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Báo cáo y học: " Extension of Murray's law using a non-Newtonian model of blood flow"

Tuyển tập các báo cáo nghiên cứu về y học được đăng trên tạp chí y học quốc tế cung cấp cho các bạn kiến thức về ngành y đề tài: "Extension of Murray's law using a non-Newtonian model of blood flow | Theoretical Biology and Medical Modelling BioMed Central Research Extension of Murray s law using a non-Newtonian model of blood flow Rémi Revellin t1 Francois Roussel1 David Baud2 and Jocelyn Bonjour1 Open Access Address 1Université de Lyon CNRS INSA-Lyon CETHIL UMR5008 F-69621 Villeurbanne France Université Lyon 1 F-69622 France and 2Department of Obstetrics and Gynaecology University Hospital of Lausanne Maternity-CHUV CH-1011 Lausanne Switzerland Email Rémi Revellin - remi.revellin@insa-lyon.fr Francois Rousset - francois.rousset@insa-lyon.fr David Baud - David.Baud@chuv.ch Jocelyn Bonjour - jocelyn.bonjour@insa-lyon.fr Corresponding author tEqual contributors Published 15 May 2009 Received 9 April 2009 Theoretical Biology and Medical Modelling 2009 6 7 doi 10.1186 1742-4682-6-7 Accepted 15 May 2009 This article is available from http www.tbiomed.cOm content 6 1 7 2009 Revellin et al licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 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 .