³He lung morphometry technique: accuracy analysis and pulse sequence optimization

Abstract

The (3)He lung morphometry technique (Yablonskiy et al., JAP, 2009), based on MRI measurements of hyperpolarized gas diffusion in lung airspaces, provides unique information on the lung microstructure at the alveolar level. 3D tomographic images of standard morphological parameters (mean airspace chord length, lung parenchyma surface-to-volume ratio, and the number of alveoli per unit lung volume) can be created from a rather short (several seconds) MRI scan. These parameters are most commonly used to characterize lung morphometry but were not previously available from in vivo studies. A background of the (3)He lung morphometry technique is based on a previously proposed model of lung acinar airways, treated as cylindrical passages of external radius R covered by alveolar sleeves of depth h, and on a theory of gas diffusion in these airways. The initial works approximated the acinar airways as very long cylinders, all with the same R and h. The present work aims at analyzing effects of realistic acinar airway structures, incorporating airway branching, physiological airway lengths, a physiological ratio of airway ducts and sacs, and distributions of R and h. By means of Monte-Carlo computer simulations, we demonstrate that our technique allows rather accurate measurements of geometrical and morphological parameters of acinar airways. In particular, the accuracy of determining one of the most important physiological parameter of lung parenchyma - surface-to-volume ratio - does not exceed several percent. Second, we analyze the effect of the susceptibility induced inhomogeneous magnetic field on the parameter estimate and demonstrate that this effect is rather negligible at B(0) ≤ 3T and becomes substantial only at higher B(0) Third, we theoretically derive an optimal choice of MR pulse sequence parameters, which should be used to acquire a series of diffusion-attenuated MR signals, allowing a substantial decrease in the acquisition time and improvement in accuracy of the results. It is demonstrated that the optimal choice represents three not equidistant b-values: b(1)=0, b(2)∼2 s/cm(2), b(3)∼8 s/cm(2).

Figure 1

Left panel: schematic structure of two levels of acinar airways. Open spheres represent alveoli forming an alveolar sleeve around each airway. Each acinar airway can be considered geometrically as a cylindrical object consisting of a tube embedded in the alveolar sleeve. Middle and right panels: two cross sections of the acinar airway model used in our simulations, with two main parameters: external radius R and depth of alveolar sleeve h. The other parameters, the internal radius r and the alveolar length L, are: r = R − h, L = 2R sinπ / 8 = 0.765 R [6].

Figure 2

Two airway configurations used in computer simulations. The internal alveolar structure of the airways is not shown and the aspect ratio is changed for better view of the structures. The highlighted airway (grey shading) at left is an airway duct and at right an airway sac.

Figure 3

Examples of diffusion attenuated MR signals from a random distribution of acinar airways: symbols - simulated signals; curves - signals calculated using Eq. (1) with D_L and D_T defined by Eqs. (13), (14), (16), (17).

Figure 4

(a) The dependence of the relative uncertainty estimate of the surface-to-volume ratio, ε = δ (S / V) / (S / V), on b₂ in the 3b experiment for R = 300 μm, r = 140 μm, and SNR = 100; b₁ = 2 s/cm². (b) The dependence of ε on the internal radius r at R = 300 μm, SNR = 100, b₁ = 2 s/cm², b₂ = 10 s/cm². The dashed curves in (a) and (b) corresponds to ε in the 6b experiment with equidistant b-values (0, b₂ / 5, 2b₂ / 5, …, b₂).