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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 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).

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.

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A diagram illustrating two-dimensional geometry of the model, detailing surface labels.
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RSPA20140955F2: A diagram illustrating two-dimensional geometry of the model, detailing surface labels.

Mentions: The boundary-integral formulation derived in §2 is very general, applicable in both two and three dimensions. Due to the computational expense, however, we follow [14] and consider a two-dimensional regime, where the vessel is modelled as a channel. Notation specific to this geometry is given in figure 2. We solve the governing integral equations using a BEM scheme, the particulars of which can be found in the electronic supplementary material, S4, alongside validation details.Figure 2.


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)

A diagram illustrating two-dimensional geometry of the model, detailing surface labels.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSPA20140955F2: A diagram illustrating two-dimensional geometry of the model, detailing surface labels.
Mentions: The boundary-integral formulation derived in §2 is very general, applicable in both two and three dimensions. Due to the computational expense, however, we follow [14] and consider a two-dimensional regime, where the vessel is modelled as a channel. Notation specific to this geometry is given in figure 2. We solve the governing integral equations using a BEM scheme, the particulars of which can be found in the electronic supplementary material, S4, alongside validation details.Figure 2.

Bottom Line: 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).

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