# Stereological Estimates of Alveolar Number and Size and Capillary Length and Surface Area in Mice Lungs.

код для вставкиСкачатьTHE ANATOMICAL RECORD 292:113–122 (2009) Stereological Estimates of Alveolar Number and Size and Capillary Length and Surface Area in Mice Lungs JULIANE KNUST,1,2 MATTHIAS OCHS,2,3 HANS JØRGEN G. GUNDERSEN,1 1 AND JENS R. NYENGAARD * 1 Stereology and Electron Microscopy Research Laboratory and MIND Center, University of Aarhus, Aarhus, Denmark 2 Department of Anatomy, Division of Electron Microscopy, University of Göttingen, Göttingen, Germany 3 Institute of Anatomy, Experimental Morphology Unit, University of Bern, Bern, Switzerland ABSTRACT The major function of the lung is gas exchange and depends on alveolar and capillary parameters such as surface area and volume. The number of alveoli may report on the nature of structural changes in lung parenchyma during development, illness or changing environmental factors. We therefore developed an efficient and easily applicable stereological design for estimating and monitoring these structural parameters in the mouse lung. The estimation of volume fractions of different lung compartments has been carried out by point counting. A combination of cycloid grids superimposed on vertical sections was used to estimate the capillary surface area with isotropic test lines. Capillary length could be measured using the harmonic mean of the surface weighted diameter. The Euler characteristic applied in the physical fractionator with varying but known sampling fractions (Horovitz-Thompson estimator) enabled us to estimate alveolar number. In adult mice lungs, we obtained total values for alveolar number of 2.31 3 106 alveoli in a pair of lungs, alveolar surface area of 82.2 cm2, capillary surface area of 124 cm2, and capillary length of 1.13 km. All values are corrected for tissue shrinkage. With this study we present a highly efficient combination of several design-based stereological tools for the unbiased estimation of alveolar number and volume as well as length, surface area, and diameter of capillaries in the mice lung. Anat Rec, 292:113–122, 2009. Ó 2008 Wiley-Liss, Inc. Key words: disector; Euler number; fractionator; quantitative microscopy; vertical sections Gas exchange is the main purpose of the lung based on the diffusion of oxygen and carbon dioxide through the thin air-blood barrier between the alveolar airspace and the capillary blood in the alveolar septa. The smallest functional unit in the lung is the alveolus consisting of its airspace and its septa carrying numerous capillaries (Caduff et al., 1986; Weibel and Taylor, 1998). Functional and structural changes in the lung can be detected, evaluated and interpreted by monitoring the changes in absolute number and in different parameters of alveoli and various compartments of the lung. With the objective of evaluating different parameters of an Ó 2008 WILEY-LISS, INC. Grant sponsors: European Union (Marie Curie fellowship), Eva and Henry Frænkels Mindefond, Danish Council for Strategic Research, Lundbeck Foundation. *Correspondence to: Jens R. Nyengaard, Stereology and Electron Microscopy Research Laboratory, University of Aarhus, Building 1185, DK-8000 Aarhus C, Denmark. E-mail: Nyengaard@ki.au.dk Received 18 September 2008; Accepted 12 February 2008 DOI 10.1002/ar.20747 Published online in Wiley InterScience (www.interscience.wiley. com). 114 KNUST ET AL. Fig. 1. Fixed mouse lung pair with vertical axis defined according to the natural vertical axis. Fig. 3. Cutting machine with agar embedded mouse lung. The lung is embedded in agar and cut into slices of exactly the same thickness by using this cutting machine. All slices are made parallel to the vertical axis. Fig. 4. Fig. 2. Sampling scheme showing all sampling stages from the whole embedded lung to fields of view for the light microscopic evaluation of the sections. I. 1 II: The right lung (r) is rotated a random angle around a predefined vertical axis (VA), the left lung (l) is rotated a further 90 degrees. Both are embedded overlapping in agar and systematically cut in slices of the same thickness parallel to the vertical axis beginning from a random point. III: Slices are placed on their surface, grouped in two or three new blocks and embedded in paraffin. T is the slice thickness of the unprocessed tissue; MA is the microtome advance. All cuts in the paraffin blocks are parallel to the vertical axis. IV: Systematically, uniformly randomly chosen 2Dunbiased counting frames are observed using a light microscope on single sections cut with a MA of 4 mm. The agar embedded lungs cut in uniform slices. organ, including structural quantities, it is most efficient to do all observations in the same specimen. The efforts for processing and observing the tissue should be kept as low as possible. A newly developed unbiased method for the estimation of alveolar number in lungs based on the Euler number has recently been published (Hyde et al., 2004; Ochs et al., 2004). Even though described for the application in placenta, the capillary length estimation using thin vertical sections and the surface-weighted diameter (Clausen et al., 2000) has not been employed in lung research so far. In this study we aimed at developing an efficient and practical design-based combination of stereological tools for the estimation of various parameters of lung structure in mice. This includes total alveolar number, sur- STEREOLOGIC DESCRIPTION OF FUNCTIONAL UNITS IN MICE LUNG 115 Fig. 5. Estimation of section sampling fraction ssf and shrunken tissue thickness T* by exhaustive sectioning of one block. The paraffin block containing the lung slice is seen edge-on and the lines x, y, and z mark points in the slice where optically prominent parts of the tissue can be well observed and followed throughout the whole thickness of the slice. As all incomplete sections of one block are mounted on slides one has to identify those that precisely represent the appear- ance and disappearance of one well-defined point in the tissue. In our example, these are sections nx1 and nx2, ny1 and ny2 and nz1 and nz2 showing the appearance and disappearance of tissue at the points x, y, and z, respectively. The number of sections N in-between them, say the difference n2–n1, represents the slice thickness T* of the shrunken slice and enables us to determine the exact section sampling fraction, ssf, of an arbitrary number of sections per block. face area, and volume as well as capillary surface area, whereas the estimation of capillary length is a modelbased method. The sampling and counting steps are described in sufficient detail to allow researchers to adopt these methods to study the lung phenotype in gene manipulated mice models using appropriate design-based stereological methods. lungs were embedded overlapping to achieve a unimodal area distribution on the systematic set of sections (Ogbuihi and Cruz-Orive, 1990). Lungs were systematically cut in slices starting at a uniform random point. We used a cutting machine and chose a slice thickness of 1.7 mm, providing about seven slices from each pair of lungs (see Figs. 3 and 4). Sampling was done by using a multistage physical fractionator (Gundersen, 1986) with a varying sampling fraction being a general Horovitz-Thompson estimator that enabled us to estimate the alveolar number disregarding shrinkage. The first sampling level is the cutting and sampling of blocks, the block (slice) sampling fraction (bsf) which is 1 because all blocks are sampled. The second sampling step is the section sampling fraction (SSF). One complete section is taken from each block. It is not necessary to section all the blocks exhaustively to estimate the average section sampling fraction. We embedded the agar slices in two to three different paraffin blocks and sectioned a systematic, uniformly random fraction of these blocks exhaustively, which yielded an average number of sections N per block representing the block thickness (see Fig. 5). All sections from the very beginning of the tissue in the block until the first complete profile are mounted on slides. At the end all sections from the last complete profiles until the very end of the tissue are also mounted. These are stained with Mayer’s haematoxylin. In the part where every section covers the whole area of the slice, sections are taken for the purpose of our estimations. On the haematoxylin stained serial sections, one fixed point in the section is defined and followed through the tissue from the very first time of its appearance until it disappears. During embedding one has to make sure that the agar slice really contains tissue throughout its whole thickness and on all—or at least a well-known part—of the area seen on the upper surface. The number of sections N between the appearance and disappearance of this very point in the tissue represents the shrunken slice thickness T* in a dimensionless way (see Fig. 5). MATERIALS AND METHODS We used female mice of the strain CL 57 B6 that were purchased from Bomholtgaard (Ry, Denmark). The study has been approved by the Danish Animal Inspectorate. Five mature animals were taken from different litters, three of them were 46- and two were 69-days old. The animals were weighed and anaesthetised by injecting 3 mL per kg body weight Mebumal (50 mg/mL pentobarbital) intraperitoneally. The trachea was cannulated through a midline cervical incision while the animal was still breathing. A bilateral pneumothorax was produced by puncturing the diaphragm from its abdominal surface. We infused 4% phosphate-buffered formaldehyde pH 5 7 into the trachea at a transpulmonary pressure of 20 cm H2O. The trachea was ligated when the flow ceased (Weibel, 1984). Lungs were removed from the thorax and then placed in fresh fixative at 48C for another 4 hr to complete fixation while intrapulmonary pressure was still maintained. The fixed pair of lungs was separated and carefully dried on its outer surface. We defined the vertical axis according to the natural vertical orientation of the lungs in vivo and all further cuttings were made parallel to the vertical axis (see Figs. 1 and 2). To avoid artificial edges the lungs were rotated as a whole to get slices that still possess their natural borders, that is, are totally surrounded by pleura. The angle of rotation for the right lung around the vertical axis was randomly chosen and the left lung (see Fig. 2) was rotated 908 with respect to the right lung. Both lungs were embedded in agar in one block. If possible both 116 KNUST ET AL. Fig. 6. Sectioning of the block. Sections are only taken in that part of the block were one can make sure that all slices may contribute full intersections. In the figure this part is defined by the thick lines. Inside this range, taking sections in different heights may influence whether a lung slice is (e.g., slice 4 in sect. b) or is not (e.g., slice 4 in sect. a) contributing tissue to the section. Taking one complete section out of every slice we know that the sampling fraction at this moment is 1/N. According to their tissue distribution in the agar at the ends of the organ, the first and the last lung slice may or may not provide a tissue section (Fig. 6). In the pilot study, it was noted for all slices at which depth (section number) a complete tissue profile was always seen. The maximal, first complete section number is then sampled from all slices, with its following look-up section, and most of the blocks are not sectioned further. For the alveolar counting we employed a stain with orcein and a nominal disector height of 4 mm, that is, the disector is two consecutive sections. This seems rather small given an expected alveolar diameter of about 45 mm (Faffe et al., 2002). However, we are actually not counting alveoli themselves, meaning the whole alveolus as a particle, but instead counting the alveolar openings. When we keep track of the appearance or disappearance of alveolar openings we need a much smaller disector height. Examining disectors under the microscope 2D unbiased counting frames are sampled in a known and predetermined distance from each other (Gundersen, 1977). Knowing the frame area and the step length between the counting frames we calculate the final area in which the counting was performed on each section and can accordingly derive the area sampling fraction (asf) from this. We estimated lung volume with the Cavalieri principle (Michel and Cruz-Orive, 1988) on the embedded and cut tissue and had to correct for shrinkage afterwards to achieve values for unshrunken lung volumes. With a 1.253 Olympus objective (Olympus, PlanApo 0.04) and at a final magnification of 23.83 a point grid was superimposed on the sections and thus area of the section estimated. Having taken the sections in a fixed distance from the tissue surface we know the distance between the sections will be equal to the shrunken slice thickness. Under these circumstances we are able to calculate lung volume after shrinkage by the Cavalieri principle: a X V ðlung; shrÞ ¼ T PðlungÞ ð1Þ p T* being the slice thickness after shrinkage, P(lung) the number of points hitting the shrunken lung tissue and a/p the area per test point of the counting grid. Alveolar Number Estimation by Means of the Euler Number Before we can count anything we have to get an idea of what we actually want to count, for alveoli as air spaces have no precise spatial definition and border that would make them countable in ordinary sections (Burri et al., 1974; Blanco et al., 1989). The disector offers the opportunity to solve these problems as it is a 3D probe sensitive to particle of which Euler number is just an especially simple case (Gundersen, 1986). Still it is necessary to define a feature that can unmistakably be recognized and counted in a disector and is characteristic for alveoli and only for them. Alveolar openings are such a feature (Hyde et al., 2004; Ochs et al., 2004), unique of the alveolus, but the question remains, how to count them? Alveolar openings are characterized by bundles of elastic fibres outlining them, visible at the very edge of the alveolar septum on the section (Burri et al., 1974). Inside an acinus one can imagine these interconnected elastic fibres as a net in whose meshes the alveoli are fixed. The very basis for quantitations in a strict mathematical sense is additivity. In a net, the feature that can be determined additively is connectivity. The mathematical idea underlying connectivity and the instrument that enables us to measure it in an object by specific counting rules is the Euler number (Hadwiger, 1959). The Euler characteristic of an object provides information about the connections of complicated 3D structures. Connections in their very meaning are never ever isolated or separated from the structure in question. For a structure of a certain dimension the Euler number is defined as the sum of significant topological changes of the Euler number in a probe of one dimension less swept through the structure disregarding its orientation. For the estimation of the Euler number of the original structure, it is necessary to define changes of the Euler number in the probe (Fig. 7). In a two-dimensional structure a segment can appear as a point in the reference section of the appropriate probe when it is not visible in the look-up section and it is then counted as 11. We refer to this as a new Island. If one line in the reference section splits into two different new ones in the look-up section this is counted as 21. We refer to this as a new Bridge. Bridges and Islands are significant topological changes and contribute to the Euler number of the 2D object (Fig. 7). For the alveolar number estimation we use, as aforementioned, the abstraction of a 2D elastic fibre net of alveolar openings or the net of alveolar wall ridges. This 2D net is expanded in a 3D space. Consequently, we are never able to make statements about it using just isolated, single 2D sections. The disector is the instrument which can sample counting events by sweeping a 2D plane through a 3D space (Gundersen, 1986). According to the situation in a 2D object one can observe certain significant topological changes between the reference section and the look-up section in a 3D object as well. When there is a septal segment in the reference section that has disappeared in the look-up section this is referred to as an Island. When the look-up section shows two (septal) lines in direct neighborhood that form one uninterrupted line in the reference section this is called a Bridge (Fig. 8). v is the disector contribution to the Euler number v3 of the 2D net in 3D space and is defined as: v ¼ #ðislandsÞ #ðbridgesÞ ð2Þ STEREOLOGIC DESCRIPTION OF FUNCTIONAL UNITS IN MICE LUNG 117 aðframeÞ dxdy ; asf ¼ where a(frame) is the frame area of the counting frame and dx and dy are the step lengths between counting frames. Consequently we get the final estimator equation: P ðTi vi Þ P ðvi Þ dx dy X v3 ¼ 1 v ð6Þ MA aðframeÞ This is a ratio unbiased estimate P of the varying SSF. It is therefore important that (1) vi 100, so CE(vi) < 0.1; and (2) enough slices are used when Ti is quite varying. The Euler number of a 3D object can in a more structural way be defined as: v3 ¼#ðisolated partsÞ #ðextra connectionsÞ þ #ðinternal cavitiesÞ Fig. 7. Changes in the Euler number in a 2D object, observed from opposite directions. If we consider the object to be a net we can clearly see it has four holes. Estimating the number of holes, that is, connectivity, by the Euler number we should obtain the same result. A line is taken as a one-dimensional probe and for reasons of efficiency swept through the object from opposite directions. Applying the counting rules for Euler number the topological changes in the probe are summed up. From this we may derive the connectivity of the object which corresponds to the number of holes. In total nine bridges (B) and three islands (I) are sampled contributing each by 21 or 11, respectively, to the Euler number. Dividing the sum by two, because we count in two directions, the Euler number equals (3 2 9)/2 5 23. Inserting this value in the connectivity equation Eq. (7) we obtain: connectivity 5 # holes 5 # isolated objects – Euler number 5 12(23) 5 4. Our final result is in accordance with what common sense tells us, that there are four holes in the observed object. Counting in disectors and for reasons of efficiency we always count in both directions in the reference and the look-up sections and then divide our estimate by two. v¼ #ðislandsÞ #ðbridgesÞ 2 ð3Þ In this fractionator design the Euler number v3 of the 3D structure is calculated as follows: P v ð4Þ v3 ¼ F P where v is summed over all disectors in all sections and F is the aggregate sampling fraction: F ¼ bsf ssf asf ð5Þ where bsf is the block sampling fraction, ssf the slice sampling fraction and asf the area sampling fraction. bsf 51; because we sample all lung blocks. ssf ¼ PMA ; where MA is the constant microtome PðTi vi Þ ðvi Þ advance, Ti is the shrunken slice thickness of slice i, and vi is the Euler number in slice i. ð7Þ Trying to apply this equation to our example of the 2D elastic fibre net we can obviously exclude the number of internal cavities. As connectivity W is the number of extra connections we may transform the equation as follows: W ¼ #ðisolated partsÞ v3 ð8Þ When alveolar number in terms of connectivity is estimated for the whole lung one has to keep track of the number of isolated parts. Isolated parts mean the number of separate 2D elastic fibre nets in one pair of lungs which equals the number of acini. Thus we finally derive the alveolar number N(alv): NðalvÞ ¼ W ¼ #ðaciniÞ v3 ð9Þ equals: NðalvÞ ¼ W ¼ #ðaciniÞ 3 2PðT v Þ Pi i X ðvi Þ dx dy #ðislandsÞ #ðbridgesÞ7 6 4 5 ð10Þ 2 MA aðframeÞ How this equation really can reflect the alveolar number becomes more graphic if one realizes that gaining or loosing one extra connection exactly reflects the existence or nonexistence of one hole or mesh in the net, that is, one alveolus in the acinus. There remains one unknown factor in Eq. (10) and that is the number of acini. The pulmonary acinus can be defined as the sum of all respiratory bronchioles (nonexistent in mice lungs) and alveolar ducts with appendant alveoli peripheral to a terminal bronchiole. The transition from a terminal bronchiole to a respiratory bronchiole is marked by the change from a purely conductive airway with high cuboidal epithelium into respiratory airspace outlined with the typical flat epithelium that is crucial for gas exchange (Rodriguez et al., 1987; Randell et al., 1989; Ten Have-Opbroek, 1991). Randell et al. (1989) found about 5,000 acini in rat lungs using serial reconstructions. We cannot transfer this value to mice lungs offhand, but assuming a similar dimension a number of a few thousand would not significantly influence the alveolar number which is in the range of millions in mice. 118 KNUST ET AL. Fig. 8. Disector image of orcein stained lung tissue in the CAST system. The reference section and the look-up section are corresponding areas on two adjacent sections that show significant structural changes concerning the Euler number estimation. Counting can be performed in both directions taking each section as reference and look-up section. Bridges, B, are counted where two alveolar wall end points are interconnected in the reference section but appear to be in- dependent in the look-up section. The counting frame determines the counting area where significant changes situated inside the frame or touching the inclusion line (thinner black line on the top and to the right) have to be counted while changes touching the exclusion line (thick black line on the bottom and to the left) have to be ignored (thick arrow). Immunohistochemical Staining of Capillaries Dell Monitor and had the CAST vers. 2.158 stereology software (Visiopharm, Hørsholm, Denmark) installed. To avoid edge effects in our estimations in the CAST we used rather large counting frames although this would somehow affect overall sampling efficiency, but due to the fact that we expect distribution of alveoli in the lung to be rather homogeneous it should not turn out to be a problem for the overall sampling efficiency. The point counting of all volume densities and the counting for alveolar number and surface area estimation were performed using a 203 objective (NA 0.70) at a final magnification of 4733. The estimation of capillary surface area and length required a 403 objective (NA 0.75) at a final magnification of 13703. Adjacent sections were mounted on one slide to improve the efficiency of the counting process. For the Euler number counting procedure in the physical disector the CAST provided, after the delineation of the two sections, a fast and precise automatic switch between corresponding fields of view on the two sections. For every lung we aimed at a number of counting events of about 100 for alveolar number and between 150 and 200 for all other counted parameters. The system chose fields of view by systematic, uniformly random sampling. Anti-Aquaporin-1 (AQP-1) was used for the staining of lung capillaries. AQP-1 water channels are known to be expressed in mammalian lung microvascular endothelium (King et al., 1996; Effros et al., 1997; Bai et al., 1999). In lung, AQP-1 is not expressed in alveolar type I cells but is in rare occasions and small amounts detectable on type II cells (King et al., 1996; Effros et al., 1997). As type II cells are in their morphology distinctively different from endothelial cells we can probably trust the immunohistochemical identification of capillaries. Immunohistochemical Treatment Peroxidase is blocked with 30% H2O2 and methanol and afterwards the sections are microwave treated at 450 W in citrate buffer three times for 5 min. Incubation with AQP-1 (Chemicon; rabbit anti-AQP-1; polyclonal) is performed at a dilution of 1:500 for 1 hr at 378C. Then the sections are treated with the secondary antibody (anti-rabbit IgG; Vector; dilution 1:100) at room temperature for 2 hr, stained with DAB and counterstained with Mayer’s haematoxylin. Microscopical Evaluation All observations were made with a modified Olympus BH2 microscope equipped with a MT12 microcator and ND281 readout (Heidenhain, Germany), a motorised specimen stage (Märzhäuser, Germany) and an object rotator (Olympus, Denmark). A CCD camcorder (JAI-2040, Protec, Japan) connected to a PC was mounted on the top of the microscope. The computer was connected to a 2100 Point Counting In the observed lung tissue we collected data about the changes in the distribution of volume fractions on different subtypes of tissue. Airspace in the parenchyma and airspace of the conductive airways down to terminal bronchioles were point counted separately. 119 STEREOLOGIC DESCRIPTION OF FUNCTIONAL UNITS IN MICE LUNG Fully aware of the fact that we possibly cannot unambiguously distinguish between air space in alveoli and airspace in alveolar ducts we still regarded it necessary to make this difference in order to be able to calculate some value of mean alveolar volume for reasons of comparison and to get an idea of how the distribution of airspace in those two compartments changes. Thus, we defined alveolar airspace as the area seen on the section which is surrounded by alveolar septa and an imaginary straight line between the free edges of the alveolar opening. We decided to distinguish between points hitting parenchymal tissue and those hitting nonparenchymal tissue. Parenchymal tissue includes all tissue that could be identified as belonging to alveolar septa, including capillaries, epithelial, and interstitial cells and extra cellular matrix. Nonparenchymal tissue is defined as all tissue not being part of alveolar septa, that is, the large connective tissue septa, walls of larger vessels and conductive airways with endothelial, epithelial, interstitial, muscle, and cartilage cells and their surrounding connective tissue. Vessels above a diameter of 10-mm make up one separate compartment as well. Surface Area of the Gas Exchange Tissue For the estimation of surface area, S, one can usually count intersections of structure boundaries on the section with straight 3D isotropic test lines of a superimposed counting grid. Alveolar surface area is estimated on the sections as follows: SðalvÞ ¼ ! P 1 I ðalvÞ 2 l P ð1 Shrinkage3D Þ3 VðunshrÞ PðlungÞ p ð11Þ where I(alv) is the number of intersections between test lines and alveolar septa, l/p is the length per test point on the counting grid and P(lung) is the number of points hitting lung tissue, V(unshr) the volume of the unshrunken lung and Shrinkage3D is the volume shrinkage, see Eq. (16). With this combination of vertical sections and cycloids it is possible to create IUR test lines. Capillary Length and Surface Area Capillary length and surface area were observed on single thin (2 mm) sections. Surface area of the capillaries was estimated according to the estimation of alveolar surface area by counting intersections of cycloids with the capillary walls on systematically, uniformly, randomly chosen fields of view (Fig. 9). The equation is identical to the alveolar surface area estimation Eq. (11) except that I(alv) is exchanged with I(cap), which is the number of intersections between cycloids and capillary walls. For the estimation of capillary length we superimpose a cycloid counting grid on the section and measure the diameter of every capillary profile that is intersected by a cycloid test line. If the capillary is hit twice by the test line its diameter is sampled and recorded twice as well. To measure the capillary diameter an imaginary line perpendicular to the direction of the largest profile dimension is drawn and measured at its greatest width. The calculated mean over all measured diameters is an estimate of the surface-weighted mean diameter of the Fig. 9. A cycloid grid superimposed on an image of alveolar septa. The sections are stained with AQP- 1 to make the identification more reliable, which is not visible in this black and white image. Every time a cycloid intersects the boundary of a capillary wall, it is registered and the capillary diameter is measured. If a capillary is hit one time (thin arrow) or two times (thick arrow) by the cycloids the capillary diameter is measured once or twice, respectively. capillaries in our sample. As this surface weighted mean diameter, dS(cap), is not equal to the ordinary lengthweighted mean capillary diameter, d(cap), we cannot simply derive length from the equation length 5 surface area/diameter p, but we have to convert our surfaceweighted mean diameter, dS(cap) to the ordinary lengthweighted diameter, d(cap), by computing the harmonic h mean, dS (cap) (Clausen et al., 2000): h dðcapÞ ¼ dS ðcapÞ ¼ 1 mi 1 P 1 di ðcapÞ ð12Þ here di(cap) is every diameter that is sampled with cycloids in the fields of view and mi is the total number of times cycloid test lines intersect the boundaries of sampled capillary profiles (Fig. 9). The total length of the capillaries in a lung is then: 2 SV ðcap=lungÞ LðcapÞ ¼ ð1 Shrinkage3D Þ3 VðunshrÞ ðcapÞ p d ð13Þ here SV(cap/lung) is the estimated surface area density of capillaries and dðcapÞ the estimated mean lengthweighted diameter. Both Eqs. (12) and (13) are modelbased estimators and require the capillary cross sections to be circular. If capillaries are collapsed, Eq. (12) pro vides an underestimate of dðcapÞ and LðcapÞ is overestimated using Eq. (13). Shrinkage Measurements As mentioned earlier we had to embed the sections into paraffin because of the immunohistochemical treatment. This makes of course the problem of tissue deformation even more prominent because paraffin embedded tissue is usually affected by pronounced tissue deforma- 120 KNUST ET AL. tion. Where shrinkage is no problem for number estimation, because cardinality is unaffected by deformation, estimations of length, surface and volume must be corrected for shrinkage to preserve unbiasedness (DorphPetersen et al., 2001). Performing exhaustive cutting with a calibrated microtome we have the possibility of estimating shrinkage on these sections. Knowing the exact thickness of the slices made in the cutting machine and having exact knowledge about the microtome advance we can compute the thickness of the shrunken tissue and the linear shrinkage that occurred during the histological processing (see Fig. 5). For the determination of the sampling fraction the average number of sections N one slice provides has already been identified. Multiplying the number of sections with the exact microtome advance we calculate the thickness of one slice after embedding and tissue deformation. Thickness T* after shrinkage: T ¼ N MA ð14Þ where N is the number of sections one slice provides on average and MA is the microtome advance. The difference between the original slab thickness and the value after cutting is the measured linear shrinkage, Shrinkage (linear): Shrinkage ðlinearÞ ¼ T T T ð15Þ where T is the original thickness of a slice, T* is the thickness after shrinkage. Assuming isotropic shrinkage, we can estimate volume shrinkage Shrinkage3D: 3 T Shrinkage3D ¼ 1 ð16Þ T The volume of the unshrunken lung tissue is: V ðunshrÞ ¼ V ðshrÞ Shrinkage3D mm3 (0.22) [77 mm3, 130 mm3] making up 31% (0.08) [29%, 35%] of total lung volume. Every pair of lungs comprised on average 2.31 106 alveoli (0.23) [1.68 106, 2.96 106]. Left and right lung showed in accordance with their volume shares different absolute numbers of alveoli. The left lung contained 740 103 alveoli (0.23) [550 103, 940 103] which corresponds to a relative share in total alveolar number of 32% (0.10) [0.29%, 0.36%]. With a number 1.57 106 alveoli (0.25) [1.13 106, 2.1 106] the right lung consisted of more than twice as many alveoli, namely 68% (0.05) [0.66%, 0.71%] of the total amount. The observed lungs showed an alveolar number density N(alv) per mm3 parenchyma of 9.55 103 alv/mm3 (0.31) [7.25 103 alv/mm3, 14.8 103 alv/mm3] in the unshrunken lung with a mean alveolar volume of 59.5 103 mm3 (0.26) [34.5 103 mm3, 75.0 103 mm3]. Surface area of total alveolar airspace was 82.2 cm2 (0.17) [63.3 cm2, 101 cm2] in unshrunken tissue, which resulted in a mean surface area of one alveolus of 3,620 mm2 (0.14) [2,870 mm2, 4,260 mm2]. The observed lungs comprised a volume of alveolar airspaces of 138 mm3 (0.29) [102 mm3, 205 mm3], alveolar duct airspace of 37.0 mm3 (0.30) [22.9 mm3, 48.1 mm3] and alveolar septal tissue of 72.6 mm3 (0.21) [50.1 mm3, 90.3 mm3]. We obtained a capillary surface area corrected for shrinkage that was 124 cm2 (0.13) [109 cm2, 143 cm2]. Capillaries in these mice lungs had a length of 1.13 km (0.13) [0.98 km, 1.35 km]. DISCUSSION Mice We present a way of effectively combining different stereological estimators for the evaluation of lung alveoli and capillaries in mice. We used the whole lungs of five adult female mice from different litters. Female mice were chosen because they are used in a bigger study of lung development. We expect that female mice have smaller lungs than male mice and that growth of female lungs will reach a plateau in contrast to male mice. ð17Þ Statistics Results are shown as mean (CV 5 SD/mean) and [min; max]. The evaluation of the error variance, coefficient of error (CE), has for the Cavalieri principle and alveolar number estimate been estimated from the equations provided in Gundersen et al. (1999). The CE’s for the ratio estimates of alveolar surface area and capillary surface area and length were estimated from Kroustrup and Gundersen (1983). RESULTS Mean body weight of the mice was 20.6 g (0.13) [18.3 g, 23.8 g]. Mean lung volume estimated by the Cavalieri principle and corrected for volume shrinkage of 35% was 307 mm3 (0.17) [264 mm3, 395 mm3]. The right lung comprised four lobes and made up 69% (0.04) [65%, 71%] of total lung volume with an absolute volume of 210 mm3 (0.15) [187 mm3, 264 mm3]. The left lung consisted of only one lung lobe with a mean volume of 97 Tissue Processing Lungs were fixed by instillation fixation in situ to allow evenly expansion and unfolding of the delicate interalveolar walls and to minimize the time between death and complete fixation of the tissue, avoiding post mortal tissue variances (Randell et al., 1989; Gil, 1990). Instillation via the airways is the method of choice for all investigations on lung tissue except for the occasions whenever the preservation of the physiologically normal status of the airspace side of alveolar septa is required, what would be the case in, for example, research on intraalveolar surfactant or intraalveolar pulmonary oedema (Fehrenbach and Ochs, 1998). We decided to apply the Cavalieri principle instead of fluid displacement for the estimation of lung volume (Michel and Cruz-Orive, 1988) because the volume estimated by this method is closest to the volume all further observations are made in (Yan et al., 2003). Yan et al., measured 13%–25% lower lung volume in guinea pigs and dogs with the Cavalieri method than with the fluid displacement and concluded that VCav measured on lung slices after relaxation of pressure more precisely repre- STEREOLOGIC DESCRIPTION OF FUNCTIONAL UNITS IN MICE LUNG sents the state of the tissue to be used for subsequent morphometric analysis (Yan et al., 2003). We are aware of the fact, that a 4 hr fixation in 2% formaldehyde does not prevent tissue deformation due to elastic recoil after releasing pressure when cutting the slabs. Oldmixon et al. found a 30%–40% lower airspace dimension after releasing airway pressure and only fixation in glutaraldehyde and dehydration by perfusing the lung with ethanol would prevent tissue from shrinkage (Oldmixon et al., 1985). As we need to use antibodies for the estimations of capillaries we are not able to apply this fixation technique. Neither could we embed the tissue in methacrylate instead of paraffin for quality improvement of the thin sections, because plastic would as well prevent the use of antibodies. Knowing at least two circumstances which produce shrinkage in our samples: fixation and the embedding in paraffin, estimation and monitoring of the magnitude of shrinkage and afterwards correction of our results for shrinkage are inevitable to get hold of reasonably reliable results for length, surface and volume estimations, as these parameters are affected by shrinkage in contrast to number (Yan et al., 2003). However, our shrinkage correction is less than perfect because we assume isotropic shrinkage. Tissue Sampling The fractionator sampling by Gundersen (2002) enables us to estimate alveolar number without any regard to shrinkage. Very simple and unbiased in itself its efficiency in lung tissue is increased by the relative homogeneous particle density of alveoli. Moreover, the sampled number of particles is rather high and the size of the pieces that are sampled on each sampling step only varies negligibly. The alveolar number estimation can be carried out on sections using a combination of the disector and the Cavalieri principle for lung volume estimation as well (Ochs et al., 2004). Still, this method may produce biased results and overestimate alveolar number as far as shrinkage is not monitored and corrected for. Mice are commonly used as models to study the mechanisms involved in lung development and disease by manipulating their well-known genome. The mouse is a very small mammal and presents good opportunities for a rigorous sampling design. On the level of block sampling we can still include all blocks and achieve a block sampling fraction, bsf, of 1. On the level of section sampling it is then enough to take only one section per slice for further observations and to survey it in about fifty fields of view. The combination of the disector as 3D sampling probe and the Euler number as a counting principle allows unbiased estimation of the alveolar number. On a trial run, we adjusted the superimposed counting grids with the different probes and the size of the counting frame to the lung size. This small effort makes it possible to estimate lung volume and surface area densities parallel to the Euler number count in the same sampling session, thus avoiding a considerable loss of time by repeated delineations of tissue and sampling of fields of view. Whereas alveolar number in terms of Euler number was always estimated in both the reference and the look-up section, we could skip the look-up section for the estimation of all other parameters. 121 Alveolar Number and Size Weibel and Gomez developed a formula to estimate the number of alveoli in lungs assuming a particular shape and size distribution of alveoli that enter the calculation as K the size distribution coefficient and b the shape coefficient for alveoli (Weibel, 1984). This has for a long time been of great use in lung research but nowadays falls behind in comparison with the new unbiased stereological tools. The mean chord length Lm obtained from single histological sections as an index of alveolar size has been a common way of deriving the total number of alveoli from alveolar size and total lung volume (Tomkeieff, 1945; Weibel and Gomez, 1962). However, this method entails bias as alveolar airspace and airspace of alveolar ducts are not distinguishable on single sections and therefore mean chord length would always be an intermediate value of Lm in acinar ducts and alveoli (Hansen and Ampaya, 1974; Blanco et al., 1989). Moreover the ratio of airspace in ducts and alveolar airspace can vary and shows different responses to experimental conditions. In addition, any estimation of size in single sections is influenced by size, shape, and distribution of alveoli. Weibel and Gomez developed a formula to estimate the number of alveoli in lungs assuming a particular shape and size distribution of alveoli that enter the calculation as K the size distribution coefficient and b the shape coefficient for alveoli (Weibel and Gomez, 1962; Weibel, 1984). This has for a long time been of great use in lung research but nowadays falls behind in comparison with the new unbiased stereological tools. Blanco et al. (1989) first used the selector method (Cruz-Orive, 1987) on stacks of serial sections to determine alveolar volume in rat lungs and indirectly derived alveolar number from mean alveolar volume, alveolar airspace density and lung volume (Blanco et al., 1989; Massaro and Massaro, 1996). The method is fraught with nearly the same problems as the Lm-based estimator. Mercer et al. (1994) first used the disector for alveolar number estimation but the identification of one single alveolus was only possible by employing the rather time consuming observation of serial sections and three dimensional reconstruction as well (Mercer et al., 1987) and could not be ensured to be unambiguous because the definition of alveoli for the counting procedure was insufficient. The first approaches combining the disector and the Euler number was made by Hyde et al. (2004) and Ochs et al. (2004) for Rhesus monkey and rat and human lung, respectively. The mean total number of alveoli of 2.3 106 we estimated for mice lungs is about in the same order of magnitude as the values Mercer et al. found in their study (1994). Those mice lungs comprised 4.2 106 alveoli, but the animals weighed about 1.5 times as much as ours and had a 2.7 times larger lung volume. The lung volume estimated by Mercer et al. is uncorrected for shrinkage, but shrinkage should not be too pronounced as the lungs were embedded in epoxy resin. Capillary Length If one wants to apply the described method of capillary length estimation one should meet four major 122 KNUST ET AL. requirements: (1) The surface area has to be obtained from vertical sections using a cycloid counting grid. (2) The diameter has to be measured according to the explained procedure as a surface-weighted diameter. (3) To perform all further calculations the surface-weighted diameter has to be transformed to the ordinary lengthweighted diameter by calculating its harmonic mean. (4) The length estimator requires that the capillaries are circular. With our way of lung fixation via the airways we may not entirely fulfil the fourth requirement. It is therefore usually an advantage to choose isotropic sections so the length estimation can be performed with a single profile count. Synopsis We have demonstrated the reliable and efficient application of a combination of unbiased stereological tools for the estimation of various parameters of lung structure. The estimation of alveolar number by the means of Euler number in a fractionator design is an easily applicable tool. The combination with the capillary length estimation on vertical sections using the surface weighted diameter provides us with a method that renders an easy, fast and essentially unbiased way of monitoring structural changes in lung tissue under whatever experimental circumstances possible. 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