The advent of prostate-specific membrane antigen (PSMA) tracers has led to the increasing adoption of PET as the modality of choice in diagnosing recurrent prostate cancer (1). For this patient group, [⁶⁸Ga]GaPSMA-11 PET/MR has been shown to have similar diagnostic performance to [⁶⁸Ga]Ga-PSMA-11 PET/CT in nodal and osseous metastasis (2–4) and superior performance in the detection of local recurrences due to the higher soft-tissue contrast provided by MR (2, 5). However, attenuation correction (AC), which is the most important correction required for quantitatively accurate PET imaging, remains a challenge in PET/MR imaging (6–8).

For PET/CT, the contrast of the CT images is dependent on the electron density of the imaged tissue, which in turn is related to the linear attenuation coefficient (LAC) of the PET photons (6, 9). A piecewise linear transformation of the CT Hounsfield units can be used to estimate the LAC at the PET photon energy of 511 keV (10). This approach is widely accepted as AC for PET/CT in clinical practice (6, 11). Since the signal in MR comes from proton densities and tissue relaxation times, no such straightforward relationship between the MR intensity values and LAC at the PET photon energy exists (6, 9, 11).

In current clinical practice, whole-body PET/MR AC is typically derived from Dixon MR sequences. These sequences are time-efficient to acquire and are available in all commercially available clinical PET/MR scanners (12). In four-class Dixon-based AC, Dixon MR images are segmented into four components: fat, lung, soft tissue, and background air, and each component is subsequently assigned a respective predefined LAC (13). Bone, although highly attenuating, is not accounted for in this four-class attenuation correction model. Disregarding the bone can lead to an underestimation of the standardized uptake values in and near the bone. For the pelvic region in particular, errors as large as 30% have been found in the most impacted bone lesions (14). In the staging of prostate cancer recurrence after definitive therapy, bone lesions are also fairly common and can be expected in more than 20% of the cases (15). In restaging after salvage radiotherapy, bone lesions are even more common and are observed in as many as 45% of cases (16).

The short T 2 * relaxation times and low proton density of cortical bone cause the MR signal to decay quickly in bone tissue (17) and make bone hard to distinguish from air in conventional MR images. Thus, in the four-class Dixon-based AC model, bone is classified as soft tissue. To tackle this issue, Paulus et al. (18) proposed the five-class Dixon-based AC model. This model is an atlas-based approach for whole-body PET AC based on individual registration of the major bones (skull, femur, hips, and spine, including sacrum) from a bone atlas consisting of paired Dixon MR images and bone masks. However, this method is prone to registration errors and misses bones entirely in some cases (19, 20). In a recent retrospective study of 200 patients, it was advised not to use this form of AC for PSMA PET/MR without great caution and thorough inspection of the resulting µ-maps (20).

Several deep learning-based approaches have also been suggested to improve AC in PET/MR. These approaches can broadly be categorized into those that only use the Dixon images (7, 21), those that require other MR sequences than the standard Dixon images (22–25), and approaches that only use the PET data (26). A different way to categorize these approaches is by whether their goal is to create a pseudo-CT image or a µ-map (21–23, 25, 27) or to directly correct or predict the corrected PET image itself (26).

An obvious limitation of the acquisition of additional MR sequences for AC purposes is that it requires additional scan time. Approaches that rely on the PET data itself as input data, either for µ-map prediction or for direct prediction of the corrected PET image itself, are dependent on the tracer for which the model is trained. These models are thus not directly applicable to multiple tracers without retraining the model.

We introduce a novel, deep learning-based approach to improving AC in pelvic PET/MR acquisitions. The proposed method aims to directly correct the errors in the PET images caused by bones not being included in the four-class AC model rather than predicting new µ-maps. For this purpose, a voxel-wise correction map is predicted by a convolutional neural network using Dixon MR and the four-class µ-map as input. The predicted correction map can subsequently be applied as a postprocessing step directly in the PET image space to correct PET images reconstructed with the four-class µ-map without re-reconstruction of the images. Additionally, the proposed model requires no additional sequences beyond the standard Dixon MR images and does not require retraining to be used with multiple tracers. In this work, we evaluated the quantitative impact of the proposed method on PSMA uptake in the pelvic region of patients suspected of recurrence of prostate cancer.

From the 49 included patients, two patients were removed from the dataset due to severe artifacts in the PET images and eight were removed due to suboptimal coregistration between CT and MR. This resulted in a training set consisting of 18 patients scanned with FDG, a validation set of four patients scanned with FDG, and a test set consisting of 17 patients scanned with [⁶⁸Ga]Ga-PSMA-11 or [¹⁸F]PSMA-1007. An overview of the dataset is presented in Table 2 , and a flow diagram of patient inclusion can be found in the Supplementary Material (S1) . From radiology reports of patients in the test set, 16 soft tissue lesions and four bone lesions were extracted.

Training the convolutional neural network took approximately 4 h on a single NVIDIA GeForce GTX 1080 Ti. An example of a corrected PET image can be seen in Figure 3 . The corrected PET images were found to closely resemble the reference standard PET_CT+MR images.

The voxel-based RMSPE and MAPE were 12.1% [8.6%, 15.4%] and 6.2% [4.0%, 10.3%], respectively, for the PET_4C images and 8.6% [5.3%, 11.5%] and 3.5% [2.3%, 5.1%], respectively, for the PET_5C images. In the PET_cor images, the RMSPE was 6.2% [4.1%, 8.6%] and the MAPE was 3.3% [2.3%, 4.6%]. The error in PET_cor is thus approximately reduced by half compared to the PET_4C images. A significant difference was found between the RMSPE of the PET_cor images and the PET_4C images (p < 0.0001) and between PET_cor images and the PET_5C images (p < 0.0001). A significant difference was also found between the RMSPE values for [⁶⁸Ga]Ga-PSMA-11 and [¹⁸F]PSMA-1007 patients individually between PET_cor and both PET_4C and PET_5C, as shown in Figure 4 . No significant difference was found when comparing the RMSPE of PET_cor between patients acquired with [⁶⁸Ga]Ga-PSMA-11 and [¹⁸F]PSMA-1007.

The lesion performance is summarized in Table 3 and Figure 5 . Performance in soft tissue lesions improved marginally from a MAPE of 2.9% [0.8%, 6.5%] in PET_4C to 2.2% [0.1%, 8.1%] for PET_cor. For bone lesions, we observed more than a fivefold decrease in MAPE from 20.0% [12.0%, 30.4%] in PET_4C to 3.8% [1.0%, 9.2%] in PET_cor. PET_5C, in comparison to the proposed model, had lower MAPE in soft tissue lesions and higher MAPE in bone lesions.

We observed a decrease in performance with increasing postinjection time (PI) in the test set. In a simple linear regression model, a significant linear trend (p < 0.05, r ² = 0.30) was found between the voxel-based RMSPE measurements and the PI time (see Supplementary Section 5 for further details).

In this study, we propose a novel attenuation correction method that seeks to directly correct for the errors obtained by not including bone when using the conventional four-class Dixon-based AC. We show that the model reduces quantification errors in a voxel-based analysis and in bone lesions compared to four- and five-class Dixon-based methods. For soft tissue lesions, the performance remains similar to that of the four-class Dixon-based AC model.

Our method can be directly applied as a correction filter in the image space to PET_4C images without the need for additional reconstruction or the acquisition of additional MR sequences. It can thus also be used to correct PET_4C images retrospectively, as long as Dixon MR images are available. This distinguishes it from other models that seek to improve pseudo-CT generation. The model also only relies on Dixon MR images, which are fast to acquire. Furthermore, like the models that predict pseudo-CT images from MR series (21–23, 25, 27), but unlike the models that predict the pseudo-CT images or AC and scatter-corrected PET directly from non-attenuation corrected PET (26, 38, 39), the predicted correction maps are not tracer-dependent.

We observed that the proposed method is robust to variations in tracer type and scatter correction method. The training and validation sets consisted of FDG images, whereas the test set consisted of [⁶⁸Ga]Ga-PSMA11 and [¹⁸F]PSMA-1007 images. Since there were no [⁶⁸Ga]Ga-PSMA-11 images in the training data, the model had only seen images reconstructed using relative scaling during scatter correction in training. Nevertheless, no differences in performance were seen between [⁶⁸Ga]Ga-PSMA-11 and [¹⁸F]PSMA-1007 patients in the test set.

A decrease in performance was seen with increasing PI. This trend can be explained by the higher number of counts acquired at lower PI, making the correction map that the model tries to predict less noisy. All patients had PET/MR and PET/CT acquisition performed on the same day. For around half of the patients in the test set, the PET/CT images were acquired at what was considered the optimal PI for the given tracer, and the PET/MR images were acquired once the PET/CT examination was finished. If all PET/MR had been acquired closer to the recommended PI, we would expect to see a slight increase in performance.

Multiple other methods have been suggested for improving PET/MR attenuation correction in the pelvic region (7, 22, 23, 25, 27). Bradshaw et al. (25) proposed a model based on the Deep Medic CNN architecture (40). In this model, T2 and T1 Lava Flex images were used for the prediction of pseudo-CT images, resulting in an RMSPE of 4.9% in the reconstructed PET image. Leynes et al. (23) used Dixon-based images and zero-echo-time images as input to a deep learning model based on the UNET architecture to generate µ-maps. The resulting PET reconstruction had an RMSPE of 2.85%. Similar to Bradshaw et al. (25), Torrado-Carvajal et al. (7) used a UNET-like architecture to create a pseudo-CT image using solely Dixon MR images as input. Their approach resulted in an absolute mean relative change of 1.83%.

A different family of models is composed of models that use non-attenuation corrected PET images as input and either the pseudo-CT (41) or the attenuation and scatter-corrected PET as output (26, 38). Though good performance can be obtained with these models, they are tracer-dependent and would likely need to be retrained for optimal performance with each new tracer. In addition, the models proposed in the literature (26, 38, 41) have only been trained and validated on PET/CT data so far, and their performance is yet to be assessed using data acquired on the PET/MR system.

Though many methods have been proposed, it is difficult to directly compare their performance. As pointed out by Lee (42), there is substantial heterogeneity in the choice of PET reconstruction parameters and performance metrics. There is also no reference dataset that can be used to benchmark the performance of different models. What is considered gold standard AC also varies between studies. In this study, we directly estimate the error of not including bones in the four-class Dixon-based µ-maps. The most common is to use registered CT images translated to LAC at 511 keV as the gold standard µ-map. This does, however, rely on a close-to-perfect coregistration between CT and MR images, which can be difficult to obtain in practice (25, 43, 44). We adopted a method similar to Bradshaw et al. (25) in which soft-tissue classes and air in the µ-map are derived from the MR images, and bone and osseous tissues are derived from the CT images.

A primary limitation of this study is the limited number of patients. The training set consisted of only 18 patients, and the test set consisted of 17 patients. Since the model was trained using a 2D network, this still constituted a considerable number of images, but we do not expect that the limited training set was able to capture all the expected interpatient variability. The number of lesions was also limited. In bone, where the model had the largest impact in our testing, only four lesions were found.

The current method is also limited to pelvic imaging only. Adapting to a different clinical application would require retraining of the model. Additionally, in the current work, only a limited subset of reconstruction parameters was used, and we did not evaluate the robustness of the method toward changes in reconstruction parameters. However, since the method is trained to predict correction maps for the PET images directly, we suspect the model to be subject to similar variability between reconstruction parameters as SUV_max measurements themselves (45, 46). Lastly, the model is only tested on a specific patient cohort consisting of elderly male patients. Consequently, the model must be evaluated on a larger and more diverse patient cohort before implementation in clinical practice is justified.

Direct correction of four-class Dixon-based AC PET in the image space is a viable method for improving AC of pelvic PSMA PET/MR imaging. The method is tracer-independent, requires only the Dixon MR series and the four-class Dixon-based µ-map, and can be retrospectively applied to PET data without the need for re-reconstruction. It gives superior performance to the four- and five-class Dixon-based AC in a voxel-based RMSPE analysis and for quantification of bone lesion uptake.

The datasets presented in this article are not readily available because The data are not publicly available because they contain information that could compromise research participant privacy/consent. Requests to access the datasets should be directed to bendik.s.abrahamsen@ntnu.no.

The studies involving humans were approved by Regional Committee for Medical and Health Research Ethics Mid Norway (FDG data: identifier REK2014/1289 and PSMA data: identifier REK2020/83009). The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.

All authors contributed to the study conception and design. The data collection of the FDG lymphoma and lung cancer dataset was performed by LE. Data collection of the [18F]PSMA-1007 and [68Ga]Ga-PSMA-11 images was performed by IK and BA. Analysis and interpretation of data was performed by ME, TB and BA. The first draft of the manuscript was written by BA and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.