Morphometry of the Respiratory Tract: Avoiding the Sampling,Size,Orientation,and Reference Traps

Abstract

The extrapolation to humans of studies of infectious or toxic agents injurious to the respiratory system using animal models assumes comparability in the structure and function of animal models and humans. Measurement of conducting airways and parenchyma yields quantitative data for parameters like volume, surface area, length, cell number and cell size. Over the past few decades, there has been an evolution of rigorous uniform sampling designs of stereology that ensure unbiased estimates of number, length, surface area, and volume. This approach has been termed ‘design-based’ stereology because of the reliance on sampling design rather than geometric model-based stereology that makes assumptions. The aim of this paper is to define new design-based stereological approaches for the direct estimation of anatomical structures and epithelial, interstitial and endothelial cells of specific regions of the lung independent of the sampling, size, orientation and reference traps. An example is provided using wildtype and transgenic mice expressing transforming growth factor-α to show the importance of the reference trap in stereologic estimates of postnatal lung growth.

Introduction

Measurement of conducting airways and parenchyma yields quantitative data for parameters like volume, surface area, length, cell number and cell size. While measurement of structure in general is known as morphometry, the methods to obtain these data in microscopy are referred to as stereological methods. Stereology can be defined as the science of sampling structures with geometric probes. Over the past few decades, there has been an evolution of rigorous, uniform sampling designs of stereology that ensure unbiased estimates of number, length, surface area and volume. This approach has been termed ‘design-based’ stereology because of the reliance on sampling design rather than geometric model-based stereology that makes assumptions (Gundersen et al., 1988a, 1988b). The aim of this paper is to define new design-based stereological approaches for the direct estimation of anatomical structures and epithelial, interstitial and endothelial cells of specific regions of the respiratory system independent of the sampling, size, orientation, and reference traps.

Materials and Methods

We use the following guiding principles for quantitation: (1) design-based methods to quantify structure, (2) structural hierarchies to link and interpret structural features, and (3) collection of data with statistical efficiency.

Design-Based Methods

A sample is considered unbiased when all the compartments of the structure have an equal chance of being sampled. One of the most reliable methods of satisfying this need for unbiased sampling is to introduce randomness in the sampling process. If a structure such as the lung does not have a uniform distribution of all of its components, such as the airways, then one of the best ways to avoid sampling bias is to collect samples with a design-based approach (Gundersen and Jensen, 1987; Ogbuihi and Cruz-Orive, 1990). Design-based sampling ensures unbiased sampling at all magnifications and even when the components exhibit striking anisotropy. Design-based sampling allows experimental questions, data and interpretations to be related to the 3-dimensional space of real world biology. Systematic sampling is a more efficient method for taking replicated spatial samples than random sampling (Howard and Reed, 2005). However, there may be a problem with systematic sampling if there is a natural periodicity in the structure that coincides with the period of the systematic sample. This overlap in sampling and natural periodicity in a structure can be avoided by using a random start in the first period of sampling, and this is called Systematic, Uniform Random Sampling (SURS). SURS is a sampling strategy that has been used extensively in stereological sampling and estimation procedures. SURS is the basis of the smooth fractionator that is much more efficient than random sampling (Gundersen, 2002). The fractionator can be used to sample the entire lung (Figure 1; (Hyde et al., 2004) or subcompartments of the lung, such as specific airway generations (Figure 2). The sampling designs in Figures 1 and 2 illustrate that the fractionator may be combined with other sampling requirements, such as specific orientation of the sections (vertical sections) critical for unbiased estimates of surface area and length of lung and airway components.

The interface of probes and structural features that enable investigators to estimate quantitative values requires isotropic orientation of either the tissue section or the test probe. Thus, the intersection of probes and features gives countable events that provide efficient estimators of volume by point hits, surface by line intersections, length by plane transects and number by volume sampling (Figure 3). Surface and length estimates are influenced by the orientation of the probe relative to the feature, but estimates of volume and number are orientation independent. Figure 1 illustrates one method of obtaining isotropically oriented tissue (Orientator) (Mattfeldt et al., 1990), while Figure 2 illustrates a method of orienting the tissue with a known (correctable bias) relative to the probe (vertical sections) (Baddeley et al., 1986). A coherent test system of probes should be simple for easy counting of probe/feature interactions and use an unbiased counting frame when counting features (Gundersen, 1977). Isotropically oriented tissue, sampled by a fractionator satisfies all the requirements of stereologic sampling, which is isotropic uniform randomness (IUR).

Collecting the Critical Data of Volume, Surface, Length and Number

Critical data required to detect and interpret quantitative data in the lung include the measures of volume (V), surface (S), length (L), and number (N) and their ratios or densities. Ratio densities to a reference volume (Vv, Sv, Lv, and Nv) can be misleading independent of the knowledge of changes in the reference compartment and have been called the “reference trap” by Gundersen (Braendgaard and Gundersen, 1986). To make this point about the reference trap absolutely clear, Gundersen stated “never ever not measure the reference space.” Densities are defined by symbols (i,ref) that define the ratio of the two compartments for the densities (eg., Vv (i, ref)). The compartment of interest,“I″, is related to the reference compartment, “ref.”

Volume

There are 2 direct methods of estimating lung volume. The first method uses volume displacement or buoyant weight in saline (Scherle, 1970). This method is accurate except with hollow organs, for which there is a possibility of volume underestimation, such as open airways or vessels in the lung. The second method is to systematically cut the lung into slabs of equal thickness and determine their cumulative area by point counting and multiplying by the average slab thickness (Cavalieri method) (Michel and Cruz-Orive, 1988).

The Cavalieri method is named after the Italian mathematician Bonaventura Cavalieri (1598–1647), a pupil of Galileo, who first proposed the method for estimating volume. In the lung, the Cavalieri method has the advantage of interfacing directly with fractionator sampling and of estimating other subcompartment volumes, such as conducting airways and large vessels, while estimating the volume of the entire lung.

Surface

Surface is estimated by surface density, Sv, and is influenced by both the sectioning angle and the shape of anisotropic structures. For IUR sampled structures, surface density can be defined as follows:

$$S{\nu }_{i,r}=\frac{2*I_i}{L_r}$$

where I _i is the number of intersections of the object surface by a linear probe and L _r is the total probe length in the reference component (Smith and Guttman, 1953). This equation is valid for test lines that are IUR relative to the structure of interest in 3-dimensional (3D) space. To meet this requirement when using a lattice grid, the structures of interest must be distributed uniformly and randomly, and their orientation must be isotropic. Both the orientator (Mattfeldt et al., 1990) and the Isector (Nyengaard and Gundersen, 1992) are approaches that ensure tissue isotropy and when mixed with a smooth fractionator, uniform randomness can be achieved. The fractionator approach also directly provides total surface of the feature of interest within the lung.

Other methods of estimating total surface require multiplication of the appropriate volumes and subcomponent volumes (multicascade design) in the lung. For tissues with evident anisotropy, the use of vertical sections, defined along the plane of preferred orientation for anisotropic microstructures, and a cycloid test system, gives surface density estimates that correct for anisotropic orientation directly using the Sv equation above (Baddeley et al., 1986) (Figure 4). This approach can be used with local vertical sections of the conducting airways sampled by a fractionator (Figure 2).

Length

Length is estimated by length density, Lv, and is influenced by both the sectioning angle and the shape of anisotropic structures. For isotropic structures, length density can be defined as follows:

$$L_{V(i,r)}=2*\frac{Q_i^{-}}{A_r}$$

where $Q_i^{-}$ is the number of profiles (feature transects) per unit area of the reference space (A _r ) (Smith and Guttman, 1953). The estimation of length density requires estimates of the number of profiles per unit area using IUR sections and the unbiased counting rule of Gundersen for profile counting (Gundersen, 1977).

In thick vertical sections a virtual IUR surface can be generated by projecting a cycloid line through the section if the major axis of the cycloid is parallel with the vertical direction (Gokhale, 1990). Uniform random sampling and isotropic rotation around the vertical axis of the thick vertical section are still required. For thick vertical sections use the formula:

$${\widehat{L}}_{V(i,r)}=\frac{2}{t}*\frac{p}{l}*\frac{\sum Ii}{\sum Pr}$$

where t is section thickness, $\frac{p}{l}$ is the length per point on the test system, I i is the number of intersections observed through the thick vertical section and Pr is the number of points that hit the reference space (Figure 5).

Number

Counting the number of structural features in the lung, whether they are cells, organelles, airways, vessels or nerves, should be done in 3D space. Profile counts are not equivalent to number counts in volume and should be avoided as an endpoint because of their inherent bias. In microscopy, a “disector” is used as a volume probe to estimate numbers in 3D (Sterio, 1984). The disector approach can be used with thick sections and viewed with a brightfield or laser confocal microscopes that optically focus through the section (Postlethwait et al., 2000). The usual section thickness is 30 to 50 μm, and a short depth of focus (usually about 1 μm) is essential to optically section the tissue using a light microscope.

A length gauge is required to record the distance moved in the Z direction. This unbiased counting method, called an optical disector, is direct and efficient, provided we use an unbiased counting frame (Gundersen, 1977) and extend the counting frame concept by excluding structures counted on either the top or bottom of the counting cube. We estimate the reference volume by point counting an optical section at the top of the disector that provides us with a reference area that is multiplied by the distance traveled in the Z direction for counting structures. We use the following formula:

$$N_{V(i,r)}=\frac{Q_i^{-}}{A_r*h}$$

where $Q_i^{-}$ is the feature count, A _r is the reference area and h is the height of the disector. An optical disector requires feature identification because of lack of resolution and, therefore, immunohistochemistry is often used to identify specific cell types.

A physical disector is used when we rely on higher resolution and morphological characteristics for feature identification (Figure 6). In general, disector height should not be greater than 0.75h of the smallest feature to be counted. The same formula is used as for the optical disector discussed above. The sections of a physical disector are as thin as possible for the greatest resolution, and the top section is used as the counting section. The bottom section is used as the lookup section.

Only those features intersecting the counting section are counted, thus, the height of the disector is the thickness of the counting section and the distance to the lookup section. An unbiased counting frame is also used on the counting section (Gundersen, 1977). A disector count can be combined with a fractionator to provide an unbiased estimate of the total number of features in the lung or airway generation:

$$N=\frac{1}{\mathit{bsf}}*\frac{1}{\mathit{ssf}}*\frac{1}{\mathit{asf}}*\frac{1}{\mathit{hsf}}*\sum Q^{-}$$

where the fractions are bsf = block sampling fraction, ssf = section sampling fraction, asf = area sampling fraction, hsf = height sampling fraction and Q ⁻ = feature count within the sampled fraction.

Structural Hierarchies

From molecules to tissues, the respiratory system is a complex organ composed of numerous compartments. Hierarchies allow the data to be organized according to the size of the structures, while the equations define relationships and link data within and across hierarchical levels. This approach has been called “multicascade sampling” and has been used to estimate the number and composition of nonciliated bronchiolar cells in respiratory bronchioles in response to inhaled oxidants (Fujinaka et al., 1985; Moffatt et al., 1987).

There are 2 general guidelines for multicascade sampling: (1) use the lowest reasonable magnification (acceptable resolution) to increase sample size for measurements; and (2) if major compartments and their subcompartments cannot be measured at the same magnification, then the magnification should be increased to optimize resolution in the subcompartment. Multicascade sampling integrates well with fractionator sampling. For example, the number of alveoli can be directly estimated using fractionator sampling, while alveolar volume and diameter estimates require use of a modest multicascade sampling scheme for determination of the volume of the lung in which alveoli reside (Hyde et al., 2004).

Statistical Efficiency

Knowing the components that comprise biological variation in the lung is the key to the design of an experiment (number of animals, tissue samples, fields per slide, frame size, points and line length per test system to estimate a particular structural feature). The equation for optimal statistical efficiency in stereology is

$${\mathit{OCV}}^2(\widehat{X})={CV}^2(X)+\text{mean}[{CE}^2(\widehat{X})]$$

where OCV ²(&Xcirc;) is the observed coefficient of variation, CV ²(X) is the true biological variation (unknown) and mean[CE ²(&Xcirc;)] is the estimate of the sampling and stereological variation (Gundersen and Osterby, 1981). A general goal in this equation should be

$${CE}_{\text{stereological}}^2\le \frac{1}{2}{CV}_{\text{biological}}^2$$

Estimation of the contributions to sampling and stereological variation to direct volume estimates using the Cavalieri method has been provided by Cruz-Orive (Cruz-Orive, 1999) and in a nomogram by Gundersen and Jensen (1987). Contributions to stereological variation for ratio estimators like volume, number, surface and length densities have also been derived (Cruz-Orive, 1980). Some simple guidelines will usually suffice for stereological sample size within an animal (primary sampling unit) as follows: 100–200 probe interactions (e.g., point hits), 50 fields and 10 blocks. This approximation is based on the t-test for significant differences between groups as follows:

$$\begin{array}{l}{(t-\text{test})}^2=\left(\frac{{\mathit{diff}}^2}{{\mathit{SEM}}^2(\mathit{diff})}\right)>4\\ n_{\text{blocks}}>2\frac{{\mathit{OCV}}_{\text{blocks}}^2}{{CV}_{\text{animals}}^2}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{then\hspace{0.28em}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{n}_{\text{blocks}}\sim 10\\ n_{\text{fields}}>2\frac{{\mathit{OCV}}_{\text{fields}}^2}{{CV}_{\text{blocks}}^2}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{then\hspace{0.28em}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }n\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{fields}\sim 50\\ n_{\text{probes}}>2\frac{{\mathit{OCV}}_{\text{probes}}^2}{{CV}_{\text{fields}}^2}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{then\hspace{0.28em}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }n\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{probes}\sim 100-200\\ {\mathit{OCV}}_{\text{probes}}^2\sim \frac{1}{\sum \text{hits}}\end{array}$$

While 200 point hits per animal seems to be minimal sampling, 50 fields and 10 blocks seems to be over-sampling per animal. If we apply the principle of doing more less well, then we sample widely within the organ, embed 10 small blocks (selected by a smooth fractionator) in one block so we only cut 1 section per animal and sample the 50 fields and 200 point hits throughout the 10 blocks (Hyde et al., 2004). This sampling approach is not only precise but highly efficient, especially when a computer assisted approach with an automated microscope is used (Gundersen et al., 1999).

Transgenic Mice Expressing Transforming Growth Factor-α (TGF-α)

The importance of the reference trap in stereologic estimates of postnatal lung growth is used to illustrate the critical errors that can occur when reference volume is not measured or included in making conclusions about quantitative measures in the lung. Methods for generating transgenic mice expressing human TGF-α under control of the human SP-C 3.7-kb promoter/enhancer sequences have been previously described (Korfhagen et al., 1994). Transgenic mice, of the FVB/N strain, were identified by a diagnostic 1.4-kb band ongenomic Southern blots of Pst1-digested genomic tail DNA (Korfhagen et al., 1994).

A conditional doxycycline regulatable transgenic system was used to induce TGF-α expression in the lungs of newborn mice during early alveogenesis (Le Cras et al., 2004). Mice were maintained in virus-free containment and handled in accordance with the Institutional Animal Care and Use Committee of UC Davis. Six wild-type and 6 transgenic mice (FVB/N strain) expressing TGF-α were used to examine the influence of TGF-α on lung development. All studies conformed to applicable provisions of the Animal Welfare Act and other federal statutes and regulations relating to animals (Guide for the Care and Use of Laboratory Animals; National Institutes of Health, 1985).

At necropsy, 8-week-old mice were sacrificed with an overdose of pentobarbital sodium and the lungs removed for intra-tracheal instillation of 1% glutaraldehyde-1% paraformaldehyde in 0.1 M cacodylate buffer (pH 7.4, 400 mosm). Mouse lung volumes were estimated by their buoyant weight in PBS (Scherle, 1970). Mouse lungs were sliced and sampled using a fractionator design for estimation volume densities of lung components (nonparenchyma (airways and blood vessels) and parenchyma) (Gundersen, 2002). Lung tissue was dehydrated and embedded in paraffin, sectioned at 7 um and stained with hematoxylin and eosin.

Results

In experimental pathology of the lung we usually ask the following morphometric questions: (1) Was tissue lost?, (2) Was tissue added?, (3) Are there more cells?, (4) Are there fewer cells?, (5) Is there an inflammatory/immune response? (6) Is there an apoptotic or necrotic response? Transgenic mice are used extensively in lung research. One of the questions that all investigators should ask is “Does the gene that is ablated or over expressed affect lung development?” An example is a transgenic (FVB/N strain) mouse expressing TGF-α.

The volume reduction in transgenic expressing TGF-α mice compared with wildtype mice appears evident when looking at the entire fixed lung (Figure 7), but is not always as clear when looking at individual sections through the lungs where sections from transgenic expressing TGF-α mice sometimes appear larger than those from wild-type mice (Figure 8). However, when we used morphometric methods to determine fixed lung volumes, the decrease in lung volume of transgenic expressing TGF-α compared with wild-type mice is confirmed (Figure 9).

A fractional difference of significantly less blood vessels but more parenchyma is provided by a volume density estimate (Figure 10), but when we avoid the reference trap and multiple by lung volume, we observe a different result with a smaller volume of parenchyma and significantly smaller volumes of airways and blood vessels in the transgenic as compared with the non-transgenic mice (Figure 11). These differential results in volume densities versus absolute volumes, underscores the misinformation provided by the reference trap.

Another common problem observed in lung morphometry is profile counting of cells as a representation of cell number. An example of the problems associated with profile counting either per unit area or per unit length of the epithelial basal lamina was demonstrated during development of the bronchiolar epithelium in rabbits (Table 1) (Hyde et al., 1983). Ciliated cells have nuclei with a larger volume than nonciliated bronchiolar cells during most of bronchiolar development. This results in more ciliated cell profiles than nonciliated cell profiles simply because of the size difference. This bias can introduce as much as a 6% overestimation error in the number of ciliated cells even though they only represent a third of the cell population. Whether we estimate numbers per airway generation or total numbers within the lung, we must use design-based methods and make sure the numbers represent the whole unit.

Discussion

It is clear from the methods and examples provided that design-based quantitation of the conducting airways and parenchyma either in transgenic expressing TGF-α animals or after exposure to inhaled toxicants provides a robust, unbiased assessment of the structural components of the lung. These design-based methods interface well with in vivo imaging (Magnetic Resonance Imaging or Computed Tomography Imaging) of the conducting airways that provide useful anatomical detail.

Careful sampling using a smooth fractionator for the components of the lung allows us to efficiently and precisely evaluate the effects of inhaled toxicants on the epithelium and submucosal cells and extracellular matrix. The fractionator has the advantage of being free of assumptions of shrinkage and, thus, is the most desirable method for estimating the total number of cells in an airway or the lung as a whole. If we use normalization of the epithelial basal lamina, we can compare changes in compartments among animals at the same airway generation or among different airway generations.

Failure to adhere to these principles leads to flawed and biased methods that disregard the essential principles of stereology. In a recent letter to the editor of the Journal of Applied Physiology, Dr. Ewald Weibel and colleagues challenged the stereologic methods used in a recently published article on quantitation of airspace enlargement in emphysema (Weibel, 2006). The debate of appropriate methods for quantitating airspace enlargement centered on the need for mathematically rigorous approaches versus expediency using image analysis that ignores years of relevant literature on stereology (Baddeley and Vedel Jensen, 2005). The stereologic methods discussed in this paper provide a morphologic assay that is efficient, precise and statistically rigorous, but are still easy to use. Use of these methods avoids many of the “traps” that investigators fall into with the best intentions of doing the best science.