Abstract
Experimental data of the radial incorporation of labeled cholesterol [14C-4] into the artery wall is regressed against a mathematical model that predicts macromolecular transport in this biological system. Data is obtained using excised canine carotid arteries that are perfusedin vitro under pulsatile hemodynamic conditions for 2 hr. Vessels are exposed to either normotensive hemodynamics, hypertensive hemodynamics, or simulations in which the rate of flow or vessel compliance is deliberately altered. Several arteries are studied under normotensive conditions following balloon catheter deendothelialization. Transmural concentration profiles of [14C-4] activity are determined by microcryotomy of longitudinal sections of perfused vessels. Nonlinear Marquardt regression on 12 experimental cases yields parameter estimates of effective diffusivity,D and solute filtration velocity,V. Results of this experimental investigation support our hypothesis that hemodynamics and the endothelial lining influence wall flux in intact vessels. Exposure to altered (vs normotensive) hemodynamics is associated with increased incorporation of labeled cholesterol. A similar observation is made for deendothelialized vessels (e.g. a greater accumulation of label and a rise in convective flux). Based upon our companion measurements of vessel wall forces and endothelial cellular morphology accompanying hemodynamic simulations, we suggest that hemodynamically induced alterations to endothelial structures lead to the increased permeability, convection and incorporation that we observe in this work.
Similar content being viewed by others
Literature
Barja, F., M. Blatter, R. W. James, D. Pometta and G. Gabbiani. 1989. Actin stress fiber content of regenerated endothelial cells correlate with intramural retention of intermediate plus low density lipoproteins in rat aorta after balloon injury.Atherosclerosis 76, 181–191.
Brant, A. M., J. F. Chmielewski, T. K. Hung and H. S. Borovetz. 1986. Simulationin vitro of pulsatile vascular hemodynamics using a CAD/CAM designed cam disc and roller follower.Artif. Organs 10, 419–421.
Brant, A. M., M. F. Teodori, R. L. Kormos and H. S. Borovetz. 1987. Effect of variations in pressure and flow on the geometry of isolated canine carotid arteries.J. Biomechanics 20, 831–838.
Brant, A. M., S. S. Shah, V. G. J. Rodgers, J. Hoffmeister, I. M. Herman, R. L. Kormos and H. S. Borovetz. 1988. Biomechanics of the arterial wall under simulated flow conditions.J. Biomechanics 21, 107–113.
Brant, A. M. and H. S. Borovetz. 1987. Hemodynamic and mass transfer aspects of arterial disese. InArtificial Organs, J. D. Andradeet al. (eds.) New York: VCH.
Bratzler, R. L., C. K. Colton and K. A. Smith. 1977. Endothelium and permeability: theoretical models for transport of low-density lipoproteins in the arterial wall. InAtherosclerosis, G. W. Manning and M. Daria-Haust (eds) pp. 943–951. New York, Plenum.
Bratzler, R. L. 1975. Low density lipoprotein transport and metabolism in the arterial wall. Ph.D. thesis, Massachusetts Institute of Technology.
Burton, A. C. 1954. Relation of structure to function of the tissues of the wall of blood vessels.Physiol. Rev. 34, 619–642.
Carew, T. E., R. C. Pittman, E. R. Marchand and D. Steinberg. 1984. Measurementin vivo of irreversible degradation of low density lipoprotein in the rabbit aorta: predominance of intimal degradation.Arteriosclerosis 4, 214–224.
Carnahan, B., H. A. Luther and J. O. Wilkes. 1969.Applied Numerical Methods. New York: Wiley.
Caro, C. G., M. J. Lever, Z. Laver-Rudich, F. Meyer, N. Liron, W. Ebel, K. H. Parker and C. P. Winlove. 1980. Net albumin transport across the wall of the rabbit common carotid artery perfusedin situ.Atherosclerosis 37, 497–511.
Colton C. K., R. L. Bratzler, K. A. Smith and R. S. Lees 1979. Transport of protein and lipid into the arterial wall.Adv. Exp. Med. Biol. 115, 299–352.
Curmi, P. A. and A. Tedgui. 1989. Effect of transmural pressure on the transport and distribution of low density lipoproteins in the arterial wall.C. r. Acad. Sci. (III) 308 149–154.
Frank, P. M. 1978.Introduction to System Sensitivity Theory. New York: Academic Press.
Friedman, M. H., G. M. Hutchins, C. B. Bargeron, O. J. Deters and F. M. Mark. 1981. Correlation between intimal thickness and fluid shear in human arteries.Atherosclerosis 39, 425–436.
Fry, D. L. 1985. Mathematical model of arterial transmural transport.Am. J. Physiol. 248, H240-H263.
Fry, D. L. 1987. Mass transport, atherogenesis and risk.Arteriosclerosis,7, 88–100.
Glagov, S., C. Zarins, D. P. Giddens and D. N. Ku. 1988. Hemodynamics and atherosclerosis.Arch. Pathol. Lab. Med. 112, 1018–1031.
Herman, I. M., A. M. Brant, V. S. Warty, J. Bonaccoroso, E. C. Klein, R. L. Kormos and H. S. Borovetz. 1987. Hemodynamics and the vascular endothelial cytoskeleton.J. Cell Biology 105, 291–302.
Johnson, G. A., T. K. Hung, A. M. Brant and H. S. Borovetz. 1989. Experimental determination of wall shear rate in canine carotid arteries perfusedin vitro.J. Biomechanics 22, 1141–1150.
Ku, D. N., D. P. Giddens, C. K. Zarins and S. Glagov. 1985. Pulsatile flow and atherosclerosis in the human carotid bifurcation.Arteriosclerosis,5, 293–302.
Marquardt, D. W. 1963. An algorithm for least-squared estimation of non-linear parameters.SIAM J. 11, 431–440.
Melissinos, A. C. 1966.Experiments in Modern Physics. New York: Academic Press.
Nerem, R. M. and M. J. Levesque. 1987. Hemodynamics and the arterial wall. InVascular Diseases. New York: Grune and Stratton.
Neumann, S. J. 1987. Application of a mathematical model to experimental data of arterial wall transport. Master's thesis, Carnegie Mellon University.
Pittman, R. C., T. E. Carew, C. K. Glass, S. R. Green, C. A. Taylor and A. D. Attie. 1983. A radioiodinated intracellularly trapped ligand for determining the sites of plasma protein degradationin vivo.Biochemistry J. 212, 791–800.
Ross, R. 1986. The pathogenesis of atherosclerosis—an update.New Engl. J. Med. 314, 488–500.
Saidel, G. M., E. D. Morris and G. M. Chisolm. 1987. Transport of macromolecules in arterial wallin vivo: a mathematical model and analytical solutions.Bull. math. Biol. 49, 153–169.
Sevick, E. M. 1985. Mathematical model of arterial macromolecular transport: application to experimental studies of cholesterol uptake. Master's thesis, University of Pittsburgh.
Smith, E. B. and R. Slater. 1970. The chemical and immunological assay of low density lipoproteins extracted from human thoracic aortic intima.Atherosclerosis 11, 417–438.
Smith, E. B. and E. M. Staples. 1982. Plasma protein concentrations in interstitial fluid from human aortas.Proc. R. Soc. Lond. B217, 59–75.
Tedgui, A. and M. J. Lever. 1985. The interaction of convection and diffusion in the transport of131I-albumin within the rabbit thoracic aorta.Circ. Res. 57, 856–863.
Tompkins, R. G., J. J. Schnitzer, M. L. Yarmush, C. K. Colton, K. A. Smith and M. B. Stemerman. 1989. Low density lipoprotein transport in the blood vessel walls of the squirrel monkey.Am. J. Physiol. 257 (Heart Circ. Physiol.,26) H452-H464.
Truskey, G. A., C. K. Colton and K. A. Smith. 1981. Quantitative analysis of protein transport in the arterial wall. InStructure and Function of the Circulation, Vol. 3, C. J. Schwartz, N. T. Werthessen and S. Wolf (eds), pp. 287–355. New York: Plenum.
Tzeghai, G., P. Ganatos, R. Pfeffer, S. Weinbaum and A. Nir. 1986. A theoretical model to study the effect of convection and leaky junctions on macromolecule transport in artery walls.J. theor. Biol. 121, 141–162.
Weinbaum, S., G. Tzeghai, P. Ganatos, R. Pfeffer and S. Chien. 1985. Effect of cell turnover and leaky junctions on arterial macromolecular transport.Am. J. Physiol. 248, H945-H960.
Wen G. B., S. Weinbaum, P. Ganatos, R. Pfeffer and S. Chien. 1988. On the time dependent diffusion of macromolecules through transient open junctions and their sub-endothelial spread. 2. Long time model for interaction between leakage sites.J. theor. Biol. 135, 219–253.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Neumann, S.J., Berceli, S.A., Sevick, E.M. et al. Experimental determination and mathematical model of the transient incorporation of cholesterol in the arterial wall. Bltn Mathcal Biology 52, 711–732 (1990). https://doi.org/10.1007/BF02460805
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02460805