Probing Lung Microstructure with Hyperpolarized Noble Gas Diffusion MRI: Theoretical Models and Experimental Results

Abstract

The introduction of hyperpolarized gases (³He and ¹²⁹Xe) has opened the door to applications for which gaseous agents are uniquely suited–lung MRI. One of the pulmonary applications, diffusion MRI, relies on measuring Brownian motion of inhaled hyperpolarized gas atoms diffusing in lung airspaces. In this article we provide an overview of the theoretical ideas behind hyperpolarized gas diffusion MRI and the results obtained over the decade-long research. We describe a simple technique based on measuring gas apparent diffusion coefficient (ADC) and an advanced technique, in vivo lung morphometry, that quantifies lung microstructure both in terms of Weibel parameters (acinar airways radii and alveolar depth) and standard metrics (mean linear intercept, surface-to-volume ratio, and alveolar density) that are widely used by lung researchers but were previously available only from invasive lung biopsy. This technique has the ability to provide unique three-dimensional tomographic information on lung microstructure from a less than 15 s MRI scan with results that are in good agreement with direct histological measurements. These safe and sensitive diffusion measurements improve our understanding of lung structure and functioning in health and disease, providing a platform for monitoring the efficacy of therapeutic interventions in clinical trials.

Approximately 12 million Americans suffer from chronic obstructive pulmonary diseases (COPD) including chronic bronchitis and emphysema as well as asthma. It is the fourth leading cause of chronic morbidity and mortality in the United States, and is projected to rank fifth in 2020 in burden of disease caused worldwide, according to a study published by the World Bank/World Health Organization (1). Numerous diagnostic tools have been developed to evaluate the presence and the stage of these diseases. The traditional classification for the severity of COPD is based on measurements of airflow limitation during forced expiration (1). Each stage is characterized by the volume of air that can be forcibly exhaled in 1 s (FEV₁) and by the ratio of FEV₁ to the forced vital capacity (FVC). Abnormalities in these tests reflect both the reduction in the force available to drive air out of the lung as a result of emphysematous lung destruction (2) and obstruction to airflow in the smaller conducting airways (3–5). However, the specific pathophysiologic role and contribution of emphysema and small airways abnormalities in expiratory airflow obstruction in COPD has been under debate (6,7). While the role of pathologic changes in small airways has received much attention in recent years (8–10), the early-emphysema component of COPD has not. Conventional pulmonary function tests are insensitive to the onset and initial stages of emphysema (11); the same is valid for conventional chest radiography (12); X-ray CT has substantially greater value for evaluation of emphysema (13); there, enlargement of airspaces and destruction of alveolar walls reduces X-ray attenuation and allows the detection of emphysema, especially in advanced stages (14,15). Studies have shown good correlation between the amount of emphysema determined by this method and the amount measured in pathology specimens (15–17) though smoking-related inflammation and lung remodeling can also alter CT attenuation (18–20).

The major function of the lung, of course, is delivery of oxygen to the body and removing CO₂ from it. The efficiency of oxygen delivery through the lung airspaces 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 (e.g. (10,17,21–30)). These studies provided invaluable information on lung microstructure that is the basis of the current knowledge on lung structure and function. Such geometrical parameters as mean linear intercept (or mean chord length), L_m, lung parenchyma surface-to-volume ratio, S/V, and number of alveoli per unit lung volume, N_v, are most commonly used to characterize lung morphometry (see definitions of these parameters in “An official research policy statement of the ATS” (31)). Although lung stereology has been in use for more than a half century and is considered a gold standard (see recent overviews (32,33)), intense debates about its accuracy in estimating lung morphometry continue (34–41). This is mostly due to the objective problems of lung specimen preparation and the subjective bias in selection of “random” regions of lung parenchyma. The problem is so important that the American Thoracic Society and European Respiratory Society have commissioned a Joint Task Force to define the “Standards for Quantitative Assessment of Lung Structure” (31). However, the clinical and even research utility of “standard” lung morphometry is limited by its invasive nature.

The rapid development during the past two decades of hyperpolarized ³He and ¹²⁹Xe gas MR imaging of lung air spaces has resulted from combined advances in the spin physics of optical pumping, affordable high-power diode laser arrays, and MRI strategies for optimum use of the non-renewable spin magnetization. MR imaging with hyperpolarized gas requires the MRI scanner to be equipped with broadband RF amplifiers and specially designed RF coils to transmit and receive signals at the ³He and ¹²⁹Xe frequencies and equipment to hyperpolarize ³He and ¹²⁹Xe gases. Even though these gases have three orders of magnitude smaller nuclear spin density (at standard pressure) compared with water, by using special laser equipment, they can be hyperpolarized to achieve a polarization almost five orders of magnitude more than the polarization of water protons at room temperature (42–46). This increase in polarization compensates for the decreased density of the gas although it also places some limitations on the MRI acquisition scheme. As a result, very intense MRI signals, compared with those of water, can be achieved from hyperpolarized ³He and ¹²⁹Xe gases. This has opened the door to applications for which gaseous agents are uniquely suited, such as lung imaging. The MRI measurements with ³He and ¹²⁹Xe gases are safe and well-tolerated (47,48) and can be repeated in vivo on a regular basis to serve as a tool for research, clinical, and drug development studies.

The first use of the technology was to produce ventilation images which display the distribution of a single bolus of inhaled ³He gas at breath-hold. For example, high spatial resolution ³He-gas imaging in animals has yielded anatomical images showing many levels of airway branching (49–51); anatomical images of human lungs have been reported from healthy subjects (52) and patients with several types of lung pathology (53). Subsequently, dynamic ³He MRI was used to show the time evolution of gas distribution, with sub-second time resolution (e.g. (54,55)). A quantitative method for measurement of the local fractional ventilation (the fraction of gas replaced with each breath) has also appeared (56). The local oxygen concentration and its decrease during breath-hold have been determined (57,58) from the ³He T₁, allowing the local ventilation–perfusion ratio to be calculated (59). ¹²⁹Xe gas exchange processes between gas and tissue-dissolved phases have also been studied (60–64). Various improvements and new techniques of hyperpolarized gas MRI in lung imaging have been developed over the years (see, for example, review articles (65–81) and references therein).

Our review is focused on one specific pulmonary application in hyperpolarized gas imaging—diffusion MRI.

DIFFUSION LUNG IMAGING (BACKGROUND)

Diffusion MRI with hyperpolarized gases is based on measurements of hyperpolarized gas diffusion introduced in the lung airspaces during inhalation. Initial applications have focused on studying ³He gas and subsequently progressed to ¹²⁹Xe. We will discuss ³He first.

In any fluid medium, the atoms or molecules diffuse; that is, the atoms perform a Brownian-motion random walk. In time interval Δ (diffusion time), in the absence of restricting walls or barriers the molecules will move a root mean-square distance L₁ = (2D₀Δ)^1/2 along any axis. The parameter D₀ is termed the free diffusion coefficient, which for highly diluted ³He in air at 37°C is about 0.88cm²/s. Hence ³He gas atoms can wander distances on the order of 1 mm in times as short as 1 ms. The alveolar walls as well as the walls of bronchioles, alveolar ducts, sacs and other branches of the airway tree serve as obstacles to the path of diffusing ³He atoms and limit their displacement. Indeed, for diffusion times around 2 ms, the MR-measured average ³He apparent diffusion coefficient (ADC) in healthy human lungs is approximately 0.20 cm²/s, more than a factor of four smaller than D₀ (82–84). For short diffusion times (a few milliseconds) the ³He gas can explore mostly alveoli and individual acinar airways and thus is primarily reporting on only those structures. This millisecond diffusion time range is used in most hyperpolarized ³He gas studies (see, e.g. (8,74,78,79,82–111)).

The simplest MR measurement of diffusion is the Stejskal-Tanner-type pulsed field gradient (PFG) experiment (112) in which a free-induction decay MR signal is acted upon by two opposite-polarity gradient pulses (Fig. 1)—the so-called diffusion-sensitizing gradients. This method is restricted by MRI signal T2* decay (on the order of 15–30 ms for ³He and 20–50 ms for ¹²⁹Xe (113,114)) and can only be used to study short range diffusion. Measurements of the ³He diffusion coefficient at longer diffusion times (seconds) proposed by Owers-Bradley et al. (115) (see also (116–120)) allow exploring the “connectivity” of acinar airways and alveoli thus providing information on airway and alveolar wall integrity (i.e., holes through the walls) and collateral ventilation pathways (118,119). This approach will be discussed later in this review.

FIG. 1.

Diffusion sensitizing pulse gradient waveform employed in diffusion MRI with hyperpolarized gases at short diffusion times. In this diagram G_m is the gradient lobe amplitude, Δ is the spacing between the leading edges of the positive and negative lobes (the diffusion time), δ is the full duration of each lobe, and τ is a ramp-up and ramp-down time.

In the presence of gradient pulses, nuclear spins suffer a net phase shift proportional to their displacement during the diffusion time Δ, resulting in decreased signal amplitude. In the case of unrestricted diffusion, the MR signal S decays as S = S₀exp (−bD₀). Here, S₀ is the MR signal intensity in the absence of diffusion-sensitizing gradients, and the b-value is determined by the gradient waveform shape. For the gradient pulses in Figure 1, the corresponding b-value is (84,121):

$$b={(\gamma G_{\mathrm{m}})}^2\left[{\delta }^2\left(\Delta -\frac{\delta }{3}\right)+\tau \left({\delta }^2-2\Delta \delta +\Delta \tau -\frac{7}{6}\delta \tau +\frac{8}{15}{\tau }^2\right)\right]$$ [1]

In the presence of barriers such as alveolar walls and walls of lung airways, the diffusive motion is restricted and the MR signal decay is often described in terms of the ADC:

$$S=S_0\exp (-b\cdot \mathrm{ADC})$$ [2]

Contrary to the free diffusion case where ADC is equal to D₀ and depends only on the molecular diffusion properties, the ADC for restricted diffusion evaluated from Eq. [2] depends also on the tissue structure and on the timing details of the gradient waveform and gradient strength.

ADC MEASUREMENTS IN HEALTHY AND EMPHYSEMATOUS LUNGS

ADC measurements are usually done with two b-values thus allowing coverage of a substantial part of the lungs in a single breath-hold. Already initial publications (82–84,87) demonstrated that the ADC of hyperpolarized ³He gas in the lungs dramatically increases in emphysema (compared with normal lungs), suggesting a large potential as a diagnostic tool for clinical applications. Figure 2 shows examples of ventilation images (MRI-measured distribution of ³He gas inhaled by a subject) and ³He gas ADC maps of normal human lungs and lungs with severe emphysema.

FIG. 2.

Images of normal and emphysematous human lungs. Left to right–proton MRI, ³He ventilation maps, ³He gas ADC maps and histological slices (the latter adapted from Ref. 122); first row–normal lungs, second row–lung with emphysema. ADC in a normal lung is rather homogeneous except for large airways (trachea and its first branches) and is about 0.17 cm²/s. In the emphysema lung ³He gas penetrates only into ventilated regions (lower portion of the lung in this case) and has an ADC about three times bigger (0.55 cm²/s) than the ADC in the normal lung.

The remarkable differences in the ADC values between healthy (0.17 cm²/s) and diseased (0.52 cm²/s) lung indicate that diffusion imaging of the lung with hyperpolarized helium could provide a very sensitive tool for clinical evaluation of emphysema. Indeed, Figure 3 demonstrates the correlation between ADC and (a) mean alveolar internal area (AIA) in rats with elastase induced emphysema (90); (b) mean chord length (MCL) in elastase-induced emphysematous rabbit lungs (102); (c) mean linear intercept (L_m) in healthy and emphysematous human lungs with data obtained at different diffusion times (123); (d) mean linear intercept (L_m) in healthy human lungs and lungs with severe emphysema (124).

FIG. 3.

Correlation between ADC and (a) mean alveolar internal area (AIA) in rats with elastase induced emphysema (adapted from Ref. 90); (b) mean chord length (MCL) in elastase-induced emphysematous rabbit lungs (adapted from Ref. 102); (c) mean linear intercept L_m in healthy and emphysematous human lungs with data obtained at different diffusion times (in ms, shown by number by the lines) (■) −1.6 ms; (•) −5 ms; (▴) −10 ms) (adapted from Ref. 123); (d) mean linear intercept L_m in healthy human lungs and lungs with severe emphysema (adapted from Ref. 124).

In addition to correlation with histology seen in Figure 3, ADC in healthy subjects showed correlation with lung inflation level (125) and subjects’ age (96,98,125) (see Fig. 4).

FIG. 4.

ADC dependence on age: (a) (adapted from Ref. 98), (b) (adapted from Ref. 125); and lung inflation (c) (adapted from Ref. 125).

Salerno et al. (83) studied correlations between ³He ADC and spirometric indices (Fig. 5). ADC images were homogeneous in volunteers, but demonstrated regional variations in emphysema patients. The mean and SD of the ADCs for patients were significantly larger than those for volunteers. The mean ADCs for all subjects correlated with the percentage of predicted FEV1 and the ratio FEV1/FVC. Correlations between mean ADC values and pulmonary function test were also reported by Fain et al. (126).

FIG. 5.

Scatter plots depict the relationship between the ADC parameters and spirometric indexes obtained from 16 healthy volunteers and 11 patients with emphysema (adapted from Ref. 83). The 95 % CIs for the regressions are shown as dotted lines. For all subjects, the mean ADCs correlated with the percentage of predicted FEV1 (r =−0.797, P < 0.001) (left) and FEV1/FVC (r = −0.930, P < 0.001) (right).

Although Figure 3 shows rather good correlations between ADC and morphometry, several important issues need to be clarified. Even in healthy human lungs ADC exhibits rather broad variability, with different studies (82,88,95,97–99,123,127) reporting results between 0.15 cm²/s and 0.25 cm²/s. This is due to the fact that ADC depends not only on lung microstructure but on pulse sequence parameters (diffusion time Δ, b-value). Besides, even for fixed pulse sequence parameters, there is no one-to-one correspondence between ADC and lung morphometric parameters (see below Fig. 14). That is why ADC, though quite sensitive and useful, cannot characterize lung microstructure in standard morphometric terms.

FIG. 14.

ADC versus L_m found for 30 subjects from study (104) (adapted from Ref. 189). a: The average (over each subject) values of the parameters ADC and L_m. b: ADC and L_m calculated on a pixel-by-pixel basis (grey symbols). The lines represent the dependence of ADC as a function of L_m, theoretically calculated at fixed values of the ratio h/R (given by numbers near the lines). Importantly, each value of Lm can be associated with numerous values of ADC, and vice versa.

Most of the studies above were based on ³He gas measurements. Quite a few authors have also reported measurements of ¹²⁹Xe-based ADC in healthy and emphysematous lungs (48,102,128–132). Kirby et al. (131) demonstrated a significant correlation between ³He ADC and ¹²⁹Xe ADC as well as between ADCs and CT measurements. In healthy lungs, ³He ADC and ¹²⁹Xe ADC were found to be ~0.20 cm²/s and ~0.055 cm²/s, respectively; in lungs with COPD, the corresponding values are ~0.55 to 0.6 cm²/s and 0.07 to 0.09 cm²/s. In Ref. 130, the mean ¹²⁹Xe ADC in healthy volunteers was reported ~0.04 cm²/s. Such a difference in ¹²⁹Xe ADC could be explained by different experimental conditions, including concentration of ¹²⁹Xe in gas mixtures. The substantially smaller ADC values for ¹²⁹Xe as compared with ³He are explained by the considerably smaller free diffusion coefficient of ¹²⁹Xe versus ³He (see detailed discussion in Theory of Gas Anisotropic Diffusion in Acinar Airways as a Background for Lung Morphometry Technique section).

ADC MEASUREMENTS-OTHER PULMONARY APPLICATIONS

Diffusion MRI with hyperpolarized gases in non-COPD pulmonary diseases has lagged significantly behind, in part because there is no clear biophysical model for what the diffusion changes mean. For example, asthma, which is the second most commonly studied pulmonary disorder using MRI, has primarily been studied using ventilation imaging. Asthma is considered an airways disease and therefore the effect on the alveolar space is uncertain. Further, as the airways disease manifests as ventilation defects in the airways distal to the flow restriction or obstruction, this lack of signal in the most affected regions precludes diffusion quantitation. Reports of diffusion values in these populations indicate normal values for the ³He or ¹²⁹Xe ADC and are limited in number, presumably because of the lack of a significant finding. Fain et al. (133) studied 21 asthmatics versus 24 never smokers and 16 COPD and found that the asthma group had slightly lower ADC values. However, since these subjects were also younger than the other groups, which would also decrease ADC, the differences were no longer significant after accounting for age. The age-normalized ADC in asthmatics correlated with FEV1 (% predicted) but not FEV1/FVC.

Wang et al. (120) compared the short and long range ³He ADC in asthmatics, COPD, and healthy subjects. While there was no statistical difference between the asthmatics and age-matched healthy controls, there was a trend toward elevated ADC values in the asthmatics, with a larger effect in the long-range ADC. Since the regions of elevated ADC were focal, the authors hypothesized that the elevated ADC was the result of chronic air trapping due to small airways disease. A mouse model of allergic-sensitization studied by Emami et al. (134) also showed no difference in ADC compared with controls, though there was more population variation in the ADC of the asthmatic mice compared with controls.

Diffusion gas MRI has also found a limited application in studying bronchiolitis obliterans in post-transplantation lungs. Bink et al. (135) reported that in this population, the ³He ADC of healthy transplanted lungs was elevated compared with controls and was further increased in transplanted lungs undergoing chronic rejection. While the increased ADC of the healthy transplanted lungs in this study may be age related (96) (the age of the lung donors was unknown), there is a suggestion that the diffusion coefficient is sensitive to the pulmonary changes post-transplantation.

In humans with pulmonary fibrosis, an elevated ³He ADC was detected by Bink et al. (135), suggesting a dilation of peripheral air spaces. However, a study of the rat bleomycin fibrosis model by Stephen et al. (136) detected a decrease in ADC along with lower variability across the lung, though there was no correlation between ADC and PFT. While these results seem contradictory, they are presumably due to differences between clinical pulmonary fibrosis and the mouse bleomycin model.

In addition to COPD, lung cancer is another major complication of smoking. Mathew et al. (137), using hyperpolarized ³He MRI, examined fifteen patients with lung cancer (in one lung) before radiation therapy. While there were increased ventilation defects in the lung with cancer, there was no difference in ADC between the ipsi-lateral and contralateral lungs, suggesting that there were no changes in lung microstructure beyond the border of the cancerous tissue.

Treatments for cancer also have the potential to change the pulmonary microstructure. Mathew et al. (138) found no statistical difference in ³He ADC between the irradiated and contralateral lung in subjects with radiation-induced lung injury; however, there was a trend toward lower ADC in the contralateral lung. After six months, the contralateral lung showed an increase in ADC and received an increased percentage of the helium dose on ventilation image, whereas no change was observed in the ADC of the irradiated lung. In contrast, Ward et al. (139) had measured decreased ³He ADC in the irradiated lung of a rat, which was associated with fibrosis. It was suggested that the regions of heavy fibrosis in the clinical study could be masked by ventilation defects (138). A more recent small study by Hegarty et al. (140) measuring anisotropy of ¹²⁹Xe diffusion in a rat model of radiation induced lung injury found decreased D_T in the irradiated rat lungs and a trend towards decreased D_L (see definitions below).

Recently Narayanan et al. (141) and Cadman et al. (142) have demonstrated pediatric applications in lung microstructure measurements using a q-space technique (143) In particular, the results in Ref. 142 demonstrate a higher degree of restriction to gas diffusion in children with asthma compared with those seen in children without asthma.

THEORETICAL MODELS OF GAS DIFFUSION IN LUNG AIRWAYS

To advance diffusion measurements to research and clinical practice, a fundamental question—what aspects of lung microstructure are being measured by ³He or ¹²⁹Xe ADC—needs to be answered. To obtain quantitative information on lung microstructure at the acinar level, geometrical parameters describing the lung microstructure should be related to the parameters extracted from MR measurements independent of pulse sequence parameters and/or gas concentration. Obviously, such a complicated structure as lung cannot be analyzed without some simplifications and assumptions. To date numerous models for lung microstructure have been explored to simulate diffusion attenuated MRI signal using Monte-Carlo approach or finite difference methods. A modified Weibel model (23,24) has been used in Refs.(84,144–147). Other examples include porous media approach proposed by Mair et al. (148,149); cylindrical model with semi-spherical alveolar shape and two-dimensional grape-like structures used by Fichele et al. (150); Kitaoka model (three-dimensional labyrinth filling a cubic volume (151)) used by Grebenkov (152); tree-like branching structures used by Verbanck et al. (153,154), Perez-Sanchez et al. (155), Conradi et al. (67), and Bartel et al. (119). Models based on morphological images or high-resolution X-ray tomography were used by Miller et al. (156) and Tsuda et al. (157). A geometrical model utilizing Voronoi meshing techniques (158) was simulated by Plotkowiak et al. (80). These publications provided important insights into gas diffusion properties in lung airways, some of them were discussed in detail by Plotkowiak et al. (80).

For these approaches to become a useful research and clinical tool in studying lungs in health and disease they need to allow solution of the inverse problem—evaluating lung geometrical parameters from specially designed MRI experiments. Such approaches should satisfy at least two requirements. They must reflect salient features of lung microstructure geometry, which affects the MR signal formation and the number of parameters characterizing the lung model should be small enough to be able to be determined from MR data. Currently there is only one approach that meets both criteria—in vivo lung morphometry—that was developed in Refs. (84,144–147). It is based on a well-accepted Weibel geometrical model of lung microstructure at the acinar level that is based upon stereological methods (23,24) and theoretical equations relating MR diffusion signal to acinar airways geometric parameters. Based on multi-b measurements of MR diffusion attenuation of signal (usually five to six b-values (84)), this approach not only provides information on gas diffusion properties, but more importantly, it allows evaluation of lung geometrical parameters from a rather simple and fast MRI experiment. Theoretical parameters used in this approach also allow calculation of standard lung morphological parameters analogous to those extracted from direct histological measurements, hence the term “in vivo lung morphometry.” Details on multi-b sequence requirements and optimization are provided in Refs. (145,147).

IN VIVO LUNG MORPHOMETRY TECHNIQUE

Lung Geometrical Model (Weibel Model) as a Basis for In Vivo Lung Morphometry

To better understand the relationship between the measured ADC and lung microstructure at the alveolar level, we first need to describe lung in terms of some basic geometrical elements. The structure of lung airways is usually considered as a branching tree structure (22) or as confluent rivers (159) beginning at the trachea and leading through bronchi and bronchioles to the terminal bronchiole that feeds each acinus—the major gas exchange unit in the lung. In humans there are 14 generations of airways before the terminal bronchioles and another nine inside the acinus, with an average acinar volume of about 187 mm³ (22). Gas ventilation in the trachea, bronchi, bronchioles, and terminal bronchioles occurs by convection (bulk flow), while diffusion is the primary ventilation mechanism beyond the terminal bronchioles—in the acini, where about 90 to 95% of gas resides (160). Functionally, the acinus is defined as the largest airway unit in which all airways participate in gas exchange (22). Geometrically, it represents the complex of all airways distal to a terminal bronchiole, starting with a first order respiratory bronchiole. A large number of studies have been devoted to acinar geometry (see for example (23,161–163)). According to (23,24) essentially all airways in the acinus are decorated by alveoli forming an alveolar sleeve (see example in Fig. 6).

FIG. 6.

a: Distal portion of airways as seen with SEM. Terminal bronchiole (tb), respiratory bronchiole (rb), alveolar duct (ad), alveolar sacs (as), and alveoli (a) are seen in continuity as the airway branches to the pleura (p) (adapted from Ref. 163). b: Schematic drawing of acinar airway cross section representing eight alveoli surrounding the lumen (L) (adapted from Ref. 164). c: Schematic structure of two levels of acinar airways. Open spheres represent alveoli forming an alveolar sleeve around the lumen of each cylindrical airway. d: Cross-section of the acinar airway model (146) with two main parameters: external radius R and internal radius r (lumen radius) The other parameters, the depth of alveolar sleeve, h, and the alveolar length, L, are: h = R − r, L = 2R sin(π/8) = 0.765 R (8-alveolar model—see discussion below).

In humans, the intra-acinar airways branch dichotomously over about nine generations. Both the internal acinar airway radius r and the outer radius R (including the sleeve of alveoli) vary depending on the position and branching level of the acinar airway tree; however, the variation is rather small—the standard deviation for R is about 60 μm and for r is about 30 μm with mean values of 350 μm and 160 μm correspondingly (23). The “narrowness” of the distributions of parameters R and r creates a solid basis for characterizing acinar airways by the mean values of R and r.

Another important parameter in Figure 6 is the “effective alveolar diameter” L, which is not specified in Ref. 23. 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. 21 and discussion therein). Here we adopt a model in which each alveolus occupies 1/8 of the annular ring (eight-alveolar model (164,165)). In this model we also assume that the alveolar effective diameter L is equal to the length of the cord corresponding to 1/8 of the annular ring, L = 2R · sin (π/8) = 0.765R reducing the number of geometrical parameters in the model to only two: R, and the depth of alveolar sleeve h = R − r. If we scale the values from (23) collected at 0.9 TLC (total lung capacity) to 0.6 TLC (usually quoted in the literature) and make the realistic assumption that lung volume scales as the cube of linear dimensions, the mean values of the parameters become R = 300 μm, r = 140 μm, and L = 230 μm. These results are consistent with literature values for average alveolar diameter ranging from 200 to 260 μm (21,25–27). 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.

Using these parameters, we can estimate the alveolar surface area S_a, lung volume per alveolus V_a, alveolar number density N_v—the number of alveoli per unit lung volume based upon geometry, and the mean linear intercept L_m (146) (see Supporting Information):

$$\begin{array}{cc}\hfill S_{\mathrm{a}}=& \frac{\pi }{4}R\cdot L+\frac{\pi }{4}h\cdot (2R-h)+2h\cdot L,V_{\mathrm{a}}=\frac{\pi }{8}{R}^{2}L\hfill \\ \hfill L=& 2R\cdot \sin \frac{\pi }{8},N_{\mathrm{v}}=\frac{1}{V_{\mathrm{a}}},S∕V=S_{\mathrm{a}}∕V_{\mathrm{a}}=4∕\mathit{Lm}\hfill \end{array}$$ [3]

Theory of Gas Anisotropic Diffusion in Acinar Airways as a Background for Lung Morphometry Technique

It is important to emphasize that the diffusion time Δ used for lung morphometry technique is a crucial parameter and only the specified diffusion time interval should be used in experiments (145–147). This parameter is selected such that the corresponding r.m.s. free displacement in one direction, (2D₀ · 2Δ)^1/2, should be larger than the average alveolar radius but smaller than the mean length of alveolar ducts or alveolar sacs (in human lung, about 0.76 mm and 1 mm, correspondingly (23)). In other words, diffusing gas atoms are expected to diffuse away from single alveoli but remain mostly in the same alveolar duct or sac throughout the duration of the bipolar diffusion-sensitizing gradient pulse – i.e., 2Δ should be short enough but not too short. Since the diffusion coefficient D₀ is different for ³He and ¹²⁹Xe, and also depends on gas concentration in lung airspaces (see Supporting Information), this diffusion time should be selected for each specific experimental condition. For ³He in human lungs this sets the upper limit of diffusion time Δ to ~1.8 ms for highly diluted ³He gas (D₀ = 0.88cm²/s) and to ~0.8 ms for lungs filled with pure ³He gas (D₀ = 2 cm²/s). For ¹²⁹Xe gas, this limit is ~10 ms for highly diluted ¹²⁹Xe gas (D₀ = 0.14 cm²/s) and 24 ms for pure ¹²⁹Xe (D₀ = 0.06 cm²/s). In small animal lungs, where the alveolar ducts and sacs are shorter, the diffusion time Δ should be much shorter (147,166–168). This constraint recognizes acinar airways (respiratory broncheoli, alveolar ducts and alveolar sacs) as the elementary geometrical units contributing to the gas diffusion MR signal. Under these conditions, the branching structure of acinar airways play little role in diffusion MR signal formation (145) (see also the detailed discussion later in this review).

The alveolar walls as well as the walls of alveolar ducts and other branches of the airway tree serve as obstacles to the path of diffusing atoms and reduce the gas diffusivity. Crucially, these restrictions are substantially less along the airway axis than perpendicular to it; consequently, diffusion in the airway is anisotropic (84). Therefore, the ADC describing signal attenuation in a single airway depends on the angle α between the direction of the diffusion-sensitizing gradient G and the airway’s principal axis:

$$S=S_0\cdot \exp (-b\cdot \mathrm{ADC}(\alpha ))$$ [4]

Due to the cylindrical symmetry of the airway,

$$\mathrm{ADC}(\alpha )=D_{\mathrm{L}}{\cos }^2\alpha +D_{\mathrm{T}}{\sin }^2\alpha$$ [5]

where apparent diffusion coefficients, longitudinal D_L and transverse D_T, correspond to diffusion along the airway principal axis and in the transverse plane, respectively (84).

With the spatial resolution of several millimeters currently available with ³He or ¹²⁹Xe MRI, each voxel contains hundreds of airways with different orientations. Due to the large number of acinar airways in each imaging voxel, their orientation distribution function can be taken as uniform, and the total signal S can be written as (84):

$$\begin{array}{cc}\hfill S(b)=& S_0\exp (-b{D}_{\mathrm{T}}){\left(\frac{\pi }{4b{D}_{\mathrm{AN}}}\right)}^{1∕2}\cdot \Phi \left[{(b{D}_{\mathrm{AN}})}^{1∕2}\right],\hfill \\ \hfill D_{\mathrm{AN}}=& D_{\mathrm{L}}-D_{\mathrm{T}}\hfill \end{array}$$ [6]

where Φ(x) is the error function. This macroscopically isotropic but microscopically anisotropic model predicts non-exponential dependence of diffusion attenuated MRI signal on b-value. The validity of Eq. [6] was confirmed in vivo by experimental measurements in humans (84,146), canines (101), mice (166,167), and rats (127,168) using hyperpolarized ³He gas. It was also recently confirmed in humans (169,170) and rats (132,140) using hyperpolarized ¹²⁹Xe gas. Example of the data obtained by Jacob et al. from a rat for a broad range of b-values up to 40 s/cm² (127) is shown in Figure 7 where the authors compared fitting their data to the model in Eq. [6], a kurtosis model S(b) = S(0) · exp [−bD + K/6 · (bD)²], and a monoexponential ADC model, Eq. [2].

FIG. 7.

³He diffusion MRI signal intensity measured from a rat lung for nine b-values in a region of interest (right lung in the inset) (adapted from Ref. 127). The solid line is a fit to the model in Eq. [6], the dashed line is a fit to the kurtosis model, and the dotted line is a fit of the first four data points to a mono-exponential ADC model, imitating the acquisition of only a few low b-values.

Importantly, the diffusivities D_L and D_T determined from the MR experiment depend on both lung microstructure and the details of the Stejskal-Tanner pulse sequence (144) (therefore they are termed “apparent” diffusivities, ADC). Although general expressions for D_L and D_T are unavailable, it was demonstrated by means of computer simulations (144–147) that in a physiological range of geometrical parameters r and R, and “realistic” gradients used in MRI experiments, a linear approximation with respect to b-values is sufficient to describe the dependence of apparent diffusion coefficients D_L and D_T on b-values:

$$\begin{array}{cc}\hfill D_{\mathrm{L}}=& D_{\mathrm{L}0}\cdot (1-{\beta }_{\mathrm{L}}\cdot b{D}_{\mathrm{L}0})\hfill \\ \hfill D_{\mathrm{T}}=& D_{\mathrm{T}0}\cdot (1+{\beta }_{\mathrm{T}}\cdot b{D}_{\mathrm{T}0})\hfill \end{array}$$ [7]

The dimensionless coefficients β_L and β_T reflect the non-Gaussian diffusion effects in each individual airway and are usually defined in terms of the so-called kurtosis K—the second-order term in the general cumulant expansion of the MR signal (e.g., (171–174)); (K_L = 6β_L, K_T = −6β_T). It should be noted that the signal S(b) in Eq. [6] also demonstrates “primary” non-monoexponentiality in b-value, which is due to orientation averaging of the signals from individual airways. The non-monoexponentiality in b-value described by the coefficients β_L and β_T is a feature of individual airways and is additional to this “averaging” effect.

Lung Morphometry with Hyperpolarized ³He Gas

In Ref. 146, using the method developed in Ref. 144, the apparent diffusion coefficients D_L and D_T characteristic of ³He gas diffusion were related to the geometrical parameters of acinar airways, R and r, in human lungs by means of phenomenological expressions:

$$\begin{array}{cc}\hfill \frac{D_{\mathrm{L}0}}{D_0}=& \exp [-2.89\cdot {(h∕R)}^{1.78}],\hfill \\ \hfill {\beta }_L=& 35.6\cdot {(R∕L_1)}^{3∕2}\cdot \exp [-4∕\sqrt{h∕R}]\hfill \end{array}$$ [8]

$$\begin{array}{c}\hfill \frac{D_{{\mathrm{T}}_0}}{D_0}=\exp [-0.73\cdot {(L_2∕R)}^{1.4}]\cdot [1+u(h,R)]\hfill \\ \hfill u(h,R)=\exp \left(-A\cdot {(h∕R)}^2\right)\cdot [\exp \left(-5{(h∕R)}^2\right)+5\cdot {(h∕R)}^2-1]\hfill \\ \hfill A=1.3+0.25\cdot \exp [14\cdot {(R∕L_2)}^2]\hfill \end{array}$$ [9]

Here L₁ = (2D₀Δ)^1/2 and L₂ = (4D₀Δ)^1/2 are the characteristic free-diffusion lengths for one- and two-dimensional diffusion, respectively. In the physiological range (h/R < 0.6), parameter β_T remains practically constant at approximately 0.06. The relationships in Eqs. [8] and [9] are illustrated in Supporting Information. Diffusion coefficient D₀ in these equations should also be used according to gas mixture in the lungs (see Supporting Information). For a typical human experiment where about 0.5 L of ³He gas is inhaled to a total lung volume of about 4 L D₀ is 0.93 cm²/s.

Fitting Eqs. [6-9] to multi-b measurements of the ³He diffusion-attenuated MRI signal in lung airways on a voxel-by-voxel basis makes possible the evaluation of mean geometrical parameters for lung acinar airways (in spite of the airways being too small to be resolved by direct imaging). As a result, parametric maps for airway radii R and alveolar depths h and physiologically important parameters L_m, S/V, and N_v can be generated.

It is important to emphasize that the phenomenological expressions, Eqs. [8] and [9], are not universal, they are derived for specific values of model parameters and diffusion time Δ. Namely, they are valid with accuracy of a few percent for Δ = 1.5 to 2 ms and R = 280 to 400 μm (145). This interval of R covers both the typical radii of acinar alveolar ducts in healthy human lungs and those in lungs with mild emphysema. For larger R corresponding to lungs with advanced emphysema our approach can produce larger estimation errors and the Weibel geometrical representation of lung airways used in our approach also may become inadequate due to lung tissue destruction. For airway sizes characteristic of small animal lungs (mice, rats), where a typical radius is substantially smaller (R = 100 μm) a modified version of Eqs. [8] and [9] were derived (166) for the diffusion time Δ = 0.3 to 0.4 ms. The corresponding expressions are provided in Supporting Information to this article.

Lung Morphometry with Hyperpolarized ¹²⁹Xe

To develop the lung morphometry technique with hyperpolarized ¹²⁹Xe, we need to take into account differences in magnetic and diffusion properties of ¹²⁹Xe as compared with ³He gas. With proper selection of ¹²⁹Xe diffusion time, Eqs. [6] and [7] can still be used, but Eqs. [8] and [9] should be modified due to the differences in the gyromagnetic ratios (γ = 7.452 rad/(G ms) for ¹²⁹Xe vs. γ = 20.379 rad/(G ms) for ³He) and in the free diffusion coefficients (D₀ = 0.88 cm²/s for diluted ³He in air vs. D₀ = 0.14 cm²/s for diluted ¹²⁹Xe in air). Generally speaking, one can modify the gradient pulse sequence parameters (diffusion time Δ, gradient amplitude G_m) in such a way that the dimensionless combinations R/L₁ and bD₀ would be the same as for ³He (147). For a typical gas mixture in human lungs (1 L of ¹²⁹Xe + 3 L of air), the ¹²⁹Xe diffusion coefficient D₀ is about 0.1 cm²/s (see Supporting Information). Hence diffusion time Δ should be increased by a factor of 9. However this would lead to a substantial increase in the imaging time and signal loss due to T2* decay of the MR signal. To address these issues, it was proposed in Ref. 147 to use a smaller diffusion time by simultaneously increasing the diffusion gradient strength. For state-of-the-art human scanners allowing diffusion gradient strengths up to 30–40 mT/m, as shown in Ref. 147, the “optimal” value of the diffusion time is Δ = 5ms , while for small animal scanners, allowing 10-fold stronger gradients, this time is about 1 ms. In Ref. 147, phenomenological expressions similar to Eqs. [8] and [9] were derived for ¹²⁹Xe gas both for humans and small animals. Corresponding equations are provided here in Supporting Information, Eqs. [S5] to [S7]. However, further theoretical and experimental studies are needed to optimize the parameters of multi-b sequences for the lung morphometry technique with hyperpolarized ¹²⁹Xe gas.

It should also be noted that the gas concentration may vary across the lung which could lead to bias in estimating both standard ADC values and lung morphometric parameters. This effect could be especially pronounced for ¹²⁹Xe gas due to its higher atomic weight and viscosity.

Validation of ³He Lung Morphometry Technique

In Ref. 146 the MRI-based measurements of lung morphometric parameters were validated in explanted human lungs against direct invasive morphometric measurements, the current gold standard. The results, shown in Figure 8, demonstrate images of L_m in healthy lungs and lungs with different levels of emphysema (mild, moderate, and severe). Figure 8 also demonstrates an excellent agreement between direct histological and ³He-based measurements of L_m. It should be noted that the MRI experiment provides for much higher statistical power since the data are collected from practically the entire lung as compared with very few regions (20 to 40) from histological cores.

FIG. 8.

Upper row: examples of the L_m (in mm) maps obtained from normal human lung (left) and lungs with different stages of emphysema (mild–middle and severe–right) (adapted from Ref. 146). Lower row: examples of histological slices obtained from the same lungs as above. Right panel: plot of mean linear intercept obtained by means of lung morphometry with hyperpolarized ³He diffusion MRI versus direct measurement. Each point represents one lung. L_m (³He) is median calculated across entire lung; L_m (histology) is median calculated across all lung specimens corresponding to this lung.

The variation of ADC, anisotropic diffusion coefficients (D_L0 and D_T0 from Eqs. [8] to [9]) and acinar airway geometrical parameters with histological emphysema severity, obtained from six lung specimens (146), are shown in Figure 9.

FIG. 9.

Summary of data obtained for six human lung specimens. a: D_L0, D_T0, and ADC (in cm²/s); b: R and h (in mm); c: S/V (in cm⁻¹); d: N_v (in mm⁻³) (adapted from Ref. 146). Markers (•) represent two control healthy lungs, markers (▴)–two lungs with mild emphysema, markers (▾)−two 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 L_m obtained from direct histological measurements on the same lungs.

Figure 9a demonstrates that the longitudinal diffusivity D_L0 grows rapidly at initial stages of emphysema and soon approaches the “free” limit (about 0.88 cm²/s) for severe cases. Such a behavior is the result of reduced alveolar sleeve depth h with emphysema progression, as seen in Figure 9b. This destruction or retraction of the septa separating alveoli belonging to the same airway leads to lessening of the restrictions to ³He gas diffusion along (parallel to) airways, practically removing them in severe emphysema cases.

Figure 9b 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 (164) and was later confirmed in elastase-induced emphysema in rodents (175,176). More recent studies (177) also demonstrated shortening of alveolar walls and effacement of inter-alveolar septa. The results in Ref. 146 observed this phenomenon by a non-invasive technique for the first time and quantified such changes with emphysema progression.

The results for surface-to-volume ratio from diffusion MRI shown in Figure 9c are in good agreement with the results of morphometric measurements (17) obtained from excised lung specimens: S/V = 256 ± 24 cm²/mL for control human subjects, 165 ± 23 cm²/mL for subjects with mild emphysema, and 43 ± 6 cm²/mL for severe emphysema.

Measurements of N_v in two healthy lung specimens (120 and 146 per mm³) in Figure 9d are in agreement with a direct morphometric approach (26) in healthy human lungs (the average N_v varies between 132 and 177 per mm³). In addition to the above-cited measurements in healthy lungs, data in Figure 9d demonstrate changes in the number density of alveoli with emphysema progression—N_v decreases to about 60 per mm³ in mild emphysema and even further to about 10 per mm³ in lungs with severe emphysema. Such decreases in alveolar density are expected due to lung dilation and alveolar coalescence.

Osmanagic et al. (166) applied the lung morphometry technique with hyperpolarized ³He diffusion MR to study explanted lungs in mice. The MR protocol and empirical relationships relating diffusion measurements to geometrical parameters of lung acinar airways were adjusted to acquire data with much shorter diffusion times as compared with humans to accommodate the substantially smaller acinar airway length. This measurements yielded mean values of lung surface-to-volume ratio of 670 cm⁻¹, alveolar density of 3200 per mm³, alveolar depth of 55 μm, and mean chord length of 62 μm, all consistent with various results from the literature obtained by stereological analysis of mouse lungs (40,178–185). The technique was further implemented by Wang et al. (167) for in vivo lung imaging in mice. Results indicated a very good agreement between in vivo morphometry via ³He MRI and microscopic morphometry after sacrifice.

Application of In Vivo Lung Morphometry to Study Human and Animal Lungs

Quirk et al. (104) used the in vivo ³He lung morphometry technique to quantitatively characterize early emphysematous changes in lung microstructure of current and former smokers. Thirty subjects with over 30 pack-year histories and mild or no abnormalities on pulmonary function tests (PFT) were studied. The results were compared against clinical standards: PFT and low-dose computed tomography (CT). Results (see Fig. 10) demonstrate that the non-invasive ³He lung morphometry detected alterations in acinar structure in smokers with clinically normal PFTs. Compared with smokers with FEV_a/FVC >80 %, those with COPD (FEV_a/FVC <70 %) had statistically significantly reduced alveolar depth h (0.07±0.02 vs. 0.13±0.02 mm, P = 0.016) and enlarged acinar ducts radius R (0.36±0.02 vs. 0.304±0.005 mm, P = 0.016). The mean alveolar geometry measurements in the healthiest subjects were in excellent quantitative agreement with literature values obtained using invasive techniques (R = 0.30 mm, h = 0.14 mm at 1 L above FRC (23)). Importantly, ³He lung morphometry detected greater abnormalities than either PFT or CT.

FIG. 10.

Examples of the maps of acinar airways geometric parameters obtained with ³He lung morphometry and CT images for a GOLD 0 former smoker (left, FEV₁ = 93 % predicted, FEV₁/FVC = 80 %), a GOLD 0 smoker (middle, FEV₁ = 94 % predicted, FEV₁/FVC = 71 %), and a GOLD 2 former smoker (right, FEV₁ = 62 % predicted, FEV₁/FVC = 56 %) (adapted from Ref. 104). These images illustrate the heterogeneity of disease across the lungs and the significant increases in R and L_m, and decreases in h and N_v with COPD. Red pixels on the CT images indicate regions of emphysema (attenuation less than −950 HU). Charts on the right summarize results obtained from 30 current and former smokers; they show the increase in (a) mean chord length, (b) %EI₋₉₅₀, and (c) acinar duct radius, and decrease in (d) alveolar depth h with decreasing prebronchodilator FEV₁/FVC by PFT. The FEV₁/FVC <70 % group is statistically significant against all other groups for all measurements shown (*P < 0.05). The FEV₁/FVC 70 to 80 % group is also statistically significant against all other groups on the ³He lung morphometry measurements (*P < 0.05), but not on the CT-based %EI₋₉₅₀. Error bars are standard deviations.

The important feature of all these maps is their relative homogeneity in the GOLD 0 former smoker’s lungs versus significant disease-related heterogeneity even in early emphysema. In the latter case a clear contrast is seen between central portion of the lung and lung periphery. This “bimodal” behavior (two-peak feature) is especially obvious if data are presented as histograms, as in Figure 11.

FIG. 11.

Histograms of the lung geometrical parameters and CT images in HU for the subjects in Figure 10.

First we note that while lung density reflected in CT histogram is different in emphysema as compared with normal lungs, the relative shift in practically all parameters determined by ³He MRI is substantially larger. Probably the most interesting is behavior of L_m that demonstrates a pronounced “bimodal” feature that is also seen in alveolar depth histogram and only hinted in other ³He-derived parameters, but is not seen in CT data at all.

Another population where one expects a change in alveolar microstructure is post pneumonectomy. After removal of a lung, the remaining lung usually increases in size to fill the space in the thoracic cavity. While the extent of this increase depends on the shifting of other organs, primarily the heart and liver, some degree of expansion is commonly noted. When the lung increases in size, it is uncertain whether this is the result of stretching of the existing alveoli, the growth of new alveoli, or a combination of both effects. If the lung responded purely by stretching, we would expect that the number of alveoli would be the same as for a single lung, the alveolar number density N_v would decrease, and the values of R and L_m would be elevated. A recent study by Butler et al. (186) using helium lung morphometry found that a woman 15 years post pneumonectomy had normal values for R with a uniform distribution of values across the lung, and slightly decreased values for h. These results suggest that the lung responded to the mechanical forces by forming new alveoli. These results were supported by Wang et al. (187) in a longitudinal mouse study where compensatory growth was found to restore the lung volume, compliance, and alveolar number to pre-surgery values by a month following surgery.

Hajari et al. (188) used in vivo lung morphometry to study the mechanisms of lung inflation and deflation in humans. Despite decades of research, there is little consensus about whether lung inflation occurs due to the recruitment of new alveoli or by changes in the size and/or shape of alveoli and alveolar ducts. In this study Hajari et al. measured the average alveolar depth and alveolar duct radius at three levels of inspiration in five healthy human subjects and calculated the average alveolar volume, surface area, and the total number of alveoli at each level of inflation. The results indicated that during a 143 ± 18 % increase in lung gas volume, the average alveolar depth decreases 21 ± 5 %, the average alveolar duct radius increases 7 ± 3 %, and the total number of alveoli increases by 96 ± 9 % (results are means ± SD between subjects). These results indicated that in healthy human subjects the lung inflates primarily by alveolar recruitment and, to a lesser extent, by anisotropic expansion of alveolar ducts.

The first ¹²⁹Xe applications of in vivo lung morphometry technique have been demonstrated by Ruppert et al. (169) (see example in Fig. 12) and Ouriadov et al. (170) in humans, and Boudreau et al. (132), and Hegarty et al. (140) in rats.

FIG. 12.

Examples of axial maps of alveolar sleeve depth h (left panel) mean linear intercept L_m (middle panel), and acinar-duct radii R (right panel) obtained with ¹²⁹Xe lung morphometry in a healthy human volunteer at 3 T (adapted from Ref. 169).

Accuracy of In Vivo Lung Morphometry Technique: Effects of Acinar Airways Branching and Distribution of Airway Geometrical Parameters (Theoretical Analysis)

While lung morphometry technique with hyperpolarized ³He diffusion MRI has been validated experimentally in human (146) and mice (166,167) lungs, questions related to its “theoretical accuracy” were discussed in detail by Sukstanskii et al. in Ref. 145. As for any approach dealing with a complicated structure, the lung morphometry technique with hyperpolarized gas diffusion MRI is based on assumptions and simplifications that potentially might bias the measurements. The core of the technique is a model that incorporates the salient feature of gas diffusion in acinar airways on the time scale when diffusing gas molecules have a chance to diffuse in and out from single alveoli but still spend most of their time in the same acinar airway. This leads to diffusion being anisotropic on microscopic (single airway) scale-the diffusivity D_L along airway axis is bigger than the diffusivity D_T perpendicular this axis. Since the measured MR signal originates from a large number of acinar airways with almost homogeneous distribution of their direction, diffusion MR signal has very little dependence on diffusion sensitizing gradient direction, i.e. it has macroscopically isotropic character. This microscopically anisotropic feature of the technique has been confirmed in numerous publications (84,101,127,132,146,166–169).

To address the accuracy of this theoretical model, Sukstanskii et al. (145) conducted Monte-Carlo simulations of gas diffusion in lung acini in a more general model, accounting for (a) the branching structure of the acinar airways and the finite length of alveolar ducts and sacs, (b) the distribution of airway geometrical parameters R and r of 17 % about the mean values, and (c) the effects of internal inhomogeneous magnetic fields. These results were then fitted by the model in Eqs. [6] to [9].

Simulations were conducted for diffusion time Δ = 1.8 ms used in ³He lung morphometry technique in humans (146). For this short diffusion time the probability to cross two branching nodes and to diffuse into the next-to-adjacent airway is negligibly small—about 1 %. Hence it is sufficient to consider for simulations only two types of basic airway configurations as shown in Figure 13 and weight them appropriately for calculating MRI signal. Of course, such a simplification is not valid for long diffusion times.

FIG. 13.

Two types of basic airway configurations contributed to MRI signal (adapted from Ref. 145). The internal alveolar structure of the airways is not shown and the aspect ratio is changed for better view of the structures. The first configuration with two nodes (a) corresponds to an alveolar duct of generation Z (shaded airway), surrounded by a “parent” duct of generation (Z − 1), a “sister” airway of generation Z, and two “daughter” airways of generation (Z + 1). Symmetrical branching with half-angle α = 40° is assumed. The second configuration with one node (b) corresponds to an alveolar sac of terminal generation Z (shaded airway), surrounded by a “parent” duct of generation (Z − 1) and a “sister” airway of generation Z.

The input values of the geometrical parameters (typical for healthy lungs and lungs with mild emphysema) used in simulations and those from the fits to the data are presented in Table 1. For SNR equal or bigger than 100, fitting differences associated with noise are much smaller than that related to other sources.

Table 1.

Results Obtained for Lung Acinar Airway Structure Depicted in Figure 13

Input Parameters			Fitting Parameters
R0, μm	r0, μm	(S/V)0, cm−1	R, μm	r, μm	S/V, cm−1
300	140	225	286 (−5%)	135 (−4%)	235 (4%)
300	180	190	296 (−1%)	163 (−9%)	210 (8%)
350	180	183	314 (−10%)	171 (−5%)	196 (7%)
350	220	156	330 (−6%)	199 (−9%)	172 (9%)

The numbers in parenthesis represent the relative difference (%) between the value found from the fitting analysis and the corresponding input value (adapted from (145)).

According to Table 1, all the parameters (R, r, S/V) found from fitting the model to simulated data using Eqs. [6] to [9], representing an idealized structure of branching acinar airways, are very close to the input values. In particular, for the surface-to-volume ratio, the average difference is 6.5 %. For a non-invasive technique able to measure microstructural parameters across the lung, this degree of potential error is easily tolerable.

One of the main assumptions of the model was the ability to describe the total MR signal from an acinus as the sum of signals from individual acinar airways. This assumption holds only if a diffusing ³He atom resides primarily within the same airway throughout the diffusion gradient pulse. Our simulations demonstrate that ³He atoms spend most of their diffusion time (typically, 75%) within a single airway. This may explain why our approach, based on the assumption of “noncommunicating” or infinite-length airways, describes data very well, as shown in Table 1. It is important to emphasize once again that only specified diffusion times should be used when applying lung morphometry technique. For example, applying this technique to study human lungs using hyperpolarized ³He gas with diffusion times different than those prescribed in Ref. 146 (1.6–1.8 ms) may lead to bias in estimates of lung geometrical parameters.

ADC VERSUS LUNG MORPHOMETRY WITH HYPERPOLARIZED GAS–AMBIGUITY OF ADC RELATIONSHIP WITH LUNG MICROSTRUCTURE

As mentioned in the Introduction, ADC is an important but insufficient parameter to characterize lung microstructure in standard morphometric terms because there is no one-to-one correspondence between ADC and histological parameters, e.g., L_m. To demonstrate this, in Figure 14 (adapted from Ref. 189, the results of the study (104) for 30 subjects are accumulated and plotted as ADC vs. Lm (all data for diffusion time 1.8 ms). The lines represent the dependence of ADC as a function of mean linear intercept L_m, theoretically calculated at fixed values of the ratio h/R (given by numbers near the lines) by using Eqs. [8], [9] and

$$\mathrm{ADC}=\frac{1}{3}{D}_{\mathrm{L}0}+\frac{2}{3}{D}_{\mathrm{T}0}$$ [10]

As we see, each value of L_m can be associated with numerous values of ADC, and vice versa. It means that the correlation between these two parameters is very limited.

LONG-RANGE DIFFUSION

All of the methods discussed above have used diffusion times of about 2 ms, corresponding to free displacements under 1 mm. Thus, most gas atoms start and end the diffusion-interval (determined by the gradient pulse) in the same acinar airway. Additional information about the lung airways is available from long-range ADC (LRADC) measurements.

Diffusion over longer distances (1–3 cm, for example) requires much longer diffusion time intervals (several seconds). This is much longer than the intravoxel T2* of approximately 20 ms at 1.5 T, which determines the life-time of transverse magnetization in gradient-echo images. The solution is to let the longitudinal spin magnetization M_z carry the position information. To achieve this, a sequence of two π/4 RF pulses is used, separated by a gradient pulse in the x-direction (116). The M_z is modulated from relative value 1 to 0 as a function of x,

$$M_z=\frac{1}{2}[1-\cos (2\pi x/\lambda )]$$ [11]

where the wavelength of modulation λ is determined by the area of the gradient pulse λ = 2Π/γGt. A small-flip angle inspection image taken afterwards in the XY plane reveals a stripe pattern superimposed on the lung image. An example of stripe images obtained from a dog with unilateral elastase-induced emphysema is shown in Figure 15.

FIG. 15.

Time sequence of tagged images in dog with emphysema in the right lung only (right side of each image) (adapted from Ref. 116). The images have a tagging wavelength of 3 cm and were acquired 0 to 4.1 s after tagging, in equal increments of 1.36 s. The images presented are all from the same slice, out of a total of 10 slices. The LRADC map at lower right is calculated from the decay rate of the fractional modulation on a pixel-by-pixel basis, and shows a substantial difference in LRADC between the two lungs. The fast diffusion is evident from the rapid disappearance of the modulation in the right lung. An ADC map of short-range diffusion is also shown for comparison; note the different scales for LRADC and ADC.

Brownian motion (diffusion) of the gas will mix the bright (magnetized) and dark (unmagnetized) spins, leading to a decay of the spatial modulation (115). That is, the stripes fade without losing average intensity, as in Figure 15. To reveal only the effect of diffusion on the stripes, a normalizing scheme that corrects for overall T₁ decay of the signal as well as consumption of M_z by the RF imaging pulses is usually used (67,116,117).

Woods et al. (116) found that in healthy canine lungs the average LRADC was 0.015±0.004cm²/s, which is about 10 times smaller than the average measured value for the traditional short-range ADC measured over milliseconds and hundreds of microns. In the emphysematous lung, the average LRADC varied from animal to animal, with significant increases from the normal lung in four of five dogs. An average increase in LRADC by a factor of 2.7 in the emphysematous canine lungs implies that the technique may be used as a measure of tissue destruction, airway connectivity, and collateral ventilation over large distances.

The relevant length scale for diffusive motion is λ/2, about 1 to 1.5 cm in Ref. 116. In healthy lungs, the airways form a network of bifurcating paths over about 23 levels (21). Thus the airways are singly connected with a unique path between any two points: a journey from one location at, e.g., level 21 to level 22 at a point 1.5 cm away necessarily requires going from one acinus to another, since acini have maximum linear dimensions of about 7 mm. Thus, the atom must move from level 21 to at least level 16 (the level where acini commence and interconnect) and back to level 22. At each of many junctions, the atom must make the correct turn if it is to leave its starting acinus. This tortuous path will make the long-range ADC quite small (0.02 cm²/s has been measured in vivo in normal human lungs) if gas motion is restricted to along the airway tree. Further discussion of the diffusion physics behind LRADC measurements can be found in Refs. 67,119,153,154,190.

In emphysema, collateral ventilation pathways develop and can become as important for peripheral gas flow as the more usual (airway) routes (191–193). This occurs as some collateral paths will have less resistance to gas flow than through diseased airways, allowing for ventilation and gas exchange to partially adapt to the structural and physiological abnormalities imposed by the disease. Thus, there are now an increased number of diffusion paths that are functioning routes for long-distance convective transport or diffusion of gas. In essence, collateral paths are short-circuits (bypasses) and will result in substantial increase in the long-range diffusivity. Thus, we believe that long-range ADC measurements provide information on the extent of collateral pathways.

Increased collateral ventilation will be required for the success of some (although not all) airway bypass procedures proposed to ameliorate emphysema. In one such scenario (194), an artificial airway is made by piercing an airway wall to connect a patent airway to a previously under-ventilated or gas-trapped region of lung parenchyma. The desired situation is that a large volume of hyperinflated lung that intercommunicates effectively through collateral pathways could be emptied through a small number of artificial airways, producing many of the benefits of lung volume reduction surgery but with minimal invasiveness. Without collateral paths, this proposed procedure is unlikely to succeed, as only the region immediately adjacent to the connection to the new airway would be emptied of its trapped gas.

Different approaches to studying LRADC have also been published. Fichele et al. proposed monitoring filling-in of magnetization from neighboring slices (195). Mugler et al. (196) and Wang et al. (120) have used through-slice magnetization modulation reporting measurements for diffusion times ranging from milliseconds to seconds. In healthy subjects, they found that the apparent diffusion coefficient decreased by about 10-fold, from approximately 0.2 to 0.02 cm²/s, as the diffusion time increased from approximately 1 ms to 1 s. Such a decrease is similar to result by Woods et al. (116). Boudreau et al. (132) used PGSE method at low static magnetic field strength of 73.5 mT for diffusion measurements at Δ = 6, 50, and 100 ms.

CONCLUDING REMARKS

Numerous diagnostic tools have been developed to evaluate the presence and the stage of chronic obstructive pulmonary diseases. The introduction of hyperpolarized gas MRI (³He and ¹²⁹Xe) has opened the door to developing new diagnostic tools for studying lung function and structure. Most applications to date have used hyperpolarized ³He as it has a higher nuclear magnetic moment than¹²⁹Xe (thus providing stronger MRI signal), is easier to polarize and is more biologically inert. However, a major problem tempering clinical implementation of hyperpolarized ³He gas MRI techniques is a shortage of the gas and its increasing cost (197), although recapture/reuse systems are being implemented (198) and will help to extend the gas supply. An alternative “hyperpolarizable” gas, ¹²⁹Xe, is cheaper and more readily available suggesting that it can become the gas of choice for these new techniques.

In this review we discussed MRI methods that are based on measurements of hyperpolarized gas (³He or ¹²⁹Xe) diffusion in the lung airspaces of humans and animals. These methods, being sensitive to changes in lung microstructure at the alveolar level, have a great potential to improve our understanding of lung structure and function in health and disease.

Numerous studies have demonstrated changes in hyperpolarized gas ADC in different diseases, especially in emphysema suggesting the use of ADC as a biomarker for disease progression. Advantages of the ADC approach are its relative simplicity and speed (only two b-values are needed for measurement as compared with minimum three for lung morphometry). However, the ADC is not an inherent property of the lung microstructure (as is L_m) and depends on the details of MRI protocol (diffusion time and b-value) that are not always described in scientific publications. This makes it impossible to directly compare data from different laboratories. Establishing guidelines for studying lung with hyperpolarized gases, similar to those established by the American Thoracic Society and European Respiratory Society for lung morphometry (31), would be of great value. Part of this effort should also be standardizing breathing protocols as MRI measurements substantially depend on lung volume.

An advanced technique-in vivo lung morphometry-allows evaluation of the geometrical parameters of acinar airways and alveoli from hyperpolarized gas diffusion MRI measurements. It reports on lung microstructure using data metrics (L_m, S/V, alveolar density, acinar airways radii) that are established markers used by lung physiologists for decades but were previously available only from invasive biopsy studies. Compared with PFTs that provide only “global” assessment of the disease, in vivo lung morphometry offers three-dimensional tomographic information on lung microstructure and may substantially aid in accurate diagnostic and treatment options. Compared with CT (which provides information only on lung tissue density and may be used to infer aspects of lung structure), in vivo lung morphometry provides information on gas ventilation and tissue microstructure at the alveolar level without the use of ionizing radiation. The safety and sensitivity of this technique suggests that it is well suited to improving our understanding of the mechanisms and development of pulmonary diseases and has the potential for monitoring the efficacy of therapeutic interventions in clinical trials.

Another issue that can streamline the adoption of hyperpolarized gas MRI into the clinical arena is accelerating data acquisition. For example, such techniques as radial acquisition (e.g. (199)) or widely available parallel imaging can substantially speed up clinical protocols potentially allowing whole lung coverage within a few seconds easily tolerable for breath-hold sessions. Both ADC and lung morphometry techniques could benefit from these advances.