Biomedical Engineering Reference
In-Depth Information
7.5 TRANSPORT THROUGH POROUS MEDIA
Porous media are solid materials that are composed of pore structures, which are typi-
cally fluid filled in biological applications. Porous media can have very different topo-
graphical and morphological properties, based on the internal organization of the pores.
The most common porous media in biological systems is the interstitial space, which is
composed of the extracellular matrix and interstitial fluid. As we have learned, the extra-
cellular matrix is mostly composed of proteins and functions as a mechanical scaffolding
for cells. This structure is required for the normal functioning of cells, including migration,
proliferation, and apoptosis.
It is common to describe porous media based on the porosity, which is defined as
volume assoicated with voids
total volume
ε
5
ð
7
:
22
Þ
The values that comprise porosity may need to be approximated from microscopy images
of scaffolds or tissues, and porosity can be dependent on the loading conditions of the
porous media. For instance, the extracellular matrix is deformable and thus the porosity
may change under particular conditions because both the volume associated with voids
and the total volume can change. The porosity of the interstitial space, neglecting blood
vessels and cells, approaches 0.9, whereas the porosity of general biological
tissues
(including blood vessels and cells) would be closer to 0.25.
Porous media can also be classified based on the body's tortuosity, which is a measure
of the random orientation and random spacing of pores. Clearly, not all pores will be able
to be classified as straight channels through the media, and tortuosity is a measure of this
bending and/or twisting (
Figure 7.5
). Tortuosity is defined as
L
actual
L
T
5
ð
7
:
23
Þ
FIGURE 7.5
Tortuosity is defined as the
actual minimum distance between two points
connected by a pore divided by the straight
line path between the points. This value can
only be greater than or equal to 1.
X
2
D
1
X
4
L
1
X
1
L
2
D
2
X
3
Porous Media
D
1
L
1
D
2
L
2
,T
X
3
→
X
4
=
T
X
1
→
X
2
=
Search WWH ::
Custom Search