Undersampled Diffusion-Weighted 129Xe MRI Morphometry of Airspace Enlargement: Feasibility in Chronic Obstructive Pulmonary Disease

Multi-b diffusion-weighted hyperpolarized gas MRI measures pulmonary airspace enlargement using apparent diffusion coefficients (ADC) and mean linear intercepts (Lm). Rapid single-breath acquisitions may facilitate clinical translation, and, hence, we aimed to develop single-breath three-dimensional multi-b diffusion-weighted 129Xe MRI using k-space undersampling. We evaluated multi-b (0, 12, 20, 30 s/cm2) diffusion-weighted 129Xe ADC/morphometry estimates using a fully sampled and retrospectively undersampled k-space with two acceleration-factors (AF = 2 and 3) in never-smokers and ex-smokers with chronic obstructive pulmonary disease (COPD) or alpha-one anti-trypsin deficiency (AATD). For the three sampling cases, mean ADC/Lm values were not significantly different (all p > 0.5); ADC/Lm values were significantly different for the COPD subgroup (0.08 cm2s−1/580 µm, AF = 3; all p < 0.001) as compared to never-smokers (0.05 cm2s−1/300 µm, AF = 3). For never-smokers, mean differences of 7%/7% and 10%/7% were observed between fully sampled and retrospectively undersampled (AF = 2/AF = 3) ADC and Lm values, respectively. For the COPD subgroup, mean differences of 3%/4% and 11%/10% were observed between fully sampled and retrospectively undersampled (AF = 2/AF = 3) ADC and Lm, respectively. There was no relationship between acceleration factor with ADC or Lm (p = 0.9); voxel-wise ADC/Lm measured using AF = 2 and AF = 3 were significantly and strongly related to fully-sampled values (all p < 0.0001). Multi-b diffusion-weighted 129Xe MRI is feasible using two different acceleration methods to measure pulmonary airspace enlargement using Lm and ADC in COPD participants and never-smokers.


Introduction
Hyperpolarized 129 Xe pulmonary MRI [1,2] provides physiologically relevant biomarkers of obstructive lung disease [3][4][5]. Recently, the 129 Xe MRI pulmonary apparent diffusion coefficient (ADC) [6] was shown to be strongly related to ex vivo histological measurements of airspace enlargement in lung tissues harvested from COPD participants. In addition, 129 Xe ventilation MRI was shown to be feasible using naturally abundant 129 Xe [7]. Moreover, dissolved-phase 129 Xe MRI may be employed for simultaneous ventilation/perfusion lung imaging [8][9][10][11], and there is a stable supply of 129 Xe and commercially available polarizers capable of generating the necessary volumes of highly polarized gas for clinical investigations [12,13]. However, the low gyromagnetic ratio of 129 Xe and the gradient strengths typical for clinical scanners (5 G/cm) dictate that rapid MRI acquisition strategies be developed [9]. This is especially true for multi-b diffusion-weighted MRI, as whole lung datasets are currently difficult to acquire during the relatively short 10-18 s breath hold timeframe [14] that is feasible in participants with lung disease. For participants with obstructive lung disease stemming from abnormal lung airspace enlargement, multi-b diffusion-weighted MRI [15,16] provides ADC and other acinar duct morphometric measurements that estimate mean linear intercept (L m ) values. This is important for young adults with bronchopulmonary dysplasia (BPD) [17] and alpha-1 antitrypsin deficiency (AATD) [18] in whom preliminary diffusion-weighted MRI studies [19,20] have been performed. Because emphysema leads to the destruction of the lung microstructure and a subsequent decrease in surface area of the alveolar walls, gas motion in the lungs is less restricted, leading to higher ADC values. Moreover, since L m is inversely proportional to the lung surface-to-volume ratio, destruction or damage of the lung microstructure leads to larger L m values. As ADC and L m values increase, normal/healthy gas exchange diminishes, making these measurements clinically practical for evaluating lung function in emphysema.
Three-dimensional multi-b diffusion-weighted MRI [21], requiring a number of independent doses of gas for each slice or each b value, has been performed using 129 Xe [14] and 3 He [21,22]. While all these approaches are feasible in the research setting, the increased time for acquisition, the potential for lung volume mismatch, and repeated doses of hyperpolarized gas are not compatible with clinical examinations. Half-Fourier RARE-type or TrueFISP [23,24], parallel imaging [25], simultaneous slice acquisition [26], and compressed sensing (CS) [27] are promising options for decreasing image acquisition time. Recently, 3 He ventilation MRI was shown using CS [27], and multi-b diffusion-weighted MRI was demonstrated using conventional k-space sampling [28], parallel imaging [29], CS [30] and undersampling in the spatial and in b-value directions [31].
We hypothesized that, by using k-space undersampling, whole lung three-dimensional multi-b diffusion-weighted 129 Xe MRI can be achieved in a single 16 s breath-hold. Therefore, in this proof-of-concept evaluation, our objective was to retrospectively evaluate and compare ADC and morphometry estimates [32,33] in never-smokers and COPD study participants using partial Fourier reconstruction [34] and compressed sensing [35].

Theory
The signal dependence related to diffusion-sensitization can be determined through the probability density function or diffusion propagator (P) for fluid diffusion in confined media with unknown geometry [20,32,33]: where D is diffusivity, S(b) is the signal at a particular b-value, and S 0 is the MR signalintensity in the absence of diffusion-sensitizing gradients. The diffusion propagator can be ascertained through the inverse Laplace transform of S(b) [33]. To apply this, the analytical representation for S(b) is required. Thus, experimental S(b) values can be fitted, as demonstrated for multi-b diffusion-weighted 3 He MRI [20,30,31] as follows: where D is the apparent diffusivity and α is the heterogeneity index (0 < α ≤ 1.0). The diffusion propagator can be determined through substitution of Equation (2) into Equation (1) and then applying the inverse Laplace transform [33]: and where f (D) is the auxiliary function, and parameters B and C are functions of the heterogeneity index [33]. Mean D estimates can be determined using the probability density function distribution to calculate mean airway length maps [32] (Lm D = √ 2∆D, where ∆ is the diffusion time). For multi-b diffusion-weighted 3 He MRI, L m is empirically observed to be proportional to Lm D [20]: Mean airway length depends on both ∆ and diffusivity, so Equation (5) cannot be used for 129 Xe MRI-based L m estimates. In order to extend Equation (5) to 129 Xe gas, the empirical relationship in Equation (6) was previously determined and proposed [36]: where D He 0 is the free diffusion coefficient of 3 He in a nitrogen gas mixture (0.88 cm 2 /s), ∆ He = 1.46 ms [20], D Xe 0 is the free diffusion coefficient of 129 Xe (0.12 cm 2 s −1 /0.14 cm 2 s −1 [37]), and ∆ Xe is the diffusion time. To validate our approach, a single participant (COPD-5) was evaluated using both 3 He and 129 Xe MRI. Stretched-exponential model 3 He MRI L m values for participant COPD-5 (Lm D = 290 ± 50 µm and L m = 700 ± 180 µm) were similar to previously published estimates [20].

Study Participants
Four never-smokers, four COPD ex-smokers with emphysema, and one AATD study participant with COPD provided written informed consent to an ethics board-approved protocol (The University of Western Ontario Health Sciences Research Ethics Board, approval ID 18130 and 18131) that was compliant with the Health Insurance Portability and Accountability Act (HIPAA, USA). Ex-smokers with COPD and AATD participants with COPD were enrolled between 50-80 years of age as part of the Thoracic Imaging Network of Canada (TinCan) cohort [38]; never-smokers without a history of tobacco smoking or chronic respiratory disease were enrolled between 45-80 years of age. Some of the participants evaluated here were previously reported [14,37] as a part of the TINCan study.

Pulmonary Function Tests and CT
Spirometry, plethysmography, and the diffusing capacity of the lung for carbonmonoxide (DL CO ) were performed according to American Thoracic Society (ATS) guidelines [39] using a plethysmograph and attached gas analyzer (MedGraphics Corporation. 350 Oak Grove Parkway, Saint Paul, MN, USA). CT was also performed in supine (64-slice Lightspeed VCT scanner GEHC, Milwaukee, WI, USA; 64 × 0.625 mm, 120 kVp, effective mA = 100, tube rotation time = 500 ms, pitch = 1.0), using a spiral acquisition in breath-hold after inhalation of 1 L N 2 from functional residual capacity (FRC). A slice thickness of 1.25 mm and a standard convolution kernel were used.

Image Analysis
As shown in Figure 1, two k-space masks, mimicking the acceleration factor 2 (AF = 2; half-echo sampling in the phase-encoding direction), and AF = 3, were applied to the fully sampled multi-b diffusion-weighted 129 Xe k-space data. A partial Fourier reconstruction (MATLAB R2013b MathWorks, Natick, MA, USA) [41] was used to reconstruct diffusionweighted images with AF = 2, while compressed sensing (MATLAB) [35] was used to reconstruct diffusion-weighted images with AF = 3. All fully sampled k-space data for 129 Xe MRI were reconstructed into a 128 × 128 matrix (Fourier transform, IDL6.4, ITT Visual Information Solutions, Boulder, CO, USA). Therefore, the nominal voxel size was 3.1 × 3.1 × 15 mm 3 for the static ventilation images and 3.1 × 3.1 × 30 mm 3 for the diffusion-weighted images. Diffusion-weighted 3 He MRI k-space data were zero-filled to a 128 × 128 matrix and then Fourier transformed (IDL6.4). Therefore, the nominal image voxel size was 3.1 × 3.1 × 30 mm 3 .
To generate D and α maps, a nonlinear least squares algorithm (MATLAB) was used to fit Equation (2) on a voxel-by-voxel basis. In turn, D and α were used to compute P(D) for the 0 < D ≤ D 0 interval based on Equations (3) and (4) on a voxel-by-voxel basis (IDL 6.4).
A semi-automated segmentation approach was used to generate ventilation defect percent (VDP), as previously described [42]. ADC maps were generated for two b-values (0 and 12 s/cm 2 ) on a voxel-by-voxel basis, as previously described [3] The relative area of the CT density histogram with attenuation values ≤−950 Hounsfield units (RA 950 ) [43] and low attenuating clusters were determined using Pulmonary Workstation 2.0 (VIDA Diagnostics Inc., Coralville, IA, USA).

Statistics
Differences between ADC and Lm values generated from fully and undersample space were calculated on a voxel-by-voxel basis [30] using Equation (7): where N and M were the corresponding map matrix sizes. Multivariate analysis of v ance (MANOVA) and independent t tests were performed using SPSS Statistics, V (SPSS Inc., Chicago, IL, USA). For all participants and for the COPD subgroup, repea measures of ANOVA with AF = [1, 2, and 3] as repeated ADC/Lm measurements w corrected using a Greenhouse-Geisser correction and used to determine any main eff for the acceleration factor regarding ADC or Lm. Relationships between voxel-wise A and Lm with acceleration factor were determined using Spearman correlation coefficie (ρ). Agreement between acceleration factors for both ADC and Lm were determined us the Bland-Altman method [44] by using GraphPad Prism version 7.00 (GraphPad S ware Inc., San Diego, CA, USA). Results were considered significant when the probab of two-tailed type I error (α) was less than 5% (p < 0.05). Table 1 summarizes pulmonary function, CT, and demographic measurements all participants. Never-smokers reported significantly different FEV1/FVC, TLC, and D as compared to COPD participants.

Discussion
Hyperpolarized gas 129 Xe MRI was approved by the Food and Drug Administration (FDA) for clinical use in December 2022, opening the doors for wide clinical adoption and usage of this imaging modality. Diffusion-weighted hyperpolarized gas 129 Xe MRI, along with static ventilation and gas exchange measurements, should be useful for the diagnosis, observation, and treatment outcome assessment of various pulmonary diseases, including smoking-related emphysema, AATD, and bronchopulmonary dysplasia. As 129 Xe MRI is a radiation-free non-invasive imaging modality, it could potentially become the main lung imaging method for young adults and newborns.
In this proof-of-concept study, we investigated the influence of k-space undersampling on 129 Xe MRI ADC and L m values using three different sampling approaches and a stretched exponential model. We retrospectively evaluated nine participants, including never-smokers, COPD ex-smokers, and a single AATD participant to explore the feasibility of this approach.
COPD ex-smokers and AATD participants were previously studied using 3 He MRI ADC and morphometry measurements [20,[45][46][47][48]. However, to our knowledge, this is the first demonstration of undersampled 129 Xe MRI ADC and L m across a spectrum of emphysema severity and using the stretched exponential method. Previous 129 Xe morphometry studies [49,50], in mainly healthy participants, provided a framework for this examination in participants with emphysema. Several factors are expected to influence ADC and L m values, such as severity of emphysema and lung aging, due to the fact these measurements are an indirect reflection of the lungs' and alveoli's ability to move and transfer gasses: L m is the lung microstructure dimension and ADC describes the motion of gasses within the lungs and the airway restrictions. As such, any destruction of the airways and alveoli leads to a change in ADC and L m values, but the destruction pattern and the distribution of these ADC and L m values differ from normal lung aging compared to emphysematous lungs [28].
Across a wide range of emphysema severity, partial Fourier reconstruction (AF = 2) and compressed sensing (AF = 3) did not significantly alter ADC and L m values (p > 0.05) compared to those generated using fully-sampled Fourier transform reconstruction. In other words, for the never-smoker and COPD subgroups, fully and under-sampled estimates of ADC, Lm D , and L m were not significantly different. For both participant subgroups, the difference in L m values calculated based on Equation (7) was the same for AF = 2/AF = 3, indicating that the two different image reconstruction methods led to similar morphometry estimates. Moreover, for all participants and for the COPD subgroup, there was no relationship for acceleration factor with ADC or L m . The strong and significant voxel-wise correlations for AF-1 ADC and L m values with AF-2 and AF-3 values also support the notion that undersampling does not alter or bias ADC or L m values and can be considered for participant studies.
It is important to note that, for the never-smoker subgroup, Lm D estimates were smaller (140 µm vs. 160 µm) than previous estimates [49] for four healthy volunteers at 1.5 T (same ∆ = 5 ms and b-values). The difference may be due to the smaller D Xe 0 used here and previously described [37] (0.12 cm 2 /s vs. 0.14 cm 2 /s [49]), and this further demonstrates the need for a time-and gas-independent airspace morphometry estimate, such as L m . The correlation between DL CO and ADC values has previously been studied by Kirby et al. [51], but such a correlation has not yet been reported for L m values.
The empirical equation (Equation (6)) was developed based on Equation (5), which, in turn, was previously validated in COPD participants with a wide range of emphysema severity [20]. For the single AATD participant evaluated here using both 3 He and 129 Xe, mean 3 He MRI L m estimates [20], based on Equation (5), and mean 129 Xe MRI L m estimates, based on Equation (6), were similar (700 ± 180 µm vs. 690 ± 210 µm, for 3 He and 129 Xe, respectively); the approximate 1-2% difference in 3 He-and 129 Xe-derived L m values likely reflected potential differences in slice location and in-plane resolution. At the same time, for the AATD participant, there was a 25% difference between Lm He D and Lm Xe D estimates (290 ± 50 µm vs. 220 ± 40 µm, for 3 He and 129 Xe, respectively), likely due to the ∆/D 0 dependence of the mean airway length scale [49]. Unfortunately, there are no published 129 Xe L m values for comparison in participants with similar age or with the image matrix size used here. Previous 129 Xe L m estimates for young healthy volunteers were smaller [52] than the values reported here (200 µm vs. 280 µm), which is consistent with the fact that the participants evaluated here were significantly older than in the previous study. 129 Xe L m values for never-smokers and COPD participants were not significantly different from the SEM-based L m values estimated using 3 He MRI previously reported [20]; this suggests that Equation (6) may be considered for 129 Xe MRI SEM morphometry estimates, although the relationship between L m and Lm D still needs to be confirmed in a larger study.
We acknowledge a number of study limitations, including the retrospective nature of this work and the small sample size: although this sample size would not be sufficient for clinical diagnostics conclusions, it should be sufficient for this methodology development and confirmation study. Generally, acceleration factors are guided by image matrix size, the number of b-values, and breath hold duration. For example, the in-plane resolution of multi-b diffusion-weighted 129 Xe k-space used for the AATD participant (64 × 64) could be matched with multi-b diffusion-weighted 3 He k-space (128 × 128) used for the same participant by using AF = 2 or half-echo partial Fourier reconstruction. Compressed sensing with at least AF = 3 can be considered to increase the in-plane resolution and number of b values. Moreover, acceleration with AF = 2 is not complicated to implement on FGRE acquisitions [53], and image reconstruction is also relatively straightforward. In contrast, the compressed sensing acquisition scheme we utilized cannot be implemented with FGRE methods and likely requires non-Cartesian [54] or pseudo non-Cartesian [55] sampling methods, which are more complex, requiring application of k-space regridding/interpolation and density-weighting algorithms. Recently, an ingenious compressed sensing approach [31] was pioneered that combined undersampling in both spatial and diffusion-sensitising directions using 3 He MRI with an acceleration factor of 7. It is this type of novel approach that will help translate MRI morphometry methods to clinical use.
In summary, in elderly volunteers and participants with emphysema, we evaluated two different acceleration techniques with diffusion-weighted 129 Xe MRI. All sampling methods generated ADC and stretched-exponential model lung Lm D and L m values that were strongly related and not significantly different. The results of this retrospective feasibility analysis provide support for the notion that undersampled single-breath diffusionweighted 129 Xe MRI may be considered for studies of emphysema in participants.
The clinically-conducted ADC and L m measurements should allow for accurate regional probing of the alveolus sizes and surface-to-volume estimates for a wide range of age groups: this information could then be used for the treatment decision and therapy outcome assessments.
Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/diagnostics13081477/s1, Table S1: Participant listing of imaging measurements and estimates.  Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Written informed consent has been obtained from the patients to publish this paper. Data Availability Statement: Data are not available due to the ethical restrictions.

Conflicts of Interest:
The authors declare no conflict of interest.