Metal artifact correction strategies in MRI-based attenuation correction in PET/MRI

In hybrid positron emission tomography (PET) and MRI systems, attenuation correction for PET image reconstruction is commonly based on processing of dedicated MR images. The image quality of the latter is strongly affected by metallic objects inside the body, such as e.g. dental implants, endoprostheses, or surgical clips which all lead to substantial artifacts that propagate into MRI-based attenuation images. In this work, we review publications about metal artifact correction strategies in MRI-based attenuation correction in PET/MRI. Moreover, we also give an overview about publications investigating the impact of MRI-based attenuation correction metal artifacts on the reconstructed PET image quality and quantification.


iNtRoductioN
To reconstruct positron emission tomography (PET) images with correct regional contrast and absolute quantification, correction for photon attenuation is essential. Commonly, attenuation correction (AC) is performed by using a 511 keV transmission scan in standalone PET systems or by multilinear rescaling of a CT image in hybrid PET/CT systems. In hybrid PET/MRI systems, where no direct information about photon attenuation is available, AC is currently based on processing of MR images (MRI-based attenuation correction, MRAC). On top of the classical MRAC problems such as the difficulty to reliably represent cortical bone in MR images or the limited transaxial field of view of MRI systems, the presence of metallic implants poses a major challenge for MR imaging and thus for MRAC. In this review about metal artifact correction strategies in MRAC for PET/MRI, we first give an introduction to metal artifacts in MR imaging and briefly summarize the state of the art for MRAC in clinical systems and research in the "Introduction" section. The following section describes the prevalence and impact of MRAC metal artifacts on the reconstructed PET image quality and quantification. In the "Correction strategies for MRAC metal artifacts" section, we review published correction strategies for MRAC metal artifacts before closing with a discussion and outlook. Since MRAC processing and its impact on the reconstructed PET images is substantially different for brain compared to whole-body PET/MRI acquisitions, we discuss them separately.

Metal artifacts in MR imaging
Metallic objects inside the body pose a severe challenge for MR imaging. Despite the fact that many metal implants are MRI safe, they strongly interfere with the MRI signal acquisition and thus affect the MR image quality that can be reconstructed. In the following, we briefly summarize the most common MR image artifacts that are caused by metal implants such as, e.g. dental fillings, surgical clips, screws or endoprostheses. For a more detailed problem description, we refer to the review of Hargreaves et al. 1 First, due to the lack of hydrogen nuclei in metal implants, no transverse magnetization, which is used as the imaging signal in MRI, is created. Consequently, the metal implant itself appears without signal (black) in the reconstructed MR image. Second, the presence of metal can cause strong variations in the static magnetic B 0 field due to susceptibility changes between the metal implant and the surrounding tissue. Those B 0 field variations depend on size, shape, type, and orientation of the metal implant and lead to local variations in the Larmor (resonance) frequency causing dephasing and signal loss. In the vicinity of metal objects, the spatial variations in the Larmor frequency can be so strong that magnitizations within a single voxel precess at different frequencies leading to complete dephasing and signal loss. As a consequence, regions around metal implants also often appear without signal in the reconstructed MR images. Commonly, the superposition of the first two effects results in a region without any MRI signal that is bigger than the metal implant itself (signal void or halo effect). The underlying dephasing of the magnetization can be reduced by using spin echo sequences or gradient echo sequences with very short echo times. 1 The spatial variations in the resonance frequency can lead to displacement of signal during excitation and readout which can shift signal away from regions (signal loss) but also to signal accumulation in other regions (signal pile-up). Another consequence of the resonance frequency variations can be geometric distortions and failure of water fat separation. Dixon techniques that are often used in MRAC can detect low frequent variations in the B 0 field but also fail to separate water and fat close to metal implants. 1 A typical example showing different MRI artifacts induced by a metal screw is shown in Figure 1.

MRI-based attenuation correction in clinical PET/ MRI systems and research
Since the introduction of PET/MRI for clinical use almost a decade ago, there has been a dedicated focus on improving MRAC. [2][3][4][5][6][7] The majority of the focus has been on the brain, which can be attributed to two main factors. First, the brain is, due to its rigid nature, an easier task for registration methods compared to the rest of the body. 8 Second, the initial MRAC problem of ignoring higher attenuation values of bone has more impact in the brain compared to the rest of the body. This is because the entire organ of interest (the brain) is completely enclosed by bone (the skull) making the exclusion of bone result in major PET bias in PET/MR imaging both close to and distant from the skull. 9 The main motivation for the advances in brain MRAC has been the acknowledgment of the importance of correctly accounting for bone during MRAC.
Today, MRAC is generally considered a solved topic for adult brains with normal anatomy. 7 However, an often neglected problem is MRAC in the presence of metal objects. Whereas a metal implant tends to produce streak artifacts in CT images, 10 it affects the MR images by inducing a susceptibility void with a reduced or complete lack of MRI signal. 11 As mentioned before, the size of the artifact area depends on the type of metal, and the MRI sequence used, 12 but is often greater than the extent of the metal itself. 12 The distortion can in some cases make the image anatomically unrecognizable. 12 The resulting local errors in the MR-based attenuation image introduced by neglecting tissue and metal in the affected area in the MR image processing translate into a bias in the reconstructed PET images. 6,[13][14][15][16][17][18] Patients referred for a PET/MRI examination are requested to remove all metal where possible, 19 but some metal cannot easily be removed. The main sources of the remaining metal-induced artifacts in brain PET/MRI are dental implants and surgical materials and devices.
MRAC in the body is in general more challenging compared to MRAC in the brain. This is because, first, most organs within the body move non-rigidly. Examples for non-rigid organ motion or deformations are respiratory or cardiac motion, flexible positioning of the arms, or non-rigid compression of the body caused Figure 1. Examples of artifacts due to presence of stainless steel screws in healthy 37-year-old male. A and B, In gradient-echo image with ±62.5 kHz receive bandwidth (A) and spin-echo image with ±16 kHz receive bandwidth (B), solid arrows show signal loss that can be due to dephasing or from signal being shifted away from region. Dotted arrow in B shows geometric distortion of femoral condyle, and dashed arrows show signal pile-up, which can be combination of in-plane and through-slice displacement of signal from multiple locations to one location. Reprinted from "Metal-induced artifacts in MRI", B. Hargreaves  by whole-body MRI coils. Second, the anatomic variability in the body is much bigger than within the brain which complicates the use of atlas-based techniques in whole-body MRAC for a wide range of patients.
That is why, all vendors started to use segmentation-based techniques to generate 3-class (Philips: air, lung, soft-tissue segmentation of T 1 weighted MR image 20,21 ) or 4-class (Siemens, GE: air, lung, fatty tissue soft-tissue segmentation of Dixon type MR images 22 ) attenuation images with fixed attenuation values assigned to the different tissue classes in whole-body PET/MRI. Note, that the missing bone problem is also present in wholebody MRAC. However, the introduced bias is much more localized to structures within or close to bone 23,24 and thus in general less severe than in brain applications. Recently, Paulus et al. 25 evaluated a model-based bone segmentation algorithm of Dixon images using a set of prealigned MR image and bone mask pairs for all major bones in the body. This technique is now implemented in the latest version of the Siemens mMR.
In general, all MRI segmentation-based methods for the generation of PET attenuation images face problems in regions with no MRI signal or contrast. Examples for those regions are: • Regions outside the MRI field of view, which is smaller than the field of view of whole-body PET scanners (ca 45 vs 60cm), lead to truncation artifacts in MRI segmentation-based attenuation images. Completion of those regions with the soft tissue attenuation coefficients is commonly done by using information from PET images reconstructed without or with imperfect AC. 26,27 • Cortical bone regions with extremely short T2 times. The latter and the fact that trabecular bone can show a variety of signals in different MRI sequences due to its fat content, currently impedes reliable segmentation of bones in T1 or Dixon-based MRI sequences without prior information • Regions inside the lung containing lung tissue with low MRI signal. Segmentation of the lungs is usually performed by using anatomical prior knowledge (regions with low MRI signal above a certain volume in the chest). Segmentation of the lungs is in general quite stable unless the low signal regions of the lungs are connected to other low signal regions such as the background, e.g. due to metal artifacts caused by sternal cerglages. • Regions inside and around metal implants such as hip, knee, or shoulder endoprotheses, spinal disk implants, sternal cerclages, surgical clips, or injection ports used for chemotherapy. As discussed in the "Metal artifacts in MR imaging" section, metallic implants produce susceptibility artifacts in MRI scans that lead to signal voids in and around the implant. Usually, those artifact regions are assigned with the air attenuation coefficient due to their low MRI signal. This in turn produces regions in the attenuation images where the attenuation is locally underestimated. 28,29 The magnitude and size of the introduced bias (usually underestimation) in the reconstructed attenuation corrected PET images depends on the size of the artifact and the time of flight (TOF) resolution that is available in the PET reconstruction. An example of a typical metal implant induced MRAC artifact is shown in Figure 2in reference. 30 In the following section, we briefly discuss the impact of metalimplant induced MRAC artifacts on the reconstructed PET images.
the PRevaleNce aNd iMPact of Metal-iMPlaNt iNduced MRac aRtifactS oN the RecoNStRucted Pet iMaGe quality aNd quaNtificatioN Theoretical considerations In clinical practice and research, PET image reconstruction is commonly performed using the iterative early-stopped (ordered subset) maximum likelihood expectation maximization algorithm (OSEM). In OSEM, the update of the activity concentration λ in a voxel j is given by where y it denotes the measured coincidence data in TOF bin t on line of response (LOR) i and c itj denotes the system matrix.
is the estimated coincidence data based on the current image estimate given by where s it are additive contaminations such as scattered and random coincidences. The system matrix elements c itj are commonly factorized into where p ij are geometric forward projection weights, g itj is the TOF kernel, n i is a normalization (sensitivity) factor, and the AC factor a i for LOR i given by where µ j is the 511-keV linear photon attenuation coefficient (LAC) in voxel j. Note that local errors in the attenuation image µ lead to errors in part of the AC factors and hence to inconsistencies in part of the system matrix. As an example, local underestimations in the attenuation image, which are common for metal-implant based MRAC artifacts, lead to overestimations of part of the attenuation factors and system matrix elements.
The specific impact of metal-based MRAC inconsistencies in the system matrix on the reconstructed activity image λ is in general hard to predict, since it depends on different factors such as the distribution of activity and attenuation and the available TOF resolution. Conti et al. 31 already noticed in 2011 that TOF PET reconstruction is more robust in the presence of inconsistent data. In this work, the authors concluded that TOF PET reconstruction "is less sensitive to mismatched attenuation correction, erroneous normalization and poorly estimated scatter correction. The spatial weighting derived from the TOF information competes, when conflicting, with other spatial weighting (normalization and attenuation), and during reconstruction partially corrects the accumulation of activity in parts of the image that are inconsistent with the data timing information. Such robustness is directly dependent from the time resolution of the TOF PET scanner, so we expect new generations of PET scanners, with improved time resolution, to be less and less sensitive to poor quality normalization, scatter and attenuation corrections. Moreover, TOF reconstruction can be beneficial in multimodalities, such as PET/MRI, where a direct attenuation measurement is not available and attenuation correction can only be approximated. " To visualize the potential impact of typical MRAC metal artifacts as a function of the available TOF resolution, we performed reconstructions of noise-free simulated PET emission data using the true attenuation image (the one that was used for data generation) and an attenuation image containing a typical metal MRAC artifact, namely a misclassification of the metal implant and its surrounding as air. The PET scanner geometry used in this three-dimensional simulation was the one of the GE SIGNA PET/MRI. Data of a head (dental implant artifact) and pelvic bed position (unilateral hip endoprosthesis) were simulated and reconstructed without TOF information and with a TOF resolution of 400 ps using 3 OSEM iterations with 28 subsets and 4.5 mm gaussian post-smoothing. As expected, the reconstructions shown in Figure 2 demonstrate that locally the simulated metal MRAC artifacts lead to a substantial underestimation of the reconstructed activity concentration in both the non-TOF and 400 ps TOF reconstruction. In line with the results shown in Conti et al., 31 the magnitude and the extent of the local underestimations is smaller in the 400 ps TOF reconstruction. The simulated lesion close to the implant is obscured in the non-TOF reconstruction, but remains visible in the TOF reconstruction-although with a substantial negative bias. Interestingly, the local underestimation of the attenuation around the implant in the pelvis also leads to local positive bias in the horizontal direction outside the artifact region. This bias is again more pronounced in the non-TOF reconstruction.  Figure 3. Buchbender et al. 13 investigated the likelihood of MRAC artifacts based on the presence of MRI artifacts. The authors found that out of 20 dental implants, 12 of them presented with visual artifacts on the MR images, and all but one of these impacted the MRAC images to a degree that resulted in decreased PET uptake. An example of the introduced bias was illustrated by Gunzinger et al., 33 who simulated dental artifacts of varying sizes inserted into the attenuation image in or near a carcinoma in the right tonsil, and found maximum SUV differences in the range of 8-33% from metal implants of 1-5 cm diameter for the GE trimodality PET/MRI system with 544 ps TOF resolution. Metal objects such as surgical materials and devices can be present especially when examining brain tumor patients post surgery. 34 The impact on MRAC of a metal-induced artifact in an MR image depends on the type of MRAC utilized, which can in large be split into three categories: segmentation-based, atlas-based and emission-based. Since the methods utilize and depend on the MR images differently, the influence of artifacts therefore also affect the methods in each category differently.
In the segmentation-based methods, where the image is separated into tissue classes based on the relative signal intensity, a signal void will most often be assigned to the air class, 13 whereas high intensity areas at the border of the signal void 12 will be assigned to the bone class when segmentation is based on UTE 14 or ZTE MRAC sequences. 16 The attenuation of the metal itself is not accounted for using the segmentation-based methods. A metal artifact-induced signal void therefore typically underestimates the PET uptake due to both the metal and soft tissue areas being set to air in the attenuation map, 13 that can impact the clinical setting when evaluating pathology close to the metal implant. 14 In the atlas-based methods, the MR image is used for registration and database matching. In the registration step, the MR image is non-linearly registered to one or more of the database-MRIs. [35][36][37][38] Larger artifacts with complete signal voids diminish the accuracy of the registration locally. 36 The corresponding CTs are typically combined into a pseudo-CT by averaging over a patch. The CTs are selected based on the corresponding MRIs similarity to the subject's MRI. When the subject MRI is lacking signal, finding the best matching MRIs in the database is challenging. 36 Confidently obtaining a matching MRI patch that in fact represents the same area is near impossible.
In the emission-based methods, where the MR image is only used as an anatomical prior, metal artifacts influences the predicted MR-based attenuation image to a lesser degree. 39

Whole-body PET/MRI
The prevalence of metal artifacts in whole-body MRAC strongly depends on the clinical indication, previous treatments (e.g. surgeries, chemotherapy) and age (prevalence of hip, knee and spine implants) of the examined patients. Brendle et al. 40   showed artifacts due to dental implants. Reading by two certified radiologists/nuclear medicine physicians revealed that the impact on the perceived image quality of the reconstructed PET images was less severe in TOF vs non-TOF PET reconstructions. In a patient with thoracolumbar spinal fusion, a bone metastasis was obscured in the non-TOF reconstruction, but could still be identified in the TOF reconstruction. Svirydenka et al. 45 studied the detectability of lesions close to simulated signal voids in non-TOF and TOF reconstructions in 27 patients with 51 lesions adjacent to the signal voids. In nine and one lesions, the detectability changed for non-TOF and TOF reconstructions, respectively. Two lesions were no longer visible in the non-TOF reconstructions. In all lesions, the SUV underestimation was decreased in TOF compared to non-TOF reconstructions. For example, in a lesion close to a simulated hip implant, the bias decreased from ca. 82% in the non-TOF reconstruction to ca. 42% in the TOF reconstruction. Attenberger et al. 46 showed two clinical examples of MRAC metal implant artifacts caused by surgical clips and a port used for chemotherapy and concluded "Since there are currently no sufficient technical solutions for the reduction of metal artifacts in PET/MRI, the best practice at this point is to simply perform PET-CT imaging if pathology is suspected adjacent to metallic implants. " Delso et al. 47 also concluded that at this moment (2015), there is no standard way to compensate for MRAC metal artifacts. In their PET/MRI study of myocardial viability, Lassen et al. 48 found that the attenuation images in 10 out of 20 cardiac patients (50%) suffered from susceptibility artifacts caused by sternotomy or other metallic objects such as stents. An example where an MRAC metal artifact changed the interpretation of a polar map in cardiological PET/MRI is shown in Figure 4.
Olin et al. 49 investigated the reproducibility of MRI-based thoracic attenuation images in the Siemens mMR. 1 of the 11 analyzed patients showed metal artifacts in each of the two generated attenuation images of all four PET/MRI examinations. The reproducibility of the SUV max in the second of the two lesions in that patient was not better than ca. 18%. Kuttner et al. 50 analyzed the reproducibility of lesion quantification in 25 lung cancer patients using the Siemens mMR. Three cases were affected by susceptibility artifacts that led to an underestimation of the reconstructed activity of up to 20% and "large inconsistencies between test-retest scans. " Despite that most of the focus in PET/MRI AC research has been on the brain, the amount of metal artifact correction methods are limited. The methods are, roughly put, based on dedicated sequences, an (un)intended feature of the MRAC method, or a post-processing of the traditional MRAC images. The advances within each area are described in the following.

Dedicated MRI sequences
Metal artifacts in MR images appear differently depending on the acquisition sequence utilized-they are most severe in gradient echo sequences, and most reduced in spin echo sequences with short TE. 51 In a prospective study, Gunzinger et al. 33 examined the effect of using MAVRIC to reduce dental artifacts. The authors acquired PET/CT and MRI scans for 25 patients, including standard MAVRIC and an adapted version optimized for speed. The artifacts present in the images were manually measured using the largest diameter in the axial direction and assuming ellipsoidal shape. Using the MAVRIC sequences, it was found that the size was significantly reduced (−75%) compared to a standard MRAC LAVA-Flex sequence.
In a retrospective study, Burger et al. 57 extended this, by similarly utilizing a diagnostic MAVRIC sequence to correct the Dixon-based attenuation maps in areas with dental implants. The method relies on the tissue intensity of the MAVRIC image in artifact areas where the Dixon in-and opposed-phase MR images have a lack of signal. By superimposing either fatty or soft tissue values in the artifact area, based on the MAVRIC image intensity, the authors obtained a corrected attenuation map. An illustration of the performance can be seen in Figure 5. In eight patients, the artifacts in the MRAC maps were reduced on average from 698 to 203 mm 2 when using the semiautomatic correction method.
The added accuracy of the specialized sequences also comes at the cost of increased acquisition time which is usually too high for pure MRAC purposes-the acquisition time of the MAVRIC sequence is between 3.5 and 6 min, depending on the version, compared to 14 s for a LAVA-Flex MRAC sequence. 33 It could, however, be of interest in specialized occasions, e.g. when examining patients with tumors in the oropharynx. 33

Part of the attenuation method
Metal artifact correction is in some MRAC methods already a feature by the very nature of the method type, either coincidentally or by design. The following highlights how novel MRAC methods handle metal artifacts.

Joint estimation of emission and attenuation: When
AC is based on emission data, the influence of the MR image is less or non-existing compared to a segmentation-based method, making such methods robust to metal artifacts. 58 Mehranian et al. 39 utilized an MRI prior for brain MRAC using maximum likelihood activity and attenuation (MLAA) reconstruction, and found that the emission-based method had a high potential to differentiate metallic implants from soft tissues when using TOF scanners, and even to recover the high valued linear attenuation coefficients (LACs) of dental implants. In general, joint estimation of activity and attenuation methods are not yet accepted as a clinically feasible MRAC technique, mainly due to the fact that they require sufficient TOF resolution, due to the limited accuracy compared to segmentation-or atlas-based methods, 7,39 and due to the absence of reliable implementations into clinical PET/ MRI scanners. With it being an active field of research, the former limitations are likely to be overcome. Recently, a publication by Razaei et al. 59 showed improved performance of a TOF-based MLAA MRAC method in brain PET/MRI, with accuracy similar to a state-of-the-art ZTE-based attenuation method for data from the GE SIGNA TOF PET/MRI. The authors demonstrated the ability of their method to recover most of the jaw, including bone and metal, in a patient with metal implant-induced artifact in the dental region, despite using an MRI-based intensity prior as input (Figure 4 in Rezaei 59 ).
Atlas-based: In the case of smaller metal artifacts occurring at a common location, as in dental artifacts, the atlas-based MRAC methods could be a viable solution. By matching to the database MRIs, the atlas-based methods can select cases with similar artifacts. The use of pattern or patch matching might even introduce metal into the attenuation map in the cases of moderate dental artifacts. 39, 60 Hofmann et al. 61 showed how an atlas-based method reduced the effect of dental artifacts from 40% PET underestimation to <10% compared to conventional segmentation-based MRAC. Atlas-based methods are, due to this relative insensitivity to metal, superior to segmentationbased methods in the case of smaller dental artifacts. 4 In the case of larger artifacts, completely removing the MRI signal, or artifacts from surgical materials occurring at uncommon locations, atlas-based methods are challenged by the lack of training data. Especially atlas-based 35,36,38 or patternrecognition methods 37 that synthesize the CT image within local patches that might be completely corrupted are challenged. In such cases, a template-based method, which is a subtype of the atlas-based methods only utilizing a single MRI-CT pair, might provide more accurate and anatomically correct results for the missing artifact region, as it retains the spatial relative information. 62,63 It is worth noting that the atlas-based methods are further challenged by a lack of a true gold-standard, since CT images also suffer from metal implants resulting, e.g. in streak artifacts. Moreover, the rescaling of CT Hounsfield units of metals to 511 keV attenuation coefficients is non-trivial.
Deep learning-based: Recently, several methods for brain MRAC have been proposed utilizing the advances within deep learning and convolutional neural networks. [64][65][66][67][68] These networks excel in noise reduction, and could therefore contain an untapped potential for metal artifact correction, as has been explored towards CTAC metal artifact reduction. 69,70 Ladefoged et al. 68 showed that a deep learning-based MRAC method was able to achieve a performance comparable to CTAC in pediatric patients with metal clip implanted into the skull causing both artifacts and abnormal anatomy in the used MR images.
Recently, Hwang et al. 71 trained a deep learning model with the activity and transmission outputs of a TOF-based MLAA algorithm to improve the accuracy of the attenuation map, and achieved relative PET errors comparable to other state-of-the-art MRAC methods. 7 Similar to the emission-based methods, this method works independent of the MR images, making it insusceptible to metal artifacts. It remains to be shown whether deep learning-based methods can play a role in correcting larger metal artifacts.

Post-processing of the attenuation maps
Post-processing of the attenuation map is the only remaining strategy to correct for metal artifacts when neither specialized sequences is an option or the chosen MRAC method manages to overcome the artifact. Ladefoged et al. 72 proposed a twofold method to correct dental artifacts by first delineating the outer contour of artifacts breaching the anatomical surface using statistical models of possible dental shapes, and then classifying internal air cavities based on their position relative to anatomical landmarks. This type of method is limited to inserting soft tissue in the signal voids, failing to compensate for the metal implant itself. When comparing the PET signal after filling the artifact region with soft tissue, which is still an underestimation of the true density, the mean PET signal increased by 48% in the affected region, and up to 7% in the cerebellum. 32 Here, it was concluded that the artifact region could potentially obliterate a tumor in the dental region.
Arabi and Zaidi 73 proposed to use deep convolutional neural networks for completion of artifact areas. The authors used co-registered PET, CT, and MR data from 15 patients examined with FDG-PET for staging of head and neck malignancies, to train a network for completion of the MR images. The evaluation was performed using 10 patients with metal-induced artifacts, where using the proposed deep learning architecture improved segmentation accuracy in the area incorrectly segmented as air, decreasing SUVmean bias from −60 ± 11% (without correction) to −24 ± 9% (with correction).
A study by Fuin et al. 74 proposed to use emission data in non-TOF systems to correct the artifacts in the attenuation map.
Here, the authors first semiautomatically segmented the artifact region, and then fixated the LACs outside the region during the reconstruction. The method appears to recover not only the shape but also the LAC of the metal implant, and if so, being the only method available to do so. The method was only tested on 11 patients, of which 2 were dental implants, and therefore remains to be tested on a larger patient cohort.

BJR|Open
Review article: Metal artifact correction in MRAC in PET/MRI Whole-body MRAC Similar to brain MRAC, strategies for metal artifact correction in whole-body MRAC can be classified into different groups that are described in the following.

Dedicated MRI sequences
As in the case of brain MRI, dedicated MRI sequences that reduce the size of the signal voids around metal implants such as SEMAC or MAVRIC 1,75-78 can help to reduce the size of the artifact regions in the MRI-based attenuation images and thus lower the bias introduced in the reconstructed PET images. However, to the best of our knowledge, there are currently no publications that evaluate the performance of those sequences in the context of whole-body MRAC.

Inpainting methods
The basic idea of inpainting methods is to fill the signal voids caused by metal implants in the attenuation MRI with the softtissue LAC in the corresponding attenuation image. In this way, the bias introduced in the attenuation factors (negative exponential of the forward projected attenuation image) is strongly reduced.
Ladefoged et al. 29 showed that manual inpainting of the artifact regions with the soft tissue LAC can restore the uptake pattern in non-TOF PET reconstructions in the vicinity of the metal artifact and concluded that this "method can be recommended as a first-line retrospective correction of artifacts resulting from endoprostheses present during WB PET/MRI imaging. " The authors also showed that inpainting with the soft-tissue LAC leads to less bias compared to inpainting with the much higher metal LAC. The latter leads to substantial local overestimations of the reconstructed activity concentration since the signal void in the commonly used attenuation MRI sequences is much bigger than the metal implant itself.
Based on this work, Schramm et al. 42 presented a method for automatic inpainting of MRAC metal artifact regions with the soft tissue LAC. The proposed method consists of three steps. First, the outer contour of the attenuation MRI is closed based on information obtained from an initial TOF PET reconstruction with a simple segmentation-based attenuation image. This contour closing is needed for lung segmentation in the case of sternal cerclages or for the inpainting of MRI signal voids that are connected to the background such as, e.g. caused by knee implants. In the second step, the lung is segmented as low MRI intensity regions at a certain distance to the shoulders. In the final step, all other internal low MRI intensity regions are filled with the soft tissue LAC. The authors demonstrated the stability of the algorithm in 13 patients with sternal cerclages, hip implants and knee implants. A potential drawback of this method is the fact that all internal air cavities outside the lungs are also filled the soft-tissue LAC which leads to local overestimations of the reconstructed activity concentration close to those regions.

Atlas-based methods
As discussed before, atlas-based methods for the generation of MRI-based attenuation images, especially those relying on pattern or patch matching, are challenged by bigger regions without any MRI signal.
While the atlas registration and pattern recognition method presented by Hofmann et al. 61 was able to strongly reduce the bias in the reconstructed PET images close to metal artifacts caused by a postoperative clip and a dental implant, it failed to compensate the signal void caused by a sternal wire and thus  Figure 6.
Based on the work in Hofmann et al., 61 Bezrukov et al. 79 developed two advanced methods for the compensation of MRAC metal artifacts that use a combination of segmentation-and atlas-based prior knowledge. The first method (SEG2) uses an atlas of potential metal artifact regions to fill signal voids caused by metal implants with the soft tissue LAC. The artifact location atlas was derived from 11 patients with metal implants and contained prior information about the location of hip prostheses in the pelvis and about sternal cerclages and portal catheters in the thorax. In the second method (SEG2wBone), information about higher bone attenuation was superimposed on the attenuation images generated with SEG2. Using the developed methods, the bias in nine lesions located close to the metal artifacts regions could be reduced from −54 ± 38.4% to −15.0 ± 12.2% (SEG2) and to 0.6 ± 11.1% (SEG2wBone). A representative example is shown in Figure 7. As mentioned before, the performance of any atlas-based method strongly depends on the number and quality of data sets available in the atlas.

Joint estimation of emission and attenuation
An interesting alternative to all previous methods is the estimation of attenuation properties from the acquired PET data itself. Defrise et al. 80 could prove that the availability of TOF determines the attenuation sinogram up to a constant. Rezaei et al. 81 proposed the MLAA estimation algorithm that allows to jointly reconstruct the emission and attenuation image (instead of the attenuation sinogram). The authors could show that with TOF data the cross-talk between emission and attenuation image can be strongly reduced, 82 provided that the object diameter is bigger than the spatial width of the TOF kernel.
Since MLAA does in general not rely on MRI or CT information, it is not directly affected by metal-induced signal voids in attenuation MR images nor by metal artifacts in attenuation CT images. Note, however, that all joint estimation methods need prior information since the attenuation sinogram is only determined up to a constant. This prior information can be, e.g. implemented as an absolute intensity prior for the linear attenuation coefficients of a certain tissue class (e.g. soft-tissue) in a given region.
Ahn et al. 58,83 proposed to combine MLAA with a quadratic intensity prior for the attenuation coefficients based on an initial standard MRI segmentation-based attenuation image. High prior weights were used in regions with known attenuation (regions with high MRI signal) and low prior weights were used in regions with low MRI signal which are potentially lung, air cavities, cortical bone, or metal artifact regions. The authors could show in 12 TOF data sets using 3 different tracers that their proposed method is able to recover the shape and the higher metal attenuation coefficients of a hip implant and pedicle screws in the spine (see Figure 8). Moreover, lower attenuation values in abdominal air cavities could be recovered. The authors could also show that the MRI-based prior substantially reduced residual cross-talk artifacts as observed in the bladder.   74 demonstrated that their algorithm "implant PET-based attenuation map completion" works well with non-TOF data sets from the Siemens mMR (see Figure 9). To circumvent the cross-talk problem, Fuin et al. initialized their joint reconstructions with a MRI segmentation-based attenuation image where the metal artifact regions were manually inpainted with the softtissue LAC (similar to 29 ). Moreover, in the optimization of the joint cost function using the L-BFGS-B optimizer, the attenuation image was strongly constrained by keeping all attenuation coefficients outside the metal artifact regions fixed. On top of that, the attenuation coefficients within the metal artifact regions were constrained to be within 0.08 and 1 cm −1 . The analysis of 11 patients with 13 metal implants showed that the bias introduced by MRAC metal artifacts could be reduced from 80.1% ± 27.1% to 20.3% ± 23.1% using CTAC as a reference.

diScuSSioN
All in all, publications on techniques for correction of metalimplant induced artifacts in MRAC are still scarce and no reliable and stable solution has been implemented in any of the currently available PET/MRI systems. As discussed in "The prevalence and impact of metal-implant induced MRAC artifacts on the reconstructed PET image quality and quantification" section, the MRAC metal artifacts can have a severe impact on PET image quantification and lesion detectability in the vicinity of bigger metal implants-typically seen in the body-depending on the available TOF resolution. While artifacts caused by bigger metal implants are visually easy to detect in the reconstructed PET images, small artifacts as, e.g. caused by stents or surgical clips might be missed and might lead to misinterpretations of the reconstructed PET images as shown in Figure 4 depending on the clinical task. It should be once again emphasized that attenuation images should always be inspected for potential (metal) artifacts when reading PET images from PET/MRI acquisitions. Unfortunately, studies evaluating the impact for a given clinical task such as, e.g. lesion detection or quantification in bigger patient cohorts with metal implants are still missing.
Given the fact that the available TOF resolution of new PET scanners is steadily improving (nowadays between 300 and 400ps), we are convinced that joint estimation methods for emission and attenuation are probably the most promising candidate to solve the MRAC metal problem in current and upcoming TOF PET/MRI systems. The proof of concept results obtained by Ahn et al. 58,83 and Fuin et al. 74 using constrained MLAA to estimate the attenuation of metal implants are very promising for TOF and even non-TOF PET/MRI systems, respectively. To validate and improve the performance and stability of those methods in bigger studies, implementations of these algorithms on the commercially available systems by the vendors would be highly desirable. On top of the ability to estimate attenuation values of metal implants correctly, MLAA type methods also have the advantage that they are by design not susceptible for motion-induced misalignments between emission and attenuation images, e.g. caused by respiratory motion. Nevertheless, more research needs to be done to reliably solve the inherent scaling problem of MLAA (e.g. by using dedicated MRI-based prior knowledge) and to deal with the increased sensitivity of MLAA with respect to inconsistencies in TOF scatter estimation and scanner calibrations. 59,84 The future potential of atlas-or deep learning-based methods to predict correct attenuation values from MR images with bigger metal artifacts is at the moment hard to predict. This is due to the fact that (a) the problem is very ill-posed since there is no information in the signal void to distinguish the metal implant itself from surrounding tissue and (b) the success of any atlas or deep learning method strongly depends on the availability of a large number of high quality training data sets which are the moment not available for MRAC metal artifacts. Deep learning generative adversarial networks using unpaired data might be a solution to overcome this limitation. Moreover, the generation of ground truth attenuation images is challenging to the presence CT metal artifacts and the non-trivial scaling CT Hounsfield units to 511 keV attenuation values for metals. Undoubtedly, all classical-or deep learning-based approaches would benefit from reducing or avoiding the signal loss, signal pile-up and geometric distortions around metal implants. Whether this can be achieved with MRI sequences such as MAVRIC or SEMAC within a given amount of available acquisition time, remains to be tested.
From the view point of the current clinical PET/MRI user, there is still no vendor solution to correct for metal MRAC artifacts which means that reliable image reconstruction in the vicinity of bigger metal implants is currently not possible. Until more sophisticated correction methods become available, a manual inpainting method implemented in the clinical systems would be very helpful to correct the major part of the bias caused by MRAC metal artifacts.
ackNowledGMeNt Georg Schramm would like to acknowledge the helpful discussions with Johan Nuyts and Ahmadreza Rezaei.