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Higuchi T, Haga A. X-ray energy spectrum estimation based on a virtual computed tomography system. Biomed Phys Eng Express 2023; 9. [PMID: 36623292 DOI: 10.1088/2057-1976/acb158] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 01/09/2023] [Indexed: 01/11/2023]
Abstract
This paper presents a method for estimating the x-ray energy spectrum for computed tomography (CT) in the diagnostic energy range from the reconstructed CT image itself. To this end, a virtual CT system was developed, and datasets, including CT images for the Gammex phantom labeled by the corresponding energy spectra, were generated. Using these datasets, an artificial neural network (ANN) model was trained to reproduce the energy spectrum from the CT values in the Gammex inserts. In the actual application, an aluminum-based bow-tie filter was used in the virtual CT system, and an ANN model with a bow-tie filter was also developed. Both ANN models without/with a bow-tie filter can estimate the x-ray spectrum within the agreement, which is defined as one minus the absolute error, of more than 80% on average. The agreement increases as the tube voltage increases. The estimation was occasionally inaccurate when the amount of noise on the CT image was considerable. Image quality with a signal-to-noise ratio of more than 10 for the basis material of the Gammex phantom was required to predict the spectrum accurately. Based on the experimental data acquired from Activion16 (Canon Medical System, Japan), the ANN model with a bow-tie filter produced a reasonable energy spectrum by simultaneous optimization of the shape of the bow-tie filter. The present method requires a CT image for the Gammex phantom only, and no special setup, thus it is expected to be readily applied in clinical applications, such as beam hardening reduction, CT dose management, and material decomposition, all of which require exact information on the x-ray energy spectrum.
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Affiliation(s)
- Takayuki Higuchi
- Department of Biomedical Sciences, Tokushima University, Tokushima 770-8503, Japan
| | - Akihiro Haga
- Department of Biomedical Sciences, Tokushima University, Tokushima 770-8503, Japan
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Ha W, Sidky EY, Barber RF, Schmidt TG, Pan X. Estimating the spectrum in computed tomography via Kullback-Leibler divergence constrained optimization. Med Phys 2018; 46:81-92. [PMID: 30370544 DOI: 10.1002/mp.13257] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Revised: 09/03/2018] [Accepted: 10/09/2018] [Indexed: 01/13/2023] Open
Abstract
PURPOSE We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. METHODS Spectrum estimation is posed as an optimization problem with x-ray spectrum as unknown variables, and a Kullback-Leibler (KL)-divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated-gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation-maximization (EM) method is also discussed. RESULTS In simulations, the proposed algorithm is seen to yield x-ray spectra that closely match the ground truth and represent the attenuation process of x-ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization-based approach and EM. CONCLUSIONS Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL-divergence constraint can include a prior spectrum and appears to capture important features of x-ray spectrum, allowing accurate and robust estimation of x-ray spectrum in CT imaging.
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Affiliation(s)
- Wooseok Ha
- Department of Statistics, UC Berkeley, 473 Evans Hall, Berkeley, CA, 94720, USA
| | - Emil Y Sidky
- Department of Radiology, The University of Chicago, Chicago, IL, 60637, USA
| | - Rina Foygel Barber
- Department of Statistics, The University of Chicago, Chicago, IL, 60637, USA
| | - Taly Gilat Schmidt
- Department of Biomedical Engineering, Marquette University, Milwaukee, WI, 53201, USA
| | - Xiaochuan Pan
- Department of Radiology, The University of Chicago, Chicago, IL, 60637, USA
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Gualdrini G, Ferrari P. Monte Carlo variance reduction techniques: an overview with some practical examples. RADIATION PROTECTION DOSIMETRY 2011; 146:425-433. [PMID: 21775319 DOI: 10.1093/rpd/ncr240] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Since the first developments of Monte Carlo radiation transport codes, the importance of solving deep penetration problems in the phase space was pointed out. Whilst natural Monte Carlo radiation transport models are rather easy and straightforward to be implemented, apart from geometry extreme complexities that could limit the modelling capabilities of the user, the possibility to obtain results with high precision and reasonable CPU time, when the scored events contributing to the response of interest are characterised by a low probability of occurrence, can be guaranteed only through biased games for which the user needs a robust expertise. The present paper wanted to present in a concise way the main aspects of the variance reduction techniques and some practical application to help the users in becoming more familiar with such a necessary tool.
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Affiliation(s)
- G Gualdrini
- ENEA, IRP-Radiation Protection Institute, 16 via dei Colli I-40136, Bologna, Italy.
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Duan X, Wang J, Yu L, Leng S, McCollough CH. CT scanner x-ray spectrum estimation from transmission measurements. Med Phys 2011; 38:993-7. [PMID: 21452736 DOI: 10.1118/1.3547718] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
PURPOSE In diagnostic CT imaging, multiple important applications depend on the knowledge of the x-ray spectrum, including Monte Carlo dose calculations and dual-energy material decomposition analysis. Due to the high photon flux involved, it is difficult to directly measure spectra from the x-ray tube of a CT scanner. One potential method for indirect measurement involves estimating the spectrum from transmission measurements. The expectation maximization (EM) method is an accurate and robust method to solve this problem. In this article, this method was evaluated in a commercial CT scanner. METHODS Two step-wedges (polycarbonate and aluminum) were used to produce different attenuation levels. Transmission measurements were performed on the scanner and the measured data from the scanner were exported to an external computer to calculate the spectra. The EM method was applied to solve the equations that represent the attenuation processes of polychromatic x-ray photons. Estimated spectra were compared to the spectra simulated using a software provided by the manufacturer of the scanner. To test the accuracy of the spectra, a verification experiment was performed using a phantom containing different depths of water. The measured transmission data were compared to the transmission values calculated using the estimated spectra. RESULTS Spectra of 80, 100, 120, and 140 kVp from a dual-source CT scanner were estimated. The estimated and simulated spectra were well matched. The differences of mean energies were less than 1 keV. In the verification experiment, the measured and calculated transmission values were in excellent agreement. CONCLUSIONS Spectrum estimation using transmission data and the EM method is a quantitatively accurate and robust technique to estimate the spectrum of a CT system. This method could benefit studies relying on accurate knowledge of the x-ray spectra from CT scanner.
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Affiliation(s)
- Xinhui Duan
- Department of Radiology, Mayo Clinic, 200 First Street Southwest, Rochester, Minnesota 55905, USA
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Delgado V. Determination of x-ray spectra from attenuation data by imposinga prioripositiveness and bounded support: Theory and experimental validation. Med Phys 2007; 34:994-1006. [PMID: 17441246 DOI: 10.1118/1.2436971] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
The determination of the spectral distribution of an x-ray beam from attenuation measurements in a narrow beam has aroused great interest since it was first proposed by Silberstein in 1932. Since then, it has become clear that this is an ill-conditioned problem. Then, due to the intrinsic difficulties of the problem, care has been taken to improve the mathematical and numerical inversion techniques. Alternative ways to circumvent the explicit inversion by using the attenuation curve itself to calculate directly generalized moments of the solution have also been found. In this work, the explicit reconstruction of the spectral distribution is carried out by an expectation-maximization method that satisfies the a priori condition of positiveness of the solution and allows us to impose the boundness of its support easily, conditions which are known to be fulfilled by physically acceptable solutions. The simulations made and the experimental validation of the proposed method allow us to prove its scope and limitations.
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Affiliation(s)
- Victor Delgado
- FaMAF Laboratorio de Espectroscopía de Radiaciones, Universidad Nacional de Córdoba, Ciudad Universitaria (5010)-Córdoba, Argentina.
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Iwasaki A, Kubota M, Hirota J, Fujimori A, Suzaki K, Aoki M, Abe Y. Characteristic features of a high-energy x-ray spectra estimation method based on the Waggener iterative perturbation principle. Med Phys 2007; 33:4056-63. [PMID: 17153385 DOI: 10.1118/1.2359227] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
We have redeveloped a high-energy x-ray spectra estimation method reported by Iwasaki et al. [A. Iwasaki, H. Matsutani, M. Kubota, A. Fujimori, K. Suzaki, and Y. Abe, Radiat. Phys. Chem. 67, 81-91 (2003)]. The method is based on the iterative perturbation principle to minimize differences between measured and calculated transmission curves, originally proposed by Waggener et al. [R. G. Waggener, M. M. Blough, J. A. Terry, D. Chen, N. E. Lee, S. Zhang, and W. D. McDavid, Med. Phys. 26, 1269-1278 (1999)]. The method can estimate spectra applicable for media at least from water to lead using only about ten energy bins. Estimating spectra of 4-15 MV x-ray beams from a linear accelerator, we describe characteristic features of the method with regard to parameters including the prespectrum, number of transmission measurements, number of energy bins, energy bin widths, and artifactual bipeaked spectrum production.
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Affiliation(s)
- Akira Iwasaki
- School of Health Sciences, Hirosaki University, 66-1 Hon-cho, Hirosaki, Aomori 036-8564, Japan.
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A practical method for estimating high-energy X-ray spectra using the iterative perturbation principle proposed by Waggener. Radiat Phys Chem Oxf Engl 1993 2003. [DOI: 10.1016/s0969-806x(03)00012-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Abstract
This note (1) provides references to recent work that applies computer algebra (CA) to the life sciences, (2) cites literature that explains the biological background of each application, (3) states the mathematical methods that are used, (4) mentions the benefits of CA, and (5) suggests some topics for future work.
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Fix MK, Manser P, Born EJ, Mini R, Rüegsegger P. Monte Carlo simulation of a dynamic MLC based on a multiple source model. Phys Med Biol 2001; 46:3241-57. [PMID: 11768503 DOI: 10.1088/0031-9155/46/12/312] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Detailed knowledge of the characteristics of the radiation field shaped by a multileaf collimator (MLC) is essential in intensity modulated radiotherapy (IMRT). A previously developed multiple source model (MSM) for a 6 MV beam was extended to a 15 MV beam and supplemented with an accurate model of an 80-leaf dynamic MLC. Using the supplemented MSM and the MC code GEANT, lateral dose distributions were calculated in a water phantom and a portal water phantom. A field which is normally used for the validation of the step and shoot technique and a field from a realistic IMRT treatment plan delivered with dynamic MLC are investigated. To assess possible spectral changes caused by the modulation of beam intensity by an MLC, the energy spectra in five portal planes were calculated for moving slits of different widths. The extension of the MSM to 15 MV was validated by analysing energy fluences, depth doses and dose profiles. In addition, the MC-calculated primary energy spectrum was verified with an energy spectrum which was reconstructed from transmission measurements. MC-calculated dose profiles using the MSM for the step and shoot case and for the dynamic MLC case are in very good agreement with the measured data from film dosimetry. The investigation of a 13 cm wide field shows an increase in mean photon energy of up to 16% for the 0.25 cm slit compared to the open beam for 6 MV and of up to 6% for 15 MV, respectively. In conclusion, the MSM supplemented with the dynamic MLC has proven to be a powerful tool for investigational and benchmarking purposes or even for dose calculations in IMRT.
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Affiliation(s)
- M K Fix
- Institute for Biomedical Engineering, University of Zurich, Switzerland.
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Fix MK, Stampanoni M, Manser P, Born EJ, Mini R, Rüegsegger P. A multiple source model for 6 MV photon beam dose calculations using Monte Carlo. Phys Med Biol 2001; 46:1407-27. [PMID: 11384062 DOI: 10.1088/0031-9155/46/5/307] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
A multiple source model (MSM) for the 6 MV beam of a Varian Clinac 2300 C/D was developed by simulating radiation transport through the accelerator head for a set of square fields using the GEANT Monte Carlo (MC) code. The corresponding phase space (PS) data enabled the characterization of 12 sources representing the main components of the beam defining system. By parametrizing the source characteristics and by evaluating the dependence of the parameters on field size, it was possible to extend the validity of the model to arbitrary rectangular fields which include the central 3 x 3 cm2 field without additional precalculated PS data. Finally, a sampling procedure was developed in order to reproduce the PS data. To validate the MSM, the fluence, energy fluence and mean energy distributions determined from the original and the reproduced PS data were compared and showed very good agreement. In addition, the MC calculated primary energy spectrum was verified by an energy spectrum derived from transmission measurements. Comparisons of MC calculated depth dose curves and profiles, using original and PS data reproduced by the MSM, agree within 1% and 1 mm. Deviations from measured dose distributions are within 1.5% and 1 mm. However, the real beam leads to some larger deviations outside the geometrical beam area for large fields. Calculated output factors in 10 cm water depth agree within 1.5% with experimentally determined data. In conclusion, the MSM produces accurate PS data for MC photon dose calculations for the rectangular fields specified.
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Affiliation(s)
- M K Fix
- Institute for Biomedical Engineering, University of Zurich and Swiss Federal Institute of Technology (ETH)
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