Non‐rigid motion‐compensated 3D whole‐heart T2 mapping in a hybrid 3T PET‐MR system

Simultaneous PET‐MRI improves inflammatory cardiac disease diagnosis. However, challenges persist in respiratory motion and mis‐registration between free‐breathing 3D PET and 2D breath‐held MR images. We propose a free‐breathing non‐rigid motion‐compensated 3D T2‐mapping sequence enabling whole‐heart myocardial tissue characterization in a hybrid 3T PET‐MR system and provides non‐rigid respiratory motion fields to correct also simultaneously acquired PET data.


INTRODUCTION
][6] The clinical potential of myocardial T 2 mapping has been shown in several studies.Wicks et al. showed that T 2 mapping improves the detection of active myocarditis compared to late gadolinium enhancement (LGE) alone. 7yocardial T 2 abnormalities in combination with LGE findings have been also shown to additionally predict arrhythmias and electrocardiographic (ECG) abnormalities better than each technique separately. 8T 2 mapping alongside LGE has been suggested to be superior to LGE alone in the diagnosis of cardiac sarcoidosis. 7,9Furthermore, T 2 mapping has been shown to distinguish between irreversible (fibrotic) and reversible (inflamed) myocardial damage, both for diagnosis and evaluation of response to treatment in cardiac sarcoidosis. 9,10The introduction of the hybrid PET-MR scanners and the development of targeted PET radiotracers have opened new opportunities to enable a more comprehensive assessment of cardiac disease from the complementary information provided by quantitative cardiac MRI and PET imaging. 11However, whereas PET imaging is intrinsically a 3D imaging technique, and is performed under free-breathing, cardiac MR T 2 mapping is conventionally performed as a series of short-axis 2D images under breath-hold (to minimize the effect of respiratory motion), raising challenges due to potential mis-registration between datasets and different coverage of the heart.Furthermore, most of the T 2 mapping techniques have been developed for 1.5T systems and use balanced SSFP (bSSFP) readouts. 5,12Such sequences are not directly applicable to hybrid 3T PET-MR systems due to banding artifacts and different hardware characteristics.
To address some of these limitations, novel techniques have been introduced for free-breathing 3D whole-heart T 2 mapping at 3T. [13][14][15] The 3D radial acquisitions, which allow acceleration and self-navigation to correct for respiratory motion, were used to perform free-breathing 3D T 2 mapping at 3T, 13 however, the acquisition remained lengthy, with an ∼18 min scan for isotropic 1.7 mm spatial resolution.Yang et al. 15 proposed a free-breathing 3D gradient echo T 2 mapping method with adiabatic T 2 preparation.In this approach, the effect of respiratory motion was addressed by using a 3D affine motion model derived from the respiratory diaphragmatic navigator signals.The final T 2 maps were obtained using a mono-exponential fitting, which is known to produce a bias of T 2 values. 16urthermore, the method relies on stable heart rates to produce accurate T 2 maps.Yang et al. have included saturation recovery pulse after each heartbeat to null the longitudinal magnetization in their later work. 17This approach was tested on the PET-MR scanner in dogs and healthy volunteers.The voxel size used in this approach was 2.0 × 2.0 × 6.0 mm 3 ; however, high isotropic resolution may be beneficial especially in diseases such as cardiac sarcoidosis, where the inflammation can be patchy and easily missed without high-resolution whole-heart coverage. 18To minimize heart rate dependency, additional saturation preparation pulses have been proposed for T 2 mapping at 3T in work by Ding et al. 14 However, this approach uses respiratory diaphragmatic navigator gating, resulting in long scan times for moderate non-isotropic resolution (1.25 × 1.25 × 5 mm 3 within ∼9 min), as well as using mono-exponential fitting to obtain the T 2 maps.Efficient high-spatial resolution (1.5 mm 3 isotropic, ∼6 min scan time) 3D whole-heart T 2 -mapping with image-navigator (iNAV) based translation respiratory motion compensation has been shown in healthy subjects and patients with myocarditis; however, this approach was proposed and evaluated at 1.5T. 1,19Furthermore, this approach only considers 2D translational respiratory motion correction.][22] Here we extend the iNAV-based 3D whole-heart T 2 -mapping to hybrid 3T PET-MRI and incorporate 3D nonrigid respiratory motion correction directly in the multi-contrast image reconstruction.The proposed approach uses a gradient echo readout for robustness at 3T, and a variable density Cartesian trajectory with spiral profile reordering 23 to enable undersampled acquisitions for reduced scan time.A virtual 3D image navigator 24 is integrated into the sequence to enable 3D respiratory motion tracking and non-rigid motion correction. 25T 2 maps are obtained using a dictionary-based mapping. 26urthermore, this technique provides non-rigid respiratory motion fields, that can be used to correct simultaneously acquired PET data 27 in a 3T hybrid PET-MR system, to produce co-registered motion-corrected PET and 3D T 2 mapping images that could facilitate image fusion and clinical interpretation.

Acquisition and reconstruction framework
The proposed 3D whole-heart T 2 mapping research sequence consists of an ECG-triggered 3D T 2 -prepared The 3D free-breathing T 2 -mapping pulse sequence diagram including three T 2 preparation pulses, saturation pulse and fat saturation (not shown).The 2D image-navigator (iNAVs) are acquired for translational motion estimation and correction.right-left (RL) and anterior-posterior (AP) motion is estimated with autofocus approach.Respiratory binning using the foot-to-head (FH) motion estimated from the iNAVs is performed and beat-to-beat 3D translational respiratory motion is applied to each bin.The 3D non-rigid motion is estimated and included into the reconstruction.Extended phase graph (EPG)-based dictionary matching is performed voxel-by-voxel to estimate the T 2 -maps.PET list-mode data are acquired simultaneously as the MR images.Non-rigid v3D iNAV motion fields estimated from MR are used to motion-correct PET data to the same respiratory position as MR, enabeling direct fusion of both datasets.To improve alignment between the μ-map and PET image position, the breath-held μ-map is registered to the last contrast of the 3D T 2 -mapping.This image is also used to perform MR-guided motion-corrected PET reconstruction.gradient echo sequence, where three datasets are sequentially acquired with three different T 2 -preparation durations (Figure 1A).The sequence includes a saturation pulse performed immediately after each R-wave to render the sequence heart rate insensitive, and a fat saturation pulse immediately prior to the imaging sequence.The 2D iNAVs are integrated into the sequence, 20 to enable 100% respiratory scan efficiency (no data rejection) and predictable scan time.The low-resolution 2D iNAVs are acquired at each cardiac cycle by adding spatially encoded low flip-angle lines at the beginning of each heartbeat of the T 2 -prepared gradient echo acquisition using 14 low-flip angle excitations (flip angle 3 • ), resulting in an iNAV duration of 50 ms.For 2D iNAV acquisition, high-low Cartesian trajectory with coronal orientation and right-left (RL) phase encoding is used.iNAV FOV matched the FOV of the T 2 mapping acquisition, resulting in a 1.5 mm × 22.3 mm acquired in-plane resolution.The 3D data are acquired with an undersampled variable-density golden-step Cartesian trajectory with spiral profile order sampling (VD-CASPR) 23 to further reduce scan time.
The iNAVs are used to estimate translational respiratory motion in the foot-head (FH) and RL directions in a beat-to-beat fashion by tracking a rectangular template placed over the apex of the left ventricle (LV) myocardium.The positioning of the iNAV window within which the motion patterns are estimated is selected for all three contrasts and is placed at the border of the myocardium and lungs.These estimates are used to create a virtual 3D (v3D) iNAVs based on autofocus, 24,28 so that FH, RL, and anterior-posterior (AP) beat-to-beat translational motion is obtained (Figure 1B).The FH translational motion is then used to bin the 3D data into four respiratory bins, and the v3D beat-to-beat motion is used to correct the data to the center of the corresponding bins.Respiratory-resolved 3D bin images are then reconstructed with soft-gating iterative SENSE 29 and used to estimate 3D non-rigid motion fields (Figure 1C).The motion fields are then incorporated into a non-rigid motion-compensated reconstruction 25 with multi-contrast patch-based low-rank regularization 30 to produce three motion-corrected datasets (one per T 2 -preparation).
To obtain the final T 2 maps, after the three datasets are aligned, an extended phase graph (EPG) simulation is used to generate a multidimensional dictionary of signal evolution based on the physical properties of the tissues (T 1 and T 2 relaxation values) and the parameters specific to the proposed pulse sequence.The dictionary was created for T 2 relaxation values ranging from 5 to 300 ms with a step of 1 ms, and for T 1 relaxation values ranging from 1100 to 1700 ms with a step of 100 ms in in-vivo studies and for T 1 relaxation values ranging from 1800 to 2700 ms with a step of 100 ms in phantom studies.These were selected to approximately cover the range of T 2 and T 1 values of normal and diseased myocardium and surrounding tissues and the approximate values of the phantom.A voxel-wise dictionary-matching approach is used to obtain the maps, where the reconstructed motion-corrected multi-contrast 3D images are first registered and normalized based on the first contrast data (acquired with T 2 prep = 0 ms) to account for any residual misalignment between the contrast due to the sequential acquisition approach.The 3D images are then used as input for the dictionary matching step, where for each voxel a T 2 value is retrieved by minimizing the difference of the signal of the dictionary over all the entries and the acquired data using least squares 26 (Figure 1D).
To reconstruct PET data, the v3D iNAV respiratory motion is used to bin the PET data into the same respiratory positions as the MR data (Figure 1E).To improve the alignment between the μ-map and PET image position, the conventionally breath-held μ-map is registered to the last contrast of the 3D T 2 -mapping.The third 3D T 2 -map contrast is also used to perform MR-guided motion-corrected PET reconstruction, 31 incorporating the non-rigid motion fields estimated from the MR reconstruction.This approach enables motion-correction for both the MR and PET data to the same respiratory position, 27 enabling direct fusion of both datasets for analysis and interpretation.

Experiments
The proposed 3D T 2 -mapping sequence was implemented as a prototype on a hybrid 3T PET-MR system (Biograph mMR, Siemens Healthineers, Erlangen, Germany).All acquisitions were performed on this system using a 6-channel body coil and a 24-channel spine coil.Written informed consent was obtained from all subjects according to institutional guidelines and the institutional ethics committee approved the study (REMAS 8700 for healthy subjects and REC 15/NS/0030 for patients).Data were acquired on phantom, healthy subjects, MR only patients and PET-MR patients with known or suspected cardiovascular disease with the proposed 3D T 2 -mapping method.The 2D multi-echo spin-echo mapping (phantom only, (TR = 10s, TE = 12, 28 and 55 ms, matrix size = 128 × 128, resolution 2 × 2 × 8mm 3 , acquisition time = 21 min 10 s for each TE) and conventional breath-held 2D T 2 prep-bSSFP mapping were also performed for comparison purposes.PET-MR patients received an [ 18 F]-FDG injection of 330 and 374.4 MBq and were scanned ∼2.5 h post injection.
Relevant imaging parameters for the proposed 3D T 2 mapping include coronal orientation, spatial resolution 1.5 mm 3 isotropic, 3× undersampling, flip angle 15 • , TR/TE = 3.45/1.57ms, bandwidth = 670 Hz/px, T 2 -prep durations of 0, 28, and 55 ms.2D iNAVs were acquired using 14 low-flip angle excitations (flip angle 3 • ).To decide the optimal flip angle, empirical optimization was performed before the sequence was validated with a range of flip angles, considering similar approaches found in the literature, where best flip angle of 15 • was determined.The optimal T 2 prep-delays were determined based on the literature research of similar approaches. 1,15,32atient-specific trigger delay and acquisition window was determined from a free-breathing 2D transverse cine scan right before the 3D T 2 mapping sequence to coincide with the mid-diastolic quiescent period of the cardiac cycle.Compared to our previous work at 1.5T, 1 the proposed approach acquisition time was increased to ∼10 min (reducing undersampling factor from 5× to 3×) to ensure enough data for the simultaneous PET acquisition.
Conventional breath-held 2D T 2 prep-bSSFP T 2 -maps were acquired at the myocardial apex, mid, and base.Imaging parameters include in-plane resolution = 1.5 × 1.5 mm (phantom and healthy subjects) or 1.9 × 1.9 mm (patients, clinical protocol), slice thickness 8 mm, T 2 -preparation pulses = 0, 28, 55 ms, flip angle = 12 • , bandwidth = 1155 Hz/px.MR image reconstruction for the proposed 3D T 2 mapping, including motion estimation, non-rigid motioncompensated image reconstruction, and dictionary-based T 2 mapping was implemented offline in MATLAB (MathWorks, Inc., Natick, Massachusetts, USA).PET image reconstruction was performed offline using MAT-LAB and e7 Tools (Siemens Healthcare, Knoxville, TN, USA) using MR-guided motion-correction. 31,33ramework for PET image reconstruction integrates μ-map alignment, respiratory motion correction, cardiac gating, and MRI guidance to further improve image quality.The PET images were reconstructed into 3D arrays of 127 × 344 × 344 voxels, with voxel size 2.03 × 2.08 × 2.08 mm 3 .Only the PET list-mode data acquired within the duration of the MRI were considered, in order to allow use of the MRI respiratory trace for PET data binning.

Phantom study
Phantom studies were performed to evaluate the accuracy of the proposed 3D T 2 mapping approach.An in-house built phantom with 7 different mixtures of water and agarose (0, 0. diseased myocardium and surrounding tissues.The T 1 values of the in-house built phantom were in the range of T 1 = 1850 ms-T 1 = 2750 ms.The dictionary was created for T 2 relaxation values ranging from 5 to 300 ms with a step of 1 ms, and for T 1 relaxation values ranging from 1800 to 2700 ms with a step of 100 ms.All phantom experiments were performed with a simulated heart rate of 60 beats per minute. Images were acquired with the proposed 3D T 2 -mapping method as described above.Additional imaging parameters include saturation time (T SAT ) = 550 ms, and acquisition time = 3 min 43 s.
The values obtained with the proposed 3D mapping and conventional 2D mapping were compared to the gold standard 2D multi-echo spin-echo images (TR = 10s, TE = 12, 28, 55, 80, 120, 250 & 480 ms) with acquisition times of 21 min 10s for each TE.The multi-echo spin-echo acquired images were mono-exponentially fitted.
Repeatability studies were performed acquiring two datasets on three consecutive days (6 acquisitions in total) with the proposed 3D T 2 mapping approach and the conventional 2D T 2 mapping.These values were compared to the spin-echo gold standard.The phantom was kept in the scanner room, to keep a constant temperature during the study.

Healthy subjects
Healthy subjects (N = 10, 5 males, 29 ± 2 y old) with no history of cardiovascular disease underwent the proposed 3D T 2 mapping sequence.Data were acquired during mid-diastole using a subject-specific trigger delay, acquisition window, and saturation time (longest possible).The average T SAT time and acquisition window in healthy subjects was T SAT = 650 ± 92 ms, acquisition window = 115.4± 11 ms, and heart rate = 70 ± 14 bpm.Additional imaging parameters included: FOV = 312 × 312 × 60-72 mm 3 .
To assess the impact of the non-rigid motion correction (NRMC) approach, 3D T 2 maps were also reconstructed without motion correction (No MC) and with v3D translational motion correction only (TRMC) for comparison purposes.1.Similar to healthy subjects, 3D T 2 mapping data were acquired during mid-diastole using a subject-specific trigger delay, acquisition window, and saturation time (longest possible).The average T SAT time and acquisition window in the patients was T SAT = 521 ± 84 ms, acquisition window = 111.5 ± 5 ms, and heart rate = 66 ± 13 bpm.Additional imaging parameters include FOV = 312 x 312 x 108 − 132 mm 3 .The proposed NRMC images were compared to the clinical 2D T 2 maps.

PET-MR patients
Two male patients, ages 58 and 53 y, with suspected cardiac sarcoidosis referred for clinically indicated cardiac PET-CT were recruited.Patients were eligible to participate if they were > 18 y of age and agreed to an additional PET-MR imaging after their clinical PET-CT imaging protocol.MR imaging parameters matched the parameters of MR-only patients.

Phantom study
Circular regions of interest (ROIs) for each vial of the phantom of 1 cm diameter were manually drawn in the center slice of the proposed 3D T 2 mapping.For each ROI, the mean value, and the SD of T 2 relaxation times were calculated.A repeatability study was performed for both the proposed 3D T 2 mapping and the conventional 2D T 2 mapping, where intra-and inter-scan variation were calculated for assessment of scan/rescan reproducibility and accuracy.An analysis of variance (ANOVA) test was performed to evaluate statistically significant differences between the six acquisitions (two acquisitions, 3 days).Paired t-tests were performed between scans, including Tukey correction for multiple comparisons.T 2 bias in the phantom was quantified with Bland-Altman analysis.
T 2 values obtained with the proposed 3D T 2 mapping and the conventional 2D T 2 mapping were also compared to the values obtained by the reference 2D spin-echo reference technique.

Healthy subjects
The performance of the proposed non-rigid motion (NRMC) corrected 3D T 2 mapping was compared against TRMC and No MC reconstruction.Image quality scores were ranked by a clinical expert (4 y of experience in cardiovascular MRI) to quantitatively compare the three motion correction approaches (NMC, TRMC, and NRMC) using the 5-point Likert scale (1: non-diagnostic, 5: excellent diagnostic quality).To further compare the motion correction approaches, T 2 values from the mid-cavity septum have been compared using NMC, TRMC, and NRMC.Mean and SD were calculated for all the healthy subjects.To assess the quantitative T 2 values obtained with the proposed method, the 3D T 2 maps obtained from NRMC images were reformatted into the short-axis view to be compared with the conventional 2D T 2 maps.The LV myocardium was segmented slice by slice (∼40 slices for 3D T 2 maps and 3 slices for 2D T 2 maps) semi-automatically using a supervised in-house developed deep learning segmentation. 34The third contrast was used for the segmentations and masking of the images, which is intrinsically aligned with the T 2 map and has very good delineation between myocardium and blood.Slices were grouped into apical, mid-ventricular, and basal sections for region-based analysis following 16-segment AHA guidelines. 35T 2 values quantified within each segment were obtained as mean ± SD.T 2 bias in healthy subjects was quantified with Bland-Altman analysis comparing the proposed 3D T 2 mapping and conventional breath-held 2D T 2 maps.
To study the uniformity of the resulting T 2 maps in healthy subjects, SD across segments was computed for each subject in both proposed 3D T 2 mapping and conventional breath-held 2D T 2 maps.The T 2 SD bias across all the segments was compared using the Bland-Altman analysis.

MR-only patients
The 3D T 2 maps obtained with the proposed approach were reformatted into the short-axis view to be compared with the clinically indicated 2D T 2 maps using the 16-segment American Heart Association (AHA) model.Elevated T 2 segments, recognized by a clinical expert, were excluded from the statistical analysis so that only values from remote myocardium are considered.Paired two-tailed t-tests were then performed for each segment to compare the 3D and 2D approaches.Additionally, high-resolution bullseye plots of the myocardium were generated from the proposed 3D and conventional 2D T 2 maps to visually compare the extent of T 2 elevation findings.T 2 bias in patients of the mean T 2 values over all the segments was quantified with Bland-Altman analysis.All statistical analysis was performed using Prism Graphpad (Version 9.1.0).T 2 values for all the segments for 2D and 3D T 2 maps were compared with a two-way ANOVA with the Geisser-Greenhouse test to assess statistical differences.Values of p < 0.05 were considered statistically significant differences.

Phantom study
T 2 values obtained with the proposed 3D T 2 mapping sequence in phantom are summarized in Figure 2. On average, intra-session variation was 0.53 ± 0.4 ms for 3D T 2 mapping compared with 1.38 ± 0.7 ms for the conventional 2D T 2 map.Similarly, inter-session variation was 1.17 ms with the proposed 3D T 2 mapping compared with 1.37 ms for the conventional 2D T 2 mapping.
(A) (B) The T 2 values obtained with the proposed 3D T 2 -mapping sequence were compared to the gold standard values obtained with 2D multi-echo spin echo sequence for each of the vials.We can see that we achieve good intra-session and inter-session repeatability in both 3D and 2D T 2 mapping.On the right we see the mean T 2 value (and SD) for each vial averaged over the six acquisitions acquired as part of the repeatability study for both 3D and 2D T 2 mapping.A linear correlation with R2 = 0.99 was observed between the proposed technique and the gold standard values.
Excellent linear correlation with a high coefficient of determination (R 2 > 0.9999) was found between 3D T 2 mapping and the gold-standard spin-echo (SE) technique T 2 values.A similar, slightly lower, coefficient of determination (R 2 > 0.9994) was observed for the conventional 2D T 2 mapping.When compared to the gold-standard SE technique, T 2 bias was 5.3 ± 4.8 ms for the conventional 2D T 2 mapping versus 2.2 ± 1.1 ms for the proposed 3D T 2 map.

Healthy subjects
All experiments with healthy subjects were successful.The average acquisition time for the 10 healthy subjects was 9.25 ± 1.1 min.Example reconstruction results (third contrast and T 2 maps) for NRMC and TRMC are shown in Figure 3 for two representative subjects.Improved delineation and sharpness of structures can be observed with NRMC in the third contrast.Similarly, a clear improvement in the homogeneity of the blood pool and myocardium is observed in the proposed 3D T 2 map with NRMC.NRMC reconstruction for two additional healthy subjects is shown in Figure 4 for all three contrast and the resulting T 2 map in mid short axis.The average quality score for NMC was 4.25 ± 0.4, for TRMC it was 4.4 ± 0.4 and for NRMC it was 4.8 ± 0.3.The difference between NMC and TRMC was not statistically significant, however the difference between TRMC and NRMC and also NMC and NRMC was statistically significant.To compare the motion correction approaches, all the T 2 values obtained by selecting a ROI at the mid-cavity septum were averaged and compared against the conventional 2D T 2 values.Average T 2 values were 36 ± 4.7 ms for NMC, 36.6 ± 2.5 ms for TRMC, and 36.8 ± 2.6 ms for NRMC, whereas for the conventional 2D images it was 37 ± 2.4 ms.T 2 values for all segments (apical, basal, mid-cavity) with the proposed 3D NRMC approach and the conventional 2D T 2 mapping are shown in Figure 5A.Good agreement was observed between the proposed technique and conventional T 2 mapping, with average values of Images from two representative healthy subject showing the translational motion correction and proposed virtual 3D (v3 image-navigator (iNAV) non-rigid motion correction for third 3D T 2 -prepared volume in coronal view, and T 2 maps in coronal view and reformatted to short axis Remaining motion artifacts are observed translational motion correction, improved quality is observed non-rigid motion correction.The non-rigid motion fields provided with the proposed approach can be used for motion correction of simultaneously acquired PET data.

F I G U R E 4
Images from two representative healthy subjects and a representative patient showing the three 3D T 2 -prepared volumes reformatted to short axis and the associated T 2 map.
39.0 ± 1.4 ms vs 38.6 ± 1.2 ms in healthy subjects, respectively.The values are in good agreement with the literature range. 36The bias of 1.8 ms and 95% limits of agreement (LOA) of −2.4 to 6 ms was observed when comparing the mean 3D T 2 values to the mean conventional 2D T 2 values across all the segments.We observe good homogeneity with low SD for the values across all the segments for both 2D and 3D techniques with a bias of 0.3 ms.

MR-only patients
All experiments in patients were successful.The average acquisition time for the 14 patients was 10.5 ± 4 min with a reconstruction time of ∼250 min.Reconstruction results for the proposed NRMC 3D T 2 mapping are shown in Figure S1 for two representative subjects, showing similar image quality to healthy subject scans.The proposed 3D T 2 mapping is compared against conventional 2D T 2 mapping for two representative patients in Figure 6, showing four short axis slices from base to apex.Similar visual image quality is observed for the proposed 3D T 2 mapping, while improving volumetric coverage compared to the conventional 2D acquisition.Since the 3D whole heart T 2 mapping framework has an isotropic spatial resolution, the T 2 maps can be reformatted in any view.This is demonstrated in Figure 7, where T 2 map reformats in the standard orientations are displayed (two-chamber, three-chamber, and four-chamber, short axis (3D and 2D)) in three additional representative patients for the proposed 3D T 2 mapping.

F I G U R E 5
The violin plots show average T 2 values in basal slices, mid-cavity, and apex for healthy subjects all segments, in patients in just non-elevated segments.
(A) (B) Comparison of the conventional 2D T 2 map and 3D T 2 map reformatted to the same table position from base to apex.
T 2 values for all non-elevated segments (apical, basal, mid-cavity) with the proposed 3D T 2 mapping approach and the conventional 2D T 2 mapping are shown in Figure 5B for all patients.Good agreement was observed between the proposed T 2 map and conventional T 2 mapping.T 2 mapping average values were measured at 39.1 ± 1.4 ms for the proposed 3D T 2 mapping approach and 40.3 ± 1.7 ms with the conventional 2D T 2 mapping in remote segments for patients (p value = 0.97).The bias of 1.3 ms and 95% LOA of −1.9 to 4.6 was observed for patients using Bland-Altman analysis.For segments that were elevated in the three patients, T 2 values were averaged and compared between 2D (44.6 ± 0.7 ms) and 3D (44.5 ± 2.8 ms), showing good agreement between the two techniques.The 16-segment maps of the LV obtained with 3D T 2 mapping and 2D T 2 mapping are shown in Figure 8 for two patients with non-elevated myocardium values and two patients diagnosed with acute myocarditis, showing elevated T 2 values.LV coverage was the same for both 3D and 2D methods, but the number of slices covering the LV was higher for the isotropic 3D approach in comparison to the conventional 2D T 2 mapping (∼40 slices for 3D T 2 maps and 15 slices for 2D T 2 maps).The advantage of the isotropic 3D coverage of the proposed approach can be observed in patient 7, where elevated values are more visible with the 3D 16-segment plot compared to the conventional 2D plot.Good agreement is observed for the proposed 3D T 2 mapping in comparison to conventional 2D T 2 maps, with higher detail in high-resolution 16-segment AHA plots computed from the 3D T 2 mapping values due to higher spatial resolution.No significant difference was found between 2D and 3D T 2 values for each segment in all the patients (p = 0.9857).T 2 values per segment measured from all the patients can be found in Table S1.

PET-MR patients
The proposed protocol was completed successfully.Motion correction visually improved the quality of the PET images and improved correspondence to the 3D MR data compared to conventional uncorrected PET reconstructions (white arrows on Figure 9).There was no T 2 elevation, LGE or [ 18 F]-FDG uptake in these subjects (Figure S5), which suggests these subjects do not have active cardiac sarcoidosis at the time of examination.

DISCUSSION
In this study, we have introduced a free-breathing non-rigid motion-compensated 3D whole-heart T 2 -mapping that enables the detection of myocardial inflammation and provides non-rigid respiratory motion fields to correct simultaneously acquired PET data in a 3T PET-MR system.The feasibility of this technique was investigated in phantom and healthy subjects.The proposed approach was also evaluated on 14 patients with suspected cardiovascular disease in comparison to conventional clinical 2D T 2 mapping in MR only acquisitions The 3D T 2 mapping images shown in two-, three-, and four-chamber views and short axis for 3D and 2D T 2 mapping for three representative cases.The 3D T 2 mapping extends the volumetric coverage, which can be beneficial for diagnosis of patchy diseases such as cardiac sarcoidosis.

F I G U R E 8
The 16-segments American Heart Association (AHA) model plots for the conventional 2D T 2 -mapping sequence using 9 slices and 3D T 2 -mapping sequence using 45-55 slices to compute the plot.Comparable T 2 values can be observed between both techniques with no significant differences found between the averaged basal, mid-cavity, and apical slices.Patients 9 and 5 (bottom of the figure) have been diagnosed with acute myocarditis.More patient information can be found in Table 1.
and on two patients with PET-MR acquisitions.Comparable T 2 values to conventional 2D T 2 mapping were achieved with the proposed 3D whole-heart T 2 mapping in phantoms, healthy subjects, and patients.
In phantom studies, good agreement was found between the proposed 3D T 2 mapping and the gold-standard spin-echo sequence.We observed some underestimation when using the clinical T 2 mapping sequence.That sequence is tuned for the T 1 values in the myocardium, thus the T 2 value can deviate in substances with out-of-range T 1 .This specifically can be observed in the vials with the higher concentration of water, where the T 2 and T 1 values were higher.In the proposed approach, the higher T 1 values were considered when generating the dictionary.Low intra-session and inter-session variability were obtained with the proposed 3D T 2 mapping Fused PET-MR image, showing the conventional no motion correction maximum-likelihood expectation-maximization reconstruction and the proposed motion corrected MR-guided maximum a posteriori expectation maximization.The third column shows the corresponding 3D T 2 maps.Improvements in the correspondence between PET and MR are highlighted with the white arrows.approach, showing no significant difference with conventional 2D T 2 mapping.Slight differences in the intra-and inter-session variability between the investigated sequence compared with conventional 2D T 2 mapping technique could be explained by the increased isotropic resolution, the use of saturation pulses at every heartbeat, which make the sequence more sensitive to noise, and scanner instability.Similar observations were found in previous work. 1This is consistent with the results observed in our recent study performed at 1.5T. 19he difference in T 2 values of healthy myocardium and diseased tissue has been reported to be relatively small, around 11 to 13 ms, which makes T 2 mapping challenging. 13,32,36,37The ability to estimate the T 2 values more precisely would make the T 2 mapping more reliable and clinically relevant.Improved non-rigid motion-corrected reconstruction was investigated in this study as one of the proposed improvements to the previously introduced 3D T 2 mapping approach at 1.5T. 19For single-contrast images, it has been previously shown that non-rigid motion correction can significantly improve image quality. 21,27,38In this work, non-rigid motion correction was integrated into the reconstruction framework, instead of translational motion correction only.We further included a novel autofocused-based virtual 3D iNAV approach that enables improved 3D beat-to-beat and intra-bin non-rigid respiratory motion corrected reconstruction for free-breathing 3D cardiac MRI, which has shown improvement in cases with challenging breathing cycles and irregular heart rate for single contrast images. 20Results showed that the proposed 3D T 2 mapping approach achieves comparable T 2 values to reference methods in healthy subjects and patients with suspected cardiovascular disease.
The reason for the slight, however not significant, variation of the 3D T 2 mapping values compared to 2D T 2 mapping values lies behind the shortcomings of the 2D T 2 mapping technique and bias when compared against the gold standard in phantoms, due to the simplified exponential model used in the conventional method, which can be attested by the bias observed when comparing the conventional 2D T 2 mapping values to the gold standard T 2 values obtained with the SE sequence (Figure S2). 16Another reason for slight overestimation of T 2 values observed with respect to the conventional breath-hold 2D T 2 mapping sequence could be the use relatively thick slices, between 8 and 10 mm, with the conventional 2D sequences may result in T 2 times underestimation due to partial volume averaging effects, thereby potentially lowering sensitivity or resulting in an underestimation of the extent of tissue injury.Underestimation with the conventional 2D T 2 mapping has previously reported in several studies. 1,39,40ther novel 3D whole-heart T 2 mapping techniques at 3T have been introduced to achieve higher SNR with larger coverage of the heart [13][14][15] ; however, they have certain shortcomings, such as a lengthy acquisition time of ∼18 min for isotropic 1.7 mm spatial resolution, 13 a mono-exponential fitting, which is known to produce a bias of T 2 values and relying on stable heart rates to produce accurate T 2 maps 15 or using respiratory diaphragmatic navigator gating, resulting in long scan times for moderate non-isotropic resolution (1.25 × 1.25 × 5 mm 3 within ∼9 min). 14Those limitations are addressed in the proposed technique, as the acquisition time is more predictable and shorter due to motion compensation and undersampling.In our approach dictionary matching is used for more accurate T 2 values and additional saturation preparation pulses have been implemented to minimize heart rate dependency.
It should be noted that even though the acquisition time has been reduced compared to previously proposed 3D T 2 mapping approaches at 3T, the scan time remains lengthy.This could be further reduced by further acceleration.Similarly, reconstruction time, which currently takes approx.250 min could be further improved by implementing the reconstruction on multiple graphics processing units (GPUs) and using coil compression strategies.Deep learning reconstruction could also be considered for faster reconstruction time.
The ability of the proposed framework to produce high-resolution 3D images holds promise for wider cardiac applications, such as high-resolution motion-compensated 3D joint T1-T 2 mapping, 41 which was preliminary tested at the 3T PET-MR system in healthy subjects. 42Nevertheless, further clinical studies are required.
Additionally, PET-MR imaging has shown promise for enhanced characterization of cardiovascular disease.Motion correction of PET data using MR has demonstrated to improve the PET images. 43,44One of the approaches was proposed by Kolbitsch et al., 45 where PET data were corrected using single contrast MRI making cardiac PET results more reproducible.In our work, T 2 mapping adds diagnostic value to the simultaneous PET-MR acquisition, which is especially useful in patients with inflammatory diseases like cardiac sarcoidosis.By acquiring MR images that can provide cardiac and respiratory motion information, the simultaneously acquired PET data has been shown to benefit from motion correction, resulting in improved delineation and quantification for cardiac PET images.In this work, respiratory motion correction was performed for both 3D T 2 map MR and PET data.However, the proposed approach can be extended to consider cardiac ECG-gating and MR guided image reconstruction as previously proposed for single contrast images by Munoz et al. [45][46][47] The feasibility of simultaneously acquired non-rigid motion corrected [ 18 F]-FDG PET and 3D T 2 mapping data has been evaluated in two patients with suspected cardiac sarcoidosis.Improved PET images call for future studies in more patients with cardiac sarcoidosis undergoing simultaneous PET-MR.

CONCLUSIONS
Here, we introduced a free-breathing non-rigid motion-compensated 3D T Patient information including sex, age, and diagnosis.
8, 1, 1.5, 2, 3, and 5% agarose concentration) was used with a range of T 2 values between 20 and 150 ms to approximately cover the T 2 values of normal and T A B L E 1 2 -mapping at a 3T hybrid PET-MR enabling whole-heart myocardial tissue characterization and providing non-rigid respiratory motion fields to correct simultaneously acquired PET data.An MR-only validation of the proposed 3D whole-heart T 2 -mapping sequence was demonstrated in phantom, healthy subjects, and patients with suspected cardiovascular disease.Repeatability studies in phantom showed good agreement with reference standard sequences.Furthermore, good image quality with T 2 -values comparable to the clinical 2D T 2 -mapping sequence was achieved in healthy subjects and patients.Proof-of-concept simultaneous PET-MR acquisitions were performed in two patients, showing improved PET image quality.Future studies will evaluate the proposed method in a cohort of patients in simultaneously acquired cardiac PET-MR data.ACKNOWLEDGMENTSThis work was supported by EPSRC (EP/L015226/1, EP/P032311/1, EP/P007619/1, and EP/P001009/1).This research was supported by the National Institute for Health Research (NIHR) Cardiovascular Health Technology Cooperative (HTC) and the Biomedical Research Centre based at Guy's and St. Thomas' NHS Foundation Trust and King's College London.This research was funded in part, by the Wellcome Trust NS/A000049/1.For Open Access, the author has applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission.