Biomedical Engineering Reference
In-Depth Information
The effects of diffusion, convection, and electrostatic interactions can be
combined by summing the fluxes due to each effect. For example, the one-
dimensional flux
N
of a molecular solute through a tissue is given by
¬
s
cz
-
-
N
=
'
D
xz
N
+
cE
+
cU
,
[4]
-
-
-
s
®
where
0
is the porosity of the tissue,
c
is the concentration of the solute at posi-
tion
x
,
z
is the valence of the solute (if the solute is charged),
U
is the average
fluid velocity relative to the tissue, and
E
is the electric field within the matrix.
D
is the diffusivity of the solute, N is the electrical mobility of the solute, and
W
is the hindrance factor for convection (25).
Oxygen is the most basic of nutrients, and investigations into oxygen trans-
port are common. The response of cells to oxygen gradients can be finely meas-
ured (2), and numerical models can be used to design devices where oxygen
transport to all cells is controlled (66).
2.4. Centimeter-Meter Scale
Biological phenomena typically encompass a range of time and length
scales whose intrinsically complex interactions are critical to system function
(37). For example, in the study of arterial disease, one needs to understand how
the entire cardiovascular system responds to a variety of external factors that
impact local flow characteristics. The fluid dynamic and solid stresses experi-
enced by the vascular wall tissues lead to a cascade of critical biological events,
which may contribute to disease progression. At the cellular level, these stresses
produce deformations of the cytoskeletal network, the cell membrane, and the
nuclear envelope, which lead, in turn, to conformational changes in individual
proteins that elicit the biological response. Along with understanding what goes
on within an organ, it is necessary to know how the organ interacts with the rest
of the body.
2.5. Multiscaled Systems
To fabricate a functioning device, it is necessary to combine systems of
different scales. This has been achieved in some experiments, most notably
bioartificial liver systems. In such a system, hepatocytes are cultured on a scaf-
fold and under continuous flow. The overall device provides liver function, and
can be used to assist patients with liver disorders (Figure 19).
