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A least‐squares error minimization approach in the determination of ferric ion diffusion coefficient of Fricke‐infused dosimeter gels
Author(s) -
Tseng Y. J.,
Huang SungCheng,
Chu W. C.
Publication year - 2005
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.1879452
Subject(s) - ferric , diffusion , analytical chemistry (journal) , dosimeter , materials science , ion , chemistry , agarose , dosimetry , chromatography , inorganic chemistry , physics , thermodynamics , nuclear medicine , medicine , organic chemistry
A least‐squares error minimization approach was adopted to assess ferric ion diffusion coefficient of Fricke‐agarose gels. Ferric ion diffusion process was modeled as a Gaussian‐shaped degradation kernel operating on an initial concentration distribution. Diffusion coefficient was iteratively determined by minimizing the error function defined as the difference between the theoretically calculated and the experimentally measured dose distributions. A rapid MR image‐based differential gel dosimetry technique that time resolves the evolution of the ferric ion diffusion process minimizes smearing of the dose distribution. Our results showed that for a Fricke‐agarose gel contained 1 mM ammonium ferrous sulfate, 1% agarose, 1 mM sodium chloride, and 50 mM sulfuric acid, its ferric ion diffusion coefficient is ( 1.59 ± 0.28 ) × 10 − 2cm 2h − 1at room temperature. This value falls within the 1.00 – 2.00 × 10 − 2cm 2h − 1range previously reported under varying gelling ingredients and concentrations. This method allows a quick, nondestructive evaluation of the ferric ion diffusion coefficient that can be used in conjunction with the in situ gel dosimetry experiment to provide a practical diffusion characterization of the dosimeter gel.