Solutions to the diffusion equation with no solute elimination or generation

4 SOLUTIONS TO THE DIFFUSION EQUATION WITH NO SOLUTE ELIMINATION OR GENERATION 

When appropriately applied, the equations derived in the section above can be used to predict variations in drug concentration within a tissue following administration. Por the description of molecular transport in cells or tissues, the mass conservation equations must be simplified by making appropriate 

The concentration of A as a function of time and distance from the site of initial injection can be predicted by solving Equation 3-31, expressed in a onedimensional rectangular coordinate system  

Typical problems of diffusive transport. Many real examples of diffusion in organs and tissues ean be analyzed in terms of simple solutions to the diffusion equation in rectangular, cylindrical, or spherical coordinates (a) a bolus of molecules is injected into a cylindrical volume of infinite extent (b) a cylindrical source of molecules in an infinite volume (c) a spherical source of molecules in an infinite volume or (d) drug concentration is maintained at a constant value at the surface of a semi-infinite medium. 

The error function occurs frequently in solutions to the diffusion equation extensive tables of error functions are available as well as series expansions for approximation [12]. Some values are tabulated in Appendix B. Equation 3-37 can be used to examine the penetration of drug molecules into a tissue when suddenly presented at a surface (Eigure 3.6). 

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