A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta

Abstract

The pulmonary artery (PA) wall, which has much higher hydraulic conductivity and albumin void space and approximately one-sixth the normal transmural pressure of systemic arteries (e.g, aorta, carotid arteries), is rarely atherosclerotic, except under pulmonary hypertension. This study constructs a detailed, two-dimensional, wall-structure-based filtration and macromolecular transport model for the PA to investigate differences in prelesion transport processes between the disease-susceptible aorta and the relatively resistant PA. The PA and aorta models are similar in wall structure, but very different in parameter values, many of which have been measured (and therefore modified) since the original aorta model of Huang et al. (23). Both PA and aortic model simulations fit experimental data on transwall LDL concentration profiles and on the growth of isolated endothelial (horseradish peroxidase) tracer spots with circulation time very well. They reveal that lipid entering the aorta attains a much higher intima than media concentration but distributes better between these regions in the PA than aorta and that tracer in both regions contributes to observed tracer spots. Solutions show why both the overall transmural water flow and spot growth rates are similar in these vessels despite very different material transport parameters. Since early lipid accumulation occurs in the subendothelial intima and since (matrix binding) reaction kinetics depend on reactant concentrations, the lower intima lipid concentrations in the PA vs. aorta likely lead to slower accumulation of bound lipid in the PA. These findings may be relevant to understanding the different atherosusceptibilities of these vessels.

Fig. 1.

Schematic of the periodic wall unit in terms of a cartoon of the physiological wall structure with nondimensional variables (A) and in terms of an idealized mathematical diagram with dimensional variables (B) for the filtration and macromolecular transport models in the arterial wall. C: finer scale model of Ref. of the leaky cleft for our equations (Eq. A17 and Eq. A18); Eq. A18 enters our problem as a boundary condition at the endothelial surface. EC, endothelial cell; SI, subendothelial intima; IEL, internal elastic lamina; SMC, smooth muscle cell; EL, elastic lamellae. For all figures, see Table 2 for definitions of parameters.

Fig. 2.

Nondimensional tissue low-density lipoprotein (LDL) concentration profile for the pulmonary artery. Normal distance is in the direction perpendicular to the endothelial surface. Discrete points are experimental data from Ref. . Continuous curve is the best-fit result with the one-dimensional model, where the segment with high values near z = 0 corresponds to the subendothelial intima.

Fig. 3.

Nondimensional pressure in the subendothelial intima (P_SI) at z = 0 and at the interface of the IEL and media (P_Im), and the normal velocity (W*_I) across the IEL for the pulmonary artery (PA, solid lines) and the aorta (dash lines) as functions of radial distance r from the center of the leaky cell. Radial distance r* in this and subsequent plots is normalized by the radius of an endothelial cell (R*₁; thus the leaky junction is at r*/R*₁ = 1), as opposed to r: = r*/L*_p2 (Eq. A1), to focus on the junction region. Pressure is normalized by the transmural pressure drop (ΔP*), 100 mmHg for the aorta and 16 mmHg for the PA (45).

Fig. 4.

Local Peclet number in the radial direction in the SI for the PA (solid line) and the aorta (dash line).

Fig. 5.

Concentration distributions of horseradish peroxidase (HRP) at 4-min circulation in the SI (C_SI) at z = 0 and at the IEL-media interface (C_Im) for the PA and the aorta. The radial distance (r*) is normalized by the radius (R*₁) of an endothelial cell, and thus the leaky junction is at r*/R*₁ = 1.

Fig. 6.

Theoretical predictions from current theory vs. the data of Ref. for LDL vs. z for curves from normal (A and B) and enhanced (C) permeability regions. C: assumed endothelial denudation and blood in vessel during early fixation to obtain such high LDL concentration at lumen boundary. Calculation scenarios described in text.

Fig. 7.

Evolution with HRP circulation time of SI tissue-to-plasma HRP concentration distribution for the PA (solid lines) and aorta (dash lines). Four curves for the each vessel represent (left to right) 30-, 60-, 120-, and 240-s circulation. Best data fits obtain for time lags t₀=15 sec (PA) and 25 s (aorta) for HRP to travel from the femoral vein to the vessel. Visibility threshold HRP concentrations, chosen as in the text, are 0.02 (PA) and 0.05 (aorta).

Fig. 8.

HRP spot growth at 4 min circulation in the PA and aorta. Experimental results: discrete points from Refs. and 46; theoretical predictions: continuous curves. Curves 1 and 2: aorta; curves 3, 4, and 5: PA. Curves 1 and 3 from SI HRP concentrations; curves 2, 4, and 5 from integration of HRP concentrations across vessel wall. Curves 2 and 4 use Int_th = 1 × 10⁻⁵ cm; curve 5 uses Int_th = 1.2 × 10⁻⁵ cm. Curve 1 uses C_th = 0.05; curve 3 uses C_th = 0.02.

Fig. 9.

Radial distribution of A(r*/R*₁;λ)/ε(λ) = ∫0LC(r*/R*₁;z)dz, the integral of the HRP concentration dz across the SI and the media. Curves (solid line, PA; dashed line, aorta) from left to right are at HRP circulation times 30, 60, 120, and 240 s. Horizontal threshold, Int_th, = 1 × 10⁻⁵ cm of A/ε intersects the concentration profiles to give the HRP spot edge vs. circulation time.

Fig. 10.

Distribution of LDL concentration (C) in the subendothelial intima, normalized by the plasma LDL concentration, as a function of r at 10 min LDL circulation time for the normotensive aorta (solid line) and the PA with normal (16 mmHg, dashed line) and elevated (40 mmHg, dotted line) transmural pressure. Parameters: L*₁ = 1 μm (23); media LDL distribution volumes γ₂ estimated from HRP values and molecular radii: 0.025 (aorta), 0.074 (PA); PA parameters at 16 and 40 mmHg same except for L*_pt(L*_pnj) = 1.60 × 10⁻⁷ (3.35 × 10⁻⁷) cm·s⁻¹·mmHg⁻¹ at ΔP* = 40 mmHg (45). L*_pnj is 41% lower than at 16 mmHg (24, 45).

Fig. 11.

Short-term growth of SI total liposome mass, normalized by the ratio of the rate constant for lipid binding to extracellular matrix to that for the (assumed j-independent) growth of a liposome comprised of j LDL particles by the appending of a single unbound particle. Model includes these 2 kinetic processes plus the formation of liposomes comprised of j LDL particles by the merging of particles of size i (i < j) with those of size j-i (for details of the equations and calculation methods, see Refs. , , and .