Magnetic Resonance-Based Attenuation Correction and Scatter Correction in Neurological Positron Emission Tomography/Magnetic Resonance Imaging—Current Status With Emerging Applications

In this review, we will summarize the past and current state-of-the-art developments in attenuation and scatter correction approaches for hybrid positron emission tomography (PET) and magnetic resonance (MR) imaging. The current status of the methodological advances for producing accurate attenuation and scatter corrections on PET/MR systems are described, in addition to emerging clinical and research applications. Future prospects and potential applications that benefit from accurate data corrections to improve the quantitative accuracy and clinical applicability of PET/MR are also discussed. Novel clinical and research applications where improved attenuation and scatter correction methods are beneficial are highlighted.


INTRODUCTION
Hybrid positron emission tomography/magnetic resonance (PET/MR) systems for clinical imaging have been first introduced nearly a decade ago, with systems capable of either sequential or simultaneous image acquisition. The first concept studies for successful combined PET/MR measurements were initially performed in 1996 [1]. After solving several technical challenges due to the complexity of integration of PET and MR, the first commercial whole-body PET/MR systems were installed in 2010 [2,3]. PET/MR instrumentation has been an active field and has been discussed in several review articles [4][5][6][7][8][9]. The introduction of simultaneous PET/MR systems for clinical use has been suggested to mark a paradigm shift for neuroimaging, and the combination of both systems offers a multitude of advantages [10][11][12]. As can be seen in several clinical and research scenarios, PET/MR offers many advantages over positron emission tomography/computed tomography (PET/CT) or standalone MR.
Fusion information of MR and PET provides advantages over PET and computed tomography (CT) in neurological applications, as overlaying MR and PET image supplies improved diagnostic information in characterization of many conditions [13]. Beyond image fusion, MR offers a library of multiparametric imaging information from morphology, function to even metabolism that cannot be obtained from CT. MR has also an excellent sensitivity in capturing the small changes in brain structure and function [14]. PET on the other hand, offers a high specificity and a wide quality of radiotracers applicable for investigation of numerous molecular targets [14]. Potential applications include metabolism, receptor function, neurotransmitter distribution, inflammation, antigen targeting, and tissue perfusion. Thus, PET/MR unlocks a multitude of novel research and diagnostic applications. To improve data synergy between PET and MR, the focus from hardware integration has shifted to development of integrated data processing and analyses [14]. It is clear that both the research and the diagnostic capabilities of hybrid PET/MR could be extended from that of PET/CT, once fusion information from PET and MR is realized in a more complementary fashion.
However, as PET imaging is severely affected by both photon attenuation and scatter, effective data corrections for both physical phenomena are needed to produce quantitative images reflecting the true spatial distribution of the radiotracer. The physical basis of both scatter and attenuation is explained in detail in review papers of Zaidi and Hasegawa [15], Zaidi and Montandon [16], and Martinez-Möller and Nekolla [17]. Thus, a prerequisite to these corrections is the availability of an accurate attenuation map containing the attenuation coefficients for 511-keV photons at each voxel [17], which makes attenuation correction fundamental to produce visually and quantitatively accurate PET images. Shortly after the introduction of the first commercial PET/MR systems, this became a fundamental limitation of the modality, until the methodological challenges were addressed and effective methods were introduced.
Rotating transmission sources and a bilinear scaling procedure with CT can be applied for attenuation correction on standalone PET and PET/CT systems, respectively [18]. On PET/MR, there are two basic methodological challenges related to attenuation correction. First, MR-based attenuation correction (MRAC) is a challenge due to the very basic idea of what MR images represent-proton density and relaxation time properties of biological tissues [17]. However, for attenuation correction purposes, tissue electron density information needs to be resolved. Therefore, there is no standardized transformation procedure that can translate the MR tissue intensities to tissue attenuation properties as in CT-based attenuation correction (CTAC). An equally important second challenge is the short T2 * relaxation time of bone, which makes it hard to delineate bone, unless MR sequences based on ultrashort echo time (UTE) or zero echo time (ZTE) sequences are used [19].
Thus, the main challenges in MRAC originated from deriving bone density information on an individual basis and differentiating bone in MR images. These two challenges led to the first clinically implemented MRAC methods ignoring bone entirely in the body and brain region and replacing bone with soft tissue. However, neglecting bone in attenuation map in the head region was shown to cause large, spatially varying bias in regions close to bone, such as in the cortical regions of the gray matter with errors of magnitude across the brain ranging from −10 to −25% [20,21]. These errors could also be visually regarded as cortical hypometabolism, representing a potential factor for misdiagnosis, thus impairing the diagnostic quality of the PET/MR images [20,21]. This led to a large and active field of methodological development in MRAC.
To account for these challenges, a multitude of innovative methods for MRAC were developed over the course of years following the introduction of the first simultaneous PET/MR systems. These methods are well-summarized in the excellent review papers of Martinez-Möller and Nekolla [22], Hofmann et al. [23], Berker and Li [24], Bezrukov et al. [18], Chen and An [25], Izquierdo-Garcia and Catana [26], Keereman et al. [17], Wagenknecht et al. [27], and Mehranian et al. [28] and partially in Teuho [29]. These methods have been proven to be fairly accurate, as a recent multicenter study with 11 MRAC methods and three radiotracers including [ [30]. To illustrate this, Figure 1 shows the reported global bias and standard deviation of the methods reported in the MR-Based Attenuation Correction for PET/MR Neuroimaging section, where applicable.
Thus, while the challenge of improving accuracy of MRAC with adult brains with normal anatomy can be considered to be solved [30,47], future methodological advances are of interest. It seems that the focus of methodological research in MRAC is now shifting on improving the accuracy of the existing methods and applying them to novel clinical and research applications. While the accuracy of MRAC is no longer the major methodological problem, increasing accuracy is always desirable [36] in combination of the assessment and application of MRAC methods for more challenging clinical and research applications. Therefore, any application that involves detection of subtle changes in the brain, such as dementia trajectory or epilepsy lesion detection, will benefit from increased accuracy of MRAC and subsequently from accurate scatter correction.
In addition to attenuation correction, scatter correction is one of the major quantitative corrections performed in PET, as the fraction of scattered photons in three-dimensional (3D) PET acquisitions in the brain region can be increased to over 30% [48]. Both attenuation and scatter correction are related, as the attenuation sinogram is used in the calculation of the scattered photons when performing single scatter simulation (SSS). A few reports have investigated the effects of the accuracy of the attenuation map on scatter correction. These investigations unanimously concluded that the errors in the attenuation map introduced to calculated scatter sinograms are much smaller than errors produced by incorrect attenuation correction [49][50][51][52]). While scatter correction has not been a major issue to be addressed for neurological PET/MR imaging, developments in scatter correction are FIGURE 1 | A scatter plot diagram that contains the reported global average bias and standard deviation in percentage of the methods included in this review. It can be seen that majority of the published methods perform with a mean bias up to ±5% in positron emission tomography (PET) evaluation. Most of the methods also have a mean bias in the range of the difference (−6 to +4%) to what was previously reported in a phantom study between different positron emission tomography/computed tomography (PET/CT) and positron emission tomography/magnetic resonance (PET/MR) systems [31]. Segmentation-based methods: 1-4 [ also beneficial for increasing the quantitative accuracy of PET images. Consequently, methodological developments that increase the accuracy of attenuation correction will also result in minimization of errors in scatter correction.

MR-BASED ATTENUATION CORRECTION FOR PET/MR NEUROIMAGING
A multitude of MRAC methods have emerged, and significant methodological advances have been made in the PET/MR field of neuroimaging, since the introduction of the first PET/MR systems. Attenuation correction for PET/MR can be performed based on anatomical MR images, PET datadriven approaches, or a combination of both. The attenuation correction strategies can be roughly divided into (a) methods based on image segmentation, (b) atlas or database approaches including machine learning methods, and (c) emission datadriven approaches, which use PET data alone or in synergy with existing magnetic resonance imaging (MRI) data. A strict division between methods is challenging, as some of the methodology can be used in combination, e.g., segmentation and template.  [26], and Mehranian et al. [28]. The physical basis of attenuation correction concerning PET/MR is addressed in Martinez-Möller and Nekolla [17]. In this section, we will focus on methods that allow for bone delineation for brain imaging applications, as methods that ignore bone should be avoided.

MRAC Methods Based on Image Segmentation
The aims of any segmentation-based MRAC method are to divide the tissues from MR images into specific classes and to assign the attenuation coefficients either based on predefined value or determining that value individually. The number of classes used depends on the method, where three tissue classes (bone, soft tissue, air) are considered the minimum, while additional classes might improve the accuracy. The first methodological challenge is to ensure that tissues are segmented and classified in an accurate and reproducible manner, so that the overlap between tissues that have large differences of attenuation coefficients is minimized, such as bone (0.151 cm −1 ) and air (0.0 cm −1 ). Challenging regions to segment are those that include, e.g., tissue interfaces such as the sinus region. Challenges for image segmentation for UTE and ZTE can be found, e.g., in Delso et al. [54,55] and Aasheim et al. [56].
The tissues in the head region might be roughly divided into the following classes: soft tissue (0.094-0.100 cm −1 ), adipose tissue (0.086-0.093 cm −1 ), air cavities, and bone. A further division can be made between the nasal cavities (sinus region), 1 | Generalized summary of the methodology between (a) segmentation-, (b) template-, and (c) emission-based MRAC methods. Essential concerns, potential solutions, and future directions are highlighted.
Need to ensure Quality of the segmented images (no signal voids, artifacts) and the accuracy of segmentation.
High number of subjects for database creation and method validation, especially for deep learning.
High quality of the emission data by accurate corrections and calibrations.
Specific advantages Subject-specific anatomy and anatomical variation is accounted for, fast and simple to implement.
Continuous attenuation coefficients for the entire head region.
Can estimate attenuation in the presence of signal voids and implants.
Specific disadvantages Robustness in challenging anatomical regions (e.g., sinuses) or presence of MRI artifacts.
Accounting anatomical and attenuation coefficient variability.
Non-emitting objects remain invisible.
Issues that have been addressed since previous reviews different classes of bone (spongy and cortical: 0.130-0.172 cm −1 ), and different brain tissues (gray and white matter: 0.099 cm −1 , cerebrospinal fluid: 0.096 cm −1 ). Each of these tissues has a different attenuation coefficient, which might vary on an interor intrapatient basis. Thus, the most preferable way would be to account and assign the attenuation coefficients on an individual basis. This would reduce the variation caused by the differences in individual anatomy and different patient groups. Thus, the second methodological challenge is to account for the variation of attenuation coefficients in tissues and in patients. Segmentation-based methods are popular due to ease of implementation and low computational cost. Multiple methods based on segmentation of T1-weighted images have been proposed. Zaidi and Fei proposed using T1-weighted MRI images, which are co-registered to PET data and segmented by fuzzy C-means clustering to air, scalp, skull, gray matter, white matter, and nasal sinuses [57,58]. Statistical parametric mapping version 8 (SPM8) has also been applied to extract the bone component from T1-weighted images, which is added to the Dixon-based attenuation map [59,60] or by deriving a threeto six-class attenuation map from T1-images alone [32,61]. The advantage of these methods is that they are straightforward to apply across multitude of datasets, as the only requirement is access to T1 data, which is collected routinely. In addition to T1weighted MR images, methods based on segmentation of [ 18 F]sodium fluoride ([ 18 F]-NaF) PET [62] or on a combination of segmentation and a fixed point source have been applied [63].
Methods based on bone delineation from short echo time (STE) sequences such as UTE or ZTE have become one of the most popular fields in segmentation-based MRAC. To visualize and account for bone, UTE-based methods were introduced in Keereman et al. [64], Catana et al. [65], and Berker et al. [66]. While these methods showed improvements in the visual and quantitative accuracy of PET images, inconsistencies in bone delineation were reported with UTE [21,56,67,68], which later resulted in improved segmentation methods and MRI sequences. After the introduction of UTE, methods based on ZTE emerged [55,69,70]. With both UTE and ZTE, the development of more advanced segmentation techniques and new MRI sequences has been an active field of research, to increase the accuracy of bone delineation and segmentation.
To improve the quality of segmentation, several techniques have been applied. One is to use regional masks [71] or anatomical templates [36] to assist in the delineation of different tissues. Specific masks for challenging regions such as the sinus cavities have been also proposed [72,73]. Delineation of tissues based on tissue clusters from dual echo UTE has also been applied [54]. Recently, improved segmentation with UTE was achieved by using custom templates and tissue probability maps with statistical parametric mapping version 12 (SPM12) segmentation engine to improve the delineation of both air and bone [74]. Machine learning techniques have also been used to refine the quality of the attenuation maps derived with UTE and could potentially be applied in any segmentation-based MRAC method [75].
Improved MRI sequences for UTE include STE/Dixon and fuzzy clustering [76], improved UTE using point-wise encoding time reduction with radial acquisition (PETRA) [77] or likewise a fast dual-echo ramped hybrid encoding (dRHE) [78], and reduction of eddy current artifacts [79]. Sequences based on triple-echo UTE have also been applied [66,79,80]. These methods have shown improvements in terms of accuracy of the attenuation map, PET image quality, and quantitative accuracy, compared to UTE-based methods introduced previously. Recent developments include also the use of 3D radial ZTE imaging [81], which is primarily a proton density-weighted sequence. Several studies on successful use of ZTE-based methods on MRAC have been published recently [55,69,70,72] in addition to assessment of repeatability [82].
Nevertheless, all previously described methods assign discrete linear attenuation coefficients to each class. Methods that apply continuous attenuation coefficients for bone have been introduced to address the limitations with discrete attenuation coefficients. A common factor for these methods is to apply a calibration curve (sigmoid, polynomial, or linear function) between the relationship of Hounsfield unit (HU) values vs. R2 * values or ZTE intensities. This allows for mapping of the MR intensities in the bone region to HU values on a voxel basis. HU to R2 * mapping has been successfully applied in Navalpakkam et al.; [41], Ladefoged et al. [71], Baran et al. [74], and Juttukonda et al. [83], while HU to ZTE intensity transformation has been applied in Khalifé et al. [84] and Yang et al. [72]. The performance of methods using continuous attenuation values is generally considered superior over discrete-tissue methods.
In summary, it can be seen that methods based on UTEs, such as UTE and ZTE, have become a very popular option for segmentation-based MRAC as they allow us to visualize and segment bone with fairly good accuracy, addressing the first challenge, which is the delineation of skull bones. Previously, segmentation-based methods were limited by assigning fixed attenuation coefficients to bone, but lately, this problem has been circumvented by implementing calibration curves between HU and R2 * or HU and ZTE intensities, addressing the second methodological challenge. However, there are several regions, such as air-tissue interfaces in the sinus cavity, which are still challenging for segmentation-based methods. To account for this challenge, a multitude of techniques from improved MR acquisition to masks and templates to assist segmentation have been applied, helping to improve the accuracy of the available methods.

Methods Based on Atlas or Database Approaches Including Machine Learning
Atlas-or template-based methods are typically based on using a co-registered database or atlas of CT and MR images. Methods can be further divided into approaches applying a single probabilistic atlas or a multiple atlas. To create a substitute CT, the subject MR image is matched to an MR image in the database or a predefined template. The best match is determined using a predefined similarity metric. Thereafter, the purpose is to create a CT substitute corresponding to subject anatomy with continuous attenuation coefficients for the whole image volume, usually referred to as pseudo-CT. The substitute pseudo-CT is usually created in a volume-by-volume, slice-by-slice, or voxel-by-voxel basis, using a trained classifier, image intensity mapping, or registration techniques. Recently, methods based on machine learning or deep learning techniques have also become increasingly popular.
The most straightforward implementation is to use a single atlas in combination of a predefined template. Templates can be created by taking an average of multiple co-registered CTAC or transmission-based attenuation correction (TXAC) images to represent mean attenuation coefficients and anatomical variability in a given population [85]. Template-based approaches using registration and nonlinear wrapping of a predefined TXAC or CTAC template to the individual subject anatomy using SPM have been proposed [44,86]. SPM8 has also been used to perform segmentation and state-of-the-art registration with a probabilistic template to derive a pseudo-CT [87]. Similar approaches have been implemented by either wrapping of a CT atlas to the patient MR image using a two-step registration [88] or registering a subject MR image to an MR template and mask pair, followed by a two-step registration to delineate bony regions with the mask [89]. Limitations of the single-atlas approaches include ignoring the intersubject variation of attenuation coefficients and that the anatomical transformation might be prone to errors in registration between the template and subject images, especially with non-conventional anatomy or in the presence of disease.
Several methods based on a multiatlas approach have been introduced, where an atlas of multiple pairs of CT and anatomical MR images is used to derive patient-specific substitute pseudo-CT either by intensity mapping or by registration. Several approaches to derive the pseudo-CT substitute exist, such as using patches to match CT and MRI intensities [90,91] or image registration techniques [50,[92][93][94]. The substitute pseudo-CT can be also derived by linking the intensities between CT and MR images with a trained model, such as using a Gaussian mixture regression model with probabilistic measures [40,95,96] or a Gaussian mixture model based with patches [97]. While methods using multiple atlases are inherently more complex and computationally intensive, they are able to overcome the limitations of single-atlas approaches [98].
Probabilistic measurers in combination of atlases have been also applied for pseudo-CT creation, which can be used to improve the quality of segmentation or to generate continuousvalued attenuation maps [39,53,99]. In addition, pattern recognition [38] or machine learning techniques [41] have been successfully applied. Machine learning applying a random forest regression with patch-based anatomical signatures was used to generate pseudo-CT from T1-weighted images in Yang et al. [100]. Recently, several methods based on deep learning have also become increasingly popular in the creation of a suitable attenuation maps for MRAC.
Santos Ribeiro et al. [101] proposed a feed-forward neural network to directly output a continuous-valued head attenuation map by nonlinear regression of several UTE images and a template-based MRAC map. Gong et al. [102] used a convolutional neural network with Dixon images only or in a combination of Dixon and ZTE images to generate a continuous valued attenuation map. Similarly, a deep convolutional neural network that derived attenuation maps based on ZTE images was shown to outperform both ZTE and atlas-based method in Blanc-Durand et al. [43]. Interestingly, while most evaluations have been performed with adults with normal anatomy, Ladefoged et al. [103] evaluated deep learning methods in pediatric brain tumor patients, with robust performance. The preliminary results obtained with these methods are encouraging.
However, it would be advantageous if conventional MR images collected routinely or PET data could be used to obtain an attenuation map. The use of deep convolutional neural networks with T1 images only has been reported in Han [104] and Liu et al. [105], and they have been applied also to synthetize a pseudo-CT from patient-specific transmission data [106]. Recently, Liu et al. [107] proposed to use only uncorrected PET images with a deep convolutional encoder-decoder network to generate a pseudo-CT. Very recently, a multiparametric MRI model was also suggested to generate pseudo-CT maps based only on Dixon MRI images and was evaluated on head and pelvic images [108]. Among other benefits, these methods also show a great potential for whole-body applications. Finally, any deep learning methodology conventionally requires a large dataset of paired CT and MRI images. Recently, methods based on unpaired image-toimage translation using Cycle-Consistent Generative Adversarial Networks (CycleGan) [109] have been applied to pseudo-CT generation [110,111], which might circumvent this requirement.
In summary, the atlas or database approaches range from simple single-template methods to complex approaches, allowing us to derive continuous attenuation coefficients not just in bone but also in a range of tissues. There is also a multitude of good methods available. Most of these methods, however, have been solely applied in research context. Until recently, a few promising studies in using atlas-based approaches on non-normal populations such as pediatric patients and in brain tumors have emerged. Naturally, pediatric patients require that an atlas fit for different anatomy will be created. In this regard, the research questions on the applicability of the atlas-based methods for more challenging clinical and research applications is being addressed.
Recently, several machine learning approaches have emerged, which can be applied in a flexible manner. They can be applied in conjunction with segmentation-or emission-based methods, to refine the quality of the segmentation or the resulting attenuation maps. A very promising aspect is that machine learning methods might be able to create accurate attenuation maps solely on conventional T1 and T2 data or from non-attenuation-corrected PET images alone, without requiring specific sequences such as UTE or ZTE. While these methods have initially shown promising results, they need to undergo further validation studies to investigate their applicability in larger patient groups, different datasets, and a variety of radiotracers, in case PET images are used to derive an attenuation map.

Emission-Based Attenuation Correction Approaches for PET/MR
Emission-driven methods allow for estimating attenuation maps (a) based on reconstruction of emission data alone, (b) based on a combination of jointly reconstructed emission and transmission data, and (c) by the use of information from scattered coincidences, background radiation, or radiating sources. An extensive and thorough review of the methods that apply emission data for attenuation correction in PET and singlephoton emission computed tomography (SPECT) was conducted by Berker and Li [22]. In this section, we will focus mainly on emerging PET/MR-specific approaches applied for clinical imaging of the head region.
A popular approach for emission-based attenuation correction is the maximum likelihood reconstruction of attenuation and activity (MLAA), which was originally proposed by Nuyts et al. [112], based on a concept introduced by Censor et al. [113]. The MLAA method is based on simultaneous reconstruction of both attenuation and activity using maximum likelihood expectation maximization (MLEM) algorithm and enables deriving an attenuation sinogram up to a constant using measured emission data only. The accuracy of the method is improved if high quality of the emission data can be guaranteed.
To reduce the cross-talk and dependence on count statistics in MLAA, the use of time-of-flight (TOF) information with MLAA has been shown to be beneficial [114]. In addition, incorporating spatial constraints or prior information, e.g., from MR data, can be used to improve the MLAA estimate [115]. MRguided MLAA imposes MR spatial and CT statistical constraints with a Gaussian mixture model and Markov random field smoothness prior to improving the quality of the attenuation map [116]. Another approach is to jointly estimate the emission distribution and the attenuation correction factors, avoiding the reconstruction of the attenuation map. Rezaei et al. [117] proposed a maximum likelihood algorithm to jointly estimate the activity distribution and attenuation correction factors (MLACF), up to a scaling constant.
Advanced MLAA methods with additional penalty functions might offer better performance in brain imaging as shown in Ahn et al. [118] and Mehranian et al. [46], which could overcome the limitations of earlier MLAA methods for brain imaging when compared to, e.g., atlas-based methods [42]. Recent developments in the methodology have allowed for reaching <5% of error in brain PET quantification with TOFbased MLAA using an MRI prior [46]. Deep learning has been also applied to improve the quality of the MLAA for attenuation correction in the brain using nonconventional tracers, such as 18F-radiolabeled N-(3-fluoropropyl)-2β-carboxymethoxy-3β-(4-iodophenyl) nortropane ([ 18 F]-FP-CIT) used for brain dopamine transporter imaging [119]. Thus, it would seem that most of the limitations in the emission-based methods are being addressed.
Methods that use either transmission sources or background radiation have been also introduced. Improvement of the accuracy of the attenuation maps with an external transmission source was shown in Mollet et al. [120] and Mollet et al. [121], with supplemental transmission sources [122], and using different source geometries [123]. External radiation, such as 176Lu emitted by lutetium oxyorthosilicate/lutetium-yttrium oxyorthosilicate (LSO/LYSO) scintillation crystals, could also be used to acquire transmission data [124], or the scattered background radiation could be used to derived an attenuation map [125]. However, these methods have been mostly applied solely in research context. Recently, an integrated approach that includes a moving point source on a helical path around a 24-channel MR-receiver coil to perform a transmission scan was introduced in Navarro de Lara et al. [126] and Renner et al. [127], which might offer a clinically feasible approach for transmission imaging on brain PET/MR. Finally, several authors have highlighted the benefits of TOF in reducing the errors in the PET images reconstructed with MRAC [84,128,129]. This is due to TOF reconstruction being less sensitive to inconsistencies in emission data and data corrections such as attenuation, normalization, and scatter [130].
It can be seen that emission-based attenuation correction is an active field of research, where large clinical validation studies have begun to emerge. A scale-corrected MLACF has recently been shown to provide images that quantitatively and visually correspond to CTAC-reconstructed PET images in 57 patients [131]. Benoit [45]. The authors suggested that MLAA might be useful in patients where metal implants or other imaging challenges hinder the use of traditional segmentation-based methods.
In summary, emission-based attenuation correction has been an active field of research, and the methods proposed have begun to show both increases in quantitative accuracy (errors below 5%) and advantages compared to segmentation-or atlasbased methods. For example, emission-based methods might be able to estimate the attenuation coefficients in the presence of metal implants, which would pose a problem for segmentation-or atlas-based methods due to large signal voids. Thus, they would be able to complement both segmentation-or atlas-based methods in challenging cases where they fall short.
There have been traditionally two challenges in emissionbased MRAC, which have been addressed in recent methodological studies. Originally, most methods were validated using [ 18 F]-FDG only and a small group of patients. Very recently, however, the applicability of the emission-based methods to a variety of radiotracers has been shown. Moreover, the sensitivity of MLAA to the quality of emission data has been addressed in the following manners. For example, by carefully improving and ensuring the quality of both TOF calibrations and accuracy of data corrections and by the implementation of anatomical priors from MRI, the accuracy of the attenuation map estimation can be improved. Deep learning methods can be also applied to improve the quality of the emission estimate in non-conventional radiotracers.

Status of PET/MR Attenuation Correction for Neuroimaging for Research and Clinics
As can be seen from above, a multitude of MRAC methods are available for research settings, where most of the presented methods perform with good accuracy [30,133]. While the problem concerning the availability of accurate attenuation correction in research settings has been solved, investigation of new attenuation correction methods still is of interest to improve the accuracy of the available methods for more challenging research applications. Most of the methods presented in the previous chapters might be also applied on PET/MR systems of different vendors, unless a specialized, vendor-dependent sequence or software is required.
However, it seems that there is still an ongoing discussion whether reasonably accurate methods have become commercially available, especially in challenging clinical applications [134], while the accuracy of MRAC can be considered adequate for the majority of routine clinical situations [47]. Furthermore, future efforts for standardization and quality control are important for accurate and robust results in both research and clinics and are needed for PET/MR as well [135]. In addition to technical efforts, knowledge sharing in terms of new guidelines and procedures for PET interpretation and reading will help to improve clinical confidence [28,136]. Finally, promising methods available for research use might be eventually translated to commercial platforms and thus result in further benefit for clinical applications.
Perhaps the greatest challenge so far has been to present the knowledge gained in the evaluation of different MRAC methods in terms of clinically interpretable information. Impact of MRAC on clinical reading is generally determined by visual analysis, presence of visible artifacts in MRAC or PET, lesion detectability, and standardized uptake value (SUV) quantification accuracy in PET [28]. Recent studies have proposed that standardized, clinical metrics need to be taken into use for MRAC method evaluation, to make direct comparison of method performance less challenging [30,137]. Implementing more advanced vendor-based attenuation correction methods will certainly result in an increase in the clinical evaluations performed with MRAC.
Concerning the availability of accurate MRAC methods outside the research setting, there are currently two state-of-theart vendor-based attenuation correction methods for imaging of the brain region on the Siemens mMR and General Electric (GE) Signa PET/MR system. The Philips Ingenuity TF is the only PET/MR system that does not account for bone, as it uses the method described in Schulz et al. [138]. In this regard, while it seems that there is an overflow of MRAC methods to be selected in the research setting, there are also vendorbased methods available that have been successfully applied in a multitude of evaluations in clinical setting. Increasing the amount of clinical evaluations will undoubtedly result in increased clinical confidence in applying the vendor-based methods in clinical routine imaging of, e.g., dementia, epilepsy, and other diagnostic applications. The Siemens mMR system implements a UTE-based method with fixed attenuation coefficients (bone: 0.151 cm −1 , soft tissue: 0.100 cm −1 , air: 0 cm −1 ) for delineating bone for the head region, described in the paper of Aasheim et al. [56] from the internal software version of VB20P and above. Another method for delineating bone with continuous attenuation coefficients using a Dixon sequence and superimposed model-based bone compartment is presented in the paper of Koesters et al. [89]. Similarly, the GE Signa system has two methods routinely available. The first method is based on atlas registration to delineate bone with continuous attenuation coefficients for the head region [88]. The second method is based on a ZTE sequence, which derives bone in the head region by segmentation of ZTE images and assigns continuous attenuation coefficients using a ZTE-intensity vs. HU calibration curve [69], available from the internal software version of MP26 and above.
Clinical evaluations of the impact on MRAC with the vendor-based methods have been performed on the Siemens mMR using the Dixon, UTE, and model-based attenuation correction. In the study of Werner et al., 13 patients suspected of having dementia were imaged with [ 18 F]-FDG. Both UTE and Dixon-based attenuation correction were assessed for differentiating hypometabolism [139]. In a similar study consisting of 16 patients, both model-based and Dixon attenuation corrections were assessed for the visual interpretation of regional hypometabolism [140]. Both studies concluded that the typical patterns of hypometabolism were not significantly changed when even the most inaccurate MRAC was used. Furthermore, several research and clinical methods were recently assessed in terms of z-scores, with 27 patients with suspected dementia [141]. The study concluded that while the research methods proved superior, the model-based attenuation correction should be preferred for diagnostic assessment in the clinical routine.
Similar methods have also been applied in the diagnostic evaluations in brain tumors and amyloid imaging. A study from Rausch et al. evaluated Dixon-based attenuation correction and the model-based method described in Koesters et al. [89], where the authors showed no significant change in diagnosis even when an attenuation map without bone was used [137] in brain tumors.
Su et al. [80] showed that an attenuation map without bone is also sufficient for visual interpretation and clinical diagnosis when using [ 18 F]-Florbetapir to determine either amyloid positive or negative status. In a very recent study, Rausch et al. [142] assessed three vendor-based attenuation correction methods, where the authors found no significant changes in time-activity curve (TAC) pattern categorization in [ 18 F]-FET PET and that tumor grading seems to be feasible, regardless of the choice of the MR-AC method. Thus, the accuracy of the vendor-based attenuation correction has been shown to be feasible for both amyloid and tumor imaging.
Evaluations of the template-based method described in the paper of Wollenweber et al. [88] have been performed against CTAC [37,143], a multiatlas method [98], and ZTE-based attenuation correction [70]. The ZTE method has also been evaluated against Ge-68 transmission sources [34], in dynamic PET [33], and in MR-based radiotherapy of the head [35]. In these evaluations, the ZTE-based method proved superior to the template-based method, especially if the intent is to perform kinetic analysis. These studies have shown that the ZTE-based methods can be considered to be feasible in clinical PET/MR imaging applications. Undoubtedly, more evaluations on the vendor-based methods presented above will follow in the near future.
As can be seen, there are a wide range of MRAC options from the first-generation of segmentation-, atlas-, and emissionbased methods to second-generation machine learning and deep learning methods. However, the current application of these methods for PET/MRI in multicenter clinical trials is a challenge contrary to PET/CT in population multisite studies such as Alzheimer's Disease Neuroimaging Initiative (ADNI) or Open Access Series of Imaging Studies (OASIS). Since the methods developed for research used perform, to some extent, differently in terms of different magnitude of residual bias and regional accuracy, the community still needs to work on the standardization of MRAC methods in PET/MR neuroimaging. These challenges could be potentially overcome by using either a commonly available and acceptable library of well-established MRAC methods or by using one comparable, integrated method from either of the PET/MR vendors.

SCATTER CORRECTION FOR PET/MR NEUROIMAGING
A 30-35% scatter fraction in brain studies can be expected [16], which makes scatter correction one of the fundamental data corrections in addition to attenuation correction. The majority of the scattered events originate from the patient, whereas the physical hardware components contribute from 5 to 15% of the scatter [144]. The physical basis for scatter correction in PET/MR is addressed in the review paper of Martinez-Möller and Nekolla [17]. In this section, we will summarize the current approaches and highlight some emerging applications for scatter correction in brain PET/MR imaging.
While scatter correction has not been a major issue to be addressed for neurological PET/MR imaging, developments in accuracy of scatter correction are considered beneficial especially in regard to quantitative PET imaging. Furthermore, advanced scatter correction methods would be beneficial also in wholebody imaging applications. The current approaches for scatter correction can be divided into (a) historical approaches; (b) simulation or model-based methods, which estimate the single Compton scatter events; and (c) emerging Monte-Carlo-based scatter correction methods and methods based on machine learning. In Table 2, a flowchart describing the main steps in both SSS and Monte-Carlo scatter correction is described.

Scatter Correction, Historical Approaches
Historically, a multitude of methods were introduced for PET scatter correction, which are summarized in the following books and reviews: [16,48,85,[151][152][153][154]. These methods were based on either using (1) multiple energy windows to acquire PET data, e.g., Grootoonk et al. [155]; (2) scatter modeling based on convolution and subtraction, e.g., Bergstrom et al. [156] and Bailey and Meikle [157]; and (3) performing Monte Carlo (MC) simulation, e.g., Levin et al. [158]. In addition to software-based methods, hardware approaches such as coarse septa or beam stoppers made from lead were suggested [16]. These methods are no longer in use, with the exception of emerging MC approaches discussed later in this paper.
Much effort was also put into the development of approximate scatter correction techniques for PET, when shifting from twodimensional (2D) to 3D PET imaging. These techniques are summarized in the following articles: Bailey and Meikle [157], Adam et al. [159], Barney et al. [160], Chen et al. [161], Cherry [162] and Zaidi [163]. The use of full MC methods to derive a "gold standard" approach for scatter modeling was also investigated, although they were considered computationally too intensive to be implemented in clinical routine at the time [158,164,165]. Interestingly, MC-based methods have recently reemerged due to the availability of parallel graphics processing units (GPUs), which offer a boost in computing power at a reasonable cost and availability [166].
In the gradual shift from 2D imaging to 3D imaging in PET, most methods were superseded by mainly two approaches based on direct calculation of scatter distribution, which we will refer to as simulation-based approaches.

Scatter Correction, Simulation-and Model-Based Methods
Simulation-based approaches proved most successful for calculation of scatter in 3D PET. Two methods based on direct estimation of scatter distribution became most widely adopted, generally denoted as the SSS algorithm of Watson et al. [146] and the model-based single scatter approach of Ollinger [147], which are incorporated as part of the iterative reconstruction loop in clinical PET/CT and PET/MR systems. The algorithm implementations vary to some extent across different PET system vendors, e.g., comparing the approaches of Siemens Healthcare [167], Philips Healthcare [145], and GE Healthcare [168].
Both the simulation-based [146] and the model-based approaches [147] are essentially based on the direct calculation of the single scatter distribution, which considers emission and attenuation sinograms as input data and is scaled to match the emission distribution. While there are differences in implementation of how single Compton scattered events are modeled between these two approaches, some common principles can be identified. These are as follows: (1) scatter is due to single Compton scatter events, (2) single scatter distribution can be calculated by application of the Klein-Nishina formula using the known emitter density and attenuation coefficients from emission and attenuation sinogram data, and (3) the derived scatter estimate can be scaled to the emission data tails for subtraction (tail fitting) and to account TABLE 2 | Flowchart of single scatter simulation following the methodology in Accorsi et al. [145], Watson et al. [146], and Ollinger [147] in comparison to Monte Carlo simulation-based scatter correction shown in Kim et al. [148], Magota et al. [149], and Ma et al. [150].

Single scatter simulation Monte Carlo simulation
(1) Define activity and attenuation distribution from the scatter uncorrected emission and transmission image.
Provide a scatter uncorrected emission and transmission image and initialize random number generator for Monte Carlo simulation.
(2) Randomly distribute scatter points within the scatter volume. Generate annihilation photon pairs according to the activity distribution of the input emission image. Generate a table of the information from the materials and physical properties.  Simulate physical effects such as photoelectric effect and Compton scattering using the Klein-Nishina formula for the emission volume, with potential inclusion of the physical effects occurring in the detector. Repeat the steps from (3) to (4) until two photons are either detected or rejected.
Update the corresponding LOR value.
Interpolate in LOR space to obtain the scatter sinogram. Perform coincidence sorting to simulated trues, scattered and random events. Frontiers in Physics | www.frontiersin.org for multiple scattered photons. For discussion in differences in scatter correction approaches and potential relation of scatter correction to MRAC, we refer the interested reader to Teuho [29].
Both simulation-and model-based methods have been extended and modified since the original publications. The details of the modifications in the model-based method are described in detail in the following references: Ollinger [147], Wollenweber et al. [168], Iatrou et al. [169], and Iatrou et al. [170]. Extensions and modifications to the original work in the simulation-based method are described in the following references: Watson et al. [167,[171][172][173][174]. A major extension of the original work was to include the calculation of scatter for TOF PET, described in the works of Werner et al. [175], Watson [173], and Iatrou et al. [170], by inclusion of double scatter in the model, which also excludes the need for tail fitting [174,176].
While the currently available scatter correction methods for PET neuroimaging in general do not pose problems for the majority of neuroimaging studies on PET/MR, there might be specific applications where more accurate methods for scatter correction would be beneficial. As in the case of MRAC, increasing accuracy of the available methods is always seen beneficial.

Emerging Methods Based on MC Simulation and Machine Learning
Methods based on MC simulation and machine learning have recently gained interest. MC methods offer potential improvements in increasing the accuracy of scatter estimation or tail fitting in cases of challenging acquisition conditions. Machine learning methods allow potentially new approaches to be implemented in scatter correction, where the computationally intensive process of scatter calculation could be ignored entirely. In addition to these, several groups have investigated how current scatter correction methods could be improved in terms of tail scaling [177], out-field of view scatter compensation [178], multiple scatters [179], or speed [180].
Improved scatter correction methodology might prove useful in several applications. Data-driven methodologies such as MLAA benefit from accurate data corrections. Recently, it was shown that improved scatter correction is helpful for increasing the visual and quantitative accuracy of PET and could also result in improved attenuation correction with data-driven methodologies using PET and MRI [45]. Furthermore, accurate scatter correction methods could be useful in improving the quantitative accuracy of dynamic PET data with low count statistics [150], which is often the case in neuroimaging research. While studies in the head region do not suffer from the same effects from, e.g., truncation or large bladder-to-background ratio as PET/MR studies in the body region, accurate methodologies developed for the head region might eventually become useful for whole-body PET/MR as well.
With the introduction of fast GPUs that could be implemented in parallel, promising methods based on MC simulation have been proposed. Doing a full MC simulation combined with a GPU implementation could offer a feasible way to implement a very accurate method for scatter correction [166]. Recently, a method based on the paper of Gaens et al. [166] was further refined and applied in a phantom and patient study using a brain PET/MR imaging system [150], with promising initial results. MC simulation has been also applied to implement more robust scaling of the scatter sinograms in the presence of high activity in [ 15 O]-inhalation studies [149]. Combining MC simulation in both scatter calculation and scaling would be beneficial for neurological applications as well as whole-body studies, and the availability of GPU-based methods might enable just that.
Finally, several groups have investigated deep learning methods for scatter estimation to calculate both scatter and attenuation estimates without requiring conventional attenuation map generation and time-consuming scatter correction. The works of Qian et al. [181] and Berker et al. [182] have shown promising early results in using deep learning to calculate scatter estimates for PET, which could offer increases in both accuracy and computational speed. Interestingly, both papers discussed that a deep learning network trained with MCsimulated data would offer further improvements in accuracy [181,182]. Finally, a very recent work proposed performing both scatter and attenuation corrections in image space using non-corrected PET [183]. Undoubtedly, it is expected that more deep learning-based methods for both attenuation and scatter correction will emerge in the upcoming years, given the popularity of the research topic. An intriguing possibility might be to combine the best of both worlds-by the use of fast GPU-based MC for accuracy and deep learning for computational speed.
Finally, concerning PET/MR neuroimaging, the current status for vendor-based, clinically available scatter correction methods could be summarized very shortly. The SSS algorithm and the model-based SSS with current extensions form the basis of vendor-based scatter correction in PET/MR systems, which offer a well-validated and reasonable accurate solution for a multitude of neurologic applications. Although the challenges in traditional approaches, e.g., related to tail fitting, are well-known in wholebody applications, these generally do not pose a problem, with the exception of very specific neuroimaging applications, such as It could also be argued, as with MRAC, that the increase of accuracy in scatter correction is beneficial in both research and clinical settings, resulting in improved visual quality and quantitative accuracy. With the increasing appeal of using either a GPU-based MC or a deep learning-based approach for scatter correction, it remains to be seen whether these methods will be implemented as an alternative approaches in future clinical PET/MR systems.

EMERGING CLINICAL AND RESEARCH APPLICATIONS
Finally, there are several clinical and research applications where accurate attenuation and scatter correction methods will prove to be beneficial. Eventually, the success of PET/MR depends on the level of confidence revealed by current and future reports on clinical and research applications where combined PET/MR provides useful additional information.
This might lead to more widespread acceptance of PET/MR in clinical setting, particularly in neurology and oncology [28]. However, at the same time, it should be emphasized that PET/MR is much more than mere attenuation and scatter correction.
For emerging applications in neurological PET/MR, we wish to highlight recent reports where accurate data corrections are beneficial. These include, e.g., PET measurements of cerebral blood flow (CBF) using [ 15 O]-labeled water ([ 15 O]-H2O) PET [184] and receptor binding studies with [18F]-(E)-N-(3iodoprop-2-enyl)-2β-carbofluoroethoxy-3β-(4-methyl-phenyl) nortropane ([ 18 F]-PE2I) [33]. When PET is used to derive the arterial input function for quantification and kinetic modeling, it should be ensured that the method delivers consistent performance in terms of regional bias, accuracy, and precision. The impact of accuracy of attenuation correction on dynamic PET studies in PET/MR has been studied for 3,4-dihydroxy-6-[ 18 [106]. The methods evaluated in these studies have proven to perform with sufficient accuracy for both dynamic and static PET studies. Furthermore, they have highlighted the importance that bias between the reference region (e.g., cerebellum) and the analyzed region should be kept minimal to ensure accurate quantification in kinetic analysis.
Using an image-derived input function (IDIF) for kinetic modeling on PET/MRI will certainly benefit from accurate data corrections and will be further improved by the complementary nature of both modalities. MRI data could be used to assist and complement PET data in several ways [188]. Using TOF MR angiography can improve the delineation of the arterial volume in PET [184,[189][190][191]. The IDIF could be implemented in an automated pipeline to provide absolute values of cerebral glucose metabolism in a clinically feasible manner [192]. The IDIF measured from either MRI and PET could also be used interchangeably [193]. The need to measure IDIF could also be circumvented entirely by the measurement of global CBF by phase-contrast MRI [194]. Another approach is to incorporate information from arterial spin labeling (ASL) into PET pharmacokinetic modeling [195]. Thus, methods using complementary information from MR with PET for defining IDIF might be beneficial for kinetic modeling in PET, as MRdriven or MR-assisted approaches might be less dependent on accuracy of data corrections.
In regard to emerging applications and new opportunities that complement the neuroimaging field in PET/MR, we wish to briefly highlight the following review papers. A review of the neurologic applications where the complementary natures of PET and MRI are beneficial in both research and clinics has been provided in Chen et al. [14], Chen et al. [196], Catana et al. [197], Hope et al. [198], Miller-Thomas and Benzinger [199]. The clinical applications where PET/MR might clinically excel are brain tumor imaging, epilepsy, stroke, and a number of neurodegenerative conditions, to name a few. Another new clinical field where PET/MR might excel is the study of movement disorders [200]. There are also numerous research applications related to neuroreceptor studies, cerebral metabolism, and blood flow, which are not yet explored extensively. From a technical viewpoint, deep learning has several potential applications, although it has been used mainly for attenuation correction. A very recent review of potential applications of artificial intelligence for PET/MR neuroimaging was given in Zaharchuk [201]. Although out of the scope of this review, synergistic PET and MRI reconstruction might be also be applied to improve PET image quality in terms of noise or resolution.
In addition, we would like to specially mention pediatric PET/MRI imaging, which presents a number of specific challenges [202,203] but also has the utmost benefits [204,205]. Clinical applications for PET/MR in pediatrics have been highlighted in Gatidis et al. [206], Kwatra et al. [207], Lee et al. [208]. Accurate PET quantification is crucial in this population, and the use of combined PET/MR with accurate attenuation and scatter corrections could lead to reduced injected doses, as well as reduced exposure to CT radiation burden. This aspect has significance for pediatric cancer patients, who may need to undergo repeated diagnostic imaging sessions. In regard to novel applications, a recent study showed the benefit of PET/MR in low activity imaging (14 MBq) of [ 15 O]-H2O PET for quantitative relative cerebral blood flow (rCBF) assessment in unsedated healthy newborn infants [209]. In this regard, applying and modifying existing MRAC methods to pediatric cohorts such as in Ladefoged et al. [103] are encouraged.
Finally, MR-based radiotherapy treatment (MR-RT) and PET/MR have a lot in common in terms of methodological applications. PET/MR could be even used to improve radiotherapy treatment planning, after the challenges related to patient positioning for radiotherapy planning have been sufficiently addressed [210,211]. This requires designing MR compatible and PET transparent radiotherapy (RT) equipment [212] and accounting the attenuation of immobilization devices and flat table tops [213]. The information from MR and generated pseudo-CT images could give a better insight for particle RT where the beam range depends strongly on chemical composition [28]. Numerous accurate MRAC methods exist, which could be used for MR-RT, with careful investigation and application of the methodology for more challenging populations undergoing radiotherapy. Similarly, there are a multitude of methods that are used for MR-RT and could be applied for attenuation correction in PET/MR [214,215]. The methodological advances in both MR-RT and PET/MR could be applied to derive pseudo-CT images on both platforms to improve the PET quantification or accuracy of RT treatment planning.

DISCUSSION-CONCLUDING REMARKS AND OUTLOOK
In research settings, the accuracy of the attenuation correction is no longer the major methodological factor to be solved, and promising state-of-the-art methods are in the process of being implemented in vendor-based attenuation correction as well. The remaining issues in research settings are being slowly overcome in all major fields of (a) segmentation-based, (b) template-based, and (c) emission-based attenuation corrections. In this regard, the state of MRAC is very positive, with the major focus on improving the accuracy of the existing methods. This would indicate that in the future, MRAC will no longer be considered as an issue, at least in terms of its impact on the clinical interpretation of the images.
In clinical setting, the next challenge to overcome is for the PET/MR community to work on standardization of the use of different MRAC methods in neuroimaging applications. This concerns especially the application of MRAC in PET/MRI in multicenter clinical trials, as there are a wide range of MRAC options available with varying accuracy and regional bias. These challenges could be potentially overcome by using either a commonly available and acceptable library of well-established MRAC methods with similar accuracy or one comparable, integrated method from either of the PET/MR vendors.
While the currently available scatter correction methods for PET neuroimaging in general do not pose problems for the majority of neuroimaging studies on PET/MR, it could be argued that increasing accuracy for scatter correction would be beneficial in a range of clinical and research studies. Methods based on MC calculation might become clinically feasible for accurate scatter scaling and estimation. GPU-based approaches might eventually be implemented in vendor-based methods for scatter calculation.
Deep learning is an emerging trend in medical imaging in general, where both attenuation and scatter corrections are no exception, and where several methods applying deep learning in both attenuation and scatter estimation have emerged. Undoubtedly, more methods will emerge in the near future. However, for the introduced methods to become eventually popular, the applicability of the methods between different PET/MR systems, different MR sequences, PET tracers, and patient populations should be carefully investigated.
Currently available clinical and research methods for attenuation and scatter corrections will be useful in numerous emerging applications in neurological PET/MR, such as dynamic PET studies with different radiotracers, IDIF used for kinetic modeling, clinical applications for neurology, pediatric imaging, and MR-based radiation therapy. Thus, development, application, and refinement of advanced methods for attenuation and scatter correction methods in these fields are further encouraged, with the focus on taking into account fully the simultaneous acquisition of both PET and MRI.

AUTHOR CONTRIBUTIONS
JT contributed to the conception and design of the content, conducted the review, and wrote the manuscript. AT-C, HH, and UA contributed to the content design, conducting the review, and writing and revising the manuscript. RK, HI, and MT supervised the work and participated in writing and revising the manuscript. All authors contributed to manuscript revision, read, and approved the submitted version.

FUNDING
This study was financially supported by the Alfred Kordelin Foundation and the Finnish Cultural Foundation, Varsinais-Suomi Regional fund. Financial support was also received from the Hospital District of Southwest Finland (ERVA-project, number 13236) and the funding from the University of Turku Graduate School in the Doctoral Programme in Clinical Research. Finally, the Academy of Finland is acknowledged for the strategic Japanese-Finnish research cooperation program on Application of Medical ICT Devices supported by the Academy of Finland (project number 269977), University of Turku, Turku University Hospital, and the Åbo Akademi University. This project was also partially supported by Real Colegio Complutense at Harvard University Research Fellowships.

ACKNOWLEDGMENTS
JT acknowledges Prof. Ronald Boellaard for the review and feedback received during the pre-examination phase of his thesis, which eventually evolved into this review paper. In addition, M. D. Terhi Tuokkola was acknowledged for providing her clinical expertise, comments, and viewpoint for the manuscript.
This study was conducted within the Finnish Center of Excellence in Molecular Imaging in Cardiovascular and Metabolic Research supported by the Academy of Finland, University of Turku, Turku University Hospital, and Åbo Akademi University.