Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic).

The lung parenchyma provides a maximal surface area of blood-containing capillaries that are in close contact with a large surface area of the air-containing alveoli. Volume and surface area of capillaries are the classic stereological parameters to characterize the alveolar capillary network (ACN) and have provided essential structure-function information of the lung. When loss (rarefaction) or gain (angiogenesis) of capillaries occurs, these parameters may not be sufficient to provide mechanistic insight. Therefore, it would be desirable to estimate the number of capillaries, as it contains more distinct and mechanistically oriented information. Here, we present a new stereological method to estimate the number of capillary loops in the ACN. One advantage of this method is that it is independent of the shape, size, or distribution of the capillaries. We used consecutive, 1 μm-thick sections from epoxy resin-embedded material as a physical disector. The Euler-Poincaré characteristic of capillary networks can be estimated by counting the easily recognizable topological constellations of "islands," "bridges," and "holes." The total number of capillary loops in the ACN can then be calculated from the Euler-Poincaré characteristic. With the use of the established estimator of alveolar number, it is possible to obtain the mean number of capillary loops per alveolus. In conclusion, estimation of alveolar capillaries by design-based stereology is an efficient and unbiased method to characterize the ACN and may be particularly useful for studies on emphysema, pulmonary hypertension, or lung development.

Willführ A ，Brandenberger C ，Piatkowski T ，Grothausmann R ，Nyengaard JR ，Ochs M ，Mühlfeld C ... -  《-》

Is length an appropriate estimator to characterize pulmonary alveolar capillaries? A critical evaluation in the human lung.

Mühlfeld C ，Weibel ER ，Hahn U ，Kummer W ，Nyengaard JR ，Ochs M ... -  《-》

Stereological estimates of alveolar number and size and capillary length and surface area in mice lungs.

Knust J ，Ochs M ，Gundersen HJ ，Nyengaard JR ... -  《-》

The number of glomerular capillaries estimated by an unbiased and efficient stereological method.

Nyengaard JR ，Marcussen N 《-》

Digital 3D reconstructions using histological serial sections of lung tissue including the alveolar capillary network.

Grothausmann R, Knudsen L, Ochs M, Mühlfeld C. Digital 3D reconstructions using histological serial sections of lung tissue including the alveolar capillary network. Am J Physiol Lung Cell Mol Physiol 312: L243-L257, 2017. First published December 2, 2016; doi:10.1152/ajplung.00326.2016-The alveolar capillary network (ACN) provides an enormously large surface area that is necessary for pulmonary gas exchange. Changes of the ACN during normal or pathological development or in pulmonary diseases are of great functional impact and warrant further analysis. Due to the complexity of the three-dimensional (3D) architecture of the ACN, 2D approaches are limited in providing a comprehensive impression of the characteristics of the normal ACN or the nature of its alterations. Stereological methods offer a quantitative way to assess the ACN in 3D in terms of capillary volume, surface area, or number but lack a 3D visualization to interpret the data. Hence, the necessity to visualize the ACN in 3D and to correlate this with data from the same set of data arises. Such an approach requires a large sample volume combined with a high resolution. Here, we present a technically simple and cost-efficient approach to create 3D representations of lung tissue ranging from bronchioles over alveolar ducts and alveoli up to the ACN from more than 1 mm sample extent to a resolution of less than 1 μm. The method is based on automated image acquisition of serially sectioned epoxy resin-embedded lung tissue fixed by vascular perfusion and subsequent automated digital reconstruction and analysis of the 3D data. This efficient method may help to better understand mechanisms of vascular development and pathology of the lung.

Grothausmann R ，Knudsen L ，Ochs M ，Mühlfeld C ... -  《-》