Abstract
A mathematical model has been developed to simulatein vivo transmural accumulation of an intravenously injected tracer in the aortic wall of experimental animals. Parameters have been included to represent the following processes that affect tracer distribution: permeation of the blood-tissue interface, diffusion through the layers of the artery wall,convective solute drag through the same, and degradation. Of particular interest for thein vivo situation situation is the inclusion of boundary conditions that account for the variation in the plasma concentration of injected tracer as a function of time. Two analytical solutions are presented. The first describes a system in which two boundaries must be delineated; it pertains if the tracer is allowed to circulate until it enters the avascular media of the artery wall both across its luminal boundary and from the capillaries in its outer layer. The second applies to shorter duration experiments in which entry across only the luminal boundary is considered. A limiting case of the solution for short circulation times is presented, compared with a previously published solution, and examined for its potential utility in parameter estimation. Because of its treatment of time-dependent boundary conditions, the model has unique application toin vivo experiments related to macromolecular transport in atherosclerosis that may otherwise elude proper interpretation.
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This work was supported by National Institutes of Health Grants HL-29582 and HL-07242.
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Saidel, G.M., Morris, E.D. & Chisolm, G.M. Transport of macromolecules in arterial wallin vivo: A mathematical model and analytical solutions. Bltn Mathcal Biology 49, 153–169 (1987). https://doi.org/10.1007/BF02459696
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DOI: https://doi.org/10.1007/BF02459696