A Method for determining the diffusion coefficient in Fe(II/III) radiation dosimetry gels using finite elements

Magnetic resonance imaging (MRI) may be used to image three-dimensional dose distributions of ionizing radiation in tissue equivalent gels infused with ferrous sulphate solutions, commonly known as Fricke gels. In this technique, ferrous (Fe2+) ions are oxidized to ferric (Fe3+) ions by free radicals produced by ionizing radiation. A limitation on this technique is the diffusion of ferric (Fe3+) ions in the gel. A method is presented for evaluating the diffusion coefficient in Fricke gels. Finite elements are used to model variations of the concentration in space, coupled with an analytical scheme to integrate the resulting system of equations through time. This method may be used for problems with one, two or three space dimensions and with arbitrary initial and boundary conditions. Results are presented for one- and two-dimensional data.