Magnetization Tagging Decay to Measure Long-Range ³He Diffusion in Healthy and Emphysematous Canine Lungs

Abstract

Spatial modulation (tagging) of the longitudinal magnetization allows diffusive displacements to be measured over times approximately as long as T₁ and over correspondingly long distances. Magnetization tagging is used here with hyperpolarized ³He gas in canine lungs with unilateral elastase-induced emphysema. A new scheme for analyzing images subsequent to tagging determines the spatially-resolved fractional modulation and its decay rate, using a sliding window. The diffusivity so determined over seconds and centimeter lengths, D_sec, is smaller in all cases than the diffusivity measured over milliseconds and hundreds of microns, D_msec (in healthy lungs, this ratio is about 0.1). While D_msec is sensitive to lung microstructure on the alveolar level, D_sec reflects airway connectivity and provides new information on lung structure. The results show substantial increases in D_sec in the lungs of four dogs with clear evidence of emphysema. For these dogs, the fractional increase in long-range diffusivity D_sec in the emphysematous lungs was greater than that in short-range diffusivity D_msec.

The free diffusivity D_o of ³He, dilute in air or N₂, is exceptionally large at 0.88 cm²/s. Thus, the root mean square (RMS) free displacement of a typical ³He atom during several milliseconds is larger than the diameter of the acinar airways, with the result that the apparent diffusivity measured over such times is restricted by collisions with airway walls and is near 0.2 cm²/s in healthy lung (1– 4). Airway expansion and destruction of airway and alveolar walls in emphysema (5) result in reduced restriction of diffusion (D ≈ 0.55 cm²/s in a group of severely diseased subjects) (3). Nearly all of the work to date has measured D_msec, taken from the decay of transverse magnetization measured at two b-values (that is, with and without a pulsed, diffusion-sensitizing field gradient) (3,4,6 – 8). The experiment is sensitive to displacements during the gradient waveform that is typically several milliseconds in duration, corresponding to displacements of a few hundred microns. This time is limited by the short $T_2^{\ast }$ of ³He in lung (about 20 ms in 1.5 T) (9,10). The small length scale associated with this method limits the motion to individual acinar airways where 95% of the gas resides; the time is not sufficient for many of the atoms to move from one airway to the next. Multi-b-value measurements of the decay of transverse magnetization over times of milliseconds have been understood in terms of anisotropic diffusion, with different values longitudinal and transverse to the airways (D_L and D_T) (1). Diffusion values so measured are sensitive indicators of the changes in localized lung morphology that accompany emphysema.

However, by probing gas diffusion over longer times, one can examine the structure of the airway network over longer length scales. In the canonical description of lung (11), there are 24 levels of branching airways, where the trachea is Z = 0 and the alveolar sacs are Z = 23. The acinar units are the primary regions of gas exchange and comprise the highest-numbered eight airway levels. The mean linear size of an acinar unit is about 7 mm, with individual acinar airways having lengths of approximately 1 mm (11). Because the average acinar-airway length is small, and the acini contain the vast majority of gas in the lung, diffusion between arbitrary points that are centimeter(s) apart requires that atoms must travel from one acinus to another, connecting via a common conducting airway node. From the alveolar sacs, for example, this is a path through eight or more airway levels. The diffusion coefficient measured over such long distances will necessarily be smaller than that measured over submillimeter distances, due to the negotiation of the tortuous path of airways from one acinus to another. Thus, long-range diffusion is sensitive to different aspects of the lung’s structure, compared to those affecting short-range diffusion. In particular, long-range diffusivity is sensitive to the connectivity of the airways.

Long-range diffusion and airway structure may indeed be relevant to lung disease. Two of the current authors (J.D.C. and C.K.C.) and other research groups are exploring the possibility of ameliorating emphysema by installing a few artificial airways to connect poorly ventilated lung regions to well ventilated regions (12). Good communication within each region is essential for the success of this approach, so that a realistic, limited number of artificial airways can improve the ventilation to a significant volume of lung (12,13). Probing diffusion over longer length-scales, spanning multiple acini and/or multiple lobules, may provide a means of measuring this internal communication.

The tagging of longitudinal magnetization is limited by the longest relaxation time in the spin system, T₁, which allows diffusion over much greater times and distances to be probed. Sinusoidal spatial modulation of the longitudinal magnetization (magnetization tagging) can be prepared with two RF pulses separated by a gradient pulse (14). The result is periodically modulated magnetization with wavelength λ. For a gradient pulse of amplitude G and effective duration t, λ is given by γGλt = 2π. If the two RF pulses are each of flip angle θ with the same RF phase, the fraction of longitudinal magnetization M remaining at position x after the second RF pulse is obtained from Bloch’s equations:

$$M=co{s}^2\theta -si{n}^2\theta \mathit{cos}(\gamma \mathit{Gxt}).$$ [1]

The case with θ = 45° gives, with k ≡ γGt = 2π/λ:

$$M=[1-\mathit{cos}(kx)]/2,$$ [2]

This delivers 100% modulation of the magnetization while avoiding the ambiguity of sign reversal that occurs with gradient-echo (magnitude) imaging. RF pulses <45° generate a smaller amplitude of modulated magnetization, but with the same wavelength.

After the magnetization tagging pulses, the spatially modulated magnetization is homogenized by diffusion according to the diffusion equation (15)

$$\partial M/\partial t=D_{\mathit{sec}}{\nabla }^{2}M.$$ [3]

Here the notation D_sec serves as a reminder that the apparent diffusivity is expected to depend on the time scale of the measurement (16). T₁ relaxation has not been included. Assuming a trial solution with the cosinusoidal spatial dependence of Eqs. [1] and [2] with only the modulated part of the magnetization being attenuated by diffusion,

$$M=A+B(t)\hspace{0.17em}\mathit{cos}(kx)=A+B(0)\mathrm{\hspace{0.17em} }\mathit{cos}(kx)\mathrm{\hspace{0.17em} }\mathit{exp}(-Rt).$$ [4]

The decay rate constant R is determined by Eq. [3] as

$$R=D_{\mathit{sec}}{k}^2=4{\pi }^2{D}_{\mathit{sec}}/{\lambda }^2.$$ [5]

We note that the decay rate and resulting D_sec are independent of the modulation depth B(0) in Eq. [4]; thus, an exact calibration of the RF tagging pulses is not necessary.

Diffusion over distances of approximately λ/2 connects points of maximum and minimum magnetization, and thus is most effective at destroying the spatial modulation. Hence, diffusion over different length-scales may be measured by the selection of different k (or λ) in the magnetization tagging sequence. As displayed in Fig. 1a, the effect of diffusion is to transport magnetization from crests to troughs without changing the average magnetization. The effect of both T₁ and the consumption of longitudinal magnetization M by subsequent RF imaging pulses (used to inspect the decaying modulated magnetization) is to drive M uniformly toward zero, independently of position x, as in Fig. 1b. Here we recall that the thermal equilibrium magnetization is essentially zero compared to the initial hyperpolarized state. Thus, the fractional modulation (B(t)/A from Eq. [4]) is unaffected by T₁ and RF pulses, which allows long-range diffusion to be measured without corruption from these effects. This is valid provided that T₁ and RF pulses are uniform over the length scale λ. The RF field amplitude B₁ is a slowly varying function of position in the RF coil, so B₁ inhomogeneity is not expected to distort the decaying sinusoidal magnetization over the relevant scale of λ (2–3 cm). $T_1^{-1}$ is known to be proportional to O₂ concentration, and the O₂ concentration may not be uniform— especially in some disease states. This is expected to exert at most a minor effect on the fractional modulation, as T₁ in lungs is typically 20 s, and the modulated magnetization was followed out to times no longer than 10 s (typically 6 s). In addition, in the reported case of healthy subjects, the regional variations in T₁ over centimeter distances are small (usually much less than 20% (17)).

FIG. 1.

Idealized representation of the cross section of a tagged image at increasing times: 0 < τ₁ < τ₂. In a, diffusion alone is represented, without the influence of T₁ processes or RF consumption of magnetization by imaging pulses. The spatial magnetization is unchanged, but the extent of modulation is attenuated by the diffusion. In b, the influence of T₁ and the RF imaging pulses is depicted, with no diffusion. Here the shape of the cross section is unchanged, because the magnetization is reduced everywhere by the same factor. Depicted in c is the combination of the two effects (where τ₁/T₁ = 0.2, τ₁R = 0.7, and τ₂ = 2τ₁), from Eq. [6].

In the case in which D and T₁ are both non-negligible, Eq. [4] can be rewritten, with RF-pulse effects on M being subsumed into the effective T₁:

$$M=e^{-t/T_1}[A+B·e^{-Rt}\mathit{cos}(kx)]$$ [6]

The variation of M upon x at three values of t is presented in Fig. 1c for such a case.

The first magnetization tagging measurements with hyperpolarized ³He in lung were recently reported by Owers-Bradley et al. (18,19). The tagging was used to image respiratory motion, and diffusion was measured from the decay of tagged magnetization across the entire lungs, without imaging. Their method calculated D_sec from decay rates at several different tagging wavelengths. The result of D_sec = 0.02 cm²/s in a healthy subject is one-tenth of typical D_msec values. This dramatic decrease in diffusivity over larger distances is in accord with the explanation offered above, in which motion over centimeters involves gas traveling from one acinus to another through the maze of airways via the common node on the airway tree. We note that the canonical model of airways implies that only one unique airway path exists between any two points (20). The uniqueness makes the long-range diffusivity small.

Gas diffusion has also been measured in vessels by the similar method of selective inversion or saturation of single slices, with xenon or hyperpolarized ³He (21,22). Particularly slow diffusion in an intense field gradient has been measured in supercooled glycerol by means of a multiple hole-burning method (23). We note that the method of stimulated echoes involves spatially modulated longitudinal magnetization, similar to the magnetization shown in Fig. 1.

Collateral pathways are defined as all paths other than the canonical airway tree (24,25), and are essentially orifices that connect one airway to another through the intervening wall. Collateral ventilation in healthy lung is relatively small, but is substantially enhanced in emphysema (26). Thus, collateral pathways are expected to provide alternate routes for long-distance diffusion in emphysema. Consequently, the long-range diffusion D_sec is expected to increase in emphysema, because of both airway expansion and the increase in collateral pathways. We note that the restriction ratio D_o/D_sec is much larger than D_o/D_msec in healthy lung; thus, there is a larger range for a possible increase for D_sec. Such measurements should also shed light on the regional communication (possibly via collateral pathways) required for the success of the artificial airways discussed above.

Here we present spatially resolved maps of long-range diffusion D_sec as measured by the decay of sinusoidally tagged ³He images in dogs with one healthy lung and one emphysematous lung. This strategy allowed simultaneous control experiments to be performed in each animal. We also present a new method for locally quantifying the decay of magnetization-tagged images. For comparison, diffusion over short times and distances, D_msec, was also measured.

MATERIALS AND METHODS

Emphysema was induced in five mongrel dogs, in the right lung only, by instillation of porcine pancreatic elastase through one side of a double-lumen tube. Simultaneous control experiments were performed in the unaffected, healthy left lung of each animal. To ensure that the elastase penetrated deeply into the right lung, we first made the lung atelectatic by ventilating it with pure O₂ and then isolating the lung for elastase lavage. The dogs were generally imaged after three lavage treatments (usually spaced 3 weeks apart), and were also tested with high-resolution CT as part of a separate study. Both CT and ³He MR revealed large mediastinal shifts to the left in four of five dogs, indicative of hyperinflation and emphysema in the right lung (3). All work was approved by the local animal studies committee.

Three separate 500-mL boluses of hyperpolarized ³He gas with 35–50% polarization were prepared with the use of an in-house-built apparatus (6). Each bolus was mixed in a flexible plastic bag with 200 – 400 mL of N₂ for a full breath-hold, to ensure that all possible areas of the lung received enough gas for the diffusion maps. The dogs were ventilated on air with a mechanical piston-cylinder ventilator through a cuffed trachea-tube, anesthetized with isoflurane and/or propofol, and monitored with pulse oximetry via the tongue. At a lung volume of approximately functional residual capacity, the mechanical ventilator was halted and we removed 200 mL of air from the lungs by opening the valves to a partially evacuated 2-L container. Pressures during this maneuver were never below −5 cm H₂O. We then delivered the gas mixture by manually squeezing the ³He/N₂-containing bag (maximum distending pressure = 15 cm H₂O), and imaging was started.

An in-house-built, 30-cm-diameter Helmholtz pair operating at 63.63 MHz (¹H) and 48.47 MHz (³He) was used with a 1.5 T whole-body Magnetom Vision imager (Siemens, Erlangen, Germany) to obtain 10 coronal or 25 transverse slices of proton scout scans and 2-b-value diffusion scans (3). Maps of the ³He short-range diffusivity (D_msec) were generated by the ratio of two gradient-echo fast low-angle shot (FLASH) images, with b = 0 and 1.375 s/cm² (3). The image slices were 8 mm thick, with 5 × 5 mm in-plane resolution, 6-ms echo times (TEs), and a 160 mm × 320 mm field of view (FOV). The diffusion time for ³He atoms in this pulse sequence is about 1.8 ms, corresponding to a free diffusion RMS length of 500 μ. The D_msec measurement involved a breath-hold of typically 15 s.

Magnetization tagging was achieved by means of two nominally 45° RF pulses separated by a gradient pulse, as described in the Introduction. Flip angles were calibrated from the magnetization consumption of four RF pulses, each with a nominal flip angle of 20°. However, as noted above, exact calibration is not essential for obtaining long-range diffusivity maps. Usually, the magnetization tagging was in sagittal planes with λ = 2–3 cm. Six or seven subsequent multislice sets of FLASH images for inspection of the decaying tagged magnetization were taken out to about 6 s. A flip angle of approximately 7° was chosen to retain adequate SNR for the final image set. The 20-mm-thick axial slices were 320 mm × 160 mm FOV, with 5 mm × 2.5 mm pixels. The resolution was better in the readout direction, normal to the tagging planes and thus in the direction along which diffusion is probed. The wavelength λ was selected to correspond to an integer number of readout pixels. The selection of 2–3 cm for λ was made to yield a decay rate R in Eqs. [4] and [5] in the measurable range. Overly large values of λ lead to negligible decay of the tagging in the healthy lung, where D_sec is small. Too-small values of λ result in nearly complete decay of the tags in the first or second image sets in emphysematous regions with rapid gas diffusion.

We measured long-range diffusion D_sec using Eq. [5] from the decay rate constant R of the fractional sinusoidal modulation (proportional to B(t)/A in Eq. [4]). We defined the fractional modulation at each pixel from a discrete Fourier sum, involving only neighboring pixels extending from −λ to λ in the readout/tagging direction about the central pixel. Clearly, the fractional modulation so determined is not independent for pixels separated by less than one wavelength, since their integrals share common data elements. In other words, one cannot expect to determine the Fourier amplitude in a distance smaller than λ. Nevertheless, the use of a sliding window provides a smooth presentation of the data by assigning a value of fractional modulation to each pixel.

We determined both cosine and sine components for the image intensity, as well as the average intensity over the one wavelength. Mathematically, the fractional modulation FM at position x is

$$FM(x)=\frac{\sqrt{C{(x)}^2+S{(x)}^2}}{a(x)}.$$ [7]

Here C, S, and a (average) are each defined for the pixel at x from the image intensities

$$a(x)=\sum I(x+\mathrm{\Delta }x),$$ [8]

$$C(x)=\sum I(x+\mathrm{\Delta }x)\mathit{cos}\left[\frac{2\pi (x+\mathrm{\Delta }x)}{\lambda }\right],$$ [9]

$$S(x)=\sum I(x+\mathrm{\Delta }x)\mathit{sin}\left[\frac{2\pi (x+\mathrm{\Delta }x)}{\lambda }\right];$$ [10]

the sums over Δx run from −λ/2 to λ/2, without end-point redundancy. The fractional modulation defined in Eq. [7] is not sensitive to uniform T₁ decay or consumption of magnetization by the RF imaging pulses, because FM(x) is defined as a ratio of modulated to average signal components.

The above analysis results in five to eight image sets with fractional modulation FM(x) defined for each pixel. For each pixel, the FM values are fitted to a monoexponential decay to determine the decay rate constant R (Eq. [4]) on a pixel-by-pixel basis. The procedure automatically excludes pixels that are outside the lung and/or have FM values of inadequate SNR.

RESULTS AND DISCUSSION

Four of the five dogs displayed an extreme shift of the mediastinum due to hyperinflation of the right, lavaged lung (dog 2 showed a smaller shift). Lower x-ray attenuation at CT was also found in the lavaged lungs. Short-range ³He diffusivity measurements (D_msec) indicate emphysema in the right lung by an average increase of 75% compared to the healthy left lung (Fig. 2 and Table 1) (3). We note, however, that dog 2 shows little evidence of emphysema from D_msec in Table 1. The average D_msec in the control (healthy) dog lungs is 0.17 cm²/s, which is quite close to the average value reported for healthy adult humans (0.20 cm²/s) (1– 4). This is also very close to the average value of D_msec (0.18 cm²/s) measured in two dogs prior to any elastase lavage. While spatial heterogeneity of disease in the emphysematous dog lungs is generally less pronounced than in smoking-induced emphysema in humans, heterogeneity is clearly evident in the short- and long-range diffusivity maps.

FIG. 2.

Axial 2-b-value ³He diffusion maps (D_msec) for animals 4 and 5, taken just below the carina. The left, healthy lung is on the left, and the emphysematous right lung is on the right in the images. The diffusion map of dog 5 is incomplete due to low SNR in some poorly ventilated regions, which are represented as gray; the right lung is outlined from the corresponding proton image (not shown). Violet corresponds to nearly free diffusion of ³He, as present in the largest airways. Emphysema in the right lungs is evident from the substantial increases in D_msec in both dogs.

Table 1.

Diffusivity Results

Dog no.	No. lavages	〈Dsec〉	λ (cm)	〈Dmsec〉
1L (H)	0	0.012	3	0.19
1R (E)	3	0.047	3	0.27
2L (H)	0	0.019	2	0.19
2R (E)	6	0.015	2	0.22
3L (H)	0	0.017	2	0.19
3R (E)	3	0.034	2	0.28
4L (H)	0	0.017	3	0.18
4R (E)	6	0.07	3	0.36
5L (H)	0	0.010	2	0.19
5R (E)	3	0.033*	2	0.45*

Summary of diffusivity values (D_sec and D_msec, both in cm²/s) in canine lungs, both healthy (H, left lung) and with elastase-induced emphysema (E, right lung). The values 〈D_sec〉 and 〈D_msec〉 are averages across all ventilated regions of each lung. The tagging wavelengths λ refer to the measurements of D_sec. (*) denote that significant portions (≥20%) of the right lung of animal no. 5 were not sufficiently well ventilated for diffusion measurements.

In all of the healthy canine lungs, only a small amount of tagging decay occurs during the approximate 6-s duration of the experiment, at our 2–3-cm wavelengths (Fig. 3, left lung). The average diffusion coefficient measured by such decay, D_sec, is 0.015 ± 0.004 cm²/s—approximately one-tenth the value of D_msec in the same dogs. We believe that some of the variation in D_sec seen in the healthy lungs (Table 1) is due to the small extent of decay of the modulation and resultant imprecision in the extracted decay rate. Experimental parameters of time duration and wavelength were better optimized for the larger diffusivity in the emphysematous lungs. Our results of average D_sec in healthy dog lungs are consistent with previous findings in a healthy human, where the diffusivity over centimeter distances was 0.02 cm²/s, again a factor of 10 smaller than D_msec (18,19). The substantial restriction of long-range diffusivity reflects the fact that diffusion over centimeter distances requires the ³He atoms to negotiate the branching airway network over several levels.

FIG. 3.

Time sequence of tagged images in dog 4 with emphysema in the right lung only (right side of each image). The images have a tagging wavelength of 3 cm and were acquired 0 – 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 diffusion (D_sec) 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 D_sec between the two lungs. The fast diffusion is evident from the rapid disappearance of the modulation in the right lung. A map of short-range diffusion (D_msec) is shown for comparison; note the different scales for D_sec and D_msec. The steps in the color bars linearly span the indicated ranges.

The average long-range diffusivity D_sec varies widely from animal to animal in the emphysematous lung, with significant increases from the normal lung in four of five dogs. The increase in <D_sec> in the five lavaged lungs over the healthy (untreated) lungs is by an average factor of 2.7 (compared to a factor of 1.75 for <D_msec>), and at particular locations is as high as a factor of 10 (e.g., Fig. 3; emphysema was not homogeneously distributed in the right lungs of these animals). The average diffusivities are summarized in Table 1. In one of the five dogs (dog 2), <D_msec> was only slightly increased in the right lung, showing little MR evidence of emphysema. In this animal <D_sec>is actually slightly smaller in the right lung compared to the left lung.

In some cases, the decay of modulation in the emphysematous lung is so rapid that it is plainly evident in the raw images, in contrast to the adjacent healthy lung (Fig. 3); presumably, these are areas of more severe disease. In Fig. 3, for example, the diffusivity D_sec is so large in regions of the right lung of dog 4 that the modulation has decayed to nearly zero in the second image— only 1.36 s after the first image was acquired. Compared to the average across the healthy left lung in this case, D_sec is elevated by a factor of 10 in some regions while D_msec has increased by a factor of 3 in the same regions.

In the emphysematous lungs, D_sec generally increases by a larger factor (compared to the value in the control lung) compared to D_msec (see Table 1). The maximum possible value for any measure of the diffusion of dilute ³He in air is the free diffusivity D_o, 0.88 cm²/s. Values of D_msec near this unrestricted limit are measured in the trachea and in some areas of severe disease in humans (3,27). Because D_sec is much smaller than D_msec in healthy lungs, the upper limit set by D_o allows for a larger possible factor of increase of the long-distance diffusivity.

We used paired t-tests to assess differences between healthy lungs and lungs with emphysema. The differences tended to be normally distributed (Shapiro-Wilk W-tests, P > 0.05). The mean for D_sec was 0.046 ± 0.017 (mean ± standard deviation) in emphysematous lungs, and 0.014 ± 0.004 (P = 0.03) in healthy lungs. The mean for D_msec was 0.34 ± 0.08 in emphysematous lungs, and 0.188 ± 0.005 (P = 0.04) in healthy lungs. The ratio of D_msec values (emphysema/healthy) was 1.82 ± 0.45, and the same ratio for D_sec was 3.33 ± 0.96 (P = 0.05). Because dog 2 did not have a significant increase in D_msec (our usual inclusion criterion for emphysema), the results from this dog were excluded from the above statistical analyses. The analyses show that the increase in D_sec in the emphysematous lungs is statistically significant. Furthermore, a statistically significant, larger fractional increase in D_sec than in D_msec is observed when one compares the emphysematous lungs to healthy lungs.

In one measurement, the RF-preparation pulses were slightly misadjusted and exceeded 45°. This generated regions of negative magnetization that appear positive in the magnitude images, giving the tagging profile a somewhat rectified appearance (see Eq. [1]). This nonlinear distortion of the modulation profile interferes with the determination of the modulation decay rate and D_sec, while the magnetization is negative. To avoid this effect, one should use only later images in which the magnetization has become non-negative everywhere through diffusion. The diffusion coefficient can then be determined as usual. In other cases in which pulses <45° were used, the initial fractional modulation was decreased, which simply reduced the tagging contrast. Aside from issues involving the contrast-to-noise ratio (CNR), a reduced modulation depth will not alter the decay rate analysis, and the maps of D_sec will be unaffected. In some cases, one or more regions of the emphysematous lung were so poorly ventilated that analysis of the tagged magnetization could not be performed there. This problem is encountered with all ³He measurements of diffusion (see right lung of dog 5 in Fig. 2, for example).

In summary, we used spatial modulation of longitudinal magnetization to measure the diffusion of hyperpolarized ³He gas over lengths of centimeters and times of seconds. In addition, we created a method for analyzing the magnetization-tagged images that assigns a fractional modulation at each pixel with the aid of a sliding window. This allows one to fit the fractional modulation to a pixel-by-pixel decay rate R, which is related to D_sec by R = D_seck², with k = 2π/λ. Because the fractional modulation is defined as a ratio, the calculated decay rate R is unaffected by uniform T₁ processes and uniform consumption of spin magnetization by RF imaging pulses. We compared D_sec to the more typical D_msec (measured over a few milliseconds and hundreds of microns) in dogs with unilateral, elastase-induced emphysema. We found that in the healthy lungs the average D_sec was 0.015 cm²/s, which is about 10 times smaller than the average measured value for D_msec. This decreased ADC over long distances is due to gas atoms diffusing up and down many levels in the airway tree, to travel from one acinar unit to another. In emphysema, an increase in D_sec is expected, both from airway expansion and the development of collateral ventilation paths. An average increase in D_sec by a factor of 2.7 in the present elastase-induced, emphysematous canine lungs implies that the technique may be used as a measure of tissue destruction and airway connectivity over large distances.