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), 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 inter- or 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 three- to 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 T1-weighted MR images, methods based on segmentation of [¹⁸F]-sodium fluoride ([¹⁸F]-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.

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, 92–94]. 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 continuous-valued 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-to-image 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-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 single-photon 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]. MR-guided 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 TOF-based 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 ([¹⁸F]-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 et al. [132] studied a modified non-TOF MLAA algorithm with a relatively large group of patients, i.e., with 204 [¹⁸F]-FDG patients, 35 [¹¹C]-PiB patients, and 1 O-(2-[18F]-fluoroethyl)-l-tyrosine ([¹⁸F]-FET) patient. Moreover, in a study consisting of 34 dementia patients imaged with [¹⁸F]-FDG, an MLAA method was compared with state-of-the-art MRAC and CTAC, producing errors within a few percent [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 atlas-based 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 emission-based MRAC, which have been addressed in recent methodological studies. Originally, most methods were validated using [¹⁸F]-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.

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-the-art 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 vendor-based 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 [¹⁸F]-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 [¹⁸F]-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 [¹⁸F]-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 emission-based 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.

Historically, a multitude of methods were introduced for PET scatter correction, which are summarized in the following books and reviews: [16, 48, 85, 151–154]. 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 two-dimensional (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.

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 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, 171–174]. 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.

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 [¹⁵O]-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 MC-simulated 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 whole-body applications, these generally do not pose a problem, with the exception of very specific neuroimaging applications, such as [¹⁵O]-inhalation studies.

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.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.