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

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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.

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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.

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Authors and Affiliations

  1. Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK

    Amy F. Smith

  2. Department of Mechanical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK

    Rebecca J. Shipley

  3. Department of Biomedical Engineering, St. Thomas’ Hospital, King’s College London, London, SE1 7EH, UK

    Jack Lee & Nicolas P. Smith

  4. Department of Physiology, Faculty of Medical and Health Sciences, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Gregory B. Sands & Ian J. LeGrice

  5. Faculty of Engineering, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Nicolas P. Smith

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  1. Amy F. Smith
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Correspondence to Nicolas P. Smith.

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Associate Editor Dan Elson oversaw the review of this article.

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Smith, A.F., Shipley, R.J., Lee, J. et al. Transmural Variation and Anisotropy of Microvascular Flow Conductivity in the Rat Myocardium. Ann Biomed Eng 42, 1966–1977 (2014). https://doi.org/10.1007/s10439-014-1028-2

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