1. Semi-empirical Monte Carlo optical-gain
modelling of Nuclear Imaging scintillators
E. M. Vlamakis, X. A. Argyriou, T. J. Sevvos, A. A. Fotopoulos, N. N.
Chatzisavvas, P. H. Yannakopoulos, N. Kalyvas, I. Valais, I. Kandarakis,
D. Nikolopoulos

2. Aim
Develop a theoretical model of the optical gain of single-
crystal scintillators, via Monte Carlo methods. Compare
theoretical results to experimental data for photon energies of
140keV and 364keV. The presented results could be useful in
designing nuclear medicine imaging systems.

3. Introduction
Scintillation detector applications
Conventional and digital x-ray
radiography,
x-ray computed tomography,
single-photon emission
tomography (SPECT)
positron emission tomography
(PET)

4. Introduction +
The emission of light of granular and non-granular
scintillators has been investigated through analytical
modelling [9-14].
These models take into account scintillator thickness as the
main influencing parameter, while the other dimensions (e.g
area or lateral thickness) are assumed to be infinite. For the
application of scintillators in nuclear medicine systems, the
analytical models [9-15] are insufficient in scoring gamma
radiation deposited energy.
The stochastic processes of radiation transport have been
studied efficiently through Monte Carlo simulation [16-28].
Several general Monte Carlo packages are available (e.g.
TART, PENELOPE, MCNP, GEANT4, GATE, EGSnrcMP) [16,
17, 22, 23, 25].

5. Introduction ++
Recent reports have employed general Monte Carlo
packages in studying radiation and optical photon transport in
medical imaging scintillators [26-27].
The combination however of analytical optical modelling and
simulation of radiation transport with general Monte Carlo
codes has not been attempted for single crystal scintillators.
In such an attempt, the present study employs a hybrid
semi-empirical method for the estimation of the optical output
of scintillator crystals in terms of Detector-Optical-Gain
(DOG). The method uses specially developed Monte-Carlo
EGSnrc codes for scoring the gamma ray photon and energy
redistribution within certain crystal scintillators.

6. Introduction +++
The EGS (Electron–Gamma–Shower) platform is a general
purpose package for the Monte Carlo simulation. The new
enhanced version of EGS is called EGSnrc.
The outputs of the EGSnrc simulations are utilised as inputs
into a semi-empirical analytical model which predicts DOG.
Semi-empirical model adjustments are based on scintillator
measurements in the energy range of Nuclear Medicine.
The model is used for the estimation of the effective optical
photon loss per mm. The latter parameter is employed in the
estimation of an optimum scintillator thickness, between 5mm
and 25mm, per incident gamma ray energy for the
Gd2SiO5:Ce (GSO:Ce), Lu2SiO5:Ce (LSO:Ce) and
YAlO3:Ce (YAP:Ce) scintillators.

7. Materials & Methods
Modelled scintillators
single crystal blocks
10x10 mm2 entrance area
varying z-thickness
zb equally spaced slabs
140, 364 and 511 keV

8. Materials & Methods +
Single-crystal scintillator
divided in N layers
a fraction was absorbed to
each layer
Optical photons propagate
either in the forward or in
the backward direction
per crystal layer only a
fraction, hereafter called k,
was propagated to the next
layer

9. Materials & Methods ++
Qn(E) is calculated via the EGS4rnc Monte Carlo code. The
absorbed X-ray energy is transformed into optical photon energy in
the scintillator. The number of the produced optical photons in the
nth layer, Ln can be calculated as:
E
Ln ( E ) = Qn ( E )nC (1)
Eλ
where nC is the intrinsic conversion efficiency and Ελ is the optical
photon energy [5], [8]. It is assumed that half of the produced optical
photons are propagating forward and half backwards. To the next layer,
n+1, only a fraction, k, of the produced optical photons arrives. That is:
Lnn + 1 ( E ) = Ln ( E )k (2)

10. Materials & Methods +++
The optical photons in Forward direction are calculated as:
1
Lnf ( E ) = (1 − R) Ln ( E )k N− n
(3)
1− k R
2N 2
The optical photons in Backward direction are calculated as:
1 k 2N R 2
Lm ( E ) = Lnf ( E ) + Lnb ( E ) = (1 − R) Ln ( E )k N − n + (1 − R) Ln ( E ) Rk n k N
1 − k 2N R 2 1 − k 2N R 2
(4)

11. Materials & Methods +++
If all the layers as well as equation (1) are considered then the total number of
optical photons produced per absorbed gamma ray (i.e. DOG) equals to:
N
E  k N− n k 2N R 2 
DOG ( E ) = ∑ Qn ( E )nC (1 − R )  + Rk n + N 2 
 1− k R 1− k R 
2N 2 2N
n= 1 Eλ
where the values of Qn(E) is calculated by EGSnrc. (5)
The value of the reflectance, R, when a light ray propagates from a medium with
index of refraction n1, to a medium of index of refraction n2 (equals to 1 for air),
depends upon the polarization of the incident ray.The total reflectance can be
calculated as R(θ i ) = Rs (θ i ) + Rp (θ i ) and the mean reflectance used in the
2
estimation of equation 5 was found as: θ crit
∑ R (θ )
R= θ =0
noa
where noa is the number of angles used in the summation and θcrit is the critical
angle above which total reflection occur. In the calculation of R it was assumed
that the input and exit surfaces of the crystal were perfect planes and any
existed surface anomalies [26] were not considered.

12. Results & Discussion
Qn(E) values for gamma ray energies of 140keV and 364keV for LSO:Ce, GSO:Ce and
YAP:Ce. The curves represent exponential fits at the 99% confidence interval. The errors are
below 0.5%. The legend presents the dimensions of the modeled scintillator block

13. Results & Discussion +
Crystal Energy (keV) DOG k DOG DOG
experimental theoretical k - 1%
LSO:Ce 140 323±16 0.80 248 227
364 644±45 790 753
GSO:Ce 140 150±8 0.86 146 133
364 275±19 291 275
YAP:Ce 140 57±3 0.74 50 48
364 95±7 111 107
Experimental and semi-empirical method predicted DOG values. In the last two columns the
sensitivity of the method in k values is demonstrated

14. Results & Discussion ++
DOG values for different scintillator total thickness (T) and gamma ray energies of
140keV, 364keV and 512keV for (a) GSO:Ce, (b) LSO:Ce and (c) YAP:Ce

15. Results & Discussion +++
Predicted DOG values of GSO:Ce, LSO:Ce and YAP:Ce for gamma ray energy of 140keV.

16. Conclusion
A semi-empirical theoretical model, describing light transport
in single crystals was developed.
The model was used in conjunction with a Monte Carlo
generated gamma ray absorption data to describe the
Detector Optical Gain (DOG) of single crystal scintillator
materials excited by gamma rays.
The model was checked against experimental results and
the fraction of the optical photons propagating through crystal
layers (named k) was determined.
The model was used to find an optimum crystal thickness
per gamma ray energy application. It was found that the
optimum thickness is a function of the scintillator material and
the gamma ray energy

17. Thank you!
http://env-hum-comp-res.teipir.gr/

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