Skip to main content
Journal cover image

Green's function methods for analysis of oxygen delivery to tissue by microvascular networks.

Publication ,  Journal Article
Secomb, TW; Hsu, R; Park, EYH; Dewhirst, MW
Published in: Ann Biomed Eng
November 2004

Delivery of oxygen to tissue is an essential function of the circulatory system. The distance that oxygen can diffuse into oxygen-consuming tissue is small, and so tissue oxygenation is critically dependent on the spatial arrangement of microvessels in tissue. Theoretical methods have been developed to simulate the spatial distribution of oxygen levels in tissue surrounding a network of microvessels. Here, numerical methods based on a Green's function approach are presented, for realistic three-dimensional network geometries derived from observations of skeletal muscle, brain, and tumor tissues. Relative to finite-difference methods, the Green's function approach reduces the number of unknowns in the numerical formulation and allows rapid computations even for complex vascular geometries. Generally, the boundary conditions on the exterior of the computational domain are not known. Imposition of a no-flux boundary condition can lead to exaggerated estimates of the extent of hypoxia in the tissue region. A new version of the method is described that avoids this problem and can be applied to arbitrarily shaped tissue domains.

Duke Scholars

Published In

Ann Biomed Eng

DOI

ISSN

0090-6964

Publication Date

November 2004

Volume

32

Issue

11

Start / End Page

1519 / 1529

Location

United States

Related Subject Headings

  • Oxygen Consumption
  • Models, Cardiovascular
  • Microcirculation
  • Humans
  • Biomedical Engineering
  • Animals
  • 4003 Biomedical engineering
  • 11 Medical and Health Sciences
  • 09 Engineering
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Secomb, T. W., Hsu, R., Park, E. Y. H., & Dewhirst, M. W. (2004). Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann Biomed Eng, 32(11), 1519–1529. https://doi.org/10.1114/b:abme.0000049036.08817.44
Secomb, Timothy W., Richard Hsu, Eric Y. H. Park, and Mark W. Dewhirst. “Green's function methods for analysis of oxygen delivery to tissue by microvascular networks.Ann Biomed Eng 32, no. 11 (November 2004): 1519–29. https://doi.org/10.1114/b:abme.0000049036.08817.44.
Secomb TW, Hsu R, Park EYH, Dewhirst MW. Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann Biomed Eng. 2004 Nov;32(11):1519–29.
Secomb, Timothy W., et al. “Green's function methods for analysis of oxygen delivery to tissue by microvascular networks.Ann Biomed Eng, vol. 32, no. 11, Nov. 2004, pp. 1519–29. Pubmed, doi:10.1114/b:abme.0000049036.08817.44.
Secomb TW, Hsu R, Park EYH, Dewhirst MW. Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann Biomed Eng. 2004 Nov;32(11):1519–1529.
Journal cover image

Published In

Ann Biomed Eng

DOI

ISSN

0090-6964

Publication Date

November 2004

Volume

32

Issue

11

Start / End Page

1519 / 1529

Location

United States

Related Subject Headings

  • Oxygen Consumption
  • Models, Cardiovascular
  • Microcirculation
  • Humans
  • Biomedical Engineering
  • Animals
  • 4003 Biomedical engineering
  • 11 Medical and Health Sciences
  • 09 Engineering