PREDICTION OF MACROMOLECULAR TRANSPORT THROUGH THE DEFORMABLE POROUS MEDIA OF AN ARTERY WALL BY PORE THEORY

Kim WS; Tarbell JM

Korean Journal of Chemical Engineering, Vol.13, No.5, 457-465, September, 1996

To determine the transport properties of macromolecules in media of an artery wall deformed inhomogeneously by the transmural pressure, we combine a simple mechano-hydraulic model based on a two parameter strain-dependent permeability function, which was developed by Klanchar and Tarbell [1987], with a pore theory. The combined theory allows us to calculate the spatial distributions of porosity, solute partition, pore radius and macromolecular solute concentration in the media and their dependence on the transmural pressure. The predictions from the pore theory are in good agreement with experimental measurements of sucrose space, albumin space and albumin concentration profiles in the media of rabbit aortas at transmural pressures of 70 and 180 mmHg. The prediction indicates that albumin transport through the aortic media is dominated by convection rather than diffusion. It is further de- monstrated that the transport properties of planar tissue samples, which are often used in vitro experimentals, may be quite different from those of intact vessels in their natural cylindrical configuration because of the variation in tissue deformation. Using the pore theory we are also able to calculate the interstitial shear stress associated with transmural volume flow which may act on the smooth muscle cells residing in the media and find it to be on the order of several dyne/cm2. This level of shear stress will stimulate endothelial cells and may also affect smooth muscle cells.

Keywords:Deformable Media;Pore Theory;Macromolecular Transport;Sucrose Porosity;Albumin Porosity

[References]

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Bratzler RL, "The Transport Properties of Arterial Tissue," Ph.D. Thesis, Massachusetts Institute of Technology (1974)
Caro CG, Lever MJ, Tedgui A, J. Physiol., 38P (1981)
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Fry DL, Mathematical Modellings, 6, 353 (1985)
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Harrison RG, Massaro TA, Atherosclerosis, 24, 363 (1976)
Jo H, Dull RO, Hollis TM, Tarbell JM, Am. J. Physiol., 260, H1992 (1991)
Kim WS, Tarbell JM, J. Biomech. Eng., 16, 156 (1994)
Klanchar M, Tarbell JM, Bull. Math. Biology, 49(6), 651 (1987)
Lai WM, Mow VC, Biorheology, 17, 111 (1980)
Lodge TP, Markland P, Polymer, 28, 1377 (1987)
McKinley RM, Jahns HO, Harris WW, Greenkorn RA, AIChE J., 12(1), 17 (1966)
Muhr AH, Blanshard JMV, Polymer, 23, 1012 (1982)
Ogston AG, Preston BN, Wells JD, Proc. R. Soc. Lond. A, 333, 297 (1973)
Patel DJ, Varishnay RN, "Basic Hemodynamics and Its Role in Disease Processes," University Park Press, Baltimore, MD, 183 (1980)
Phillies GDJ, Gong J, Li L, Rau A, Zhang K, Yu LP, Rollings J, J. Phys. Chem., 93(16), 6219 (1989)
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Tedgui A, Lever MJ, Am. J. Physiol., 247, H784 (1984)
Tedgui A, Lever MJ, Circulation Res., 57(6), 856 (1985)
Tedgui A, Lever MJ, Am. J. Physiol., 250, H1530 (1987)
Truskey GA, Colton CK, Smith KA, "Quantitative Analysis of Protein Transport in the Arterial Wall," Structure and Function of the Circulation, Vol. 3, edited by Schwartz, C.J., Werthessen, J.T. and Wolf, S., Plenum Publishing Corporation, New York, N.Y., 287 (1981)
Yuan F, Chien S, Weinbaum S, J. Biomech. Eng., in press (1991)

[1] Anderson JL, Quinn JA, Biophys. J., 14, 130 (1974)

[2] Baldwin AL, Wilson LM, Simon BR, Atherosclerosis Thrombosis, 12(2), 163 (1992)

[3] Bratzler RL, "The Transport Properties of Arterial Tissue," Ph.D. Thesis, Massachusetts Institute of Technology (1974)

[4] Caro CG, Lever MJ, Tedgui A, J. Physiol., 38P (1981)

[5] Curmi PA, Juan L, Tedgui A, Circulation Res., 66(6), 1692 (1990)

[6] Curry FE, Circulation Res., 59(4), 367 (1986)

[7] Curry FE, "Mechanics of Thermodynamics of Transcapillary Exchange," Handbook of Physiology, Section 2, the Cardiovascular System, Vol. IV, Microcirculation, American Physiology Society, 309, Bethesda, MD (1984)

[8] Curry FE, Michel CC, Microvascular Res., 20, 96 (1980)

[9] Deen WM, AIChE J., 9, 1409 (1987)

[10] Fry DL, Mathematical Modellings, 6, 353 (1985)

[11] Garay R, Rossella R, Rosati C, "Non-Laminar Flow as Initiating Factor of Atherosclerosis: Evidence for a Role of Membrane Ion Transport," in Membrane Technology (Ed. Verna, R.), Raven Press, New York, pp. 137-139 (1989)

[12] Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Martinus Nijhoff Publishers, Dordrecht, Netherland (1986)

[13] Harrison RG, Massaro TA, Atherosclerosis, 24, 363 (1976)

[14] Jo H, Dull RO, Hollis TM, Tarbell JM, Am. J. Physiol., 260, H1992 (1991)

[15] Kim WS, Tarbell JM, J. Biomech. Eng., 16, 156 (1994)

[16] Klanchar M, Tarbell JM, Bull. Math. Biology, 49(6), 651 (1987)

[17] Lai WM, Mow VC, Biorheology, 17, 111 (1980)

[18] Lodge TP, Markland P, Polymer, 28, 1377 (1987)

[19] McKinley RM, Jahns HO, Harris WW, Greenkorn RA, AIChE J., 12(1), 17 (1966)

[20] Muhr AH, Blanshard JMV, Polymer, 23, 1012 (1982)

[21] Ogston AG, Preston BN, Wells JD, Proc. R. Soc. Lond. A, 333, 297 (1973)

[22] Patel DJ, Varishnay RN, "Basic Hemodynamics and Its Role in Disease Processes," University Park Press, Baltimore, MD, 183 (1980)

[23] Phillies GDJ, Gong J, Li L, Rau A, Zhang K, Yu LP, Rollings J, J. Phys. Chem., 93(16), 6219 (1989)

[24] Renkin EM, Curry FE, "Transport of Water and Solutes Across Capillary Endothelium," in Membrane Transport in Biology (Eds., Giebisch, G., Toteson, D.C. and Ussing, H.H.) Springer-Verlag, Berlin, Chapter 1 (1979)

[25] Tedgui A, Lever MJ, Am. J. Physiol., 247, H784 (1984)

[26] Tedgui A, Lever MJ, Circulation Res., 57(6), 856 (1985)

[27] Tedgui A, Lever MJ, Am. J. Physiol., 250, H1530 (1987)

[28] Truskey GA, Colton CK, Smith KA, "Quantitative Analysis of Protein Transport in the Arterial Wall," Structure and Function of the Circulation, Vol. 3, edited by Schwartz, C.J., Werthessen, J.T. and Wolf, S., Plenum Publishing Corporation, New York, N.Y., 287 (1981)

[29] Yuan F, Chien S, Weinbaum S, J. Biomech. Eng., in press (1991)