Extension of Murray's law including nonlinear mechanics of a composite artery wall
2015 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 14, no 1, 83-91 p.Article in journal (Refereed) Published
A goal function approach is used to derive an extension of Murrays law that includes effects of nonlinear mechanics of the artery wall. The artery is modeled as a thin-walled tube composed of different species of nonlinear elastic materials that deform together. These materials grow and remodel in a process that is governed by a target state defined by a homeostatic radius and a homeostatic material composition. Following Murrays original idea, this target state is defined by a principle of minimum work. We take this work to include that of pumping and maintaining blood, as well as maintaining the materials of the artery wall. The minimization is performed under a constraint imposed by mechanical equilibrium. We derive a condition for the existence of a cost-optimal homeostatic state. We also conduct parametric studies using this novel theoretical frame to investigate how the cost-optimal radius and composition of the artery wall depend on flow rate, blood pressure, and elastin content.
Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2015. Vol. 14, no 1, 83-91 p.
Goal function; Murrays law; Constrained mixture theory; Artery
IdentifiersURN: urn:nbn:se:liu:diva-113721DOI: 10.1007/s10237-014-0590-8ISI: 000347250500008PubMedID: 24817182OAI: oai:DiVA.org:liu-113721DiVA: diva2:784659
Funding Agencies|Swedish Research Council [621-2012-3117]2015-01-302015-01-292016-05-04