A scaling law of vascular volume

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Scaling of Engineered Vascular Grafts Using 3D Printed Guides and the Ring Stacking Method
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Published on: March 27, 2017

Yunlong Huo1, Ghassan S Kassab

  • 1Department of Biomedical Engineering, Surgery, and Cellular and Integrative Physiology, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana, USA.

Biophysical Journal
|January 27, 2009
PubMed

Vascular volume is of fundamental significance to the function of the cardiovascular system. An accurate prediction of blood volume in patients is physiologically and clinically significant. This study proposes what we believe is a novel volume scaling relation of the form: V(c)=K(v)D(s)(2/3)L(c), where V(c) and L(c) are cumulative vessel volume and length, respectively, in the tree, and D(s) is the diameter of the vessel segment. The scaling relation is validated in vascular trees of various organs including the heart, lung, mesentery, muscle, and eye of different species. Based on the minimum energy hypothesis and volume scaling relation, four structure-function scaling relations are predicted, including the diameter-length, volume-length, flow-diameter, and volume-diameter relations, with exponent values of 3/7, 1(2/7), 2(1/3), and 3, respectively. These four relations are validated in the various vascular trees, which further confirm the volume scaling relation. This scaling relation may serve as a control reference to estimate the blood volume in various organs and species. The deviation from the scaling relation may indicate hypovolemia or hypervolemia and aid diagnosis.

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