Semi-empirical determination of the diffusion coefficient of the Fricke Xylenol Gel dosimeter through Finite Difference methods.
Keywords:
Finite difference, Diffusion coefficient, Simulation, Gel dosimeters, Fricke Xilenol Gel.Abstract
Partial Differential Equations (PDE) can model natural phenomena, such as related to physics, chemistry and engineering. For these classes of equations, analytical solutions are difficult to be obtained, so a computational approach is indicted. In this context, the Finite Difference Method (FDM) can provide useful tools for the field of Medical Physics. In this study, is described the implementation of a computational mesh, in order to be used in determining the Diffusion Coefficient (DC) of the Fricke Xylenol Gel dosimeter (FXG). The initial and boundary conditions both referred by experimental factors are modelled in FDM, thus making a semi-empirical study in determining the DC. Together, the method of Reflection and Superposition (SRM) and the analysis of experimental data, served as first validation for the simulation. Such methodologies interface generated concordant results for a range of error of 3% in concentration lines for small times when compared to the analytical solution. The result for the DC was 0.43 mm2/h. This value is in concordance with measures parameters range found in polymer gels dosimeters: 0.3-2.0 mm2/h. Therefore, the application of computer simulation methodology supported by the FDM may be used in determining the diffusion coefficient in FXG dosimeter.References
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2. Oliveira LN, Calcina CSG, Parada MA, Almeida CE, Almeida A. Ferrous Xylenol Gel Measurements for 6 and 10 MV Photons in Small Fiel Sizes. Braz. J. Phys. 2007; 27:1141-1146.
3. Alva-Sánchez MS, Oliveira LN, Petchevist PC, Moreira MV, Almeida A. Beta planar source quality assurance with the Fricke xylenol gel dosimeter. Radiat. Phys. Chem. 2014; 96:56-59.
4. Oliveira LN, Calcina CSG, Parada MA, Almeida CE, Almeida A. 6 MV Wedge Photon Beam Profiles with the Fricke Xylenol Gel Dosimeter. Braz. J. Phys. 2009; 39:615-618.
5. Caldeira AMF, De Almeida A, Neto AM, Baesso M, Bento AC, Silva MA. Fricke Xylenol Gel characterization using a photoacustic technique. Nucl. Instr. Meth. Phys. A. 2007; 582:484-488.
6. Calcina CSG, Oliveira LN, Almeida CE, Almeida A. Dosimetric parameters for small field sizes using Fricke xylenol gel, thermoluminescent, film dosimeters and an ionization chamber. Phys. Med. Biol. 2007; 52:1431-1439.
7. Davies JB, Bosi SG, Baldock C. Dosimetry aspects of a non-diffusing genipin–gelatin gel. Radiat. Phys. Chem. 2013; 83:19-27.
8. Maeyama T, Fukunishi N, Ishikawa KL, Furuta T, Fukasaku K, Takagi S, Noda S, Himeno R, Fukuda S. A diffusion-free and linear-energy-transfer-independent nanocomposite Fricke gel dosimeter. Radiat. Phys. Chem. 2014; 96:92-96.
9. Oliveira LN, Zimmerman RL, Moreira MV, Ila D, Almeida A. Determination of diffusion coefficient in Fricke Xylenol gel dosimeter after electron beam bombardment. Surf. Coating. Tech. 2009; 203:2367-2369.
10. Iserles A. First Course in the Numerical Analysis of Differential Equations. 2.ed. New York:Cambridge University Press; 2009. 459 p.
11. Ióri V. EDP um curso de graduação “Coleção matemática universitária”. 3.ed. Rio de Janeiro:IMPA; 2012. 275 p.
12. Crank J. The Mathematics of Diffusion. 2.ed. Bristol,Inglaterra: Oxford University Press; 1975. 414 p.
13. Feynman RP, Leighton R, Sands M. Feynman Lectures on Physics. Addison-Wesley Boston, 1994.
14. Balluffi RW, Samuel MA, Craig WC. Kinetics of Materials. 1.ed. Hoboken,New Jersey:Wiley-Interscience; 2005. 645 p.
15. Jaroslav Š, Václav Spěváček. New 3D radiochromic gel dosimeters with inhibited diffusion. J. Phys.: Conf. Ser. 2009; 164:123-125.
16. Evans LC. Partial Differential Equations, Vol.12: Graduate Studies in Mathematics. Providence,Rhode Island:American Mathematical Society. 2010. 749 p.
17. Morton KW, Mayers DF. Numerical Solution of Partial Differential Equations. 2.ed. New York:Cambridge University Press; 2005. 278 p.
18. Olsen-Kettle L. Numerical solution of partial differential equations Lectures book. Australia:The University of Queensland,Earth Systems Science Computational Centre; 2005. 206 p.
19. Courant R. Methods of Mathematical Physics,Vol.2: Partial Differential Equations. NewYork, Wiley-Interscience; 1962. 560 p.
20. Vretblad A. Fourier analysis and its applications. Graduate texts in Mathematics 223, Springer; 2003. 279 p.
21. Kron TD, Jonas D, Pope JM. Fast T1 imaging of dual gel samples for diffusion measurements in NMR dosimetry gels. Magn. Reson. Imaging. 1997; 15:211-221.
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Published
2014-10-08
How to Cite
de Oliveira, L. N., & Nascimento, E. O. (2014). Semi-empirical determination of the diffusion coefficient of the Fricke Xylenol Gel dosimeter through Finite Difference methods. Scientia Plena, 10(10). Retrieved from https://www.scientiaplena.org.br/sp/article/view/1919
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