Extension of Murray's law including nonlinear mechanics of a composite artery wall
(English)Manuscript (preprint) (Other academic)
A goal function approach is used to derive an extension of Murray’s 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 growth and remodel in a process that is governed by a target state defined by a homeostatic radius and a homeostatic material composition. Following Murray’s original idea, this target state is defined by a principle of minimum work. We take this work to includes 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 depends on flow rate, blood pressure and elastin content.
Goal function, Murray’s law, Constrained mixture theory, Artery
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-104187OAI: oai:DiVA.org:liu-104187DiVA: diva2:695191