Metrics of lung tissue heterogeneity depend on BMI but not age

Abstract

Altered parenchymal microstructure and complexity have been observed in older age. How to distinguish between healthy, expected changes and early signs of pathology remains poorly understood. An objective quantitative analysis of computed tomography imaging was conducted to compare mean lung density, tissue density distributions, and tissue heterogeneity in 16 subjects, 8 aged >60 yr who were gender and body mass index matched with 8 subjects aged <30 yr. Subjects had never been smokers, with no prior respiratory disease, and no radiologically identified abnormalities on computed tomography. Volume-controlled breath hold imaging acquired at 80% vital capacity (end inspiration) and 55% vital capacity (end expiration) were used for analysis. Mean lung density was not different between the age groups at end inspiration (P = 0.806) but was larger in the younger group at end expiration (0.26 ± 0.033 vs. 0.22 ± 0.026, P = 0.008), as is expected due to increased air trapping in the older population. However, gravitational gradients of tissue density did not differ with age; the only difference in distribution of tissue density between the two age groups was a lower density in the apices of the older group at end expiration. The heterogeneity of the lung tissue assessed using two metrics showed significant differences between end inspiration and end expiration, no dependence on age, and a significant relationship with body mass index at both lung volumes when heterogeneity was calculated using quadtree decomposition but only at end expiration when using a fractal dimension.

NEW & NOTEWORTHY Changes to lung tissue heterogeneity can be a normal part of aging but can also be an early indicator of disease. We use novel techniques, which have previously not been used on thoracic computed tomography imaging, to quantify lung tissue heterogeneity in young and old healthy subjects. Our results show no dependence on age but a significant correlation with body mass index.

INTRODUCTION

Understanding the normal radiological appearance of the older lung and its relationship to lung function is important for discriminating lung disease from normal senescence. During mature aging, the lung undergoes microstructural changes that affect its mechanical (1a, 5, 22, 39) and gas exchange function (43). These changes to the lung are most marked over the age of 50 yr (14, 15) and include alveolar “airspace enlargement” (8a, 38) which reduces the gas exchange surface area and is associated with a loss of tissue elastic recoil (18, 42. Senescent microstructural remodeling differs from the pathologic destruction of the alveoli that defines pulmonary emphysema (17, 37) (a component of chronic obstructive pulmonary disease, which has age-related prevalence). While the normal age-related changes in gross lung structure on pathology and their functional consequences have been well documented, the computed tomography (CT) appearance and densitometry of lung tissue in the normal older nonsmoker have been described in relatively few studies. Similarly, the effect of increased body weight on respiratory function has been studied (25, 28b, 44), whereas the association between body mass index (BMI) and metrics of lung tissue density remains unclear. BMI has been reported to differ by ~2 kg/m² in young (20–30 yr) and older (>50 yr) adults (7); therefore, any comparison of lung appearance in these age groups should consider the potential contribution of BMI.

Automated quantitative methods are increasingly being used on high-resolution chest CT for identifying lung pathology. CT studies using a simple measure of the lung tissue, the mean lung density (MLD), have suggested a decrease in MLD of ~50 Hounsfield units (HU) (0.05 g/cm³) between 20 and 70 yr of age (45). This implies an increase in air volume, which may be the result of normal alveolar airspace enlargement (17, 38) or pathologic destruction of the alveolar walls. More detailed subjective assessments have suggested an increase in tissue and airway abnormalities in older age. Copley et al. (3) compared the presence and extent of CT features on prone imaging from subjects with no known respiratory disease, aged >75 and <55 yr. They noted limited predominantly subpleural basal reticular pattern in the majority of the older group but none in the younger group and more frequent incidence of cysts, bronchial dilation, and wall thickening in the older subjects. Similarly, Winter et al. (46) reported a higher prevalence of abnormal scans in subjects aged >65 yr in comparison with subjects aged <50 yr. They suggested that parenchymal bands, interlobular septal thickening, and lung nodules may represent normal lung aging. In a subgroup of subjects who had never been smokers from the study of Copley et al. (3), it was found that the lung tissue of the younger cohort had a larger fractal dimension (FD) than the older subjects, suggesting an “increased complexity” in lung tissue in comparison to the older group. A limitation of previous studies is the reliance on imaging that is acquired as part of routine clinical diagnosis or screening. Clinical protocols do not explicitly control the lung volume during imaging; instead patients are instructed to maximally inhale or exhale followed by a breath hold. Intersubject variability in lung volumes could introduce error into the comparison of lung densitometry between subject groups, potentially influencing study interpretation.

The main purpose of the current study is to determine whether microstructural parenchymal changes to the lung manifest as quantifiable differences in metrics of lung tissue density in older (>60 yr) and younger (<30 yr) nonsmoking adults who have normal lung function and no radiological abnormalities on CT. Based on prior studies of age-related changes in lung parenchyma, it was hypothesized that lung complexity would decrease with age. Both the older and younger cohorts in this study consist of subjects with a range of BMIs, so that the association between BMI and tissue density can be assessed. Several different metrics of lung tissue density are quantified, to assess mean tissue density, its distribution within the chest wall, and heterogeneity.

METHODS

Subject data.

Imaging and pulmonary function test data were acquired retrospectively from the University of Iowa Comprehensive Lung Imaging Center. Subjects were selected from a previous study of healthy volunteers with normal lung function (under National Institutes of Health Grants R01-HL-064368 and R01-EB-005823) (10, 19, 36). The University of Iowa Institutional Review Board and Radiation Safety Committees approved the study and subsequent use of the data, and all subjects gave informed consent. The data comprised volumetric multidetector row computed tomography imaging, pulmonary function tests (PFTs), and radiology reports. Imaging was acquired in the supine posture at end expiration (EE; volume controlled at 55% vital capacity) and end inspiration (EI; at 80% vital capacity). Multidetector row computed tomography scan parameters were 120 kV, 100 mAs, and a pitch of 1.2. Subject data were acquired during the years 2004–2011, and all data were acquired in the same center under the same imaging protocols with regular scanning calibration. Each volumetric image set contained 500–800 images, with a distance between slices of 0.50 mm and a reconstruction matrix of 512 × 512 pixels.

All subjects in the imaging study who were 60 yr of age or older were considered for inclusion (33 subjects). Subjects were excluded on the basis of ever smoking, previous lung disease or lung injury, PFTs that did not meet American Thoracic Society criteria for normal lung function (2, 28a), or radiologist-identified parenchymal abnormalities. Two female subjects were excluded to maintain equal numbers of males and females. The >60-yr cohort in this study then comprised four male and four female subjects, with mean age 70.8 ± 9.2 yr, and mean BMI of 27.1 ± 4.4 kg/m² (range: 21–32 kg/m²). A further eight subjects aged 30 yr or younger who met the same exclusion criteria were selected from the database, to gender and BMI match the older cohort. The less than 30-yr group were aged 24.5 ± 4.7 yr, with mean BMI of 26.9 ± 3.9 kg/m². Table 1 summarizes the subject physiological data that are relevant to the current study. Upright lung volumes (from plethysmography) were not significantly different between the groups [P = 0.497 and 0.460 for functional residual capacity (FRC) and total lung capacity, respectively]. Forced expiratory volume in 1 s (FEV₁), forced vital capacity (FVC), and their ratio were all significantly smaller in the >60-yr group compared with the <30-yr group (see Table 1).

Table 1.

Subject demographics, including lung air volumes and capacities measured using seated body box plethysmography

	Subjects Aged <30 yr	Subjects Age >60 yr	P Value (Paired t-Test)
Age	24.5 (4.7)	70.8 (9.2)
BMI	26.9 (4.2)	27.1 (4.7)	0.35
FRC, liter	2.92 (0.90)	2.70 (0.69)	0.49
TLC, liter	6.44 (1.51)	6.11 (1.05)	0.46
FEV1, liter	4.48 (1.54)	2.90 (0.83)	0.023*
FVC, liter	5.30 (1.49)	3.61 (0.98)	0.018*
FEV1/FVC	0.83 (0.04)	0.80 (0.05)	0.25
FEV1% Predicted	116.98 (23.97)	123.18 (10.97)	0.51

BMI, body mass index. FRC, functional residual capacity; TLC, total lung capacity; FVC, forced vital capacity; FEV₁, forced expiratory volume in 1 s.

^*Significance for the paired t-test at the 5% level.

The lungs, major airways, and blood vessels were automatically segmented from the volumetric imaging for each subject, using custom-written software [PASS: the Pulmonary Analysis Software Suite, University of Iowa (12)]. Further image analysis was performed using MATLAB (version 2010a, The MathWorks). The segmented images were used to subtract “nontissue” structures from the raw images (large airways, large blood vessels). An erosion filter was then used to perform a “peel” function on the resultant images. This operation was performed along the jagged boundary of the segmented lung parenchyma where any residual nonlung-tissue pixels were removed, effectively shrinking the region of interest by two to three pixels. The filter was applied to all of the images, along the craniocaudal axis.

Supine EE and EI total lung volumes (V_EE and V_EI, respectively) were calculated from the reconstructed images (Table 2). The maximum distance along the mediolateral axis (total lung “width”) and the minimum distance along the craniocaudal axis (lung “height”) were measured directly on the images using caliper measurement tools in PASS.

Table 2.

Lung volumes and dimensions from volumetric MDCT imaging

	Subjects Aged <30 yr	Subjects Aged >60 yr	P Value (Paired t-test)
VEE supine, from MDCT, liter	2.10 (0.54)	2.48 (0.50)	0.15
VEI supine, from MDCT, liter	5.27 (1.14)	4.98 (1.16)	0.43
Difference in supine VEE from upright FRC, liter	−0.81 (0.72)	−0.22 (0.35)	0.04*
Difference in supine VEI from upright TLC, liter	−1.17 (0.66)	−1.13 (0.29)	0.90
Lung craniocaudal height at EE, mm	160 (15)	154 (19)	0.14
Lung craniocaudal height at EI, mm	201 (17)	199 (21)	0.73
Lung mediolateral width at EE, mm	260 (19)	260 (30)	0.93
Lung mediolateral width at EI, mm	283 (23)	280 (35)	0.68

End expiratory and end inspiratory lung air volumes (V_EE and V_EI) are given from volumetric image reconstruction (supine) by subtraction of tissue and blood volumes. MDCT, multidetector row computed tomography; FRC, forced residual capacity; TLC, total lung capacity.

^*Significance for the paired t-test at the 5% level.

Densitometry.

The tissue density (ρ, in g/cm³) was calculated from the Hounsfield units (HU) at each voxel using

$$\text{ρ}=\frac{\text{HU}}{1\text{,}000}+1.$$

ρ was evaluated at three different scales of interest: 1) at the whole organ level by its mean value for each age group; 2) by its spatial variation along the craniocaudal, mediolateral, and dorsoventral (i.e., gravitational) axes; and 3) by assessment of its heterogeneity.

The MLD and its SD were calculated for each subject using intensity values from every voxel within the filtered images (including all CT slices). To quantify the spatial distribution of ρ, a custom-written MATLAB program was used to calculate the mean ρ ± SD within 5-mm sections of tissue that were oriented perpendicular to the three axes.

Heterogeneity in ρ was quantified using two different methods: 1) the FD for ρ, calculated by fitting a straight line to the log-log relationship between coefficient of variation (CoV) and sampling window size (1, 9); and 2) quadtree decomposition (QtD) (4, 23, 33, 35), which accounts for the spatial clustering of tissue with similar ρ. Figure 1 illustrates how two images can result in the same values for CoV but different values for QtD. Further detail on each method is given in the appendix and in Subramaniam et al. (35). Essentially, the QtD algorithm recursively divides an image into quadrants that are considered regions of homogeneous tissue if the pixel intensity values within that quadrant are within a certain range. If the pixel intensity range is greater than the threshold, the quadrant is further decomposed. Thus the number of quadrants, or boxes, resulting from this technique serves to indicate how heterogeneous an image is. A threshold range of 100 HU was used for the QtD method in this study. To allow comparison between subjects and between image slices within a subject, the number of boxes for each image’s decomposition was normalized by the total area taken up by lung tissue in the image slice. The QtD algorithm was programmed to exclude regions of high density (corresponding to blood) that occur at the interfaces between vessel walls and parenchymal tissue. The number of boxes created for one execution of the algorithm on one image ranged from 10,000 to 20,000, with a higher number of boxes indicating an image that contained more heterogeneous lung tissue.

Fig. 1.

A simple schematic illustrating the difference in output between the coefficient of variation (CoV) and the quadtree decomposition (QtD) for 2 sample images. The CoV is identical in both cases since both images have 50% black squares and 50% gray squares. QtD gives different values (4 blocks for the bottom image and 64 for the op) because it groups “like” regions together. The QtD method recursively divides the image into quadrants, until each quadrant bounds a block of pixels that have similar intensity. The more heterogeneous the image, the larger the number of QtD quadrants that will be required.

The two heterogeneity assessment methods were implemented in custom-written MATLAB code. Each analysis method was applied to three image slices that were positioned at 25, 50, and 75% of the distance along the craniocaudal axis, where 0% was defined as the location of the dome of the diaphragm, and 100% was the most apical point of the lung. Results present the mean of values calculated for all three image slices. FD and QtD were compared by age, lung volume (EE and EI), and BMI.

RESULTS

Table 2 lists lung air volumes and dimensions calculated from volumetric imaging at EE and EI. The only significant difference between the two age groups was a smaller change in lung volume from upright functional residual capacity (FRC; as measured in PFTs) to supine EE volume in the older compared with younger subjects (P = 0.04). The EE and EI air volumes (V_EE and V_EI, respectively) and the dimensions along each of the three axes were not significantly different between the two groups. The MLD (Table 3) was significantly smaller at EE in the >60-yr group (P = 0.008), but was not different at EI. The proportion of lung at EE with Hounsfiled units less than −850 (to approximate air trapping) was 3.7 ± 2.4 and 16.4 ± 9.6% for the <30- and >60-yr groups, respectively (P = 0.01, paired t-test; P = 0.003, unpaired t-test).

Table 3.

Densitometric values from volumetric MDCT imaging

	Subjects <30 yr	Subjects >60 yr	P Value (Paired t-Test)
MLD and lung attenuation at end expiration, g/cm3	0.26 (0.033)–742 (33)	0.22 (0.026)–784 (26)	0.01*
MLD and lung attenuation at end inspiration, g/cm3	0.12 (0.008)–883 (8)	0.12 (0.011)–885 (11)	0.81

MDCT, multidetector row computed tomography; MLD, mean lung density.

^*Significance for the paired t-test at the 5% level.

Figure 2, A–C, illustrates the distribution of ρ in three orthogonal axes at the two imaged lung volumes. ρ Is shown normalized by the respective mean MLD for the volume and cohort. The dependent variable in these figures is shown on the x-axis, and the independent variable (percentage of distance along axis) is on the y-axis. The craniocaudal (Fig. 2A) distribution at EI is very similar for both age groups: ρ is close to MLD between ~10 and 80% distance, it increases by 30% in the most apical 20% (by distance) of the lung and decreases by 20% in the most basal 10% (tissue largely within the costodiaphragmatic recess). The EE distribution for the <30-yr group is similar to the EI distributions, except for the lack of increase in ρ from 80 to 100% distance (apical). The EE distribution in the >60-yr group is noticeably different from the other curves. There is an approximately linear decrease in tissue density of ~30% from 5 to 90% distance from the base and a small increase in density in the remaining 10% of lung height.

Fig. 2.

Craniocaudal (A), dorsoventral (B), and mediolateral (C) distributions of lung tissue density in subjects aged <30 and >60 yr of age at end expiration and end inspiration volumes. Note that the dependent variable (density in a 5-mm section of tissue normalized by mean lung density) is graphed on the horizontal axis, and the independent variable (distance to tissue section normalized by total distance) is graphed on the vertical axis such that the density values correspond to the lung orientation in the insets.

The dorsoventral axis aligns with the direction of gravity during supine imaging. The EI and EE distributions of ρ both show a gravitational influence for both age groups (Fig. 2B), with ρ decreasing with increased distance along the dorsoventral axis. There are no obvious differences between the ρ distributions for the two age groups at the respective volumes. That is, for both age groups at EE the normalized ρ decreases approximately linearly (over a range of ± 50% from the mean) with increasing distance over the entire range, whereas at EI the normalized ρ decreases approximately linearly from 30 to 100% distance and increases in the most dependent 30% of the lung (by distance).

The mediolateral axis is shown running from the left lateral surface (0%) to the mediastinum (~50–60%) to the right lateral surface (100%). The distribution for each volume and age group is similar (Fig. 2C): ρ increases with distance from the lateral surface (of either lung) to ~30% of the distance into the lung (i.e., ~60% of the distance into a single lung) and then decreases to the medial surface.

The mean FDs at EI (expiration) were 1.43 ± 0.08 (1.15 ± 0.06) and 1.41 ± 0.11 (1.15 ± 0.04) for the younger and older groups, respectively. There was no significant difference in FD between the two age groups at either volume (P = 0.27 and 0.85 for EI and EE, respectively). In contrast, the FDs at the two volumes were significantly different in both age groups (P < 0.0001 for subjects < 30 and P = 0.0003 for subjects > 60). The relationships between FD and age at each volume are shown in Fig. 3.

Fig. 3.

The relationship between fractal dimension and age for end expiration and end inspiration inflation volumes. No significant relationship was found between the 2 age groups at either volume.

The number of boxes per unit area calculated using QtD was not significantly different between the two age cohorts for either of the two lung volumes, and there was no trend of QtD with age (Fig. 4). QtD at EI (expiration) was 0.24 ± 0.035 (0.35 ± 0.073) for the younger group and 0.24 ± 0.049 (0.33 ± 0.066) for the older group, with P = 1.0 and P = 0.7030 for EI and EE, respectively. QtD was significantly different at the two lung volumes in both age groups (P = 0.0021 and 0.0040, for subjects < 30 and subjects > 60, respectively).

Fig. 4.

The relationship between quadtree decomposition heterogeneity and age for end expiration and end inspiration inflation volumes. No significant relationship was found between the 2 age groups at either volume.

When all subjects from the two groups were pooled, MLD at EE, but not EI, was proportional to BMI, although this was a relatively weak relationship (with an R² of 0.16 for EE and 0.079 for EI). Tissue volume was also weakly proportional to BMI (Fig. 5) with R² = 0.15 and 0.14 for EE and EI, respectively. Normalizing tissue volume by subject height (34) or total lung capacity did not strengthen its relationship with BMI. Figure 6 shows the relationship of the lung percent predicted volume to BMI. Data are shown for imaged EE volumes (supine) and FRC plethysmographic volumes (upright). For both postures, the data show a trend for volume to decrease with increasing BMI. Both trends were weak, particularly that with imaged EE volume; R² for upright FRC was 0.39 and R² for imaged EE was 0.16. FD and QtD both showed significant relationships with BMI (Figs. 7 and 8 for FD and QtD, respectively). FD decreased with increasing BMI at both EE and EI; and QtD increased with increasing BMI. R² values of >0.6 indicate relatively strong relationships between FD or QtD and BMI, for all but FD at EI (R² = 0.19).

Fig. 5.

The relationship between tissue volume and body mass index (BMI) for end expiration and end inspiration lung volumes for pooled data from both age groups. Tissue volume increases with increasing BMI but with relatively weak correlations.

Fig. 6.

The relationship between lung volume and body mass index (BMI) for end expiration (EE; imaged supine) and functional residual capacity (FRC; plethysmographic, upright) volumes, for pooled data from both age groups. Volume decreases with BMI for both supine and upright postures. Note that FRC only measures the air volume, whereas EE also includes tissue and small blood vessels.

Fig. 7.

The relationship between fractal dimension and body mass index (BMI) for end expiration and end inspiration (EI) inflation volumes, for pooled data from both age groups. The EI data result in higher fractal dimension (FD) values. FD decreases with increasing BMI at both lung volumes, but the data spread for EI is relatively large and the correlation is weak.

Fig. 8.

The relationship between quadtree decomposition (QtD) heterogeneity and body mass index (BMI) for end expiration (EE) and end inspiration (EI) inflation volumes for pooled data from both age groups. The QtD at EE is higher than at EI. Both lung volumes show trends of increased heterogeneity with BMI.

To confirm that the location of images selected for analysis did not unduly impact the results, QtD was compared for the three image locations, calculated using images located 25, 50, and 75% of the distance along the craniocaudal axis (Table 4). The EI and EE QtD values at each image location were significantly different from each other (P < 0.01 for all three locations). QtD tended to be largest in the 25% image but was not significantly different from the other two image locations. This analysis was repeated using additional axial images and using reconstructed images from other planes (results not shown). The trends were the same therefore to minimize the analysis time only three image locations were used.

Table 4.

Statistics for the three slice locations for QtD measurements

	Slice 1: 25%	Slice 2: 50%	Slice 3: 75%
End Expiration
Means	0.37	0.34	0.34
SD	0.08	0.07	0.06
Slice 1–2	P = 0.26
Slice 1–3	P = 0.23
Slice 2–3	P = 1.00
End Inspiration
Means	0.25	0.23	0.23
SD	0.04	0.03	0.03
Slice 1–2	P = 0.12
Slice 1–3	P = 0.12
Slice 2–3	P = 1.00

The quadtree decomposition (QtD) of the 3 slice locations were not significantly different from each other, within each volume. Between end expiration (EE) and end inspiration (EI), the P values for corresponding slice locations all proved significantly different from each other i.e., at 25, 50, and 75%; P_QtDEE-EI < 0.0001.

DISCUSSION

The lung undergoes changes to its tissue microstructure with age that are reflected in an age-related decline in most standard measurements of lung function. Studies based on subjective assessments of thoracic CT agree that the older lung has airway and/or tissue appearances that would be considered abnormal if present in the younger adult lung. What has not been clear is whether there are subtle age-related changes to the CT appearance of the lung tissue that could be detected using quantitative methods. The current study used an objective quantitative assessment to determine whether never-smoking younger (<30 yr) and older (>60 yr) subjects with no significant prior respiratory disease have differences in tissue density distribution and tissue heterogeneity (quantified by FD and QtD) on supine volumetric CT. In contrast to previous studies no age-related differences in the lung tissue were found. However, strong relationships were observed between BMI and FD or QtD.

The two age groups that were selected for comparison differ by >45 yr. The younger group represents early maturity, at an age at which lung function has peaked or has entered the early stage of decline (44) The older group is well into the age at which significant lung tissue remodeling is expected to have occurred (44). Static (breath hold) volumes in the upright and supine postures did not differ with age, whereas dynamic volumes (from forced spirometry) were significantly smaller in the older subjects. The lack of difference in static volumes along with the smaller dynamic volumes in the older subjects indicates age-related differences in the lung tissue and/or airway mechanics. Percent predicted FEV₁ was high in both groups (117 and 123% for younger and older, respectively) but not significantly different between them (P = 0.51). FEV₁/FVC was not significantly different with age (P = 0.25); that is, the ratio for the younger group was the same as predicted (83% compared with 81%, P = 0.19), whereas the older group was larger than predicted (80% compared with 68%, P = 0.0003). The high percent predicted FEV₁ and relatively high FEV₁/FVC in the older group are consistent with the older subjects representing a healthy subgroup of elderly with no airflow limitation.

The MLD at EI did not differ with age, whereas MLD was 0.04 g/cm³ smaller in the older group at EE. Well et al. (45) showed a decrease in lung attenuation from approximately −840 HU at 20 yr of age to approximately −890 HU at 90 yr of age, which is presumably associated with increased airspace enlargement. Our mean lung attenuations of −883 and −885 HU for the younger and older group, respectively, correspond to their fitted relationship between attenuation and age at ~80 yr of age. Genevois et al. (8) showed a mean attenuation across men and women aged 21–73 yr of −866 HU, and like our study did not find a significant decrease in attenuation with age. That is, the EI lung attenuation in this study was lower than the average attenuation in the previous studies. However, the images in this study were obtained from volume-controlled imaging whereas participants in both previous studies were encouraged to breath maximally, rather than to a controlled volume.

Static elastic recoil of the lung decreases at a rate of ~0.1–0.2 cmH₂O/yr. Deformation of the lung tissue within its semirigid “container” could therefore be expected to be different with age. Elastic recoil was not measured directly in these subjects; however, the smaller FEV₁ and FVC (and elevated residual volume, not shown here) in comparison to the younger subjects suggests a change in tissue and/or airway mechanics with age that is consistent with other studies (15). It is therefore reasonable to assume that the loss of tissue elastic recoil would also be consistent with previous studies. If hyperinflation was significant in the older group, then the tissue density gradient would be expected to be smaller. Conversely, in the absence of significant chest wall remodeling in older age, loss of elastic recoil (i.e., increased tissue compliance) could result in a larger tissue density gradient or appear as increased air trapping due to airway closure. However the distribution of tissue density (Fig. 2) in the gravitational direction (the dorso-ventral axis) was not noticeably different between the two age groups at either lung volume nor was there any difference in the distribution medio-laterally. Figure 2A shows similarity in the craniocaudal density distribution at EI but not EE. For the younger subjects at both lung volumes and the older subjects at EI, the density was relatively constant through the middle 10–90% of lung height (base to apex). For the older subjects at EE, a gradient in density was observed over the same height range, with lowest density in the lung apices. Variation from these trends in the most apical and basal 10% of tissue is probably because this represents relatively small volumes of tissue, and the basal tissue is adjacent to the diaphragm (or in the recess) so could experience some motion during imaging.

Two metrics to quantify properties of the lung tissue heterogeneity were calculated: a FD, which is a function of the CoV, and the number of boxes by QtD divided by lung area. The simplest measure of heterogeneity (and one that is often employed in image analysis) is the CoV, defined simply as the SD divided by the mean. While CoV can be used to analyze data from a single cohort (obtained at common spatial and temporal intervals), it depends heavily on scale and thus does not provide information on the relationship between large and small scale heterogeneities. FD does not quantify the magnitude of heterogeneity but instead quantifies the relative changes in CoV with a change in spatial (or temporal) scales. The FD is calculated as the slope of the log-log relationship between CoV and scale, therefore the higher the FD the more “complex” the structure. If FD is constant across all spatial scales, then the system is fractal, but absolute constancy in FD is not a requirement: systems can be quasifractal if the log-log relationship between CoV and scale is almost linear over the range of possible spatial scales (as is the case in this imaging), or multifractal if it is linear with different slopes across ranges of spatial scales. The QtD is an index of spatial clustering of similar structures; in this case regions of the lung with similar densities. The greater the value of the QtD the smaller the clusters of like regions in imaging.

For the data set considered, FD was larger at EI than EE, and the opposite relationship with volume was found for QtD. FD at EE for the younger group (1.15 ± 0.05) is consistent with FD calculated from MRI measurement of specific ventilation in supine humans during tidal breathing (32) and FD for PET-imaged perfusion in dog lungs (41). FD at EI (1.43 ± 0.08 and 1.41 ± 0.11 for the younger and older groups, respectively) approached 1.5, suggesting that as the lung inflates the variability of tissue density approaches that of a random distribution. This was also observed by Venegas and Galletti (41) for FD in dog lung perfusion when the vertical gradient was removed (by approximating the gradient as linear). In this case, removing the vertical gradient (which is similar to the effect of expanding to EI). The appendix provides an explanation for how FD and QtD are affected by characteristic changes to the distribution of lung tissue density with lung volume change. At EI the tissue density is expected to be less dense and more uniformly distributed than at EE; at EE the greater density of the lung tissue means that it experiences greater deformation due to gravity, and therefore develops a distinct gravitational gradient (as in Fig. 2B, and represented by the pattern in Fig. A1C). Although the CoV is largest for the pattern with a gradient (Fig. A1E), the FD (calculated as the magnitude of the slope of the log-log plot of CoV against box) is smaller than for the more uniform case. Quadtree decomposition divides the uniform pattern in Fig. A1A into fewer boxes than the pattern with a gravitational gradient (Fig. A1C), thus implying greater small scale heterogeneity when the gravitational gradient is present. QtD calculated for the uniform pattern is lower than for the pattern with a gradient. QtD is therefore smallest when the tissue is most uniform at EI.

Neither FD nor QtD differed with age in our study. This contrasts with Copley et al. (3) who found a higher fractal dimension in the lung tissue of younger (<55 yr) compared with older (>75 yr) subjects. There are several methodological differences between the two studies. Copley et al. (3) analyzed prone imaging whereas our study used supine volumetric images. Gravitational tissue deformation is less pronounced in the prone posture (29, 30), which is similar to the reduction in gravitational deformation in the lung at EI. While both age groups in Copley et al. (3) were older than in the current study (39.4 ± 7.5 and 80.9 ± 4.2 yr, compared with 24.5 ± 4.7 and 70.8 ± 9.2 yr), the difference in age was similar. If the change in MLD with age is linear with time [as suggested by Well et al. (45)], then it is not likely that this would contribute to the difference in study outcomes; on the other hand, if changes in MLD accelerate in older age, then this could result in differences between the two studies. Copley et al. (3) examined selected regions of interest at five thoracic levels on bands of tissue 25 pixels wide and more than 15 pixels from the lung/pleural interface. Our analysis was applied to images at three locations and included all nonairway and nonvessel pixels in the images. FD and QtD did not differ between image location, despite the images being sampled in regions that have different proportions of airway and blood vessel to alveolar tissue. It is therefore unlikely that the different study outcomes are due to erroneous inclusion of airways and vessels in the analysis. The method for calculation of a fractal dimension differs between the two studies. Copley et al. used a topological analysis of the image “surface,” whereas the current study used a more simple calculation. While the different methods would give different quantitative results, it is not likely that they would have other systematic differences.

The higher proportion of air trapping in the older subjects could influence the lack of difference in FD and QtD with age. That is, if air trapping is present in sufficiently large “clusters” of voxels, then this could increase FD and potentially decrease QtD. However, we found only a small weak relationship between QtD and proportion of air trapping, which suggests that the influence of this relationship on our results is minor.

In contrast to the absence of an age effect on tissue FD and QtD, there was a strong relationship between BMI and the two heterogeneity metrics: with increasing BMI, FD decreased and QtD increased. Increased adipose tissue with BMI has been suggested to attenuate signal in thoracic CT (13); however, this would not be expected to affect either FD or QtD. A number of techniques have been suggested for increasing signal strength in obese patients (28); however, these guidelines are generally recommended for those with a BMI >40 (well above the highest BMIs used in this study). In general, if the patient can fit into the scanner, the quality of imaging is unlikely to be greatly reduced (40). If the same radiation dose is used as for a thinner patient, then signal attenuation may occur, although in general this results in reduced contrast overall, and this effect was not seen in our images. Thus, either signal attenuation was minor, or the radiation dose was increased to compensate for abdominal fat and create better contrast. Noise in the form of quantum mottle (13, 28) was not present in our images, and neither was truncation noise. Our analysis was repeated on the darker areas surrounding the lung parenchymal tissue to check if specular noise might influence results; however, no influence from these regions was found. Specular (high intensity) noise was also removed as part of the segmentation and filtering preprocessing steps and would therefore have played no part in the QtD algorithm. In addition, a histogram analysis was done on all images to ensure that their histograms were similar and occupied the same range of intensities.

MLD at EE (but not EI) was proportional to BMI, albeit with a weak relationship. MLD depends on the amount of air in the lung and the amount of tissue (including inflammation) and blood in the parenchyma and small vessels. MLD could therefore increase with BMI (at EE) due to a lower proportion of air in the lung during imaging, which is consistent with findings in the literature that FRC (i.e., EE air content in the upright lung) decreases exponentially with increasing BMI (16). Figure 6 shows decrease in lung volume at EE and in air volume during (upright) measurement of FRC. MLD could also be higher than normal in the presence of inflammation (6, 21), or because of larger blood volume. Figure 5, which shows a positive relationship between tissue volume and BMI [consistent with a previous study comparing controls and obese subjects with BMI ~47 kg/m² (34)], suggests that if the former, then the FD and QtD trends with BMI (which are stronger than the BMI relationship with MLD) could be reflecting the relationship to imaged lung volume seen in Figs. 7 and 8 for EE and EI. If inflammation was present this would increase MLD, but for it to affect QtD and FD would require that inflammation was heterogeneously distributed in proportion to BMI, for which there is no evidence.

MLD could also increase with BMI because of larger blood volume. It has been suggested that obesity results in an increase in total blood volume, with the additional pulmonary blood being accommodated by recruitment of otherwise under-perfused vessels (20, 31). This is likely to be a consequence of the BMI-related decrease in lung volume (16): when lung volume decreases, the stretch on the pulmonary capillaries also decreases, which increases capillary sheet height, reduces pulmonary vascular resistance, and contributes to increased pulmonary blood volume. If the increase in pulmonary blood volume was heterogeneous, this would affect both FD and QtD. Finally, there was a trend in our subjects for females to have lower BMI. Some of the apparent relationship between BMI and heterogeneity metrics could therefore be associated with gender differences. Larger numbers of subjects would be required to assess this.

Study limitations.

A relatively small number of subjects was used for the current study (8 in each age group). The number of subjects was constrained by access to volume-controlled imaging from healthy nonsmoking subjects. Data are available for more subjects in the younger age group but not the older group. To increase the study numbers, the current methods could be tested on clinical imaging; however, as this would not be volume controlled, the variability of heterogeneity metrics within each age group would be expected to be larger.

Unlike previous studies we excluded subjects with radiologist-identified abnormalities. Considering that the presence of some airway and tissue abnormalities is considered “normal” for the older lung, it is possible that we selected “super-normal” subjects that are not representative of the typical older subject. Further study would be required to evaluate whether there are differences between the older subjects used here, and older subjects identified with mild abnormalities.

To derive values for FD we calculated CoV in a grid of regions of interest of specific size. This method might not be as precise as others [for example, low-pass filtering (41)] that do not have a mismatch in shape between the analysis grid and the lung shape. However, the consistency of our FD results with previous studies suggests that the trends of FD with lung inflation in the current study are not unduly affected by using this more simple method. It is also unlikely that volume change, age, or BMI would have a systematic relationship with the accuracy of the method.

GRANTS

This work was supported by the Royal Society of New Zealand Marsden Grant 14-UOA-308.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

K.S. conceived and designed research; K.S. and E.A.H. performed experiments; K.S., A.R.C., and M.H.T. analyzed data; K.S., A.R.C., and M.H.T. interpreted results of experiments; K.S. prepared figures; K.S. drafted manuscript; K.S., A.R.C., E.A.H., and M.H.T. edited and revised manuscript; M.H.T. approved final version of manuscript.

APPENDIX

The fractal dimension.

The FD is calculated as one minus the gradient of the log-log plot of CoV against sample window size (FD = 1 − slope). The CoV is a measure of the SD relative to the mean of the intensities in an image, or sampling window. As such it directly quantifies the variability of ρ with respect to the MLD. The CoV can be calculated for any sized sampling window. In the FD calculation in the current work the CoV was calculated for sampling window sizes ranging from 1 × 1 pixels to 8 × 8 pixels. It is important to distinguish between the CoV calculation for a single window and the FD as calculated by taking into account all the windows. The variation (heterogeneity) within a window can be independent of the FD (the slope), since the slope reflects how much variation can be observed as window size changes.

The quadtree decomposition.

The QtD algorithm reflects the spatial distribution of image intensities. In the QtD the image is recursively divided into quadrants. The range of intensities within each quadrant is evaluated, and if the range is less than a user-defined threshold (here 100 HU), then the pixels in the quadrant are considered homogeneous. The quadrant is considered to be heterogeneous if the range of pixels is greater than the user-defined threshold, and hence, the quadrant is divided into four subquadrants. This process is performed recursively until the image has been reduced to the minimum number of homogeneous quadrants.

Figure A1 provides a schematic illustration of the quadtree decomposition. Figure A1A shows a uniform grid, analogous to an EI lung volume where parenchyma can be considered maximally stretched and relatively uniform. In Fig. A1C, the grid is “compressed” in the vertical direction, and is analogous to the end expiratory lung volume where parenchyma is greatly influenced by gravity, and considerable deformation of the spongy tissue takes place. Figure A1E shows the calculation of FD for the illustrative examples. Figure A1, B and D, illustrates the results of a quadtree decomposition on their sample images. The QtD metric has been calculated for both sample images, as well as the fractal dimensions.

Gradients in lung tissue and FD.

Increased vertical gradients in lung density do not in themselves relate to increases in FD, although they can lead to increased CoV overall. As an illustrative example we consider an image with an equal number of the values 1 to 8 (Fig. A2). If the image has a gradient (Fig. A2A), the CoV does not decrease with decreasing resolution as one might expect. This is consistent with the lower FD in EE images in this study compared with EI images, as well as that larger lung tissue density gradients with higher BMI do not increase the FD. Figure A2B has a gradient as well as some additional heterogeneity. This results in a higher FD than in Fig. A2A. As a further (more extreme) example, Fig. A2C shows an image with no gradient and considerable heterogeneity, and results in a higher FD than Figs. A2A or A2B.

Gradients in lung tissue and QtD.

We consider the same examples as above and work through the steps of QtD (assuming we do not split boxes when the range of values in a box is 2 or less); Fig. A3 illustrates the progression of the QtD for each scenario.

It is clear from the examples in Figs. A2 and A3 that an image with a gradient but the same overall CoV can result in a higher QtD than an image without a gradient but with a clustering of “like” values. The larger the clusters of like values, the lower the QtD. If airtrapping was represented in these examples it would appear as a cluster (or clusters) of like values; one would therefore expect a higher FD metric and potentially a decrease in QtD as a result.

Fig. A1.

Simple schematic to illustrate the quadtree decomposition (QtD) and fractal dimension (FD) methods. A: the image is divided into equal sized blocks that decompose to the grid on the image in B, with QtD metric = 0.074. C: the image has a gradient in block size that decomposes to the grid in D, with QtD metric = 0.136. E: the log-log plot of coefficient of variation (CoV) against box size for the images in A and C. The uniform grid in A has lower CoV values overall than the gradient grid in C, but the slope is steeper and therefore the FD is higher.

Fig. A2.

Coefficient of variation (CoV) and fractal dimension calculations for various degrees of heterogeneity coupled with gravitational gradients. A: regular structure with a gravitational gradient. B: gradient with some heterogeneity. C: structure dominated by heterogeneity, with no gradient.

Fig. A3.

Quadtree decomposition calculations for the same example images used in Fig. A2. A: regular structure with a gravitational gradient. B: gradient with some heterogeneity. C: structure dominated by heterogeneity and no gradient.

Fig. A3.—Continued.