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A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx.

Sumets PP, Cater JE, Long DS, Clarke RJ - Proc. Math. Phys. Eng. Sci. (2015)

Bottom Line: We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer.This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL).In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Science , University of Auckland , Auckland 1142, New Zealand.

ABSTRACT

We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic-mobility problems using boundary element methods. We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL). In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

No MeSH data available.


Related in: MedlinePlus

Varicose vessels ((a–d) cases I–IV and (e) IX, respectively) showing flow fields and shear stresses exerted by the flow. The first colour bar indicates the magnitude of the shear stresses on the vessel walls, whereas the scale beneath corresponds to the stresses on the cell. Corresponding translational and angular velocities are: (a) W=(0.98,0), ωp=0; (b) W=(0.88,0), ωp=0; (c) W= (0.7,0), ωp=0; (d) W=(0.6,0), ωp=−0.1. Regions inside dashed boxes in (b,d) are shown magnified in figure 7.
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RSPA20140955F5: Varicose vessels ((a–d) cases I–IV and (e) IX, respectively) showing flow fields and shear stresses exerted by the flow. The first colour bar indicates the magnitude of the shear stresses on the vessel walls, whereas the scale beneath corresponds to the stresses on the cell. Corresponding translational and angular velocities are: (a) W=(0.98,0), ωp=0; (b) W=(0.88,0), ωp=0; (c) W= (0.7,0), ωp=0; (d) W=(0.6,0), ωp=−0.1. Regions inside dashed boxes in (b,d) are shown magnified in figure 7.

Mentions: In figure 5, we examine the flow fields and FSSs for the varicose geometry in the presence of a cell. When the cell is located in the geometric constriction (case I), in figure 5a, we observe a local amplification of stresses and flow velocities, over that seen when the cell is absent (figure 5e). However, immediately above the cell we observe a reduction in the shear stress. This is highlighted further in figure 6, which shows that the presence of the cell leads to increased wall stress (as compared with the cell-free vessel) immediately upstream and downstream of the cell, but decreased stress directly above the cell (i.e. x=−2). When the particle is located on the centreline of the vessel, and in the widest part of the vessel (figure 5c), we observe that the influence of the cell upon the FSSs on the wall is fairly minimal.Figure 5.


A boundary-integral representation for biphasic mixture theory, with application to the post-capillary glycocalyx.

Sumets PP, Cater JE, Long DS, Clarke RJ - Proc. Math. Phys. Eng. Sci. (2015)

Varicose vessels ((a–d) cases I–IV and (e) IX, respectively) showing flow fields and shear stresses exerted by the flow. The first colour bar indicates the magnitude of the shear stresses on the vessel walls, whereas the scale beneath corresponds to the stresses on the cell. Corresponding translational and angular velocities are: (a) W=(0.98,0), ωp=0; (b) W=(0.88,0), ωp=0; (c) W= (0.7,0), ωp=0; (d) W=(0.6,0), ωp=−0.1. Regions inside dashed boxes in (b,d) are shown magnified in figure 7.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4528650&req=5

RSPA20140955F5: Varicose vessels ((a–d) cases I–IV and (e) IX, respectively) showing flow fields and shear stresses exerted by the flow. The first colour bar indicates the magnitude of the shear stresses on the vessel walls, whereas the scale beneath corresponds to the stresses on the cell. Corresponding translational and angular velocities are: (a) W=(0.98,0), ωp=0; (b) W=(0.88,0), ωp=0; (c) W= (0.7,0), ωp=0; (d) W=(0.6,0), ωp=−0.1. Regions inside dashed boxes in (b,d) are shown magnified in figure 7.
Mentions: In figure 5, we examine the flow fields and FSSs for the varicose geometry in the presence of a cell. When the cell is located in the geometric constriction (case I), in figure 5a, we observe a local amplification of stresses and flow velocities, over that seen when the cell is absent (figure 5e). However, immediately above the cell we observe a reduction in the shear stress. This is highlighted further in figure 6, which shows that the presence of the cell leads to increased wall stress (as compared with the cell-free vessel) immediately upstream and downstream of the cell, but decreased stress directly above the cell (i.e. x=−2). When the particle is located on the centreline of the vessel, and in the widest part of the vessel (figure 5c), we observe that the influence of the cell upon the FSSs on the wall is fairly minimal.Figure 5.

Bottom Line: We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer.This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL).In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Science , University of Auckland , Auckland 1142, New Zealand.

ABSTRACT

We describe a new boundary-integral representation for biphasic mixture theory, which allows us to efficiently solve certain elastohydrodynamic-mobility problems using boundary element methods. We apply this formulation to model the motion of a rigid particle through a microtube which has non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to scenarios such as the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an endothelial glycocalyx layer (EGL). In this context, we examine the impact of geometry upon some recently reported phenomena, including the creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells.

No MeSH data available.


Related in: MedlinePlus