title: Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic).
abstract: 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.
authors.affiliation: Institute of Functional and Applied Anatomy, Hannover Medical School, Hannover, Germany;
authors.forename: Alper
authors.initials: A
authors.lastname: Willführ
authors.affiliation: Institute of Functional and Applied Anatomy, Hannover Medical School, Hannover, Germany;
authors.forename: Christina
authors.initials: C
authors.lastname: Brandenberger
authors.affiliation: Institute of Functional and Applied Anatomy, Hannover Medical School, Hannover, Germany; Department of Cardiac Development and Remodelling, Max-Planck-Institute for Heart and Lung Research, Bad Nauheim, Germany;
authors.forename: Tanja
authors.initials: T
authors.lastname: Piatkowski
authors.affiliation: Institute of Functional and Applied Anatomy, Hannover Medical School, Hannover, Germany;
authors.forename: Roman
authors.initials: R
authors.lastname: Grothausmann
authors.affiliation: Stereology and Electron Microscopy Laboratory, Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, Aarhus, Denmark;
authors.forename: Jens Randel
authors.initials: JR
authors.lastname: Nyengaard
authors.affiliation: Institute of Functional and Applied Anatomy, Hannover Medical School, Hannover, Germany; Biomedical Research in Endstage and Obstructive Lung Disease Hannover, Member of the German Center for Lung Research, Hannover, Germany; and Cluster of Excellence REBIRTH, Hannover, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Ochs
authors.affiliation: Institute of Functional and Applied Anatomy, Hannover Medical School, Hannover, Germany; Biomedical Research in Endstage and Obstructive Lung Disease Hannover, Member of the German Center for Lung Research, Hannover, Germany; and Cluster of Excellence REBIRTH, Hannover, Germany muehlfeld.christian@mh-hannover.de.
authors.forename: Christian
authors.initials: C
authors.lastname: Mühlfeld
mesh_terms: D000818:Animals; D002196:Capillaries / Q000033:anatomy & histology* / Q000648:ultrastructure; D002452:Cell Count; D021621:Imaging, Three-Dimensional; D010827:Physiology / Q000379:methods*; D011650:Pulmonary Alveoli / Q000098:blood supply*; D051381:Rats
keywords: Euler number; capillary number; stereology