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Extension of Murray's law including nonlinear mechanics of a composite artery wall
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1503-8293
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-8460-0131
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
Abstract [en]

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 grow 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 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 Berlin/Heidelberg, 2015. Vol. 14, no 1, 83-91 p.
Keyword [en]
Goal function, Murrays law, Constrained mixture theory, Artery
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:liu:diva-113721DOI: 10.1007/s10237-014-0590-8ISI: 000347250500008PubMedID: 24817182OAI: oai:DiVA.org:liu-113721DiVA: diva2:784659
Note

At the time for thesis presentation publication was in status: Manuscript

Funding Agencies|Swedish Research Council [621-2012-3117]

Available from: 2015-01-30 Created: 2015-01-29 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Goal Function Approach to Growth and Remodeling of Arteries
Open this publication in new window or tab >>Goal Function Approach to Growth and Remodeling of Arteries
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we develop a new goal function approach to investigate stability of the growth processes in blood vessels and cost-optimal composition and geometry of these vessels. In the vascular system of a healthy individual, the living composition of the arterial wall must regenerate and remodel continuously during the entire lifetime to maintain itself. In some cases the system destabilizes due to disease, injury or other complex processes. To understand how and when this happens, several mathematical models have been developed. These models have included an evolution equation for mass fractions of the vessel wall, describing how the vessel develops from an actual state to a target state. These works are based on constrained mixture theory (CMT), which takes care of production and removal of arterial constituents. The cost-optimal design of blood vessels has been studied previously by Murray.

The aim of this thesis is to contribute to stability analyses of the growth process by formulating a new goal function approach, making it possible to examine under which conditions instability arises. We also aim to analyze changes in the optimum material composition and geometry of the vessel wall, using a more realistic, nonlinear material model.

The blood vessel is modeled as a thin-walled tube and the constituents that form the vessel wall are assumed to deform together (CMT). The growth dynamics of the composite material of the vessel wall is described by an evolution equation, where the effective area of each constituent changes in the direction of steepest descent of a goal function. This goal function is formulated in such way that the constituents grow toward a target potential energy and a target composition. The response of the evolution equation is simulated for several dierent material models. These simulations suggest that elastin-decient vessels are more prone to growth instability, but that increased vessel stiness gives a more stable growth process. Another important nding is that an increased rate of degradation of materials impairs growth stability.

By extending Murray's law to include effects of nonlinear mechanics of the artery wall and a growth and remodeling mechanism based on CMT, and at the same time having the system satisfy an equilibrium equation, we study cost-optimal compositions and geometries of the vessel wall. This gives new insight into the wall's architecture under optimal conditions.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2014. 19 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1639
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-104188 (URN)10.3384/lic.diva-104188 (DOI)LIU-TEK-LIC-2013:73 (Local ID)978-91-7519-433-2 (ISBN)LIU-TEK-LIC-2013:73 (Archive number)LIU-TEK-LIC-2013:73 (OAI)
Presentation
2014-02-28, A32, A-huset, Campus Valla, Linköpings universitet, Linköping, 13:15 (Swedish)
Opponent
Supervisors
Available from: 2014-02-10 Created: 2014-02-10 Last updated: 2017-05-15Bibliographically approved

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Lindström, StefanSatha, GanarupanKlarbring, Anders

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