Monte Carlo Simulation and a Review of the Physics of the Positron Annihilation Process in PET

Abstract

In this paper, we investigate the physics of the positron annihilation process, which occurs in a PET imaging system. In particular, the diffusion of beta particles (positrons) within water was addressed. Beta particles are emitted isotropically from the same source point with random directions and randomly chosen energy levels. After traversing a certain distance within water, beta particles lose a certain amount of its energy. The inelastic collisions with atomic electrons are mainly responsible for the energy dissipation of charged particles, such as electrons and positrons (that have low mass). The energy loss rate due to inelastic process is estimated by using the Beta-Bloch formula. These results help in understanding how to develop and implement a computationally efficient Monte Carlo Simulation of the positron annihilation process.

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Muhammed, H. and Zengin, Z. (2013) Monte Carlo Simulation and a Review of the Physics of the Positron Annihilation Process in PET. Engineering, 5, 12-17. doi: 10.4236/eng.2013.510B003.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. Barba, J. Sempau, J. M. Ferntidez-Varea and F. Salvat, “PENELOPE: An Algorithm for Monte Carlo Simulation of the Penetration and Energy Loss of Electrons and Positrons in Matter,” Nuclear Instruments and Methods in Physics Research B, Vol. 10, 1995, pp. 100:31-46. http://dx.doi.org/10.1016/0168-583X(95)00349-5
[2] H. Bethe, “Moliere’s Theory of Multiple Scattering,” Physical Review, Vol. 89, 1953, pp. 1256-1266. http://dx.doi.org/10.1103/PhysRev.89.1256
[3] I. Buvat and I. Castiglioni, “Monte Carlo Simulations in SPET and PET,” Quarterly Journal of Nuclear Medicine, Vol. 46, No. 1, 2002, pp. 48-61.
[4] I. Buvat and D. Lazaro, “Monte Carlo Simulations in Emission Tomography and GATE: An Overview,” Nuclear Instruments and Methods in Physics Research A, Vol. 569, 2006, pp. 323-329. http://dx.doi.org/10.1016/j.nima.2006.08.039
[5] J. Cal-Gonzalez, J. L. Herraiz, S. Espana, M. Desco, J. J. Vaquero and J. M. Udias, “Positron Range Effects in High Resolution 3D PET Imaging,” Nuclear Science Symposium Conference Record, 2009.
[6] A. Cengiz and E. Almaz, “Internal Bremsstrahlung Spectra of β-Particle Emitters Using the Monte Carlo Method,” Radiation Physics and Chemistry, Vol. 70, 2004, pp. 661-668. http://dx.doi.org/10.1016/j.radphyschem.2004.03.008
[7] J. C. L. Chow, M. K. K. Leung and D. A. Jaffray, “Monte Carlo Simulation on a Gold Nanoparticle Irradiated by Electron Beams,” Physics in Medicine and Biology, Vol. 57, 2012, pp. 3323-3331. http://dx.doi.org/10.1088/0031-9155/57/11/3323
[8] K. Contractor, A. Challapalli, G. Tomasi, L. Rosso, H. Wasan, J. Stebbing and Others, “Imaging of Cellular Proliferation in Liver Metastasis by [18F]Fluorothymidine Positron Emission Tomography: Effect of Therapy,” Physics in Medicine and Biology, Vol. 57, 2012, pp. 3419- 3433.
[9] H. Daniel, “Shapes of Beta-Ray Spectra,” Reviews of Modern Physics, Vol. 40, 1968, pp. 659-672. http://dx.doi.org/10.1103/RevModPhys.40.659
[10] S. Espana, J. L. Herraiz, E. Vicente, J. J. Vaquero, M. Desco and J. M. Udias, “PeneloPET, a Monte Carlo PET Simulation tool Based on PENELOPE: Features and Validation,” Physics in Medicine and Biology, Vol. 54, 2009, pp. 1723-1742. http://dx.doi.org/10.1088/0031-9155/54/6/021
[11] R. D. Evan, “The Atomic Nucleus,” McGraw-Hill, New York, 1955, Chaps 18-22.
[12] E. Fermi, “Towards the Theory of β-Rays,” Zeitschrift für Physik, Vol. 88, 1934, p. 161. http://dx.doi.org/10.1007/BF01351864
[13] L. Jodal, C. Le Loirec and C. Champion, “Positron Range in PET Imaging: An Alternative Approach for Assessing and Correcting the Blurring,” Physics in Medicine and Biology, Vol. 57, 2012, pp. 3931-3943. http://dx.doi.org/10.1088/0031-9155/57/12/3931
[14] G. F. Knoll, “Radiation Detection and Measurement,” Wiley, New York, 1989, Chap 2.
[15] E. J. Konopinski, “The Theory of Beta Radioactivity,” Clarendon Press, Oxford, 1966.
[16] W. R. Leo, “Techniques for Nuclear and Particle Physics Experiments,” Springer, New York, 1987, Chap 2. http://dx.doi.org/10.1007/978-3-642-96997-3
[17] C. S. Levin, M. Dahlbom and E. J. Hoffman, “A Monte Carlo Correction for the Effect of Compton Scattering in 3-D PET Brain Imaging,” IEEE Transactions on Nuclear Science, Vol. 42, 1995, pp. 1181-1185. http://dx.doi.org/10.1109/23.467880
[18] C. S. Levin and E. J. Hoffman, “Calculation of Positron Range and Its Effect on the Fundamental Limit of Positron Emission Tomography System Spatial Resolution,” Physics in Medicine and Biology, Vol. 44, 1999, pp. 781- 799. http://dx.doi.org/10.1088/0031-9155/44/3/019
[19] W. E. Meyerhof, “Elements of Nuclear Physics,” Mc-Graw-Hill, New York, 1967.
[20] A. Murray and D. L. Williams, “Organic Synthesis with Isotopes,” Interscience, New York, 1958.
[21] D. G. Ott, “Synthesis with Stable Isotopes,” Wiley-Interscience, New York, 1981.
[22] H. Paganetti, “Range Uncertainties in Proton Therapy and the Role of Monte Carlo Simulations,” Physics in Medicine and Biology, Vol. 57, 2012, pp. R99-R117. http://dx.doi.org/10.1088/0031-9155/57/11/R99
[23] H. Peng and C. S. Levin, “Study of PET Intrinsic Spatial Resolution and Contrast Recovery Improvement for PET/ MRI Systems,” Physics in Medicine and Biology, Vol. 57, 2012, pp. N101-N115.
[24] D. M. Ritson, “Techniques of High Energy Physics,” Interscience, New York, 1961, Chap 1.
[25] A. F. G. Rocha and J. C. Harbert, “Text-book of Nuclear Medicine: Basic Science,” Lea and Fekigur, Philadelphia, 1978.
[26] L. G. Strauss and P. S. Conti, “The Applications of PET in Clinical Oncology,” Journal of Nuclear Medicine: Official Publication, Society of Nuclear Medicine, Vol. 32, No. 4, 1991, p. 623.
[27] R. M. Thomson and I. Kawrakow, “On the Monte Carlo Simulation of Electron Transport in the Sub-1 keV Energy Range,” Medical Physics, Vol. 38, 2011, pp. 4531- 4534. http://dx.doi.org/10.1118/1.3608904
[28] C. S. Wu and S. A. Moskowski, “Beta Decay,” Interscience, New York, 1966.
[29] S. Yamamoto, M. Imaizumi, T. Watabe, H. Watabe, Y. Kanai, S E. himosegawa and J. Hatazawa, “Development of a Si-PM-Based High-Resolution PET System for Small Animals,” Physics in Medicine and Biology, Vol. 55, 2010, pp. 5817-5831. http://dx.doi.org/10.1088/0031-9155/55/19/013

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