Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease

Abstract

Increases in the low attenuation areas (LAA) of chest x-ray computed tomography images in patients with chronic obstructive pulmonary disease (COPD) have been reported to reflect the development of pathological emphysema. We examined the statistical properties of LAA clusters in COPD patients and in healthy subjects. In COPD patients, the percentage of the lung field occupied by LAAs (LAA%) ranged from 2.6 to 67.6. In contrast, LAA% was always <30% in healthy subjects. The cumulative size distribution of the LAA clusters followed a power law characterized by an exponent D. We show that D is a measure of the complexity of the terminal airspace geometry. The COPD patients with normal LAA% had significantly smaller D values than the healthy subjects, and the D values did not correlate with pulmonary function tests except for the diffusing capacity of the lung. We interpret these results by using a large elastic spring network model and find that the neighboring smaller LAA clusters tend to coalesce and form larger clusters as the weak elastic fibers separating them break under tension. This process leaves LAA% unchanged whereas it decreases the number of small clusters and increases the number of large clusters, which results in a reduction in D similar to that observed in early emphysema patients. These findings suggest that D is a sensitive and powerful parameter for the detection of the terminal airspace enlargement that occurs in early emphysema.

Figure 1

(A) Original CT image of the middle lung slice in a representative COPD patient. LAA% is 55.1. (B) The same image as in A, but the individual clusters comprising contiguous LAA regions are shown in contrasting colors. The lung field was identified from the rest of the image, and the lumen of the trachea and large bronchi were excluded. The white regions are smaller airways and vessels. (C) LAA image of a normal subject. (D) LAA image of a COPD patient. The LAA% and exponent D of the cluster distribution of the two images in C and D are 7.2 vs. 7.1 and 2.97 vs. 1.71, respectively.

Figure 2

Log-log plot of representative cumulative frequency distributions of LAA size. The five lung slices analyzed had LAA% values of 5.1 (1), 15.6 (2), 30.9 (3), 42.3 (4), and 60.4 (5). Eq. 1 then was fitted to the plots by linear regression. In these five cases, r has a value of 0.991, 0.997, 0.987, 0.998, and 0.998, respectively. The corresponding D values are 1.71, 1.87, 1.26, 1.10, and 0.64, respectively.

Figure 3

Relationship between LAA% and D. Open and closed circles represent normal subjects and COPD patients, respectively. The LAA% in the normal subjects were all <30 (dotted lines).

Figure 4

Relationship between LAA% and D. Open and closed symbols represent data from in vivo lung and excised lobe, respectively. The inset shows the correlation between D obtained from in vivo CT images and from excised lobes. Dotted line is the line of identity.

Figure 5

Log-log plots of the cumulative distribution functions of the LAA clusters obtained from the spring network model. The cases 1, 2, and 3 have LAA% values of 12, 29, and 55%, respectively. The corresponding exponents D of the distributions are 2.2, 1.3, and 0.88, respectively. The inset shows the variation of D with LAA%. Small values of LAA% are generated by using S_max = 10, and medium and large values of LAA% are obtained with S_max = 20 whereas NP was increased from 1 to 16%.

Figure 6

Images obtained from simulations using a square lattice (500 × 500) of nodes connected by springs. The lattice constant is 1. The different colors represent LAA clusters in which several nodes have been removed from the network. (A) A 250 × 250 zoom in to the lattice. (B) Zoom into a small area (50 × 50) of the lattice in A. Notice that the three larger red clusters and the smaller neighboring green clusters are separated by tissue (gray). (C) The same network as in B but after 554 additional springs (whose tension was higher than 80% of the maximum tension) have been cut out of the 500 × 500 network. The tension in the walls separating the red and green clusters in B was high, and the alveolar walls broke. As a result, the green clusters are now part of the larger red clusters.