Reproducibility of 3D thoracic aortic displacement from 3D cine balanced SSFP at 3 T without contrast enhancement

Aortic motion has direct impact on the mechanical stresses acting on the aorta. In aortic disease, increased stiffness of the aorta may lead to decreased aortic motion over time, which could be a predictor for aortic dissection or rupture. This study investigates the reproducibility of obtaining 3D displacement and diameter maps quantified using accelerated 3D cine MRI at 3 T.


INTRODUCTION
Aortic motion has been shown to have a direct impact on the mechanical stresses acting on the aorta. 1 Large aortic displacement may be tolerated in a compliant aorta but could be the cause of dissection or rupture in a patient with stiffer aortic tissue.Therefore, it is possible that aortapathy is expressed through decreased aortic displacement over the cardiac cycle, for example in Marfan disease. 2 Because aortic dimensions, such as diameter and cross-sectional area, alone are inaccurate predictors of aortic dissection, 3 aortic displacement might be a valuable complementary measure.An increased stiffness of the aortic wall results in increased resistance to motion; consequently, change in the displacement of the aorta over time could be a predictor of aortic dissection and aortic dilatation.
Previous studies have investigated rigid longitudinal displacement of the aortic annulus in the general population, 4 personalized aortic root support patients, 5 and aortic valve replacement patients 6 and its effect on aortic wall stress 1,5,7 using angiography or 2D cardiovascular MR (CMR).The average longitudinal displacement of the aortic annulus in the general population was reported to be 11.6 mm (range 3-19 mm). 4 Also, 2D in-plane displacement of the aortic cross-sectional centroid has been quantified on CT 8 and MRI. 9 The extension of these longitudinal or purely in-plane measurements to a 3D map would allow for more local investigation.In 3D, CMR-derived displacement of the aortic arch has been studied using affine and elastic registration 10 and showed significant displacement of the arch.The current study aims to extend this 3D measurement to the larger displacement of the entire thoracic aorta using an iterative closest point (ICP) registration of segmentations. 11ine balanced SSFP (bSSFP) CMR provides excellent blood-tissue contrast to study motion of the heart and aorta.In clinical routine, multi-slice 2D cine is performed under multiple breath-holds, which requires patient cooperation and can result in slice misalignments as a result of different breath-hold positions. 12Additionally, the anisotropic nature of these thick sliced cines hinders the high-resolution reformatting into arbitrary orientations and accurate 3D segmentation of the aorta.High and isotropic resolution is essential to provide accurate information on the 3D displacement and diameter of the aorta.
To meet the above criteria, a free-breathing 3D cine bSSFP sequence with undersampled Cartesian trajectory at 3 T is proposed to provide high isotropic resolution with coverage of the thoracic aorta.This approach does not require contrast agent administration.Furthermore, a method is proposed to determine the displacement between end-systolic and mid-diastolic 3D segmentations of the thoracic aorta.To assess the validity of these methods, this study aims to investigate the interexamination and interobserver reproducibility of the resulting 3D diameter and displacement maps of the thoracic aorta.

Study population
Fourteen healthy control subjects (6 women, 8 men, age range from 25 to 44 years, mean: 30 ± 5 years) were prospectively enrolled in the study.Each subject underwent three MRI examinations.The first two examinations were on the same day, separated by a break of 2-5 min (test, retest) that included repositioning of the subject and replanning of the FOV, and the third examination was 12-19 days later (rescan) (mean: 14 ± 2 days).The exams were scheduled in the evening between 16:00 and 19:30, and subjects were instructed to avoid caffeine intake 5 h prior to the exam.The study was approved by the local medical ethics review committee.Informed consent was obtained from all subjects.

MRI
A block diagram of the complete proposed framework is presented in Figure 1.

Acquisition
All 3D cine bSSFP exams were acquired in a sagittal oblique volume covering the entire thoracic aorta and performed during free breathing.Figure 2 illustrates the acquisition and reconstruction pipeline.A variable density pseudo-spiral Cartesian pattern was sampled with prospective undersampling in multiple dimensions (PROUD) functionality enabled on the scanner, as previously proposed. 13PROUD allows for a free running scan that samples from a precalculated trajectory list.This trajectory is calculated a priori based on the matrix size and is not electrocardiogram (ECG)-triggered or associated in advance to the expected breathing pattern or heart rate.The ECG signals were, however, used to store the acquisition time points within each cardiac cycle to allow for retrospective binning.Due to the physiological heart rate variability, a random filling of k-t space is created. 13he used trajectory spirals out from the center of k-space and then back in again along the same spiral arm A block diagram of the complete proposed framework from acquisition to analysis.Steps that currently require a manual intervention are highlighted with an asterisk.
to minimize eddy current effects (Figure 2A) (Video S1).Each subsequent spiral starting from the center of k-space is rotated with a tiny golden angle of  ∼23.63 • with respect to the previous spiral arm.The trajectory can be described in polar coordinates (r, ) as where T is the number of spiral turns; N is the total number of sampling locations in each spiral arm, that is, frequency encoding lines; and n is an index of the sampling location. 13To realize the pattern of sampling out and back in, the first N/2 sampling locations n were chosen as {n = 2 m| m∈ {0, 1, … , N∕2} and the second half as {n = 2 m − 1| m ∈ {N∕2, N∕2 − 1, … , 1}}.For this study, N = 100 and T = 3.In the process of stretching to match the size of k-space and gridding to Cartesian coordinates by rounding off to nearest integers, some duplicate locations were created and removed, 13 which led to an effective total sampling number N eff = 78 per spiral arm.
MRI acquisitions were done on an Ingenia 3 T MRI scanner (Philips Healthcare, Best, Netherlands) in combination with a 16-channel torso and eight-channel posterior coil.For two of the examinations, a peripheral pulse signal was used instead of ECG because of poor behavior of the ECG signal.Scan parameters for the 3D cine bSSFP scan were: FOV = 256 × 256 × 88 mm 3 , acquired and reconstructed spatial resolution = 1.6 × 1.6 × 1.6 mm 3 , TE/TR = 1.7/3.4ms, flip angle (FA) = 30 • , free-running acquisition time ∼3 min:48 s.Temporal resolution ∼67 ms (15 cardiac frames).
The scans were acquired with a target acceleration factor of ∼10.This acceleration factor, R proud , was calculated based on a theoretically fully sampled scan: R proud = , where N ky and N kz are the matrix size along k y and k z in the phase-encoding plane, and N card and N resp are the number of cardiac and respiratory bins for a fully sampled scan.N proud is the total number of acquired k-space lines in the undersampled acquired k-space. 13The factor ∕4 represents the elliptical scanning region related to PROUD sampling (elliptical k-space shutter). 13

Reconstruction
An overview of the reconstruction steps is depicted in Figure 2B,C.Video S1 shows a movie of Figure 2 with cardiac and respiratory motion.The aim of the reconstruction is to retrieve a respiratory motion-corrected and cardiac motion-resolved series of images to be able to distill the aortic motion over the heart cycle.The data was reconstructed offline in MatLab 2021a (MathWorks, Natick, MA) using ReconFrame 4.2.0 (Gyrotools, Zurich, Switzerland).The respiratory signal was extracted from the Fourier-transformed and bandpass-filtered k-space center lines (k 0,0 ) in the foot-head direction (sampled at ∼3.9 Hz) via principal component analysis on the readout matrix of size , followed by manual selection of the component containing the respiratory signal. 14Amplitude-based respiratory binning was performed while at the same time enforcing approximately equal number of readouts per respiratory bin to ensure comparable acceleration factors for all motion states.This consequently leads to variable respiratory bin widths, as can be seen in Figure 2B.No view-sharing or soft-weighting was applied.Finally, this resulted in the binned and subsampled k-space Y ∈ C N k x ×N k y ×N k z ×N card ×N coils ×N resp with cardiac bins N card = 15 and respiratory bins N resp = 4. Fifteen cardiac bins were chosen as a proof of concept for suitable temporal resolution able to capture the motion of the aorta.As in previous publications, [15][16][17] four respiratory bins for expiration, inspiration, and two in-between states were deemed a natural choice for maintaining a balance in respiratory motion resolving and undersampling factor.
From this k-space Y , a 5D complex image X was reconstructed with a nonlinear compressed sense algorithm, 18,19 available from the Berkeley Advanced Reconstruction Toolbox, 20 according to where P denotes the subsampling operator, F the Fourier transform, and S the multiplication with the sensitivities.The coil sensitivities S were estimated from the k-space data using the eigenvector-based iterative self-consistent parallel imaging reconstruction (ESPIRiT) calibration method available in the Berkeley Advanced Reconstruction Toolbox. 21A sparsifying total variation operator (TV) was included along the cardiac and respiratory dimensions with respective regularization parameters  C =  R = 0.1 and number of iterations equal to 20.These parameters were determined empirically.This reconstruction resulted in a 5D image volume containing three spatial, one cardiac, and one respiratory dimension.
We seek to retrieve the 4D image after correction of the respiratory motion.Therefore, a respiratory motion-resolved image was made by averaging over the cardiac dimension (N card = 1 cardiac phase) in order to estimate the nonrigid 3D motion fields needed for correction toward end-expiration.The respiratory phase corresponding to end-expiration was selected manually after inspection, and the nonrigid transformations of all bins to end-expiration were calculated using image registration with the demons algorithm. 22These motion fields were subsequently applied to the 5D image X for all cardiac phases per corresponding respiratory bin to warp all images to the end-expiration phase.Averaging over the respiratory dimension then resulted in a 4D was used for further analysis.

Preprocessing and 3D segmentation
The end-systolic cardiac phase of both scan and rescan was selected by finding the latest phase of left ventricular contraction, and a corresponding diastolic phase was systematically selected ∼35% later in the cardiac cycle using N Card−Dia = N Card−Sys + 5.This was done to reflect that 30%-40% and 70%-75% of the R-R interval represent the systolic and diastolic phases, respectively. 23The aortas were segmented once by the first observer (1 year of experience) on the test, retest, and rescan; and once by a second observer (half a year of experience) on the rescan.Segmentation was performed in Materialise Mimics Medical (Materialise, Leuven), version 24.0.0.427 from the sinotubular junction (or the slice above the branching coronaries if coronary branch was visible) to the descending aorta (DAo) below the aortic root and above the liver dome, excluding the subclavian and carotid arteries.After manually segmenting the aorta, the resulting mask was transformed to a 3D object and smoothed with a threshold value of 0.4 and 100 iterations within Materialise Mimics.This smoothed 3D volume was in turn saved as a binary mask and used for further analysis.The similarity of segmentations S made by observers 1 and 2 after equalizing the DAo length was gauged with the Dice similarity coefficient (DSC):

Diameter and displacement estimation
Next, the measurements on the aortic segmentations were automatically calculated using in-house-developed Mat-Lab 2021a software (MathWorks).Figure 3 illustrates the quantification pipeline, which is animated to show the registration iterations in Video S2.The 3D segmentations were transformed into surface objects, and a diameter measurement was computed per surface vertex as the length between the vertex and the opposing side of the surface along its corresponding normal vector, as previously proposed. 24It is important to note that this results in large values at the cross sections at the ends of the segmentation.The values of these cross sections do not represent aortic wall diameter and were discarded in subsequent diameter analysis by semiautomatic delineation.
Aortic displacement was calculated following nonrigid registration of the systolic segmentation surface to the diastolic segmentation surface using an ICP method. 25The Euclidean distance in 3D between the registered systolic and source systolic surface vertex represents its displacement.The ICP algorithm approximates vector displacements by mapping the systolic source vertices to the diastolic target mesh modeled as a sum of N s Gaussian radial basis functions with variable  defining the width of the Gaussian function. 25For this study, 30 iterations were used with N s = 10 k 1 , and where k 1 and k 2 linearly increased/decreased from 1-1.5 to 3-1.5, respectively, over these 30 iterations.D mean is the mean distance between the source and target meshes.

Regional analysis of mean and maximum displacement and diameter
The reproducibility of mean and maximum displacement and diameter values was studied for regions of interest (ROIs) of different sizes to see how this behaved at different scales.For the segmentations, the same start and end locations along the aorta were used between systole and diastole.However, between observers or between scan sessions, the end point of the DAo could deviate.For the regional analysis, the length of the DAo of the aortic segmentations was equalized to the shortest DAo length of all four segmentations (test, retest, rescan (observer 1 (obs1)), rescan (observer 2 (obs2))).This was done by first calculating the length of each from the top of the arch to the lowest point of the descending aorta, followed by removal of vertices from the descending aorta of segmentations more than 2 mm longer than the shortest aorta segmentation.The test and retest segmentations were rigidly registered to the rescan segmentation location.A total of five ROIs were used for analysis as depicted in Figure 4: the entire thoracic aorta (TAo), the ascending aorta (AAo), the upper half of the ascending aorta (UH-AAo), the lower half of the ascending aorta (LH-AAo), and a mid-ascending aorta (M-AAo) slice with a width of 10 mm.

2.3.4
Voxel-by-voxel comparison of the displacement field and diameter maps Voxel-by-voxel analysis allows for the pairwise assessment of local reproducibility of displacement and diameter measurements.Again, for each voxel-by-voxel analysis pair, the DAo lengths were equalized to the shortest DAo length.
Rigid registration and region of interest determination.The test and retest segmentation are rigidly registered to the rescan segmentation.Here, five regions of interest are defined: TAo, AAo, UH-AAo, LH-AAo, and a slice with a width of 10 mm on their boundary (M-AAo).AAo, ascending aorta; LH-AAo, lower half of the ascending aorta; M-AAo, mid-ascending aorta; TAo, thoracic aorta; UH-AAo, upper half of the ascending aorta.
To be able to calculate voxel-wise interscan or interobserver variability between measurements, they must be mapped to one geometry.This was done using rigid registration with FLIRT (Functional Magnetic Resonance Imaging of the Brain [FMRIB] Linear Image Registration Tool 26 ) and nearest neighbor interpolation. 27

Statistical analysis
All continuous parameters are expressed as mean ± SD unless indicated otherwise.The interexamination and interobserver differences of mean and maximum displacement were tested with a Wilcoxon signed-rank test (with Bonferroni correction for the two interexamination comparisons), and p < 0.05 was considered statistically significant.The maximum displacement and diameter were calculated as the average over the 5% maximum voxel values.For the regional analysis, the mean difference and limits of agreement (LoA; mean difference ± 1.96 × SD of difference (SD difference )) of the mean displacement and their 95% confidence interval per ROI were calculated for Bland-Altman analysis.Shapiro-Wilk test was used to confirm the assumption of normality of the difference distributions.The smallest detectable change at 95% confidence interval (SDC 95 ) is equal to the distance between the mean difference and LoA and can be deduced directly from the Bland-Altman analysis: SDC 95 = 1.96 × SD difference. 28The within-subject coefficient of variation (CV) from duplicate measures was calculated using the RMS approach.
Additionally, the complementary voxel-by-voxel analysis was done to allow a more local inspection of the displacement measurement.Orthogonal regression and Bland Altman analysis was done per volunteer and their results plotted for qualitative inspection of the distribution of the voxel-pair values around the equality line.To summarize this behavior for all volunteers, the corresponding mean difference, LoA, slope, and intercept of all volunteers were averaged.

Scan and segmentation results
Figure 5 shows the reconstruction results for the test, retest, and rescan of two volunteers for a single sagittal slice in diastole and systole.Similarities in anatomy as well as some variation in hyper-and hypointensity were A sagittal slice of the reconstruction of two volunteers in diastole and systole for the test, retest, and rescan.Volunteer A shows an exemplary case, where retest and rescan are reoriented for optimal comparison of the anatomy, which can be done for isotropic reconstructions.Volunteer B shows a worse case where the signal of the blood is lost toward the inferior descending aorta.observed between scans.Additionally, though smaller, some variations between systole and diastole in signal within the aortic lumen were observed.These hyper-and hypointensities are presumably a result of the variable blood signal intensity as a function of off-resonance angle for a FA of 30 degrees.Small changes in shim efficacy, positioning of the patient in the magnetic field, and orientation of the FOV will lead to different off-resonance profiles over the anatomy, thus leading to these intensity differences.Finally, some residual ghosting of the chest wall was observed in the aorta.
The mean and maximum displacement and diameter measures averaged over all subjects for the test, retest, rescan (obs. 1 and obs.2) per ROI can be found in Table 1.As expected, both average displacement and diameter increased for ROIs closer to the heart.For the test scan, the maximum displacement measured in the lower half of the ascending aorta was 11.0 ± 3.4 mm (range: 3.0-17.5mm).Between test, retest, rescan (obs. 1 and obs.2), this average maximum displacement in LH-AAo ranged between 10.0 and 11.0 mm.The average mean displacement in this ROI ranged between 6.9 and 7.4 mm for test retest and rescan.

Regional analysis
Pairwise Wilcoxon signed-rank tests with Bonferroni correction for test-retest (within-day) and test-rescan (between-day) resulted in no significant differences in mean or maximum displacement and diameter for any of the ROIs.The mean difference, SDC 95 , and CV are reported in Table 2 for both displacement and diameter measurements.Figures S1 and S2 show the within-and between-day Bland-Altman analysis results for mean displacement.Generally, the mean displacement was larger and had larger LoA for ROIs closer to the aortic root.The SDC 95 was smaller based on the within-day comparisons (SDC 95 = 3.1 mm or smaller for the different ROIs) than on the between-day comparisons (SDC 95 = 4.7 mm or less).
The CV values for displacement are five to 10 times larger than those for diameter measurements.

Voxel-by-voxel analysis
Figure 6 shows the voxel-by-voxel displacement analysis of one exemplary volunteer.The gray-shaded geometries in Figure 6A depict the 3D test and retest diastolic segmentations of the aorta, and the colored arrows show the displacement from diastole to the end-systolic phase scaled to the largest measured displacement.In Figure 6B, the results of the Bland-Altman analysis and orthogonal regression analysis are shown.
The displacement was larger in the AAo than in the arch or DAo.The voxel-by-voxel mean difference was close to zero with LoA less than the voxel width of 1.6 mm.The maximum displacement values were ∼14 mm, and the orthogonal regression in Figure 6 displays a strong correlation between the local test-retest voxel values along the entire range of displacement values, again reflecting the small mean differences.

Interobserver analysis
The mean DSC between segmentations from observer 1 and 2 for the rescan was 0.90 ± 0.03, indicating good agreement between the segmentations of the two observers.

Regional analysis
The average displacement and diameter measured from the rescan by observer 1 and observer 2 per ROI are shown in Table 1.There were no significant interobserver differences in displacement measurements for any of the ROIs, but observer 2 consistently made larger segmentations, as indicated by the negative diameter mean differences in Table 3.
Figure S3 shows the Bland-Altman plot for interobserver mean displacement.Again, the mean displacement was larger closer to the aortic root with larger LoA for decreasing ROI size and location closer to the heart.The SDC 95 was 2.9 mm (M-AAo) or less for the other ROIs, which is less than two voxel lengths.For the diastolic diameter, the SDC 95 = 2 mm or less; and for the systolic diameter, SDC 95 = 2.9 mm or less.The CVs for displacement are two to five times larger than that of diameter.

Voxel-by-voxel analysis
Figure 7 shows the voxel-by-voxel displacement analysis of one exemplary volunteer.Again, the gray-shaded geometries in Figure 7A depict the 3D observer 1 and observer 2 diastolic segmentations of the rescan of the aorta, and the colored arrows show the displacement from diastole to

T A B L E 2
Interexamination mean difference, smallest detectable change, and CV of regional mean displacement and diameter.the end-systolic phase scaled to the largest measured displacement.In Figure 7B, the results of the Bland-Altman analysis and orthogonal regression analysis are shown.Averaged over all volunteers, the voxel-by-voxel mean difference = −0.3± 0.5 mm with LoA = 2.3 ± 0.5 mm, slope = 0.93 ± 0.26, and intercept = 0.5 ± 0.6 mm.The mean difference for diameter measurements (−1.0 and −1.4 mm) deviated further from zero than the mean difference for displacement (−0.3 mm) with larger LoA (4.4 and 5.2 mm vs. 2.3 mm).

DISCUSSION
In this study, we investigated the reproducibility of aortic diameter and systolic to diastolic displacement assessed with an accelerated, high isotropic resolution and noncontrast-enhanced 3D cine bSSFP sequence.We found that the mean diameter measurements were reproducible for all ROIs with SDC 95 smaller than or equal to 3 mm for both interexamination and interobserver systolic and diastolic diameter.As a single aorta specialist may obtain, at different sessions, measurements that differ by up to 3 mm from identical images, 29 this finding is in accordance with current clinical standards.
The displacement reproducibility showed SDC 95 < 3.1 mm (within-day interexamination) and SDC 95 < 4.7 mm (between-day interexamination) and interobserver SDC 95 < 2.9 mm.The higher SDC 95 for between-day interexamination analysis is strongly affected by at least one outlier, with high difference in test and rescan displacement values.Upon closer investigation, this is the result of inaccurate segmentation ends at the sinotubular junction.It is expected that correcting these segmentation ends would improve outcomes.A calculation of the SDC 95 without taking this one outlier into consideration supports this because its value decreases from 4.7 mm to 3.7 mm.This might be an indication that the 3 mm SDC found for both within-day interexamination and interobserver is the practical limit of this technique.The relatively larger CVs for displacement than diameter measures are a result of comparable variability over lower mean values.
Plonek et al. 4 previously reported an average longitudinal displacement of the aortic annulus of 11.6 mm (range: 3-19 mm) for the general population in all age groups.The maximum displacement of the LH-AAo is the metric in the current study that most resembles this measurement and was 11.0 ± 3.4 mm (range: 3.0-17.5mm) for the test scan.This result is comparable with these previous findings.A 3D displacement calculation of the entire thoracic aorta or the aortic root has to our knowledge not been performed before.
The remaining differences in measurements between repeated scans leading to the non-zero SDC 95 can potentially be ascribed to variability in image quality, physiological variation, and/or the variability introduced by manual segmentation.Generally, the interobserver analysis gave better agreement parameters than the interexamination analysis.This might indicate that the main source of variation in measurement outcome is the scan quality or physiological variation over time.
It is important to realize that for an evaluative measure, as we envision the displacement metric to be, variability between persons in the population sample is less important as opposed to the measurement error.This measurement error should be smaller than the changes that one wants to detect. 30Based on the current results, we are able to measure changes in mean displacement larger than ∼3 mm where the average mean displacement is ∼7 mm in the LH-AAo.The size of displacement change in increasingly stiffening aortas in, for example, Marfan, a patient group that suffers from aortic dilation and sudden dissection/rupture, is still unknown.Because aortas in disease conditions are generally stiffer than in healthy subjects, it can reasonably be expected that these measures might be smaller, and that measurement precision should be enhanced through further optimization of scan quality and the use of automated techniques.
Variation in signal intensities in the arterial lumen in these 3D bSSFP scans is one of two main aspects to further address in future work.At the used FA of 30 degrees, the intensity profile as a function of off-resonance angles first increases before decreasing completely into a dark bank.The contribution of these off-resonance intensities increases for longer TRs.The maximum achievable FA angle and minimum TR for 3D cine bSSFP scans at 3 T are balanced and bounded by specific absorption rate safety restrictions (implemented on the scanner).The resulting higher TR, as compared to what is achievable at 1.5 T, makes bSSFP at 3 T more vulnerable to banding artifacts due to field inhomogeneities.The lower part of the thoracic descending aorta in Figure 5 (volunteer B, test) shows the impact of such banding artifacts on the image.In future studies, the TR of the sequence might be further shortened by implementing simpler, shorter RF pulses while at the same time implementing a higher FA of 40 degrees, which gives a more constant signal behavior of the blood pool as a function of off-resonance.
Secondly, adipose tissue can introduce strong ghosting in highly accelerated free-breathing 3D cines as a result of chest motion. 31The major attributions to these effects are addressed by the current respiratory motion binning and registration to expiration.The residual artifacts could be further minimized by combining the sequence with a fat-suppression strategy decreasing the chest fat signal. 17,32owever, this will be at the cost of scan time because fat suppression typically interrupts the steady-state.Also, the signal from fat around the aorta can be useful for the delineation of the aorta because of its higher signal intensity.Alternatively, implementing additional respiratory compensation techniques, such as, for example, intrabin correction or a focused navigation type of approach, could further address these residual artifacts. 33,34he majority of the abovementioned artifacts can be recognized by the human eye and therefore do not affect the segmentations.The 3D cine bSSFP datasets (42 in total) were of adequate quality to perform manual segmentations.The precision of the delineation of the aorta might in future work be improved after the above-mentioned optimizations have been applied.To the same end, reconstruction to higher spatial and temporal resolution could be an interesting avenue for future improvement.
Even though the mean DSC of 0.90 indicates good agreement between segmentations, the consistent difference in segmentation sizes of the manual segmentations illustrates that it is still a factor of variability in this methodology.The 3D cine bSSFP images are segmented manually, and the lack of contrast between tissue and blood pool hampers the use of semiautomated segmentation methods such as thresholding, which makes them more vulnerable to interobserver variability.Additionally, upon further exploration, the outlier previously described seemed to be caused by the incorrect determination of the end-descending aorta landmark.These sources of variable and erroneous segmentation could most likely be decreased in future studies by the implementation of an automated segmentation method.For example, adaptation of existing software to 3D cine bSSFP, [35][36][37] an atlas-based strategy, 38 or a deep-learning strategy using a convolutional neural network [39][40][41] could be used.
Automating the segmentation process will also give access to the segmentations of the remaining phases of the cardiac cycle.The strenuous segmentation process limited the current analysis for the displacement measurements to two cardiac phases, namely end-systole and diastole, as has been previously done in 2D. 1,5,6This limitation to two phases is a result of the displacement calculation being segmentation-based and not gray level-based.A benefit of this strategy is that the displacement calculation is not affected by signal variations as long as segmentations can be retrieved.Future research will focus on training a convolutional neural network for automated segmentations to quantify the displacement over the entire cardiac cycle, as done in 2D by, for example, Weber et al. 8 This will allow for an even more in-depth insight into the displacement path of the aorta.
Generally, the manual interactions currently required for extraction of the self-gating signal, selection of the expiratory respiratory phase, and segmentation will in future work be automated such that this entire acquisition, reconstruction, and analysis pipeline for the calculation of displacement measures will require no more manual user input.This will render the method more clinically applicable.
The blood SNR of the 3D bSSFP can be reduced in 3D cine due to blood pool saturation and the inflow of saturated blood into the atrial pool. 31Although the use of contrast agents has been shown to improve SNR, the decision was made to focus on imaging without contrast agents because this will allow use in a broad patient population, including those with contrast contraindication.

CONCLUSION
In this work, a free-running free-breathing Cartesian PROUD 3D cine bSSFP sequence was proposed with high isotropic resolution.The resulting 3D segmentations of end-systole and diastole allowed for the reproducible quantification of aortic displacement and diameter that allows for the measurement of displacement change within acceptable limits compared to current clinical practice for diameter measurements.At the same time, there is potential to improve the technique further to increase its relevance for future studies investigating aortic motion in health and disease.

ACKNOWLEDGMENTS
For this study we used the Amsterdam UMC 'PROspective Undersampling in multiple Dimensions' (PROUD) software patch.This publication is part of the project Comprehensive Assessment of 4D

2
Data acquisition and reconstruction pipeline.(A) A free-running prospectively undersampled variable density PROUD 3D cine based on bSSFP scan acquires data in ∼4 min.(B) From the center k-space readouts, respiratory self-gating is performed, and data are sorted into a 5D dataset with 15 cardiac and 4 respiratory phases.Compressed sense reconstruction uses total variation over cardiac and respiratory dimensions.(C) Images are averaged over the cardiac dimension, followed by 3D nonrigid registration to end-expiration (vector overlays).Respiratory displacements are then applied to the 5D images and data is respiratory-averaged. bSSFP, balanced SSFP; PROUD, prospective undersampling in multiple dimensions.

F I G U R E 3
Diameter and displacement quantification pipeline.(A, B)The diastolic and end-systolic aorta segmentations are loaded as a surface into MatLab 2021a (MathWorks, Natick, MA), and for each surface vertex the diameter is calculated.(C) The systolic surface is nonrigidly registered to the diastolic surface using an iterative closest-point method, and the displacement for each vertex is calculated as the 3D Euclidean distance between its original and registered location.

F I G U R E 6
Interexamination voxel-by-voxel analysis.(A)Full 3D rendering in sagittal and transversal view of the displacement field used for the voxel-by-voxel analysis.(B) Voxel-by-voxel analysis: Bland Altman plot (left), orthogonal regression (right).
Mean and maximum displacement and diameter.
T A B L E 1 Interobserver mean difference, smallest detectable change, and CV of regional mean displacement and diameter.Abbreviation: AAo, ascending aorta; LH-AAo, lower half of the ascending aorta; max, maximum; M-AAo, mid-ascending aorta; obs., observer; TAo, thoracic aorta; UH-AAo, upper half of the ascending aorta.
Thoracic Aorta Biomechanics Using Novel Cardiac MRI Technology (project number 18402) of the research program Applied and Engineering Sciences, funded by the Dutch Research Council (NWO).Part of the research program Applied and Engineering Sciences, and the project Comprehensive Assessment of 4D Thoracic Aorta Biomechanics Using Novel Cardiac