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complete description of the very complicated geometry and dynamics of the stomach. However, it was created to provide indications of the concentration and duration of radon in regions that may contain radiosensitive cells. These efforts were necessary because no other theoretical or experimental information is available. By varying the parameters, it was possible to obtain a range of results and to identify extreme values that could serve as bounds for radon concentrations in the stomach wall.
For simplicity, the lumen of the stomach was considered to be a sphere. The sphere was surrounded by concentric spherical shells representing the mucous layer and the wall. The stomach was filled with water containing a unit concentration of radon at time t = 0. The radon concentration in the mucous and wall was zero at t = 0. The radon concentration at the outer surface of the wall was considered to be zero at all times because of the removal of radon by blood flowing through the stomach wall.
The time-dependent equation describing the concentration of radon can be derived from Fick's law:
C = the concentration of radon,
D = the effective diffusion coefficient, 2 = the Laplacian operator, and
λ = the radioactive-decay constant associated with 222Rn.
Since the intervals associated with events in the stomach are generally much less than the half-life of 222Rn, radioactive decay is neglected. Using spherical symmetry, the Laplacian operator can be expressed in terms of only the radius, r:
One procedure for solving the equation is to separate C into the product of two components, one in radius only, R(r), and another in time only, T(t) (Andrews 1986). Thus,
where K is referred to as a separation constant. Initial and boundary conditions are expressed as