## Abstract

The mean linear intercept (chord) length (*L*_{m}) is a useful parameter of peripheral lung structure as it describes the mean free distance in the air spaces. It is often misinterpreted as a measure of “alveolar size,” and its estimation is fraught with a number of pitfalls. We present two methods for the accurate estimation of *L*_{m}: *1*) the indirect method, which derives *L*_{m} from the volume-to-surface ratio of air spaces estimated by point counting methods, and *2*) the direct method, which uses a set of random intercepts and calculates *L*_{m} from their frequency distribution, for which we introduce a new and accurate method. Both methods are efficient and, with proper precautions, unbiased. The meaning of *L*_{m} is assessed in two different examples. In a physiological study, the effect of different inflation levels is studied, showing that *L*_{m} critically depends on lung inflation. In an experimental study on emphysema-like changes in a genetic mouse model, the effect of heterogeneity of air space size is assessed; these results are obtained partly because of differences in lung volume due to altered recoil in the emphysematous lungs. In conclusion, although *L*_{m} is not a robust parameter of internal lung structure because it crucially depends on lung volume, it is still a valid measure for which accurate and efficient methods are available that yield additional parameters such as size distribution or alveolar surface area.

- lung
- alveoli
- morphometry
- stereology
- mean linear intercept
- emphysema
- lung mechanics

the functional impact of lung structure is particularly felt when alveolar surface area is lost and distal air spaces are enlarged. One of the most popular measures of such changes is the mean “alveolar” intercept or mean chord length (*L*_{m}). The crux is that *L*_{m} is not a robust measure of internal lung structure as it is significantly affected by lung volume changes, be this due simply to inflation conditions or to altered elastic recoil (43). Also, *L*_{m} is not a measure of alveolar size, as is often implied; rather, it is a measure of the entire acinar air space complex, alveoli and alveolar ducts combined, since in the probing line explores the entire inner complexity of the air space. This measure is nevertheless appealing because it gives a simple and direct notion of size of the structural lung units and its changes, be it in human or experimental pathology or in genetic studies relevant to human lung disease (e.g., Refs. 15, 21, 24, 29); however, it is fraught with a number of pitfalls with respect to both the methods of measurement and its real meaning, mainly when used as the single estimator of structural changes in lung parenchyma (10, 17, 18, 53, 55).

*L*_{m} was introduced by Campbell and Tomkeieff in 1952 as a measure of the volume-to-surface ratio (V/*S*) of the alveolar complex of lung parenchyma (3), based on the original proposal of Tomkeieff (44) that the V/*S* of (convex) bodies was directly proportional to *L*_{m}. Independently, Chalkley et al. (4) proposed a simple method for estimating the V/*S* of particles: by using a set of short test line segments of known length, V/*S* is obtained from the ratio of the number of end points hitting the particle (proportional to the volume) to the number of intersections of the line with the particle surface trace (proportional to surface area) from which *L*_{m} can be derived.

These two related approaches were picked up and applied to the estimation of alveolar surface area in an attempt to characterize the morphometry of the normal human lung (42, 45, 46, 52). In these studies, the “mean linear intercept” was not considered per se as a parameter of structure but merely as an intermediary tool to obtain internal alveolar surface area. Thurlbeck (43) then applied this method to the study of emphysema and reported the estimates of *L*_{m} as an additional parameter to alveolar surface area, remarking that it was not only dependent on the absolute surface area but also on the lung volume that may be increased in emphysematous lungs due to loss of elastic recoil. This interesting observation means that *L*_{m} is not a robust parameter of internal lung structure but a variable that crucially depends on the inflation state at which the lung was fixed. This will be discussed further.

The concept of intercept length as a parameter of structure gained increased attention with the advent of automatic image analysis (27, 39), mainly in view of novel in vivo imaging techniques such as MRI and high-resolution computed tomography (41). Image analysis algorithms offer the possibility to automatically and exhaustively measure “alveolar,” or rather air space, intercepts along the scan lines. Provided that bona fide intercepts can be generated, this appears as an interesting approach to obtain an estimate of *L*_{m} with high precision and seemingly little effort, although automatic image interpretation must be guided or aided by some observer intervention (27, 36, 39), by “blacking” undesirable areas on the slides or by touching up the scanned image. This approach has received considerable attention in relation to MRI-based studies of gas diffusion in the parenchymal air spaces (8, 56, 57, 58) because here *L*_{m} is indeed a direct estimator of the mean free path within the alveolar complex. This important application calls for a critical appraisal of the methods used to estimate *L*_{m}.

The methodological problems at hand are threefold. First, the potentials and pitfalls of the two basic methods of estimating *L*_{m}, namely, the indirect, counting-based method of Chalkley and Tomkeieff or the direct, measuring-based method via the length distribution of random intercepts, must be clearly worked out to allow a decision on which method is to be used under given circumstances. Second, the sampling of intercepts poses problems with the direct method, which must be overcome by suitable test system designs, particularly to avoid edge effects that cause underrepresentation of very long intercepts as they occur, in normal lungs, when the test line lies in the direction of alveolar ducts, or, in emphysema, when it traverses areas with focal enlargement of distal air spaces. Third, the dependence of *L*_{m} on the degree of lung inflation needs particular attention as it must be realized that *L*_{m} is a parameter of structure only if the reference volume of the lung is precisely defined. This paper addresses all three problems.

The dimensions of the distal air spaces vary for several reasons: *1*) because of dynamic or functional changes, *2*) because of constitutional or structural alterations, and *3*) as a result of a combination of the two. Therefore, the respiratory cycle under physiological conditions has a direct effect on the dimensions of distal air spaces (1). Also influencing distal air space dimensions are chronic and acute pathological alterations involving destructive lung disease in pulmonary emphysema, with the loss of elastic recoil, and acute surfactant dysfunction in acute lung injury (30). Therefore, quantification and interpretation of these changes represent a special challenge in lung morphometry.

Here, the application of these methods is tested using two different animal models: a physiological rabbit lung model with varying degrees of lung inflation (1) and an experimental mouse lung model [the surfactant protein D (SP-D)-deficient mouse] with a well-characterized emphysema-like pathology (22, 33).

## MATERIALS AND METHODS

### Methods of Intercept or Chord Length Estimation

*L*_{m} is the mean length of straight line segments (“chords”) on random test lines spanning the air space between two sequential intersections of the alveolar surface with the test line (Fig. 1). It is important to note that chord lines often cross from one alveolus through an alveolar duct to an opposite alveolus, indicating that *L*_{m} characterizes the entire acinar air space complex and not just alveoli. In simplest terms, *L*_{m} is therefore an estimator of V/*S* of acinar air spaces [(V/*S*)_{asp}; alveoli and alveolar ducts together]:
*S*(a) is alveolar surface area (3, 4, 7, 44–47, 52). Two methods can be used to estimate *L*_{m}: *1*) indirectly estimating *L*_{m} from V/*S* according to *Eq. 1* and *2*) directly estimating *L*_{m} from measurement of a set of random intercepts (*L*_{x}). These two approaches are complementary and have different advantages and limitations. In addition to *L*_{m}, the direct approach allows different moments of the *L*_{x} distribution, and hence the variance of air space size measures, to be estimated. This is not obtained from the indirect method, which in turn provides direct information on the alveolar surface area and the distribution of volumes of air, tissue, and so forth. The choice of the method should therefore depend on the study goal: which are the most useful additional parameters?

#### Indirect method, based on point and intersection counting.

In analogy to the estimation of alveolar surface density in lung volume, V/*S* and thus *L*_{m} can be estimated indirectly by simple point and intersection counting using a suitable coherent test line system with unit length *d* (Fig. 2), counting points hitting air spaces [P(asp)] and intersections of the test line system with alveolar surface [I(a)] to obtain
*k* depends on the geometry of the coherent test system and determines the number of test line segments of length *d* per test point (48). In Fig. 2, two test points are associated with the test line *d* so that k = 1/2 (48). With proper sampling of sections and microscope fields, this method of estimating L_{m} is unbiased (18).

#### Direct method based on L_{x} distribution.

With the use of a set of random test lines superimposed on a sample of sections (Fig. 1), *L*_{x} can be measured, allowing *L*_{m} to be calculated from their distribution. In this method, the test line contains two parts: a short stretch beginning with a start point, marked as a solid line, which is used to sample the intercepts, and an (infinitely) long continuation of the test line, marked as a broken line. Intercepts are measured along the entire test line from the intersection of the solid line with alveolar surface to the next intersection. This test line design, with what has been called a guard zone (13, 51), ensures unbiased sampling of intercepts irrespective of their length, which may be very long when the line lies along the alveolar duct or traverses emphysematous air space enlargements: without a guard zone long intercepts would be preferentially undersampled. The procedure is to scan along the line from the start point (on the left) and to determine the initial intersection with the alveolar surface and then measure the intercept length to the next surface intersection (on the right), which can occur on the sampling line or on the extension line (Fig. 1). If an intercept extends beyond the image boundary, the distance from the sampling intercept to the end of the extension line is recorded; even though this is an underestimate of *L*_{x}, it is better to record it than to eliminate the measurement altogether. All intercepts sampled by the sampling line are measured. The intercepts can be measured with a ruler, but digitization of images combined with computer-assisted image analysis allows chord lengths to be measured automatically. From these measurements, the chord length distribution, the arithmetic mean *L*_{m}, and other moments of the distribution, such as the variance or the harmonic mean (54), can be calculated. Because the distributions are skewed, it might be useful to plot them as a function of the log of intercept length.

The method can also be used with automatic image analysis, but the problem with this approach is the automated recognition of bona fide air space intercepts: non-air space voids such as vessels (Fig. 1) or bronchioles and others must be excluded. Thresholding and setting lower cut-offs (39) are approximations that introduce unknown biases, and blocking areas by “painting” (27) is not satisfactory. Observer intervention is required to ascertain the true intercepts on a limited sample of random test lines, with the computer suggesting intercepts and measuring those accepted. This is feasible because it suffices to perform measurements only on a limited number of loosely placed test lines (Fig. 1). In view of large variability between pulmonary regions and individuals, there is no gain in precision by measuring, on single images, all or even a large number of intercepts generated by the scan (27). This direct approach is more laborious than the indirect method based on point and intersection counting described above, but it is a justified approach if more information is sought than *L*_{m}.

It should be pointed out that both the indirect and direct method to estimate *L*_{m} rely on the use of test lines. For counts or measurements involving test lines, isotropy is required. To account for this, the sampling procedure needs to randomize for spatial orientation. This can be achieved either by randomization of test line orientations in three dimension (e.g., with the help of computer-assisted stereology systems) or by randomization of tissue sample orientations (26, 32).

### Implementation of the Methods

The stereological assessment was carried out using a Zeiss microscope with a primary magnification of ×10 equipped with a computer-assisted stereological toolbox (CAST, Olympus, Ballerup Denmark). In a first step, a coherent test grid consisting of a short line of length *d* with two endpoints as test points (Fig. 2) was used to count on microscopic images generated by systematic uniform random sampling test points falling on alveolar [P(a)] and ductal air space [P(duct)] or on septal tissue [P(sep)], as well as I(a). This allows estimation of the volume fractions of ductal air space [V_{V}(duct,par)], alveolar air space [V_{V}(a,par)], and septal tissue within parenchyma [V_{V}(sep,par)] (35, 48) such that, e.g.,
*L*_{m} of air spaces was estimated according to *Eq. 2* as

In a second step, random linear intercepts were measured on microscopic images generated according to systematic random sampling by the computer-assisted stereological toolbox CAST. The test line, as described (Fig. 1), consisted of a sampling line segment of 80 μm that was projected on the left side of the image with the orientation from left to right; the test line continued to the right as a long dashed line about four times the length of the sampling line. Reading from left to right, a measurement was performed each time the upper edge of the sampling line segment intersected an alveolar surface: the distance from this intersection to the next intersection of the upper edge with an alveolar surface was determined as intercept length *L*_{x}. Note that this sometimes generated more than one intercept on the same line. With a mean of 50 test fields (containing a single test line) per section and sections from three to four tissue blocks per lung, we obtained on average 300 measurements per lung. From these data, frequency distributions of intercept length were constructed by means of the program S-Plus 7.0 (Insightful 2005) for linear and log_{10}-transformed data.

### Materials

The application of the proposed methods was tested on materials from two previous studies: a physiological study on rabbits (1) and an experimental pathology study on mice (22), which had included an extensive stereological assessment of lung structure.

In the physiological study, the effect of different expansion levels of the lung on its structure was assessed on rabbit lungs fixed by vascular perfusion at different degrees of inflation and deflation (1). Here, we evaluated histological sections from two lungs: one lung was deflated from total lung capacity (TLC) to 80% (D80), with the other deflated to 40% TLC (D40). Tissue preparation has been described in detail elsewhere (1). Briefly, the lungs were perfusion fixed starting with a 1% solution of osmium tetroxide buffered with sodium cacodylate and 3% dextran T70 for 15 min followed by 0.5% uranyl acetate in maleate buffer and 3% dextran T70 for 10 min. Afterward, dehydration and stiffening of elastic fibers were achieved by perfusing ethanol solutions in rising concentrations. Lung volume was measured by fluid displacement, and, following a systematic uniform randomization rule, 12 tissue blocks were sampled, embedded in Epon, and sectioned. Gomori-stained sections of 5 μm thickness of three or four of the tissue blocks were chosen randomly and analyzed in the present study.

As a model of emphysema-like pathology, we used two SP-D knockout mice back-crossed 10 generations into C57BL/6 background, which causes an emphysematous phenotype to emerge (22). From age 3 wk on, one of the two animals was subjected to daily intranasal therapy with a recombinant fragment of human SP-D (rfhSP-D), which has been shown to be effective in correcting the emphysematous phenotype (22). The procedures regarding cloning, expression, and purification of rfhSP-D have been described in detail elsewhere (40). The other mouse served as control and received only PBS. At the age of 12 wk, (i.e., 9 wk after starting therapy), the animals were killed for stereological assessment. Using a mixture of 1.5% glutaraldehyde-1.5% formaldehyde (from freshly depolymerized paraformaldehyde) in 0.15 M HEPES buffer, instillation fixation was carried out with a constant instillation pressure of 20 cmH_{2}O (22, 31, 35). The total lung volume was determined by means of the buoyancy-based fluid displacement method (38). Afterward, a systematic uniform randomization was performed following an established procedure, guaranteeing that every part of the lung had the same chance of being chosen for analysis, thereby achieving a representation of the whole organ (35). Four tissue blocks per lung were sampled, processed, and embedded in glycol methacrylate (Technovit 7100; Heraeus Kulzer, Wehrheim, Germany) so that shrinkage could be neglected (Refs. 6, 11 and online supplement of Ref. 34). Slices were cut from each tissue block (thickness: 1.5 μm), mounted on a slide, and stained with toluidine blue.

### Statistical Analysis

Frequency distributions of intercept length were constructed by means of the program S-Plus 7.0 (Insightful 2005) for linear and log_{10}-transformed data. The distributions obtained after log transformation were tested for normality, applying the Kolmogorow-Smirnow test, with *P* > 0.05 indicating that the distribution does not differ significantly from a hypothetical normal distribution. The means of the distributions were tested for significant differences using the *t*-test. A *P* value below 0.05 was accepted as statistically significant. To further compare the results of the direct and indirect method, the 95% confidence intervals of *L*_{m} measured with the direct method and indirect method [*L*_{m}(dir) and *L*_{m}(indir)] were calculated for three (D40) and four (D80, SP-D^{+}, SP-D^{−}) sections per lung from the mean and standard error of the mean (48).

## RESULTS

Both the indirect point and intersection counting method and the direct intercept length measurement method introduced here turned out to be very efficient; with an average of 1.5 h/animal, these methods were not time consuming. The stereological data are summarized in Table 1. Additional features of the distributions of *L*_{x} are given in Table 2 and Table 3.

When we compared representative images of the rabbit lung deflated either to 40% TLC (Fig. 3*A*) or 80% TLC (Fig. 3*A*), it was evident that the distal air spaces appeared homogenously enlarged in the more inflated lung; however, the alveolar ducts seemed to be more involved. In contrast, the emphysematous phenotype that developed in the untreated SP-D knockout mouse lung showed heterogeneous air space enlargement, with some regions appearing quite normal and others affected to a larger extent, with clear focal enlargements of distal air spaces (see Fig. 5*B*). The therapy with rfhSP-D led to a normalization of lung architecture (see Fig. 5*A*).

Regarding the general stereological data derived from point and intersection counting (Table 1), both deflation (from 80 to 40% TLC in the rabbit lung model) and the correction of the emphysema-like pathology in the SP-D knockout mouse by rfhSP-D were associated with a decrease of V_{V}(duct,par), whereas V_{V}(sep,par) and V_{V}(a,par) were increased. The total surface area of the alveolar epithelium on the other hand demonstrated an increase in the rabbit lung at the higher inflation degree (D80) due to stretching of alveolar walls, whereas it was not different in the emphysema-like phenotype of the untreated SP-D knockout mouse compared with the treated lung. *L*_{m}(indir) demonstrated a 1.6-fold increase in the rabbit lung with the higher degree of inflation (D80) compared with the lung with the lower degree of inflation (D40). When we compared the *L*_{m}(indir) of the untreated mouse lung with the effectively treated SP-D knockout mouse, this ratio was also 1.6. With regard to these findings, a closer look to the reference spaces is important. The difference in total lung volume in the two groups of rabbits (Table 1) was the result of controlling the degree of air inflation; accordingly, the total volume of air space was doubled in the rabbit lung analyzed at an inflation degree of 80% TLC compared with 40% TLC. Although the pressure used during instillation fixation of the two mouse lungs was exactly the same (20 cmH_{2}O), both the total lung volume and total volume of air space of the untreated SP-D knockout mouse was increased 1.6-fold compared with the treated SP-D knockout mouse.

The distribution of the chord length *L*_{x} (used to determine *L*_{m} with the direct method) is heavily skewed (Fig. 4*A* and Fig. 6*A*). Considering the rabbit lungs, the density curve had a slimmer but higher peak in the lung analyzed at 40% TLC compared with at 80% TLC (Fig. 4*A*). In these lungs, fixed by vascular perfusion in the air-filled state, we observed shifts in the volume fractions of alveolar space and alveolar duct space: there was an increase of V_{V}(duct,par) and a decrease of V_{V}(a,par) in D80 compared with D40 (Table 1). This strongly suggests that more measurements of chord lengths included alveolar ducts in D80, thus contributing to the shift of the distribution toward higher values (Fig. 4*B*) and an increase of the standard deviation (Table 2). Both the direct and the indirect methods to determine *L*_{m} yield comparable results (see Fig. 7).

In the untreated SP-D knockout mouse lung with the emphysema-like pathology, the density curve of the raw data had a wider and lower peak than that shown in the treated lung (see Fig. 6*A*); these conditions were comparable to the rabbit lung model: the shape of the distribution of *L*_{x} of the treated mouse lung resembled the rabbit analyzed at an inflation degree of 40% TLC, whereas the density curve of measurements obtained from the untreated mouse lung looked like the one obtained from the rabbit analyzed at 80% TLC (see Figs. 4*A* and 6*A*). Considering qualitatively the size of alveoli in the treated SP-D knockout mouse (Fig. 5*A*), the value of 41.1 μm at the 75th percentile (Table 2) suggests that most measurements represent chords traversing the alveolar portion, whereas higher values represent measurements of the alveolar ducts and alveoli taken together linked by the alveolar opening. In the untreated SP-D knockout mouse, there were less measurement events with smaller values, as indicated by the more than doubled value at the 75th percentile. Because this was accompanied by a decrease of V_{V}(a,par) and an increase of V_{V}(duct,par), this might at least in part be attributed to more measurements traversing the enlarged alveolar ducts. Additionally, the emphysema-like lesions with destroyed alveolar septa (focal enlargements of distal air spaces) (Fig. 5*B*) contributed longer chord lengths, although the exact contributions of these different mechanisms to the changes in the distribution of the chord lengths cannot be distinguished. The higher standard deviation in the untreated SP-D knockout mouse reflects the heterogeneity of alterations.

The means of these *L*_{x} distributions correspond to the *L*_{m}(dir), which show between-group differences comparable to the *L*_{m}(indir) (see Fig. 7). The surface area of alveolar epithelium was nearly the same in the treated and untreated animal in the presented cases, in accordance with our previous study in which the total surface area did not differ between the treated and untreated groups (22). However, as shown in our previous study, there was a decline of alveolar number accompanied by an increase of mean alveolar size in the untreated SP-D knockout mouse, strongly suggesting that there is a destruction of alveolar walls resulting in larger alveoli possessing more alveolar surface area each.

Figures 4*B* and 6*B* show the distribution of *L*_{x} on a logarithmic scale. In both models, the curves show a near log-normal distribution that is supported by the comparable values of median and mean as well as the symmetries of the 25th and 75th percentile in relation to the median after log transformation of the raw data. Moreover, the statistical analysis based on the Kolmogorow-Smirnow test demonstrated that all four distributions obtained in this study did not differ from a hypothetical log-normal distribution (Table 3). Both the higher degree of expansion in the rabbit lung and the emphysematous phenotype in the mouse lung led to a shift of the log-distribution curves to the right. In the treated mouse lung, the log-distribution curve of *L*_{x} resembles very closely a bell-shaped curve (Fig. 6*B*). In the untreated mouse lung, there is a suggestion of a bimodal distribution with one peak coinciding with the peak of the treated lung. The appearance of a second peak to the right could most likely be attributed the occurrence of emphysematous lesions that are embedded in regions with normal architecture (Fig. 5*B*).

The results of estimating *L*_{m} by the direct and indirect method are compared in Fig. 7. In all four cases, the results are comparable since the group means are pairwise not statistically different: the SE values overlap. With only two exceptions, the paired estimates per section (sample) are rather close; this is remarkable since these estimates are based on only 50–100 intercept measurements per sample in the direct method and an average of 50–100 intersections with alveolar surface in the indirect method. Even with this small sample, the differences between the experimental groups are found to be significant by both methods, as shown by the 95% confidence intervals.

## DISCUSSION

The mean linear intercept length *L*_{m} is a widely used parameter to characterize the dimensions of the distal air spaces on histological lung sections. Frequently, it is used in quantitative assessment of pulmonary emphysema, in human pathology, or in animal models. Concerns of this parameter regarding its properties to assess pulmonary emphysema quantitatively are partly related to the fact that the reference volume is frequently not considered making its interpretation difficult (17, 28, 53). Moreover, this parameter involves both alveolar space and alveolar duct space taken together; in addition, because it is only a mean, it cannot reflect the heterogeneity of pathological alterations, a typical feature of pulmonary emphysema (20, 37). The *L*_{m} can be determined either indirectly from V/*S* by point and intersection counting (45, 46) or directly by measuring wall-to-wall intercepts using a ruler or an automatic image analyzer. The direct method is affected by the so-called edge effect, since measurements depend on the occurrence of two surface hits so that air space chords extending beyond the sampled field cannot be measured; larger chords are more affected by this than short ones, leading to a biased measurement. This bias can be avoided by dividing the test line into a short sampling line segment followed by a guard zone measuring line that is three to four times as long as the sampling segment (Fig. 1) (13, 51).

In the present study, we addressed both the problem of the edge effect, as mentioned, and the problem of assessing the heterogeneity in air space size. For that purpose, the direct measurement of intercept lengths provided a frequency distribution of chord lengths, which proved to be represented by a log-normal distribution in all cases (Figs. 4*B* and 6*B*). This procedure has previously been used to characterize the air-blood barrier in the lung (51, 54) and the basement membrane thickness in the glomeruli of the kidney (13). The changes in these distributions observed between the experimental groups are descriptive of the structural alterations, but it is difficult to translate this into three-dimensional models of the complex air space structure. Algorithms for the conversion of such linear intercept distributions into spatial size distribution parameters may have to be developed, as they exist for sheet-like structures such as the air-blood barrier (49). The method of determining the intercept length measurements proposed in the present study turned out to be very efficient as the evaluation of one entire lung with four sample sections lasted <2 h. The question regarding how many samples should be used and how dense the test lines should be arranged cannot be answered from this study. It is, however, remarkable that, with no more than 100 test lines per section, consistent measurements were obtained by both methods, as shown in Fig. 7. Definitive recommendations would have to be worked out in targeted studies, but some general rules of stereology can be advanced, namely, that the variance between samples is much greater than the measuring error on the section so that there is little or no gain in using dense test systems (14, 25). In a thorough study on structural heterogeneity in the mouse lung, Mitzner et al. (27) compared the effect of test line spacing in an automatic analysis; this shows that the SD of the measurements is lower with dense test lines but that the variance of the estimate of *L*_{m} across all sections and animals is not different if the lines are spaced at 280 μm or 3 μm.

The *L*_{x} distribution curve of the treated SP-D-deficient mice resembled a log-normal distribution (Fig. 6*B*), as did the distribution curve at the lower inflation level D40 in the rabbit model (Fig. 4*B*). Both the pulmonary emphysema in the untreated SP-D-deficient mouse and the higher degree of inflation (80% of TLC) in the rabbit lung model led to a shift of the distribution curve to the right accompanied by almost a doubling of the *L*_{m} in both cases despite completely different underlying causes of the structural changes. In the one case, it was due to heterogeneous emphysematous alterations as a consequence of an ongoing inflammatory state (33); in the other case, it was a consequence of the effect of surface tension at different degrees of deflation from TLC (1). Therefore, neither the indirect point and intersection counting method to determine *L*_{m} nor the direct approach by measuring intercept lengths presented in this study is able to distinguish simple physiological air space enlargement due to different degrees of lung deflation/inflation from pathological air space enlargement resulting from septal wall destruction. This remains an apparent limitation of the method presented in this study and should be considered in future applications.

The shift in the intercept length distribution observed in the rabbit lungs (Fig. 4*B*) is related to a change in the distribution of air space between alveoli and ducts (Table 1) and is a consequence of different effects of surface tension at different inflation levels (2). In these preparations, the lungs had been fixed by vascular perfusion at controlled levels of air inflation (1) so that the surface forces remained active up to tissue fixation. At the higher level of air inflation (D80), the surface force generated at the free edge of the alveolar septa due to high curvature tends to push the septal edge outward, thus preferentially enlarging the ducts more than alveoli compared with the lower inflation level (1, 2, 50). This functionally important effect then results in a higher frequency of long values of *L*_{x} and a right skew in the distribution curve at the higher inflation level (Fig. 4*B*).

In all our previous studies on SP-D knockout mice, the SP-D-deficient animals had increased lung volumes compared with the wild-type groups (16, 22, 23, 33). In all cases, instillation fixation was carried out with a constant pressure of 20 cmH_{2}O. Measurements of respiratory mechanics revealed a decreased elastance in SP-D-deficient Swiss black mice compared with wild-type littermates (5). Although the animals in our previous study had a different genetic background (C57BL/6), the emphysematous alterations and disturbances of the surfactant homeostasis might affect the pulmonary compliance in this animal model. Instillation of the fixative at a given pressure can therefore lead to different lung volumes in SP-D knockout and wild-type animals accompanied by an enlargement of the distal air space and an increased *L*_{m} accompanied with a shift of the distribution curve to the right. These problems can be addressed by applying alternative tools of unbiased stereology in which all parameters are calculated per total lung. These parameters include for example the number of alveoli together with their individual mean volume or the total surface area of the alveolar epithelium (18, 19, 34). With the use of these methods, a real loss of tissue due to destruction can be distinguished from simple air space enlargement.

*L*_{m} is not related to alveolar air space alone, as is often assumed, since chords can also traverse the ductal air space. Therefore, *L*_{m} cannot distinguish between processes affecting either the dimensions of alveolar air spaces or ductal air spaces or both. If one is interested in alveolar size, alternative stereological tools such as the so-called point sampled intercepts (12) for determination of the volume-weighted mean volume of either alveoli or acinar pathways can give additional information (9, 16). The heterogeneity of alterations of alveolar size is taken into account when using this method because the volume-weighted mean volume (obtained from point sampled intercepts) and the number-weighted mean volume of alveoli (obtained from total alveolar volume and alveolar number) are related to each other via the coefficient of variance of the number-weighted mean volume (12).

Hyperpolarized ^{3}He diffusion magnetic resonance imaging of the lung, a noninvasive method to analyze the dimensions of the distal air spaces, has recently become available (57, 58). Based on the apparent diffusion coefficient (ADC) of ^{3}He in the lung, conclusions can be drawn considering the mean free path in different parts of the lung. The mean free path of ^{3}He is restricted by alveolar septa but does not differentiate between ductal space and alveolar space, just like *L*_{m}. This has recently been analyzed in great detail on the basis of realistic model assumptions on acinar airway geometry (58). An increase of ADC reflects an increase of the mean free path as a consequence of distal air space enlargement; it is evident that ADC measurements are also subjected to effects of lung inflation as demonstrated here. This MRI technique turned out to be very efficient to detect early emphysematous alterations in the human lung, also taking the heterogeneity of this disease into account (8). As studied by Woods et al. (56) in human lung tissue in detail, the ADC displayed a correlation with the *L*_{m}; this is plausible because the functional meaning of *L*_{m} is indeed the mean free path of the air spaces, irrespective of their geometry. Furthermore, the distribution of the ADC in pulmonary emphysema samples demonstrated an increased standard deviation of this parameter, presumably reflecting the heterogeneity of the pathological alterations together with a shift toward higher values (56). The distribution of the intercept length as determined in our study reflects the distribution of the mean free path distance on a light microscopic level rather than the distribution of alveolar size.

### Comparison of Direct and Indirect Method to Determine L_{m}

The two approaches to the estimation of *L*_{m} of acinar air spaces have their specific merits and problems. Both are efficient with no differences regarding time consumption.

The indirect estimation of *L*_{m} from the ratio of point and intersection counts on a coherent test system of lines and points is quick and easy, and it is unbiased if proper precautions are taken for isotropic orientation of the test lines. In particular, there is no danger of an edge effect and thus no need for a guard frame. The method is easy to apply because it requires no measurement; all that is needed is to count point hits on air space and intersections with the alveolar surface; computer-assisted counting tools help but are not essential. It is also convenient to perform the counts at reasonably high magnification, thus providing adequate resolution of structure. The drawback of this method is that it provides only the mean linear intercept length and cannot give information on the variation in air space dimensions. On the other hand, since this indirect approach is based on point and intersection counts, the estimation of *L*_{m} can be obtained without additional effort when embedded in stereological studies assessing total air space volume and alveolar surface area as parameters describing the structural conditions for gas exchange (48, 51); vice versa, when estimating *L*_{m} by the indirect method, one obtains an estimate of alveolar surface and air space volume for free.

Estimating *L*_{m} directly from the set of *L*_{x} measurements is more informative only with respect to air space size variations but is also more demanding and fraught with a number of pitfalls. Because actual measurements must be performed, care must be taken that very long *L*_{x}, as they occur when the test line courses along an alveolar duct, are properly sampled; this requires a test line design with a guard zone where sampling and measurement are separated. Likewise, very short chords must also be assessed, and this requires adequate microscopic resolution. To define a lower cut-off of *L*_{x} (39) is not suitable, as this introduces arbitrary bias (in theory, the shortest *L*_{x} should be infinitely small; i.e., the *L*_{x} distribution must go to 0). The efficiency of these measurements is improved by using either computer-assisted measuring devices or applying a log-scale ruler for manual recording (48, 51). However, the greatest gain in efficiency is to use a small number of test lines per field (1 to 4) and to apply this to a larger number of fields from different sections and from different samples. There is no gain in accuracy or in precision in analyzing a very large number of scan lines per field, as they can be produced by scanning programs because the greatest contribution to variance is not the variation of air space size within a field of view but between regions, and between individuals, as discussed above. Examples include pathological cases such as smoke-induced pulmonary emphysema in humans, which often affects the upper zones to a larger extent, whereas in patients with α_{1}-antitrypsin deficiency, lower zone dominated emphysema can occur (37).

A word of caution is needed with respect to automatic image analysis and intercept length measurement, which have serious limitations. It is very difficult, if at all possible, to automatically generate bona fide air space intercepts: air spaces and empty blood vessels, bronchiolar lumina, or interstitial spaces have about the same optical density and cannot be discriminated by the automatic scan, thus generating spurious intercepts. In contrast, any particle contained in the air space image (a speck of dust for example) may intersect the scan line and thus cut an intercept in half so that two short chords are recorded instead of one longer one. Finally, the edge effect is more difficult to control: here again the test lines must be provided with a guard zone to avoid sampling bias due to large intercepts. It is therefore essential that automation is limited to the measuring process, whereas image interpretation depends on quality control by an educated observer.

### Conclusions

The determination of the *L*_{x} distribution is clearly more demanding than the indirect estimation of *L*_{m}, but it is also more informative regarding heterogeneity. On the other hand, the information value of *L*_{x} distributions is limited because the measure is not directly related to “size” of an air space unit: long values of *L*_{x} are due to long alveolar ducts in the normal lung and enlargements of distal air spaces in emphysema, which cannot be differentiated by this simple linear measure. Advanced statistical analysis may however provide new insight. Above all, it must be remembered that intercept lengths measured on microscopic slides are primarily determined by the inflation level at which the specimen has been held during tissue preparation. The meaning of *L*_{m} is therefore conditional on lung volume and cannot be interpreted per se, even in the comparison of two different groups. The same holds true for ADC measurement by MRI.

Finally, the decision on what method for estimating *L*_{m} should be preferred depends on the study goal, in particular on what additional information may be useful. If an estimate of *L*_{m} is sought in a context of functional studies, it may be more useful to obtain an estimate of alveolar surface area and then the indirect method is preferable. The same may hold in certain cases for characterizing emphysema where the question of loss of surface and tissue may be pertinent. In lung pathology, one may, however, chose to know more about the heterogeneity of air space alterations and then the direct method is the method of choice. Because, as shown, both approaches can be designed as very efficient methods, they may well be combined because the effort for measurement is, in fact, not the major cost factor in such studies, and the same preparations can be used for both approaches.

## GRANTS

Parts of this work have been funded by the Swiss National Science Foundation (SNF 3100A0-116417 to M. Ochs).

## ACKNOWLEDGMENTS

The authors express thanks to Barbara Krieger (Bern) for help with the preparation of the figures.

- Copyright © 2010 the American Physiological Society