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TECHNICAL PAPERS

A Biphasic, Anisotropic Model of the Aortic Wall

[+] Author and Article Information
Mark Johnson

Northwestern University, Evanston, IL

John M. Tarbell

Pennsylvania State University, University Park, PA 16802

J Biomech Eng 123(1), 52-57 (Aug 29, 2000) (6 pages) doi:10.1115/1.1339817 History: Received July 02, 1999; Revised August 29, 2000
Copyright © 2001 by ASME
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References

Vargas,  C. B., Vargas,  F. F., Pribyle,  J. G., and Blackshear,  B. L., 1979, “Hydraulic Conductivity of the Endothelial and Outer Layers of Rabbit Aorta,” Am. J. Physiol., 236, pp. H53–H60.
Fry,  D. L., 1983, “Effect of Pressure and Stirring on the in Vitro Aortic Transmural 125I-Albumin Transport,” Am. J. Physiol., 245, pp. H977–H991.
Parker,  K. H., and Winlove,  C. P., 1984, “The Macromolecular Basis of the Hydraulic Conductivity of the Arterial Wall,” Biorheology, 21, pp. 181–196.
Tedgui,  A., and Lever,  M., 1985, “The Interaction of Convection and Diffusion in the Transport of 131I-Albumin Within the Media of the Rabbit Thoracic Aorta,” Circ. Res., 57, pp. 856–863.
Klanchar,  M., and Tarbell,  J., 1987, “Modeling Water Flow Through Arterial Tissue,” Bull. Math. Biol., 49, pp. 651–669.
Baldwin,  A., Wilson,  L., and Simon,  B., 1992, “Effect of Pressure on Aortic Hydraulic Conductivity,” Arterioscler. Thromb., 12, pp. 163–171.
Kim,  W.-K., and Tarbell,  J., 1994, “Macromolecular Transport Through the Deformable Porous Media of an Artery Wall,” ASME J. Biomech. Eng., 116, pp. 156–163.
Simon,  B., Kaufmann,  M., McAfee,  M., Baldwin,  A., and Wilson,  L., 1998, “Identification and Determination of Material Properties for Porohyperelastic Analysis of Large Arteries,” ASME J. Biomech. Eng., 120, pp. 188–194.
Bergel,  D. H., 1961, “The Static Elastic Properties of the Arterial Wall,” J. Physiol. (Lond), 156, pp. 445–457.
Fenn, W. O., 1957, “Changes in Length of Blood Vessels on Inflation,” in: Tissue Elasticity, J. W. Remington, ed., American Physiological Society, Washington, DC, pp. 154–167.
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Whale,  M. D., Grodzinsky,  A. J., and Johnson,  M., 1996, “The Effect of Aging and Pressure on the Specific Hydraulic Conductivity of the Aortic Wall,” Biorheology, 33, pp. 17–44.
Kenyon,  D. E., 1979, “A Mathematical Model of Water Flux Through Aortic Tissue,” Bull. Math. Biol., 41, pp. 79–90.
Whale,  M. D., Grodzinsky,  A. J., and Johnson,  M., 1996, “The Effects of Age and Pressure on the Specific Hydraulic Conductivity of the Aortic Wall,” Biorheology, 33, pp. 17–44.
Loree,  H. M., Kamm,  R. D., Stringfellow,  R. G., and Lee,  R. T., 1992, “Effects of Fibrous Cap Thickness on Peak Circumferential Stress in Model Atherosclerotic Vessels,” Circ. Res., 71, pp. 850–858.
Lehknitskii, S. G., 1963, Theory of Elasticity of an Anisotropic Body, Holden-Day, San Francisco, CA.
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Lai,,  W. and Mow,  V., 1980, “Drag Induced Compression of Articular Cartilage During a Permeation Experiment,” Biorheology, 17, pp. 111–123.
Baldwin,  A., and Wilson,  L., 1993, “Endothelium Increases Medial Hydraulic Conductance of Aorta, Possibly by Release of EDRF,” Am. J. Physiol., 264, pp. H26–H32.
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Figures

Grahic Jump Location
Biphasic and single-phase 12 model predictions of aortic wall volume (normalized to unpressurized volume) as a function of perfusion pressure in a cylindrical geometry for parameter values of E=460 kPa,E=20 kPa,ν=0.3,M=6.0, and 0<ν<0.05
Grahic Jump Location
Biphasic and single-phase 12 model predictions of aortic radius as a function of perfusion pressure for parameter values of E=460 kPa,E=20 kPa,ν=0.3,M=6.0 and ν=0.038 (biphasic) or ν=0.0 (single-phase)
Grahic Jump Location
Comparison of biphasic (solid line) to single-phase model (dashed line) 12 for the tangential (σt) and radial (σr) stress distribution in the aortic wall at a perfusion pressure of 70 mmHg for parameter values of E=460 kPa,E=20 kPa,ν=0.3,ν=0.038 and M=6.0.
Grahic Jump Location
Comparison of biphasic (solid line) to single-phase model (dashed line) 12 for the tangential (εt) and radial strain (εr) distribution in the aortic wall at a perfusion pressure of 70 mmHg for parameter values of E=460 kPa,E=20 kPa,ν=0.3,ν=0.038 and M=6.0
Grahic Jump Location
Data (symbols) from rabbit aorta Baldwin et al. 6 for vessel radius as a function of perfusion pressure. The solid line is from the nonlinear biphasic model as described in the text
Grahic Jump Location
Modulus in the plane of symmetry (E) of the rabbit aorta as a function of tangential strain as determined by the biphasic model in combination with the data from Baldwin et al. 6
Grahic Jump Location
Modulus in the plane of symmetry (E) of the rabbit aorta as a function of perfusion pressure as determined by the biphasic model in combination with the data from Baldwin et al. 6
Grahic Jump Location
Thickness of the rabbit aortic wall as predicted by the nonlinear, biphasic model (solid line) for the parameters given in the text. Data shown are from Baldwin et al. 6
Grahic Jump Location
Hydraulic conductivity of the rabbit aortic wall as predicted by the nonlinear, biphasic model (solid line) for the parameters given in the text. Data shown are from Baldwin et al. 19

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