A fractional derivative model to describe arterial viscoelasticity

Arterial viscoelasticity can be described with a complex modulus (E*) in the frequency domain. In arteries, E* presents a power-law response with a plateau for higher frequencies. Constitutive models based on a combination of purely elastic and viscous elements can be represented with integer order...

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Autores principales:	Craiem, D., Armentano, R.L.
Formato:	JOUR
Lenguaje:	English
Materias:	Arterial wall mechanics Complex modulus Constitutive models Fractional calculus Viscoelasticity animal experiment animal tissue artery artery wall article experimental model in vivo study nonhuman prediction pressure theoretical model viscoelasticity Animals Aorta Arteries Elasticity Humans Models, Cardiovascular Muscle, Smooth, Vascular Sheep Stress, Mechanical Viscosity
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0006355X_v44_n4_p251_Craiem
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_0006355X_v44_n4_p251_Craiem
record_format	dspace
spelling	todo:paper_0006355X_v44_n4_p251_Craiem2023-10-03T14:05:10Z A fractional derivative model to describe arterial viscoelasticity Craiem, D. Armentano, R.L. Arterial wall mechanics Complex modulus Constitutive models Fractional calculus Viscoelasticity animal experiment animal tissue artery artery wall article experimental model in vivo study nonhuman prediction pressure theoretical model viscoelasticity Animals Aorta Arteries Elasticity Humans Models, Cardiovascular Muscle, Smooth, Vascular Sheep Stress, Mechanical Viscosity Arterial viscoelasticity can be described with a complex modulus (E) in the frequency domain. In arteries, E presents a power-law response with a plateau for higher frequencies. Constitutive models based on a combination of purely elastic and viscous elements can be represented with integer order differential equations but show several limitations. Recently, fractional derivative models with fewer parameters have proven to be efficient in describing rheological tissues. A new element, called "spring-pot", that interpolates between springs and dashpots is incorporated. Starting with a Voigt model, we proposed two fractional alternative models with one and two spring-pots. The three models were tested in an anesthetized sheep in a control state and during smooth muscle activation. A least squares method was used to fit E. Local activation induced a vascular constriction with no pressure changes. The E results confirmed the steep increase from static to dynamic values and a plateau in the range 2-30 Hz, coherent with fractional model predictions. Activation increased E, affecting its real and imaginary parts separately. Only the model with two spring-pots correctly followed this behavior with the best performance in terms of least squares errors. In a context where activation separately modifies E, this alternative model should be considered in describing arterial viscoelasticity in vivo. © 2007 - IOS Press and the authors. All rights reserved. JOUR English info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0006355X_v44_n4_p251_Craiem
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language	English
orig_language_str_mv	English
topic	Arterial wall mechanics Complex modulus Constitutive models Fractional calculus Viscoelasticity animal experiment animal tissue artery artery wall article experimental model in vivo study nonhuman prediction pressure theoretical model viscoelasticity Animals Aorta Arteries Elasticity Humans Models, Cardiovascular Muscle, Smooth, Vascular Sheep Stress, Mechanical Viscosity
spellingShingle	Arterial wall mechanics Complex modulus Constitutive models Fractional calculus Viscoelasticity animal experiment animal tissue artery artery wall article experimental model in vivo study nonhuman prediction pressure theoretical model viscoelasticity Animals Aorta Arteries Elasticity Humans Models, Cardiovascular Muscle, Smooth, Vascular Sheep Stress, Mechanical Viscosity Craiem, D. Armentano, R.L. A fractional derivative model to describe arterial viscoelasticity
topic_facet	Arterial wall mechanics Complex modulus Constitutive models Fractional calculus Viscoelasticity animal experiment animal tissue artery artery wall article experimental model in vivo study nonhuman prediction pressure theoretical model viscoelasticity Animals Aorta Arteries Elasticity Humans Models, Cardiovascular Muscle, Smooth, Vascular Sheep Stress, Mechanical Viscosity
description	Arterial viscoelasticity can be described with a complex modulus (E) in the frequency domain. In arteries, E presents a power-law response with a plateau for higher frequencies. Constitutive models based on a combination of purely elastic and viscous elements can be represented with integer order differential equations but show several limitations. Recently, fractional derivative models with fewer parameters have proven to be efficient in describing rheological tissues. A new element, called "spring-pot", that interpolates between springs and dashpots is incorporated. Starting with a Voigt model, we proposed two fractional alternative models with one and two spring-pots. The three models were tested in an anesthetized sheep in a control state and during smooth muscle activation. A least squares method was used to fit E. Local activation induced a vascular constriction with no pressure changes. The E results confirmed the steep increase from static to dynamic values and a plateau in the range 2-30 Hz, coherent with fractional model predictions. Activation increased E, affecting its real and imaginary parts separately. Only the model with two spring-pots correctly followed this behavior with the best performance in terms of least squares errors. In a context where activation separately modifies E, this alternative model should be considered in describing arterial viscoelasticity in vivo. © 2007 - IOS Press and the authors. All rights reserved.
format	JOUR
author	Craiem, D. Armentano, R.L.
author_facet	Craiem, D. Armentano, R.L.
author_sort	Craiem, D.
title	A fractional derivative model to describe arterial viscoelasticity
title_short	A fractional derivative model to describe arterial viscoelasticity
title_full	A fractional derivative model to describe arterial viscoelasticity
title_fullStr	A fractional derivative model to describe arterial viscoelasticity
title_full_unstemmed	A fractional derivative model to describe arterial viscoelasticity
title_sort	fractional derivative model to describe arterial viscoelasticity
url	http://hdl.handle.net/20.500.12110/paper_0006355X_v44_n4_p251_Craiem
work_keys_str_mv	AT craiemd afractionalderivativemodeltodescribearterialviscoelasticity AT armentanorl afractionalderivativemodeltodescribearterialviscoelasticity AT craiemd fractionalderivativemodeltodescribearterialviscoelasticity AT armentanorl fractionalderivativemodeltodescribearterialviscoelasticity
_version_	1807321145883492352

A fractional derivative model to describe arterial viscoelasticity

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