Annals of Biomedical Engineering

, Volume 42, Issue 9, pp 1966–1977 | Cite as

Transmural Variation and Anisotropy of Microvascular Flow Conductivity in the Rat Myocardium

  • Amy F. Smith
  • Rebecca J. Shipley
  • Jack Lee
  • Gregory B. Sands
  • Ian J. LeGrice
  • Nicolas P. Smith
Article
First Online:
Received:
Accepted:

Abstract

Transmural variations in the relationship between structural and fluid transport properties of myocardial capillary networks are determined via continuum modeling approaches using recent three-dimensional (3D) data on the microvascular structure. Specifically, the permeability tensor, which quantifies the inverse of the blood flow resistivity of the capillary network, is computed by volume-averaging flow solutions in synthetic networks with geometrical and topological properties derived from an anatomically-detailed microvascular data set extracted from the rat myocardium. Results show that the permeability is approximately ten times higher in the principal direction of capillary alignment (the “longitudinal” direction) than perpendicular to this direction, reflecting the strong anisotropy of the microvascular network. Additionally, a 30% increase in capillary diameter from subepicardium to subendocardium is shown to translate to a 130% transmural rise in permeability in the longitudinal capillary direction. This result supports the hypothesis that perfusion is preferentially facilitated during diastole in the subendocardial microvasculature to compensate for the severely-reduced systolic perfusion in the subendocardium.

Keywords

Myocardial blood flow Microvascular networks Transmural functional differences Homogenization Darcy flow Flow conductivity 
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Notes

Acknowledgments

The authors acknowledge support from the Virtual Physiological Rat Project (NIH1 P50 GM094503-1), the EPSRC (Engineering and Physical Sciences Research Council) under grant numbers EP/F043929/1 and EP/G007527/2, and Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). The authors would also like to thank Prof. Timothy W. Secomb (University of Arizona) for helpful scientific discussions.

Supplementary material

10439_2014_1028_MOESM1_ESM.pdf (975 kb)
Supplementary material 1 (PDF 976 kb)

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Copyright information

© Biomedical Engineering Society 2014

Authors and Affiliations

  • Amy F. Smith
    • 1
  • Rebecca J. Shipley
    • 2
  • Jack Lee
    • 3
  • Gregory B. Sands
    • 4
  • Ian J. LeGrice
    • 4
  • Nicolas P. Smith
    • 3
    • 5
  1. 1.Oxford Centre for Collaborative Applied Mathematics, Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Department of Mechanical EngineeringUniversity College LondonLondonUK
  3. 3.Department of Biomedical Engineering, St. Thomas’ HospitalKing’s College LondonLondonUK
  4. 4.Department of Physiology, Faculty of Medical and Health SciencesThe University of AucklandAucklandNew Zealand
  5. 5.Faculty of EngineeringThe University of AucklandAucklandNew Zealand

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