A least-squares error minimization approach in the determination of ferric ion diffusion coefficient of Fricke-infused dosimeter gels.
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) x 10(-2) cm2 h(-1) at room temperature. This value falls within the 1.00-2.00 x 10(-2) cm2 h(-1) range 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.
Tseng
Y J
YJ
Institute of Biomedical Engineering, University Systems of Taiwan-National Yang Ming University, Pei-Tou, Taipei, Taiwan, Republic of China.
Huang
Sung-Cheng
SC
Chu
W C
WC
D004058:Diffusion; D004307:Dose-Response Relationship, Radiation; D005296:Ferrous Compounds / Q000737:chemistry; D005583:Fourier Analysis; D005782:Gels; D006801:Humans; D007477:Ions; D008279:Magnetic Resonance Imaging; D015233:Models, Statistical; D008962:Models, Theoretical; D016011:Normal Distribution; D019047:Phantoms, Imaging; D000644:Quaternary Ammonium Compounds / Q000737:chemistry; D011874:Radiometry / Q000379:methods*; D016634:Radiosurgery; D011880:Radiotherapy Planning, Computer-Assisted; D012685:Sepharose / Q000737:chemistry; D012965:Sodium Chloride / Q000737:chemistry; D013464:Sulfuric Acids / Q000737:chemistry; D013997:Time Factors
D005296:Ferrous Compounds; D005782:Gels; D007477:Ions; D000644:Quaternary Ammonium Compounds; D013464:Sulfuric Acids; D012965:Sodium Chloride; D012685:Sepharose; C038178:ammonium ferrous sulfate; C033158:sulfuric acid