A Fiber Matrix Model for the Growth of Macromolecular Leakage Spots in the Arterial Intima

Abstract

A new model is presented for the growth of cellular level macromolecular leakage spots in the arterial intima. The theoretical approach differs from the recent study by Yuan et al. [19] in that it directly models and calculates the intimal transport parameters based on Frank and Fogelman’s [22] ultrastructural observations of the extracellular subendothelial proteoglycan matrix that their rapid freeze etching technique preserves (see Addendum). Using a heterogeneous fiber matrix theory, which includes proteoglycan and collagen components, the model predicts that the Darcy permeability Kp and macromolecular diffusivity D of the subendothelial intima is two orders of magnitude larger than the corresponding values measured in the media, and supports the observations in Lark et al. [24] that the proteoglycan structure of the intima differs greatly from that of the media. Numerical results show that convection parallel to the endothelium is a very significant transport mechanism for macromolecules in the intima in a large region of roughly 200 μm diameter surrounding the leaky cleft. The predictions of the new model for the early-time spread of the advancing convective-diffusive front from the leakage spots in the intima are in close agreement with our experimental measurements for the growth of HRP spots in [20]. The regions of high concentration surrounding the leaky cell, however, are much more limited and cover an area that is typically equivalent to 20 cells. This prediction is consistent with the recent measurements of Truskey et al. for LDL spot size in rabbit aorta [21] and the hypothesis advanced in [19] that there is a colocalization of subendothelial liposome growth and cellular level leakage. Finally, comparison of predicted and experimentally-measured average LDL concentration in leakage spots strongly suggests that there is significant local molecular sieving at the interface between the fenestral openings in the internal elastic lamina and the media.