Abstract
A mathematical model of diffusive transport of macromolecules across the arterial wall was developed in order to analyze the enhancement of molecular transport into the media in the presence of the endothelial injuries. The model is based on the continuum description of the distribution of macromolecules in the arterial wall with multiple injuries periodically dispersed on the endothelial surface. A boundary element method is successfully employed to model the problem geometry along with the relevant boundary conditions. The concentration and surface flux are computed for various physical conditions of the artery. Among other factors, the proper estimation of the mass transfer resistance, characterized by the Biot number, of the endothelial surface is crucial for the analysis. In addition the curvature effects are negligible when the vessel radius is larger than 10 times the wall thickness.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beskos, D. E.,“Boundary Element Methods in Mechanics”, North Holland, Amsterdam, 1987.
Cowper, G. R.,“Gaussian Quadrature Formulas for Triangles”,Int. J. Num. Meth. Eng.,114, 405 (1973).
Fung, Y. G,“Biodynamics-Circulation”, Springer Verlag, New York, 1984.
Getz, G. S.,“The Involvement of Lipoproteins in Atherogenesis”,Ann. N. Y. Acad. Sci.,598, 17 (1990).
Jawson, M. A. and Symm, G. T.,“Integral Equation Methods in Potential Theory and Electrostatics”, Academic Press, New York, 1977.
Kellogg, O. D.,“Foundations of Potential Theory”, Dover, New York, 1953.
Lever, M. J. and Jay, M. T.,“Transport of Materials through the Walls of Different Blood Vessels”, Biomechanical Transport Processes, Mosora, F., Caro, C. G., Krause, E., Schmid-Schönbein, H., Baquey, C. and Pelissier, R., Plenum, New York, 1990.
Nerem, R. M.,“Vascular Fluid Mechanics, the Arterial Wall, and Atherosclerosis”,J. Biomech. Eng.,114, 274 (1992).
Nir, A. and Pfeffer, R.,“Transport of Macromolecules Across Arterial Wall in the Presence of Local Endothelial Injury”,J. Theor. Biol.,81, 685 (1979).
Pfeffer, R., Ganatos, P., Nir, A. and Weinbaum, A.,“Diffusion of Macromolecules Across the Arterial Wall in the Presence of Multiple Endothelial Injuries”,J. Biomech. Eng.,103, 197 (1981).
Ross, R.,“The Pathogenesis of Atherosclerosis-An Update”,N. Engl. J. Med.,314, 488 (1986).
Tedgui, A. and Lever, M. J.,“Effect of Pressure and Intimai Damage on I-albumin and [14C]Sucrose Spaces in Aorta”,Am. J. Physiol.,253, H1530 (1987).
Tomlin, S. G.,“Vesicular Transport Across Endothelial Cells”,Biochim. Biophys. Acta,183, 559 (1969).
Weinbaum, S. and Caro, C. G.,“A Macromolecule Transport Model for the Arterial Wall and Endothelium Based on the Ultrastructural Specialization Observed in Electron Microscopic Studies”,/.Fluid Mech.,74, 611 (1976).
Weinbaum, S. and Chien, S.,“Lipid Transport Aspects of Atherogenesis”,J. Biomech. Eng.,115, 602 (1993).
Ylä-Herttuala, S.,“Biochemistry of the Arterial Wall in Developing Atherosclerosis”,Ann. N. Y. Acad. Sci.,623, 40 (1991).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kim, J.Y., Yoon, B.J. Diffusive transport of macromolecules across the arterial wall. Korean J. Chem. Eng. 14, 198–203 (1997). https://doi.org/10.1007/BF02706095
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02706095