Aarhus University Seal / Aarhus Universitets segl

Jens Randel Nyengaard

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

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Standard

Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic). / Willführ, Alper; Brandenberger, Christina; Piatkowski, Tanja; Grothausmann, Roman; Nyengaard, Jens Randel; Ochs, Matthias; Mühlfeld, Christian.

In: American Journal of Physiology: Lung Cellular and Molecular Physiology, Vol. 309, No. 11, 01.12.2015, p. L1286-93.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Harvard

Willführ, A, Brandenberger, C, Piatkowski, T, Grothausmann, R, Nyengaard, JR, Ochs, M & Mühlfeld, C 2015, 'Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic)', American Journal of Physiology: Lung Cellular and Molecular Physiology, vol. 309, no. 11, pp. L1286-93. https://doi.org/10.1152/ajplung.00410.2014

APA

Willführ, A., Brandenberger, C., Piatkowski, T., Grothausmann, R., Nyengaard, J. R., Ochs, M., & Mühlfeld, C. (2015). Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic). American Journal of Physiology: Lung Cellular and Molecular Physiology, 309(11), L1286-93. https://doi.org/10.1152/ajplung.00410.2014

CBE

Willführ A, Brandenberger C, Piatkowski T, Grothausmann R, Nyengaard JR, Ochs M, Mühlfeld C. 2015. Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic). American Journal of Physiology: Lung Cellular and Molecular Physiology. 309(11):L1286-93. https://doi.org/10.1152/ajplung.00410.2014

MLA

Willführ, Alper et al. "Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic)". American Journal of Physiology: Lung Cellular and Molecular Physiology. 2015, 309(11). L1286-93. https://doi.org/10.1152/ajplung.00410.2014

Vancouver

Willführ A, Brandenberger C, Piatkowski T, Grothausmann R, Nyengaard JR, Ochs M et al. Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic). American Journal of Physiology: Lung Cellular and Molecular Physiology. 2015 Dec 1;309(11):L1286-93. https://doi.org/10.1152/ajplung.00410.2014

Author

Willführ, Alper ; Brandenberger, Christina ; Piatkowski, Tanja ; Grothausmann, Roman ; Nyengaard, Jens Randel ; Ochs, Matthias ; Mühlfeld, Christian. / Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic). In: American Journal of Physiology: Lung Cellular and Molecular Physiology. 2015 ; Vol. 309, No. 11. pp. L1286-93.

Bibtex

@article{c3eb47e639844608984f50ad4b075a62,
title = "Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincar{\'e} 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-Poincar{\'e} 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-Poincar{\'e} 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.",
author = "Alper Willf{\"u}hr and Christina Brandenberger and Tanja Piatkowski and Roman Grothausmann and Nyengaard, {Jens Randel} and Matthias Ochs and Christian M{\"u}hlfeld",
note = "Copyright {\textcopyright} 2015 the American Physiological Society.",
year = "2015",
month = dec,
day = "1",
doi = "10.1152/ajplung.00410.2014",
language = "English",
volume = "309",
pages = "L1286--93",
journal = "American Journal of Physiology: Lung Cellular and Molecular Physiology",
issn = "1040-0605",
publisher = "American Physiological Society",
number = "11",

}

RIS

TY - JOUR

T1 - Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic)

AU - Willführ, Alper

AU - Brandenberger, Christina

AU - Piatkowski, Tanja

AU - Grothausmann, Roman

AU - Nyengaard, Jens Randel

AU - Ochs, Matthias

AU - Mühlfeld, Christian

N1 - Copyright © 2015 the American Physiological Society.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

U2 - 10.1152/ajplung.00410.2014

DO - 10.1152/ajplung.00410.2014

M3 - Journal article

C2 - 26432874

VL - 309

SP - L1286-93

JO - American Journal of Physiology: Lung Cellular and Molecular Physiology

JF - American Journal of Physiology: Lung Cellular and Molecular Physiology

SN - 1040-0605

IS - 11

ER -