviour in (Am,U)O 2-x pins irradiated in the separated effect test MARIOS are currently available and show that: helium was totally released from the fuels. Fission Gas release rates are strongly temperature dependent and Cs release follows FG trend.

The semi-prototypic irradiation MARINE including pelletized and spherepacked (U,AM)O 2 fuels, to be implemented in HFR is almost ready to start.

The investigations to extend Minor Actinide bearing fuel fabrication processes to alternative routes, that are the Weak Acid Resins and micro-wave technologies, have given promising results.

Upgrades in models and correlations used to describe conventional fuels behaviour under irradiation, taking into account the specific issues related to MA-bearing fuels and sphere-packed fuels, are underway. Recalculations with several codes of the SPHERE and SUPERFACT-1 irradiation have been initiated.

Key issues of core physics, design and safety performance for sphere-packed MA-bearing driver fuels have been addressed.

At the end of the project that could be later than initially planned due to unexpected difficulties met in experiments, a new stage will have been reached in the long-term fuel qualification approach thanks to the skills, the involvement and the staunch determination of the PELGRIMM consortium.

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Fission Gas release results versus temperature for MARIOS pins

Fig. 4 .

 4 Visual aspect (a) and ceramography (b) of a MARINE pelletThe synthesis of the 2 diameter size beads (50 and 800µm) for the MARINE 2 mini-pin was much more challenging than expected and the two fractions were prepared by the external gelation method. (U,Am)O 2 sol-gel broth solutions were prepared and dispersed in droplets. After calcination, the beads for the large fraction (Figure5) were sieved, Proceedings of Global 2015 September 20-24, 2015 -Paris (France) Paper 5058

Fig. 7 .

 7 Fig. 7. Flowchart of the internal gelation route through a microwave cavity (right) compared to a silicon oil bath gelation step (left).

Fig. 11 .

 11 Fig. 11. Principle of the WAR process applied to Uranium dioxide based materials synthesis

Fig. 12 .

 12 Fig. 12. FEG-SEM micrographs of U 0.90 Am 0.10 O 2-x beads prepared by WAR technology [13] IV. MODELLING AND SIMULATION OF FUEL BEHAVIOUR UNDER IRRADIATION Most of fuel performance codes have been originally developed, verified and validated to model standard fuels for Light Water Reactor and Fast Reactor types. Upgrades of codes such as MACROS (developed by SCKƔCEN), TRANSURANUS[START_REF] Lassmann | TRANSURANUS: a fuel rod analysis code ready for use[END_REF], SPHERE&SPACON[START_REF] Wallin | The sphere-pac nuclear fuel behaviour modelling at high burnup[END_REF] started within the frame of FP-6 EUROTRANS, FP-7 FAIRFUELS and FP-7 F-BRIDGE to consider some of the specificities for Am-bearing fuels and for spherepacked fuels. The objective of the work within PELGRIMM, is to capitalize on previous investments and to go further in the capabilities of the codes already mentioned plus GERMINAL[START_REF] Bouineau | Toward an improved GERMINAL V2 code to model oxide fuel for sodium fast reactor[END_REF], to describe the behaviour under irradiation of (U,Pu,Am)O 2 and (U,Am)O 2 fuels shaped as pellets or spherepacs.

ACKNOWLEDGMENTS The authors appreciate the financial support of the European Commission through the PELGRIMM grant agreement 752 295 664. NOMENCLATURE BOL: Beginning Of Life DE : Destructive Examinations EFPD : Equivalent Full Power Days FG: Fission Gas MA : Minor Actinide NDE : Non Destructive Examinations PIE: Post Irradiation Examinations SFR: Sodium cooled Fast Reactor ULOF: Unprotected Loss of Flow WH: Working Horse