Extension of Murray's law using a non-Newtonian model of blood flow.

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serval:BIB_F9839BCD2C62
Type
Article: article from journal or magazin.
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Publications
Institution
Title
Extension of Murray's law using a non-Newtonian model of blood flow.
Journal
Theoretical Biology and Medical Modelling
Author(s)
Revellin R., Rousset F., Baud D., Bonjour J.
ISSN
1742-4682 (Electronic)
ISSN-L
1742-4682
Publication state
Published
Issued date
2009
Volume
6
Pages
7
Language
english
Notes
Publication types: Journal ArticlePublication Status: epublish
Abstract
BACKGROUND: So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n.
RESULTS: We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature.
CONCLUSION: It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.
Keywords
Animals, Arteries, Capillaries, Entropy, Hemorheology, Humans, Models, Anatomic, Models, Biological, Models, Theoretical, Regional Blood Flow
Pubmed
Web of science
Open Access
Yes
Create date
09/02/2010 14:46
Last modification date
20/08/2019 16:25
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