Twelve oncology patients were included in the study that were scheduled for a 18Fluoride-fluorodeoxyglucose (18F-FDG)-PET/CT for regular clinical care. Each patient was injected with 3 MBq/kg body weight of the tracer. These patients underwent an additional PET/MRI examination. Of the 12 patients injected with 18F-FDG, 2 patients did not complete the scan due to discomfort and therefore these patients were excluded. Data from 2 more scans could not be used due to corruption of the listmode file and distortion of the respiratory signal. Furthermore, another 15 patients suffering from coronary artery disease (CAD) that underwent an 18F-FCH cardiac PET/MRI examination were also included in the study. Each patient was injected with 4 MBq/kg body weight of the tracer. Of the 15 patients injected with 18F-FCH, data from 2 patients could not be used due to an erroneously highly undersampled CMRA and a distorted belt respiratory signal, respectively. The tracer was administered extravascularly for another 2 patients, therefore the data from these patients was also not analyzed.

The approval for both studies was obtained from the Institutional Review Board and the local medical ethical research committee (METC Academisch Ziekenhuis Maastricht) with reference numbers METC 164156 and 162043 respectively. All patients provided written informed consent.

Each patient was scanned with an integrated 3T PET/MRI scanner (Biograph mMR, Siemens Healthineers, Erlangen, Germany). The patients were scanned in headfirst supine position with the 6-channel body matrix coil and the 12-channel spine radiofrequency coils (Siemens Healthineers, Erlangen, Germany). A Dixon-based attenuation map (µ-map) was acquired at the end-expiration position during a breath-hold for attenuation correction of the PET data [26]. To prevent truncated MR-based attenuation correction maps due to the smaller MRI FOV, B0 homogenization using gradient enhancement (HUGE) was used [27]. Subsequently, a 3D-CMRA sequence with a 2D iNAV was acquired, which consists of a 3D spoiled gradient echo sequence with a fully sampled golden-angle step Cartesian trajectory with spiral profile ordering such that one spiral-like interleaf is acquired per heartbeat [25]. Sequence parameters include FOV = 304 × 304 × 96–104 mm3 (based on the patient’s anatomy, the field of view can differ slightly and therefore a range is provided in the feet-head direction), acquired resolution = 1.0 × 1.0 × 2.0 mm3, flip angle = 15°, repetition time (TR) = 3.72 ms, echo time (TE) = 1.7 ms, patient-specific trigger delay, preferably targeting the end-diastole phase, with an acquisition window ranging between 90 and 130 ms (corresponding to 24–32 lines per spiral interleaf). Just before the 3D CMRA acquisition window, a 2D iNAV is acquired which provides a low-resolution image of the heart in coronal view. As part of the imaging protocol, other cardiac MRI sequences, including cardiac cine MRI are acquired as well. Simultaneously, listmode cardiac PET data is acquired and the respiratory signal is recorded via the respiratory belt for the entire duration of the scan. PET image reconstruction was performed using e7 Tools (Siemens Healthineers, Knoxville, TN, USA), using the ordinary Poisson-ordered subset expectation maximization (OP-OSEM) algorithm with 3 iterations and 21 subsets [28]. Images were reconstructed with a voxel size of 2.08 × 2.08 × 2.03 mm3 and a matrix size of 344 × 344 × 127. For PET attenuation correction the MR-based (Dixon) µ-maps were used which provided segmentation of air, lung, fat, and soft tissue.

Respiratory motion in the left–right (LR) and feet head (FH) direction is estimated using the position of the left ventricle of the heart in the iNAV images for each heartbeat. Based on the FH position, the CMRA data is allocated to certain respiratory phases (bins). In our study, we used 4 bins. K-space data inside each bin is corrected to the center of the bin using the FH and LR position estimates derived from the iNAV. Afterwards, each bin is reconstructed. Using the end-expiration bin as a reference, 3D non-rigid deformation fields are generated based on free form deformations using voxel based normalized mutual information as a similarity measure [29, 30]. These deformation fields are subsequently applied to transform each bin to the end-expiration position generating the motion-compensated CMRA image [25].

A schematic representation of PET respiratory motion correction is displayed in Fig. 1. The motion correction pipeline was developed in MATLAB (MATLAB (2018) 9.7.0.1190202 (R2019b); Natick, Massachusetts: The MathWorks Inc.). To utilize the entire PET dataset acquired during the complete PET/MRI exam, the respiratory signal from the respiratory belt is used. The respiratory signal from the iNAV, respiratory belt, and the bins to which the data are allocated are visualized in Fig. 2. The two signals (FH motion signal derived from the iNAV and respiratory belt signal, respectively) are synchronized as described in more detail below. For the time period where iNAV signal is acquired (CMRA acquisition), the respiratory signal from the belt is initially divided into the same bins (bin start and end time) as those that were used for the CMRA motion correction. The scale on the y-axis of the respiratory belt signal is adjusted to the same order of magnitude as the iNAV signal, which allows the use of the same bin thresholds (FH displacement ranges that determine to which bin the acquired data are allocated) for CMRA motion correction and the respiratory belt signal binning as a first input in an iterative procedure. The iNAV signal is acquired every heartbeat. Therefore, using ECG R-R wave intervals as reference, corresponding bins from the iNAV and respiratory belt are compared to determine the bin match percentage between the 2 signals. Subsequently, the bin threshold ranges for the respiratory belt signal are manually adjusted to provide the highest bin match percentage between the 2 signals. Once the final threshold ranges are determined, they are used to bin the respiratory belt signal for the remaining part of the PET acquisition.

PET and MRI data are acquired simultaneously. The 2D iNAV is only available for part of the complete examination (i.e. during the CMRA acquisition). The feet-head (FH) motion signal is derived from the iNAV to generate the iNAV respiratory signal. The different colors (green, black, red, and cyan) each represent the bin in which the data acquired during this time window will be allocated. The breathing signal from the respiratory belt (thoracic motion) is available for the entire duration of the scan. By co-registration of the iNAV and belt respiratory signal in the period in which they are acquired simultaneously, the respiratory signal in the entire time period can be used to bin the PET data of the entire PET examination. The µ-map is deformed using the inverse motions fields to match the position of each bin. The deformed µ-map is used to reconstruct PET data for each bin. Next, these PET images are transformed to the end-expiration position using the motion fields again and combined to create the final motion-corrected PET image

a Feet head motion recorded by the iNAV. b Thoracic motion recorded with the respiratory belt. c Overlapping signal from the iNAV (a) and the respiratory belt (b). The solid vertical lines represent the R-peak in the ECG signal. The dots on curve in sub-plot a represent the time points at which the iNAV was acquired in the R–R wave. The crosses on curve in sub-plot b represent the corresponding time points signal from the respiratory belt. The shaded horizontal regions in panel a and b represent the 4 bins. All PET data acquired in an R-R interval is allocated to one of the 4 bins. The bin to which the data is allocated is based on the displacement of the heart as determined by the iNAV. For example, in panel a, the data in the first panel is allocated to bin 2 as the iNAV acquired for the R–R interval falls within the bin 2 thresholds. The four colors represent the 4 bins. Red represents bin 1, cyan bin 2, black bin 3 and green bin 4

Based on the binning threshold ranges, PET counts are divided into four bins. For each bin, a listmode file is created. PET images, µ-maps and MRI-derived deformation fields have different dimensions. To enable application of the deformation fields to µ-maps and PET images the data were interpolated and zero-padded to the largest dimension in each direction, resulting in matching matrices where each point represents the same physical position. The µ-map is deformed to reconstruct 4 µ-maps that match the position of each bin using the inverse of the deformation fields that were generated previously to reconstruct the CMRA. To reconstruct the cardiac gated PET images, data for each bin is cardiac gated to include only the PET data that was acquired simultaneously with the CMRA acquisition window (acquired preferably in end-diastolic phase). Using the listmode files and the µ-maps, PET data is reconstructed for each bin as described above. Finally, using the same deformation fields, each PET image is transformed to the reference position (end-expiration) and, subsequently, combined (corresponding pixels from each of the four reconstructed bins are averaged) to create the final motion-corrected PET image.

For each patient in the 18F-FDG and 18F-FCH study, PET data were reconstructed in four ways: a dataset with neither respiratory nor cardiac motion correction (NMC), a dataset with only respiratory motion correction using the framework provided in this manuscript (MC), a dataset with no respiratory motion correction but with end-diastolic gating (NMC_G) and a dataset with respiratory motion correction using the framework provided in this manuscript combined with end-diastolic gating (MC_G).

For the 18F-FDG datasets, volumes of interest (VOIs) were drawn in the 5 middle CMRA slices delineating the left ventricular wall and the middle of the left ventricle cavity (Fig. 3). The corresponding PET images were overlaid on the CMRA images in color. The VOI on the myocardial wall was used to calculate the maximal myocardial 18F-FDG uptake, expressed as maximal Standardized Uptake Value (SUVmax). The SUVmax is defined as the maximum voxel activity within the VOI. The myocardial SUVmax were normalized to the mean blood pool activity concentration obtained from the VOI in the center of the left ventricular cavity (SUVmean blood pool). The resulting normalized values were expressed as maximum target-to-background ratio (TBRmax). Blurring of the image due to respiratory motion is expected to reduce the myocardial SUVmax and TBRmax values. Therefore, higher TBRmax values are expected for the respiratory motion-corrected images. We also calculated the SNR, defined as the ratio of the signal intensity in the VOI in the myocardial wall and the standard deviation of the SUV in a VOI with low uptake (lung) as the inhomogeneous uptake in the myocardium does not allow to quantify the noise reliably in the VOI in the myocardium [31]. The SNR is calculated using the following equation.

$$SNR = \left( \right)/\left( \right)$$

MR and 18F-FDG PET/MR images of the myocardium. a CMRA image, b CMRA image with the volumes of Interest (VOIs) that encompasses the left ventricular wall (yellow), a VOI in the middle of the left ventricular cavity (red) and a VOI in the lung close to the myocardium (green) c shows a color overlay of the PET image projected on the CMRA image. d PET/MR image with the three VOIs

The statistical noise in PET images is related to the number of PET counts [32]. The motion-corrected images have the same number of PET counts as the non-motion corrected images and therefore these images are expected to have a similar SNR. Cardiac gating leads to a large reduction in the number of PET counts which reduces the SNR. Therefore, we expected a higher SNR for the MC compared to the MC_G images and also a higher SNR for the NMC versus NMC_G image.

To qualitatively assess the PET images, line profiles were drawn through a high tracer uptake region (myocardial walls) for the 18F-FDG dataset and these line profiles were visually inspected.

For the 18F-FCH datasets, a volume of interest was drawn that delineates a vulnerable atherosclerotic lesion, which was selected based on a vascular section with a vulnerable plaque, defined as a plaque with a fibrous cap thickness of < 70 µm on optical coherence tomography (OCT). The OCT slice position of the vulnerable plaque was identified on the CMRA images, using vessel side branches as landmarks, in consensus by a cardiologist (BR) and nuclear medicine physician (JP). Another VOI was drawn in the left ventricle cavity. The CMRA images were fused with the corresponding PET images. The TBRmax was determined as described above. Since the small size of the atherosclerotic lesions and low 18F-FCH uptake in the plaques prevented accurate SNR assessment, a VOI in the liver was drawn to calculate the SNR values for the 18F-FCH datasets. To calculate the SNR, the mean value of the signal from the liver VOI was used while the standard deviation of the VOI in a low uptake region (lung) was used to determine the noise since inhomogeneous uptake in the liver prevented accurate noise assessment (Additional file 1: Figure Appendix A). The VOI in the liver was also used to assess the SUVmax for the 18F-FCH datasets. To qualitatively assess the 18F-FCH PET images, line profiles were drawn through a high tracer uptake region (at the lung-liver interface) and these line profiles were visually inspected.

The SUVmax, TBRmax and SNR values for the 4 reconstructions were compared using a repeated measures ANOVA test with post hoc tests. The values are presented as the mean ± standard error (SE) of the measurements. A p-value < 0.05 was considered statistically significant.