Marinković, Predrag

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  • Marinković, Predrag (6)
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Author's Bibliography

Application of the Monte Carlo method and the empirical approximate formulas by Taylor and Berger for the calculation of the build-up factor in the fields of gamma and X radiation

Stanković, Srboljub; Ilić, Radovan; Marinković, Predrag; Nikolić, Dragana; Kržanović, Nikola; Radenković, Mirjana

(Niš : Sievert Association, 2019)

TY  - CONF
AU  - Stanković, Srboljub
AU  - Ilić, Radovan
AU  - Marinković, Predrag
AU  - Nikolić, Dragana
AU  - Kržanović, Nikola
AU  - Radenković, Mirjana
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12139
AB  - During the construction of nuclear facilities, radiotherapy centers, hospitals with radiological diagnostic facilities, and radioactive waste storage facilities, complex requirements for protection against ionizing radiation have been set up. In its basic principles, modern approaches in the design of radiation protection procedures were derived from empirical conclusions that were obtained by solving practical problems encountered by nuclear engineers and physicists. In the radiation protection projections, as well as in the formation of different technical and technological procedures in the radiation environment, one of the most important characteristics is the build-up factor of the material used. Based on experimental and theoretical research, empirical formulas for calculating the build-up factors are used to solve practical problems in radiation protection. With the development of information and computer technologies for calculating the build-up factor, other numerical methods are also used, of which a very attractive and efficient Monte Carlo calculation method is used. In this paper, the calculations with the empirical approximate formulas by Taylor and Berger, as well as the results obtained by using the software based on the Monte Carlo method, were used to determine the build-up of the factors in the protection of gamma and X radiation for several selected materials (lead, water, iron, etc.). By comparing the results obtained with the empirical approximations and Monte Carlo calculations, certain conclusions have been drawn that direct us to new critical considerations about the usefulness of using the chosen method of calculation for the build-up factor of materials found in modern technological processes using sources of gamma and X radiation.
PB  - Niš : Sievert Association
C3  - RAP 2019 : International conference on radiation applications : Book of abstracts
T1  - Application of the Monte Carlo method and the empirical approximate formulas by Taylor and Berger for the calculation of the build-up factor in the fields of gamma and X radiation
SP  - 93
EP  - 93
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12139
ER  - 
@conference{
author = "Stanković, Srboljub and Ilić, Radovan and Marinković, Predrag and Nikolić, Dragana and Kržanović, Nikola and Radenković, Mirjana",
year = "2019",
abstract = "During the construction of nuclear facilities, radiotherapy centers, hospitals with radiological diagnostic facilities, and radioactive waste storage facilities, complex requirements for protection against ionizing radiation have been set up. In its basic principles, modern approaches in the design of radiation protection procedures were derived from empirical conclusions that were obtained by solving practical problems encountered by nuclear engineers and physicists. In the radiation protection projections, as well as in the formation of different technical and technological procedures in the radiation environment, one of the most important characteristics is the build-up factor of the material used. Based on experimental and theoretical research, empirical formulas for calculating the build-up factors are used to solve practical problems in radiation protection. With the development of information and computer technologies for calculating the build-up factor, other numerical methods are also used, of which a very attractive and efficient Monte Carlo calculation method is used. In this paper, the calculations with the empirical approximate formulas by Taylor and Berger, as well as the results obtained by using the software based on the Monte Carlo method, were used to determine the build-up of the factors in the protection of gamma and X radiation for several selected materials (lead, water, iron, etc.). By comparing the results obtained with the empirical approximations and Monte Carlo calculations, certain conclusions have been drawn that direct us to new critical considerations about the usefulness of using the chosen method of calculation for the build-up factor of materials found in modern technological processes using sources of gamma and X radiation.",
publisher = "Niš : Sievert Association",
journal = "RAP 2019 : International conference on radiation applications : Book of abstracts",
title = "Application of the Monte Carlo method and the empirical approximate formulas by Taylor and Berger for the calculation of the build-up factor in the fields of gamma and X radiation",
pages = "93-93",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12139"
}
Stanković, S., Ilić, R., Marinković, P., Nikolić, D., Kržanović, N.,& Radenković, M.. (2019). Application of the Monte Carlo method and the empirical approximate formulas by Taylor and Berger for the calculation of the build-up factor in the fields of gamma and X radiation. in RAP 2019 : International conference on radiation applications : Book of abstracts
Niš : Sievert Association., 93-93.
https://hdl.handle.net/21.15107/rcub_vinar_12139
Stanković S, Ilić R, Marinković P, Nikolić D, Kržanović N, Radenković M. Application of the Monte Carlo method and the empirical approximate formulas by Taylor and Berger for the calculation of the build-up factor in the fields of gamma and X radiation. in RAP 2019 : International conference on radiation applications : Book of abstracts. 2019;:93-93.
https://hdl.handle.net/21.15107/rcub_vinar_12139 .
Stanković, Srboljub, Ilić, Radovan, Marinković, Predrag, Nikolić, Dragana, Kržanović, Nikola, Radenković, Mirjana, "Application of the Monte Carlo method and the empirical approximate formulas by Taylor and Berger for the calculation of the build-up factor in the fields of gamma and X radiation" in RAP 2019 : International conference on radiation applications : Book of abstracts (2019):93-93,
https://hdl.handle.net/21.15107/rcub_vinar_12139 .

Toward utilization of MCNP5 particle track output file for simulation problems in photon spectrometry

Stanković, Jelena S.; Marinković, Predrag; Ciraj-Bjelac, Olivera; Kaljević, Jelica; Aranđić, Danijela; Lazarević, Đorđe R.

(2015)

TY  - JOUR
AU  - Stanković, Jelena S.
AU  - Marinković, Predrag
AU  - Ciraj-Bjelac, Olivera
AU  - Kaljević, Jelica
AU  - Aranđić, Danijela
AU  - Lazarević, Đorđe R.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/650
AB  - Pulse height distribution (PHD) registered by a spectrometer is influenced by various physical phenomena such as photon interactions as well as disturbance produced by the electronic circuits inside the spectrometer. Therefore, spectrometry measurements of gamma and X-ray radiation inaccurately represent primary spectra. In order to overcome spectrum disruption, spectrum unfolding has to be applied. One of the common tools used in the unfolding process is Monte Carlo simulation of spectrometer response to monochromatic photons. The purpose of this work is to develop a new method for simulating CdTe semiconductor spectrometer response to monochromatic photons that can be further used for the spectrum unfolding procedure. The method is based upon post-processing of the particle track (PTRAC) output file generated by the MCNP5 program. In addition to the spectrometry output, this method provides information for each specific photon interaction inside the spectrometer active volume, which is required when taking into account spectrometer charge collection. The PTRAC generated detector response and the measured spectrum were in good agreement. The results obtained showed that this method can be used to generate precise response functions of gamma and X-ray spectrometers.
T2  - Computer Physics Communications
T1  - Toward utilization of MCNP5 particle track output file for simulation problems in photon spectrometry
VL  - 195
SP  - 77
EP  - 83
DO  - 10.1016/j.cpc.2015.05.003
ER  - 
@article{
author = "Stanković, Jelena S. and Marinković, Predrag and Ciraj-Bjelac, Olivera and Kaljević, Jelica and Aranđić, Danijela and Lazarević, Đorđe R.",
year = "2015",
abstract = "Pulse height distribution (PHD) registered by a spectrometer is influenced by various physical phenomena such as photon interactions as well as disturbance produced by the electronic circuits inside the spectrometer. Therefore, spectrometry measurements of gamma and X-ray radiation inaccurately represent primary spectra. In order to overcome spectrum disruption, spectrum unfolding has to be applied. One of the common tools used in the unfolding process is Monte Carlo simulation of spectrometer response to monochromatic photons. The purpose of this work is to develop a new method for simulating CdTe semiconductor spectrometer response to monochromatic photons that can be further used for the spectrum unfolding procedure. The method is based upon post-processing of the particle track (PTRAC) output file generated by the MCNP5 program. In addition to the spectrometry output, this method provides information for each specific photon interaction inside the spectrometer active volume, which is required when taking into account spectrometer charge collection. The PTRAC generated detector response and the measured spectrum were in good agreement. The results obtained showed that this method can be used to generate precise response functions of gamma and X-ray spectrometers.",
journal = "Computer Physics Communications",
title = "Toward utilization of MCNP5 particle track output file for simulation problems in photon spectrometry",
volume = "195",
pages = "77-83",
doi = "10.1016/j.cpc.2015.05.003"
}
Stanković, J. S., Marinković, P., Ciraj-Bjelac, O., Kaljević, J., Aranđić, D.,& Lazarević, Đ. R.. (2015). Toward utilization of MCNP5 particle track output file for simulation problems in photon spectrometry. in Computer Physics Communications, 195, 77-83.
https://doi.org/10.1016/j.cpc.2015.05.003
Stanković JS, Marinković P, Ciraj-Bjelac O, Kaljević J, Aranđić D, Lazarević ĐR. Toward utilization of MCNP5 particle track output file for simulation problems in photon spectrometry. in Computer Physics Communications. 2015;195:77-83.
doi:10.1016/j.cpc.2015.05.003 .
Stanković, Jelena S., Marinković, Predrag, Ciraj-Bjelac, Olivera, Kaljević, Jelica, Aranđić, Danijela, Lazarević, Đorđe R., "Toward utilization of MCNP5 particle track output file for simulation problems in photon spectrometry" in Computer Physics Communications, 195 (2015):77-83,
https://doi.org/10.1016/j.cpc.2015.05.003 . .
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Radiography simulation based on point-kernel model and dose buildup factors

Marinković, Predrag; Ilic, Radovan

(2009)

TY  - JOUR
AU  - Marinković, Predrag
AU  - Ilic, Radovan
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3691
AB  - Three-dimensional point-kernel multiple scatter model for radiography simulation, based on dose X-ray buildup factors, is proposed and validated to Monte Carlo simulation. This model embraces nonuniform attenuation in object of imaging (patient body tissue). Photon multiple scattering is treated as in the point-kernel integration gamma ray shielding problems via scatter voxels. First order Compton scattering is described by means of Klein-Nishina formula. Photon multiple scattering is accounted by using dose buildup factors. The proposed model is convenient in those situations where more exact techniques, like Monte Carlo, are not time consuming acceptable.
T2  - Journal of X-Ray Science and Technology
T1  - Radiography simulation based on point-kernel model and dose buildup factors
VL  - 17
IS  - 1
SP  - 41
EP  - 59
DO  - 10.3233/XST-2009-0215
ER  - 
@article{
author = "Marinković, Predrag and Ilic, Radovan",
year = "2009",
abstract = "Three-dimensional point-kernel multiple scatter model for radiography simulation, based on dose X-ray buildup factors, is proposed and validated to Monte Carlo simulation. This model embraces nonuniform attenuation in object of imaging (patient body tissue). Photon multiple scattering is treated as in the point-kernel integration gamma ray shielding problems via scatter voxels. First order Compton scattering is described by means of Klein-Nishina formula. Photon multiple scattering is accounted by using dose buildup factors. The proposed model is convenient in those situations where more exact techniques, like Monte Carlo, are not time consuming acceptable.",
journal = "Journal of X-Ray Science and Technology",
title = "Radiography simulation based on point-kernel model and dose buildup factors",
volume = "17",
number = "1",
pages = "41-59",
doi = "10.3233/XST-2009-0215"
}
Marinković, P.,& Ilic, R.. (2009). Radiography simulation based on point-kernel model and dose buildup factors. in Journal of X-Ray Science and Technology, 17(1), 41-59.
https://doi.org/10.3233/XST-2009-0215
Marinković P, Ilic R. Radiography simulation based on point-kernel model and dose buildup factors. in Journal of X-Ray Science and Technology. 2009;17(1):41-59.
doi:10.3233/XST-2009-0215 .
Marinković, Predrag, Ilic, Radovan, "Radiography simulation based on point-kernel model and dose buildup factors" in Journal of X-Ray Science and Technology, 17, no. 1 (2009):41-59,
https://doi.org/10.3233/XST-2009-0215 . .
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Radiography Simulation Based on Exposure Buildup Factors for Multilayer Structures

Marinković, Predrag; Pešić, Milan P.

(2009)

TY  - JOUR
AU  - Marinković, Predrag
AU  - Pešić, Milan P.
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3736
AB  - Monte Carlo techniques were usually used to study the effect of scattered photons on a radiographic X-ray image, Such approach is accurate, but computer time consuming. On the other hand, the exposure buildup factors can be used as approximate and efficient assessment to account for the scattering of X-rays. This method uses the known radiography parameters to find the resulting detector exposure due to both scattered and un-collided photons. A model for radiography simulation, based on X-ray dose buildup factor, is proposed. This model includes non-uniform attenuation in voxelized object of imaging (patient body tissue). Composition of patient body is considered as a multi-layer structure. Various empirical formulas exist for multi-layer structure calculations and they all calculate multi-layer buildup factors by combining single-layer buildup factors. The proposed model is convenient in cases when more exact techniques (like Monte Carlo) are not economical. (C) 2009 The Japan Society of Applied Physics
T2  - Japanese Journal of Applied Physics
T1  - Radiography Simulation Based on Exposure Buildup Factors for Multilayer Structures
VL  - 48
IS  - 6
DO  - 10.1143/JJAP.48.066002
ER  - 
@article{
author = "Marinković, Predrag and Pešić, Milan P.",
year = "2009",
abstract = "Monte Carlo techniques were usually used to study the effect of scattered photons on a radiographic X-ray image, Such approach is accurate, but computer time consuming. On the other hand, the exposure buildup factors can be used as approximate and efficient assessment to account for the scattering of X-rays. This method uses the known radiography parameters to find the resulting detector exposure due to both scattered and un-collided photons. A model for radiography simulation, based on X-ray dose buildup factor, is proposed. This model includes non-uniform attenuation in voxelized object of imaging (patient body tissue). Composition of patient body is considered as a multi-layer structure. Various empirical formulas exist for multi-layer structure calculations and they all calculate multi-layer buildup factors by combining single-layer buildup factors. The proposed model is convenient in cases when more exact techniques (like Monte Carlo) are not economical. (C) 2009 The Japan Society of Applied Physics",
journal = "Japanese Journal of Applied Physics",
title = "Radiography Simulation Based on Exposure Buildup Factors for Multilayer Structures",
volume = "48",
number = "6",
doi = "10.1143/JJAP.48.066002"
}
Marinković, P.,& Pešić, M. P.. (2009). Radiography Simulation Based on Exposure Buildup Factors for Multilayer Structures. in Japanese Journal of Applied Physics, 48(6).
https://doi.org/10.1143/JJAP.48.066002
Marinković P, Pešić MP. Radiography Simulation Based on Exposure Buildup Factors for Multilayer Structures. in Japanese Journal of Applied Physics. 2009;48(6).
doi:10.1143/JJAP.48.066002 .
Marinković, Predrag, Pešić, Milan P., "Radiography Simulation Based on Exposure Buildup Factors for Multilayer Structures" in Japanese Journal of Applied Physics, 48, no. 6 (2009),
https://doi.org/10.1143/JJAP.48.066002 . .

Primena virtuelng voksela pri upotrebi CT podataka u modelovanju trajektorije čestice tehnikama Monte Karlo

Ilić, Radovan; Marinković, Predrag; Stanković, Srboljub; Kaljević, Jelica

(Beograd : Institut za nuklearne nauke "Vinča" : Društvo za zaštitu od zračenja Srbije i Crne Gore, 2007)

TY  - CONF
AU  - Ilić, Radovan
AU  - Marinković, Predrag
AU  - Stanković, Srboljub
AU  - Kaljević, Jelica
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12261
AB  - U simulaciji prolaza čestica tehnikama Monte Karlo aktuelni geometrijski moduli upotrebljavaju površine prvog i drugog reda (FOTELP, PENELOPE, SHIELD, GEANT), a nekad i četvrtog reda(MCNP5), da opišu složene geometrijske forme.. Sve veća primena tehnika Monte Karlo u medicini oslanja se na vokselizovane geometrijske forme koje se dobijaju vokselizaciom fantoma ili iz CT podataka. Ogroman broj tela (voxela) u tom slučaju otežava primenu konstruktivne geometrije. Eefikasniji pristup tom problemu zasniva se na primeni virtuelnog voksela.Ovde se saopštavaju rezultati upotrebe virtuelnog voksela na anatomiju tela i organa upotrebom CT podataka.
AB  - Geometry modules in particle transport simulation codes with Monte Carlo techniques use surfaces of first and second order, sometimes even a fourth order surfaces, to be able to describe complex geometrical shapes. Constructive quadric geometry dominates in all leading software packages. Increasing application of Monte Carlo techniques in medicine is associated with voxelized geometry forms. Huge number of bodies present in this case makes the use of constructive geometry more difficult. The paper describes an efficient approach to this problem by virtual voxel application, where optical distance to the boundary is obtained, and 3D voxel indices give information about the materials present in voxel.
PB  - Beograd : Institut za nuklearne nauke "Vinča" : Društvo za zaštitu od zračenja Srbije i Crne Gore
C3  - 24. simpozijum DZZSCG : zbornik radova
T1  - Primena virtuelng voksela pri upotrebi CT podataka u modelovanju trajektorije čestice tehnikama Monte Karlo
T1  - Usage of virtual voxel with CT data in particles trajectory modeling by Monte Carlo techniques
SP  - 233
EP  - 237
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12261
ER  - 
@conference{
author = "Ilić, Radovan and Marinković, Predrag and Stanković, Srboljub and Kaljević, Jelica",
year = "2007",
abstract = "U simulaciji prolaza čestica tehnikama Monte Karlo aktuelni geometrijski moduli upotrebljavaju površine prvog i drugog reda (FOTELP, PENELOPE, SHIELD, GEANT), a nekad i četvrtog reda(MCNP5), da opišu složene geometrijske forme.. Sve veća primena tehnika Monte Karlo u medicini oslanja se na vokselizovane geometrijske forme koje se dobijaju vokselizaciom fantoma ili iz CT podataka. Ogroman broj tela (voxela) u tom slučaju otežava primenu konstruktivne geometrije. Eefikasniji pristup tom problemu zasniva se na primeni virtuelnog voksela.Ovde se saopštavaju rezultati upotrebe virtuelnog voksela na anatomiju tela i organa upotrebom CT podataka., Geometry modules in particle transport simulation codes with Monte Carlo techniques use surfaces of first and second order, sometimes even a fourth order surfaces, to be able to describe complex geometrical shapes. Constructive quadric geometry dominates in all leading software packages. Increasing application of Monte Carlo techniques in medicine is associated with voxelized geometry forms. Huge number of bodies present in this case makes the use of constructive geometry more difficult. The paper describes an efficient approach to this problem by virtual voxel application, where optical distance to the boundary is obtained, and 3D voxel indices give information about the materials present in voxel.",
publisher = "Beograd : Institut za nuklearne nauke "Vinča" : Društvo za zaštitu od zračenja Srbije i Crne Gore",
journal = "24. simpozijum DZZSCG : zbornik radova",
title = "Primena virtuelng voksela pri upotrebi CT podataka u modelovanju trajektorije čestice tehnikama Monte Karlo, Usage of virtual voxel with CT data in particles trajectory modeling by Monte Carlo techniques",
pages = "233-237",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12261"
}
Ilić, R., Marinković, P., Stanković, S.,& Kaljević, J.. (2007). Primena virtuelng voksela pri upotrebi CT podataka u modelovanju trajektorije čestice tehnikama Monte Karlo. in 24. simpozijum DZZSCG : zbornik radova
Beograd : Institut za nuklearne nauke "Vinča" : Društvo za zaštitu od zračenja Srbije i Crne Gore., 233-237.
https://hdl.handle.net/21.15107/rcub_vinar_12261
Ilić R, Marinković P, Stanković S, Kaljević J. Primena virtuelng voksela pri upotrebi CT podataka u modelovanju trajektorije čestice tehnikama Monte Karlo. in 24. simpozijum DZZSCG : zbornik radova. 2007;:233-237.
https://hdl.handle.net/21.15107/rcub_vinar_12261 .
Ilić, Radovan, Marinković, Predrag, Stanković, Srboljub, Kaljević, Jelica, "Primena virtuelng voksela pri upotrebi CT podataka u modelovanju trajektorije čestice tehnikama Monte Karlo" in 24. simpozijum DZZSCG : zbornik radova (2007):233-237,
https://hdl.handle.net/21.15107/rcub_vinar_12261 .

A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor

Marinković, Predrag; Ilic, Radovan; Spaic, Rajko

(2007)

TY  - JOUR
AU  - Marinković, Predrag
AU  - Ilic, Radovan
AU  - Spaic, Rajko
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3310
AB  - A three-dimensional (3D) point-kernel multiple scatter model for point spread function (PSF) determination in parallel-beam single-photon emission computed tomography ( SPECT), based on a dose gamma-ray buildup factor, is proposed. This model embraces nonuniform attenuation in a voxelized object of imaging ( patient body) and multiple scattering that is treated as in the point-kernel integration gamma-ray shielding problems. First-order Compton scattering is done by means of the Klein-Nishina formula, but the multiple scattering is accounted for by making use of a dose buildup factor. An asset of the present model is the possibility of generating a complete two-dimensional (2D) PSF that can be used for 3D SPECT reconstruction by means of iterative algorithms. The proposed model is convenient in those situations where more exact techniques are not economical. For the proposed models testing purpose calculations ( for the point source in a nonuniform scattering object for parallel beam collimator geometry), the multiple-order scatter PSF generated by means of the proposed model matched well with those using Monte Carlo ( MC) simulations. Discrepancies are observed only at the exponential tails mostly due to the high statistic uncertainty of MC simulations in this area, but not because of the inappropriateness of the model.
T2  - Physics in Medicine and Biology
T1  - A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor
VL  - 52
IS  - 19
SP  - 5785
EP  - 5802
DO  - 10.1088/0031-9155/52/19/004
ER  - 
@article{
author = "Marinković, Predrag and Ilic, Radovan and Spaic, Rajko",
year = "2007",
abstract = "A three-dimensional (3D) point-kernel multiple scatter model for point spread function (PSF) determination in parallel-beam single-photon emission computed tomography ( SPECT), based on a dose gamma-ray buildup factor, is proposed. This model embraces nonuniform attenuation in a voxelized object of imaging ( patient body) and multiple scattering that is treated as in the point-kernel integration gamma-ray shielding problems. First-order Compton scattering is done by means of the Klein-Nishina formula, but the multiple scattering is accounted for by making use of a dose buildup factor. An asset of the present model is the possibility of generating a complete two-dimensional (2D) PSF that can be used for 3D SPECT reconstruction by means of iterative algorithms. The proposed model is convenient in those situations where more exact techniques are not economical. For the proposed models testing purpose calculations ( for the point source in a nonuniform scattering object for parallel beam collimator geometry), the multiple-order scatter PSF generated by means of the proposed model matched well with those using Monte Carlo ( MC) simulations. Discrepancies are observed only at the exponential tails mostly due to the high statistic uncertainty of MC simulations in this area, but not because of the inappropriateness of the model.",
journal = "Physics in Medicine and Biology",
title = "A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor",
volume = "52",
number = "19",
pages = "5785-5802",
doi = "10.1088/0031-9155/52/19/004"
}
Marinković, P., Ilic, R.,& Spaic, R.. (2007). A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor. in Physics in Medicine and Biology, 52(19), 5785-5802.
https://doi.org/10.1088/0031-9155/52/19/004
Marinković P, Ilic R, Spaic R. A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor. in Physics in Medicine and Biology. 2007;52(19):5785-5802.
doi:10.1088/0031-9155/52/19/004 .
Marinković, Predrag, Ilic, Radovan, Spaic, Rajko, "A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor" in Physics in Medicine and Biology, 52, no. 19 (2007):5785-5802,
https://doi.org/10.1088/0031-9155/52/19/004 . .
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