Biomedical Engineering Reference
In-Depth Information
and to use it for this problem, pressure needs to be expressed in concentration. Assuming
an ideal gas law, at a standard temperature (273K) and pressure (1 atm), 1 mol of gas oc-
cupies 22.414L.
Ppp
(
)
4.17 * 10
−
12
(0.21
0.001)
−
−
10
2
J
mem
A
1
A
2
2.480
10
−
kgmol / s.m
=
=
=
×
local
22.414 *
d
22.414 * 0.00015
A nylon film has a much smaller permeability value for oxygen and would make a
more suitable barrier. However, for a membrane oxygenator application, polyethylene
would be more suitable.
Equation (2.14) assumes that the solute is easily soluble in the medium in which
permeability is defined. However, the molecular transfer reduces in scenarios where
solubility is limited. For example, concentration gradient exists for glucose between
the extracellular fluid and intracellular fluid but the membranes do not permit the
transfer of glucose from one compartment to the other. To cross the lipid bilayer of
the cell membrane, a substance must enter (or partition) into the chemical matrix
of the membrane. Lipids do not interact effectively with polar molecules, such as
water or substances such as glucose that readily dissolve in water. Therefore, polar
molecules experience significant resistance when entering the lipid bilayer. Conse-
quently, even in the presence of a favorable chemical concentration gradient, the
diffusion of glucose across a cell membrane is very slow. A general approach to
include the effect of solubility in the permeability calculation is by incorporating a
factor called the partition coefficient,
, which is defined as the ratio of the solubil-
ity of the compound in lipids to that in water. Then
ϕ
2
[m /s]
D
AB
(2.15)
P[m/ ]
=
ϕ
mem
δ
[m]
2.3.2 Facilitated Diffusion
The lipid bilayer is a semipermeable barrier. A number of molecules cannot dif-
fuse freely, despite the presence of electrochemical gradients, as the lipid bilayer is
impermeable. One way through which some molecules are transported in and out
of cells is by using specialized structures called transporters. This process is called
facilitated diffusion and does not require an expenditure of energy.
Transporters are typically proteins, or assemblies of proteins, embedded in the
lipid bilayer. Transporters are broadly categorized into two groups: carriers and
channels. Carriers are highly specific proteins, which interact with the molecule
to be transported at a specific sites called receptor sites. Those sites have a three-
dimensional shape, permitting interaction with molecules that have a matching
three-dimensional configuration. This arrangement provides specificity, similar to
a key specific to a lock. Molecules with a shape that does not match a binding site
