Modeling the Adaptive Permeability Response of Porcine Iliac Arteries to Acute Changes in Mural Shear A. L. HAZEL, 1 D. M. GRZYBOWSKI, 2 and M. H. FRIEDMAN 3 1 Department of Mathematics, University of Manchester, Manchester, U.K.; 2 Biomedial Engineering Center, The Ohio State University, Columbus, OH; and 3 Department of Biomedical Engineering, Duke University, Durham, NC (Received 28 January 2002; accepted 12 December 2002) Abstract—The hypothesis that much of the uptake of macro- molecules by the vascular wall takes place while the endothe- lial lining is adapting to changes in its hemodynamic environ- ment is being tested by a series of in vivo measurements of the uptake of Evans-blue-dye-labeled albumin by porcine iliac ar- teries subjected to acute changes in blood flow. The uptake data are interpreted through an ad hoc model of the dynamic per- meability response that is proposed to accompany alterations in mural shear. The model is able to correlate, with a single set of parameters, the vascular response to a variety of experimen- tal protocols, including sustained step increases and decreases in shear, and alternations in shear of various periods. The best-fit parameters of the model suggest that the adaptive re- sponse to an increase in shear proceeds with a latency of ;1.5 min and a time constant of ;90 min that is substantially shorter than the response to a decrease in shear. © 2003 Bio- medical Engineering Society. @DOI: 10.1114/1.1560633# Keywords—Atherogenesis, Hemodynamics, Endothelium, Wall shear stress. INTRODUCTION The transport of macromolecules across the arterial wall and the subendothelial accumulation of these spe- cies are important processes in atherogenesis and athero- sclerotic development. Despite a vast body of research in this area, the mechanisms and dynamics of such trans- port are still incompletely understood. An intriguing fea- ture of the process is that transport appears to be en- hanced by changes in the direction and magnitude of the shear stress exerted upon the wall by the movement of the blood. 2 This response is a transient effect, however, and it has been shown both in cell culture 1 and in vivo 4 that the increase in permeability decays if the altered shear environment is maintained. This suggests that the endothelium eventually adapts to its new external conditions. Friedman and Fry 2 presented a simple a priori math- ematical model to describe the permeability and uptake transients that might occur during such endothelial adap- tation to a new shear environment. The model was ini- tially tested by comparing its predictions with experi- ments in which porcine iliac arteries were subjected in vivo to a shear stress environment described by a square wave, 3 where the period of the square wave was varied from 1 to 180 min. The rate of uptake of Evans-blue- dye-labeled albumin by the artery increased with the period of the square wave, a result generally predicted by the model. The model predictions agreed well with the experimental data at intermediate periods of alternation, but there were noticeable differences at low and high periods. These discrepancies might reflect different en- dothelial responses to increases and decreases in shear. Such a possibility was not considered in the initial model, where the parameters of the response were as- sumed to be the same for any change in shear. Remuzzi et al. 15 conducted in vitro studies of the re- laxation of bovine aortic endothelial cells after cessation of a previously imposed shear. They found that the mor- phology of the cells was initially unchanged during the 3– 4 h period after the step decrease in shear. After this delay, however, the cells began to relax, reaching a con- figuration comparable to unstressed control cells after 72 h. In contrast, Levesque and Nerem 13 reported that en- dothelial cell morphology changes noticeably 3– 4 h after a step increase in shear in vitro. This evidence indicates that the responses of endothelial cells to an increase in shear are different from those that occur in response to a decrease. Motivated by these considerations, we now relax the assumption that the response to changes in shear is in- dependent of sign. Two additional experimental protocols are introduced to characterize the separate responses to increases and decreases in shear. The experimental data are then used to reexamine the experimental results in Friedman et al. 3 It is found that a single set of model parameters can capture the responses to all three experi- mental protocols and, indeed, provides a better fit to the previous data. Address correspondence to M. H. Friedman, Department of Bio- medical Engineering, Box 90281, Duke University, Durham, NC 27708. Electronic mail: mhfriedm@duke.edu Annals of Biomedical Engineering, Vol. 31, pp. 412–419, 2003 0090-6964/2003/31~4!/412/8/$20.00 Printed in the USA. All rights reserved. Copyright © 2003 Biomedical Engineering Society 412