Morphological characteristics of vascular systems are commonly presented in terms of Strahler order because the logarithms of quantities such as vessel diameter and length are often linearly related to Strahler order. However, the ability to interpret Strahler order geometrically or physiologically is compromised because the precision of the order number is limited to integer values. This limitation is overcome by the volume ordering scheme, in which volume order number is defined as the logarithm of the estimated perfused tissue volume for each vascular segment. While Strahler and volume order numbers are equivalent for completely symmetrical branching trees, they deviate in the presence of asymmetries. The physiology-based definition of volume ordering offers benefits in the analysis of vascular design, fractal characterization of vascular systems, and blood flow modeling. These benefits are illustrated based on arterial kidney data that show a linear relationship of logarithmic vessel diameter and conductance as a function of both Strahler order and volume order with differing proportionality constants, which are expected to depend on the branching characteristics of the particular organ investigated.
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This research is supported by the Canadian Institutes of Health Research and the National Cancer Institute of Canada. We also thank Janet Koprivnikar and Lisa Yu, who prepared the microCT specimens. R. Mark Henkelman is the recipient of a Canada Research Chair in Imaging.
Author information Authors and AffiliationsRotman Research Institute, Baycrest Centre for Geriatric Care, 3560 Bathurst St., Toronto, ON, M6A 2E1, Canada
M. Marxen
Department of Medical Biophysics, University of Toronto, Toronto, Canada
J.G. Sled & R.M. Henkelman
Hospital for Sick Children – Mouse Imaging Centre, Toronto, Canada
J.G. Sled & R.M. Henkelman
Sunnybrook Health Sciences Centre, Toronto, Canada
R.M. Henkelman
Correspondence to M. Marxen.
About this article Cite this articleMarxen, M., Sled, J. & Henkelman, R. Volume Ordering for Analysis and Modeling of Vascular Systems. Ann Biomed Eng 37, 542–551 (2009). https://doi.org/10.1007/s10439-008-9623-8
Received: 29 October 2007
Accepted: 12 December 2008
Published: 24 December 2008
Issue Date: March 2009
DOI: https://doi.org/10.1007/s10439-008-9623-8
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