Macromolecular transport in heart valves. II. Theoretical models

Abstract

This paper proposes a new, two-dimensional convection-diffusion model for macromolecular transport in heart valves based on horseradish peroxidase (HRP) experiments on rats presented in the first of the papers in this series (Part I; Zeng Z, Yin Y, Huang AL, Jan KM, Rumschitzki DS. Am J Physiol Heart Circ Physiol 292: H2664-H2670, 2007). Experiments require two valvular intimae, one underneath each endothelium. Tompkins et al. (Tompkins RG, Schnitzer JJ, Yarmush ML. Circ Res 64: 1213-1223, 1989) found large variations in shape and magnitude in transvalvular (125)I-labeled low-density lipoprotein (LDL) profiles from identical experiments on four squirrel monkeys. Their one-dimensional, uniform-medium diffusion-only model fit three parameters independently for each profile; data variability resulted in large parameter spreads. Our theory aims to explain their data with one parameter set. It uses measured parameters and some aortic values but fits the endothelial mass transfer coefficient (k(a)=k(v)=1.63 x 10(-8) cm/s, where subscripts a and v indicate aortic aspect and ventricular aspect, respectively) and middle layer permeability (K(p(2))=2.28 x 10(-16)cm(2)) and LDL diffusion coefficient [D(2)(LDL)=5.93 x 10(-9) cm(2)/s], using one of Tompkins et al.'s profiles, and fixes them throughout. It accurately predicts Part I's rapid localized HRP leakage spot growth rate in rat leaflets that results from the intima's much sparser structure, dictating its far larger transport parameters [K(p(1))= 1.10 x 10(-12)cm(2), D(1)(LDL/HRP)=1.02/4.09 x 10(-7)cm(2)/s] than the middle layer. This contrasts with large arteries with similarly large HRP spots, since the valve has no internal elastic lamina. The model quantitatively explains all of Tompkins et al.'s monkey profiles with these same parameters. Different numbers and locations of isolated macromolecular leaks on both aspects and different section-leak(s) distances yield all profiles.