Energy Spectrum of Converters and Positron Range Estimation in PET Simulation For 511-KeV Photons

Volume 8, Issue 2, February – 2023 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
Energy Spectrum of Converters and Positron Range

Estimation in PET Simulation For 511-keV Photons
Muhammad Afzaal Sadaqat1 and Dr. Ijaz Ahmed2
1,2
Riphah International University. I-14 Hajj Complex,
Islamabad, Pakistan
Abstract:- The purpose of this study was to observe the Herein, we used Geant4 to simulate the energy
energy distribution of incident 511-keV photons distribution of 511-keV photons for various electrode
produced as a result of annihilation effect e -+e+ γ+γ in materials. The Geant4 simulation package was designed
three different electrodes (of aluminum, glass, and specifically for the passage of charged particles through
Bakelite). The transmission, absorption, and reflection of matter. Ionization and excitation of gas molecules result in
particles for 511-keV photons were examined using a energy losses in charged particles, and the type of
thin or thick layer of electrodes. Moreover, the manner interaction determines the cross-section of the energy loss.
in which the energy spectrum of a single electrode The total energy loss is depicted in the following equation
changes with its thickness was explored. The positron [3].
range of the positron emission tomography (PET)
radioisotopes is responsible for the production of high- -1/ρdE/dx|col=CNA/A[lnπ2γ3(mec2 )2/I2 – a] (1)
quality images in (PET) imaging reconstruction. As a
result, the ranges and kinetic energies of positrons from Here, ‘ρ’ is the density of the particles, ‘dE/dx’ is the
three radioisotopes (F18, O15, I124) were calculated in this energy loss, and ‘C’ is a constant expressed in MeV/cm 2.
study using the Geant4 application for tomographic For electrons a=2.9 and positrons a=3.6. 'I’ represents the
emission (GATE) simulation package. Notably, the intensity, ‘me’ represents the mass of electrons, and ‘A’ is the
mass number of the absorbing material.
ranges thereof were determined via their
energies.Finally, the simulated ranges and kinetic energy In the second part of this study, we used GATE to
values were compared with the literature values estimate the ranges and kinetic energies of positrons of F18,
revealing a 0.5% difference. O15, and I124 radionuclides in PET simulations for the case of
Keywords:- Annihilation effect, Positron Emission 511-keV photons.
Tomography (PET), Imaging reconstruction, Radioisotopes. II. ENERGY DISTRIBUTION OF 511-KEV
I. INTRODUCTION PHOTONS
The growing interest in positron emission tomography Geant4 was used to examine the energy spectrum
(PET) in medical imaging reconstruction has facilitated formed upon incidence 511-keV photons on various
development of techniques allowing healthcare electrodes. Fig. 1 depicts an image of the energy deposited
professionals to see inside a patient’s body without directly on three different electrodes as a result of this simulation.
looking at a camera or performing an open surgery and Because of the photoelectric effect, the rate of energy
forming qualitative images. PET is currently the most deposition abruptly decreases at 340-keV photon energy.
preferred imaging method in clinical research. Short-lived The low electrical resistivity of aluminum (10-8Ω-cm)
radionuclides are endowed with subjective tissue that emits implies a lower resistance offered to incoming photons than
positrons at a time based on their respective half-lives in this of glass and Bakelite. As a result, there existed more events
procedure. This positron travels some distance (~mm) in a in which energy was deposited takes place at the electrode.
tissue before it annihilates with an electron to produce two
back-to-back 511-keV photons traveling at 180o to each
other. In this regard, an activity distribution in a tissue can
be created by aggregating several interaction events [1].
PET is noninvasive imaging technique, used in tomography
for small animals, that involves good time resolution, a
potentially high spatial resolution, and low cost [2].
IJISRT23FEB461 www.ijisrt.com 953

ISSN No:-2456-2165
Fig 1: Energy deposited at absorber dN/ Kinetic Energy at Exit dN/dE
Fig 2: Transmitted Compton Electrons Kinetic
Fig. 2 depicts the kinetic energy of the transmitted on the energy of the transmitted Compton electrons.
Compton electron at the exit point. Electron extraction from Moreover, energy fluctuations up to 240-keV occur for
an electrode reveals that there is no electrical resistive effect transmitted Compton photons 9 (Fig. 3).
Fig 3: Transmitted Compton Photon Kinetic Energy at Exit dN/dE
Fig 4: Reflected Compton Photon Kinetic Energy at Exit dN/De

ISSN No:-2456-2165
Because photons are produced at energies lower than electrode are depicted in Fig. 5. Because, electrons produce
this, by the photoelectric effect or multiple scattering [1]. intense ionization in the gas gap and cause avalanches at
Photons are scattered at 90° at 240-keV energy, but the higher energies, the probability rate decreases with energy;
probability rate increases at higher energy. The maximum there are very few events at higher energy.
probability of Compton photons can be seen at a very high
energy (~ 511 keV). Fig. 6 depicts the kinetic energy of the transmitted
Compton electrons and Compton photons for the Bakelite
Because of the thinness of the electrode material (2 electrode. Because of the photoelectric effect, the
mm), one out of every ten events in which incident photons probability of events for Compton electrons decreases at
with energies of 180 keV leave the crystal without 340-keV photon energy. The curve fluctuates up to photon
interacting and are thus scattered on the electrode entrance energy of 240-keV for transmitted Compton photons.
window is shown in Fig. 4. Backscattered particles are Photons with energies less than 240-keV are produced as a
thought to be very important in the simulation of single- result of the photoelectric effect or multiple scattering.
layer crystals with sufficient dimensions and their scattering Photons are scattered at 90o at 240 keV, resulting in a longer
properties [4]. The energy deposition and energy of path through the solid material before reaching the gas
Compton electrons and Compton photons for the aluminum volume [1].
Fig 5: Energy spectrum of Compton electrons Compton photons absorbed and at creation of aluminum electrode.
Fig 6: Transmitted Compton electrons and Compton photons kinetic energy at exit.
However, owing to the thinness of the glass electrode window (Fig. 7). The reflected Compton electrons have a
material (~2mm), 70% of the incident photons leave the low speed and high ionizing ability; therefore, the rate of
crystal without interacting and may enter the glass electrode reflection is extremely low [4].

ISSN No:-2456-2165
Fig 7: Reflected Compton electrons and Compton photons kinetic energy at exit
III. VARIATION OF ENERGY DISTRIBUTION electrons at creation remains constant (Fig 8 a,c,d)).
WITH ELECTRODE THICKNESS Notably, only the probability of transmission of the
Compton photons increases with electrode thickness (Fig 8
Further, we checked the alteration of the energy b). As a result, the greater is the probability of transmission
spectrum curves at the end of this process by changing the of Compton photons, the higher is the electrode material
thickness of the electrode (aluminum). Upon variation of the thickness.
thickness, the probability of transmitted Compton electrons,
energy deposited at the absorber, and energy of the Compton
(a) (b)
(c) (d)
Fig. 8: Variation of energy spectrum with electrode thickness (a) transmitted Compton electrons (b) transmitted Compton photons
(c) energy deposited at absorber (d) Compton electrons energy at creation

ISSN No:-2456-2165
IV. ESTIMATION OF POSITRON RANGE AND (2), one can estimate the mean and maximum value of the
KINETIC ENERGY positron's range.
The positron travels a certain distance in the tissue r = √x2+y2+z2 (2)

before annihilating into two photons. This is the distance
between the point of emission and the point of annihilation where, r represents the range, moreover, x, y, and z are
in Euclidean space and represents a significant advancement the position vectors of the range along the x, y, and z-axis
in PET imaging blurring. Blurred images are considerably respectively. Notably, their energies determined their ranges,
improved during imaging reconstruction through accurate and fluorine's positrons were found to be short-range ones
estimation of the positron range. We estimated the positron (~2mm) whereas, iodine’s positronswere found to be long-
range for three commonly used PET radioisotopes F18, O15, range ones (~10mm). The spatial resolution of the image can
and I125 using the GATE simulation toolkit. These be improved by using short half-lived radionuclides. As a
radioisotopes are found in a variety of biological media result of its short half-life, short positron range, and better
including striated muscle, brain, soft bone, water, lung, spatial resolution, fluorine is the most frequently used
adipose tissue, cortical bone, and skin [6]. We compared the radioisotope in the PET imaging [5].
GATE simulation results to those found in the literature
(Table 1 and 2) and our findings are observed to be F18 has half life t1/2= 110 min and disintegrates into O18
consistent with those of experiments.In this case, the by β (96.9%) and electron capture (3.1%). The emitted
+
majority of the simulations conducted previously had a positrons have Rmax= 2.3 mm and Rmean= 0.64 mm with the
mean and maximum range discrepancy of less than 20%. corresponding energies Emax= 0.63 MeV and Emean= 0.25
Based on these measurements, we conclude that a more MeV. O15 disintegrates into N15 with a half-life of t1/2= 2 min
accurate simulation setup is required particularly to by β+ (99.9%) and electron capture (0.1%). The range of its
disengage the positronium formation effect in the positron positron emission is Rmax= 8.4 mm and Rmean= 3.0 mm and
range. The spectra of positron range and kinetic energy are its corresponding energies are Emax= 1.73 MeV and Emean=
shown in Fig. 8 and Fig. 9 respectively. Three columns exist 0.73 MeV. Similarly, I124 decays under a long half-life of
in the output text: X(mm), Y(mm), and Z(mm). Each set of 100h into Te124 by β+ (22.7%) and electron capture (77.3%).
points represents the position vector of the range values as Its positron range is calculated as Rmax= 10.2 mm and Rmean=
well as their respective coordinate systems. By accurately 4.4 mm and its corresponding energies are Emax= 2.13 MeV
calculating the norm value of each data set using formula and 0.97 MeV.
Fig. 9: Positron range (mm) Fig. 10: Positron kinetic energy (MeV)
Rmax < R > : Most Probable Range

# Simulation # Data # Simulation # Data
18
F 2.04 mm 2.3 mm 0.43 mm 0.64 mm
15
O 7.2 mm 8.4 mm 4.01 mm 3.0 mm
I124 9.16 mm 10.2 mm 2.34 mm 4.44 mm
Table 1: Positron range (mm)
Emax < E > : Most Probable Energy

# Simulation # Data # Simulation # Data
F18 0.60 MeV 0.63 MeV 0.21 MeV 0.25 MeV
15
O 1.60 MeV 1.73 MeV 0.42 MeV 0.73 MeV
124
I 2.10 MeV 2.13 MeV 0.51 MeV 0.97 MeV
Table 2: Positron kinetic energy (MeV)

ISSN No:-2456-2165
V. CONCLUSION
In this study, in the case of incident 511-keV photons,

we observed the manner in which energy is distributed for
three electrode materials: aluminum, glass, and Bakelite.
Compton scattering is thought to be the primary
phenomenon governing interaction with fluctuations of the
energy distribution of Compton photons and Compton
electrons occuring at photon energies of 340 keV. In
addition, we investigated the variation in the energy
spectrum of a single electrode (aluminum) as its thickness
varies. Finally, we extracted certain GATE results that show
the ranges and kinetic energies of positrons for different
radionuclides F18, O15, and I124. The ranges and kinetic
energy values that we simulated for the F18, O15, and I124
radioisotopes resemble the literature values, indicating that
our simulation model is valid.
REFERENCES
[1.] Lippmann, C., Vincke, H., & Riegler, W. (2009).

Simulation of RPC performance for 511 keV photon
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Physics Research Section A: Accelerators,
Spectrometers, Detectors, and Associated
Equipment,602(3), 735-739.
[2.] Weizheng, Z., Ming, S., Cheng, L., Hongfang, C.,
Yongjie, S., & Tianxiang, C. (2014). Monte Carlo
Simulation of RPC-based PET with GEANT4.arXiv
preprint arXiv:1402.4544.
[3.] B. Rossi. High Energy Particles. Prentice-Hall, Inc.,
Englewood Cliffs, NJ, 1952.
[4.] Santin, G., Strul, D., Lazaro, D., Simon, L., Krieguer,
M., Martins, M. V., ... & Morel, C. (2003). GATE: A
Geant4-based simulation platform for PET and
SPECT integrating movement and time management.
IEEE Transactions on nuclear science, 50(5), 1516-
1521.
[5.] Conti, M., & Eriksson, L. (2016). Physics of pure and
non-pure positron emitters for PET: a review and a
discussion. EJNMMI Physics,3(1), 1-17.
[6.] Cal-González, J., Herraiz, J. L., España, S., Corzo, P.
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Energy Spectrum of Converters and Positron Range Estimation in PET Simulation For 511-KeV Photons

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Volume 8, Issue 2, February – 2023 International Journal of Innovative Science and Research Technology

Energy Spectrum of Converters and Positron Range

IJISRT23FEB461 www.ijisrt.com 953

Fig 1: Energy deposited at absorber dN/ Kinetic Energy at Exit dN/dE

Fig 2: Transmitted Compton Electrons Kinetic

Fig 3: Transmitted Compton Photon Kinetic Energy at Exit dN/dE

Fig 4: Reflected Compton Photon Kinetic Energy at Exit dN/De

IJISRT23FEB461 www.ijisrt.com 954

IJISRT23FEB461 www.ijisrt.com 955

IJISRT23FEB461 www.ijisrt.com 956

The positron travels a certain distance in the tissue r = √x2+y2+z2 (2)

Rmax < R > : Most Probable Range

Emax < E > : Most Probable Energy

IJISRT23FEB461 www.ijisrt.com 957

In this study, in the case of incident 511-keV photons,

[1.] Lippmann, C., Vincke, H., & Riegler, W. (2009).

IJISRT23FEB461 www.ijisrt.com 958

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