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. 2017 Jul 11;7:5149. doi: 10.1038/s41598-017-05601-9

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Relationship between the degree of vessel obstruction and blood flow. Thrombotic vessel obstruction increases the vascular resistance as described by Poiseuille’s law, which says that resistance is inversely related to the radius to the fourth power. Therefore, if the radius (or diameter) of a vascular segment is reduced by one-half, the resistance or the volumetric blood flow within that narrowed segment increases by 16-fold, which is a dramatic effect relative to the change in degree of vessel obstruction. Based on the Poiseuille’s equation: Volume flow rate = π*(pressure difference)*(radius)4/8*(viscosity)*(length) the change in the cross-sectional area corresponding to a decrease of the degree of vessel obstruction from 56% to 48% will result in an increase in the volumetric blood flow by about 30%.