Biomedical Engineering Reference
In-Depth Information
Membrane transport
In a closer view on the transport of gases through the membrane in an artificial
lung, two mechanisms can apply: diffusion through pores or solution diffusion
through a dense, solid material. Federspiel et al.
7
give a good overview of the
mechanisms involved.
In a non-porous membrane where solution diffusion is the only transport
mechanism, two basic values determine the permeability: the solubility of the
gas in the membrane material and the diffusion through the material as such,
with the permeability as the product of solubility and diffusivity. Here, the
solubility is a function of the polarity of the gas and membrane material, and for
the diffusivity as a rule of thumb smaller molecules tend to have high diffusion
coefficients, as they can move more freely and faster. The transport of gases by
solution diffusion always has a certain hysteresis: when concentrations on the
gas side are changed, this higher concentration needs to dissolve in the mem-
brane material and migrate through the membrane wall and only then will the
gases reach the blood side of the device. Depending on the thickness of the
membrane and the diffusion coefficient of the gas in the membrane material, this
hysteresis can take some minutes. This delay in concentration changes makes
the conduct of a clinical application of an artificial lung, in particular a
cardiopulmonary bypass, more difficult and contributed to the displacement of
silicone oxygenators in cardiac surgery.
In porous membranes, the diffusion of gas molecules through the pores is not
entirely clarified in detail. Commonly, only an overall permeability of a given
gas through the membrane is defined. This is a function of pore size, pore
tortuosity, wall thickness/gas path length and, of course, the size and mass of the
gas molecule, temperature and pressure gradient. This permeability is a
composite of the three contributing mechanisms:
· free diffusion comparable to that in a gas phase;
· Knudsen diffusion;
· solution diffusion.
(Formally, also convection can contribute to the permeance, but pressure
gradients in blood oxygenators need to be kept at a minimum to prevent the
build-up of gas bubbles on the blood side; therefore convection in this case can
be neglected.)
In large pores, the transport will take place according to the diffusion laws as
they are valid for a gas-in-a-gas model (Fick's model, see above): all molecules
move randomly with the speed as a function of temperature and pressure. This
leads to a concentration equilibration and thus net transport from areas of high
concentration to areas of low concentration. The narrower the pores get, the
more molecules will not only collide with other gas molecules, but increasingly
also with the pore walls, which decreases speed of exchange.
