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1Biomedical Engineering Department, Northwestern University, Evanston, Illinois 60208-3107; and 2Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
Submitted 10 December 2002 ; accepted in final form 6 May 2003
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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cell migration; cell proliferation; cell alignment; vascular morphogenesis
Given the complexity of blood flow patterns in a curved blood vessel with additional complications due to altered tensile stress, it is difficult to identify the role of nonuniform fluid shear stress in a native vascular system. To resolve such a problem, an in vivo experimental model has been developed with a polymer cylinder implanted in the rat vena cava in a direction perpendicular to blood flow, resulting in a defined field of nonuniform fluid shear stress on the implant without the influence of tensile stress (31, 34). In such a model, SMCs migrated from the vessel media into the neointima of the implant, and nonuniform blood shear stress at the neointimal surface regulated the direction of SMC migration and alignment. In contrast, uniform shear stress in a control model did not significantly influence the direction of SMC migration and alignment, as shown in our preliminary studies. These observations support the role of nonuniform blood shear stress in regulating the direction of SMC migration and alignment.
Because not all SMCs were directly exposed to blood shear stress in the present model, indirect mediating processes might be involved in the transmission of shear stress signals to SMCs. One possible mechanism may be related to the role of fluid shear stress in the regulation of mitogenic activities. Fluid shear stress has been known to inhibit cell proliferation (1, 26, 28–30, 39, 61), potentially influencing cell density. The distribution of cell density is a factor that directs cell migration and alignment (6, 16, 48–50). In cell culture models, epithelial cells and neural crest cells have been observed to migrate from a high to a low cell density location (49, 50). Enhanced cell-cell contacts in a high-density cell population may directly influence the regional activities of cell migration machineries and regulatory molecules, thus controlling the direction of cell migration. On the basis of these observations, we propose the following hypotheses: 1) nonuniform fluid shear stress may induce graded suppression of mitogenic activities and influence the distribution of cell density, resulting in the formation of cell density gradients; and 2) the gradient of cell density may in turn influence the direction of SMC migration, thus determining the pattern of SMC alignment. This investigation provides evidence for these hypotheses by using experimental models with vascular polymer implants subject to defined flow fields with uniform and nonuniform shear stress.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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Nonuniform shear stress model. Male 3-mo-old Sprague-Dawley rats
(Harlan; Indianapolis, IN) were anesthetized with an intraperitoneal injection
of pentobarbital sodium (50 mg/kg). After the abdominal cavity was opened, the
inferior vena cava was separated from surrounding tissue with side branches
tied off except for the celiac, mesenteric, renal, and common iliac veins. To
create a model for SMC migration in nonuniform blood shear stress, a
polypropylene cylinder of 0.3 mm diameter coated with polyethylene glycol was
implanted in the center of the vena cava (
3 mm in diameter) in a
direction perpendicular to blood flow (Fig.
1A). The vena cava was chosen in this study to avoid the
influence of flow pulsatility, which may complicate the pattern formation of
SMCs, and simplify computational processes. Observations were carried out at
days 3, 5, 7, and 10 after surgery with a focus on day
5 because of the presence of peak mitogen activities and SMC migration
(34). Experimental procedures
were approved by the Animal Care and Use Committee of Northwestern
University.
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Uniform shear stress model. A polytetrafluoroethylene (PTFE)
membrane patch, 3, 0.5, and 0.01 mm in length, width, and thickness,
respectively, was inserted into the vena cava and attached to the endothelium
in the circumferential direction with 10-O suture stitches
(Fig. 1B). The length
of the patch was similar to that of the cylinder in the nonuniform shear
model. Because the patch is thin, fluid shear stress on the patch is similar
to that on the endothelium. The level of shear stress on the patch was
controlled to match that in the nonuniform shear model in an area with a
Reynolds number of 10, where specimens were collected for biological
assays, by narrowing the vena cava at the site of patch implantation
(35–45% reduction in diameter with a 10-mm vascular clamp). We have
found, in preliminary studies, that SMCs migrate from the injury sites of the
vessel wall onto the rectangular polymer patch in its axial direction
(perpendicular to blood shear stress; open arrow in
Fig. 1B), whereas SMCs
rarely migrate onto the patch from the free edges without vessel wall
injury.
Zero shear stress model. To create a zero-shear model, a hollow
porous polypropylene cylinder of 0.3 mm diameter with a slit opening in the
wall (0.03 mm in width and 0.1 mm in length along the circumference
of the cylinder) was implanted in the vena cava. Such a model allows SMC
migration from the external to the internal surface of the implant. Shear
stress is zero at the internal surface of the hollow cylinder.
Assessment of Fluid Shear Stress
Nonuniform shear model. The analysis of fluid shear stress in the
model used in this study has been reported previously
(31). Briefly, a polymer
cylinder implanted in the vena cava was subject to laminar blood flow in the
leading region (from the stagnation edge at 0° to flow separation edges at
+109 and –109°, as shown in Fig.
2A) and to vortex blood flow in the trailing region (from
±109° to the trailing stagnation at 180°) with the flow pattern
symmetrical for the positive and negative sides
(Fig. 2A). A
stagnation edge is defined as a line where fluid shear stress is zero, and a
flow separation edge is that where flow detaches from a surface and is also
associated with zero shear stress. The distribution of blood shear stress
along the circumference of the implanted cylinder from 0 to ±109°
at a given axial location with a Reynolds number larger than 10 (within the
central portion 80% of the cylinder length) was estimated and analyzed on
the basis of a boundary layer theory
(51).
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To estimate the distribution of fluid shear stress on the implanted polymer
cylinder, the rate of blood flow (Q) in the vena cava was measured with a
Transonic flowmeter and used for computing the distribution of blood flow
velocity (u) along the axis of the cylinder using the following
equation (11,
34)
 | (1) |
Vascular implants were collected at specified times, fixed in 4%
formaldehyde in PBS for 20 min, and cut into serial transverse cryosections of
10 µm in thickness. A number of 20 equally spaced sections along the entire
axis of the implanted cylinder were collected for geometric measurements and
analyses. For each section selected at an axial location, the thickness of the
encapsulating thrombus was measured at 20 equally spaced locations within the
region from 0 to 109° in the circumferential direction of the implanted
cylinder (parallel to blood shear stress) and used for the calculation of the
radius and circumferential surface distance (x) of the implant (with
the encapsulating thrombus taken into account). The viscosity of blood (µ)
was measured using a capillary method as described previously
(30). The magnitude of blood
shear stress (
) along the circumference of each selected transverse
section was calculated from 0° to 109° using the following equation
(31,
34,
51)
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 | (2) |
is blood density and u is maximal blood flow velocity at
a given axial location on the implanted cylinder. A reconstruction of the
circumferential shear stress profiles at selected axial locations provides a
distribution of fluid shear stress on the surface of the implanted cylinder. A
differentiation of blood shear stress with respect to the circumferential
distance of the implanted cylinder yields a distribution of shear stress
gradients. Fluid shear stress in the trailing region from ±109 to
180° was not estimated because of the limitation of the analytic
approach.
Uniform shear model. Fluid shear stress on the PTFE membrane patch
of the uniform shear model was estimated using the Poiseuille approach. The
rate of blood flow and diameter of the vena cava were measured as described
above. Fluid shear stress () was estimated using the following equation
 | (3) |
Measurement of Cell Density
For the nonuniform shear model, whole specimens including the neointima of the implant were fixed as described above, treated with 0.5% Triton X-100 in PBS for 30 min, incubated with 20 nM of the cell nucleus-staining substance Hoechst 33258 at 37°C for 1 h (15), and observed en face using an Olympus fluorescence microscope. Previous studies (6, 16, 48–50) have shown that the gradient of cell density determines the direction of cell migration and alignment. The gradient-driven cell migration may be related to the mechanisms of cell survival. When cells reach a critical cell density within a given area, which induces a relative deficiency of oxygen and nutrients, cells may only survive by migrating to a new area with a lower cell density. On the basis of such a hypothesis, all cell types may be involved in the induction and regulation of cell density-related cell migration. Thus the total cell density was measured and analyzed in the present study. While a measurement of the density of individual cell types may provide information for the contribution of each cell type, we were not able to do so because of difficulties in the labeling of multiple cell types, possibly including endothelial cells, SMCs, leukocytes, platelets, and fibroblasts, and in the identification of individual cell boundaries in a highly packed cell population in the present model.
The density of total cell nuclei was measured at 40 equally spaced axial locations and 10 equally spaced circumferential locations from 0 to 109° at each axial location, resulting in a map of cell density on the implanted cylinder. The distribution of cell density was analyzed with respect to that of blood shear stress. For the uniform shear model, the distribution of cell density was measured using a similar approach as described above.
Measurement of SMC Alignment
For the same specimens used for cell nucleus measurements and analyses, SMC
actin was labeled simultaneously using an immunohistochemical approach
described previously (30).
Briefly, Triton X-100-treated specimens were incubated with an anti-SMC
-actin antibody (1:20, Chemicon) and subsequently incubated with a
fluorescein-conjugated secondary antibody (1:20) at 37°C for 1 h each.
SMCs were identified on the basis of positive labeling of SMC -actin.
The alignment of SMC -actin fiber bundles was measured at three
selected circumferential locations, including 0, 55, and 109° of the
implanted cylinder, with the flow direction defined as an alignment angle of
0°. Because the neointimal tissue was relatively thin (50–100
µm), SMC migration and alignment could be observed in a two-dimensional
layer. The pattern of SMC alignments was analyzed with respect to the
distribution of blood shear stress and cell density. For the uniform shear
stress model, the alignment of SMC -actin fiber bundles was measured at
three locations including the leading, middle, and trailing regions of the
implanted PTFE membrane patch, which corresponded to regions near 0, 55, and
109°, respectively, in the nonuniform shear model.
Statistics
Means ± SD were calculated for all measured parameters. Student's t-test (two tailed) was used to determine the significance of difference between two selected groups. One-way ANOVA was used to determine the significance of difference between more than two groups. Statistical significance of difference was considered at P < 0.05.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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Nonuniform shear model. To understand how fluid shear stress may
regulate SMC alignment and pattern formation, we assessed the distribution of
fluid shear stress in the nonuniform shear model. Flow patterns and the
distribution of fluid shear stress at selected axial locations of the
nonuniform shear model have been reported previously
(31). In this study, the
distribution of fluid shear stress along the entire axis of the implanted
polymer cylinder was estimated and presented using 5-day specimens as an
example. As shown in Fig. 2,
fluid shear stress is zero at the intersection of the implanted cylinder with
the vena cava wall as well as at the leading stagnation and flow separation
edges (perpendicular to blood shear stress) at 0 and 109°, respectively.
In the axial direction of the implant at a given circumferential location,
fluid shear stress increased from both ends to the center of the implant,
whereas the shear stress direction was always perpendicular to the implant
axis (Fig. 2A). In the
circumferential direction of the implant (parallel to blood shear stress) at a
given axial location, fluid shear stress increased from zero at the leading
stagnation edge to a maximum at 55° and then decreased to zero at the
flow separation edge (Fig.
2B). Over the entire implant, maximal shear stress was
found at 55° at the axial center of the implant
(Fig. 2C). The pattern
of fluid shear stress on the implant did not change apparently at various
observation times.
Uniform shear model. To test the possibility that nonuniform shear
stress may cause the formation of cell density gradients, we created a control
model with uniform shear stress for comparisons. Because we selected specimens
from the nonuniform shear model at a location with an average shear stress of
5 N/m2 (Reynolds number 10) for the measurement and
analysis of cellular activities, a comparable level of shear stress was
generated in the uniform shear model. Fluid shear stress measured at the
implanted PTFE patch was 5.18 ± 0.73 and 5.36 ± 0.66
N/m2 at days 5 and 10, respectively.
Distribution of Total Cell Density
Nonuniform shear model. Fluid shear stress has been shown to inhibit the proliferation of vascular cells (1, 26, 28–30, 39), and nonuniform shear stress possibly influences mitogenic activities in a shear level-dependent manner and causes the formation of cell density gradients, which may in turn regulate the direction of SMC migration and alignment. To test such a possibility, we examined the distribution of cell density with respect to that of fluid shear stress.
In the nonuniform shear model, the implanted cylinder was rapidly encapsulated with thrombi, forming a structure with a streamlined profile with the maximal thrombus thickness at the end and a minimal at the center of the implant. Two major cell density gradients, axial and circumferential gradients (perpendicular and parallel to blood shear stress, respectively), were found in this model (Fig. 3). The implantation of a polymer cylinder into the vena cava caused vessel wall injury, leading to cell proliferation at the injury site. Although blood cells attached to the implant after surgery, the cell density in the thrombus of the implant was significantly lower than that in the injured vessel wall, resulting in a cell density gradient from the vessel wall to the implant along the implant axis (referred to as the axial gradient of cell density) that is perpendicular to blood shear stress.
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The distribution of cell density in the axial direction of the implant (perpendicular to blood shear stress) changed significantly in a shear stress-dependent manner. The cell density along the zero-shear stagnation and flow separation edges (0 and 109°, respectively, perpendicular to blood shear stress) increased more rapidly than that in the shear stress region between the stagnation and flow separation edges, due to the shear inhibition of cell proliferation. Such an influence resulted in a nonuniform distribution of cell density in the circumferential direction of the implant with the maximal cell density at the stagnation edges and the minimal cell density at the site of maximal shear stress, resulting in the circumferential gradient of total cell density (Fig. 3). An inverse relationship was observed between blood shear stress and cell density in the circumferential direction of the implant at a given observation time (Fig. 4), suggesting that the nonuniform distribution of blood shear stress possibly caused the formation of the circumferential gradient of total cell density.
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In the shear stress region between the zero-shear stagnation and flow separation edges, the average circumferential gradient of cell density was larger than that in the axial direction at a given location of the implant, because the initial cell density on the implant at the intersection with the vena cava wall was lower in the shear stress region than that at the zero shear stagnation edges (Fig. 3B). Whereas the distribution of cell density altered dynamically with time due to progressive cell proliferation and migration, the pattern of cell density gradients did not change significantly at all observation times. Over the entire implant, a minimal cell density was found in a region near 55° at the axial center of the implant, where maximal shear stress was observed.
Uniform shear model. To verify the role of nonuniform shear stress in the formation of the circumferential gradient of total cell density, we analyzed and compared the distribution of cell density between the nonuniform and uniform shear stress models. In the uniform shear model, cell density gradients were observed from the implantation injury sites at the vena cava wall onto the PTFE patch in the axial direction of the implant (perpendicular to blood shear stress), as observed in the nonuniform shear model. However, unlike what was observed in the nonuniform shear model, SMCs migrated in a relatively constant speed in the axial direction across the entire PTFE patch. Thus no significant gradients of cell density were established in the direction of blood shear stress (perpendicular to the axis of the PTFE patch), which corresponds to the circumferential direction of the nonuniform shear model (Fig. 5).
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Direction of SMC Alignment
Nonuniform shear model. To test the hypothesis that fluid shear stress influences the direction of SMC alignment via the mediation of cell density gradients, we examined the alignment of SMCs with respect to the distribution of cell density. It was found that SMCs near the stagnation and flow separation edges of the implant were aligned in the implant axial direction (perpendicular to blood shear stress), whereas those in the shear stress region between the stagnation and flow separation edges were aligned toward the circumferential direction (parallel to blood shear stress; Fig. 6, A–C). The alignment of SMCs in each region was consistent with the dominant gradient of total cell density. Along the zero-shear stagnation and flow separation edges, the distribution of cell density was not influenced by shear stress, and the axial gradient of total cell density possibly determined the direction of SMC migration, resulting in the axial alignment of SMCs (perpendicular to blood shear stress). In the shear stress region between the stagnation and flow separation edges, the circumferential gradient of cell density was dominant and possibly directed SMC migration in the circumferential direction (parallel to blood shear stress; Fig. 3).
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Uniform shear model. The data above suggest that SMC migration and alignment are related to fluid shear stress and cell density gradients. To verify whether fluid shear stress directly influences SMC pattern formation, we assessed SMC alignment in the uniform shear model, which exhibited only cell density gradients in the axial direction of the PTFE patch (perpendicular to blood shear stress), without apparent cell density gradients in the direction of blood shear stress. Unlike that observed in the nonuniform shear model, the majority of SMCs were aligned in the axial direction of the PTFE patch (Fig. 6, D–F). The concurrent lack of cell density gradients and SMC alignment in the direction of blood shear stress supports the possibility that the establishment of cell density gradients may be a necessary step for shear-induced pattern formation of SMCs.
Zero shear model. To further identify the role of fluid shear stress and cell density gradients, we examined the pattern of SMC migration and alignment in the zero-shear model. The alignment of SMCs was consistent with cell density gradients. The pattern of SMC alignment was similar to that observed in the uniform shear model.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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The role of fluid shear stress in regulating the activities of vascular cells has been a topic of focus in vascular research. Alterations in the level and gradient of fluid shear stress have long been known to regulate the proliferation, migration, and alignment of vascular cells (3, 5, 9, 13, 14, 25, 28, 33, 42–44, 59) and the activity of related signaling molecules (2, 4, 7, 8, 17–20, 22, 23, 35–37, 40, 41, 45–47, 54–58, 60). Fluid shear stress exerts a frictional effect on cell membranes, causing conformational changes in cell membranes (12). Such changes may influence the activities of cell membrane molecules, including growth factor receptors and ion channels, which may in turn regulate cellular events such as cell proliferation and migration (7, 8, 13, 23, 29, 37, 41, 46, 54, 60). Recent investigations (1, 26, 28–30, 39) have demonstrated that fluid shearing friction inhibits mitogenic signaling activities in vascular cells, suppressing cell proliferation and migration. Thus it is possible that fluid shear stress may influence the activity of mitogenic molecules in a shear level-dependent manner, and nonuniform shear stress may induce the formation of mitogen gradients, causing graded cell proliferation and the formation of cell density gradients. Under such a hypothesis, we investigated the relationship between nonuniform shear stress and the distribution of cell density.
As shown in this study, a polymer cylinder implanted in a blood vessel is subject to a flow field with nonuniform shear stress, allowing the observation of shear influence on vascular cell migration. The level of fluid shear stress was inversely correlated with the total cell density in the neointima of the implant, supporting the possibility that fluid shear stress inhibits mitogenic activities and influences the distribution of total cell density. The presence of nonuniform shear stress possibly caused the formation of cell density gradients. In a related paper (32), we report a possible mechanism by which mitogenic molecules mediated such a process.
Role of Shear Stress and Cell Density Gradients in Regulating SMC Migration and Alignment
On the basis of the present study, it seems that SMC alignment and pattern formation are related to fluid shear stress and cell density gradients. These factors may influence SMC activities via two possible mechanisms. First, fluid shear stress may directly influence SMC migration and alignment via physical friction and cell membrane deformation. Second, nonuniform shear stress may influence these processes via the formation of cell density gradients, a necessary mediating step for shear-induced pattern formation of SMCs. To clarify these possibilities, we analyzed the relationship between fluid shear stress, cell density gradients, and the pattern of SMCs in the uniform and nonuniform shear models.
Results from the uniform shear model showed that the direction of fluid
shear stress was not consistent with the alignment of SMCs, suggesting that
fluid shear stress did not directly influence the alignment of SMCs. In a
related paper (32), it was
found that a pharmacological suppression of selected mitogenic factors,
including platelet-derived growth factor-
receptor and a nonreceptor
tyrosine kinase, Src, significantly reduced the influence of nonuniform shear
stress on SMC migration and alignment, even though the SMCs were subject to
the same field of nonuniform blood shear stress. Furthermore, SMCs were
resided underneath the endothelium and were not directly exposed to blood
shear stress. A shear-induced change may unlikely be a result of direct
physical shearing effect. These observations did not support the first
mechanism.
Directed cell migration is a complicated process, involving a variety of cellular machineries, regulatory molecules, and extracellular matrix proteins (24, 38, 52, 53). While the mechanisms of such a process remain poorly understood, a simple observation has shown that the gradient of cell density determines the direction of cell migration (6, 16, 48–50). Because fluid shear stress exerts an inhibitory effect on mitogenic activities, the presence of nonuniform shear stress possibly induces a graded suppression of cell proliferation and thus the formation of cell density gradients. The correlation of blood shear stress with the cell density, as observed in the present study, supports such a possibility. Further investigations showed that the gradient of cell density was consistent with the alignment of SMCs in either the presence or the absence of nonuniform blood shear stress. These observations suggest that the formation of cell density gradients is possibly a critical intermediate step for nonuniform shear stress-initiated pattern formation of SMCs. It should be pointed out that fluid shear stress may not be a unique factor that induces the formation of cell density gradients. Any factors, such as trauma and inflammation, that influence local cell growth may induce changes in the distribution of cell density.
Experimental Approach
In the present study, several artificial models were used to induce SMC migration on polymer implants under defined fluid shear stress. These models were introduced because of difficulties in the characterization of SMC migration and the assessment of fluid shear stress in a blood vessel in vivo. The uniqueness of these modeling systems is that the distribution of fluid shear stress can be assessed and controlled by varying the geometry and location of the implant in blood flow. Furthermore, the migration and alignment of SMCs can be characterized in vivo. Previous studies (31, 34) have demonstrated that such artificial systems can be used to assess the role of fluid shear stress in the regulation of SMC migration and proliferation. Compared with other artificial systems, such as cell and tissue culture, these in vivo models can be used to investigate cell activities under realistic vascular conditions.
In the nonuniform shear model used in this study, in addition to the gradient of blood shear stress, pressure gradients are present on the surface of the implanted cylinder in the direction of blood shear stress. In the trailing region of the implant, adverse pressure gradients develop due to divergent geometry, causing the formation of vortex flow (51). The gradient of blood pressure may be a potential factor that regulates SMC activities. This problem warrants a further investigation.
Although the present research was based on the observation that nonuniform fluid shear stress in vortex blood flow possibly influences the migration and alignment of vascular SMCs, the polymer implantation model may not represent a natural vascular system. Compared with vasculogenesis, the formation of neointima in this model is a relatively rapid process under biochemical and biomechanical conditions that differ from those during vascular development. Furthermore, the migration and proliferation of vascular SMCs due to implantation injury are pathological processes, which may not represent those during natural morphogenesis. Nonetheless, this study may provide insights into the mechanistic aspects of shear stress-induced migration and pattern formation of vascular SMCs during pathological remodeling.
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DISCLOSURES |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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FOOTNOTES |
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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.
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REFERENCES |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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-actin filaments in vascular
smooth muscle cells in response to mechanical stretch. Am J Physiol
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H1839–H1847, 2003.-receptor
and Src. Am J Physiol Heart Circ Physiol
285: H1081–H1090,
2003.This article has been cited by other articles:
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  A. L. Pyle, J. B. Atkinson, A. Pozzi, J. Reese, B. Eckes, J. M. Davidson, D. L. Crimmins, and P. P. Young Regulation of the Atheroma-Enriched Protein, SPRR3, in Vascular Smooth Muscle Cells through Cyclic Strain is Dependent on Integrin {alpha}1{beta}1/Collagen Interaction Am. J. Pathol., November 1, 2008; 173(5): 1577 - 1588. [Abstract] [Full Text] [PDF]
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 J. F. LaDisa Jr., Lars. E. Olson, R. C. Molthen, D. A. Hettrick, P. F. Pratt, M. D. Hardel, J. R. Kersten, D. C. Warltier, and P. S. Pagel Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries Am J Physiol Heart Circ Physiol, May 1, 2005; 288(5): H2465 - H2475. [Abstract] [Full Text] [PDF]
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 J. F. LaDisa Jr., L. E. Olson, I. Guler, D. A. Hettrick, J. R. Kersten, D. C. Warltier, and P. S. Pagel Circumferential vascular deformation after stent implantation alters wall shear stress evaluated with time-dependent 3D computational fluid dynamics models J Appl Physiol, March 1, 2005; 98(3): 947 - 957. [Abstract] [Full Text] [PDF]
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J. F. LaDisa Jr., L. E. Olson, I. Guler, D. A. Hettrick, S. H. Audi, J. R. Kersten, D. C. Warltier, and P. S. Pagel Stent design properties and deployment ratio influence indexes of wall shear stress: a three-dimensional computational fluid dynamics investigation within a normal artery J Appl Physiol, July 1, 2004; 97(1): 424 - 430. [Abstract] [Full Text] [PDF]
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S. Q. Liu, C. Tieche, D. Tang, and P. Alkema Pattern formation of vascular smooth muscle cells subject to nonuniform fluid shear stress: role of PDGF-{beta} receptor and Src Am J Physiol Heart Circ Physiol, August 7, 2003; 285(3): H1081 - H1090. [Abstract] [Full Text] [PDF]
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indicates the circumferential direction of the cylinder (parallel to
blood shear stress). 0, 109, and 180° indicate the leading stagnation,
flow separation, and trailing stagnation edges, respectively. B:
uniform shear stress model with a membrane patch on the vena cava endothelium.
Note that smooth muscle cell (SMC) migration was initiated from the
implantation injury sites to the patch in the direction perpendicular to blood
shear stress but not at the free edges in the direction parallel to blood
shear stress. Open arrow, direction of SMC migration on the membrane
patch.
