B1 and magnetization decay correction for hyperpolarized 129Xe lung imaging using sequential 2D spiral acquisitions

To mitigate signal variations caused by inhomogeneous RF and magnetization decay in hyperpolarized 129Xe ventilation images using flip‐angle maps generated from sequential 2D spiral ventilation images acquired in a breath‐hold. Images and correction maps were compared with those obtained using conventional, 2D gradient‐recalled echo.


INTRODUCTION
Methods to produce and detect hyperpolarized (HP) 129 Xe have advanced over the last two decades and now enable a range of MRI techniques to quantify regional changes in lung structure and function. [1][2][3][4][5][6] The most common HP 129 Xe MRI application is mapping gas distribution after inhaling a single bolus of gas. [7][8][9][10] Within these "ventilation maps," lung volume containing abnormally high inhaled HP 129 Xe density (i.e., hyperventilated) display relatively high signal relative to surrounding lung airspace. In contrast, regions containing abnormally low ventilation due to obstructed air flow display relatively low signal. Due to its sensitivity to airflow obstruction, 129 Xe MRI is increasingly used to assess impaired ventilation in a range of obstructive lung diseases, including asthma, 9,10 lymphangioleiomyomatosis, 11 chronic obstructive pulmonary disease, 7,8 and cystic fibrosis. [12][13][14] For ventilation imaging, quantification based on signal intensity is complicated because HP magnetization is created externally to the lungs and is nonrecoverable. Thus, HP signal varies spatially due to the regional physiology of interest (i.e., ventilation), local T 1 decay, and coil inhomogeneity. For most 2D acquisitions, the time required to acquire an image slice is less than 1 s; therefore T 1 relaxation (∼30 s in the lung at 3 T 15,16 ) can be neglected during a given image acquisition. However, RF excitation is unavoidable, so care must be taken when choosing flip angles that balance HP magnetization decay while ensuring sufficient recoverable signal. 1,17 Even if an optimal global flip angle is chosen, inhomogeneity in the B 1 field will cause coil sensitivity, flip angle, and RF-induced magnetization decay to vary across the lung volume. Because this coil-dependent signal variability is unrelated to the ventilation patterns of interest, it has the potential to both mask and mimic impaired ventilation, compromising the physiological interpretation and quantification of the image. To differentiate coil-dependent sensitivity variation and magnetization decay from regional physiological differences, B 1 variability across images must be corrected.
Currently, ventilation imaging is most commonly performed using 2D gradient-recalled echo (GRE) sequences with breath-hold scan durations of 16 s or less. 7-14 RF-coil sensitivity maps have been obtained for HP gases by acquiring consecutive, 2D-GRE images and reducing scan to with partial k-space acquisition. 18 The signal attenuation between images depends directly on the variations in flip angle across the FOV, allowing flip angle to be calculated from a simplified form of the Bloch equations suitable for nonrenewable HP magnetization. The resulting flip-angle maps were used to correct both coil sensitivity and RF-induced signal decay, thus more accurately representing regional physiology. However, this GRE-based correction requires longer scan durations and longer breath-holds, which increases T 1 relaxation. Furthermore, increased scan times may not be feasible in subjects who cannot perform long breath-hold maneuvers, including young children and people with severe respiratory disease. Fortunately, more efficient sampling methods (i.e., spiral sequences) enable HP gas flip-angle mapping with significantly reduced scan times. 19,20 Here, HP 129 Xe ventilation images and flip-angle maps were acquired during a single 5-s breath-hold using 2D spiral. Flip-angle maps were generated from sequentially acquired 2D spiral images using an analytical model appropriate for HP gases and center-out sampling trajectories. These maps were used to calculate and correct signal variations caused by coil sensitivity and RF-induced signal decay. Corrections were validated using simulations, HP gas phantoms, and in vivo imaging.

THEORY
In HP-129 Xe imaging, the initial longitudinal magnetization is about 10 5 orders of magnitude greater than that of thermally polarized 129 Xe at clinically relevant magnetic field strengths and temperatures. Thus, HP magnetization dynamics can be approximated as a monotonic decay to thermal equilibrium caused by T 1 relaxation and RF depletion. 1,17 In this work, we assume T 1 relaxation is negligible because the time for each 2D acquisition slice is short (<1 s for Cartesian and <0.5 s for spiral) relative to the 129 Xe T 1 (∼30 s) in the lung at 3 T. 15,16 Thus, longitudinal magnetization decay can be approximated as occurring solely due to RF excitation. Under these assumptions, the signal intensity obtained from a constant flip angle, , acquired as a function of RF pulse number (n = 1, .., N) can be approximated as follows: where f is a system-specific sensitivity factor, and M hp (0) is the initial longitudinal magnetization. For Cartesian sequences using linear phase encoding, signal is determined by the magnitude of k-zero (k 0 ), which is encoded following RF pulse number n 0 = N ph 2 + 1 where N ph is the number of phase encodes per slice. When two images are acquired sequentially during a held breath, k 0 is sampled twice, with N ph RF pulses separating the two k 0 lines. Assuming both fixed slice position and fixed , the signal intensities from the first and second images are given by (2) For center-out sampling approaches, such as spiral sequences, k 0 is sampled following each excitation. Consequently, the signal for each image can be calculated from the average k 0 magnitude. As such, the image signal intensity resulting from all spiral views (total number, N s ), 21 is given by If two spiral images are acquired sequentially within the same breath-hold, 2N s total pulses will be applied. Therefore, the signal intensity for the first (S 1 ) and second (S 2 ) image can be approximated as and (5) For both GRE and center-out sampling approaches, the flip angle at a given voxel position (r) can be calculated from the ratio of the voxel magnitudes according to where N d is the number of RF excitations separating the k 0 lines of the first and second images (N d = N ph for Cartesian and N d = N s for spiral images that are fully sampled).
To correct for signal variation caused by RF-induced decay inhomogeneity and B 1 -related sensitivity, magnitude images must be multiplied by a correction factor given by sin( (r)) for Cartesian (8) and where the factor of 1∕ (r) accounted for the receive sensitivity of the RF coil (i.e., RF reciprocity). 18,22 An analytical expression describing the uncertainty in the measured flip angle can be derived from Eq. (7) by applying the matrix expression for uncertainty propagation, 23 assuming a single channel coil is used, and that noise distribution in S 1 and S 2 is constant (i.e., S 1 = S 2 = S ) according to .
To allow direct comparison across (r) values, uncertainty can be expressed in terms of relative uncertainty percentage, , as follows:

Simulation
Simulations were performed on 2D digital phantom images (image size = 128 × 128) for GRE and spiral sampling. Magnetization dynamics during ventilation imaging were simulated in MATLAB 2021b (The MathWorks, Inc.), as shown in Figure 1. HP 129 Xe decay was incorporated by acquiring two consecutive images with magnetization that decayed from a single initial level according to Eq. (1). Regionally varying flip angles ( = 1 −25 • for GRE and = 1 −40 • for spiral) were used to examine the effect of B 1 inhomogeneity. k-Space was generated by performing a fast Fourier transform (FFT) on the attenuated images. Gaussian noise (μ = 0, = 0.1) was then added to the complex k-space data (SNR ≈ 30 for the first image). In the Cartesian case, K-space data were sampled linearly (+k to −k), with each k-space line receiving a unique level of signal decay. Inverse FFT (iFFT) was performed to obtain final images. In the spiral case, k-space data were decayed similarly, but sampled using Archimedean spirals (uniform density) and interpolated onto a Cartesian grid. Images were reconstructed using iterative density compensation, 24 Cartesian gridding, and iFFT.

Phantom and in vivo imaging
Isotropically enriched 129 Xe (85% 129 Xe; Linde Electric. & Specialty Gasses Inc.) was polarized to approximately 30%-35% (Polarean Imaging, PLC, Model 9820) and Schematic depicting simulated hyperpolarized (HP) 129 Xe flip-angle mapping and image correction using sequential imaging. (A) Flip angle was varied to mimic B 1 inhomogeneity. (B) HP signal was attenuated according to cos( ) n−1 for a given number of RF excitations (n, … , N). (C) k-Space data were then generated by performing fast Fourier transform (FFT) on the attenuated images and adding complex Gaussian noise (mean of zero). (D) k-Space was sampled using gradient-recalled echo (GRE) or spiral ordering. GRE images were reconstructed by performing inverse FFT (iFFT). Spiral images were reconstructed by regridding data onto a Cartesian matrix using iterative density compensation followed by iFFT. (E) Flip-angle maps were generated from Image 1, Image 2, and N d according to Eq. (7). (F) Image 1 was corrected using Eq. (8) for GRE and Eq. (9) for spiral. dispensed into evacuated phantoms (purged with N 2 ). An initial dose containing 25% HP 129 Xe and 75% N 2 was used to calibrate 129 Xe flip angle and resonance frequency.
Two physical, HP 129 Xe phantoms (free and restricted diffusion) were constructed (Appendix B). Before imaging, phantoms were filled with 50% HP 129 Xe and 50% N 2 . Phantom images were acquired using a 3T Philips Ingenia MRI scanner (Philips Healthcare, Best, Netherlands) with a flexible transmit/receive 129 Xe chest coil (Clinical MR Solutions). HP-129 Xe gas images and flip-angle maps were obtained during the same scan using 2D GRE or spiral. For each sequence, two consecutive, fully sampled images were acquired using the same flip angle at the same slice position by acquiring both the first and second image of a given slice before continuing to the next slice. We assume T 1 relaxation is negligible, because acquisition time was short (<1 s/slice for Cartesian and <0.5 s/slice for spiral) relative to the 129 Xe T 1 (∼2.5 h) for free-diffusion 25 and (∼7 min) restricted-diffusion phantoms ( Figure S1). Applied flip angle was prescribed depending on the number of excitations per slice, N, according to = atan( √ 2∕N). 1,18 Image acquisition parameters are given in Table 1.
Human studies were approved by the Cincinnati Children's Research Foundation Institutional Review Board and U.S. Food and Drug Administration through an investigational new drug protocol (IND 123577). HP-129 Xe ventilation MRI was performed in 1 healthy volunteer (male, 30 years) and 1 patient with cystic fibrosis (CF) (female, 21 years). Informed written consent was obtained from the participants.
Subjects were imaged (using the protocol described previously) in the supine position during a less-than 16-s breath-hold. HP-129 Xe gas was delivered to the subject while lying in the scanner and inhaled through a 0.95-cm inner-diameter Tygon tube (Saint-Gobain Performance Plastics). Each subject inhaled three imaging doses of xenon. Before each dose, subjects exhaled to functional residual capacity and then inhaled the 1-L dose. The first dose was the calibration dose. The second dose (1 L of 100% Xe) was used to acquire GRE ventilation images, and a third dose (1 L of 100% Xe) was used to acquire spiral ventilation images. Acquisition parameters are provided in Table 1.

Image reconstruction and analysis
Complex raw data were exported after DC offset correction, and images were reconstructed offline using a graphical programming interface. 26 GRE images were reconstructed by applying an iFFT. Before spiral reconstruction, all points along a projection were scaled to the mean of k 0 across all spiral interleaves to reduce artifacts caused by RF depletion. 6,20,[27][28][29] Scaled data were gridded onto a Cartesian matrix using the default graphical programming interface density compensation (iterative density compensation 24 ), and gridding settings and were reconstructed by applying 2D iFFT. Within each slice, a binary mask of the 129 Xe-containing regions was generated by signal intensity thresholding, with additional manual segmentation as needed. Only visibly ventilated portions of the phantom/lungs (excluding large airways) were included in the segmented volume for analysis. SNR was calculated for all images according to S lung ∕ BG , where S lung is mean signal amplitude within the lung mask, and BG is the SD of the noise (region of interest in the background). For both GRE and spiral, flip-angle maps were generated from the signal magnitude of images 1 and 2 (both simulated and acquired) according to Eq. (7). Flip-angle maps were smoothed using a 2D low-pass Gaussian filter with SD of 2 voxels. These maps were used to correct image 1 according to Eqs. (8) and (9) for GRE and spiral, respectively. (Note that the coil receiver sensitivity term [1∕ ] was not included in the simulations.) The mean percent difference between images and flip-angle maps was calculated for simulations, phantoms, and in vivo images. All data analysis (e.g., generating maps, calculation of means, SD, coefficient of variation [CV]) were performed in MATLAB 2021b.

Simulation
Simulated sequential GRE images (Images 1 and 2) are shown in Figure 2A,B, and applied and measured flip-angle maps are shown in Figure 2C,D, respectively. Measured flip angle showed excellent voxel-by-voxel correlation with local flip angle included in the simulation (R 2 = 0.99; Figure 2E). Similar simulations were performed with spiral sampling (Figures 2F-J), and excellent correlation was again observed between measured and local flip angles (R 2 = 0.99; Figure 2J). Additionally, the relative uncertainty in the measured flip angle, , agreed well with the analytical uncertainty predicted by Eq. (11) for both GRE and spiral ( Figure S3A,B), respectively. Figure 3 shows the results of applying flip-angle maps to correct simulated GRE and spiral 129 Xe images. For GRE, Figure 3A shows the simulated object alongside the measured flip-angle map ( Figure 3B). Using the flip-angle map, Image 1 was corrected according to Eq. (8) to compensate for regionally varying signal decay ( Figure 3C,D). Percent signal difference maps between the object and uncorrected Image 1 ( Figure 3E) and the object and the corrected image ( Figure 3F) are shown. Mean percent difference between the object image and the corrected image was 16 ± 3%, which is 35% lower relative to the mean percent difference between the object image and the uncorrected image (26 ± 19%). The percent difference map of the corrected image is also more homogeneous (CV = 0.18) with significantly reduced mean percent difference relative to that of the uncorrected image (CV = 0.73). Similarly, spiral correction (N S = 10, Figure 3G-L) resulted in improved images with lower and more homogeneous percent difference (mean = 17 ± 9% and CV = 0.52 relative to the uncorrected image [Image 1, mean = 23 ± 14% and CV = 0.60]). Figure 4 shows image 1 (A) and image 2 (B) of the physical HP 129 Xe phantoms obtained using GRE and spiral. The theoretical SNR gain in the spiral images ( Figure S2) was not fully realized, due to noise-like background artifacts. These artifacts were found primarily near high-signal edges and likely result from a combination of Gibbs ringing, long readout window, large flip angle, or off-resonance effects. The measured flip-angle maps ( Figure 4C) were relatively homogenous due to the small, sampled volume and yielded in mean flip angles that were comparable to the nominal flip angle applied, with a mean percent difference in flip angle of 5% and 13% for the GRE and spiral sequences, respectively. Given the uniform nature of the phantoms, homogenous signal is expected; however, in both GRE and spiral instances, there are focal regions of nonuniformity (arrows) and subsequently high CV (measure for GRE and spiral, respectively), which is spurious and not reflective of actual structure. Figure 4 also shows Image 1 (A) and Image 2 (B) from a healthy subject and a person with CF obtained using GRE and spiral. Also shown are the measured flip-angle maps (C), extracted correction maps (D), and the final corrected images (E) obtained for both sequences. The mean measured flip-angle values matched well with the nominal flip angle. For the healthy control, the mean percent difference in flip angle was 13% for GRE and spiral. For the person with CF, the mean percent difference in flip angle was 17% and 18% for GRE and spiral, respectively. Applying the correction map to Image 1 resulted in visible differences in the images. Regions with bias toward lower signal (i.e., smaller measured flip angles; red arrows) become brighter with correction. In other regions biased toward high signal (i.e., hyperventilated regions, larger measured flip angles; blue arrows) display reduced intensity that is more similar to the surrounding parenchyma. Moreover, the hyperintense spot on the CF subject (upper left lung; green arrows) becomes brighter after correction. Furthermore, similar Similarly, the correction process in the spiral case (N S = 10) (G-L) resulted in quantitatively more accurate images. After correction, images are more homogeneous with reduced mean percent difference, 17 ± 10% relative to the uncorrected images (Image 1, mean = 23 ± 14%). Red arrows indicate the focal differences between the uncorrected and corrected images. correction patterns are similar between GRE and spiral acquisitions.

DISCUSSION
Regional signal variation arising from B 1 inhomogeneity and RF-induced signal decay is a major limitation for quantitative 129 Xe ventilation MRI. This variation is unrelated to physiology and has the potential to both mask and mimic impaired ventilation, thus compromising image interpretation. To differentiate coil-dependent sensitivity variation and magnetization decay from the regional physiological differences, 129 Xe delivery via ventilation is necessary to measure and correct B 1 variability across images. In this study, we describe a method to acquire RF coil sensitivity maps and ventilation images during a single breath-hold scan using fully sampled 2D spiral and compared this approach with a fully sampled variant of the analogous GRE technique described by Miller et al. 18 While this analytical solution accounts for hyperpolarized-specific effects (nonrecoverable magnetization and RF-induced signal loss), it does not account for uncertainty resulting from image acquisition and reconstruction (e.g., signal variation caused by Gibbs ringing, HP magnetization decay). To address this limitation, HP-129 Xe ventilation MRI acquisition and reconstruction ( Figure 1) were simulated by explicitly including k-space sampling and longitudinal magnetization decay for both GRE and spiral acquisitions. These simulations produced similar results (i.e., minima were at the same

F I G U R E 4
Correcting HP signal variation caused by B 1 inhomogeneity in phantoms and in vivo imaging. (A,B) Representative slices from 129 Xe ventilation Images 1 and 2, acquired using GRE (top) and spiral (bottom) pulse sequences, are shown for phantoms, a healthy subject, and a patient with cystic fibrosis (CF). (C) Flip-angle map calculated according to Eq. (7). The resulting mean flip angle was comparable with the globally applied flip angle. Mean percent difference = 5% for GRE and 13% for spiral in the phantom studies. Mean percent difference = 13%, 13%, 17%, and 18%, for healthy (GRE), healthy (spiral), CF (GRE), and CF (spiral), respectively. (D,E) Correction maps were calculated according to Eqs. (8) (GRE) and (9) (spiral) and used to correct Image 1. Red arrows indicate decreased signal; blue arrows indicate increased signal; and green arrows indicate a hyperintense spot between the uncorrected (Image 1) and corrected images. place) to those predicted by the analytical model with only modestly elevated ( Figure S3). Gas phantoms further validated the approach by showing good agreement (mean percent difference <15%) between applied and measured flip-angle maps (Figure 4). The reconstructed image was successfully corrected for signal variation due to B 1 inhomogeneity and signal decay ( Figure 4D,E).
Using sequential ventilation imaging, voxel-by-voxel flip angle and correction maps were successfully obtained in 2 human volunteers in single breath-holds using both GRE and spiral acquisitions. Measured flip-angle maps revealed larger regional differences than were observed in phantom imaging (Figure 4), likely caused by RF heterogeneity of the coil across the larger lung volume. Despite substantial regional variation, the mean measured flip-angle maps agreed well with nominally applied flip angles (mean percent difference <20%). When flip-angle maps were used to correct images for regional variations in coil sensitivity and signal decay, significant improvements in signal homogeneity were observed in the appearance of the corrected images from both healthy and CF subjects. While the spiral provided comparable correction maps to the GRE, the spiral enabled 3-fold faster acquisition (15 s GRE vs. 5 s spiral) with identical resolution. In addition to being more feasible for young children or those with advanced lung disease, the shorter spiral acquisition allows regional 129 Xe signal bias to be corrected, thus providing improved sensitivity to regional pathophysiology and enhanced clinical interpretation.

Study limitation and future work SUPPORTING INFORMATION
Additional supporting information may be found in the online version of the article at the publisher's website.  [11]) for SNR = 30. The value of is minimized when SNR is at maximum (marked minima) for both GRE and spiral. Figure S3. Relative uncertainty of the measured flip angle, , derived analytically and generated by simulation. The flip-angle relative uncertainty from the simulated data agrees well with the analytical solution, showing minima of at optimal θ for both GRE (A) and spiral (B) pulse sequences. However, the relative uncertainty of the flip angle produced from the simulation exceeds that predicted analytically, due to image artifacts resulting from factors such as sampling and image reconstruction.