Morphological mechanism of the developmentof pulmonary emphysema in klotho miceAtsuyasu Sato*, Toyohiro Hirai*†, Akihiro Imura‡, Naoko Kita‡, Akiko Iwano‡, Shigeo Muro*, Yo-ichi Nabeshima‡,Bela Suki§, and Michiaki Mishima*

Departments of *Respiratory Medicine and ‡Pathology and Tumor Biology, Graduate School of Medicine, Kyoto University, Kawahara 53, Shogoin,Sakyo, Kyoto, 606-8507, Japan; and §Department of Biomedical Engineering, Boston University, Boston, MA 02215

Edited by Tasuku Honjo, Kyoto University, Kyoto, Japan, and approved December 14, 2006 (received for review September 8, 2006)

The concept of fractal geometry is useful for the analysis ofirregular and complex structures often seen in nature. Here weapply this concept to investigate the structural mechanism of thedevelopment of pulmonary emphysema in the klotho mouse,which, after milk feeding, exhibits characteristics resembling agingand develops emphysema. We calculated the relationships be-tween perimeter and size characterizing shape and between cu-mulative frequency and size of the terminal air spaces identifiedfrom histologic slides and found that both relations followed apower law with fractal properties. However, the fractal dimensionsrelated to the shape and size (Dsn) in the klotho mice weresignificantly lower than in controls. Additionally, in the klothomice, Dsn decreased with age without significant change in meanlinear intercept. These abnormal morphological changes wererestored when the klotho mice were fed with a vitamin D-deficientdiet. Previously undescribed morphological model simulationsshowed that a random destruction, in which the destructionprocess occurs homogeneously in the lungs, was more consistentwith the data than a correlated destruction that is usually seen insmoking-related human emphysema. These results suggest thatthe pathological changes in the lungs of the klotho mice arederived not from localized causes, but from systemic causes thatare related to abnormal activation of vitamin D. The morphogen-esis of emphysema in the klotho mice and morphological analysesusing fractal geometry may contribute to the understanding of theprogressive nature and cause of parenchymal destruction in humanemphysema.

chronic obstructive pulmonary disease � fractal � lung � morphometry �simulation

Chronic obstructive pulmonary disease (COPD) is a progres-sive lung disease that consists of airway obstruction and

pulmonary emphysema, which is characterized pathologically byabnormal and permanent enlargement of the air spaces distal tothe terminal bronchioles with the destruction of their walls (1).To study the mechanism of progression, several techniques havebeen proposed to evaluate air space enlargement and parenchy-mal destruction in various mouse models of emphysema. Theenlargement of air spaces has been evaluated by using the meanlinear intercept (Lm) technique, described originally by Dunnill(2). The degree of parenchymal destruction is usually deter-mined by a microscopic point counting technique called theDestructive Index (DI) (3). These morphological indexes haveproved useful in evaluating the extent and severity of emphy-sema, one form of COPD, and have been used for understandingof the relationship between pathological and clinical findings (4,5). However, these indexes are limited because they do notaccount for the irregularities and structural complexity of thelung periphery, and hence they are unable to quantify how theair spaces become enlarged and destroyed (6–8).

Recently, the concept of fractal geometry developed by Man-delbrot (9) was applied to pulmonary physiology and histology(10, 11). Fractals are self-similar structures characterized bypower-law functions and noninteger dimensions (fractal dimen-

sion). Fractal analysis has been applied to characterize theemphysematous lesions on chest x-ray computed tomography(CT) in patients with COPD, and this analysis has been usefulnot only for evaluating the severity of COPD but also fordetecting early stages of COPD (12). However, CT quantifiesonly the macroscopic lesions that reflect mainly abnormal airspace enlargement without detailed information on the micro-scopic mechanisms at the level of the alveolar walls that lead toa destruction of the tissue and enlargement of alveoli.

The purpose of the present study is to examine histologicallywhether the shape and size distributions of air spaces in the lungshave fractal properties and to investigate the differences be-tween emphysematous lungs and controls, by using a mousemodel of emphysema called the klotho mouse (13). klotho-nullmutants (kl�/�) were established by targeted gene disruptionand reveal the same phenotype as the original klotho mice (14).A defect in klotho gene expression results in a syndrome thatresembles human aging (short life span, arteriosclerosis, etc.)and obvious emphysema after milk feeding (15). The firsthistological changes in the lung of the original klotho mice appearat 4 weeks of age with both destruction of alveolar walls and airspace enlargement (13). Recently, the abnormal activation ofvitamin D was reported to be the major cause of the phenotypeof the klotho mice (14). Thus, we also performed vitaminD-deficient diet experiments to investigate its involvement in thedevelopment of emphysema in the klotho mice. Finally, weintroduced a previously undescribed structural model and ap-plied it to digital images of histological sections to reveal themechanism of parenchymal destruction in the klotho mice.

Results and Discussionklotho 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 agein 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 � 0.08ml at 4 and 7 weeks, respectively; P � 0.0001). klotho miceshowed significantly lower body weight and smaller TLC com-pared with controls (P � 0.0001).

Author contributions: T.H., S.M., Y.-i.N., B.S., and M.M. designed research; A.S., T.H.,A. Imura, N.K., A. Iwano, Y.-i.N., and B.S. performed research; A.S., T.H., and S.M. analyzeddata; and A.S., T.H., B.S., and M.M. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS direct submission.

Abbreviations: COPD, chronic obstructive pulmonary disease; TLC, total lung capacity; Lm,mean linear intercept; DI, Destructive Index; Dsp, exponent between size and perimeter ofair space; Dsn, exponent between size and cumulative frequency of air space.

†To whom correspondence should be addressed. E-mail: t�hirai@kuhp.kyoto-u.ac.jp.

© 2007 by The National Academy of Sciences of the USA

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Fig. 1 shows representative lung fields of WT and kl�/� at 4and 7 weeks of age. Each terminal air space of the lungs wasidentified as a contiguous region and, to distinguish fromadjacent regions, was represented by a different color. klothomice showed air space enlargement in the lungs compared withcontrols.

Structural Analysis. We analyzed two types of power-law functionsthat provide the exponents reflecting the shape (Dsp) and size(Dsn) distributions of air spaces. Fig. 2 shows log–log plots ofrepresentative cumulative frequencies of air space sizes for allgroups of mice. These four examples correspond to Fig. 1 A–D.The correlation coefficients (r) for Dsp and Dsn were �0.975and 0.949, respectively, in all samples, and there were nosignificant differences in the r values for Dsp and Dsn among thegroups (ANOVA). Thus, the shape and size distribution ofterminal air spaces showed fractal properties in histologicalsections of both klotho and control mice. Dsp is the fractaldimension related to the irregularity of the overall shape of theair space perimeter with high values representing a rough andirregular shape. On the other hand, Dsn is the fractal dimensionrelated to the size distribution of air spaces. A decrease in Dsnmeans that the probability of finding extremely large clusters isincreased as expected during the progression of emphysema.Next, we applied these fractal dimensions together with Lm andDI to evaluate the progression of emphysema in the klotho mice.

Effects of Age on Tissue Morphology. Fig. 3 compares the morpho-logical indexes of the four groups of mice. The Lm values weresignificantly higher in kl�/� mice than in WT mice (ANOVA,P � 0.001), although there was no statistical difference betweenthe age groups of either strain of mice. These results were thesame even when Lm was normalized by TLC. klotho mice showedsignificantly higher DI values than controls and significantincreases between 4 and 7 weeks of age (P � 0.001), whereasthere was no increase with age in WT mice.

The Dsp values were significantly lower in klotho mice at 4 weeksof age than controls at 7 weeks of age (P � 0.05), and klotho mice

Fig. 1. Representative H&E-stained sections (�40) of the lungs in WT andkl�/� 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 �m.) (E–H) Each contiguous air space was identified and is shown indifferent colors (E–H converted from A–D, respectively).

Fig. 2. 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.

Fig. 3. 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’stest, 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 distributionfunction of air spaces (Dsn). *, Significant difference between WT and kl�/� atsame age (P � 0.001); †, significant difference from the same strain of 4-week-oldmice (P � 0.05). Results are expressed as mean � SD.

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showed a tendency for increased Dsp with age. Dsn values weresignificantly lower in klotho mice than controls (P � 0.001), and Dsndecreased with age in both strains of mice (P � 0.05).

These results showed that klotho mice had larger air spaceswith alveolar wall destruction, and smaller exponents in theshape and size distribution of the air spaces. In human emphy-sema, air space enlargement and parenchymal destruction havebeen shown to increase Lm and DI, and a previous histologicalstudy reported a decrease in the fractal dimension of the alveolarperimeter in patients who died of COPD, compared withpatients who died of non-respiratory-related causes (16). Thus,based on these morphological similarities, the klotho mouse canbe considered as a possible model for investigating humanemphysema. Hence, our results may have implications for thestructural changes in the alveoli in human emphysema. In WTmice, Dsn decreased significantly with age (P � 0.01), whereasthere were no significant changes with age in Lm, DI, and Dsp.Thus, control mice have a relative increase in the number oflarger air spaces and a decrease in the number of smaller airspaces with age without alveolar wall destruction, suggestingnormal growth. On the other hand, with age, the klotho miceshowed significant increase in terminal air space size (decreasein Dsn) accompanied by tissue destruction (increase in DI)without noticeable change in shape (Dsp).

Effects of Vitamin D-Deficient Diet. To investigate the mechanismof these morphological changes in the lungs of klotho mice, fivekl�/� mice were fed a vitamin D-deficient diet after milk feedingup to 7 weeks of age. Histological analyses were performed onthe lungs at 7 weeks of age to obtain the same indexes describedabove. Fig. 4 shows a representative image of the lung of a mousefed a vitamin D-deficient diet. There were no significant differ-ences in body weight (20.7 � 1.5g) and morphological parame-ters (Lm, 75.0 � 3.5 �m; DI, 5.1 � 1.1%; Dsn, 0.84 � 0.04; Dsp,1.50 � 0.03), compared with controls. Thus, a deficiency of theklotho protein led to emphysema, which was rescued by theabsence of vitamin D. The klotho protein participates in anegative regulatory circuit of the vitamin D endocrine system,and vitamin D-deficient diets reduce the abnormally high levelsof serum vitamin D and calcium in the klotho mice (14). Calpain,which is a calcium-dependent cytosolic cysteine protease, may beinvolved in one of the causes of emphysema in klotho mice. Theaberrant activation of �-calpain caused by the klotho mutationleads to the cleavage of �II-spectrin, which is usually found onthe cytoplasmic side of the plasma membrane. Because theexpression of intact �II-spectrin is drastically decreased and

activated �-calpain is detected, significant proteolysis mustoccur in the lungs of 4-week-old klotho mice (17). These factssupport the notion that the mechanism behind the morpholog-ical changes in emphysema of klotho mice is derived from asystemic cause.

Model Simulations Using Histological Images. To interpret thesefindings, we performed two kinds of model simulations, randomdestruction and correlated circular destruction, by using binaryimages of the lungs of 4-week-old klotho mice. First, we devel-oped a random destruction model (Fig. 5A), in which the ‘‘tissue’’pixels were randomly eliminated from the image. This techniqueresulted in a destruction that proceeded homogenously in thelungs. Next, we developed a correlated circular destructionmodel (Fig. 5B). First a single pixel was randomly selected in thebinary image, and all alveolar duct and walls found within acertain radius (R) from this pixel were destroyed simultaneously,a process similar to that in emphysema induced by intratrachealadministration of elastase.

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

In the correlated circular destruction model, at first, R wasfixed to either 100 or 200 pixels during the iteration of destruc-tion process. The simulations when R was 100 pixels (Fig. 6) showthat Lm increased but Dsn did not decrease during the iteratedprocess of destructions. Similar results were obtained when Rwas 200 pixels; for example, Lm increased from 92.1 to 97.5 �mand Dsn changed from 0.80 only to 0.76, whereas Dsp increasedfrom 1.35 only to 1.41. Next, R was allowed to vary from regionto region with a range of values (5, 25, or 50 pixels), whereas the

Fig. 4. Representative H&E-stained sections (�40) of the lungs in a klothomouse fed a vitamin D-deficient diet. (Scale bar: 200 �m.)

Fig. 5. Schematic representation of model-based tissue destruction. (A)Random destruction model in which the destruction process occurs homoge-neously. When an AW pixel representing tissue was selected for destruction ina random order, the AW pixel was converted to white horizontally (in thiscase) or vertically. This magnified region shows an example of parenchymaldestruction. The definition of AW pixels is described in Methods. (B) Corre-lated circular destruction model. One pixel was randomly selected in a binaryimage of the lung, and all AW pixels that existed within a given radius (R � 200pixels in this case) from this pixel were converted simultaneously to white. Asa result, parenchymal destruction occurred in a localized and heterogeneousdestruction way. In both models, the destruction is iteratively repeated in thesame way using the last image.

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mean R was fixed to 100 pixels. Two separate trial simulationswhen 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 decreaseduring the iterated process of destructions. Again, similar resultswere obtained when R varied from 95 to 105 pixels (for example,Lm increased from 92.1 to 97.6 �m, and Dsn changed from 0.80only to 0.77) or from 75 to 125 pixels (for example, Lm increasedfrom 92.1 to 97.6 �m ,and Dsn changed from 0.80 only to 0.78).When we used a model in which the seed points for tissuedestruction were the same as in the random destruction model,then the gradual reduction of R resulted in the correlatedcircular destruction model to smoothly transitions into therandom destruction model (data not shown).

These results suggest that the morphological changes from 4 to7 weeks of age in the lungs of klotho mice are consistent with a morerandom but homogenously distributed destruction process provid-ing further support that the abnormal lung morphology in theklotho mice is related to a systemic cause. In human pulmonaryemphysema, alveolar wall destruction has been shown to increasethe heterogeneity of the terminal air space structure (18). In oursimulation studies, both the standard deviation (SD) and thecoefficient of variation of air space sizes increased with repeateddestructions demonstrating that in both models the heterogeneityof the terminal air spaces gradually increased (Fig. 7). It has beensuggested that the disease process of human emphysema progressessuch that ‘‘once the destruction occurs, it proceeds there,’’ mainlybecause of the correlated local changes in mechanical forces afterthe destruction (18). The correlated circular model should thus beable to account for the observed morphological changes. However,the random destruction model showed a considerably better agree-ment with the actual data. The possible reasons are as follows. First,the effects of gravity and tidal breathing on parenchymal structureare 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 klothomice may not be representative of the late stages of emphysema inwhich mechanical forces can significantly contribute to the destruc-tion process. Indeed, Fig. 7 demonstrates that although heteroge-neity continuously increases during the simulated random destruc-tion process, it does not follow the trajectory of maximumheterogeneity that can be achieved by the correlated destruction.This finding also may explain the discrepancy with a previous studyusing computed tomography in human COPD (12), which showedthat the progression of emphysema could be interpreted by an

elastic spring network model. Indeed, although clusters of lowattenuation area in CT images reflect macroscopic emphysematouschanges, they may not be sensitive to microscopic changes in earlystages of parenchymal destruction because of the limitation ofimage resolution. Our results therefore suggest that with respect totissue destruction, the strong systemic-induced proteolytic injuryrandomly occurring throughout the lung dominates the influence ofmechanical forces in the klotho mice.

The clinical applicability of the morphological analysis includ-ing power-law relationships established here may be limited,because the estimation of the power-law exponents require theprocessing of a large number of air spaces in the histologicalsections, which is not feasible from small biopsy samples. How-ever, such analysis may be applied to larger surgical biopsyspecimens from human lungs, and hence it may contribute to theunderstanding of the structural progression of COPD.

In conclusion, lungs of klotho mice showed larger air spaces withalveolar wall destruction, and this phenotype was restored after avitamin D-deficient diet. Our morphological assessment usingpower-law analysis and model simulations showed that the pro-gression of tissue destruction with age in klotho mice increased theheterogeneity of air space structure and followed a random ratherthan correlated local destruction pattern. Thus, the klotho mousemay prove to be a useful model for evaluating the pathogenesis oftissue destruction associated with vitamin D in human pulmonaryemphysema, especially in the early proteolysis-dominated stages.

MethodsTissue Preparation of the Lungs. Mice were anesthetized by i.p.administration of pentobarbital sodium (30 mg/kg). They weretracheostomized, and the trachea was cannulated by using a22-gauge urethane needle. After degassing by using the oxygenabsorption method (19, 20), mice were killed. Whole lungs werethen inflated with optimal cutting temperature fluid diluted tohalf concentrate to a transpulmonary pressure of 2.5 kPa for 20min according to the methods described in ref. 21. The degassingprocedure was used to avoid inhomogeneous inflation andfixation of the lungs by residual trapped air. The inflated lungvolume was determined by water displacement (22) and definedas TLC. The lungs were then flash frozen in isopentane andliquid nitrogen.

Fig. 6. Results from the random destruction and correlated circular destruc-tion model simulations. (A) Relationship between Lms and Dsp. (B) Relation-ship between the number of terminal air spaces and Dsn. Open and filledsquares with SD bars indicate the actual values of the means of 4- and7-week-old klotho mice, respectively. Open circles and open triangles showrepresentative examples obtained by applying the random destruction modelto two lung images of 4-week-old klotho mice. Filled circles show a represen-tative example obtained by applying the correlated circular destruction modelto the same image used in the random destruction model when the destruc-tion radius R was 100 pixels. Open and filled diamonds show two separatetrials applying the correlated circular destruction model to the same imagewhen R was varied from 50 to 150 pixels with a mean of 100 pixels.

Fig. 7. Changes in SD (A) and coefficient of variation (B) of air space sizeagainst the number of terminal air spaces in the random destruction andcorrelated circular destruction model simulations. Open circles represent rep-resentative examples obtained by applying the random destruction model tothe lung image of 4-week-old klotho mice. Filled circles show a representativeexample obtained by applying the correlated circular destruction model to thesame image used in the random destruction model when the destructionradius R was 100 pixels. Open diamond shows a representative exampleobtained by applying the correlated circular destruction model to the sameimage 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 airspace size.

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Lung Histology and the Quantification of Emphysema. The left lungwas cut sagittally into serial 5-�m-thick sections and stained withhematoxylin/eosin for histological examination. Five successivesections were obtained at each of three approximately equidis-tant levels through the lung and placed on a slide. The thirdsection on each slide was used for morphometry (23). Theshrinkage factors (23) of our samples were 1.05. The slides wereexamined without knowledge of the animals. One microscopicfield of each slide was digitized at �40 magnification (DXM1200; Nikon, Tokyo, Japan). The original microscopic images(1,280 � 1,024 pixels, pixel dimension 1.67 �m) were convertedinto a binary image with the modified methods described in ref.24, and all morphological parameters except DI were calculatedautomatically by using our custom software. Lm was calculatedby placing imaginary vertical and horizontal lines at every 90 �m(total 440 lines per section) and counting the intercepts asfollows:

Lm � �{2 � (length of the line�the number of intercepts)}

�(total number of the lines).

To validate our methods, Lm values in some sections weremeasured 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 eachbinary image as contiguous regions, and the numbers andperimeters were counted. Summing the number of pixels in theseregions provides the size of air spaces. The DI was measured bymanual point counting according to the methods described inrefs. 3 and 5 by using the formula

DI � D�(D � N) � 100 (%),

where D indicates ‘‘destroyed’’ and N indicates ‘‘normal’’ points.

Fractal Analysis. To assess the fractal properties of the shape anddistribution of terminal air spaces, two power-law functions wereapplied to obtain two exponents, Dsp and Dsn. The exponentDsp between size (X) and perimeter (Y) of air spaces wasobtained by the following equation:

Y � k1 X�Dsp�2,

where the k1 is constant.The exponent Dsn between the size (X) and cumulative

frequency (Z) of air space was calculated from the followingequation:

Z � k2 X�Dsn,

where the k2 is constant. Both exponents, Dsp and Dsn, wereobtained by linear regression on a log–log plot, and the corre-lation coefficients (r) were taken to indicate the goodness-of-fitof 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 horizontallycontiguous at �5 pixels were detected in the image at first. Thesepixels were called the AW pixels with the assumption thatthese pixels contributed to the alveolar duct and wall, and henceAW pixels could be destroyed. The destruction of tissue in themodel is equivalent to a conversion of the AW pixels from black(tissue) to white (air space) on an image. In the randomdestruction model simulation, AW pixels were destroyed ran-domly with a probability of 0.001 (Fig. 5A). In the correlatedcircular destruction model (Fig. 5B), one pixel in a binary imagewas selected randomly, and all AW pixels that existed within acircle of radius (R) around this pixel were destroyed simulta-neously. The value of R could be changed with each destructionprocess. In both models, the new binary image after destructionwas analyzed in the same way as described above to calculatemorphological parameters, such as Lm and fractal dimensions.The destruction process was then iteratively repeated by usingthe last image as the starting point for the next destruction.

Statistical Analysis. Results are expressed as means � SD.ANOVA (Scheffe test) was used for comparisons betweengroups. All statistical analyses were performed by using StatView software (SAS Institute, Cary, NC). P � 0.05 was consid-ered to be significant.

This work was supported in part by Japan Society for the Promotion ofScience Grant B 16390234 and National Institutes of Health GrantHL059215.

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