## Abstract

Interstitial flow through the tunica media of an artery wall in the presence of the internal elastic lamina (IEL), which separates it from the subendothelial intima, has been studied numerically. A two-dimensional analysis applying the Brinkman model as the governing equation for the porous media flow field was performed. In the numerical simulation, the IEL was modeled as an impermeable barrier to water flux, except for the fenestral pores, which were uniformly distributed over the IEL. The tunica media was modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells (SMCs) embedded in a fiber matrix simulating the interstitial proteoglycan and collagen fibers. A series of calculations was conducted by varying the physical parameters describing the problem: the area fraction of the fenestral pore (0.001–0.036), the diameter of the fenestral pore (0.4–4.0 μm), and the distance between the IEL and the nearest SMC (0.2–0.8 μm). The results indicate that the value of the average shear stress around the circumference of the SMC in the immediate vicinity of the fenestral pore could be as much as 100 times greater than that around an SMC in the fully developed interstitial flow region away from the IEL. These high shear stresses can affect SMC physiological function.

- fenestral pore
- numerical analysis

the wall shear stress of flowing blood on the endothelial lining layer of blood vessel walls has been studied extensively because of its central role in the maintenance of vascular tone, vascular remodeling, and localization of atherosclerosis (6, 16). Mean values of wall shear stress on endothelial cells are on the order of 10 dyn/cm^{2} in arteries and may be higher in capillaries and lower in postcapillary venules (13). In a previous study, Wang and Tarbell (22) revealed that smooth muscle cells (SMCs) could be subjected to significant levels of shear stress associated with normal transmural interstitial flow, even though the superficial velocity of interstitial flow is very low (on the order of 10^{−6}cm/s). In their analytic model, they assumed uniform superficial velocity at the upstream end of an array of cylindrical SMCs, neglecting the more complex entrance conditions that exist at the intimal-medial boundary, to estimate the magnitude of the shear stress imposed on the SMCs suspended in a fiber matrix. Their results show that, under physiological conditions, wall shear stress on SMCs is on the order of 1 dyn/cm^{2}, a level that has more recently been shown to affect SMC biology (1, 14).

However, for the SMCs bordering the subendothelial intima, the presence of internal elastic lamina (IEL) with leaky fenestral pores can greatly alter the flow field around the boundary SMCs. Because the area fraction of fenestral pores is in the range 0.002–0.01 and the mean diameter of the fenestral pores varies from 0.4 to 2.1 μm (8), the velocity of fluid issuing from an individual pore could be 100-fold greater than the superficial flow velocity in the tunica media, resulting in a significant change in the distribution of flow and associated shear stress on the most superficial layer of SMCs that lie just beneath the IEL. The elevated shear stresses on the cells in this layer may affect SMC biology and could play a role in SMC proliferation and migration that occur in atherosclerosis and intimal hyperplasia (17).

In this study, under realistic physiological flow conditions, two-dimensional numerical simulations of the interstitial flow in the tunica media were performed to estimate the magnitude and spatial distribution of wall shear stress on SMCs, with the influence of the IEL on distribution of the flow to the media taken into account. In addition, the effects of several physiological parameters, the area fraction of the fenestral pore, the fenestral pore diameter, and the distance between the IEL and the first SMC, were studied.

### Glossary

*a*- Distance between IEL and upstream end of SMC (m)
*D*- SMC diameter (m)
*d*- Fenestral pore diameter (m)
- F
- Volume fraction of SMC
- f
- Area fraction of fenestral pore
*K*_{p}- Permeability of media (m
^{2}) *K*_{p eff}- Effective permeability of media (m
^{2}) *L*- Distance between the centers of neighboring SMCs (m)
*l*- Fenestral pore spacing (m)
- P
- Pressure (Pa)
- Re
- Reynolds number (= ρ
*UD*/μ) *r*- Radial coordinate (m)
*U*- Mean interstitial flow velocity (m/s)
*U*_{0}- Flow velocity at fenestral pores (m/s)
**u**- Velocity vector (m/s)
*u**x*component of velocity (m/s)*u*_{r}*r*component of velocity (m/s)*u*_{θ}- θ component of velocity (m/s)
**x**- Positional vector (m)
*x**x*-Axis of Cartesian coordinate system (m)*y**y*-Axis of Cartesian coordinate system (m)- δ
- Boundary layer thickness (m)
- θ
- Angular coordinator
- μ
- Viscosity (N ⋅ s ⋅ m
^{−2}) - ρ
- Fluid density (kg/m
^{3}) - τ
- Shear stress (N/m
^{2}) - κ
- Dimensionless permeability
- Wall
- Value at the SMC surface
- *
- Dimensionless value

## NUMERICAL ANALYSIS

A schematic illustration of the typical structure of an arterial wall is shown in Fig. 1. In the intact vessel there is a pressure gradient between the blood and the tissue surrounding the vessel that drives transmural flow across the wall and exposes the SMCs to interstitial flow shear stress. SMCs are embedded in a tissue matrix beneath the subendothelial intima in most blood vessels and, under normal circumstances, are shielded from the direct shear forces of flowing blood. The IEL separates the subendothelial intimal layer from the medial layer and provides a complex entrance flow condition through the fenestral pores.

To obtain a basic understanding of the flow through the medial layer, Wang and Tarbell (22) performed an analytic study of the two-dimensional, steady-state problem by applying Brinkman's model (4) to describe flow through an infinite periodic array of cylindrical SMCs. In the present study we consider the same array of cylindrical SMCs but take into account the fact that the fluid enters the medial layer of the artery through the fenestral pores, which are randomly distributed over the IEL. The interstitial flow field in the region immediately below the IEL is investigated numerically.

The medial layer of the blood vessel wall is modeled as a heterogeneous medium composed of a periodic square array of cylindrical SMCs and a continuous interstitial fluid phase filled with proteoglycan and collagen fibers modeled as a uniform fiber matrix (22). Transmural flow is distributed into the medial layer from the intima by passing through the fenestral pores of the IEL. The IEL is assumed to be an impermeable rigid wall except for its pore openings. SMCs are treated as obstacles impermeable to fluid because of the low hydraulic conductance of the cell membrane relative to that of interstitium (22).

#### Mathematical formulation of the transmural flow problem.

In the present analysis, flow in the interstitial phase filled with fiber matrix is modeled as Newtonian fluid flow (viscosity, μ) through a homogeneous porous medium having a Darcy permeability coefficient, *K*
_{p}. The geometry of the two-dimensional flow problem is shown in Fig.2. The fenestral pore center is aligned with the SMC center to investigate the extreme case in which the shear stress around SMCs attains the maximum possible value. Although in real arteries there can be fenestral pores that are not aligned with the SMC array, this case has not been taken into account in the present calculation, because it is expected to produce minor changes in shear stress relative to the fully developed flow values computed by Wang and Tarbell (22). SMCs are arranged in a square-array configuration. This is an obvious idealization, but it is not far from real features, because the flow field is not very sensitive to array structure unless the volume fraction of SMCs is high (22).

Once the SMC diameter (*D*) and volume fraction for SMC (F) are given, the distance between centers of neighboring SMCs (*L*) can be calculated. In the same manner, the pore spacing (*l*) is also calculated when the pore diameter (*d*) and area fraction of pores (f) are given. In the present calculation, four different values of *l* (calculated from 4 different values of f) are selected (Fig. 3). In Fig. 3, *A–D*, when*d* is kept constant, f is changed according to the following definition: f = π*d*
^{2}/4*l*
^{2}. On the other hand, when we examine the effect of *d* under the condition of a constant f, values of *l* and *d* are changed simultaneously. Moreover, the distance between the IEL and upstream end of the SMC (*a*) is varied in accordance with recent experimental data.

To simplify the problem to be solved, the following additional assumptions are invoked: *1*) The flow is steady and perpendicular to the longitudinal axis of the cylindrical SMCs.*2*) The IEL is a rigid impermeable wall with zero thickness except for its fenestral openings. *3*) The circular fenestral pores are distributed with a periodic square-array configuration over the IEL surface. *4*) The no-slip condition is applied on all surfaces of the SMCs and IEL. *5*) A uniform velocity profile is specified at the entrance to the fenestral pore.

The governing equations are Brinkman's equation (4), a generalization of Darcy's law for flow in a saturated porous medium that allows for satisfaction of no-slip boundary conditions
Equation 1and the equation of continuity
Equation 2where ∇ is the Nabla operator, Δ is the Laplacian, **u** is the local flow velocity vector, P is the pressure, μ is the viscosity of the fluid, and *K*
_{p} is the Darcy permeability of the fiber matrix. The term on the left-hand side of *Eq. 1
* is the pressure gradient, which drives the flow, the first term on the right-hand side represents the viscous term, which allows satisfaction of the no-slip condition, and the last term on the right-hand side represents the Darcy-Forchheimer term, which characterizes flow in the porous medium away from the solid boundaries.

After definition of dimensionless variables
Equation 3where *D* is the diameter of the SMC, *U* is the superficial velocity of the fully developed interstitial flow, ρ is the fluid density, and **x** is the position vector in Cartesian coordinates, *Eqs. 1
* and *
2
* are rewritten in dimensionless form as
Equation 4
Equation 5where Re is Reynolds number defined as
Equation 6

#### Physical parameters and constants.

To determine physiological values of constants and parameters for the numerical analysis, data for transmural flow in the rabbit thoracic aorta have been employed. Typical values of parameters defining the flow problem are taken from a range of experimental data available from Huang and Tarbell (10). For the fiber matrix in the interstitial phase, the value of hydraulic permeability is *K*
_{p} = 1.432 × 10^{−18} m^{2}, which is consistent with the value used by Wang and Tarbell (22) based on the data of Tedgui and Lever (19) for the rabbit aorta. The mean *U* is obtained from Darcy's law
Equation 7where*K*
_{p eff} is the effective permeability defined by Wang and Tarbell and ∂P/∂*x* is pressure gradient along the flow direction. The effective permeability is given by Wang and Tarbell
Equation 8where F is the volume fraction of the SMC defined in terms of *D* and*L* (Fig. 2) and O represents order of magnitude
Equation 9Taking F = 0.4, μ = 6.86 × 10^{−3}N ⋅ s ⋅ m^{−2}(viscosity of water at 36.9°C), and ∂P/∂*x* = 0.5 mmHg/μm (10), we obtain *U* = 5.8 × 10^{−8} m/s from *Eq. 7
*.

Besides the constants mentioned above, the area fraction of fenestral pores (f), the diameter of fenestral pores (*d*), and the distance between the IEL and the upstream end of the SMCs (*a*) are considered to be important parameters defining the flow field. According to experimental data (rat thoracic aorta) at 0 mmHg pressure reported by Huang et al. (8, 9) and Roach and Song (15), f is 0.002–0.01 and *d* is 0.4–2.1 μm. The parameter*a* was estimated to be 0.36 μm from electron micrographs of rabbit aortic intima (Y. Huang, personal communication). To investigate the influence of these parameters on the flow field and associated shear stress on SMCs, we consider the values of f, *d*, and*a* within the ranges 0.001–0.036, 0.4–4.0 μm, and 0.2–0.8 μm, respectively. All the constants and parameters described above are listed in Table 1.

#### Computational method.

The FIDAP software package (version 7.62, FLUENT) was used for the numerical simulations. The set of governing equations was solved by direct Gaussian elimination. The global matrix arising from the finite element method discretization was decomposed into smaller submatrices to save memory space. Numerical simulations were carried out on the IBM RS/6000 SP system at the Penn State Center for Academic Computing. One of the finite element mesh realizations used in our calculations is shown in Fig. 4. The curvilinear grid system was generated by using FI-GEN, which is a submodule of the FIDAP solver. Velocity grid points are arranged on each nodal point of the grid system, while the pressure is solved at the centroid of each cell. In the vicinity of solid boundaries, the flow is dominated by viscosity. Therefore, a finer mesh of grid points taken perpendicular to each SMC surface was employed to ensure sufficiently high resolution within the boundary layer.

In the present problem, the Brinkman boundary layer thickness (δ) is on the order of
or, in dimensionless form, δ* = O(
). δ* is estimated to be 1 × 10^{−3}; hence, a minimum mesh size of 1 × 10^{−5} was taken next to the SMC and IEL surfaces. After it was established that the numerical results were independent of mesh density, a computational mesh consisting of 2,400 (40 × 60, radial × circumferential) four-node quadrilateral elements was applied for the half-space of each SMC. The total mesh size was changed according to the combination of f and *d*values. The maximum mesh size was ∼75,000 (containing 6 × 5 half-space SMC units); on the other hand, the minimum mesh size was ∼16,000 (containing 6 × 1 half-space SMC units). As the convergence criteria for implicit Gaussian elimination iterations, a relative error of velocity
Equation 10was applied on the value of the *n*th iteration. In each element, biquadratic interpolation functions were used to approximate the velocities. For the pressure variable, a piecewise constant approximation was applied. A symmetry boundary condition was applied on the top and bottom end lines of the computational domain. At the downstream end, a gradient-free (∂**u***/∂**x*** = 0) outlet boundary condition was applied. The effect of the location of the outlet boundary condition on the resulting flow field was examined by increasing the number of columns of SMCs parallel to the IEL surface. The vertical (*y*) component of velocity at the downstream end of the last column of SMCs was used as an indicator of the fully developed outlet flow condition. Results were independent of exit length when six or more layers of SMCs were employed.

#### Numerical validation.

To validate the present interstitial flow simulation method, the wall shear stress on an SMC (τ) was computed for several values of the SMC volume fraction (F) for an infinite periodic square array of SMC (with no IEL). The computed results were compared with the analytic solution of Wang and Tarbell (22).

The local shear stress is defined as
Equation 11where Wall represents the value taken on the SMC surface (*r** = 1),*u*
_{θ} is the angular component of the velocity, and*u*
_{r} is the radial component of the velocity when the origin of the polar coordinate system is taken at the center of the SMC; τ_{local} is calculated to first-order discretization accuracy by use of the numerically obtained velocity variables *u*
_{x} and*u*
_{y}.

The wall shear stress averaged around an SMC is defined as Equation 12 Furthermore, τ is nondimensionalized by using the reference shear stress defined by Wang and Tarbell (22) as Equation 13Figure 5 shows a comparison of the numerical results with the analytic result of Wang and Tarbell (22) calculated from the following equation For smaller values of F, the agreement is very good. However, for the largest value of F simulated, the numerical shear stress is slightly greater than the analytic result. We attribute the deviation to truncation error in the analytic infinite series expansion.

## RESULTS AND DISCUSSION

The incoming flow velocity at each fenestral pore (*U*
_{0}) is derived from the relation
Equation 15which ensures that the volumetric flow rate far away from the IEL is equal to that supplied by the fenestral pores. A schematic view of the relationship between the superficial velocity (*U*) and*U*
_{0} is shown in Fig. 6. For all results to be presented, *U* is taken to be 5.8 × 10^{−8} m/s.

To reveal basic characteristics of the interstitial flow, intermediate values of the model parameters were used to compute the results displayed in Fig. 7: *d* = 0.4 μm, f = 0.004, and *a* = 0.36 μm. F was maintained at 0.4 for all calculations, because it was expected to have a minor influence on the shear stress distribution over SMC near the IEL (Fig. 5).

#### Characteristics of the interstitial flow.

Figure 7 shows a streamline contour plot of the interstitial flow in the media. The fluid coming from the fenestral pores (located at the top and bottom of the IEL at the left end of the computational domain) is distributed into the whole region of the media. Near the IEL, fluid spreads laterally into the upstream region of the media as soon as it enters from the fenestral pore, in contrast to a conventional Stokes fluid flow with the same Re (i.e., 1.657 × 10^{−7}). The Darcy resistance tends to make the jet broader, as discussed by Friedrich and Rudraiah (7). The flow is symmetrical about the center line in the flow direction, because the volumetric flow rate at the entrance of each fenestral pore is the same. At the narrowest point in the path between neighboring SMCs, the intervals between streamlines are almost equal, suggesting that a uniform velocity distribution is established, except in a thin boundary layer near the SMC surfaces. This feature is also quite different from conventional Stokes flow, in which the fluid displays a parabolic velocity distribution. Furthermore, streamlines penetrate more deeply into the wake region behind each SMC, in contrast to those of Stokes flow.

#### Changes of shear stress for different pore diameter.

As suggested by Fig. 7, the shear stress on the first SMC is elevated as a result of the concentrated flow entering from the fenestral pore. On the other hand, the second to the sixth SMCs have an almost identical distribution. Clearly, the existence of the fenestral pore significantly affects shear stress on the SMC located directly beneath the pore but has no effect on the shear stress distribution around the second and more distal SMCs. Therefore, we will focus on the first SMC, which has elevated shear stress.

Figure 8 shows the local shear stress distribution around the circumference of the SMC directly beneath a fenestral pore for four different values of *d*. F and f are kept constant at 0.4 and 0.004, respectively; τ*_{local} is the nondimensional shear stress defined in *Eq. 13
*. To obtain a sense of the dimensional magnitude of these shear stresses, the normalization factor, μ*U*
, takes on a value of 0.52 dyn/cm^{2} on the basis of interstitial flow data in the rabbit thoracic aorta, as discussed earlier (19). The value of τ* averaged over an SMC in the fully developed flow regimen is ∼1.3 (Fig. 5). So we are observing a significant elevation of shear stress on the first SMC. A constant value of f implies that the incoming flow velocity at the pore entrance is constant, independent of *d*. It is interesting that the maximum value of the local shear stress appearing on the upstream side of the SMC increases with *d*. This reflects the fact that the inflow jet impinges on a larger fraction of the SMC surface as*d* increases. In addition, a qualitative change in the distribution of shear stress is also observed. The shear stress distribution changes from a complex one having two maxima and a minimum to a triangular shape having a steep gradient at the upstream side as*d* becomes larger. The position on the SMC surface where the maximum shear stress appears also changes. It moves downstream as*d* becomes larger. Clearly, the spatial gradient of shear stress (∇τ*_{local}) becomes large at the leading edge of the SMC. The largest value of ∇τ*_{local} is 750 for*d* = 1.6 μm; ∇τ*_{local} = 1 corresponds to 0.26 dyn ⋅ cm^{−2} ⋅ μm^{−1}. By comparison, the maximum value of ∇τ*_{local} for the fully developed flow is only ∼3.2. Clearly, the elevation of shear stress gradient on the first cell is very significant.

τ* varies almost linearly with the variation of *d* (Fig.9). This suggests that τ* around the first SMC is proportional to the area that the fenestral pore projects onto the surface of the SMC in the streamwise direction.

To obtain a more detailed understanding of the shear stress behavior, which depends strongly on *d*, another set of calculations for a large f (i.e., 0.016) was performed. *d* was varied from 0.8 to 4.0 μm, which corresponds to the diameter of the SMC. The local shear stress distributions (not shown) are similar in shape to those in Fig.8. The largest value of Δτ*_{local} is 450 for*d* = 3.2 μm.

Figure 10 shows the relationship between τ* and *d* for the case F = 0.4 and f = 0.016. The value of τ* increases linearly with *d* for *d* < 2.4 μm; however, it decreases at *d* = 4 μm after displaying a maximum at *d* = 3.2 μm. From these results, we can see that τ* increases with increasing *d* until *d* approaches the SMC diameter. Beyond that, τ* will decrease with increasing*d*. Ultimately, for *d *≫* D *(as in a damaged IEL), τ* should asymptotically approach the fully developed flow value (without the IEL) given in Fig. 5.

#### Changes of shear stress for different pore area fraction.

Figure 11 shows the relationship between τ* on the SMC directly beneath a fenestral pore and f, for constant values of F and *d*. The local shear stress distributions (not shown) are similar in shape to those shown in Fig. 8. The largest value of ∇τ*_{local} is 2,600 for f = 0.001. The value of τ* varies with 1/f^{2}, as expected. This means that the magnitude of τ* is simply proportional to the velocity of incoming flow approaching the SMC. For f = 0.001, τ* is significantly elevated, up to 135. This corresponds to a value ∼100 (135/1.3) times greater than experienced by SMC in the fully developed flow field away from the IEL. In other words, a very strong shear force can be imposed on the SMC directly beneath the pore, particularly when f is sufficiently small.

#### Changes of shear stress for different spacing between IEL and SMC.

The distance between the IEL and upstream end of the nearest SMC (*a*) is expected to be one of the most important parameters that affect the shear stress distribution over an SMC. The value of*a* = 0.36 μm was chosen as a reference value on the basis of the scanning electron microscope data (rat thoracic aorta) provided by Dr. Yaqi Huang (personal communication). However, inasmuch as *a*may vary in different blood vessels and in different species, we simulated three different values (0.2, 0.36, and 0.8 μm) to examine the dependence of the shear stress behavior on *a*.

Figure 12 displays the shear stress distribution around the circumference of the SMC directly beneath the fenestral pore for three different values of *a*. A significant change in the shear stress distribution appears at the upstream side of the SMC surface when *a* varies. The magnitude of τ*_{local} changes drastically in the region θ > 3/4π. The location where τ*_{local} takes on its maximum value moves slightly toward the upstream end as *a*becomes smaller. ∇τ*_{local} takes on a maximum value of 1,200 for *a* = 0.2 μm.

Figure 13 shows the relationship between τ* and *a*; τ* increases nonlinearly as *a* decreases. This reflects the fact that when *a *is large, the flow velocity just outside the boundary layer on the first SMC is reduced, because there is a greater distance over which the flow can spread laterally; when *a* is small, the fluid can maintain a higher velocity.

#### Concluding remarks.

The two-dimensional numerical simulations of interstitial flow immediately below the IEL reveal a fluid mechanical environment around the most proximal layer of SMCs that is quite distinct from that around the more distal cells. Depending on f and *d*, the average shear stress on this proximal layer could be 10–100 times higher than on the cells far removed from the IEL, which have been estimated to experience an average shear stress on the order of 1 dyn/cm^{2} (22). Thus the first layer of SMCs may experience shear stress levels that are even higher than that of endothelial cells exposed to normal blood flow [on the order of 10 dyn/cm^{2} (13)].

The shear stress gradients on the leading edge of the first layer of SMCs are also highly elevated relative to the distal layer. Depending on f and *d*, the maximum shear stress gradients on this layer range from 200 to 700 dyn ⋅ cm^{−2} ⋅ μm^{−1}, whereas for the distal layers the maximum gradient may only be ∼1 dyn ⋅ cm^{−2} ⋅ μm^{−1}. The maximum shear stress gradient over the surface of endothelial cells in blood flow has been computed to be on the order of 5 dyn ⋅ cm^{−2} ⋅ μm^{−1}(2). Although there is no direct evidence available to indicate that shear stress gradients affect SMC biology, analogies to endothelial cells, which are hypothesized to transduce mechanical signals through shear stress gradients (2, 6), suggest a potential role for shear stress gradients in SMCs.

The magnitudes of shear stresses estimated by two-dimensional calculations must be interpreted with some caution. They represent upper bounds on the magnitudes that would actually be obtained in a full three-dimensional calculation. With reference to Fig. 6, it should be realized that our two-dimensional calculations do not account for spreading of the jet along the axis of the SMC. Our results estimate the shear stresses on the first SMC only over an axial length scale on the order of *d*. Clearly, the velocity will be reduced along the axis of the SMC moving away from the fenestral pore. Full three-dimensional calculations are required to determine the axial distribution of shear stress along the first SMC.

Recent in vitro studies have shown that vascular SMCs are responsive to shear stress in the range 1–25 dyn/cm^{2} and increase their synthesis of transforming growth factor-β, tissue plasminogen activator (20), heme oxygenase-1 (21), nitric oxide (14), and PGs (1). These results and our simulations suggest that, in a normal artery with intact IEL, the innermost layer of SMC in the intimal-medial border may be the most active biochemically because of elevated shear stresses.

On the other hand, several in vitro studies have shown that shear stress is an inhibitor of vascular SMC proliferation (18, 20). In addition, in vivo studies in balloon-injured rabbit carotid arteries (3) have demonstrated that increasing blood flow on the injured artery inhibits matrix metalloproteinase-2 mRNA and intimal hyperplasia. These studies suggest that high levels of shear stress on SMCs are beneficial, because they suppress SMC proliferation and migration, which might otherwise contribute to intimal hyperplasia. Thus, because an intact IEL promotes high shear stresses on the superficial SMCs associated with transmural flow (as we have demonstrated in this study), an intact IEL may contribute to the suppression of intimal hyperplasia. A damaged IEL would reduce transmural flow shear stress on the superficial SMCs and upregulate mechanisms supporting intimal hyperplasia. This scenario must be considered speculative and requires additional studies to assess its physiological relevance.

## Acknowledgments

The authors are grateful to Dr. Yaqi Huang (Dept. of Mechanical Engineering, Massachusetts Institute of Technology) for providing his scanning electron micrograph experimental data to us.

## Footnotes

Address for reprint requests and other correspondence: J. M. Tarbell, 155 Fenske Laboratory, The Pennsylvania State University, University Park, PA 16802-4400 (E-mail: jmt{at}psu.edu).

The research is supported by National Heart, Lung, and Blood Institute Grant HL-35549.

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. §1734 solely to indicate this fact.

- Copyright © 2000 the American Physiological Society