Biomedical Engineering Reference
In-Depth Information
We will show in the following that diffusion in the ECS is much slower than free
diffusion. It is common to use an apparent (or effective) diffusion coefficient (ADC)
to determine the speed of diffusion of drugs in the tumor ECS [17]. Speed of diffu-
sion based on the apparent diffusion coefficient is equal to that of the real diffusion
coefficient in the restricted geometry of the ECS. The apparent diffusion coefficient
depends on the morphology of the ECS, especially on the tortuosity (Figure 5.32)—
the ratio of the real distance to the straight line distance between two points—and
also to special features of the ECS like intercleft spaces and constrictions. Real drug
delivery time will be determined by adding to the diffusion characteristic time in the
ECS the uptake characteristic time (time for the macromolecule to enter the cell),
plus the diffusion time inside the cell [13].
Remark that it is of great importance in cancer treatment to be able to esti-
mate the value of the apparent diffusion coefficient [18]. If the delivery time is
too long—it may reach 48 hours—or if some cells are not delivered, the balance
between destruction and multiplication of cancerous cells will be unfavorable. Note
also that in some cases, a change of the ADC reflects a change in the cells shape and
arrangement [19], so that an evolution of a disease may be followed.
We suppose that the fluid flow in the ECS is negligible in front of the molecular
diffusion, so we have to calculate the diffusion of a substance in a very complex
geometry. Different types of numerical approaches have been proposed for regu-
lar repetitive patterns like squares and triangles: the homogenization theory [20],
which is based on the calculation of the diffusion in a motif and extending the result
to the whole domain, and the Monte Carlo method [21] in geometry where the
boundaries are defined by analytical linear functions. It is thought that at a certain
point regular patterns calculation could be sufficient to approximate an average
ADC [22]. However this is not always the case if the ECS has intercleft spaces or
constrictions, especially if one wants to estimate the local uptake rates [23] or if
any change in cell shape and arrangement takes place [20]. So far, there have been
Figure 5.32  Schematic view of the diffusion paths in a porous media depending on the tortuosity.
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