Finite element simulations of hyperpolarized gas DWI in micro‐CT meshes of acinar airways: validating the cylinder and stretched exponential models of lung microstructural length scales

This work assesses the accuracy of the stretched exponential (SEM) and cylinder models of lung microstructural length scales that can be derived from hyperpolarized gas DWI. This was achieved by simulating 3He and 129Xe DWI signals within two micro‐CT–derived realistic acinar airspace meshes that represent healthy and idiopathic pulmonary fibrosis lungs.


| INTRODUCTION
The detection of microstructural changes to the acinar airways, the structural units of gas exchange of the lungs that are located distally to the terminal bronchioles, are crucial for the clinical evaluation and longitudinal monitoring of a range of pulmonary diseases. Multi-detector CT is the current clinical gold standard for in vivo structural evaluation of the lungs in emphysema 1-3 and interstitial lung diseases. 4,5 However, multi-detector CT cannot resolve airways smaller than approximately 1.5 mm in diameter, 6 corresponding to the seventh to ninth generation of airways. 7 The higher spatial resolution of micro-CT facilitates 3D visualization of the acinar airways in ex vivo human lung samples and has been used to investigate chronic obstructive pulmonary disease mechanisms in the small airways and terminal bronchioles that previously could not be resolved with in vivo multidetector CT. 8,9 DWI with inhaled hyperpolarized gases ( 3 He or 129 Xe) combines the advantages of both multi-detector CT and micro-CT with 3D in vivo information of the lung microstructure due to the Brownian gas atom diffusion restriction within the acinar airways. The derived ADC is a sensitive biomarker of underlying changes in acinar airway microstructure. 10,11 The cylinder airway model (CM) [12][13][14] and stretched exponential model (SEM) 15,16 are theoretical models of hyperpolarized gas DWI signal within the lungs that can derive estimates of in vivo acinar airway dimensions with both 3 He and 129 Xe gases. These two diffusion models have been used to elucidate quantitative changes in acinar airway microstructure that are additional to basic ADC or mean-square displacement � √ 2 ⋅ ADC ⋅ t � measurements associated with smokingrelated early emphysema, 17 lung inflation mechanisms, 18 post-transplant lung growth 19 and lifespan, 20 aging, 21 and idiopathic pulmonary fibrosis (IPF) disease progression. 22 The reproducibility and accuracy of derived morphometry measurements from hyperpolarized gas DWI models are crucial for their reliable use in the detection of therapeutic responses or longitudinal disease changes. Excellent short-and long-term reproducibility of diffusion model measurements have been demonstrated in healthy subjects, 23 whereas excellent same-day reproducibility has been shown in patients with IPF. 22 To date, two validation methods have been used to assess the accuracy of measurements from the CM. The first method utilized direct validation of CM-derived morphological parameters obtained from ex vivo lung specimens against equivalent histological measurements in lung cores obtained from the same specimens. 13,24,25 Good agreement between CM and histology measurements was observed for morphological parameters of mean chord length (Lm) as well as outer acinar radius (R) and alveolar sleeve depth (h) in ex vivo human 13 and canine lungs, 24 respectively. A second proposed validation method was via computer simulations of hyperpolarized gas DWI within simplified geometrical models of acinar airways, [26][27][28] where known model dimensions were compared to respective CM-derived parameters obtained from Monte-Carlo or finite element (FE) simulations of 3 He gas diffusion. Simulations across a range of different diffusion parameters were used to establish an accurate operational range of the CM.
Recently, the SEM-derived mean diffusive length scale (Lm D ) was indirectly validated with comparisons against CM-derived measurements in the same subjects across a range of acinar length scales. 29 However, the Lm D has not yet been directly validated against histology or known acinar geometries. Therefore, this work aims to validate the SEM Lm D , alongside CM-derived parameters, with FE simulations of hyperpolarized 3 He and 129 Xe DWI in realistic models of acinar airway geometry-derived from micro-CT images. Specifically, FE simulations were used to determine optimum diffusion gradient parameters for accurate measurements with 3 He and 129 Xe and to establish the operational ranges of the SEM and CM by investigating the relationship between diffusion model measurements and experimental diffusion time.

| Acinar airway geometry meshes
Two different realistic acinar airspace geometry meshes were derived from existing 3D micro-CT images of human lung samples (16 µm resolution) representing healthy 8 and IPF 30 lungs ( Figure 1). An IPF lung was chosen because IPF-related acinar airspace changes are subtle and not as well understood as emphysematous airspace enlargement, and because IPF may cause substantial deviation from the healthy alveolar duct cylindrical geometry. 7 The process used to obtain and prepare lung samples from explanted lungs for micro-CT are fully described in McDonough et al. 8 Written informed consent was obtained from the next of kin of the patients whose donated lungs served as healthy controls. 8 Written informed consent was obtained from all IPF patients, and the study was approved by the hospital ethics and university biosafety committees in Leuven, Belgium. 30 Digital micro-CT images for this work were obtained with principal investigator approval.
Segmentation of the 3D micro-CT images were performed in Simpleware ScanIP (v. 2016.09-SP1, Synopsys, Mountain View, CA) where de-noising and edge enhancement was used to first segment the alveolar walls, followed by inverting the alveolar wall mask to derive the acinar airspace. 31 A single connected region of acinar airspace (approximately the size of a single MRI voxel ~4 mm isotropic) was isolated by floodfilling the airspace mask after manual editing and Gaussian smoothing. The resulting healthy and IPF acinar airspace geometries were then meshed for FE analysis with tetrahedral elements using the Simpleware FE Module (Synopsys). The final healthy and IPF acinar airspace FE meshes, after optimization (see Supporting Information), contained ~120,000 elements and ~37,000 nodes, and ~110,000 elements and ~36,000 nodes, respectively.

| Mean linear intercept length
The mean linear intercept length (MLI) for each micro-CT acinar airspace mesh was calculated as a benchmark for subsequent FE simulation-derived acinar airway dimensions from the two diffusion models. MLI is taken as being representative of the mean free path of restricted Brownian diffusion of the hyperpolarized gas atoms within the acinar airspace. MLI was calculated automatically from the segmented isolated acinar airspace micro-CT masks, which were up-sampled to an isotropic 4 µm resolution by direct measurements of linear intercept lengths in MATLAB (R2019a, MathWorks, Natick, MA) ( Figure 2). Parallel grid lines spaced 80 µm apart were used to calculate intercept lengths across every mask image spaced 80 µm apart. This entire process is analogous to the stereologic method for chord length measurements used for estimating MLI 32,33 and was repeated for 31 different orientations in 3D space at 30° intervals, representing the different 1D diffusion-sensitizing gradient directions used in subsequent FE simulations. The MLI was obtained from the mean value of the distribution of all intercept lengths in all orientations. The MLI for the healthy and IPF acinar airway meshes were 266 µm and 371 µm, respectively, and are similar to histological MLI values reported for healthy and IPF human lung samples. 34,35 It is important to note that there is a small difference between the CM-derived Lm and histological MLI gas-space parameters. The derivation of CM Lm assumes a negligible alveolar wall or interstitium, 13 whereas in the calculation of MLI no assumptions about the interstitium are made.

| Finite element simulations
Hyperpolarized 3 He and 129 Xe multiple b value DWI experiments were simulated in the micro-CT acinar airspace meshes. The evolution of the MR signal from a Stejskal-Tanner pulsed F I G U R E 1 Representative healthy (A) and IPF (D) micro-CT images (16 µm resolution) obtained from human lung samples. Representative healthy (B) and IPF (E) acinar airspace masks after segmentation of a single connect region of acinar airspace using flood filling and manual editing. Tetrahedral FE meshes representative of healthy (C) and IPF (F) acinar airspace meshes. FE, finite element; IPF, idiopathic pulmonary fibrosis gradient diffusion experiment, 36 proportional to the integral of transverse magnetization over a voxel, can be described by the Bloch-Torrey equation 37 : where M ⃗ r , t is the spatially varying complex transverse magnetization; is the gyromagnetic ratio of 3 He or 129 Xe; G ⃗ r , t is a spatially varying magnetic field gradient; and D 0 is the 3 He or 129 Xe free diffusion coefficient. In hyperpolarized gas DWI experiments, G ⃗ r , t is typically a bipolar trapezoidal gradient waveform used to sensitize the MR signal to diffusion attenuation, and the b value (b) is given by 12 : where G is the gradient amplitude; Δ is the diffusion time; δ is the gradient lobe time; and τ is the ramp time. The diffusion time (Δ) is defined as the duration from the middle of the first gradient lobe to the middle of the second. A typical in vivo 3 He and 129 Xe DWI voxel contains numerous acinar airways of various orientations that all contribute to the measured DWI signal. Therefore, to simulate in vivo conditions, diffusion FE simulations were implemented in a single direction and solved for 31 different 1D diffusion-sensitizing gradient angles uniformly orientated in 3D space at 30° intervals. 28 A range of validation experiments were performed in the two acinar airspace meshes with both 3 He and 129 Xe gases at different diffusion times to explore the full operational range of the two theoretical hyperpolarized gas diffusion models. For each FE simulation, the same following diffusion parameters were simulated, unless otherwise stated, for either 3 He: D 0 = 0.88 cm 2 /s and b = [0, 1.6, 3.2, 4.8, 6.4, 8.0] s/cm 2 or for 129 Xe: D 0 = 0.14 cm 2 /s and b = [0, 6, 12, 18, 24, 30] s/cm 2 . The choice of D 0 reflects the D 0 of each respective gas when diluted with either N 2 or air within the lungs, whereas the selection of b values are reflective of typical in vivo experimental diffusion gradients, which have a maximum gradient strength between 30 to 40 mT/m. [12][13][14][15][16][17][18][19][20][21][22][23] All FE simulations were solved using COMSOL Multiphysics (v. 5.3, COMSOL AB, Stockholm, Sweden) on a high-powered computing cluster (Dell PowerEdge C6320) using 12 CPU cores (dual Intel Xeon Processor E5-2630 v3) with 16 GB RAM per core. Boundary conditions assumed impenetrable mesh walls (i.e., 0 flow through the acinar airway walls) on all surfaces, and the initial transverse magnetization was set as 1 to reflect acinar airspaces entirely filled with hyperpolarized gas at the start of each simulation. An entire multiple b value DWI simulation took between 8 to 16 h.
The simulated DWI signal for each b value was averaged across all 31 gradient orientations and every mesh node. The global averaged multiple b value DWI signal was fitted to the CM (with either 3 He-based 13 or 129 Xe-based 14 expressions) and SEM 15,16 in MATLAB (R2109a, MathWorks) to derive respective diffusion model estimates of acinar airway dimensions for each FE simulation (see Supporting Information for the CM and SEM equations).

| Validation of in vivo diffusion times
The first set of validation simulations were of hyperpolarized gas DWI in the healthy and IPF acinar airspace meshes with diffusion times of 3 He (Δ = 1.6 ms) and 129 Xe (Δ = 8.5 ms). For in vivo hyperpolarized gas DWI with the two gases, these respective diffusion times provide comparable diffusion model acinar airway dimensions with both the SEM and CM. 16 3 He diffusion gradient parameters were: G Max = 31.4 mT/m, Δ = 1.6 ms, δ = 1.6 ms, and τ = 0.3 ms; 129 Xe: G Max = 32.6 mT/m, Δ = 8.5 ms, δ = 2.9 ms, and τ = 0.3 ms. The 129 Xe (Δ = 8.5 ms) simulations were fitted to the 3 He CM expressions due to in vivo results demonstrating that comparable 3 He and 129 Xe CM Lm can be derived at this diffusion time using the 3 He-based expressions. 16

| Operational range of theoretical diffusion models
Nine additional 129 Xe diffusion times ranging between Δ = 5 and 20 ms were simulated for both healthy and IPF acinar airspace meshes to investigate the relationship between the derived diffusion model parameters and diffusion time and to establish operational ranges for both theoretical diffusion models. 129 Xe diffusion gradient parameters for each diffusion time simulation are summarized in Table 1. The respective bipolar gradients for each 129 Xe diffusion time were optimized such that similar diffusion gradient amplitudes (G) were implemented at each b value. This ensured that each simulation had a consistent gradient dephasing length and that the resulting diffusion regimes were only dependent upon the respective diffusion time or 1D free diffusion length to the SEM and 129 Xe-based CM expressions, and derived diffusion model parameters were benchmarked against the respective MLI of each acinar airspace mesh.

| Validation of in vivo diffusion times
A video demonstrating the evolution of the normalized transverse magnetization during a 129 Xe (Δ = 8.5 ms) diffusion simulation for each b value in the healthy acinar airspace mesh can be found in Supporting Information Video S1.  Figure 3; similar distributions of values were also observed for L Alv and Lm. In the healthy mesh, smaller acinar airspace dimensions can be observed at the periphery, whereas larger dimensions are found near the center of the mesh corresponding to larger acinar airways. Conversely, the distributions of acinar dimensions in the IPF acinar airspace mesh are more heterogeneous and elevated when compared to the healthy mesh. In both meshes, similar Lm D distributions were observed for 3 He and 129 Xe.  (Table 4). Significant correlations were also observed for R and L Alv in the healthy airspace model only. A logarithmic regression provided the best fit for the DDC and Lm D data from both acinar airspaces, suggesting a nonlinear relationship between SEM metrics and 129 Xe diffusion times ( Figure 4A). For the CM Lm metric, a linear relationship with 129 Xe diffusion time was observed ( Figure 4B). The best agreement between Lm D and MLI in the healthy acinar airspace mesh was observed at diffusion times between 8 to 10 ms. In contrast, for the IPF mesh the best agreement between Lm D and MLI was demonstrated at a 16 ms 129 Xe diffusion time. A large mismatch between Lm and MLI was   29 The simulated Lm D from the healthy acinar mesh was larger than those found in previous in vivo studies of healthy volunteers even with the same DDC and α because the integrals in Equations [S5] and [S8] now have an upper limit of infinity instead of D 0 and L 1D , respectively. The 3 He and 129 Xe diffusion metrics for the IPF mesh were smaller than those reported for in vivo patients with IPF. 22,29 However, these reported IPF lung values are global averages and are likely to be different to those derived from a single acinar airspace region selected from a single ex vivo IPF lung sample. The smaller α values found for the IPF mesh, when compared to the healthy mesh, are characteristic of the increased heterogeneity of IPF acinar airspaces. The increased heterogeneity and elevated IPF Lm D values match the results observed in IPF patients with in vivo 3 He DWI 22 and are indicative of the microstructural acinar changes related to fibrotic disease. The global 3 He and 129 Xe Lm D value in the healthy mesh at the in vivo diffusion times were in excellent agreement with the MLI of the healthy acinar mesh. The underestimation of IPF Lm D values with MLI is comparable to the bias observed previously with histological validation of 3 He Lm. 13 The larger mismatch observed between Lm D and MLI in the IPF geometry in comparison to the healthy geometry could be attributed to the larger percentage of IPF intercept lengths ( Figure 2B), which are greater than the respective L 1D derived from the 3 He (L 1D = 530 µm) and 129 Xe (L 1D = 488 µm) FE simulations, respectively. In a given diffusion experiment, gas atoms will experience D 0 in length scales far greater than L 1D . Therefore, in acinar airspace dimensions that are far at each mesh node for each respective FE simulation. The similar shapes of the p (D) and the DDC distribution confirms that the SEM p (D) does indeed reflect the underlying intravoxel diffusivities. It is important to note that the distributions in Figure 5 are representative of intravoxel distributions of diffusivity (DDC), and as such they are different to histograms of ADC or DDC values averaged across numerous voxels from images of the whole lungs typically reported in the literature. In contrast to the SEM, the CM acinar dimension metrics of L Alv and Lm were both much smaller than the healthy and IPF meshes' MLI. The mismatch of ~100 µm between simulated 3 He and 129 Xe Lm and MLI is greater than the average ~20 µm bias observed between 3 He Lm and MLI in histological validation of the CM. 13 This difference could perhaps be associated with sample bias of histological tissue samples when compared to whole lung 3 He DWI measurements or from lung inflation differences due to shrinkage of lung tissue between 3 He DWI measurements and the subsequent fixation process for histological measurements. These potential inaccuracies are absent in these FE simulations due to the calculation of MLI across the entire acinar airspace model that is compared to simulated hyperpolarised gas DWI in the same geometry.

| Operational range of theoretical diffusion models
The small difference between 3 He and 129 Xe Lm D in the healthy mesh further supports the implementation of 129 Xe Δ = 8.5 ms for in vivo 129 Xe DWI. 16 The larger discrepancy between healthy and IPF meshes could be explained by two factors. First, the 129 Xe Δ = 8.5 ms was optimized by measurements from a single healthy subject 16 ; as such, in patients with more heterogeneous distributions of acinar length scales, perhaps a different optimal diffusion time exists. The results in Table 3 suggest that for the IPF mesh the optimal 129 Xe diffusion time is 10 ms. Second, additional effects on diffusion signal from microscopic background susceptibility gradients 39 are not accounted for in these FE simulations.

| Operational range of theoretical diffusion models
The second set of validation experiments for the SEM and CM were simulations of 129 Xe diffusion times between 5 and 20 ms within the healthy and IPF meshes. This range encompasses the optimal 129 Xe Δ = 5 ms for the 129 Xe CM expressions 14 and 129 Xe Δ = 20 ms that has a L 1D corresponding to approximately the mean length of a healthy acinar duct (730 µm). 40 This mean acinar duct length is of particular significance to the CM geometrical model, where if an in vivo experiment's L 1D exceeds this length, the underlying assumption that the majority of hyperpolarized gas atoms are contained within the same acinar unit in the diffusion time is no longer correct, and the assumption of anisotropic diffusion is thus no longer valid.
Significant correlations of 129 Xe diffusion metrics from both the SEM and CM with 129 Xe diffusion time were observed, demonstrating the dependency of diffusion modelderived metrics on experimental diffusion time. The diffusion time dependency reflects the L 1D of the experiment, assuming a constant D 0 . L 1D or diffusion time is a dependent variable in both the SEM 15,16 and CM 13,14 diffusion model expressions. Therefore, it is not surprising that the majority of diffusion model metrics demonstrated a correlation with experiment diffusion time or L 1D .
The alpha heterogeneity index (α) from the SEM was the only diffusion model metric not significantly correlated with diffusion time. α represents the deviation of the diffusion signal decay from a mono-exponential decay due to different acinar structures of varying sizes and orientations that lead to different apparent diffusion rates and has been demonstrated to be independent of experimental conditions such as lung inflation. 41 Therefore, in these 129 Xe diffusion time simulations where the underlying acinar airspace structure is constant, the α value for each respective acinar airspace mesh is relatively similar across all diffusion times. The small differences in α for the range of 129 Xe diffusion times likely reflect small changes to diffusion signal behavior related to differences in L 1D .
Nonlinear logarithmic relationships were observed between some of the 129 Xe SEM metrics and 129 Xe diffusion time. The logarithmic decay of DDC is similar to that observed with 3 He and 129 Xe ADC in healthy volunteers. 16,42 For SEM Lm D , the positive logarithmic relationship suggests that with increasing diffusion time there is an asymptotic plateauing of Lm D . A linear correlation between 129 Xe diffusion time and Lm D was observed previously in vivo in one healthy volunteer. 16 This difference could be attributed to the inclusion of more diffusion times in these FE simulations, especially those greater than 129 Xe Δ = 10 ms that have not yet been explored experimentally in vivo either due to SNR or breath-hold limitations.
A linear regression fit best described the significant correlation between CM Lm and 129 Xe diffusion time. Across both acinar airspace models, a small increase in Lm can be observed with increasing diffusion time ( Figure 4B), which could be related to the relative independence of some underlying phenomenological expressions of the CM to diffusion time. 14 Larger differences between the CM Lm and MLI, when compared to SEM Lm D across this range of diffusion times, are likely related to the small optimal diffusion time range of Δ = 4 to 6 ms for the 129 Xe-based CM expressions. 14 Furthermore, the large differences between CM Lm and MLI in the IPF mesh could also be associated with the underlying CM geometrical model, which assumes the interstitial space between alveolus units is < 10µm and negligible in the derivation of Lm. 13 Therefore, the CM expressions are not necessarily valid for the thickened (fibrosed) interstitium in IPF disease and may be more relevant in chronic obstructive pulmonary disease lungs .
The best agreement between Lm D and MLI in the healthy and IPF acinar airspace meshes was observed at diffusion times of 9 ms and 16 ms, respectively. This difference can be attributed to the differences in underlying length scales of each acinar airspace model. If we define a confidence interval of Lm D values within ±10% of the MLI (Figure 4A), the operational ranges of diffusion time for the healthy and IFP meshes are defined as between 7 to 13 ms, and 13 to 20 ms, respectively. Although this may suggest that in vivo acquisitions at longer diffusion times may provide better direct correspondence with MLI, additional effects related to longer diffusion times such as increased T 2 * decay and longer acquisition times, which in turn meaning longer breath-holds, prevent this from being applied routinely for in vivo imaging. The currently implemented in vivo 129 Xe Δ = 8.5 ms allows for the 3D whole lung acquisitions in a single breath-hold. 16 Furthermore, at this diffusion time we observe excellent agreement with MLI in healthy acinar length scales, and in larger length scales systematic differences between healthy and diseased acinar airspaces are still detected.
The differences in diffusion time operational ranges for the healthy and IPF lung simulations can be attributed to inherent differences between the apparent length scale (Lm D ) from diffusion models and MLI from histology. This is illustrated in Figure 6 for the probability distribution of diffusive length scales, p L D , and MLI histogram of the healthy airspace mesh. Figure 6 represents intravoxel distributions of length scale derived theoretically with the SEM p L D (red) or from histological intercept lengths (blue). The differences in the histogram tails are related to the L 1D constraints of the diffusion experiment where there is a plateauing of L D toward L 1D . The absence of small L D (<150 µm) in the p L D can be attributed to diffusion motional averaging effects in these small airway dimensions (see Figure 3 of Yablonskiy et al 12 ). The combination of these two effects could account for the different diffusion time operational ranges for the two sets of airways. Further FE simulations in a wider range of different airway length scales could be performed in order to derive a mathematical transformation that will allow a derived p L D to be mapped to the underlying airway distribution across a variety of diffusion experimental parameters. This is akin to the approach used to establish CM phenomenological expressions (eg, Equations 3 and 4 in Ref. 43) that describe the relationship between anisotropic diffusion coefficients and cylindrical airway geometry parameters. 14,43

| FE simulations limitations and assumptions
The micro-CT-derived acinar airspace meshes are, to our knowledge, the most realistic airway geometry used to date for the simulation and validation of hyperpolarized gas DWI signal behavior within the lungs. Although these acinar airspace meshes represent single connected acinar airspace geometries approximately the size of a MR voxel, they may not be representative of the acinar airway variation across the whole lung. However, it should be noted that the linear intercept length distribution of the healthy FE model is representative of the larger (14 mm diameter) micro-CT lung core sample from which the healthy FE model was derived (see Supporting Information Figure S1). Future FE simulations could be performed in larger acinar airspace meshes that represent acinar geometry on a lobar or segmental level.
One limitation of the micro-CT MLI is the inherent resolution (16 µm) of the micro-CT imaging. To improve the accuracy of linear intercept length measurements, segmented acinar airspace masks were up-sampled to an isotropic 4 µm resolution. Even with up-sampling, intercept lengths are only accurate to the nearest 4 µm increment, which is substantially larger than the typical submicron resolution of histological section images obtained with light microscopy for MLI calculation. 32 However, the process of sampling intercept length measurements across the entire acinar airspace geometry in this work allows for the direct comparison of histology and diffusion measurements in identical regions of acinar airspace. Furthermore, this eliminates any potential sampling bias that may occur from conventional histological assessment of lung tissue samples used in previous validation studies. 13 The absence of simulated SEM and CM metrics in lung meshes representing emphysema lung disease is a limitation of this work. Future FE simulations in a micro-CT-derived emphysema lung model would be beneficial and would complement the diffusion model validations shown here in healthy and IPF lungs. In addition, the CM diffusion model may be more accurate in an emphysema lung mesh due to the optimization of the CM for evaluating emphysematous alveolar changes. 12,13 Our FE simulations of hyperpolarized gas DWI assume that the change in transverse magnetization is entirely due to diffusion of 3 He or 129 Xe gas atoms during the duration of bipolar trapezoidal waveforms. Therefore, additional effects on in vivo hyperpolarized gas DWI signal behavior such as background susceptibility gradients, RF depletion, T 1 decay, and signal change due to dissolved 129 Xe in the interstitium are not currently accounted for. Typically, with the small flip angles and short TR used for in vivo imaging, the majority of these effects have negligible influence on the hyperpolarized gas DWI signal behavior and diffusion model metrics. However, the presence of background susceptibility gradients due to the susceptibility differences between the lung parenchyma and oxygenated airspaces have been shown to influence in vivo ADC and diffusion model measurements 39 and are also field strength-dependent. 38 The absence of a tissueair susceptibility interface in the FE models means that the simulation results are not a complete mechanistic representation of the signal formation of in vivo hyperpolarized gas DWI. Future FE simulations that incorporate a susceptibility difference at the boundaries of the FE model with a B 0 term could be used to further investigate the effects of background susceptibility gradients on diffusion model-derived metrics.

| CONCLUSION
This work is the first validation of the SEM-derived Lm D and the CM Lm with FE simulations of 3 He and 129 Xe DWI in micro-CT-derived realistic acinar airway geometries representing healthy and IPF lungs. The SEM Lm D demonstrated better agreement with MLI when compared to the CM Lm across each FE simulation and acinar mesh. Excellent agreement (±10% difference) between Lm D and MLI was observed in FE simulations at 3 He (Δ = 1.6 ms) and 129 Xe (Δ = 7 to 13 ms), and 129 Xe (Δ = 13 to 20 ms) for the healthy and IPF acinar meshes, respectively. This further validates previous experimental demonstrations of the use of the SEM for accurate estimation of lung microstructural dimensions and indicates that the SEM is relatively robust across a range of experimental conditions and acinar length scales.