Ho-Fung Chan^{1}, Guilhem J. Collier^{1}, and Jim M. Wild^{1}

Lung morphometry parameters
can be derived from multiple b-value hyperpolarized gas diffusion-weighted (DW)-MRI
using the cylinder (CM) and stretched exponential (SEM) models. Mean alveolar
diameter (L_{Alv}) and diffusive length scale (Lm_{D}) are
calculated from the CM and SEM, respectively. This work compares the parameters
L_{Alv} and Lm_{D} derived from a range of subjects with both ^{3}He
and ^{129}Xe DW-MRI. Excellent linear agreement is observed between
the L_{Alv} and Lm_{D} parameters for both gases. This
indicates these parameters are equivalently representative indices of mean
alveolar diameter dimension within the range of experimental conditions considered.

Theoretical models of gas
diffusion have been proposed to derive lung morphometry parameters from the hyperpolarized
gas diffusion-weighted (DW)-MRI signal. The cylinder model (CM) is based upon infinitely long non-connected cylinders, and
has been used to obtain estimates of acinar airway radius (R) and mean chord
length (Lm) from a model of anisotropic diffusion. ^{1,2} The stretched
exponential model (SEM) is a mathematical model of the non-Gaussian diffusion
signal that derives estimates alveolar dimensions (Lm_{D}) within each
voxel from a probability distribution of diffusion length scales. ^{3,4}

Previously, in vivo comparisons
of Lm and Lm_{D} have demonstrated that the two lung morphometry
parameters are related but not identical. ^{5,6} The mean alveolar diameter (L_{Alv})
is an alternative CM parameter that is defined as the chord length of one
alveolus in the CM cylindrical airway geometry. ^{2} This work evaluates and
compares SEM-derived Lm_{D} and CM-derived L_{Alv} from a range
of subjects using ^{3}He and ^{129}Xe DW-MRI.

A
summary of global ^{3}He and ^{129}Xe lung morphometry metrics is provided in Table 1. All metrics for each patient group were
larger than those for healthy subjects reflecting the respective changes to
acinar microstructure related to fibrosis in the IPF patients, and emphysema
for the ex-smokers and COPD patients. A statistically significant linear
correlation (*P*<0.001) between Lm_{D}
and L_{Alv} was observed for both ^{3}He and ^{129}Xe
DW-MRI (Figure 1). The linear regression fit (^{3}He β_{1}=1.00,
^{129}Xe β_{1}=1.05) suggests excellent agreement between the
two parameters for both gases, and Bland-Altman analysis confirmed this with
small mean bias of +1.0% and -2.6% towards Lm_{D} for ^{3}He
and ^{129}Xe, respectively. In the representative L_{Alv} maps from
^{3}He and ^{129}Xe measurements in the same patients (Figure 2),
regions of elevated values appear to qualitatively match those observed in
corresponding Lm_{D} maps. The analogous linear correlation and lung
morphometry maps demonstrates the same microstructural information can be
obtained with both ^{3}He and ^{129}Xe.

In a
previous comparison, ^{3}He Lm_{D} was related to Lm by a
non-linear power relationship; ^{6} however, the results in this comparison
suggests that L_{Alv} is more comparable to Lm_{D} than Lm. The
two distinct relationships observed between Lm_{D} with Lm and L_{Alv}
can be associated with the different sections of the acinar airway geometry
that is measured by each parameter.

In
the CM geometry, eight alveoli units surround the acinar airway such that the
chord length of an alveolus matches typical alveolar diameter measurements from
histology. ^{2} While in the SEM, Lm_{D} represents the average distance that ^{3}He
or ^{129}Xe gas atoms diffuse within the acinar airspace. The maximum
Lm_{D} is constrained by the theoretical free diffusion length of the
respective DW-MRI experiments (~500 µm). According to histology, the mean
alveolar diameter in healthy adult lungs is approximately 200-250 µm. ^{8} Therefore,
in these experiments, gas atoms are predominantly restricted by the alveolar
geometry and as such Lm_{D}, like L_{Alv}, is reflective of
mean alveolar diameter dimensions.

In contrast, the CM-derived Lm is
calculated through an inferred relationship between the volume (alveolus and
alveolar duct) and surface area of a single alveolus unit. Therefore, the inclusion of the alveolar duct volume in the calculation might allows Lm
values that are beyond the theoretical free diffusion lengths of the diffusion
experiments, and probably accounts for the mismatch in Lm_{D} and Lm
observed previously. ^{5,6}

1. Yablonskiy, D. A., et al. (2002). Proc Natl Acad Sci USA 99(5): 3111-3116.

2. Yablonskiy, D. A., et al. (2009). J Appl Physiol (1985) 107(4): 1258-1265.

3. Parra-Robles, J., et al. (2014). Proc ISMRM:3529

4. Chan, H.-F., et al. (2017). Magn Reson Med 77(5): 1916-1925.

5. Ouriadov, A., et al. (2017) Magn Reson Med. doi:10.1002/mrm.26642.

6. Chan, H.-F., et al. (2017). Proc ISMRM:876

7. Chan, H.-F., et al. (2017). Magn Reson Med. doi:10.1002/mrm.26960.

8. Weibel, E. R. (1963). Morphometry of the human lung, Springer-Verlag.

Table 1: Summary of global ^{3}He
and ^{129}Xe DW-MRI lung morphometry metrics derived from the cylinder
model and stretched exponential model.

Figure
1: Excellent linear agreement is observed between stretched exponential
model derived mean diffusive length scale (Lm_{D}) and cylinder model derived
mean alveolar diameter (L_{Alv}) for both ^{3}He and ^{129}Xe
in all subjects.

Figure
2: Representative ^{3}He and ^{129}Xe
maps of SEM-derived Lm_{D} and CM-derived L_{Alv} for each
patient group. Maps of Lm_{D} and L_{Alv} are similar and also
comparable with both hyperpolarized gases.