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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 2007 Feb 6;104(7):2361–2365. doi: 10.1073/pnas.0607882104

Morphological mechanism of the development of pulmonary emphysema in klotho mice

Atsuyasu Sato *, Toyohiro Hirai *,†, Akihiro Imura ‡, Naoko Kita ‡, Akiko Iwano ‡, Shigeo Muro *, Yo-ichi Nabeshima ‡, Bela Suki §, Michiaki Mishima *
PMCID: PMC1892918  PMID: 17284608

Abstract

The concept of fractal geometry is useful for the analysis of irregular and complex structures often seen in nature. Here we apply this concept to investigate the structural mechanism of the development of pulmonary emphysema in the klotho mouse, which, after milk feeding, exhibits characteristics resembling aging and develops emphysema. We calculated the relationships between perimeter and size characterizing shape and between cumulative frequency and size of the terminal air spaces identified from histologic slides and found that both relations followed a power law with fractal properties. However, the fractal dimensions related to the shape and size (Dsn) in the klotho mice were significantly lower than in controls. Additionally, in the klotho mice, Dsn decreased with age without significant change in mean linear intercept. These abnormal morphological changes were restored when the klotho mice were fed with a vitamin D-deficient diet. Previously undescribed morphological model simulations showed that a random destruction, in which the destruction process occurs homogeneously in the lungs, was more consistent with the data than a correlated destruction that is usually seen in smoking-related human emphysema. These results suggest that the pathological changes in the lungs of the klotho mice are derived not from localized causes, but from systemic causes that are related to abnormal activation of vitamin D. The morphogenesis of emphysema in the klotho mice and morphological analyses using fractal geometry may contribute to the understanding of the progressive nature and cause of parenchymal destruction in human emphysema.

Keywords: chronic obstructive pulmonary disease, fractal, lung, morphometry, simulation

Chronic obstructive pulmonary disease (COPD) is a progressive lung disease that consists of airway obstruction and pulmonary emphysema, which is characterized pathologically by abnormal and permanent enlargement of the air spaces distal to the terminal bronchioles with the destruction of their walls (1). To study the mechanism of progression, several techniques have been proposed to evaluate air space enlargement and parenchymal destruction in various mouse models of emphysema. The enlargement of air spaces has been evaluated by using the mean linear intercept (Lm) technique, described originally by Dunnill (2). The degree of parenchymal destruction is usually determined by a microscopic point counting technique called the Destructive Index (DI) (3). These morphological indexes have proved useful in evaluating the extent and severity of emphysema, one form of COPD, and have been used for understanding of the relationship between pathological and clinical findings (4, 5). However, these indexes are limited because they do not account for the irregularities and structural complexity of the lung periphery, and hence they are unable to quantify how the air spaces become enlarged and destroyed (6–8).

Recently, the concept of fractal geometry developed by Mandelbrot (9) was applied to pulmonary physiology and histology (10, 11). Fractals are self-similar structures characterized by power-law functions and noninteger dimensions (fractal dimension). Fractal analysis has been applied to characterize the emphysematous lesions on chest x-ray computed tomography (CT) in patients with COPD, and this analysis has been useful not only for evaluating the severity of COPD but also for detecting early stages of COPD (12). However, CT quantifies only the macroscopic lesions that reflect mainly abnormal air space enlargement without detailed information on the microscopic mechanisms at the level of the alveolar walls that lead to a destruction of the tissue and enlargement of alveoli.

The purpose of the present study is to examine histologically whether the shape and size distributions of air spaces in the lungs have fractal properties and to investigate the differences between emphysematous lungs and controls, by using a mouse model of emphysema called the klotho mouse (13). klotho-null mutants (kl−/−) were established by targeted gene disruption and reveal the same phenotype as the original klotho mice (14). A defect in klotho gene expression results in a syndrome that resembles human aging (short life span, arteriosclerosis, etc.) and obvious emphysema after milk feeding (15). The first histological changes in the lung of the original klotho mice appear at 4 weeks of age with both destruction of alveolar walls and air space enlargement (13). Recently, the abnormal activation of vitamin D was reported to be the major cause of the phenotype of the klotho mice (14). Thus, we also performed vitamin D-deficient diet experiments to investigate its involvement in the development of emphysema in the klotho mice. Finally, we introduced a previously undescribed structural model and applied it to digital images of histological sections to reveal the mechanism of parenchymal destruction in the klotho mice.

Results and Discussion

klotho mice and their wild-type (WT) littermates (C57BL/6) were examined at ages 4 and 7 weeks (n = 5 for each group). Klotho mice showed significant decrease with age in body weight (8.2 ± 1.6 and 7.6 ± 1.2 g at 4 and 7 weeks, respectively; P < 0.0001 using ANOVA) and total lung capacity (TLC) (0.91 ± 0.11 and 0.80 ± 0.01 ml at 4 and 7 weeks, respectively; P < 0.0001), whereas WT mice showed significant increase with age in body weight (18.0 ± 1.4 and 21.3 ± 2.0 g at 4 and 7 weeks, respectively; P < 0.0001) and TLC (1.13 ± 0.06 and 1.33 ± 0.08 ml at 4 and 7 weeks, respectively; P < 0.0001). klotho mice showed significantly lower body weight and smaller TLC compared with controls (P < 0.0001).

Fig. 1 shows representative lung fields of WT and kl−/− at 4 and 7 weeks of age. Each terminal air space of the lungs was identified as a contiguous region and, to distinguish from adjacent regions, was represented by a different color. klotho mice showed air space enlargement in the lungs compared with controls.

Fig. 1.

Fig. 1.

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Representative H&E-stained sections (×40) of the lungs in WT and kl−/− mice. (A and B) Results for 4-week-old (A) and 7-week-old (B) WT mice. (C and D) Results for 4-week-old (C) and 7-week-old (B) kl−/− mice. (Scale bars, 200 μm.) (E–H) Each contiguous air space was identified and is shown in different colors (E–H converted from A–D, respectively).

Structural Analysis.

We analyzed two types of power-law functions that provide the exponents reflecting the shape (Dsp) and size (Dsn) distributions of air spaces. Fig. 2 shows log–log plots of representative cumulative frequencies of air space sizes for all groups of mice. These four examples correspond to Fig. 1 A–D. The correlation coefficients (r) for Dsp and Dsn were >0.975 and 0.949, respectively, in all samples, and there were no significant differences in the r values for Dsp and Dsn among the groups (ANOVA). Thus, the shape and size distribution of terminal air spaces showed fractal properties in histological sections of both klotho and control mice. Dsp is the fractal dimension related to the irregularity of the overall shape of the air space perimeter with high values representing a rough and irregular shape. On the other hand, Dsn is the fractal dimension related to the size distribution of air spaces. A decrease in Dsn means that the probability of finding extremely large clusters is increased as expected during the progression of emphysema. Next, we applied these fractal dimensions together with Lm and DI to evaluate the progression of emphysema in the klotho mice.

Fig. 2.

Fig. 2.

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Representative cumulative distribution functions of air space sizes. The curves A, B, C, and D correspond to the results of analysis for Fig. 1 A–D, respectively.

Effects of Age on Tissue Morphology.

Fig. 3 compares the morphological indexes of the four groups of mice. The Lm values were significantly higher in kl−/− mice than in WT mice (ANOVA, P < 0.001), although there was no statistical difference between the age groups of either strain of mice. These results were the same even when Lm was normalized by TLC. klotho mice showed significantly higher DI values than controls and significant increases between 4 and 7 weeks of age (P < 0.001), whereas there was no increase with age in WT mice.

Fig. 3.

Fig. 3.

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Morphological indexes of the lungs in WT and klotho mice. (A) Lms. (B) DI. ∗, Significant difference between WT and kl−/− at same age (ANOVA, Fisher's test, P < 0.001); †, significant difference from the same strain of 4-week-old mice (P < 0.001). (C) Fractal dimensions of perimeter and size of air spaces (Dsp). ∗, Significant difference between WT in 7 weeks of age and kl−/− in 4 weeks of age (P < 0.05). (D) Fractal dimensions between the size and cumulative distribution function of air spaces (Dsn). ∗, Significant difference between WT and kl−/− at same age (P < 0.001); †, significant difference from the same strain of 4-week-old mice (P < 0.05). Results are expressed as mean ± SD.

The Dsp values were significantly lower in klotho mice at 4 weeks of age than controls at 7 weeks of age (P < 0.05), and klotho mice showed a tendency for increased Dsp with age. Dsn values were significantly lower in klotho mice than controls (P < 0.001), and Dsn decreased with age in both strains of mice (P < 0.05).

These results showed that klotho mice had larger air spaces with alveolar wall destruction, and smaller exponents in the shape and size distribution of the air spaces. In human emphysema, air space enlargement and parenchymal destruction have been shown to increase Lm and DI, and a previous histological study reported a decrease in the fractal dimension of the alveolar perimeter in patients who died of COPD, compared with patients who died of non-respiratory-related causes (16). Thus, based on these morphological similarities, the klotho mouse can be considered as a possible model for investigating human emphysema. Hence, our results may have implications for the structural changes in the alveoli in human emphysema. In WT mice, Dsn decreased significantly with age (P < 0.01), whereas there were no significant changes with age in Lm, DI, and Dsp. Thus, control mice have a relative increase in the number of larger air spaces and a decrease in the number of smaller air spaces with age without alveolar wall destruction, suggesting normal growth. On the other hand, with age, the klotho mice showed significant increase in terminal air space size (decrease in Dsn) accompanied by tissue destruction (increase in DI) without noticeable change in shape (Dsp).

Effects of Vitamin D-Deficient Diet.

To investigate the mechanism of these morphological changes in the lungs of klotho mice, five kl−/− mice were fed a vitamin D-deficient diet after milk feeding up to 7 weeks of age. Histological analyses were performed on the lungs at 7 weeks of age to obtain the same indexes described above. Fig. 4 shows a representative image of the lung of a mouse fed a vitamin D-deficient diet. There were no significant differences in body weight (20.7 ± 1.5g) and morphological parameters (Lm, 75.0 ± 3.5 μm; DI, 5.1 ± 1.1%; Dsn, 0.84 ± 0.04; Dsp, 1.50 ± 0.03), compared with controls. Thus, a deficiency of the klotho protein led to emphysema, which was rescued by the absence of vitamin D. The klotho protein participates in a negative regulatory circuit of the vitamin D endocrine system, and vitamin D-deficient diets reduce the abnormally high levels of serum vitamin D and calcium in the klotho mice (14). Calpain, which is a calcium-dependent cytosolic cysteine protease, may be involved in one of the causes of emphysema in klotho mice. The aberrant activation of μ-calpain caused by the klotho mutation leads to the cleavage of αII-spectrin, which is usually found on the cytoplasmic side of the plasma membrane. Because the expression of intact αII-spectrin is drastically decreased and activated μ-calpain is detected, significant proteolysis must occur in the lungs of 4-week-old klotho mice (17). These facts support the notion that the mechanism behind the morphological changes in emphysema of klotho mice is derived from a systemic cause.

Fig. 4.

Fig. 4.

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Representative H&E-stained sections (×40) of the lungs in a klotho mouse fed a vitamin D-deficient diet. (Scale bar: 200 μm.)

Model Simulations Using Histological Images.

To interpret these findings, we performed two kinds of model simulations, random destruction and correlated circular destruction, by using binary images of the lungs of 4-week-old klotho mice. First, we developed a random destruction model (Fig. 5A), in which the “tissue” pixels were randomly eliminated from the image. This technique resulted in a destruction that proceeded homogenously in the lungs. Next, we developed a correlated circular destruction model (Fig. 5B). First a single pixel was randomly selected in the binary image, and all alveolar duct and walls found within a certain radius (R) from this pixel were destroyed simultaneously, a process similar to that in emphysema induced by intratracheal administration of elastase.

Fig. 5.

Fig. 5.

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Schematic representation of model-based tissue destruction. (A) Random destruction model in which the destruction process occurs homogeneously. When an AW pixel representing tissue was selected for destruction in a random order, the AW pixel was converted to white horizontally (in this case) or vertically. This magnified region shows an example of parenchymal destruction. The definition of AW pixels is described in Methods. (B) Correlated circular destruction model. One pixel was randomly selected in a binary image of the lung, and all AW pixels that existed within a given radius (R = 200 pixels in this case) from this pixel were converted simultaneously to white. As a result, parenchymal destruction occurred in a localized and heterogeneous destruction way. In both models, the destruction is iteratively repeated in the same way using the last image.

Fig. 6 shows representative trials using the random destruction model applied to two binary images of 4-week-old klotho mice. As the destruction process was repeated, adjacent air spaces coalesced to form larger air spaces, and hence, the number of air spaces per section decreased. Consequently, Dsn decreased with almost no change in Lm as the destruction was repeated. The DI values increased as the destruction repeated; for example, DI increased from 11.3 to 28.3%, whereas Dsp increased from 1.35 only to 1.42. These results were in good agreement with actual measured values.

Fig. 6.

Fig. 6.

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Results from the random destruction and correlated circular destruction model simulations. (A) Relationship between Lms and Dsp. (B) Relationship between the number of terminal air spaces and Dsn. Open and filled squares with SD bars indicate the actual values of the means of 4- and 7-week-old klotho mice, respectively. Open circles and open triangles show representative examples obtained by applying the random destruction model to two lung images of 4-week-old klotho mice. Filled circles show a representative example obtained by applying the correlated circular destruction model to the same image used in the random destruction model when the destruction radius R was 100 pixels. Open and filled diamonds show two separate trials applying the correlated circular destruction model to the same image when R was varied from 50 to 150 pixels with a mean of 100 pixels.

In the correlated circular destruction model, at first, R was fixed to either 100 or 200 pixels during the iteration of destruction process. The simulations when R was 100 pixels (Fig. 6) show that Lm increased but Dsn did not decrease during the iterated process of destructions. Similar results were obtained when R was 200 pixels; for example, Lm increased from 92.1 to 97.5 μm and Dsn changed from 0.80 only to 0.76, whereas Dsp increased from 1.35 only to 1.41. Next, R was allowed to vary from region to region with a range of values (5, 25, or 50 pixels), whereas the mean R was fixed to 100 pixels. Two separate trial simulations when R was varied from 50 to 150 pixels with a mean of 100 pixels (Fig. 6) show that Lm still increased and Dsn did not decrease during the iterated process of destructions. Again, similar results were obtained when R varied from 95 to 105 pixels (for example, Lm increased from 92.1 to 97.6 μm, and Dsn changed from 0.80 only to 0.77) or from 75 to 125 pixels (for example, Lm increased from 92.1 to 97.6 μm, and Dsn changed from 0.80 only to 0.78). When we used a model in which the seed points for tissue destruction were the same as in the random destruction model, then the gradual reduction of R resulted in the correlated circular destruction model to smoothly transitions into the random destruction model (data not shown).

These results suggest that the morphological changes from 4 to 7 weeks of age in the lungs of klotho mice are consistent with a more random but homogenously distributed destruction process providing further support that the abnormal lung morphology in the klotho mice is related to a systemic cause. In human pulmonary emphysema, alveolar wall destruction has been shown to increase the heterogeneity of the terminal air space structure (18). In our simulation studies, both the standard deviation (SD) and the coefficient of variation of air space sizes increased with repeated destructions demonstrating that in both models the heterogeneity of the terminal air spaces gradually increased (Fig. 7). It has been suggested that the disease process of human emphysema progresses such that “once the destruction occurs, it proceeds there,” mainly because of the correlated local changes in mechanical forces after the destruction (18). The correlated circular model should thus be able to account for the observed morphological changes. However, the random destruction model showed a considerably better agreement with the actual data. The possible reasons are as follows. First, the effects of gravity and tidal breathing on parenchymal structure are much smaller in the lungs of mice than in larger species. Second, the changes in lung structure from 4 to 7 weeks of age in the klotho mice may not be representative of the late stages of emphysema in which mechanical forces can significantly contribute to the destruction process. Indeed, Fig. 7 demonstrates that although heterogeneity continuously increases during the simulated random destruction process, it does not follow the trajectory of maximum heterogeneity that can be achieved by the correlated destruction. This finding also may explain the discrepancy with a previous study using computed tomography in human COPD (12), which showed that the progression of emphysema could be interpreted by an elastic spring network model. Indeed, although clusters of low attenuation area in CT images reflect macroscopic emphysematous changes, they may not be sensitive to microscopic changes in early stages of parenchymal destruction because of the limitation of image resolution. Our results therefore suggest that with respect to tissue destruction, the strong systemic-induced proteolytic injury randomly occurring throughout the lung dominates the influence of mechanical forces in the klotho mice.

Fig. 7.

Fig. 7.

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Changes in SD (A) and coefficient of variation (B) of air space size against the number of terminal air spaces in the random destruction and correlated circular destruction model simulations. Open circles represent representative examples obtained by applying the random destruction model to the lung image of 4-week-old klotho mice. Filled circles show a representative example obtained by applying the correlated circular destruction model to the same image used in the random destruction model when the destruction radius R was 100 pixels. Open diamond shows a representative example obtained by applying the correlated circular destruction model to the same image when R was varied from 50 to 150 pixels with a mean of 100 pixels. SD, standard deviation of air space size; CV, coefficient of variation of air space size.

The clinical applicability of the morphological analysis including power-law relationships established here may be limited, because the estimation of the power-law exponents require the processing of a large number of air spaces in the histological sections, which is not feasible from small biopsy samples. However, such analysis may be applied to larger surgical biopsy specimens from human lungs, and hence it may contribute to the understanding of the structural progression of COPD.

In conclusion, lungs of klotho mice showed larger air spaces with alveolar wall destruction, and this phenotype was restored after a vitamin D-deficient diet. Our morphological assessment using power-law analysis and model simulations showed that the progression of tissue destruction with age in klotho mice increased the heterogeneity of air space structure and followed a random rather than correlated local destruction pattern. Thus, the klotho mouse may prove to be a useful model for evaluating the pathogenesis of tissue destruction associated with vitamin D in human pulmonary emphysema, especially in the early proteolysis-dominated stages.

Methods

Tissue Preparation of the Lungs.

Mice were anesthetized by i.p. administration of pentobarbital sodium (30 mg/kg). They were tracheostomized, and the trachea was cannulated by using a 22-gauge urethane needle. After degassing by using the oxygen absorption method (19, 20), mice were killed. Whole lungs were then inflated with optimal cutting temperature fluid diluted to half concentrate to a transpulmonary pressure of 2.5 kPa for 20 min according to the methods described in ref. 21. The degassing procedure was used to avoid inhomogeneous inflation and fixation of the lungs by residual trapped air. The inflated lung volume was determined by water displacement (22) and defined as TLC. The lungs were then flash frozen in isopentane and liquid nitrogen.

Lung Histology and the Quantification of Emphysema.

The left lung was cut sagittally into serial 5-μm-thick sections and stained with hematoxylin/eosin for histological examination. Five successive sections were obtained at each of three approximately equidistant levels through the lung and placed on a slide. The third section on each slide was used for morphometry (23). The shrinkage factors (23) of our samples were 1.05. The slides were examined without knowledge of the animals. One microscopic field of each slide was digitized at ×40 magnification (DXM 1200; Nikon, Tokyo, Japan). The original microscopic images (1,280 × 1,024 pixels, pixel dimension 1.67 μm) were converted into a binary image with the modified methods described in ref. 24, and all morphological parameters except DI were calculated automatically by using our custom software. Lm was calculated by placing imaginary vertical and horizontal lines at every 90 μm (total 440 lines per section) and counting the intercepts as follows:

graphic file with name zpq00707-5031-m01.jpg

To validate our methods, Lm values in some sections were measured with the manual method described in refs. 25 and 26. The correlation coefficient between these two methods was 0.99 (P < 0.001). Air spaces were automatically identified in each binary image as contiguous regions, and the numbers and perimeters were counted. Summing the number of pixels in these regions provides the size of air spaces. The DI was measured by manual point counting according to the methods described in refs. 3 and 5 by using the formula

graphic file with name zpq00707-5031-m02.jpg

where D indicates “destroyed” and N indicates “normal” points.

Fractal Analysis.

To assess the fractal properties of the shape and distribution of terminal air spaces, two power-law functions were applied to obtain two exponents, Dsp and Dsn. The exponent Dsp between size (X) and perimeter (Y) of air spaces was obtained by the following equation:

graphic file with name zpq00707-5031-m03.jpg

where the k1 is constant.

The exponent Dsn between the size (X) and cumulative frequency (Z) of air space was calculated from the following equation:

graphic file with name zpq00707-5031-m04.jpg

where the k2 is constant. Both exponents, Dsp and Dsn, were obtained by linear regression on a log–log plot, and the correlation coefficients (r) were taken to indicate the goodness-of-fit of the power law.

Model Simulations Using Histological Images.

In the binary image, black and white pixels represent the tissue and air space, respectively. The black pixels that were vertically or horizontally contiguous at <5 pixels were detected in the image at first. These pixels were called the AW pixels with the assumption that these pixels contributed to the alveolar duct and wall, and hence AW pixels could be destroyed. The destruction of tissue in the model is equivalent to a conversion of the AW pixels from black (tissue) to white (air space) on an image. In the random destruction model simulation, AW pixels were destroyed randomly with a probability of 0.001 (Fig. 5A). In the correlated circular destruction model (Fig. 5B), one pixel in a binary image was selected randomly, and all AW pixels that existed within a circle of radius (R) around this pixel were destroyed simultaneously. The value of R could be changed with each destruction process. In both models, the new binary image after destruction was analyzed in the same way as described above to calculate morphological parameters, such as Lm and fractal dimensions. The destruction process was then iteratively repeated by using the last image as the starting point for the next destruction.

Statistical Analysis.

Results are expressed as means ± SD. ANOVA (Scheffé test) was used for comparisons between groups. All statistical analyses were performed by using Stat View software (SAS Institute, Cary, NC). P < 0.05 was considered to be significant.

Acknowledgments

This work was supported in part by Japan Society for the Promotion of Science Grant B 16390234 and National Institutes of Health Grant HL059215.

Abbreviations

COPD

chronic obstructive pulmonary disease

TLC

total lung capacity

Lm

mean linear intercept

DI

Destructive Index

Dsp

exponent between size and perimeter of air space

Dsn

exponent between size and cumulative frequency of air space.

Footnotes

The authors declare no conflict of interest.

This article is a PNAS direct submission.

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