ArticleBiomechanics and modeling in mechanobiology2015
Extension of Murray's law including nonlinear mechanics of a composite artery wall.
Article in Biomechanics and modeling in mechanobiology, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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7 citing papers in PubMed.
- Applications of lump, breather, rogue, and various nonlinear waves in the modeling of blood vessels: analysis of the nonlinear Murray equation with heterogeneous wall properties.Cognitive neurodynamics · 2026Article
- A microstructurally motivated framework to study autoregulation in the coronary circulation.The Journal of physiology · 2026Article
- Baseline state for pulmonary vasculature with pulmonary arterial hypertension: effect of geometric remodeling and metabolic shift.Biomechanics and modeling in mechanobiology · 2026Article
- A Microstructurally-Motivated Framework to Study Autoregulation in the Coronary Circulation.bioRxiv : the preprint server for biology · 2025Article
- Importance of Considering Temporal Variations in Pulse Wave Velocity for Accurate Blood Pressure Prediction.Annals of biomedical engineering · 2025Article
- Universal Murray's law for optimised fluid transport in synthetic structures.Nature communications · 2024Article
- A goal function approach to remodeling of arteries uncovers mechanisms for growth instability.Biomechanics and modeling in mechanobiology · 2014Article
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3 authors.
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Abstract
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.
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