Motion-Compensated Low-Rank Reconstruction (MoCoLoR) for Simultaneous Structural and Functional Ultrashort Echo Time (UTE) Lung MRI

Abstract

Purpose:

3D UTE MRI has shown the ability to provide simultaneous structural and functional lung imaging, but is limited by respiratory motion and relatively low lung parenchyma SNR. The purpose of this paper is to improve this imaging by using a respiratory phase-resolved reconstruction approach, named Motion-Compensated Low-Rank (MoCoLoR), that directly incorporates motion compensation into a low-rank constrained reconstruction model for highly efficient use of the acquired data.

Theory and Methods:

The MoCoLoR reconstruction is formulated as an optimization problem that includes a low-rank constraint using estimated motion fields to reduce the rank, optimizing over both the motion fields and reconstructed images. The proposed reconstruction along with XD and MostMoCo methods were applied to 18 lung MRI scans of pediatric and young adult patients. The datasets were acquired under free-breathing and without sedation with 3D radial UTE sequences in approximately 5 minutes. After reconstruction, they went through ventilation analyses. Performance across reconstruction regularization and motion-states parameters were also investigated.

Results:

The in vivo experiments results showed that MoCoLoR made efficient use of the data, provided higher apparent SNR compared to state-of-the-art XD reconstruction and MostMoCo reconstructions, and also yielded high-quality respiratory phase-resolved images for ventilation mapping. The method was effective across the range of patients scanned.

Conclusion:

The motion-compensated low-rank regularized reconstruction approach makes efficient use of acquired data and can improve simultaneous structural and functional lung imaging with 3D UTE MRI. It enables the scanning of pediatric patients under free-breathing and without sedation.

Introduction:

Proton ultrashort echo time (UTE) MRI has gained more attention recently in thoracic imaging because of its ability to capture fast relaxing signals with inherent motion management capabilities (1,2) and provide simultaneous structural and functional imaging (3). However, due to the limited encoding speed of MRI, and the substantial data required for volumetric images, respiratory motion remains challenging for imaging in these anatomies. Conventional MR respiratory motion management techniques include breath-holding, respiratory triggering, and gating using signals from external devices such as a bellow or MR navigators (4–7). While these approaches reduced motion artifacts, breath-holding limits the total scan time and increases patient discomfort. Respiratory gating methods suffer from prolonged scan time and low data efficiency.

3D non-Cartesian acquisition schemes such as 3D radial (8), cones (9), stack-of-stars (10), etc., can support robust respiratory motion management. These trajectories repeatedly acquire the center k-space, which serves as a self-navigator for respiratory gating. (Pseudo-)random ordering (11–13) can be easily incorporated into non-Cartesian acquisitions to increase temporal sampling incoherence. In addition, the ultrashort echo time minimizes the signal loss caused by the short T2* from the air-tissue interface susceptibility, while radial acquisition samples k-space center first which preserves the low frequency signal, and thus increases the lung parenchyma signal.

One motion management strategy is motion-resolved reconstructions (14–20) that allows for continuous free-breathing acquisitions as well as pulmonary function analysis. These methods group the k-space data based on a motion signal and reconstruct the data into multiple respiratory states or time points using compressed sensing and parallel imaging techniques. For example, XD-GRASP (10) applies the total variation (TV) constraint along the motion states dimension. An alternative to the TV constraint is to reformulate the image series into a spatiotemporal Casorati (21) matrix, then enforce low-rank on the Casorati matrix. This approach is used in free-breathing cardiac MRI and dynamic contrast-enhanced (DCE) MRI (22–24).

Several methods for motion compensation have been introduced and demonstrated for lung MRI, including iMoCo (25) and MostMoCo (26). In these methods, the motion fields are included in the data consistency term for an improved motion-resolved reconstruction. Other methods have integrated motion information into low-rank constrained reconstruction models, such as motion adaptive patch-based low-rank constrained reconstruction field (14,27) and block low-rank sparsity with motion-guidance reconstruction (28). These methods preserve the low-rank property of spatiotemporal matrices by searching similar patches locally from the image series. Recently work on free-breathing cardiac MRI has demonstrated the ability to incorporate rigid and non-rigid deformations into the reconstruction along with a patch-based low-rank penalty (29), including for 3D radial trajectories (30).

A major application of motion-resolved lung imaging is pulmonary function analysis. Developments in proton MRI-based function analysis include Fourier Decomposition (31), PREFUL (32,33), and flow-volume loop (34). These approaches utilize intensity-based specific ventilation (35) for localized lung volume function quantification. These methods are also fundamentally limited by the lung parenchyma SNR, which is low due to short T2* and low proton density, and thus will benefit from any improvements in efficient use of the acquired data.

In this work, we aim to improve simultaneous structural and functional lung imaging by reconstructing respiratory-resolved images from 3D-radial UTE MRI with a method that directly incorporates motion compensation in the low-rank constrained reconstruction model, named Motion-Compensated Low-Rank (MoCoLoR) reconstruction. This motion compensation formulation aims specifically to improve the efficiency of respiratory-resolved images by allowing data from all motion states to more effectively contribute during image reconstruction. This method was evaluated in pediatric and young adult patients with suspected lung diseases under free-breathing and without sedation. This population had a range of body size, breathing patterns, and compliance in the MRI scanner, and thus provides a challenging, real-world scenario in which to demonstrate the performance of MoCoLoR and other respiratory-resolved reconstruction methods for structural and functional imaging.

Theory:

Motion-Compensated Low-Rank Constrained (MoCoLoR) Reconstruction

In motion-compensated low-rank constrained reconstruction (MoCoLoR), we aim to reconstruct motion-resolved images from free-breathing, continuously acquired k-space data. To achieve this, we formulate the reconstruction as an optimization problem that includes data consistency across all respiratory phase states and a low-rank constraint that includes estimated motion fields to reduce the rank. This is addressed in the following optimization problem,

$${\mathit{argmin}}_X{\frac{1}{2}‖W\left(FSX-d\right)‖}_2^2+{\lambda }_L{‖MX‖}_{\mathrm{*}}$$ (1)

In the data consistency term, $W$ is the density compensation factor, $F$ is the non-uniform Fourier Transform, $\mathit{S}=\left[{ S}_i\right]$ are the sensitivity maps of coil $i,\mathrm{ }\mathit{d}=\left[d_{i,j}\right]\in {\mathbb{C}}^{B\times C\times bPE\times FE}$ are the binned data from coil $i$ and respiratory state $j$, and $\mathit{X}=\left[X_j\right]\in {\mathbb{C}}^{B\times N^3}$ are the 3D images at respiratory state $j.\mathrm{ }B$ is the number of respiratory states, $C$ is the number of coils, $\text{b}PE$ is the number of phase encodings or spokes per respiratory state, $FE$ is the number of frequency encodings or readouts per spoke, $N^3$ is the image size. In the regularization term, ${‖.‖}_{*}$ is the nuclear norm, ${\lambda }_L$ is the low-rank penalty regularization parameter, $\mathit{M}=\left[M_j\right]$ are the motion field operators.

During the iterative optimization, image $\mathit{X}$ is updated in the inner loop and $\mathit{M}$ is updated with image registration in the outer loop. The detailed iterative schemes, their derivation and a complexity analysis are included in the supplementary material.

Figure 1 summarizes the reconstruction theory of the MoCoLoR method. As shown in Fig. 1e, the addition of the motion compensation (MoCo) to the low-rank term reduces the apparent rank. When MoCo was applied, there is very little signal or structure in the 3^rd and higher spatial bases derived from SVD, whereas without MoCo there was more visible signal and structure in the 2^nd and 3^rd spatial bases. This is a major motivation for this method.

Figure 1.

Motion Compensated Low-Rank Constrained (MoCoLoR) reconstruction workflow for respiratory phase-resolved lung MRI. (a) First, a respiratory signal is required, which can be derived from the center of the k-space. (b) Based on this signal, raw data is grouped by respiratory states. (c) Respiratory phase-resolved image volumes are iteratively reconstructed by MoCoLoR, including image registration between respiratory states. (d) Singular vector decomposition (SVD) is used to enforce low rank. (e) A sample visualization of the spatial bases from SVD shows that adding in motion-compensation (MoCo) from the estimated motion fields compresses the information into fewer components, decreasing the rank. This framework can also be adapted to reconstruct time-resolved images.

Methods:

Data Acquisition

All procedures were approved by the University of California, San Francisco Institutional Review Board. Written consent or assent was acquired from guardians or patients.

The study included eighteen datasets retrospectively from fourteen pediatric and young adult patients (4–25 y/o) clinical scans between 2018 and 2022. Three of them received repeated scans at different ages (5&5.5 y/o, 4&4.5&6 y/o, 14&16 y/o). The patient population covered a variety of lung conditions, including bronchiolitis obliterans (inflammation of the airways), nodules, and atelectasis (collapse of the lung). Inclusion criteria were patients that has high resolution (~1mm) radial UTE acquired during a clinical or research chest MRI, and were under the age of 18 or were being treated in the pediatrics department. A parent companion, video goggles, and audio headphones were adopted for the younger participants to increase patient comfort and cooperation. No sedation was administered. Throughout the UTE sequence, patients maintained a supine position and practiced free tidal breathing.

All data were acquired on 3T scanners (MR750 & MR750W, GE Healthcare, Waukesha, WI, USA) with an optimized 3D radial UTE sequence (36) with golden-angle ordering. The key parameters were flip angle = 4°, resolution = 0.9 – 1.5 mm isotropic, # spokes = 80,000 – 150,000, FOV = 24 – 40 cm isotropic, TE/TR = 0.07 – 0.10/2.8 – 3.8 ms, bandwidth = 125kHz, total scan time = 3’33” - 7’55”. Depending on patient size, we used an 8-channel or 32-channel cardiac coil (GE Healthcare) or a 12 or 24-channel ultra-flexible chest coil (37) (Inkspace Inc.). A fast respiratory-gated reconstruction was available for image quality assessment at the scanner. The resolution and FOV were chosen based on patient size, while number of spokes were selected based on the time available during the clinical scan.

All reconstructions for the proposed and comparing methods were performed offline on a Linux workstation, which had 200 GB memory and a 12 – 32 GB VRAM GPU. The SigPy package (38) was used for sensitivity calibration, GPU handling, and optimization. All reconstruction scripts are available on GitHub (https://github.com/PulmonaryMRI/MoCoLoR).

Respiratory Motion Estimation & Data Binning

The position in the respiratory cycle was estimated from the center of k-space of each radial spoke. DC signal from all coils was bandpass filtered separately by cutoff frequency 0.1Hz and 0.5Hz to reduce noise and separate the respiratory contributions from cardiac motion contributions. The filtered DC signal from the coil with the highest standard deviation represented respiratory motion. The peaks or local maximum of this respiratory motion curve were chosen to represent end-expiration. The detected peaks with a value smaller than the signal mean were excluded. The data points between two adjacent peaks were separated into R respiratory states in the time dimension, where each state contained the same number of data points (Figure 1a).

The k-space data were then binned according to their corresponding time in the respiratory motion curve. The whole respiratory cycle was split into R states. R = 2 – 50 were tested on one representative patient due to computation time considerations, and R = 10 was selected for all patients in this study. Details for the number of states selection were explained in the result section.

MoCoLoR Implementation Detail

The end-expiration state (State 1 in Figure 1c) was selected as the reference state for motion field estimation because the end-expiration is lengthened in a regular breathing pattern. Thus the image in this respiratory state contains minimal within-state motion. Image registration for all approaches was performed using ANTs (39) deformable registration with the same parameters.

Due to computational time concerns, we tested the regularization parameter ${\lambda }_L=0.001, 0.005, 0.01, 0.05, 0.1, 0.5$ for all three methods on a single patient. As explained in the results section, ${\lambda }_L=0.05$ was selected for MoCoLoR. We didn’t adopt coil for the proposed or comparing methods. The algorithm convergences were reported in the supplementary material Figure S1. Based on the convergence, the number of iterations for XD Recon, MostMoCo, and MoCoLoR was selected as 25, 15, and 45, respectively.

Ventilation Quantification

Regional ventilation is derived from the registration motion field $M$. It measures the percentage of volume change during tidal breathing at each voxel. The definition of regional ventilation is as follows,

$$RV=\frac{V_{resp}-V_{end-expi}}{V_{end-expi}}=\frac{V_{resp}}{V_{end-expi}}-1=\left|\mathit{det}\left[Id+\nabla M\mathrm{ }\right]\right|-1\mathrm{ }$$ (4)

where $V_{resp},\mathrm{ }{V}_{end-expi}$, are the lung volume at each respiratory and end-expiration state. $Id$ is a 3-by-3 identity matrix, $M$ is the motion field, $\nabla$ is the Jacobian matrix, and $det$ is the matrix determinant.

A regional ventilation value greater than 0 means lung tissue expansion, and less than 0 indicates contraction. The end-expiration state is selected as the reference frame where the ventilation is by definition zero. Region ventilation reports percentage of volume change instead of volume ratio in order to be directly comparable to specific ventilation.

The specific ventilation (SV) (40) is an intensity-based approach for ventilation quantification. It assumes that the signal intensity in lung parenchyma is proportional to the proton density, T1 is independent of air volume, and that mass is conserved. Specific ventilation is defined by the following equation,

$$SV\mathrm{ }=\frac{V_{resp}-V_{end-expi}}{V_{end-expi}}\mathrm{ }=\frac{S_{end-expi}-S_{resp}}{S_{resp}}$$ (5)

where $S_{end-expi},\mathrm{ }{S}_{resp}$ are the signal intensity at each voxel in the end-expiration state and a respiratory image registered to the end-expiration image. The specific ventilation is truncated at zero for the ventilation map calculation to eliminate extreme values introduced by noise.

Lung segmentation

We adopted a 3D U-Net-based pre-trained neural network for lung segmentation (41) in its original form and weighting. 3D volumes at each respiratory state were processed separately. The lung masks maintained good visual quality and were used for ventilation map overlay.

Comparing Methods

For comparison, we reconstructed the data using the phase-resolved extra-dimension (XD) reconstruction proposed by Feng et al. (10). In addition to the original total variation regularization in the temporal dimension, we added total variation in the spatial dimension for SNR improvement. The temporal regularization parameter ${\lambda }_t=0.05$ and the spatial regularization parameter ${\lambda }_s=0.01$ were selected based on a parameter search.

We also compared with the recent work on motion-state weighted motion-compensation (MostMoCo) reconstruction by Ding et al (26). The temporal regularization parameter ${\lambda }_t=0.05$ and the spatial regularization parameter ${\lambda }_s=0.01$ were selected based on a parameter search.

Quantitative Analysis

Apparent SNR (aSNR)

Region of interest (ROIs) that covers the parenchyma, aorta, and trachea is manually drawn on a selected coronal slice that includes all structures. aSNR is calculated by $aSN{R}_{tissue} =\frac{mean\left(S_{tissue}\right)}{std\left(S_{background}\right)}$, where $S_{tissue}$ is the signal intensity within the parenchyma, aorta or trachea, and $S_{background}$ is the signal intensity within the background (25). The same ROIs are used across all three methods.

Maximum Derivative

The maximum derivative (MD) of the diaphragm is used to evaluate the sharpness of the image. A rectangular bounding box was manually drawn across the diaphragm of the selected coronal slice $n$ at the end-expiration state. MD was measured by the maximum diaphragm gradient over the mean liver signal among the 30 slices centered around slice $n$. A higher MD value represents a sharper diaphragm structure and indicates better motion correction improvement.

Paired t-test is used for significance analysis for apparent SNR and maximum derivative, where each data point represents one patient dataset.

Results:

Figure 2 demonstrates representative reconstructed images and ventilation maps of the MoCoLoR approach in 14 y/o patient with severe combined immunodeficiency (SCID). We compared the structural image of XD Recon, MostMoCo reconstruction, and motion-compensated with low-rank constraint (MoCoLoR) reconstruction. The visualization of structures such as the pulmonary vasculature was similar across methods, but the XD Recon had slightly higher noise levels.

Figure 2.

Representative structural image and ventilation maps. The dataset represents a 14 y/o patient with severe combined immunodeficiency (SCID) who presented with dyspnea on exertion in different respiratory states. The circled regions show improved structures at end-expiration and intermediate respiratory states, and the arrows point to the sharpened diaphragm.

Regional ventilation and specific ventilation maps were also calculated. The end-expiration state is selected as the reference frame where the ventilation is by definition zero. The regional and specific ventilations vary with respiratory states, with the highest ventilation appearing at the expected end-inspiration state. The ventilation maps measured with the three reconstruction methods present similar patterns. The regional ventilation method in particular shows some potential ventilation defects near the base of both lungs. The specific ventilation maps have different ranges across the reconstruction methods, which likely is because XD Recon and MostMoCo regularize intensity differences, while the proposed MoCoLoR method regularizes the absolute intensity values. Despite of the range difference, the ventilation maps show similar patterns.

Figure 3 compares the apparent SNR and sharpness of all reconstruction methods for all eighteen datasets, and a paired t-test is used for significance analysis. The aSNR box plots show that the MoCoLoR methods yield higher aSNR in the parenchyma and aorta compared to XD reconstruction and MostMoCo approaches. Since the trachea is filled with air, there’s no signal source, and in fact the aSNR should theoretically be zero in the trachea. According to the t-test, all aSNR improvements were significant. The sharpness plot suggests that the MoCoLoR approach has slightly decreased sharpness compared to the XD and MostMoCo reconstruction.

Figure 3.

Box Plots of aSNR and Sharpness Measurements of All Datasets. Apparent SNR (aSNR) of the lung parenchyma and aorta indicates an aSNR boost with the MoCoLoR approach. The Trachea aSNR measures the noise level within the trachea. Maximum Derivative (MD) of the diaphragm quantifies the sharpness. Mean and standard deviations are summarized in Table 1.

The effect of the regularization parameter on the reconstruction and ventilation analysis is summarized for a sample dataset in Figure 4. Among all the weightings for the nuclear norm ${\lambda }_L$, the highest aSNR appears at 0.05, 0.1 and 0.5. The regional ventilation appears over-smoothed when ${\lambda }_L$ is greater than 0.1. Considering these trade-offs, we selected ${\lambda }_L=0.05$ for the MoCoLoR reconstruction.

Figure 4.

Investigation of the Regularization Parameter for MoCoLoR. The figure depicts the structural and functional images of a 25 y/o patient with Leukemia. $\lambda L=0.05$ provides high parenchymal apparent SNR (SNR_p) and does not appear to over- or under-estimate the ventilation.

We further investigated the effect of the number of respiratory states on reconstruction and ventilation analysis in Figs. 5 and 6. Figure 5 shows a representative dataset where we reconstructed the dataset of 100,000 spokes into up to 50 respiratory states for all three reconstruction approaches. With the increased number of states, the diaphragm is sharper, indicating that the respiratory motion is better resolved. There was no apparent loss in resolution or apparent SNR for up to 20 states, but 32 or more states present aliasing artifact. When separated into 50 states, MoCoLoR presented higher visual quality compared to the other two approaches.

Figure 5.

Number of Respiratory States of MoCoLoR. One dataset from a 19 y/o patient with chronic cough and pulmonary nodules was reconstructed into 2–50 respiratory states. Structural images for 2, 6, 10, 20, 32, and 50 states were shown. The end-inspiration respiratory state was selected for illustration to demostrate the resolved motion blurring. With the increased number of states, the diaphragm is sharper while the aliasing artifact is more appearent.

Figure 6.

Apparent SNR, Maximum Derivative, and Ventilation measurements of a different number of states. Results from 2–50 respiratory states are included. (Top) Structural metrics compared results from all three reconstruction approaches. Note that 50-state MostMoCo did not converge in the 48-hour grid job time limit and the streaking artifacts led to an unusually high maximum derivative. (Bottom) Ventilation measurements visualize ventilation results from MoCoLoR reconsturction. The normalized phase is the respiratory state (e.g. 0…11) divided by the total number of states (e.g. 12) 0. Since respiration is cyclic, the normalized states 0 and 1 are the same and both represent the end-expiration state.

Figure 6 quantifies the effect of the number of states on structural and ventilation imaging. For XD and MostMoCo reconstruction methods, aSNR decreases with the increased number of states. While for MoCoLoR reconstruction, aSNR first increases and then decreases with the increased number of states. Consistent with Fig. 3, MoCoLoR had the highest aSNR of all methods between 6–20 number of states. The maximum derivative of MoCoLoR was slightly lower compared to the other two approaches. Note that the vertical axis of the MD diagram starts at 0.14 to show the details, and MostMoCo did not converge in the 48-hour workstation grid job time limit and likely led to an unusually high value.

The number of motion states also affects ventilation measurements. We plotted the total lung averaged ventilation of one subject calculated from MoCoLoR. The regional ventilation converges with the increased number of states, remaining relatively stable at 6 states and above. A small number of states underestimate the ventilation at end-inspiration and other intermediate respiratory states. Specific ventilation also shows a trend of convergence but has greater fluctuations in some respiratory states between the reconstructions. Considering these aSNR and ventilation results, ten respiratory states were selected for all patient reconstructions.

Lastly, we investigated the structural images and ventilation maps from MoCoLoR in longitudinal lung MRI scans (Figure 7). A subject with interstitial lung disease received MRI at ages 4 and 4.5. The ventilation is normalized by the total percentage of volume change to account for the breathing depth difference. The histogram shows the normalized ventilation is more concentrated at age 4.5, suggesting a more uniform distribution of ventilation.

Figure 7.

MoCoLoR ventilation mapping applied to Longitudinal Imaging. Repeated scans of a pediatric patient with childhood interstitial lung disease (ChILD) at ages 4 and 4.5 years old are shown. High-density suture material is visible in the left lower lobe at both time points (red arrow) because of previous wedge resection. These ventilation maps are normalized by the average ventilation, which corresponds to the total percentage volume change of the lung. Histograms of the regional ventilation and specific ventilation at both times are also shown.

Figure 8 presents MoCoLoR reconstructed images at end-expiration state for all eighteen patients included in the study. The datasets were acquired in a clinical setting and the parameters varies with patient size, age, time available. This demonstrates that our technique is appliable on a wide range of imaging parameters.

Figure 8.

MoCoLoR reconstructed images at end-expiration state for all eighteen datasets. Images were enlarged to show details.

Discussion:

This work demonstrates the feasibility of an image reconstruction method, MoCoLoR, that can simultaneously reconstruct high-resolution structural and functional images from a single 3D UTE sequence acquisition. This was evaluated in the extremely challenging scenario of pediatric patients, as young as 4 years old, who were all not sedated. All patients tolerated the scan well, and we were able to acquire the UTE sequence in a relatively quick approximately 5 minutes scan time. Structural images reconstructed with MoCoLoR showed improved apparent SNR compared to existing methods. The measured ventilation varies across respiratory states and converges to a consistent pattern with an increased number of states, which was chosen to be 10 for the lung UTE study.

In an exploratory longitudinal study with this approach, the ventilation maps reflected improved pulmonary function test results of the pediatric patient at different time points. The subject had improved forced vital capacity (FVC) from age 4 to 4.5, and the regional ventilation also showed improved uniformity.

In addition to respiratory phase-resolved imaging, the proposed MoCoLoR method was additionally able to produce time-resolved images in dynamic contrast-enhanced abdominal MRI. The results for DCE MRI were included in the Supplementary Material, showing the ability to produce time-resolved imaging with both respiratory and bulk motion correction in the MoCoLoR framework. This illustrates the flexibility of this approach, which we expect can also be applied to cardiac-resolved imaging as well with sufficiently high temporal sampling, cardiac motion signals (e.g. ECG, PG, navigators), and relevant contrast in the heart.

Total Variance and Low-Rank Constraints

The total variance regularization-based XD reconstruction is less computation-intensive than MostMoCo and the proposed MoCoLoR method, which has the additional requirement of motion state estimation. The reconstruction time comparison is in supplementary Figure S2. MoCoLoR results, however, provide higher aSNR when more states are reconstructed.

Limitations

We acknowledge that there are some limitations to our work. First, while relative peak height and width thresholding of the respiratory signal are applied to exclude irregular breathing, we did not address bulk motion during the lung MRI scans. Fortunately, bulk motion was not observed in most of our datasets, but this assumption can be challenging for the pediatric population. However, a bulk motion correction term can be added to the MoCoLoR reconstruction formulation, which we demonstrate in a pediatric 3D abdominal DCE MRI dataset in the Supplemental Material. In this result, rigid bulk motion is estimated across bins in the temporal (dynamic) dimension, and the resulting motion field is used for MoCo and the low-rank minimization. The results show that 3 distinct periods of bulk motion were corrected and improve depiction of the myocardium in DCE MRI. We could also minimize bulk motion by using other means such as a weighted blanket and providing video distractions to subjects, or through the use of image-based navigators for identification of bulk and/or irregular motion (42).

Second, the current image registration limits the speed of reconstruction. Image registration is repeated in the reconstruction; however, the toolbox we adopted only supports CPU and not yet GPU. We could further accelerate the algorithm by developing GPU-compatible registration.

Thirdly, there is a tradeoff between higher aSNR and higher sharpness (MD) for MoCoLoR approach, which is balanced by the regularization parameter. As for proton ventilation, although ground truth is unavailable in human subject studies, further validation is approachable. We plan to compare the proton ventilation results with the gold standard 129Xe MRI ventilation.

Finally, we did not include corrections for gradient non-linearity in this study. They will affect the regional ventilation in regions of gradient non-linearity. However, since the lungs are near the magnet isocenter and, especially for kids, do not likely extend into the highly non-linear gradient regions. For application of this method in clinical studies, gradient non-linearities can be incorporated as an image space correction using standard methods to correct this.

Conclusion:

In conclusion, we demonstrated that a motion-compensated low-rank (MoCoLoR) regularized reconstruction approach can be used for simultaneous structural and functional lung MRI, even in challenging pediatric scans. The MoCoLoR reconstruction approach includes motion fields to reduce the rank and better share data across motion states during iterative reconstruction, which efficiently uses the data and results in high SNR in respiratory-resolved reconstructions. We evaluated this in pediatric and young adult subjects from ages 4–25 for radial UTE lung MRI acquired without sedation. With data from a 5-minute scan, the MoCoLoR reconstructions provided 1 mm isotropic high-resolution structural images as well as respiratory-resolved images. These were used in the lung at multiple respiratory states to compute ventilation maps at the same high-resolution, where we observed anecdotal correlations between ventilation and lung function.

Supplementary Material

Supinfo

Figure S1. Convergence curve for all three reconstruction approaches from one representative dataset.

Figure S2. Comparison of Reconstruction Time for All Datasets. Median processing time for XD Recon, MostMoCo and MoCoLoR are 3.1 hours, 12.4 hours, and 5.7 hours on a 12–32 VRAM GPU machine.

Figure S3. 3D DCE MRI Reconstruction Results. DCE images zoomed in around the heart reconstructed with 4 different reconstruction strategies are plotted in (a). Images from the time frame outlined by the red rectangle that shows bulk motion artifacts are shown in (b) and Line profiles across the heart from this frame are plotted in (c). The motion compensation is also illustrated by the axial images shown in (d) and Dynamic signals of the thoracic aorta in (e), where signals clearly corrupted by bulk motion are pointed out by orange arrows. MoCoLoR with both rigid and bulk motion compensation (“both MC”) clearly outperformed the other strategies.

Figure S4. Respiratory Motion Correction Comparison on DCE data. Pre-contrast (top row) and post-contrast (bottom row) images reconstructed with different strategies are compared. The arrows point to an airway and nearby vessels in the lung (red arrows) and vessels in the liver (green arrows) that had improved delineation with MoCoLoR and using both respiratory and bulk motion compensation.

Table 1.

Summary of apparent SNR and maximum derivative values

	Parenchyma aSNR	Aorta aSNR	Trachea aSNR	Diaphragm MD
XD Recon	5.31 ± 1.94	16.92 ± 5.41	2.53 ± 0.63	0.180 ± 0.040
MostMoCo	4.12 ± 1.32	13.20 ± 3.72	2.22 ± 0.49	0.192 ± 0.043
MoCoLoR	7.98 ± 3.52	26.18 ± 9.71	3.08 ± 0.96	0.159 ± 0.033