Biomedical Engineering Reference
In-Depth Information
2.2 Convection
Convective mass transport through a porous medium can be described using the
averaged equations as formulated by Darcy or Brinkman [
27
]. These equations
express a relation between medium velocity and the applied pressure gradient
which is governed by the permeability, a factor that characterizes the influencing
matrix properties. Experimental setups are described in literature that can measure
different carrier permeabilities, either by applying a constant pressure or a constant
flow [
69
,
91
].
Several models are available that provide a link between structural carrier
properties and permeability [
49
,
53
]. Their application range is however con-
strained to approximations at the macroscopic scale since they depend on physical
and geometric idealizations of the microporous carrier [
120
]. From the theory of
mixtures and based on experimental results, it was found that the effects of induced
fluid flows (which are rather low) on solute transport in the carrier are most
significant for solutes with large molecular weight [
35
,
111
].
2.3 Compression-Induced Mass Transport
Dynamic compression of a carrier combines matrix compaction with interstitial
fluid transport [
33
]. Augmented solute transport associated with this convective
fluid transport will therefore at the same time be restricted resulting from a
decrease in matrix diffusivity. This compression-induced loss in diffusivity can
either be measured experimentally with FRAP [
38
,
66
] or estimated from struc-
tural diffusivity relations such as in Mackie and Meares [
73
,
74
,
92
], which
assumes a high dependency of matrix diffusivity on fluid volume fraction. An
interesting alternative would be the coupling of diffusive transport with structural
deformation at the microscale level [
117
].
The effect of unconfined compression on enhanced solute transport has previ-
ously been formulated in mathematical terms using the theory of incompressible
mixtures [
5
,
89
]. In agreement with experimental observations, it was established
that compression frequency and solute molecular weight are both decisive factors
for the extent of compression-enhanced solute transport [
32
,
83
]. As a major
conclusion from these studies it was shown that mechanical carrier stimulation can
significantly improve the transport of larger molecules (from glucose to large
signaling molecules). The mechanism which underlies this phenomenon is found
in the dual action of small convective flows and the increased peripheral solute
gradient during dynamic loading [
83
].
In the next sections we will give an overview on how solute molecules with
different molecular weight can influence specific cell behavior and how the
transport of these molecules is influenced by the cellular carrier components.
Solutes of interest range from small molecules (e.g., oxygen and glucose) to large
molecules (e.g., growth factors).
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