Quantification of lung microstructure with hyperpolarized ³He diffusion MRI

Abstract

The structure and integrity of pulmonary acinar airways and their changes in different diseases are of great importance and interest to a broad range of physiologists and clinicians. The introduction of hyperpolarized gases has opened a door to in vivo studies of lungs with MRI. In this study we demonstrate that MRI-based measurements of hyperpolarized ³He diffusivity in human lungs yield quantitative information on the value and spatial distribution of lung parenchyma surface-to-volume ratio, number of alveoli per unit lung volume, mean linear intercept, and acinar airway radii—parameters that have been used by lung physiologists for decades and are accepted as gold standards for quantifying emphysema. We validated our MRI-based method in six human lung specimens with different levels of emphysema against direct unbiased stereological measurements. We demonstrate for the first time MRI images of these lung microgeometric parameters in healthy lungs and lungs with different levels of emphysema (mild, moderate, and severe). Our data suggest that decreases in lung surface area per volume at the initial stages of emphysema are due to dramatic decreases in the depth of the alveolar sleeves covering the alveolar ducts and sacs, implying dramatic decreases in the lung's gas exchange capacity. Our novel methods are sufficiently sensitive to allow early detection and diagnosis of emphysema, providing an opportunity to improve patient treatment outcomes, and have the potential to provide safe and noninvasive in vivo biomarkers for monitoring drug efficacy in clinical trials.

the efficiency of oxygen delivery through the lung air spaces to the blood vessel network occupying alveolar walls depends mostly on the structure, integrity, and functioning of pulmonary acinar airways. The morphometry of the pulmonary acinus has been studied in numerous publications (see for example Refs. 8, 16, 19, 22, 26, 27, 33, 36, 42, 45, 46). These studies provided invaluable information on lung microstructure that is the basis of the current knowledge on lung structure and function. Such geometric parameters as mean air space chord length (Lm), lung parenchyma surface-to-volume ratio (S/V) and number of alveoli per unit lung volume (N_a) are most commonly used to characterize lung morphometry. Although unbiased (model free) lung stereology has been in use for more than a half-century and is considered a gold standard (see recent overviews in Refs. 32, 48 and discussions in Refs. 5, 9, 15, 20, 24, 29, 34, 38), its clinical utility is limited by its inherent invasive nature. The introduction of hyperpolarized gases (17) has opened the door to applications for which gaseous agents are uniquely suited, such as lung MRI (1). One of the important directions in hyperpolarized gas imaging is based on MRI diffusion measurements of hyperpolarized ³He gas introduced in the lung air spaces during inhalation. Already initial publications (6, 40, 41, 52) have demonstrated that the apparent diffusion coefficient (ADC) of hyperpolarized ³He gas in the lungs dramatically increases in emphysema, suggesting a large potential as a diagnostic tool for clinical applications.

In this study we demonstrate that MRI-based measurements of hyperpolarized ³He diffusivity in human lungs allow quantitative measurements of lung air spaces at the alveolar level. From a single MRI scan, our method provides quantitative values and spatial distributions of the same physiological parameters as are measured by means of “standard” stereology (Lm, S/V, N_a), as well as some other parameters characterizing lung microstructure (average radii of alveolar sacs and ducts, as well as the depth of their alveolar sleeves). These measurements have high statistical power because the MR signal in each imaging voxel is averaged over hundreds (or even thousands) of airways. Also, knowledge of the special distribution of the parameters is especially important for diseased lungs because of the well-known spatial variability of disease progression. Because of the in vivo nature of our measurements, they are obtained at normal physiological conditions and are free from possible artifacts of sample deformation during preparation for standard stereology. Our measurements are safe and well-tolerated (23) and can be repeated in vivo on a regular basis to serve as a tool for research, clinical, and drug development studies.

We validate our MRI-based measurements against direct invasive morphometric measurements, the current gold standard. We demonstrate for the first time images of commonly used microgeometric parameters in healthy lungs and lungs with different levels of emphysema (mild, moderate, and severe). Our data also suggest that the decrease in lung surface area per volume in the initial stages of emphysema is due to decreases in the depth of the alveolar sleeves that cover alveolar ducts and sacs.

MATERIALS AND METHODS

All studies were approved by the local Institutional Review Board. Responsible family members of the trauma victim and the two patients with lung cancer gave informed consent to the use of the lungs for medical research.

Theoretical background: lung model.

Because gas diffusion in lungs is strongly restricted by alveoli, especially at the acinar level, diffusion measurements can provide important insights on lung microstructure. To make the information encoded in diffusion-attenuated MRI signals quantitative, the relationships between lung microstructural parameters and signal attenuation are required. Our approach to this problem is based on a model of lung geometric structure in which lung acinar airways (alveolar ducts and sacs, where 90–95% of gas resides) are treated as a network of cylindrical passages covered with alveolar sleeves (Fig. 1). In humans, the intra-acinar airways branch dichotomously over about nine generations (16, 26). The main geometric parameters characterizing these airways are the internal acinar airway radius r and the outer radius R (which includes the sleeve of alveoli) (16, 26). Both of these parameters vary depending on the position and branching level of the acinar airway tree. However, the variation is rather small: the distribution width is ∼60 μm for R and ∼30 μm for r, with mean values of 350 μm and 160 μm, respectively (16). The “narrowness” of the distributions of parameters R and r creates a solid basis for characterizing acinar airways by their mean geometric parameters, denoted simply as R and r.

Fig. 1.

Schematic structure of an acinar airway with 8 alveoli distributed along the annular ring (8-alveolar model). Each airway (duct or sac) can be considered geometrically as a cylindrical object consisting of an alveolar sleeve with alveoli opening toward the internal cylindrical air passage. The diagram defines inner (r) and outer (R) airway radii (as in Fig. 1 in Ref. 16) and effective alveolar diameter (L). We assume that the alveolar size L along the airway is the same as in cross section: L = 2R sin(π/8). h, Alveolar sleeve depth.

Another important parameter in Fig. 1 is the “effective alveolar diameter” L, which is not specified in Ref. 16. To estimate this parameter we first note that the measurements of parameters R and r in Ref. 16 were made at lung inflation of ∼0.9 total lung capacity (TLC). Usually in the literature, lung parameters are quoted at 0.6 TLC. Making the realistic assumption that lung volume scales as the cube of linear dimensions, we can estimate that at 0.6 TLC the mean values of parameters R and r should be R = 300 μm and r = 140 μm. The parameter L roughly corresponds to the alveolar diameter. To establish a relationship between L and airway radius R we need to further specify the distribution of alveoli in the acinar airways. Numerous models have been proposed previously (see for example Fig. 41 in Ref. 46 and discussion therein). Here we adopt a model in which each alveolus occupies one-eighth of the annular ring [eight-alveolar model (18)], as shown in Fig. 1. In this model we also assume that the alveolar size (effective diameter) is the same in the directions along the airway and along the circumference. Hence, the parameter L should be equal to the length of the cord corresponding to one-eighth of the annular ring, L = 2R sin(π/8) = 0.765 R. For R = 300 μm this gives L = 230 μm, consistent with literature values for average alveolar diameter ranging from 200 to 260 μm (27, 33, 42, 46). Models that instead contain four or six alveoli per annular ring would correspond to bigger alveolar diameters (472 and 314 μm, respectively) and do not match the above-mentioned experimental data. Hence, in all further considerations we adopt the eight-alveolar model. Using the constraint L = 0.765 R reduces the number of geometric parameters in our model to only two: R and the depth of alveolar sleeve h = R − r.

Using these parameters, we can estimate the alveolar surface area S_a, lung volume per alveolus V_a, and alveolar number density N_a—the number of alveoli per unit lung volume based on geometry:

$$S_{\text{a}}=\frac{\text{π}}{\text{4}}R·L+\frac{\text{π}}{\text{4}}h·\left(2R-h\right)+2h·L;{\text{V}}_{\text{a}}=\frac{\text{π}}{\text{8}}{R}^{2}L;L=2R\sin \frac{\text{π}}{\text{8}};N_{\text{a}}=\frac{1}{{\text{V}}_{\text{a}}}$$

Note that the volume V_a comprises both the volume of alveolar duct, π(R − h)²L/8, and the volume of the alveolus proper, π[R² − (R − h)²]L/8. Using Eqs. 1 that relate airway geometric parameters R and h to alveoli surface area and volume, and the well-known relationship between mean linear intercept and surface-to-volume ratio (47), we can estimate the mean chord length Lmml:

$$S/V=S_{\text{a}}/V_{\text{a}}=4/\text{Lm}$$

We have conducted rigorous computer Monte-Carlo simulations (not shown) to confirm Eq. 2 for our model in Fig. 1. We also note that the thickness of alveolar walls, <10 μm, is much smaller than the distance between these walls and can be neglected in the calculation of mean chord length Lm, basically equating it with mean linear intercept. We will not distinguish between these two parameters in our approach.

Lung preparation.

Hyperpolarized ³He MR diffusion imaging data and histology were obtained from six human lung specimens. Two right “normal lungs” (N1 and N2) were obtained from male organ donors with no known lung disease whose lungs were not matched to a transplant recipient. One donor was a 22-year-old who smoked an unknown amount for 2 yr and the other a 21-year-old with a 1 pack·yr smoking history. Two right upper lobes of lungs with mild (M1) and moderate (M2) emphysema were removed from patients undergoing treatment for peripheral lung cancers smaller than 5 cm. One patient was a 69-year-old man [81 pack·yr smoking history, forced expiratory volume in 1 s (FEV₁) = 95% of predicted value, FEV₁/forced vital capacity (FVC) = 0.70], and the other patient was a 67-year-old woman (45 pack·yr smoking history, FEV₁ = 92% of predicted value, FEV₁/FVC = 0.62). Finally, two left lungs with severe emphysema (S1 and S2) were obtained from patients transplanted because of severe chronic obstructive pulmonary disease, one a 61-year-old man (90 pack·yr smoking history, FEV₁ = 18% of predicted value, FEV₁/FVC = 0.30) and the other a 56-year-old woman (35 pack·yr smoking history, FEV₁ = 30% of the predicted value, FEV₁/FVC = 0.25).

The lung specimens were prepared for imaging by attaching tubing to the bronchial stump to inflate the specimen and sealing any air leaks (7, 50). ³He gas was hyperpolarized by the spin-exchange technique (44) by using a lab-built polarizer or a commercial polarizer (General Electric Medical) to achieve polarization levels of ∼40%. To avoid the depolarizing effects of oxygen that would diminish the ³He MR signal (39), and thus to extend the utility of a single ³He bolus, the lungs were purged of oxygen with pure nitrogen gas immediately before imaging. For imaging, the specimens were inflated with a 1-liter syringe containing a mixture of ∼40% hyperpolarized ³He and 60% nitrogen to a pressure of 10–12 cmH₂O; the injected gas was gently withdrawn and reinjected to the same pressure two or three times to facilitate mixing throughout all of the air spaces, with final injection immediately before the MRI scan was started. For ³He gas diluted in nitrogen, the free diffusion coefficient D₀ = 0.88 cm²/s.

³He diffusion MRI for lung morphometry.

³He gas diffusion MRI measures the Brownian displacement of ³He atoms. The alveolar walls, as well as the walls of alveolar ducts, sacs, and respiratory bronchioles, serve as obstacles to the paths of diffusing ³He atoms and reduce their diffusivity. Enlargement of the air spaces distal to the terminal bronchioles with destruction of their walls, the defining characteristics of emphysema, reduces these obstacles to the motion of gas atoms and increases the diffusivity. Hence, the measured diffusivity is a function of the lung structure at the alveolar level. The quantitative theory of ³He gas diffusion in lung airways, described in the appendix, creates the basis for evaluation of lung microgeometric parameters from diffusion MRI measurements.

MR imaging was performed on a 1.5-T MRI whole body Magnetom Vision (Siemens, Erlanger, Germany) using a lab-built, transmit-receive, single-turn solenoid coil tuned to the ³He resonance frequency of 48.47 MHz. To collect diffusion MRI data we used a two-dimensional gradient echo multislice pulse sequence with embedded bipolar diffusion-sensitizing gradients (see details in Ref. 52) with 9 b values of 0, 0.95, 1.9, 2.85, 3.8, 4.75, 5.7, 6.65 and 7.6 s/cm², length of each lobe δ = 1.6 ms, rise time τ = 0.5 ms, and no gap between lobes (Δ = δ); repetition time (TR) = 11 ms, echo time (TE) = 7.2 ms. A typical signal-to-noise ratio (SNR) in our measurements is ∼100. The direction of the diffusion-sensitizing gradients is chosen to be perpendicular to the trachea. Data were collected in an interleaved centric-reordered manner, collecting the same line in k-space for all nine b-value images before stepping to the next line, ensuring reduced sensitivity to motion, signal decay due to longitudinal relaxation time (T1) effects, and radio frequency (RF) consumption during acquisition. Residual transverse magnetization before the next RF excitation was destroyed by crusher gradients and RF spoiling. Imaging parameters were 64 × 64 matrix, 35-cm field of view (5.5-mm × 5.5-mm pixel dimensions), and 10-mm slice thickness, no interslice gap; the number of slices was selected based on the lung volume. Each of the 64 lines in k-space uses the same RF excitation pulse with ∼3.5° flip angle.

Fitting Eqs. A1–A5 to multi-b measurements of the ³He diffusion-attenuated MRI signal on a voxel-by-voxel basis allows generation of parametric maps for alveolar depth h and airway radii R. Using Eqs. A4 and A5 we can then generate maps of ADC (52):

$$\text{ADC}=\frac{\text{1}}{\text{3}}{D}_{\text{LO}}+\frac{2}{3}{D}_{\text{TO}}$$

where D_L0 and D_T0 are diffusion coefficients of ³He gas along (longitudinal) and perpendicular to (transverse) the airways directions. Using Eqs. 1 and 2 we can also generate maps of Lm, S/V, and N_a. Lm estimated from ³He measurements is then compared with Lm obtained from direct measurements in tissue samples.

Lung fixation and tissue sampling.

After helium imaging, the lungs were fixed with heated formalin vapor by a method based on previously reported techniques (28, 51). In brief, each lung or lobe was ventilated under positive pressure of 12–20 cmH₂O with vapor from a 37% formalin solution heated to 46°C for 4–10 h with the use of a diaphragm pump with an electronically controlled circuit that provided a brief exhalation (<1 s) every 6–8 s. This process both fixed the samples and dehydrated the tissue. Shrinkage of the vapor-fixed tissue was minimal (<5%). While the effect of any shrinkage due to formalin on the final volume of the fixed lung is uncertain, we have found that there is very close correspondence between ADC measurements obtained before and after fixation with this method (13). While we did not assess the reason that shrinkage was less than in other studies, we suspect it may be related to the method of lung fixation with concentrated (37%) heated formalin vapor. This vapor is much more formaldehyde than water, and so likely dehydrates the tissue much more than formalin fixation. Lungs fixed in this manner are thus much lighter and dryer than when fixed by distending them with liquid formalin, and they do not deform after cutting. This suggests that ventilation with heated formalin vapor results in a fixed specimen that has already been largely dehydrated. Since shrinkage by subsequent processing of the fixed tissue normally is largely due to the removal of tissue water, a reduced amount of tissue water in heated vapor-fixed lungs may explain the minimal shrinkage we observed. Histological samples for morphometry were obtained by cutting the inflation-fixed specimens into 1- to 2-cm-thick transverse slices. Twenty tissue blocks per resected lobe and forty per whole lung were obtained from these slices in a random manner (avoiding any tumor tissue) and embedded in paraffin. Such a sampling approach is similar to those used in other imaging-pathology correlation studies of emphysema (see for example Refs. 8, 12). Histological slides of 3-μm thickness were prepared and stained with hematoxylin and eosin.

Quantitative histology: direct measurements.

Emphysema was quantified on the histological slides by means of the mean linear intercept (Lm), which is the mean length between intersections of a test line with the septa separating air spaces. To make the measurements, five random fields per slide were digitally photographed at ×4 magnification. A computer program (Image Pro Plus, Media Cybernetics) was used to overlay a grid of parallel lines on each field, automatically count the number of intersections between lines and air space walls, and divide the total length of the lines by the number of intersections, to obtain the Lm for each field. For fields comprised of pure air space (∼2% of the total number of fields), the diameter of the field (1.9 mm) was used as the Lm value. The Lm values for the five fields were averaged to obtain a single value for each histological sample. Note that the Lm value obtained by this method is different from the mean air space chord length because of the alveolar walls' finite thickness. However, this difference is practically negligible in lungs without fibrosis, as used here.

RESULTS AND DISCUSSION

Examples of parametric maps obtained from a normal lung and two lungs with different stages of emphysema are shown in Fig. 2 and demonstrate substantial differences between normal and emphysematous lungs. We note that the parametric maps of ADC and the parameters characterizing lung microstructure (R, h, Lm, N_a, and S/V) are very homogeneous in normal lungs, while the maps of these parameters in lungs with emphysema not only are different in value but, perhaps more importantly, demonstrate substantial heterogeneity that grows with emphysema progression. In our experiments, the averaged uncertainties in the estimates of the main geometric parameters are 30 μm, 20 μm, and 60 μm for R, and 30 μm, 20 μm, and 50 μm for h, for cases of normal lungs and lungs with mild and severe emphysema, respectively. A substantial increase of the uncertainty in the case of severe emphysema resulted from the significant decrease in the ratio h/R. Note also that in the latter case, our model of acinar airways becomes invalid because of significant destruction of airways. In this case, R and h found from Eqs. A3–A5 can only be considered as apparent values of these parameters.

Fig. 2.

Examples of the parameter maps obtained from normal lung (N2) and lungs with different stages of emphysema [mild (M1) and severe (S1)]. The long dimension of the lung in each of the axial images is ∼20 cm. ADC, apparent diffusion coefficient (cm²/s); Lm, mean linear intercept (mm), R, acinar airway radius (mm); h, alveolar depth (mm); N_a, alveolar density (mm⁻³); S/V, surface-to-volume ratio (cm⁻¹).

The variation of ADC, anisotropic diffusion coefficients (D_L0 and D_T0 from Eqs. A3–A5 in the appendix), and acinar airway geometric parameters with histological emphysema severity is shown in Fig. 3. Figure 3A demonstrates that the longitudinal diffusivity D_L0 grows rapidly at initial stages of emphysema and approaches the “free” limit (∼0.88 cm²/s) for severe cases. The transverse diffusivity D_T0 also substantially increases with emphysema progression. Such behavior is the result of enlarged radius R and reduced alveolar sleeve depth h with emphysema progression, as seen in Fig. 3B.

Fig. 3.

Summary of data obtained for 6 lung specimens. A: ADC and ³He gas diffusion coefficients along (D_L0) and perpendicular to (D_T0) airway direction. B: R and h. C: S/V. D: N_a. Green markers, 2 control healthy lungs; orange markers, 2 lungs with mild emphysema; red markers, 2 lungs with severe emphysema. Each data point is a median calculated across all imaging voxels for a given lung specimen. Horizontal axis is the mean Lm obtained from direct histological measurements on the same lungs.

This destruction of the septa separating alveoli belonging to the same airway leads to lessening of the restrictions to ³He gas diffusion along airways, practically removing them in severe emphysema cases. Figure 3B demonstrates that the major decrease of alveolar depth occurs already at the initial stages of emphysema—between normal and mild stages. At the same time, the airway radius R grows substantially with emphysema progression, reflecting tissue dilation and alveolar destruction and coalescence. The mechanism of “dilation of alveolar ducts with retraction of alveolar walls” was first suggested decades ago to describe the microscopic appearance of emphysema in human lungs (18) and was later confirmed in elastase-induced emphysema in rodents (21, 30). More recent studies (11) also demonstrated shortening of alveolar walls and effacement of interalveolar septa. Our studies observe this phenomenon by a noninvasive technique for the first time and quantify such changes with emphysema progression. It should be noted that the depth of the alveolar sleeve can also be affected by the alterations in the amount of surfactant that regulates alveolar surface tension. Such a phenomenon has been reported in literature discussing alveolar micromechanical properties (see, e.g., Refs. 2–4, 14, 49). A recent study (31) also suggested that a decrease in alveolar sleeve depth could be the result of inflammation and increased surface tension due to surfactant inactivation. Our imaging technique offers a unique opportunity to study these phenomena in vivo.

Our estimates of S/V from diffusion MRI shown in Fig. 3C can be compared with recent morphometric measurements by Coxson et al. (8) obtained from excised lung specimens. These authors found that S/V for control human subjects is 256 ± 24 cm²/ml, for subjects with mild emphysema 165 ± 23 cm²/ml, and for severe emphysema 43 ± 6 cm²/ml (numbers represent mean and intersubject SD). Our measurements (S/V ∼200–240 cm²/ml for healthy lungs, ∼100–140 cm²/ml for subjects with mild emphysema, and ∼50–55 cm²/ml for the case of severe emphysema) are in good agreement with these results.

Recent measurements of N_a with a new morphometric approach developed by Ochs and colleagues (33) in six healthy human lungs found that the average N_a varies between 132 and 177 per mm³, in agreement with our diffusion MR-based measurements in two healthy lung specimens, −120 and 146 per mm³. In addition to the above-cited measurements in healthy lungs, our data in Fig. 3D demonstrate changes in the number density of alveoli with emphysema progression: N_a decreases to ∼60 per mm³ in mild emphysema and even further to ∼10 per mm³ in lungs with severe emphysema. Such decreases in alveolar density are expected because of lung dilation and alveolar coalescence.

While previous animal (25, 35) and human (50) studies demonstrated correlation between ADC and Lm, the linearity of this correlation is not always expected since the increase of ADC with emphysema progression and alveolar size increase is not linear. Indeed, when alveolar size increases to approximately the level of the characteristic diffusion length L₂ = 4D₀Δ, restrictions to diffusion practically disappear and the ADC approaches its value in free space. Such a nonlinear relationship between Lm and ADC can be noted in Fig. 3A. Also, in addition to the dependence of ADC on lung microstructure, ADC values determined by standard MRI techniques substantially depend on the parameters of the MRI pulse sequence, such as diffusion time and the strength and the profile of the diffusion gradients used in the measurements (see for example Refs. 10, 52). ADC values also depend on the concentration of the ³He gas used for lung inflation—an especially important fact in animal studies, where pure ³He gas is commonly used. All these issues contribute to the subjective bias in estimation of ADC and attempts to use it for evaluation of lung tissue structure. In contrast, our approach is inherently free from such problems since our model includes the above-mentioned pulse-sequence parameters and helium gas mixture (D₀) as input parameters in the evaluation procedure that calculates lung geometric parameters.

Comparison between direct and ³He-based measurements of Lm is shown in Fig. 4. Figure 4 demonstrates a rather good agreement between ³He MRI and direct Lm measurements (correlation coefficient R² = 0.985). The small differences could be attributed to differences in the levels of lung inflation during the MRI experiment and stereological measurements. Also, the MRI experiment provides complete tissue sampling since the data are collected from thousands of voxels compared with very few regions (20–40) from histological cores. Another possible source of discrepancy may stem from a deficiency of our theoretical model in case of lungs with severe emphysema, where effects of interairway septa destruction should be taken into consideration. Nevertheless, the differences between direct Lm measurements and measurements with ³He MRI are much smaller than the differences between Lm values for normal and emphysematous lungs (mean values are 0.17 mm for normal subjects, 0.31 mm for mild emphysema, and 0.64 mm for severe cases).

Fig. 4.

Mean linear intercept obtained by means of lung morphometry with hyperpolarized ³He diffusion MRI (Lm ³He) vs. direct measurement (Lm direct). Left: Lm (median calculated across the corresponding lung specimen). Right: Lm variability (each column is 1 SD of the Lm distribution across the corresponding lung specimen).

It should be noted that, in contrast to standard unbiased stereology, which does not require assumptions on airway structure, our approach is model based. Yet, as shown above, the results obtained with our MRI approach for S/V, N_a, and Lm are in rather good agreement with direct histological measurements.

Conclusions.

Over the years, quantification of emphysema has relied on evaluation of histological sections in which lung geometric parameters have been characterized by some mean characteristics. The most widely used “traditional” parameters are mean linear intercept, surface-to-volume ratio, and alveolar density. Another approach is based on the description of lung microstructure (16, 37) in which acinar airways (ducts and sacs), rather than alveoli, are considered as the elementary building blocks of lung structure. Each unit is a cylindrical airway with radius R, covered inside with an alveolar sleeve to a depth of h so that each alveolus opens up toward the internal airway passage (see Fig. 1 in Ref. 16 and Fig. 1 in present study). However, direct measurement of these parameters is much more elaborate and labor intensive than evaluation of standard parameters such as Lm. Consequently, very few attempts have been made to quantify lung geometry by means of parameters R and h. On the other hand, knowing these parameters of the lung acinar airways would allow estimation of all other physiologically important characteristics, such as alveolar volume, surface-to-volume ratio, density of alveoli, etc. Here we demonstrated that our theory, coupled with measurements of hyperpolarized ³He MRI signal attenuation in the presence of variable diffusion-sensitizing gradients, naturally allows estimation of parameters R and h. We have validated our technique by demonstrating that our MRI measurements are in very good agreement with direct morphometric measurements on the same lung specimens.

Thus our approach—lung morphometry via hyperpolarized ³He diffusion MRI—provides a new and unique tool to study lung microstructure in health and disease without utilizing lung biopsy, a current invasive gold standard. This method offers three-dimensional tomographic information on lung microstructure at the alveolar level from a very short (<1 min) MRI scan, with more geometric details and comprehensive lung tissue sampling than random measurements of mean linear intercept in excised lung specimens. This opens the door to longitudinal studies in clinical and research trials.

GRANTS

This work was supported by National Heart, Lung, and Blood Institute Grants R01-HL-70037, R01-HL-72369, and P50-HL-084922.

APPENDIX: ³HE GAS DIFFUSION IN LUNG AIRWAYS

Our method of measuring airway geometric parameters is based on MRI measurements of hyperpolarized ³He gas diffusion. We use a rather short diffusion time, Δ = 1.6 ms. For this diffusion time, and the free (unrestricted) diffusion coefficient D₀ of ³He in air of 0.88 cm²/s, the characteristic free diffusion length L₁ = 2D₀Δ is ∼500 μm. Hence, each ³He atom will have a chance on its diffusion path to diffuse out of its initial alveolus and across the airway (the average alveolar radius is ∼100 μm). Thus, in this time regime, we consider acinar airways rather than alveoli as independent elementary geometric units. On the other hand, L₁ is smaller than the average acinar airway length [730 μm for ducts and 1,012 μm for sacs (16)]. Hence for these diffusion times the effects of the airways' finite length are not important and we can neglect both collisions with the terminal ends of sacs and branching effects when ³He atoms migrate from one airway to another. In this case, the total MR diffusion signal can be considered as a sum of the signals from individual, noncommunicating airways. Diffusion of ³He gas in each airway can be described by two distinctly different diffusion coefficients, longitudinal D_L and transverse D_T (52). With the spatial resolution of several millimeters currently available with ³He MRI, each voxel contains hundreds of acinar airways with different orientations. Under the reasonable assumption of a uniform distribution of airway orientations, the total MR signal from a voxel is (52):

$$\text{S}\left(b\right)={\text{S}}_{\text{o}}\exp \left(-b{D}_{\text{T}}\right){\left(\frac{\text{π}}{\text{4}b\left(D_{\text{L}}-D_{\text{T}}\right)}\right)}^{1/2}·\phi \left\{{\left[\text{b}\left(D_{\text{L}}-D_{\text{T}}\right)\right]}^{1/2}\right\}$$

where S₀ is the MR signal intensity in the absence of diffusion-sensitizing gradients, Φ(x) is the error function, and b is the so-called b-value depending on a gradient pulse sequence. In our experiments,

$$b={\left(\text{γ}{G}_{\text{m}}\right)}^{\text{2}}\left[{\text{δ}}^2\left(\Delta -\frac{\delta }{3}\right)+\text{τ}\left({\text{δ}}^{\text{2}}-2\Delta \text{δ}+\Delta \text{τ}-\frac{\text{7}}{\text{6}}\text{δτ}+\frac{8}{15}{\text{τ}}^{\text{2}}\right)\right]$$

where G_m is the gradient amplitude, Δ is the diffusion time (time between centers of positive and negative gradient pulses), δ is the total width of each pulse, and τ is the ramp time (52).

To infer direct information on lung microstructure from measurements of the anisotropic diffusion coefficients D_L and D_T, we need to establish their dependences on the geometric parameters of lung airways (R, h). These dependences were found by means of computer Monte-Carlo simulations as described in Ref. 43. For the present eight-alveolar model the results are summarized in Eqs. A3–A5 and Fig. 5.

$$D_{\text{L}}=D_{\text{LO}}·\left(1-{\beta }_{\text{L}}·b{D}_{\text{LO}}\right);D_{\text{T}}=D_{\text{TO}}·\left(1+{\beta }_{\text{T}}·b{D}_{\text{TO}}\right)$$

$$\frac{D_{\text{LO}}}{{\text{D}}_{\text{O}}}=\exp \left[-2.89·{\left(h/R\right)}^{1.78}\right];{\text{β}}_{\text{L}}=35.6·{\left(R/L_1\right)}^{1.5}·\exp \left[-4/\sqrt{h/R}\right]$$

$$\begin{array}{l}\frac{D_{\text{TO}}}{D_{\text{O}}}=\exp \left[-0.73·{\left(L_{\text{2}}/R\right)}^{1.4}\right]·\left(1+\exp \left(-A·{\left(h/R\right)}^{\text{2}}\right)·\left\{\exp \left[-5{\left(h/R\right)}^{\text{2}}\right]+5·\left(h/R^{\text{2}}\right)-1\right\}\right);\\ \text{A}=1.3+0.25·\exp \left[14·{\left(R/L_{\text{2}}\right)}^{\text{2}}\right]\end{array}$$

The parameters D_L0 and D_T0 are the longitudinal (D_L) and transverse (D_T) diffusivities at b = 0; D₀ is the free diffusion coefficient of ³He gas in lung air spaces, and L₁ = 2D₀Δ and L₂ = 4D₀Δ are the characteristic free-diffusion lengths for one- and two-dimensional diffusion, respectively. In the physiological range (h/R < 0.6) parameter β_T, Eq. A3, remains practically constant at ∼0.06. It should be noted that, despite the rather complicated structure of Eqs. A3–A5, the model contains only three fitting parameters: the signal amplitude S₀, the external airway radius R, and the depth of the alveolar sleeve h. The diffusion time Δ and the free diffusion coefficient D₀ are considered to be known constants. In our experiments, Δ = 1.6 ms and D₀ = 0.88 cm²/s (which corresponds to ³He gas diluted in air or nitrogen).

Fig. 5.

Plots representing data obtained by Monte-Carlo simulations of the longitudinal diffusion coefficient D_L0 (A), longitudinal kurtosis βL (B), and transverse diffusion coefficient D_T0 (C) as functions of h/R for R = 280, 300, 320, 350, 375, and 400 μm (shown by numbers next to the curve in C; in A and B symbols corresponding to different R values collapse in a single line and are indistinguishable). D: D_T0 at h = 0 (r = R) as a function of R/L₂. Solid lines are calculated according to Eqs. A4 and A5. Data are presented in the form that clearly demonstrates the scaling relationships.

Simulations showed that with an average accuracy of ∼1–3%, Eqs. A4 and A5 are valid within the interval R/L₁ < 0.7. For the typical diffusion time used in our experiments, Δ = 1.8 ms, L₁ is 563 μm, limiting R to be less than ∼400 μm. This interval covers both the typical radii of acinar alveolar ducts in healthy human lungs and those in lungs with mild emphysema. For bigger R corresponding to lungs with advanced emphysema our measurements can produce larger estimation errors and our geometric representation of lung airways also may become inadequate because of lung tissue destruction.

Applying Eqs. A1–A5 to multi-b measurements of the ³He diffusion-attenuated MRI signal in lung airways makes possible the evaluation of mean geometric parameters for lung acinar airways, despite the airways being too small to be resolved by direct imaging.