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Am J Physiol Heart Circ Physiol 292: H2195-H2201, 2007. First published January 5, 2007; doi:10.1152/ajpheart.01294.2006
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Transient diffusion of albumin in aortic walls: effects of binding to medial elastin layers

Anita R. Goriely,1 Ann L. Baldwin,2 and Timothy W. Secomb1,2

1Microcirculation Division, Arizona Research Laboratories, and 2Department of Physiology, University of Arizona, Tucson, Arizona

Submitted 27 November 2006 ; accepted in final form 18 December 2006


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The goal of this study was to measure diffusive transport of albumin through artery walls experimentally and to analyze the results theoretically, taking into account the binding of albumin to elastic lamellae. Segments of rabbit aorta were placed in solutions of fluorescently labeled albumin for periods of 30, 60, 90, and 120 min, and the distributions of fluorescence intensity through the arterial media were observed. On average, intensity increased almost linearly with time. Bands of high intensity were observed corresponding to elastin layers within the media. The temporal and spatial variations of intensity were compared with predictions of theoretical models, including effects of albumin binding and hindered diffusion resulting from the complex wall structure. Based on these analyses, it was concluded that the spatial distribution of free albumin within the media equilibrated relatively rapidly, and that the observed linear increase in intensity reflected gradual accumulation of albumin bound to medial elastin layers. The results imply that previous theoretical analyses, in which binding was neglected, substantially underestimated albumin diffusivity in the aortic wall. With respect to stent-associated delivery of inhibitors of vascular cell proliferation, the results suggest that albumin might serve as an "affinity vehicle" for drug delivery to the aorta, by attaching the drug to an abundant component of the artery wall.

arteries; drug delivery; elastic lamellae; rabbit

TRANSPORT OF SOLUTES THROUGH artery walls is important, both in the development of arterial disease (3) and in its treatment, particularly with the use of drug-eluting stents (15). A major problem with intravascular drug delivery is the rapid convective washout of the drug from the site of pathology. For this reason, extracellular matrix-directed drug delivery is being exploited for retention of high concentrations of drug within the artery wall to inhibit smooth muscle cell proliferation. A therapeutic agent is bound to an "affinity vehicle" to attach the drug to an abundant component of the artery wall (21). In the case of elastic arteries, such as the aorta, an affinity vehicle that binds to the elastic lamellae might serve this function. One previous study (24) provides qualitative evidence that albumin binds to elastic lamellae. Recent studies have indicated that the internal structure of the artery wall and the binding of solutes to artery wall components may have large effects on solute transport (8, 11, 15). A number of studies have examined the transport of albumin through artery walls (1, 3, 11, 14, 23). However, in none of these studies was the effect of albumin binding to elastic lamellae considered in the transport modeling procedures.

To optimize the use of albumin as a carrier protein for arterial drug delivery (16), it is necessary to determine its transport properties through the arterial wall. The aortic tunica media is a complex structure, in which layers of smooth muscle cells are interspersed with multiple layers of elastin (elastic lamellae) (20). The innermost of these layers is termed the internal elastic lamina (IEL). This structure results in anisotropic diffusion characteristics (11). In the smooth muscle layers, many solutes are restricted to the interstitial spaces between muscle cells, which provide tortuous pathways for diffusion. Transmural diffusion requires that solutes cross the IEL and the elastin layers, which are largely impermeable to solutes except at pores (fenestrae). As a result, the effective diffusivity of a solute through the wall may be lower than its diffusivity in free solution. The distribution of albumin through the wall may also be affected by binding of molecules to wall components, as mentioned above. In the present study, the temporal and spatial variation of fluorescently labeled albumin diffusing through aortic walls was observed experimentally. The results were compared with the predictions of theoretical models, including the effects of albumin binding and the hindrance of diffusion resulting from the complex wall structure.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Animal preparation. Experiments were performed on seven male New Zealand White rabbits (2.0–2.5 kg) anesthetized with pentobarbital sodium (30 mg/kg iv). These experiments were conducted within animal welfare regulations and guidelines for the United States of America under Institutional Animal Care and Use Committee approval. The abdomen was opened by a midline incision, the aorta was exposed, and the fascia surrounding the vessel was dissected away down the length of the vessels from the diaphragm to the aortic bifurcation. All intervening arterial branches stemming from the aorta were ligated. Heparin (1,000 IU) was administered intravenously. A cannula, which was connected, via a stopcock, to a pressure transducer and a reservoir of 4% bovine serum albumin (BSA) and 0.03% Trypan blue dye, in physiologically buffered saline (PBS), pH 7.4, 37°C, placed 80 cm above the rabbit, was inserted retrograde into the aorta, close to the aortic bifurcation, and secured. A second ligature was tied tightly around the aorta, just below the diaphragm. In this way, pressure was continuously maintained within the arterial segment, thus avoiding aortic collapse and subsequent endothelial damage (2). The height of the reservoir was lowered to 50 cm, and a second cannula, attached to a reservoir containing PBS with 4% BSA, pH 7.4, was inserted in the aorta below the diaphragm, just distal to the tight ligature. The height of this reservoir was adjusted to 5 cm to allow the blood to be flushed from the segment in a retrograde direction. Inclusion of Trypan blue dye in the perfusate allowed a visual check that ensured that all branches had been ligated. When the inner surfaces of the vessels treated in this way were later examined with a light microscope, no staining of endothelial cell nuclei was seen, indicating that the endothelium was intact. The rabbit was then killed with an overdose of anesthetic. Finally, the first reservoir was lowered to 5 cm, both stopcocks were closed, and the aortic segment was carefully excised without allowing it to collapse.

For four animals, the pressurized segment was immersed in 0.5 mg/ml tetramethylrhodamine-labeled BSA (TRITC-BSA; Molecular Probes) and then divided into five annular portions, ~5 mm long, not including the cannulated ends of the vessel. With this procedure, the sections did not collapse when cut. These annuli were immersed in the solution for 30, 60, 90, and 120 min. For three animals, each segment was placed in a TRITC-BSA solution of a given concentration, ranging from 0 to 1 mg/ml for 2 h, to determine the relationship between medial fluorescence intensity and the concentration of TRITC-BSA in the solution. Before the experiments, each batch of TRITC-BSA was tested for free TRITC, up to 2 h after preparing the solutions, by passing the product through a filtration column (Sephadex G75). Spectrophotometric analysis of elution fractions failed to detect free TRITC activity, and therefore the TRITC-BSA was used as supplied. Rhodamine was used as a label because it has a maximum wavelength of 589 nm, and the background fluorescence emission of arterial tissue is in the fluoroscein wavelength (maximum 525 nm). These maxima are sufficiently separated to allow unequivocal label detection and quantitative comparison of fluorescence intensity. Sections from control segments of artery, not exposed to TRITC-BSA, were barely visible when viewed under epifluorescence microscopy with the filters set for rhodamine. When the filters were set for fluoroscein, bright lamellae were visible due to the autofluorescence. In experiments, both the intimal and the adventitial sides of the wall were exposed to the TRITC-BSA solution. For each artery, one segment was used for each exposure time. The arterial segments were then rinsed briefly in PBS, blotted, covered with cryoprotectant, and frozen for cryosectioning. Transverse sections 20 µm thick were cut, mounted on slides, and observed under brightfield and epifluorescence microscopy (Zeiss Axioplan with a 100-W mercury lamp).

Epifluorescence microscopy. Sections were examined using a 546-nm excitation filter and a 590-nm barrier filter, and images of the whole arterial thickness were recorded using a low light level integrating video camera (Optronix DEI 750) with pixel size 8.4 x 9.8 µm, and video recorder. The camera gain was adjusted to give an optimal image, and the same gain level was used throughout the experimental series. The optical resolution of the system was ~10 µm, as judged by the fact that adjacent individual elastic lamellae were easily discernible when viewing the arterial sections under epifluorescence microscopy.

Measurement of average medial fluorescence intensity. With the use of the free software program NIH Image, the average fluorescence intensity of the media of four sections from each segment was determined. In each case, the four readings were averaged to give the mean fluorescence intensity for that concentration. The same procedure was performed in three arteries.

Measurement of intensity profiles. At a randomly chosen part of the circumference of each section, five reference lines were defined (Fig. 1). Each line spanned the media from the endothelium to the outer edge of the last lamella, which was identified by a transition from compact tissue to less compact and less organized tissue. Intensity profiles were obtained on each reference line using NIH-Image software. Background intensity values for each image were obtained by averaging 10 sampling areas outside the region of the artery and were subtracted from the measured intensity values within the artery wall.


Figure 1
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  		Fig. 1. A: fluorescence image of aortic cross section after 30-min exposure to fluorescently labeled albumin. Elastic lamellae are visible as bright irregular bands. Intensity profiles were obtained along reference lines, marked 1–5. B: example of measured intensity profiles. One pixel = 0.78 µm.

 
Measured medial intensity profiles showed a high degree of spatial heterogeneity, resulting from large differences in intensity between the elastin layers and other structures (Fig. 1), and other irregularities. To detect overall regional variations in intensity, the values in each profile were averaged in four regions representing equal intervals through the medial thickness, with region 1 adjacent to the intimal side, regions 2 and 3 in the interior, and region 4 adjacent to the adventitial side. The 10 profiles obtained from the four different segments at each time point were then combined, giving equal weight to all measured intensity values. The results for the four bins were further averaged to show intensity changes with time of the entire media (regions 1–4), the intimal regions (regions 1 and 2), the adventitial regions (regions 3 and 4), the exterior regions (regions 1 and 4), and the interior regions (regions 2 and 3).

Geometry of fenestrae. To estimate the extent of fenestrae in elastin layers, 10 segments of rabbit aorta were obtained as described above, from two more rabbits, and prepared for electron microscopy. The segments were immersed in phosphate-buffered Karnovsky's fixative, pH 7.4, containing 3.5 g/100 ml dextran 70 to bring the colloid osmotic pressure to that of plasma (25 mmHg), as measured using a 4400 Colloid Osmometer (Wescor, Logan, UT) with a 30,000 molecular cutoff membrane (Amicon, Danvers, MA). After 1 h, each segment was washed in 0.15 M phosphate buffer, postfixed in 1% OsO4 for 2 h, dehydrated in alcohols, embedded in Spurrs resin, and sectioned for light and transmission electron microscopy (Phillip's 420). From 10 images, 32 sections of elastin layers with a total length of 888 µm were found to contain 32 gaps, with a total length of 74.3 µm. The fractional area represented by fenestrae was f = 0.0836, and the length density (number of gaps per unit length) in the sections was n = 0.0360 µm–1. Under the further assumption that the fenestrae are approximately circular, the radius and area of the fenestrae and the density per unit lamellar area were estimated as r = 2f/({pi}n) = 1.484 µm, A = 6.92 µm2, and N = f/({pi}r2) = 12,150 mm–2, respectively. For fenestrae arranged in a regular square array, the corresponding spacing between fenestrae would be 9.1 µm. Corresponding observations of 12 images containing 12 sections of IEL with a total length of 370 µm were found to contain five gaps with a total length of 7.08 µm, giving f = 0.0191, n = 0.0135 µm–1, r = 0.902 µm, A = 2.56 µm2, and N = 7,490 mm–2. A similar f in IEL (f = 0.018) was found in human cerebral arteries (5). The finding that fenestrae in the elastin layers within the media have larger diameters than those in the IEL is consistent with previous results (20), where the areas of fenestrae in porcine ascending aorta were ~2 µm2 in the IEL and mainly in the range of 4–14 µm2 in the other elastin layers. Potter and Roach (18) found lower estimates for fenestra size and density in the IEL of rabbit thoracic aorta, r = 0.67 µm and N = 2,300 mm–2. These values would imply a lower value of IEL permeability. Examination of sections from three segments of each vessel examined by electron microscopy provided further evidence that the endothelium had not been damaged during the experiment.

Analysis of diffusion and binding. The goal of the theoretical analysis was to deduce information about the transport and binding properties of albumin in the aortic wall from the measured intensity profiles. A mathematical model was developed based on the following assumptions. The observed fluorescence intensity (after correction for background intensity) is assumed to be proportional to the total concentration of labeled albumin, i.e., Ct(x,t) = Ci(x,t) + Cb(x,t), where x is distance from the intimal surface, t is time, and Ci and Cb are the concentrations of free and bound albumin, respectively. Experimental measurements (see GoFig. 3) support this assumption. Both concentrations are considered as local averages with respect to the heterogeneous internal wall structure. Transport of the free component is assumed to occur by diffusion, with an effective radial diffusivity Deff. As discussed below, Deff depends on the interstitial diffusivity of albumin and on the wall structure. The component of albumin bound to the elastin layers is considered not diffusible. A linear, reversible binding process is assumed with rate constants k for binding and k' for unbinding. According to these assumptions, Ci and Cb satisfy

Formula 1(1)

Formula 2(2)
The intimal layer of the wall, consisting of the endothelium, the basement membrane, and the IEL, is assumed to present a permeable barrier to albumin diffusion, with permeability Pi. Equating the flux through the intimal layer with the diffusive flux in the adjacent media gives

Formula 3(3)
when x = 0, where C0 is the concentration of fluorescent albumin in the bathing medium, fi is the volume fraction of interstitial space in the media, and Ci/fi is the albumin concentration within the interstitial spaces. Similarly, the external elastic lamina and the adventitia are assumed to form a barrier to albumin diffusion with permeability Pa, giving

Formula 4(4)
when x = w, where w is the thickness of the media. At time t = 0, the labeled concentrations Ci and Cb were assumed to be zero throughout the media.


Figure 2
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  		Fig. 2. A: schematic view of assumed repeating artery wall structure. Light gray, smooth muscle fibers; dark gray, fenestrated elastin layer; dashed line, repeating domain used for finite element calculations of diffusivity. B: domain used for finite element calculations, showing finite element mesh. Light gray and dark gray are as described in A. White, interstitial space.

 

Figure 3
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  		Fig. 3. Plot of mean medial fluorescence intensity of transverse aortic sections vs. concentration of tetramethylrhodamine-bovine serum albumin solution in which the aortic segments were placed for 2 h. Results are from one aorta (intensities of four sections averaged per data point). Error bars indicate SE.

 
Equation 1 was solved numerically for the region 0 ≤ x ≤ w, subject to the stated boundary conditions, using a finite element package (FlexPDE, PDE Solutions, Sunol, CA). In the arteries, the intensity values could not be calibrated in terms of absolute concentration values. Ci and Cb were, therefore, normalized with respect to the external concentration, so that C0 = 1 in the simulations. With this scaling, the value of the external concentration does not enter into the model, but an unknown parameter A, the ratio of fluorescent intensity (above baseline) to concentration in the wall, must be estimated. The deviation between the model predictions and the experimental data was determined by calculating the mean squared deviation, E, defined by

Formula 5(5)
where xi are the experimental intensity values, yi are the predicted concentrations (free plus bound), and n = 16 represents the number of data points (four time points for each of the four bins). The parameter A is estimated by the linear regression through the origin of xi on yi

Formula 6(6)

Effective diffusivity of albumin. The effective diffusivity of albumin in the media was estimated based on an analysis of diffusion through a structure consisting of alternating layers of smooth muscle cells and fenestrated elastin layers surrounded by interstitial space (Fig. 2A). An idealized regularly repeating structure is assumed, such that it is sufficient to analyze diffusion in a subdomain consisting of parts of three smooth muscle cells and one elastin layer (Fig. 2B). The smooth muscle and elastin layers are assumed to be impermeable to albumin, and diffusion occurs only through the interstitium, where the albumin diffusivity is Di. The effective diffusivity across a domain of thickness hd was estimated by solving the equation {nabla}2C = 0 in a domain consisting of one repeating element of the interstitial region, with no-flux boundary conditions on the surfaces of the fiber and the elastin layer, and C = h/fi and C = 0 on opposite boundaries of the domain (Fig. 2). The finite element package FlexPDE was used. The effective diffusivity was then estimated as Deff = <D {partial}C/{partial}{xi}>, where h is the width of the domain, {xi} is the coordinate in the direction of the gradient, and the angle brackets denote the value averaged over the domain, with D = Di in the interstitial region and D = 0 elsewhere. Effective diffusivities in the axial and circumferential directions were similarly estimated by imposing gradients of solute concentration in each direction and calculating the corresponding diffusive flux.

The dimensions of the assumed wall structure were based on experimental observations from several sources. The typical wall thickness of ~150 µm contained about 15 elastin layers (Fig. 1A), so the distance between layers was assumed to be 10 µm. The fraction of the total cross-sectional area occupied by elastin layers was observed to be ~0.4, so a layer thickness of 4 µm was assumed. Fenestrae were assumed to have a minimum radius of 1.48 µm and to be spaced in a square grid at a spacing of 9.1 µm, in accordance with the morphological observations reported above. The edges were assumed to be rounded, as shown in Fig. 2. Based on these estimates, the computational domain has dimensions of 4.55 x 9.1 x 5 µm. The radius (2.77 µm) and spacing (6.07 µm) of the smooth muscle cells were chosen so that the cells fit between the elastin layers and that the volume fraction of smooth muscle was 0.4 (13, 24). Under these assumptions, the volume fraction of elastin was reduced from the apparent value of 0.4 to 0.36 as a consequence of the volume occupied by the fenestrae within the elastin layers, and the remaining volume fraction occupied by interstitium was 0.24.

To estimate the effective permeability of the IEL, the finite element method described above was modified to simulate diffusion through an elastin layer of thickness of 4 µm containing a square array of fenestrae with radius of 0.902 µm and spacing of 11.55 µm, in accordance with the morphological observations. The diffusion of solute was simulated for a structure consisting of the elastin layer embedded in the midplane of a region of interstitial space with a total thickness of 8 µm, i.e., with 2 µm of interstitial space on each side of the IEL. This calculation includes effects of lateral diffusion of solute in the vicinity of fenestrae. The effective permeability of the IEL was then estimated by calculating the permeability of a thin uniform sheet that would give the same diffusive flux when embedded in the midplane of an 8-µm interstitial layer, for a given concentration gradient.

Reported estimates for the diffusivity Di of albumin in interstitial spaces of several tissues vary widely and are, in units of 10–7 cm2/s, 0.11–0.16 in granulation tissue (17), 0.69 in mesentery (9), 3.0 in tissue surrounding implanted capsules (10), 5.8 and 6.3 in normal and tumor tissue in window chambers (7), 6.6 in lung interstitium (19), and 1.2–9.1 in two tumor types (4). The lower values reported may correspond to the slow phase of a biphasic recovery of fluorescence in the fluorescence recovery after photobleaching technique. Also, these estimates reflect hindrance of diffusion to an unknown extent by other structures embedded in the interstitium of the tissues studied. For the present study, the assumed value of the diffusivity within the interstitial spaces of artery wall is, therefore, chosen near the upper end of the reported range, at Di = 5.8 x 10–7 cm2/s (7). In comparison, estimates of the free diffusivity of albumin in aqueous solution at 37°C are in the range of 6.3–12.7 x 10–7 cm2/s (9, 10, 17, 22).


   RESULTS
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Relationship between average medial fluorescence intensity and TRITC-BSA concentration. For all three arteries, a linear relationship was observed between average medial fluorescence intensity above baseline and the concentration of TRITC-BSA in the immersion solution. The results for one artery are shown in Fig. 3.

Estimates of effective diffusivity of interstitium and permeability of IEL. The estimated Deff, expressed relative to the free diffusivity of albumin, is shown in Fig. 4 as a function of the fractional area ff of fenestrae in the elastin layers. As expected, Deff is an increasing function of ff, and, when ff = 0.0836, Deff = 0.443 x Di = 2.6 x 10–7 cm2/s, the value assumed in the analysis below. Figure 4 also shows the corresponding effective diffusivities in the axial and circumferential directions. Diffusion in the axial and circumferential directions does not depend on the presence of fenestrae and is therefore almost independent of the fenestral area. For circumferential diffusion, Deff is almost equal to Di, because the channels for diffusion between the fibers and the elastin layers are of almost uniform width in the direction parallel to the fibers. Effective diffusivity in the axial direction is lower because solutes must pass through the narrowest part of the spaces between the fibers and the elastin layers. The consequences of such anisotropic diffusion for stent-based drug delivery have been considered by Hwang et al. (12). The effective permeability of the IEL was estimated to be 0.78 µm/s.


Figure 4
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  		Fig. 4. Predicted effective diffusivity (Deff) for artery wall structure shown in Fig. 2. Diffusivities in radial, axial, and circumferential directions are shown relative to interstitial diffusivity (Di), as a function of the fractional area of fenestrae. Symbols correspond to conditions used in subsequent simulations.

 
Observations of fluorescent intensity. The medial thickness at the observation points was 151 ± 34 µm (mean ± SD, N = 39). The variation with time and vessel wall region of measured fluorescent intensity is shown in Fig. 5. Overall average intensity (Fig. 5A) increases linearly with time up to 120 min. No consistent difference is seen between the intimal and adventitial regions (Fig. 5B). However, the increase in intensity is significantly slower in the interior regions than in the exterior regions (Fig. 5C). The data for the four regions of the wall (Fig. 5D) show corresponding trends.


Figure 5
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  		Fig. 5. Variation of average fluorescence intensity in media with time. Solid lines and symbols, experimental data; dashed lines, theoretical model; dotted lines (A and C only), theoretical model with 10-fold reduced interstitial diffusivity and binding rate; dash-dotted lines (A and C only), theoretical model with no binding and best fit value for interstitial diffusivity. A: entire media (regions 1–4). B: intimal regions (regions 1 and 2) and adventitial regions (regions 3 and 4). C: exterior regions (regions 1 and 4) and interior regions (regions 2 and 3). D: bins 1, 2, 3, and 4. The error bars show the SE based on the number of measured profiles for each data point, i.e., N = 40 in A, 20 in B and C, and 10 in D.

 
Predicted intensity profiles. According to Eq. 2, the bound concentration would eventually approach an equilibrium in which k'Cb = kCi. However, the observed intensities increased linearly, with no tendency to approach equilibrium (saturate) over the interval of observation (Fig. 5). This implies that the term k'B is negligible over this interval. Equations 1 and 2 were, therefore, solved with k' = 0. Furthermore, no significant differences between average intensities in the intimal and adventitial regions were seen (Fig. 5), implying that the intimal and adventitial layers do not present significantly different barriers to albumin entry into the media under the conditions of the experiments. This unexpected finding is discussed below. For the theoretical analysis, it was, therefore, assumed that Pa = Pi.

Figure 6 shows predicted profiles of concentration within the media for two cases, Pi = 0.78 and 0.078 µm/s. In the former case, the IEL is considered to form the only barrier to albumin diffusion. This represents an upper bound on Pi. In the latter case, the permeability is reduced by a factor of 10 to represent the effect of additional resistance to albumin diffusion resulting from the endothelium and/or the basement membrane, or from a less permeable IEL (18). In each case, the value of the remaining unknown parameter k was chosen to minimize the deviation between the observed and predicted average intensities for the exterior and interior regions, as shown in Fig. 5C. The resulting estimate was k = 0.00785 s–1, independent of the value of Pi. The estimate is directly proportional to the assumed Deff, which was estimated as 2.6 x 10–7 cm2/s, as already described.


Figure 6
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  		Fig. 6. Predicted variation of interstitial and bound concentrations of labeled albumin with position in artery wall, after indicated exposure times. A and B: interstitial component. C and D: free component. Assumed permeability of endothelial and adventitial surfaces: Pi = 0.78 µm/s (A and C); Pi = 0.078 µm/s (B and D). Other parameter values are given in text.

 
Predicted interstitial concentration levels approach a steady-state profile within ~5 min (Fig. 6, A and B), in which inward diffusion from the boundaries is balanced by uptake resulting from binding. Bound albumin (Fig. 6, C and D) increases approximately linearly with time and is in proportion to the interstitial concentrations. The predicted concentration levels were lower when the smaller Pi value was used (Fig. 6, B and D), but both cases yielded equally good fits to the experimental data, with differing values of the ratio A of intensity to concentration. Therefore, it was not possible to estimate actual permeability values Pa and Pi from the available data.

Comparison of experimental and theoretical results. The observed time-dependent increases in intensities in the four regions within the media are compared in Fig. 5, with model predictions based on the fitted parameter values given above, with Pi = 0.78 µm/s. Predictions with Pi = 0.078 µm/s were virtually identical. Because it is assumed that Pa = Pi, the predicted intensities are equal in regions 1 and 4, and in regions 2 and 3. The model predictions agree with the observations within experimental uncertainty.

Effects of lower assumed interstitial diffusivity and binding on model predictions. Estimates of the diffusivity Di of albumin in interstitial spaces vary widely. To explore the sensitivity of the results to this parameter, simulations were performed with a 10-fold lower value, Di = 5.8 x 10–8 cm2/s. The corresponding binding rate that minimized the deviation between the observed and predicted average intensities was k = 7.92 x 10–4 s–1. As shown in Fig. 5, the root mean square deviation between observed and predicted values was substantially increased (more than doubled) under these conditions. Further simulations were performed for the case in which no binding is present, i.e., k = 0. The interstitial diffusivity was then chosen to minimize the deviation between observed and predicted results, giving Di = 1.06 x 10–8 cm2/s. The root mean square deviation between observed and predicted values increased sevenfold under these conditions (Fig. 5, A and C). These results show that the inclusion of effects of binding and the assumption of a relatively high interstitial diffusivity are needed to obtain good agreement between model predictions and observations.


   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The present experimental and theoretical results imply that the transport of albumin through the wall of the aorta is strongly affected by binding of albumin to elastin layers within the wall. Profiles of fluorescence show strong multiple peaks corresponding to these layers (Fig. 1). Such binding also provides an explanation for the observed linear increase in fluorescence intensity with time (Fig. 5). In the absence of binding, albumin would diffuse through the media relatively rapidly, reaching an equilibrium level, as shown by the results for interstitial albumin concentration (Fig. 6, A and B). If a much lower diffusivity were assumed, the buildup in intensity would be slower, but would still eventually reach saturation. In that case, moreover, a significant time delay would be expected before the appearance of appreciable intensity in the interior regions, but such behavior is not observed (Fig. 5C). However, the continuous binding of albumin to elastin layers results in a linear increase in the total fluorescence intensity, after the distribution of unbound albumin has come to equilibrium. The predictions of the theoretical model, which are based on independent estimates of albumin diffusivity and include effects of binding, agree well with the observed buildup of intensity.

In two previous studies, observations of albumin distribution through the rabbit thoracic aorta wall were used to deduce estimates of the effective diffusivity of albumin, without taking into account the effects of binding. The resulting estimates were 7 x 10–9 cm/s2 (3) and 5.6 x 10–9 cm/s2 (1), similar to the estimate found here for best fit with the data when binding was neglected (Di = 1.06 x 10–8 cm2/s). These estimates are much lower than the free diffusivity of albumin and lead to large deviations between model predictions and the experimental data obtained here. In the presence of binding, "apparent" values of diffusivity deduced from the observed buildup of concentration without considering binding may thus greatly underestimate its actual value.

A notable feature of the observations is that the average profiles of intensity are almost symmetrical with respect to the intimal and adventitial boundaries of the media. In the model, it was, therefore, assumed that Pa = Pi, since assuming unequal values for these parameters gives asymmetric predicted profiles. However, the physical basis for this finding has not been established. The intimal surface, consisting of endothelial cells, basement membrane, and IEL, is generally assumed to represent a significant barrier to protein diffusion. If this is the case, then a similar barrier must be present on the adventitial boundary. The adventitia itself is a relatively diffuse structure and seems unlikely to present a major barrier. However, an external elastic lamina is observed at the outer edge of the media. Little information is available about the properties of this layer, but the present results suggest that it may represent a significant barrier to albumin diffusion.

In a previous study (6), heterogeneities were demonstrated in the binding of fluorescent albumin to elastin across the vascular wall. The transmural distribution of albumin across the arterial elastin network after 4-h incubation was qualitatively similar to that observed in the present study: the relative fluorescence intensities of the intima/inner media, mid-media, and outer media being 7.8, 3.3, and 6.6, respectively. While those authors suggested that nonuniform binding resulted from heterogeneities in the structure or physicochemical properties of the elastin network, the present results provide an alternative explanation for their observations.

Care was taken to preserve the endothelial layer in the present experiments. However, the presence of a relatively small number of damaged endothelial cells may greatly increase the effective permeability of the endothelium in these experiments. For example, open junctions around endothelial cells, occupying <10–5 of the en face area, may cause a 50–100% increase in permeability to macromolecules (25). Albumin entering the media at such discrete locations may diffuse laterally throughout the wall. As suggested by our results (Fig. 4) and by other studies (11), the lateral diffusivity in the media is higher than the radial diffusivity.

No evidence of saturation was seen in the increase in fluorescent intensity with exposure times up to 2 h. Eventually, saturation of the available binding sites for albumin within the media would be expected. For instance, the data of Bratzler et al. (3) suggest near saturation of total albumin concentration at ~4 h. The time to saturation would decrease with increasing concentration of labeled albumin. The concentration used in the present studies (0.05 mg/ml) may have been too low to show effects of saturation within 2 h.

In these experiments, no hydrostatic pressure was imposed across the artery wall, and transport was by diffusion alone. However, the results can be used to estimate the Peclet number (Pe), which gives the relative importance of convection and diffusion for albumin transport, under in vivo conditions where a transmural pressure difference is present. The hydraulic conductance of the rabbit thoracic aorta is ~6 x 10–8 cm·s–1·mmHg–1 at a pressure of 70 mmHg (1). The resulting filtration velocity is u = 4.2 x 10–6 cm/s, and Pe = wu/Deff = 0.24. According to this estimate, diffusion is the dominant mechanism for albumin transport, but convection may have significant effects. This calculation assumes that the diffusivity in the wall is not affected by transmural pressure. Stretching of the wall may increase the size of pores in the IEL and elastin layers, which would increase the effective diffusivity and reduce the Pe. Conversely, a lower interstitial diffusivity Di would increase the Pe. However, as already discussed, our results do not support much lower values of Di.

Diffusion of albumin through artery walls is of interest for several applications, including as an "affinity vehicle" for stent-based drug delivery. The present results show that the aortic elastic lamellae provide a relatively high-capacity support for accumulating high concentrations of albumin and, potentially, of effector drugs bound to the albumin. In addition, the results indicate the importance of taking binding characteristics into account when analyzing the transport of solutes in artery walls. Knowledge of the different interactions that solutes have with the various components of artery walls is necessary to accurately predict their rate of transport through the media.


   ACKNOWLEDGMENTS
 
This work was supported by National Heart, Lung, and Blood Institute Grant HL07249 and the American Heart Association.


   FOOTNOTES
 

Address for reprint requests and other correspondence: T. W. Secomb, Dept. of Physiology, Univ. of Arizona, Tucson, AZ 85724-5051 (e-mail: secomb{at}u.arizona.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
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