Med Phys (2015) submitted
II. STRATEGIES FOR ATTENUATION CORRECTION IN PET/MRI A Segmentation-based AC methods
The attenuating tissues in the body consist mainly of soft tissues, adipose (fat) tissue, lungs, air cavities (sinuses, abdominal air pockets) and cortical and spongy bones. Each tissue class has a different electron density and therefore different intra/inter-patient attenuation coefficients 511 keV as summarized in Table 1. In segmentation-based MRAC methods, the aim is to segment MR images into as much tissue classes as possible and to assign representative, or if possible, patient-specific, linear attenuation coefficients at 511 keV to each tissue class. As mentioned earlier, in conventional MRI scans, bones cannot be well discriminated from air cavities in the head and most soft and fat tissues in whole-body imaging.
1) Brain Imaging. In brain PET imaging, the cortical bones of the skull substantially contribute to the attenuation and scattering of annihilation photons. For accurate PET quantification, the bones must therefore be accounted in the MRAC map. Otherwise if substituted by soft tissue, the tracer uptake might be underestimated by up to 25% in cortical regions and 5-10% in central regions of the cranium, as recently reported by Anderson et al.  using 19 brain clinical PET/MRI scans.
Table 1. Attenuation coefficients at 511-keV of different biological tissues (see Table 2 in Ref.  for relevant references).
Tissue Linear attenuation coefficient (cm–1)
Adipose tissue 0.086–0.093
Soft tissue 0.094–0.100
Spongious bone 0.110
Cortical bone 0.130–0.172
112 In a comparative study between PET, PET/CT and PET/MR using an anatomical brain phantom, Teuho et al  also reported the largest underestimations (11% to 17%) in the temporal cortex and orbito-frontal cortex.
To the best of our knowledge, the first segmentation-based MRAC method was reported by Le Goff et al.
 for brain PET/MR imaging. MRI images were classified into background air, soft tissue and bones using thresholding, morphological filtering and connect component analysis. Despite the sinuses were not classified and the eyes were mis-classified, the local relative errors in tracer uptake did not exceed 12%. Zaidi et al. 
improved upon this approach by using supervised fuzzy C-means clustering that could identify the sinus and thus segment T1-weighted MR images into air, brain tissue, skull and nasal sinuses. Predefined tissue-dependent linear attenuation coefficients were then assigned to different tissue classes. Volume-of-interest (VOI)-based quantitative analyses showed a high correlation between MRAC and 137Cs transmission-AC PET images in most regions of the brain. Wagenknecht et al.  proposed an automatic three-step approach in which neural network-based segmentation and prior knowledge about brain’s anatomical regions and their relative positions are exploited to distinguish tissue classes. Although MR segmented regions showed a high correspondence with the CT segmented regions, this technique might result into mis- or over-segmentation of bones in the case of abnormal anatomy or presence of pathology, where the anatomical pre-assumptions will no longer hold true.
The above segmentation approaches attempt to indirectly segment bones from air-filled cavities. However, in the presence of anatomical abnormalities or MRI artifacts, the probability of miss-classification errors is irreducible. Therefore, UTE MRI-based methods were explored since 2010 for bone visualization and direct segmentation of bones in brain studies. Catana et al.  and Keereman et al.  used a dual-echo UTE MRI sequence to derive 3-class attenuation maps including air, soft tissue and bones. In this sequence, bone signal is present in the first ultrashort echo time (TE1) and absent in the second longer echo time (TE2), while the signal of other tissues remains the same in both echoes. As a result, in both studies, bones intensities were enhanced using arithmetical operations based on the difference of TE images. Catana et al.  used a morphological closing and arithmetical operations based on the sum of TE images to identify the air-filled regions, while Keereman et al.  used a region-growing and thresholding scheme to segment air cavities and outer head air.
Despite the promising results, bone classification was subject to errors in bone/air or soft-tissue air interfaces due to diamagnetic susceptibility effects at these interfaces.
Berker et al.  proposed a UTE triple-echo MRI sequence, combining UTE and Dixon sequences for bone detection and fat separation in order to generate a 4-class PET attenuation map. In the Dixon sequence, the fact that fat and water protons precess at slightly different frequencies (chemical shift effect) is exploited to generate in- and out-phase images from which fat-only and water-only images are obtained. Bones were segmented from differential UTE images using empirical thresholding and multiple morphological filtering. The 4-class attenuation maps exhibited a high visual similarity to reference CT-based attenuation correction (CTAC) maps.
Despite bone misclassifications at paranasal sinuses, over 80% of voxels in 6 studied patients were correctly classified.
Recently, Delso et al.  assessed the performance of dual-echo UTE imaging for bone segmentation in head and neck imaging of 20 patients scanned on a trimodality PET/CT-MR system . Their results showed that the UTE segmented bones produce an acceptable overlap with reference CT bones over the skull, however, segmentation errors increase at (i) the base of the skull due to the presence of several unwanted structures with short echo times (e.g. facial and neck musculature), (ii) air interfaces due to diamagnetic susceptibility artifacts, (iii) posterior part of eyeballs due to eye motion during acquisition and (iv) dental arch region due to metallic artifacts. They concluded that the above artifacts can degrade the reconstructed PET images and, as such, more sophisticated approaches are necessary to compensate for these effects.
2) Whole-body Imaging. In whole-body imaging, MR images are similarly segmented into different tissue classes to which predefined LACs are assigned. Contrary to brain imaging, the segmentation of bones is much more challenging in whole-body imaging, especially the vertebra where the bones are spongy and contain either hematopoietic or fatty tissues with a moderate MR intensity. The application of UTE MRI sequences for whole-body bone segmentation is not feasible yet since it is time-consuming for routine clinical usage. Moreover, the radial k-space acquisition, used to reduce TE acquisition time as much as possible, results in a spherical reconstructed FOV, whereby the body contour can be truncated . Fat/soft-tissue to bone miss-classifications and vice versa are also inevitable in whole-body UTE images . Apart from the segmentation of bones, other challenges of segmentation-based MRAC methods in whole-body imaging include accurate segmentation of the lungs and the assignment of patient-specific attenuation coefficients to each tissue class, especially the lungs
113 Figure 2. Comparison of the attenuation maps obtained by the 4-class segmentation based method , local weighted atlas fusion  and an MRI-guided emission based method . Adopted with permission from Mehranian and Zaidi .
given their heterogeneity. The latter problem is elaborated below in the section Inter/intra-patient variability of LACs.
Current whole-body MRAC methods rely on the segmentation of the MR images into 3 or 4 tissue classes, where bones are substituted by soft-tissue. Hu et al. [30, 31] implemented a 3-class attenuation map on the Ingenuity TF PET/MR system  by segmenting MR images of a 3D T1-weighted spoiled gradient echo sequence (known as atMR) into background air, lungs and soft tissue. The atMR sequence, which takes about 3 min for a 100 cm axial coverage, is merely designed for the segmentation of body contour and lungs. The lungs are segmented using a deformable shape model initialized by an intensity-based region-growing segmentation technique. This lung-model adaptation prevents the leakage of the lungs into the stomach and intestine, and also allows for improved lung segmentation in the presence of cardiac and respiratory motion artifacts . Using 15 patients, an overall underestimation of tracer uptake by up to 10% in malignant lesions was reported. 
Schulz et al.  also proposed a 3-class segmentation of MRI images obtained from a 3D gradient and spin echo sequence with a flip angle of 2º. This sequence, essentially yielding a proton-density weighting, was chosen to equalize fat and water signals and thus increase the reliability of automatic segmentation of the MR images into 3-classes. The external body contour and lungs were segmented using thresholding of the Laplace-weighted histogram of MR images and a region-growing technique, respectively. Using 15 whole-body PET-CT/MR patients, they reported a systematic over- and under-estimations of SUV in bony and fatty regions, respectively.
Overall, the bias was <7% in most malignant lesions.
To include fat as 4th tissue class, Martinez-moller et al.  used a 2-point Dixon sequence for the separation of fat and water. In this proof-of-principle study, they used 35 clinical PET/CT scans to demonstrate the potential merit of 4-class MRAC attenuation map in PET/MRI imaging. They reported a mean SUV error of about −8%
for bone lesions and concluded that this bias in SUV estimation is clinically irrelevant. In a follow-up study using 35 PET/CT and Dixon T1-weighted MR images, Eiber et al.  demonstrated that there is no statistically significant difference between PET/MRI and PET/CT for the anatomical localization of 81 PET positive lesions.
Their quantitative results also showed that the 4-class MRAC PET images have a high SUV correlation to reference CTAC PET images. Figure 2 compares the attenuation maps of a representative study produced using the segmentation-based 4-class technique with atlas- and emission-based algorithms.
114 Hoffmann et al.  included a mixture of fat and soft tissues as 5th class (in addition to air, lung, fat and soft tissue classes) and evaluated this segmentation method and their proposed atlas-based approach using 11 PET/MRI/CT datasets. The in-phase, water and fat images were segmented in 5 classes using intensity-based thresholding, morphological filtering and connect component analysis. The authors reported mean absolute SUV errors of 8% and %14 in lesions and regions of normal uptake, respectively.
Wollenweber et al.  recently proposed a continuous fat/water (CFW) method allowing for the continuous variation of fat and soft tissue. A phase-field-based segmentation technique was employed to segment body contour, lungs and trachea in the thorax and air pockets in the abdomen. In this approach, fat and water fraction images are calculated and used to derive continuous fat and water attenuation coefficients within the interval 0.086 - 0.1 cm-1. The quantitative analysis showed that the CFW and 4 discrete-class MRAC methods result in mean SUV errors of 10.4% and 5.7% in the liver and 1.7%, and –1.6% in malignant lesions, respectively.
To evaluate the importance of bones in whole-body MRAC attenuation maps, Hofmann et al.  substituted bones in CTAC attenuation maps of 11 PET/CT patients by soft tissues. Their results demonstrated that the substitution of bones with soft tissue results in mean SUV errors of 4% in 88 VOIs defined in soft tissues adjacent to bones in the pelvic region and 3% in 28 VOIs defined in soft-tissue lesions. A similar study was conducted by Samarin et al.  using 22 PET/CT patient datasets. Their results showed an underestimation of tracer uptake of 11% and 3% in osseous and soft tissue lesions adjacent to bones, respectively. For sclerotic and osteolytic spine lesions, mean SUV underestimations of 16% and 7% were reported, respectively.
3) Segmentation of non-attenuation corrected PET images. The segmentation of NAC PET images to define 3 tissue classes (i.e. background air, lung, and soft tissues) has also been investigated . Recently, Chang et al.
 proposed a three-step iterative PET segmentation method for whole-body 18F-FDG scans. In the first step, an initial attenuation map is produced by segmenting body contour from NAC PET images using an active contour method followed by reconstruction of PET images using this attenuation map. In the second step, the attenuation map is refined by segmenting the lungs from the resulting AC PET images using a thresholding approach. PET images are then reconstructed using this updated attenuation map. Finally, the heart and liver, mis-segmented as lung tissue, are removed using a manually-seeded region growing technique. However, tissue classification from NAC PET images is generally limited to radiotracers that distribute throughout the body such as 18F-FDG and will not work for specific tracers. These techniques have been extensively employed to reduce truncation and metal artifacts in MRI-derived attenuation maps, as discussed in the following sections.