Stability against dynamic remodeling of an arterial tissue

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Abstract

Geometry and structure of the arterial wall are maintained through continuous growth and remodeling (G&R). To understand these processes, mathematical models have been proposed in which the outcome of G&R depends on a mechanical stimulus through evolution equations. Rate parameters in these equations cannot be determined easily from experimental data. Assuming that the healthy artery is stable against remodeling, a physiologically acceptable range for the two rate parameters in the framework of an existing model of arterial G&R is determined here. The model is explicitly evaluated for the example of a cylindrical blood vessel, both thick-walled and thin-walled. For the thin-walled vessel a criterion for stability against remodeling is derived by means of a linear stability approach, and is expressed in terms of the ratio of the rates of remodeling parameters. It is shown that this criterion is equivalent to the condition that the physiological healthy state of the artery can be reached, implying that if the healthy state exists then it is stable. Explicit numerical results are presented for a typical cerebral artery and an abdominal aorta.
Original languageEnglish
Pages (from-to)175-192
Number of pages18
JournalJournal of Engineering Mathematics
Volume67
Issue number3
DOIs
Publication statusPublished - 2010

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Remodeling
Arteries
Tissue
Blood vessels
Mathematical models
Aorta
Geometry
Blood Vessels
Linear Stability
Vessel
Evolution Equation
Experimental Data
Mathematical Model
Numerical Results
Model
Range of data

Cite this

@article{6bd1ed7a1c7a48b39ba627b181177125,
title = "Stability against dynamic remodeling of an arterial tissue",
abstract = "Geometry and structure of the arterial wall are maintained through continuous growth and remodeling (G&R). To understand these processes, mathematical models have been proposed in which the outcome of G&R depends on a mechanical stimulus through evolution equations. Rate parameters in these equations cannot be determined easily from experimental data. Assuming that the healthy artery is stable against remodeling, a physiologically acceptable range for the two rate parameters in the framework of an existing model of arterial G&R is determined here. The model is explicitly evaluated for the example of a cylindrical blood vessel, both thick-walled and thin-walled. For the thin-walled vessel a criterion for stability against remodeling is derived by means of a linear stability approach, and is expressed in terms of the ratio of the rates of remodeling parameters. It is shown that this criterion is equivalent to the condition that the physiological healthy state of the artery can be reached, implying that if the healthy state exists then it is stable. Explicit numerical results are presented for a typical cerebral artery and an abdominal aorta.",
author = "I. Machyshyn and P.H.M. Bovendeerd and {Ven, van de}, A.A.F. and P.M.J. Rongen and {Vosse, van de}, F.N.",
year = "2010",
doi = "10.1007/s10665-009-9336-5",
language = "English",
volume = "67",
pages = "175--192",
journal = "Journal of Engineering Mathematics",
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Stability against dynamic remodeling of an arterial tissue. / Machyshyn, I.; Bovendeerd, P.H.M.; Ven, van de, A.A.F.; Rongen, P.M.J.; Vosse, van de, F.N.

In: Journal of Engineering Mathematics, Vol. 67, No. 3, 2010, p. 175-192.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Stability against dynamic remodeling of an arterial tissue

AU - Machyshyn, I.

AU - Bovendeerd, P.H.M.

AU - Ven, van de, A.A.F.

AU - Rongen, P.M.J.

AU - Vosse, van de, F.N.

PY - 2010

Y1 - 2010

N2 - Geometry and structure of the arterial wall are maintained through continuous growth and remodeling (G&R). To understand these processes, mathematical models have been proposed in which the outcome of G&R depends on a mechanical stimulus through evolution equations. Rate parameters in these equations cannot be determined easily from experimental data. Assuming that the healthy artery is stable against remodeling, a physiologically acceptable range for the two rate parameters in the framework of an existing model of arterial G&R is determined here. The model is explicitly evaluated for the example of a cylindrical blood vessel, both thick-walled and thin-walled. For the thin-walled vessel a criterion for stability against remodeling is derived by means of a linear stability approach, and is expressed in terms of the ratio of the rates of remodeling parameters. It is shown that this criterion is equivalent to the condition that the physiological healthy state of the artery can be reached, implying that if the healthy state exists then it is stable. Explicit numerical results are presented for a typical cerebral artery and an abdominal aorta.

AB - Geometry and structure of the arterial wall are maintained through continuous growth and remodeling (G&R). To understand these processes, mathematical models have been proposed in which the outcome of G&R depends on a mechanical stimulus through evolution equations. Rate parameters in these equations cannot be determined easily from experimental data. Assuming that the healthy artery is stable against remodeling, a physiologically acceptable range for the two rate parameters in the framework of an existing model of arterial G&R is determined here. The model is explicitly evaluated for the example of a cylindrical blood vessel, both thick-walled and thin-walled. For the thin-walled vessel a criterion for stability against remodeling is derived by means of a linear stability approach, and is expressed in terms of the ratio of the rates of remodeling parameters. It is shown that this criterion is equivalent to the condition that the physiological healthy state of the artery can be reached, implying that if the healthy state exists then it is stable. Explicit numerical results are presented for a typical cerebral artery and an abdominal aorta.

U2 - 10.1007/s10665-009-9336-5

DO - 10.1007/s10665-009-9336-5

M3 - Article

VL - 67

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JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

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ER -