Spectral reconstruction of kilovoltage photon beams using generalized simulated annealing
DOI:
https://doi.org/10.15359/ru.36-1.15Keywords:
photon spectra, generalized simulated annealing, inverse reconstruction, transmission curvesAbstract
To unfold the energy spectrum of two kilovoltage (kV) X-ray beams from transmission curves through a mathematical methodology based on Laplace transform and the generalized simulated annealing algorithm. Energy spectra of photon beams and transmission data were associated by means of a mathematical expression derived from the analytical solution of Laplace transform. Transmission data was calculated by relating the air kerma of the attenuated beams, passing through aluminium plates of different thickness, to that of the non-attenuated beam. Generalized simulated annealing function, developed in an early work, was employed to find the parameters of the expression and so determine the spectra. Validation of the methodology was done by the comparison of the half-value layers obtained from transmission curves and the spectra. The mean square percentage error between transmission data and fitting curve of each spectrum defined from the parameters found was lower than 1% indicating a good adjustment. The same error was observed when the first half-value layer (HVL) from the transmission curves and those of each reconstructed spectrum were compared. Calculation time of parameters was 5 sec for 80 kV and 14 sec for 120 kV. In no case, non-realistic solution of energy spectra was obtained. These results were better than an early work where least-squares were used. The reconstruction methodology based on generalized simulated annealing employed in this manuscript can efficiently derive the spectra of two X-ray beams with comparable accuracy to previous work. A limitation is that validation was not done by comparing data with the equipment’s spectra.
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. https://doi.org/10.3390/s120608390
Archer, B. R., & Wagner, L. K. (1988). A modified X-ray spectra reconstruction technique. Physics in Medicine and Biology, 33(12), 1399-1406. https://doi.org/10.1088/0031-9155/33/12/005
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 and Biology, 30(5), 411-418. https://doi.org/10.1088/0031-9155/30/5/004
Archer, B., & Wagner, L. (1982). A Laplace transform pair model for spectral reconstruction. Medical Physics, 9(6), 844-847. https://doi.org/10.1118/1.595193
Archer, Benjamin R., & Wagner, L. K. (1988). Determination of diagnostic x-ray spectra with characteristic radiation using attenuation analysis. Medical Physics, 15(4), 637-641. https://doi.org/10.1118/1.596220
Baird, L. C. (1981). X-ray spectra vs attenuation data: A theoretical analysis. Medical Physics, 8(3), 319-323. https://doi.org/10.1118/1.594834
Bilge, H. (2004). Beam characteristics of kilovoltage radiotherapy unit. Journal of B.U.ON., 9(3), 303-306. https://pubmed.ncbi.nlm.nih.gov/17415831/
Carrera, M., Lopez-Crespo, P., Tai, Y. H., Yates, J. R., Moreno, B., Buslaps, T., & Withers, P. J. (2019). Estimation of the plastic zone in fatigue through the thickness based on synchrotron diffraction data. Procedia Structural Integrity, 17, 872-877. https://doi.org/10.1016/j.prostr.2019.08.116
Chen, S. C., Jong, W. L., & Hharun, A. Z. (2012). Evaluation of X-ray beam quality based on measurements and estimations using SpekCalc and Ipem78 models. Malaysian Journal of Medical Sciences, 19(3), 22-28. https://pubmed.ncbi.nlm.nih.gov/23610546/
Deng, J., Chen, H., Chang, C., & Yang, Z. (2004). A superior random number generator for visiting distribution in GSA. International Journal of Computer Mathematics, 81(1), 103-120. https://doi.org/10.1080/00207160310001620768
Durán-Nava, O. E., Torres-García, E., Oros-Pantoja, R., & Hernández-Oviedo, J. O. (2019). Monte Carlo simulation and experimental evaluation of dose distributions produced by a 6 MV medical linear accelerator. Journal of Physics: Conference Series, 1221(1), 012079. https://doi.org/10.1088/1742-6596/1221/1/012079
Epp, J. (2016). X-ray diffraction (XRD) techniques for materials characterization. Materials Characterization Using Nondestructive Evaluation (NDE) Methods. Elsevier. https://doi.org/10.1016/B978-0-08-100040-3.00004-3
Gonçalves, A. C., Wilches Visbal, J. H., & Martins Da Costa, A. (2020). Determinación del espectro de energía de un haz de rayos X terapéutico de kilovoltaje a partir de su curva de atenuación. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, 44(170), 142-152. https://doi.org/10.18257/raccefyn.965
Hill, R., Healy, B., Holloway, L., Kuncic, Z., Thwaites, D., & Baldock, C. (2014). Advances in kilovoltage x-ray beam dosimetry. Physics in Medicine and Biology, 59(6), 183-231. https://doi.org/10.1088/0031-9155/59/6/R183
Maeda, K., Matsumoto, M., & Taniguchi, A. (2005). Compton-scattering measurement of diagnostic x-ray spectrum using high-resolution Schottky CdTe detector. Medical Physics, 32(6Part1), 1542-1547. https://doi.org/10.1118/1.1921647
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. https://doi.org/10.1016/j.radphyschem.2015.05.008
Menin, O. H., Martinez, A. S., & Costa, A. M. (2016). Reconstruction of bremsstrahlung spectra from attenuation data using generalized simulated annealing. Applied Radiation and Isotopes, 111, 80-85. https://doi.org/10.1016/j.apradiso.2016.02.014
Nakashima, J., & Duong, H. (2020). Radiology, Image Production and Evaluation. StatPearls. https://www.ncbi.nlm.nih.gov/books/NBK553145/
Nickoloff, E. L., & Berman, H. L. (1993). Factors affecting x-ray spectra. RadioGraphics, 13(6), 1337-1348. https://doi.org/10.1148/radiographics.13.6.8290728
Pamplona, G. S. P., & 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. https://doi.org/10.29384/rbfm.2010.v4.n2.p23-25
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 and Biology, 54(19), 433-438. https://doi.org/10.1088/0031-9155/54/19/N01
Querol, A., Gallardo, S., Ródenas, J., & Verdú, G. (2010). Application of Tikhonov and MTSVD methods to unfold experimental X-ray spectra in the radiodiagnostic energy range. 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, 536-539. https://doi.org/10.1109/IEMBS.2010.5626024
Sharma, R., Sharma, S., Pawar, S., Chaubey, A., Kantharia, S., & Babu, D. A. R. (2015). Radiation dose to patients from X-ray radiographic examinations using computed radiography imaging system. Journal of Medical Physics, 40(1), 29. https://doi.org/10.4103/0971-6203.152244
Smith, F. A. (2000). A Primer in Applied Radiation Physics. En A Primer in Applied Radiation Physics (1th editio). WORLD SCIENTIFIC. https://doi.org/10.1142/3979
Tafti, D., & Maani, C. V. (2020). Radiation X-ray Production. StatPearls. https://pubmed.ncbi.nlm.nih.gov/30725731/
Thunthy, K. H., & Manson-Hing, L. R. (1978). Effect of mAs and kVp on resolution and on image contrast. Oral Surgery, Oral Medicine, Oral Pathology, 46(3), 454-461. https://doi.org/10.1016/0030-4220(78)90414-0
Visbal, J. H. W., & Costa, A. M. (2019). Inverse reconstruction of energy spectra of clinical electron beams using the generalized simulated annealing method. Radiation Physics and Chemistry, 162, 31-38. https://doi.org/10.1016/j.radphyschem.2019.04.022
Wilches Visbal, J. H., & Da Costa, A. M. (2019). Algoritmo de recocido simulado generalizado para Matlab. Ingeniería y Ciencia, 15(30), 117-140. https://doi.org/10.17230/ingciencia.15.30.6
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