A Model for Aortic Growth Based on Fluid Shear and Fiber Stresses (original) (raw)

Skip Nav Destination

Technical Papers

L. A. Taber

Department of Biomedical Engineering, Washington University, St. Louis, MO 63130

e-mail: lat@biomed.wustl.edu

Search for other works by this author on:

Crossmark: Check for Updates

L. A. Taber

Department of Biomedical Engineering, Washington University, St. Louis, MO 63130

e-mail: lat@biomed.wustl.edu

J Biomech Eng. Jun 1998, 120(3): 348-354 (7 pages)

Published Online: June 1, 1998

Stress-modulated growth in the aorta is studied using a theoretical model. The model is a thick-walled tube composed of two pseudoelastic, orthotropic layers representing the intima/media and the adventitia. Both layers are assumed to follow a growth law in which the time rates of change of the growth stretch ratios depend linearly on the local smooth muscle fiber stress and on the shear stress due to blood flow on the endothelium. Using finite elasticity theory modified to include volumetric growth, we computed temporal changes in stress, geometry, and opening angle (residual strain) during development and following the onset of sudden hypertension. For appropriate values of the coefficients in the growth law, the model yields results in reasonable agreement with published data for global and local growth of the rat aorta.

1.

, and ,

1993

, “

Control of Growth in Neonatal Pig Hearts

,”

Molecular and Cellular Biochemistry

, Vol.

119

, pp.

3

9

.

2.

, and ,

1976

, “

Effects of Hypertension on the Static Mechanical Properties and Chemical Composition of the Rat Aorta

,”

Cardiovascular Research

, Vol.

10

, pp.

437

451

.

3.

, and ,

1986

, “

On Residual Stresses in Arteries

,”

ASME JOURNAL OF BIOMECHANICAL ENGINEERING

, Vol.

108

, pp.

189

192

.

4.

,

1995

, “

Flow-Mediated Endothelial Mechanotransduction

,”

Physiological Reviews

, Vol.

75

, pp.

519

560

.

5.

, , and ,

1995

, “

A Mechanism for Heterogeneous Endothelial Responses to Flow In Vivo and In Vitro

,”

Journal of Biomechanics

, Vol.

28

, pp.

1553

1560

.

6.

Fung, Y. C., 1996, Biodynamics: Circulation, 2nd ed., Springer, New York.

7.

, and ,

1989

, “

Change of Residual Strains in Arteries Due to Hypertrophy Caused by Aortic Constriction

,”

Circulation Research

, Vol.

65

, pp.

1340

1349

.

8.

, and ,

1991

, “

Changes of Zero-Stress State of Rat Pulmonary Arteries in Hypoxic Hypertension

,”

Journal of Applied Physiology

, Vol.

70

, pp.

2455

2470

.

9.

, and ,

1993

, “

Elementary Mechanics of the Endothelium of Blood Vessels

,”

ASME JOURNAL OF BIOMECHANICAL ENGINEERING

, Vol.

115

, pp.

1

12

.

10.

Green, A. E., and Zerna, W., 1968, Theoretical Elasticity, 2nd ed., Oxford University Press, London.

11.

, and ,

1985

, “

Flow Restriction of One Carotid Artery in Juvenile Rats Inhibits Growth of Arterial Diameter

,”

American Journal of Physiology

, Vol.

248

, pp.

H540–H546

H540–H546

.

12.

, , and ,

1996

, “

Shear Stress Is Not Sufficient to Control Growth of Vascular Networks: A Model Study

,”

American Journal of Physiology

, Vol.

270

, pp.

H364–H375

H364–H375

.

13.

, and ,

1989

, “

Hemodynamics of the Stage 12 to Stage 29 Chick Embryo

,”

Circulation Research

, Vol.

65

, pp.

1665

1670

.

14.

, and ,

1980

, “

Adaptive Regulation of Wall Shear Stress to Flow Change in the Canine Carotid Artery

,”

American Journal of Physiology

, Vol.

239

, pp.

H14–H21

H14–H21

.

15.

,

1993

, “

Remodeling of Developing and Mature Arteries: Endothelium, Smooth Muscle, and Matrix

,”

Journal of Cardiovascular Pharmacology

, Vol.

21

(

Suppl. 1

), pp.

S11–S17

S11–S17

.

16.

, and ,

1995

, “

A Model for Stress-Induced Growth in the Developing Heart

,”

ASME JOURNAL OF BIOMECHANICAL ENGINEERING

, Vol.

117

, pp.

343

349

.

17.

,

1958

, “

Blood Pressure in Infant Rats

,”

Physiological Zoology

, Vol.

31

, pp.

1

9

.

18.

, and ,

1989

, “

Relationship Between Hypertension, Hypertrophy, and Opening Angle of Zero-Stress State of Arteries Following Aortic Constriction

,”

Journal of Biomechanical Engineering

, Vol.

111

, pp.

325

335

.

19.

, and ,

1996

, “

Indicial Functions of Arterial Remodeling in Response to Locally Altered Blood Pressure

,”

American Journal of Physiology

, Vol.

270

, pp.

H1323–H1333

H1323–H1333

.

20.

, and ,

1994

, “

Mechanical and Dimensional Adaptation of Rat Aorta to Hypertension

,”

ASME JOURNAL OF BIOMECHANICAL ENGINEERING

, Vol.

116

, pp.

278

283

.

21.

, , and ,

1994

, “

Passive Ventricular Mechanics in Tight-Skin Mice

,”

American Journal of Physiology

, Vol.

266

, pp.

H116–H1176

H116–H1176

.

22.

Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B.P., 1992, Numerical Recipes: The Art of Scientific Computing, 2nd ed., Cambridge Univ. Press, New York.

23.

, , and ,

1995

, “

Design Principles of Vascular Beds

,”

Circulation Research

, Vol.

77

, pp.

1017

1023

.

24.

, , and ,

1996

, “

Theoretical Study of Dynamics of Arterial Wall Remodeling in Response to Changes in Blood Pressure

,”

Journal of Biomechanics

, Vol.

29

, pp.

635

642

.

25.

Rhodin, J. A. G., 1980, “Architecture of the Vessel Wall,” Handbook of Physiology, Section 2: The Cardiovascular System, Vol. II: Vascular Smooth Muscle, Bohr, D. F., Somlyo, A. P., and Sparks, H. V., eds., American Physiological Society, Bethesda, MD, pp. 1–31.

26.

, , and ,

1994

, “

Stress-Dependent Finite Growth in Soft Elastic Tissues

,”

Journal of Biomechanics

, Vol.

27

, pp.

455

467

.

27.

, , , , and ,

1993

, “

Residual Strain in the Ventricle of the Stage 16–24 Chick Embryo

,”

Circulation Research

, Vol.

72

, pp.

455

462

.

28.

,

1995

, “

Biomechanics of Growth, Remodeling, and Morphogenesis

,”

Applied Mechanics Reviews

, Vol.

48

, pp.

487

545

.

29.

, and ,

1996

, “

Theoretical Study of Stress-Modulated Growth in the Aorta

,”

Journal of Theoretical Biology

, Vol.

180

, pp.

343

357

.

30.

,

1998

, “

An Optimization Principle for Vascular Radius Including the Effects of Smooth Muscle Tone

,”

Biophysical Journal

, Vol.

24

, pp.

109

114

.

31.

, and ,

1987

, “

Strain Energy Density Function and Uniform Strain Hypothesis for Arterial Mechanics

,”

Journal of Biomechanics

, Vol.

20

, pp.

7

17

.

32.

Thoma, R., 1893, Untersuchungen uber die Histogenese und Histomechanik des Gefassystems, Enke Verlag, Stuttgart.

33.

, , , , , and ,

1990

, “

Effect of Hypertension on Elasticity and Geometry of Aortic Tissue From Dogs

,”

ASME JOURNAL OF BIOMECHANICAL ENGINEERING

, Vol.

112

, pp.

70

74

.

This content is only available via PDF.

Copyright © 1998

by The American Society of Mechanical Engineers

You do not currently have access to this content.

Sign In

Purchase this Content

160 Views

176 Web of Science

Get Email Alerts

Cited By

Human Thermal Comfort

Electromagnetic Waves and Heat Transfer: Sensitivites to Governing Variables in Everyday Life