There is a large unmet need for in vivo biomarkers of parenchyma abnormalities that can be acquired safely, serially and non-invasively in patients. This is especially true in younger patients with emphysema related to alpha-1 antitrypsin deficiency and bronchopulmonary dysplasia for whom no biomarkers of disease progression are clinically available. Such biomarkers should allow for longitudinal measurements in patients in whom there are emphysematous findings at a very young age and in whom repeated CT poses a cumulative risk. Other measurements of emphysema severity and progression such as the diffusing capacity of the lung for carbon monoxide (DL_CO), are highly variable over time¹ and while helpful, are not sufficiently sensitive to, nor specific for emphysema in these patients. Hyperpolarized noble-gas diffusion-weighted MRI makes it possible to non-invasively estimate in vivo morphometric parameters of the alveolar ducts.² Current modelling approaches³ may not be appropriate for cases of severe tissue destruction where the geometry of the acinar ducts may not be uniform, nor cylindrical.⁴ We extend a modelling approach previously described⁵ for the evaluation of diffusion-weighted NMR fluid diffusion in porous media. This model was previously used to evaluate ¹²⁹Xe diffusion in glass beads,^{6 19}F diffusion in excised lungs⁷ and simulations of short-time diffusivity of hyperpolarized gases⁸ in emphysema. Using this model, the acinar ducts are considered as spherical single compartments which may be appropriate for evaluating severe emphysema. In this proof-of-concept study we evaluated AATD patients using ³He MRI and this single-compartment model as well as a cylindrical model to estimate gas diffusion, parenchyma surface-to-volume-ratio and mean-linear-intercepts.

Subjects: Six patients with alpha-1 antitrypsin deficiency provided written informed consent to an approved study and underwent spirometry, plethysmography, CT and ³He MRI. Imaging was performed at 3.0 T (MR750, GEHC, Waukesha, WI) using whole-body gradients (5G/cm maximum) and a rigid linear RF coil (Rapid Biomedical, Germany). In a single breath-hold, five interleaved acquisitions (TE = 3 ms, TR = 5 ms, matrix-size = 128x128, number-of-slices = 7; slice-thickness=30mm, and FOV = 40x40cm) with and without diffusion sensitization were acquired for a given line of k-space. The diffusion-sensitizing gradient pulse ramp up/down time = 500 μs, constant time = 460 μs and diffusion time (Δ) = 1.46 ms resulted in slices acquired at 0, 1.6, 3.2, 4.8 and 6.4 s/cm².

Theory: The short-time diffusivity regime assumes that a thin layer of gas molecules near the spherical walls experience restricted diffusion while the remaining molecules diffuse freely. The diffusion time of 1.46ms is likely insufficiently sensitive to longer alveolar length scales (single compartment approximation) as is the case in extremely severe emphysema that accompanies AATD. However, by subtracting the measured apparent diffusion coefficient (ADC) for each b-value from D₀ (where D₀ is the free diffusion coefficient of the gas, D₀ ≈ 0.84cm²/s) transforms the problem into the short-time diffusion regime, where the diffusion is restricted near the walls, and unrestricted within the sphere volume. It follows that:

$$\frac{D_0 - ADC(t)}{D_0} = 1 - \frac{4}{9\sqrt{\pi}}\frac{S}{V}\sqrt{D_0t}$$

where ADC(t) is the two b-value ADC(b) and the smallest diffusion time corresponds to the largest b-value. To generate the diffusion times corresponding to each b-value and fulfil the condition b=const, we assumed that 1.46ms was the longest diffusion time and b=1.6s/cm².

Image Analysis: Mean ADC was calculated for all 4 b-values (b = 1.6, 3.2, 4.8, 6.4 s/cm²). The linear relationship of $$$\frac{D_0 - ADC(t)}{D_0}$$$ and $$$\sqrt{D_0t}$$$ (t = 0.832, 0.94, 1.11, 1.46 ms) was used to generate the slope that approximated S/V. S/V and L_m estimates based on the single compartment model were also corrected using an empirical coefficient so that subtraction of ADC from D₀ would not result in 0 and negative values.

Table 1 shows demographic and morphometry estimates. Figure 1 shows static ventilation, ADC and L_m maps for two representative subjects. Figure 2-A/B shows the cylindrical and single compartment model schematics while Figure 2-C/D shows the cylindrical model relationship for S/V and R and the single compartment model relationship of (D₀-ADC)/D₀ and .We explored two different acinar duct models to explain and estimate acinar dimensions in very severe emphysema as a way to provide sensitive and specific biomarkers of emphysema progression in AATD patients.