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Am J Physiol Heart Circ Physiol 293: H126-H132, 2007. First published February 23, 2007; doi:10.1152/ajpheart.01188.2006
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In vitro study of LDL transport under pressurized (convective) conditions

Limary M. Cancel,1 Andrew Fitting,2 and John M. Tarbell1

1Department of Biomedical Engineering, The City College of New York, The City University of New York, New York, NY; and 2Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania

Submitted 30 October 2006 ; accepted in final form 21 February 2007


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
It is difficult to assess the transport pathways that carry low-density lipoprotein (LDL) into the artery wall in vivo, and there has been no previous in vitro study that has examined transendothelial transport under physiologically relevant pressurized (convective) conditions. Therefore, we measured water, albumin, and LDL fluxes across bovine aortic endothelial cell (BAEC) monolayers in vitro and determined the relative contributions of vesicles, paracellular transport through "breaks" in the tight junction, and "leaky" junctions associated with dying or dividing cells. Our results show that leaky junctions are the dominant pathway for LDL transport (>90%) under convective conditions and that albumin also has a significant component of transport through leaky junctions (44%). Transcellular transport of LDL by receptor-mediated processes makes a minor contribution (<10%) to overall transport under convective conditions.

low-density lipoprotein permeability; albumin permeability; water flux; bovine aortic endothelial cells

LOW-DENSITY LIPOPROTEINS (LDL) have been implicated in the pathogenesis of atherosclerosis (21). Their passage through the endothelium can initiate the formation of atherosclerotic lesions, and therefore it is critical that the pathways that LDL takes in crossing the endothelial barrier be well understood. Previous in vitro studies have focused on the uptake and metabolism of LDL by endothelial cells via receptor-mediated processes (11, 22, 32). Examination of animal tissue using electron microscopy following incubation with LDL has revealed the presence of vesicles containing LDL within cells that may deliver lipoproteins across the endothelium via transcytosis (28, 31). Other studies have shown that cells in a state of turnover can allow large macromolecules, including LDL and albumin, to cross the endothelium through so-called "leaky junctions" (15–17, 33). Little work has probed the transport of LDL across cultured endothelial monolayers that may serve as models for understanding and controlling transendothelial transport of LDL.

In this study, an in vitro model of bovine aortic endothelial cells (BAEC) plated onto porous polycarbonate filters was used in a series of experiments to probe LDL transport pathways. Macromolecule flux (Js) measurements were made using an automated fluorometer system, and water flux measurements were also recorded using a bubble tracker system previously developed in our laboratory (27). Experiments were conducted to determine the fraction of solute (either LDL or albumin) transport that is coupled to water flow or vesicles.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The following chemicals were obtained from Sigma Chemical (St. Louis, MO): bovine serum albumin (BSA; 30% solution, fraction V), minimum essential medium (MEM), phenol red-free MEM (PF), penicillin-streptomycin solution, L-glutamine, trypsin-EDTA solution, HEPES, sodium bicarbonate, dimethyl sulfoxide, heparin (sodium salt, grade I-A, 181 USP units/mg), and fibronectin. Fetal bovine serum (FBS) was purchased from Hyclone Laboratories (Logan, UT). Paraformaldehyde, sodium hydroxide solution (50% wt/wt), Dulbecco's PBS (1x without Ca2+ and Mg2+), and PBS (10x) were obtained from Fisher Scientific (Houston, TX). Tetramethylrhodamine-conjugated albumin was purchased from Molecular Probes (Eugene, OR). Both untagged human LDL and fluorescent DiI-LDL were obtained from Biomedical Technologies (Stoughton, MA). Transwell polycarbonate filters (24.5-mm diameter, 0.4-µm pore size) were purchased from Costar (Cambridge, MA).

Cell culture. BAEC were purchased from VEC Technologies (Rensselaer, NY). Cells were grown in T-75 flasks in 10% FBS-MEM and were kept at 37°C and 5% CO2. The medium was replaced every 2–3 days. For the transport experiments, cells were plated on fibronectin-coated polycarbonate filters in Transwell supports at a density of 2.5 x 105 cells/cm2. Experiments were carried out on monolayers 6–9 days postplating, since the cells were fully confluent and free from overgrowth during that range of days. Cells were used up to a maximum of passage 11.

Measurement of water and solute flux. An experimental apparatus was developed in our laboratory that could be used to measure both water flux and solute permeability across BAEC monolayers simultaneously (1, 6). The experimental rig was placed inside a Plexiglas box, and the temperature in the box was maintained at 37°C. The transport studies involved the placement of Costar filters seeded with cells into a black polyethylene terephthalate (PET) chamber. The BAEC were sealed within the chamber to form a luminal (top) volume that was completely isolated from the abluminal (bottom) volume. The luminal compartment was continuously fed with a flow of gas (5% CO2-95% balance air) to maintain the solution in contact with the cells at the physiological pH of 7.4. The outlet from the PET chamber was attached to Tygon and borosilicate glass tubing and an abluminal liquid reservoir. Adjustment of the height of the reservoir with respect to the height of the fluid covering the monolayers allowed for the desired hydrostatic pressure differential to be created across the filter (0 or 10 cmH2O). When a 10-cmH2O differential pressure was applied, the water flux (Jv) was measured by tracking the position of a bubble that was inserted into the glass tube. The bubble displacement data were used to compute Jv values using the following equation:

Formula 1(1)
where {Delta}d/{Delta}t is the bubble displacement per unit time, A is the area of the Transwell filter, and F is a tube calibration factor (fluid volume occupying a known length of tubing).

A fluorescent detection system was incorporated into the experimental apparatus, allowing for the simultaneous measurement of water flux and fluorescent conjugate macromolecule permeability. The concentration of fluorescent tracer molecules in the abluminal volume was measured using this system, consisting of a laser excitation source, silica optical fibers, a photomultiplier, and a data acquisition program. A Uniphase 1-mW helium-argon laser (Manteca, CA) produced excitation light at 543.5 nm. The emission signal was filtered appropriately (for LDL or albumin) and ultimately passed to a photomultiplier (C&L Instruments, Hummelston, PA). A software program (FluorMeasure) and model PC-DAQ control card (both from C&L Instruments) were used for acquisition and control of the photomultiplier. A computer-controlled mirror split the initial laser output and sent the excitation signal to one of two identical experimental chamber setups at a given instant of time. This allowed data to be collected simultaneously for two BAEC monolayers. Calibration curves were constructed allowing for fluorescence intensity to be converted to solute concentration.

Before the start of the experiments, the filters were rinsed twice with experimental medium (1% BSA-PF). In the experiments, either 10 µg/ml DiI-LDL or 100 µg/ml tetramethylrhodamine-albumin was added to the luminal chamber. A trace concentration of fluorescent conjugate macromolecule was added to the abluminal chamber so that the linear relationship of the solute concentration vs. fluorescent intensity was maintained at low solute concentrations. For a typical LDL or albumin experiment, the fluorophore was added to the luminal chamber and the system was allowed to equilibrate for 60 min, at which time a 10-cmH2O differential pressure was imposed across the monolayer. Both the fluorescence intensity in the abluminal chamber and the water flux were recorded during the hour-long pressurized period. Fluorescence data was subsequently recorded for 2 more hours under diffusive conditions.

The following equation was used to compute the solute permeability coefficient:

Formula 2(2)
where {Delta}Ca/{Delta}t is the rate of change in the abluminal solute concentration with respect to time, Va is the fluid volume of the abluminal chamber, and Cp is the luminal concentration of the solute. Changes in both Va and Cp were negligible during an experiment, and Ca << Cp.

Cell fixation protocol. Cells were fixed to block transcytosis in vesicles in the overall transport process. The fixation solution consisted of 1% (wt/vol) paraformaldehyde in PBS (6). Cell monolayers were rinsed twice with experimental medium. To the experimental monolayer, 1.5 ml of the fixative solution was added, whereas to the control monolayer, 1.5 ml of 1% BSA-PF was added. Both monolayers were placed in the incubator for 10 min. After the incubation period, the monolayers were removed and again rinsed twice with experimental medium. The protocol described earlier for the solvent drag experiments was then followed, and the diffusive solute flux of albumin or LDL for both monolayers was recorded over a 4-h period. In a different set of experiments, the Jv of fixed and control monolayers was measured over a 1-h period to determine whether the fixation had any effect on the paracellular pathway. The chamber in which the fixed monolayer was placed was alternated to eliminate bias.

Excess LDL experiments. To test the role that LDL receptors play in transport across the endothelium, we ran experiments in which an excess of untagged native LDL was added to saturate the receptors. In these experiments, 10 µg/ml DiI-LDL was added to one monolayer, and 10 µg/ml DiI-LDL plus 500 µg/ml untagged, native LDL was added to the other monolayer. The standard experimental protocol for LDL pressure experiments was then followed.

Pore model. Solute transport via diffusion and convection through a single pathway can be described using the following relations (5):

Formula 3(3)
where {sigma} is the osmotic reflection coefficient, Po is the diffusive permeability, Jv is the water flux, and Pe is the apparent permeability coefficient defined as:

Formula 4(4)
In Eq. 4, Js is the solute flux and Cp is the plasma (luminal) concentration of solute, and it has been assumed that the abluminal concentration is much less than Cp. Z is defined as:

Formula 5(5)
where NPe is the Peclet number,

Formula 6(6)
which indicates the relative importance of convection to diffusion. Note that Z -> 1 as NPe -> 0 and Z -> 0 as NPe -> {infty}.

If we allow for transcellular vesicular transport that is strictly diffusive (no water flux through vesicles) and two convective pathways, a paracellular pathway through breaks in the tight junctions surrounding all endothelial cells (8), and a leaky junction pathway associated with cells in a state of turnover or death (33), then the following three-pore model equations arise:

Formula 7(7)

Formula 8(8)
where Jvi is the water flux through pore i, Pov is the diffusive permeability of the vesicular pathway, Poi is the diffusive permeability of pore i, {sigma}i is the reflection coefficient of pore i, and Zi is defined by Eqs. 5 and 6 with the appropriate subscripts for pore i. These equations were used to analyze the experimental data.

Statistical analysis. Water and solute fluxes are presented as means ± SE. Tests for statistical significance were made using the unpaired Student's t-test with P < 0.05 considered significant.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
LDL and albumin permeability. Figure 1 shows a representative abluminal chamber solute concentration profile, and Fig. 2 shows the corresponding water flux plot for a 10-cmH2O pressure experiment. In Fig. 1, the interval from 0 to 60 min shows a slight negative slope, a feature that was present in every experiment. We believe this to be due to transient binding of the DiI-LDL initially present in the abluminal reservoir. For this reason the diffusive permeability was measured from t = 180 to 240 min. Upon application of the pressure differential at t = 60 min, a sharp increase in the slope of the concentration vs. time plot is observed as the rate of macromolecule transport increased due to convection. The concentration profile became linear within 30 min following the differential pressure application, indicating that the transport of LDL had reached steady state. At t = 120 min, the differential pressure was removed and data were recorded under diffusive conditions for 2 more hours. Regions of the data were selected, as shown in Fig. 1, and trend lines were constructed to determine dC/dt values. Data for each macromolecule (LDL or albumin) were analyzed in a consistent manner, with the same regions being selected for computing solute permeabilities.


Figure 1
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  		Fig. 1. Typical solvent drag experiment concentration plot. The system was allowed to equilibrate for an hour, at which point a 10-cmH2O differential pressure was applied across the monolayer, driving convective flux. After an hour of pressurized conditions, the liquid reservoir was raised once more, and diffusive conditions were recorded from t = 120 to 240 min. The slopes, dC/dt, were determined by linear fits of the time regions indicated by triangles (pressure) and squares (no pressure).

 

Figure 2
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  		Fig. 2. Typical water flux plot from solvent drag experiment. Typical water flux plot corresponding to the plot of LDL concentration vs. time shown in Fig. 1. Triangles indicate the points that were averaged to compute the water flux.

 
Upon application of the differential pressure, water flux data were collected in addition to the solute measurements. Because of the time required to scan the initial bubble position and because the algorithm used to calculate Jv from the raw data computes the slope of the data over a 5-min interval, the first Jv value was registered 10 min after the application of pressure, as shown in Fig. 2. Water flux profiles typically displayed an initial decrease of Jv over a course of ~10 min of data collection (20 total min of pressure), at which point they would level out. This transient decrease in Jv after application of differential pressure has been referred to as the "sealing effect" and has been observed both in vitro (6) and in vivo (14). A time interval was selected to compute an average Jv value (Fig. 2: t = 80 to 110 min) that matched the time interval used for calculating solute permeability values (Fig. 1).

Table 1 summarizes the water flux and permeability data for both LDL and albumin. The Jv values are the average water fluxes measured for all monolayers in a set (LDL or albumin). The Po values are the permeabilities under diffusive conditions after sealing, whereas the Pe values are the apparent permeability coefficients that account for both diffusive and convective contributions during the application of 10-cmH2O hydrostatic pressure differential. The Peclet numbers and osmotic reflection coefficients are based on the one-pore model (Eqs. 3–6). As can be seen, the LDL reflection coefficients are significantly larger than the albumin reflection coefficients (P < 0.001).


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  		Table 1. Summary of data from 10 cmH2O differential pressure solvent drag experiments

 
Cell fixation and receptor blocking experiments. To assess the contribution of transcellular transport in vesicles to overall solute transport, we ran experiments with both albumin and LDL on monolayers that had been fixed with 1% paraformaldehyde. Table 2 shows the diffusive permeability for control (Po) and fixed (Po,fixed) monolayers and the ratio of the two permeabilities, which was calculated from the mean values. The diffusive permeability for LDL was reduced 2.59-fold, whereas that of albumin was reduced 1.6-fold.


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  		Table 2. LDL and albumin diffusive permeability of fixed and receptor-blocked monolayers

 
To determine the effect of fixation on the paracellular pathway, we measured the Jv value on both fixed and control monolayers. The Jv value for control monolayers was 4.06 x 10–6 ± 3.04 x 10–7 cm/s, and the Jv value for fixed monolayers was 4.97 x 10–6 ± 4.57 x 10–7 cm/s. Although the Jv value of fixed monolayers was higher in five of the six experiments, the difference was not significant (P > 0.12).

To probe the role that LDL receptors play in transport across the endothelium, we incubated some monolayers with both fluorescent LDL conjugate and a 50-fold excess of native, untagged LDL. The untagged LDL competed with the fluorescent conjugates for the receptor binding sites. The results for the receptor binding experiments are provided in Table 2. The diffusive permeabilities for control monolayers (Po) and for those incubated with excess LDL (Po,excess LDL) are shown. Incubation with excess LDL reduced the permeability 2.28-fold.

Two-pore model analysis. Using data from both the fixation and receptor-blocking experiments, as well as the solvent drag experiments, we computed reflection coefficients for a two-pore model (vesicle and 1 convective pore–pore 2) as given by Eqs. 7 and 8. The fixation experiments were run under diffusive conditions, and the ratios Po/Po,fixed were determined for both albumin and LDL (Table 2). The ratio Po/Po,excess LDL from the receptor-blocking experiments was also found and is given in Table 2. The fraction of the total diffusive permeability (for LDL, based on the average of fixation and receptor blocking; for albumin, based on fixation only) that comprises the transcytosis component (Pov) was computed for each of the individual solvent drag experiments as follows:

Formula 9(9)

Using these permeability coefficients, as well as the pressurized Pe values and the water flux measurements, we computed the Peclet numbers and two-pore reflection coefficients (Eqs. 7 and 8). The coefficients for the two-pore model are summarized in Table 3.


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  		Table 3. Summary of 2-pore analysis

 
The main result to note in Table 3 is that the reflection coefficients for the two-pore model have mean values that are slightly larger than those from the one-pore analysis (Table 1); however, there is no significant difference between the values for all of the experiment sets shown (P > 0.3). The data in Table 3 can be used to compute the fraction of total transport under pressurized conditions that occurs by transcytosis (see DISCUSSION).

Three-pore model analysis. Lin et al. studied the relationship between areas of focal uptake of Evans blue-albumin and endothelial cells that were either undergoing mitosis (16) or dying (15) in the rat aorta. They found that 42% of the leaky foci were associated with mitotic cells, whereas 37% were associated with dying cells. These observations have motivated us to analyze the water flux, albumin, and LDL transport data using a three-pore model (Eqs. 7 and 8). We assume that the vesicular pore (v) does not transport water and is, therefore, nonconvective. Pore 2 represents the break in the tight junction that will allow water and albumin transport but is too small for LDL (8). Pore 3 is the leaky junction that allows water, albumin, and LDL transport and is so large that the reflection coefficient for both albumin and LDL are zero. It is assumed in this case, as by Fu et. al. (8), that the tight junction pathway (not the breaks) is so small that it not only excludes albumin and LDL but also blocks water flux because of its elevated hydraulic resistance. Therefore, all of the water flux is assumed to pass through pores 2 and 3.

There are five equations that must be solved to determine the parameters of the three-pore model: Eq. 7 for water flux, and Eq. 8 for each solute (a, albumin; L, LDL) under convective conditions (pressurized) or diffusive conditions (unpressurized). There are six unknown parameters: Jv2, Jv3, Po2a, Po3a, Po3L, and {sigma}2a. The data in Table 1 were used to determine the parameters. The average of the Jv values obtained for albumin and LDL experiments was used. PFormula 9 and PFormula 9 were determined using the methods associated with the data in Table 3. To complete specification of the problem, we assigned values to {sigma}Formula 9 and solved for the remaining parameters. The five equations had real solutions only for Formula 9 in the range of 0.29 to 0.49. Results are presented in Table 4 for the case {sigma}Formula 9 = 0.49. The results for {sigma}Formula 9 = 0.30 and 0.40 are shown in Table 5. Note that only the results for albumin are shown, since varying {sigma}Formula 9 has no effect on the model predictions for LDL and water transport.


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  		Table 4. Summary of 3-pore model predictions (Formula 12 = 0.49)

 

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  		Table 5. Effect of varying albumin reflection coefficient on 3-pore model predictions and fractional fiber volume calculation

 

   DISCUSSION
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
In vitro transport studies have been carried out on a variety of cell types, using different support substrates, culturing procedures, sampling protocols, and tracer materials. Table 6 summarizes diffusive albumin permeability coefficients measured by various investigators and lists the cell types that were used. It is clear from the data in Table 6 that the albumin permeability measurements in the present study are consistent with those of other studies and lower than most. There was only one other in vitro study of diffusive LDL transport available for comparison (13). They studied the transport of 125I-LDL as well as other modified LDLs across cultured monolayers of human umbilical vein endothelial cells (HUVEC) under diffusive conditions. They measured Po values between 0.74 x 10–7 and 0.80 x 10–7 cm/s for unmodified LDL. These permeabilities are close to those measured in the present study (2.1 x 10–7 cm/s in Table 1, 1.8 x 10–7 and 1.2 x 10–7 cm/s in Table 2). There have been no previous studies of convective (pressurized) transport of LDL in vitro. The water flux values induced by a 10-cmH2O pressure differential that were observed in this study (Tables 1 and 3) are comparable to previous in vitro studies and are of the same order of magnitude as fluxes across the aorta of rabbits at physiological pressures (7).


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  		Table 6. Summary of diffusive albumin permeabilities in vitro

 
Transport pathways for LDL and albumin. The first experiments that were run under 10-cmH2O differential pressure were initially interpreted using the description of diffusion and convection through a single pathway as defined by Eqs. 3–6 (5). The osmotic reflection coefficients ({sigma}) for albumin and LDL were computed as 0.11 and 0.768, respectively (Table 1).

To examine the possible contribution of transcytosis in vesicles to total solute transport, we ran experiments in which monolayers were fixed with 1% paraformaldehyde. The fixation prevents transcellular transport, and by comparing permeability values of chemically fixed monolayers with control monolayers, the relative contribution of this pathway was assessed. Results in Table 2 show that Po was reduced 2.59-fold for LDL and 1.60-fold for albumin in fixed monolayers. This reduction in diffusive permeability suggests that vesicular transport plays a role in transport of both albumin and LDL across the endothelium. Albumin transport across the endothelium in vesicles has been reported in several other studies (2, 10, 20, 23), and transport of LDL into endothelial cells in vesicles is well established (29, 30, 32). It may be argued that fixation also affects the paracellular pathway and that the reduction in transport after fixation cannot be attributed entirely to the vesicular pathway. However, DeMaio et. al. (6) have shown, using the same cell monolayers and fixation procedure, that the diffusive transport of 70-kDa dextran is not affected by fixation. Since 70-kDa dextran is believed to be transported exclusively through the paracellular pathway, this indicates that fixation does not affect the paracellular pathway. Additional experiments were run to determine whether fixation would affect the Jv value of cell monolayers. The results showed no significant difference between fixed and control monolayers, indicating no effect of fixation on the paracellular pathway.

To determine whether LDL receptors on BAEC are involved in vesicular transport of LDL, we ran experiments with a 50-fold excess of native, untagged LDL to saturate the receptor binding sites. A 50-fold ratio has been used in prior experiments to prevent receptor binding (29, 30, 32). The results of these receptor-blocking experiments are also shown in Table 2, where it is apparent that there is a significant difference in diffusive permeabilities (P < 0.05) between control and test monolayers, with the control monolayers having Po values 2.28-fold higher than the receptor-blocked monolayers. This ratio is not significantly different from the ratio of diffusive permeabilities of control and fixed monolayers (2.59; P > 0.3), suggesting that virtually all of the vesicular LDL transport is receptor mediated.

When a two-pore model, accounting for the vesicular transport contribution, is used to fit the pressurized transport experiments (Table 3), the reflection coefficients for albumin and LDL are slightly larger than predicted by a one-pore model. These changes in reflection coefficient are, however, not significant (P > 0.3). It is also clear from the results in Table 3 that under pressurized conditions, convective transport dominates over diffusive transport by either paracellular (Po2) or vesicular (Pov) pathways. This observation is consistent with LDL transport studies in vivo (under pressure) that indicate no significant contribution of LDL receptors to overall LDL transport in arteries (18, 28, 34).

Since previous in vivo (15–17) and theoretical (33) studies have supported the importance of leaky junctions in LDL and albumin transport, we analyzed a three-pore model. Following previous detailed modeling studies of the leaky junction (33) and the paracellular junction with breaks in the tight junction (8), we associated pore 2 with the breaks in the tight junction that would allow water and albumin, but not LDL, to pass and pore 3 with the leaky junctions that allow water and unrestricted albumin and LDL passage. The predictions, summarized in Table 4, indicate that pore 2 is the dominant pathway for water (77.7%) but that pore 3 carries most of the LDL (90.9%) and a substantial portion of the albumin (44%). These predictions are consistent with the in vivo observations that LDL receptors (vesicles) do not contribute significantly to LDL uptake in pressurized arteries (e.g., Ref. 34) and that regions of enhanced uptake of Evans blue-albumin are predictive of regions of enhanced LDL uptake (24).

If we assume that the molecular filter within the break in the tight junction is a fiber matrix associated with the glycocalyx (4), then the predicted value of the reflection coefficient can be used to estimate the fractional fiber volume by using the following relationships (19),

Formula 10(10)

Formula 11(11)

Formula 12(12)
where {Phi} is the partition coefficient, a is the radius of the solute, rf is the radius of the fibers, and Vf = 1 – {varepsilon} is the fractional fiber volume. The values predicted by these equations, using 0.6 nm for the radius of the fibers, range from 1.7 to 2.7% fractional fiber volume for a random fiber arrangement (1 – {varepsilon}) and from 1.2 to 1.5% fractional fiber volume for an ordered fiber arrangement (Vf) (Table 5). These predicted fiber volume fractions are close to values predicted for capillaries (19).

In conclusion, this study was the first to quantify transendothelial transport of LDL in vitro under pressurized conditions simulating convectively dominated transport that arises in arteries in vivo. Our results are consistent with observations in vivo indicating that leaky junctions, not vesicles, provide the dominant pathway for LDL uptake by arteries.


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
This work was supported by National Heart, Lung, and Blood Institute Grant HL-57093.


   FOOTNOTES
 

Address for reprint requests and other correspondence: J. M. Tarbell, Dept. of Biomedical Engineering, The City College of New York, Steinman Hall Rm. T403H, Convent Ave. and 140th St., New York, NY 10031 (e-mail: tarbell{at}ccny.cuny.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
 GRANTS
 REFERENCES
 

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U. Olgac, V. Kurtcuoglu, and D. Poulikakos
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