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Abstract
Many scientific and technological areas associated with industrial process, diagnostic radiation images and radiation therapy demand high levels of accuracy and practicality for the measurement of X-ray energy spectra. The energy spectra of an X-ray beam can be determined either a direct or indirect measurement. Direct measurement uses a high energy resolution detector placed along the direction of the beam. Indirect measurement is based on the transmission curve of the beam and Laplace transforms. For this, i) a complete and exhaustive description of the mathematical derivation of the energy spectrum was carried out; ii) it was used the multistart algorithm along with the lsqnonlin function of MATLAB for the reconstruction of the spectrum; iii) the reconstruction of the spectrum was validated by comparing the half-value layer of the spectrum and the attenuation curve. The results showed that the half-value layer values of the spectrum and the attenuation curve were close to each other and the calculation time of the spectrum was considerably short. Therefore, it is concluded that the indirect determination of the X-ray spectrum from its attenuation curve by means of the novelty usage of the multistart-lsqnonlin synergy is a demonstrably simpler, faster and as effective alternative as the direct spectrum measurement.
References
Abbene, L., Gerardi, G., Principato, F., Del Sordo, S., & Raso, G. (2012). Direct measurement of mammographic x-ray spectra with a digital CdTe detection system. Sensors, 12 (6):8390-8404.
AL-Jasim, A. K., Hulugalle, S. N. C. W. M. P. S. K., & Al-Hamadani, H. K. (2017). A Quality Control Test for General X-Ray Machine. World Scientific News, 90: 11-30.
Archer, B. R., & Wagner, L. K. (1982). A Laplace transform pair model for spectral reconstruction. Medical physics, 9 (6): 844-847.
Archer, B. R., Wagner, L. K., Johnston, D. A., Almond, P. R., & Bushong, S. C. (1985). Analysis of errors in spectral reconstruction with a Laplace transform pair model. Physics in Medicine & Biology, 30 (5): 411.
Archer, B. R., & Wagner, L. K. (1988a). Determination of diagnostic x‐ray spectra with characteristic radiation using attenuation analysis. Medical physics, 15 (4): 637-641.
Archer, B. R., & Wagner, L. K. (1988b). A modified x-ray spectra reconstruction technique. Physics in Medicine & Biology, 33 (12): 1399.
Attix, F. H. (2008). Introduction to radiological physics and radiation dosimetry. John Wiley & Sons.
Ay, M. R., Shahriari, M., Sarkar, S., Adib, M., & Zaidi, H. (2004). Monte Carlo simulation of x-ray spectra in diagnostic radiology and mammography using MCNP4C. Physics in Medicine & Biology, 49 (21): 4897.
Baird, L. C. (1981). X‐ray spectra vs attenuation data: A theoretical analysis. Medical physics, 8 (3): 319-323. Bell, G. E. (1936). Spectral distribution in the continuous X-ray spectrum and the specification of X-ray quality. The British Journal of Radiology, 9 (106): 680-688.
Bilge, H. (2004). Beam characteristics of kilovoltage radiotherapy unit. Journal of BU ON.: official journal of the Balkan Union of Oncology, 9 (3): 303-306.
Bonifácio, D. A., Murata, H. M., & Moralles, M. (2005, July). Monte Carlo Simulation of X-ray spectra in diagnostic radiology and mammography using Geant4. In 2005 International Nuclear Atlantic Conference-INAC. Bos, A. J. (2011, May). Fundamentals of radiation dosimetry. In AIP Conference Proceedings, 1345 (1): 5-23. AIP.
Chen, S. C., Jong, W. L., & Harun, A. Z. (2012). Evaluation of x-ray beam quality based on measurements and estimations using SpekCalc and IPEM78 models. The Malaysian journal of medical sciences: MJMS, 19 (3): 22.
Correa, E. D. L., Vivolo, V., & Potiens, M. D. P. A. (2012). Determination of the effective energy in X-rays standard beams, mammography level. Instituto de Pesquisas Energéticas e Nucleares, Brazil.
De la Vega J, M., Guirado, D., Vilches, M., Perdices, J. I., & Lallena, A. M. (2008). Obtaining the intrinsic electron spectrum of linear accelerators using the relation between the current of the bending magnet and the absorbed dose in water. Radiotherapy and Oncology, 86 (1): 109-113.
Delgado, V. (1999). Comparison between measured and predicted attenuation curves of x‐ray beams. Medical physics, 26 (10): 2183-2189.
Delgado, V. (2007). Determination of x‐ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation. Medical physics, 34(3): 994-1006.
Delgado, V. (2009). Determination of x‐ray spectra from Al attenuation data by imposing a priori physical features of the spectrum: Theory and experimental validation. Medical physics, 36(1): 142-148.
Dodson, C. T. J. (2002). Introduction to laplace transforms for engineers. School of Mathematics, Manchester University Lecture Notes.
Dössel, O., & Schlegel, W. C. (Eds.). (2010). World Congress on Medical Physics and Biomedical Engineering September 7-12, 2009 Munich, Germany: Vol. 25/IX Neuroengineering, Neural Systems, Rehabilitation and Prosthetics (Vol. 25). Springer Science & Business Media.
Dyson, N. A., & Dyson, N. A. (2005). X-rays in Atomic and Nuclear Physics. Cambridge University Press. Glover, J. L., & Chantler, C. T. (2009). A method to determine the absolute harmonic content of an X‐ray beam using attenuation measurements. X‐Ray Spectrometry: An International Journal, 38 (6): 510-512.
Kramer, H. M., & Von Seggern, H. (1983). The determination of x-ray spectra from attenuation data: Part I: The potentials of various methods. Nuclear Instruments and Methods in Physics Research, 213 (2-3): 373-380.
Kramer, H. M. (1983). The determination of x-ray spectra from attenuation data: Part II: Experimental results. Nuclear Instruments and Methods in Physics Research, 214 (2-3): 445-450.
Li, G., Wu, A., Lin, H., & Wu, Y. (2008). Electron spectrum reconstruction as nonlinear programming model using micro-adjusting algorithm. In 7th Asian-Pacific Conference on Medical and Biological Engineering (pp. 451-454). Springer, Berlin, Heidelberg.
Ma, C. C. (2014). AAPM. Measurement of radiation, Fox Chase Cancer Center, Philadelphia, PA, USA. Disponible en https://www.aapm.org/meetings/2014AM/ReviewCourses/documents/T06MaMeasurementchapter.pdf, accedida en noviembre de 2019.
Mainardi, R. T., & Bonzi, E. V. (2008). An indirect method of X-ray spectra measurement by simultaneous attenuations of the scattered beam. Radiation Physics and Chemistry, 77 (5):537-544.
Malezan, A., Tomal, A., Antoniassi, M., Watanabe, P. C. A., Albino, L. D., & Poletti, M. E. (2015). Spectral reconstruction of dental X-ray tubes using laplace inverse transform of the attenuation curve. Radiation Physics and Chemistry, 116: 278-281.
Menin, O. H., Martinez, A. S., & Costa, A. M. D. (2016). Reconstruction of bremsstrahlung spectra from attenuation data using generalized simulated annealing. Applied Radiation and Isotopes, 111: 80-85.
Nickoloff, E. L., & Berman, H. L. (1993). Factors affecting x-ray spectra. Radiographics, 13 (6): 1337-1348.
Panthi, R. (2018). Determination of the Energy Spectra of Clinical X-Ray Beams Using Dose-Depth Datasets (Doctoral dissertation). Oklahoma State University. Disponible en: https://shareok.org/bitstream/handle/11244/317776/PANTHI_okstate_0664D_15685.pdf?sequence=1, accedida en noviembre de 2019.
Pamplona, G. S., & Costa, A. M. (2010). Determinação do espectro de raios X a partir da curva de transmissão para um equipamento de radiografia dentária. Revista Brasileira de Física Médica, 4 (2): 23-25.
Pernicka, F., & McLean, I. D. (2007). Dosimetry in diagnostic radiology: an international code of practice. International Atomic Energy Agency.
Poludniowski, G., Landry, G., DeBlois, F., Evans, P. M., & Verhaegen, F. (2009). SpekCalc: a program to calculate photon spectra from tungsten anode x-ray tubes. Physics in Medicine & Biology, 54 (19): N433.
Santos, J. C., Gonzales, A. H. L., Terini, R. A., & Costa, P. R. (2016). Determinação da camada semirredutora e da tensão aplicada a partir de espectros emitidos por um tubo de raios X. Revista Brasileira de Física Médica, 10 (3):28-33.
Silberstein, L. (1933). XXXIV. Spectral composition of an X-ray radiation determined from its filtration curve. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 15 (98): 375-394.
Smith, F. A. (2000). A primer in applied radiation physics. World Scientific Publishing Company. Twidell, J. W. (1970). The determination of X-ray spectra using attenuation measurements and a computer program. Physics in Medicine & Biology, 15 (3): 529.
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