RBFM v6n1.indb

Transcrição

RBFM v6n1.indb

Expediente
A Revista Brasileira de Física Médica (RBFM)
é uma publicação editada pela Associação
Brasileira de Física Médica. Criada em 2005,
tem como objetivo publicar trabalhos originais
nas áreas de Radioterapia, Medicina Nuclear,
Radiologia Diagnóstica, Proteção Radiológica
e Dosimetria das Radiações, incluindo
modalidades correlatas de diagnóstico e terapia
com radiações ionizantes e não-ionizantes,
além de Ensino e Instrumentação em Física
Médica.
Os conceitos e opiniões emitidos nos artigos
são de inteira responsabilidade de seus autores.
É permitida a reprodução total ou parcial dos
artigos, desde que mencionada a fonte e
mediante permissão expressa da RBFM.
Corpo editoral
Editor Científico
Marcelo Baptista de Freitas – Universidade Federal de São Paulo (UNIFESP)
Editores Associados
Ana Maria Marques da Silva – Pontifícia Universidade Católica do Rio Grande do Sul (PUCRS)
Denise Yanikian Nersissian – Instituto de Eletrotécnica e Energia da Universidade de São Paulo
(IEE/USP)
Lorena Pozzo – Instituto de Pesquisas Energéticas e Nucleares (IPEN-CNEN)
Patrícia Nicolucci - Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto da Universidade de
São Paulo (FFCLRP/USP)
www.abfm.org.br/rbfm - [email protected]
Conselho editorial
Adilton de Oliveira Carneiro
Faculdade de Filosofia, Ciências e Letras de Ribeirão
Preto da Universidade de São Paulo (FFCLRP/USP)
Alessandro André Mazzola
Hospital Moinhos de Vento, Porto Alegre (RS)
Alessandro Martins da Costa
Faculdade de Filosofia Ciências e Letras de Ribeirão
Diretoria
Presidente
Edmário Antônio Guimarães Costa
Vice-Presidente
Ilo de Souza Baptista
Secretário Geral
Luiz Flávio Kalil Telles
Tesoureira
Josemilson de Menezes Bispo
Diretorias setoriais
Diretoria da Área de Medicina Nuclear
Daniel Coiro da Silva
Diretoria da Área de Radiologia Diagnóstica
Renato Dimenstein
Diretoria da Área de Radioterapia
Aluísio José de Castro Neto
Secretários regionais
Região Sul
Marcus Vinicius Bortolloto
Região Centro-Sudeste
Roberto Salomon de Souza
Região Norte-Nordeste
Francisco Luciano Viana
Endereço
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www.abfm.org.br - [email protected]
PRODUÇÃO EDITORIAL
Alexandre Bacelar
Hospital de Clínicas de Porto Alegre (RS)
Caridad Borrás
School of Medicine and Health Sciences, Washington
University, USA
Carla Rachel Ono
Centro de Medicina Nuclear do Hospital das Clínicas da
Faculdade de Medicina da Universidade de São Paulo
(HC-FMUSP)
Carlos Eduardo de Almeida
Universidade Estadual do Rio de Janeiro (UERJ)
Carlos Malamut
Centro de Desenvolvimento de Tecnologia Nuclear,
Comissão Nacional de Energia Nuclear de Minas gerais
(CDTN/CNEN-MG)
Leonardo Paschino
Centro de Diagnóstico e Análises Clínicas, São Paulo (SP)
Letícia Lucente Campos Rodrigues
Instituto de Pesquisas Energéticas e Nucleares,
Comissão Nacional de Energia Nuclear de São Paulo
(IPEN/CNEN-SP)
Linda Viola Ehlin Caldas
(IPEN/CNEN-SP)
Luiz Antonio Ribeiro da Rosa
Instituto de Radioproteção e Dosimetria, Comissão
Nacional de Energia Nuclear do Rio de Janeiro
(IRD/CNEN-RJ)
Cecil Chow Robilotta
Instituto de Física da Universidade de São Paulo (USP)
Cecília Kalil Haddad
Hospital Sírio Libanês, São Paulo (SP)
Martha Aurélia Aldred
Cláudio Hissao Sibata
East Carolina University, USA
Martin Eduardo Poletti
Cleber Nogueira de Souza
TomoTherapy Incorporated, USA
Dráulio Barros de Araujo
Edmário A.G. Costa
Radioterapia do Hospital São Rafael, Salvador (BA)
Elisabeth Mateus Yoshimura
Emico Okuno
Gabriela Hoff
Pontifícia Universidade Católica do Rio Grande do Sul
(PUCRS)
Gian-Maria A.A. Sordi
(IPEN/CNEN-SP)
Helen Jamil Khoury
Universidade Federal de Pernambuco (UFPE)
Helvécio Correa Mota
East Carolina University, USA
Rua Bela Cintra, 178, Cerqueira César
São Paulo/SP - CEP 01415-000
Tel.: 55 11 2978-6686
www.zeppelini.com.br
Laura Natal Rodrigues
(IPEN/CNEN-SP)
Maria Inês Calil Cury Guimarães
Centro de Medicina Nuclear do Hospital das Clínicas da
Faculdade de Medicina da Universidade de São Paulo
(HC-FMUSP)
Gunther Drexler
Universidade Estadual do Rio de Janeiro (UERJ)
Uma empresa do Grupo ZP
Laura Furnari
Beneficência Portuguesa, São Paulo (SP)
Homero Lavieri Martins
Hospital A.C. Camargo, São Paulo (SP)
José Carlos da Cruz
Hospital Israelita Albert Einstein, São Paulo (SP)
José Willegaignon de Amorim de Carvalho
Centro de Medicina Nuclear (HC-FMUSP)
Michael Stabin
Vanderbilt University, USA
Oswaldo Baffa Filho
Faculdade de Filosofia Ciências e Letras de Ribeirão
Paulo Roberto Costa
Regina Bitelli Medeiros
Universidade Federal de São Paulo (UNIFESP)
Ricardo Tadeu Lopes
Instituto Alberto Luiz Coimbra de Pós-Graduação e
Pesquisa de Engenharia, Universidade Federal do Rio de
Janeiro (COPPE/UFRJ)
Simone Kodlulovich Dias
Universidade Federal do Rio de Janeiro (UFRJ)
Tânia Aparecida Correia Furquim
Instituto de Eletrotécnica e Energia da Universidade de
São Paulo (IEE/USP)
Teógenes Augusto da Silva
Centro de Desenvolvimento de Tecnologia Nuclear,
Comissão Nacional de Energia Nuclear de Minas Gerais
(CDTN/CNEN-MG)
Thomaz Ghilardi Netto
Faculdade de Medicina de Ribeirão Preto da
Universidade de São Paulo (FMRP/USP)
Walter Siqueira Paes
Serviço de Engenharia de Segurança e Medicina do
Trabalho da Universidade de São Paulo (USP)
Sumário
Editorial
1
Patient safety and the medical physicist
William R. Hendee
Artigos Originais
3
Primary and scattering contributions to beta scaled dose point kernels by means of Monte
Carlo simulations
Contribuições primária e espalhada para dosimetria beta calculadas pelo dose point kernels empregando
simulações pelo Método Monte Carlo
Mauro Valente, Francesca Botta, Pedro Pérez and Guido Pedroli
7
Intrinsic spatial resolution limitations due to differences between positron emission position
and annihilation detection localization
Limitações da resolução espacial intrínseca devido às diferenças entre a posição da emissão do pósitron e a
detecção da localização de aniquilação
Pedro Pérez, Francisco Malano and Mauro Valente
13
Comparison between subjective and quantitative methods for assessing the resolution limit
of radiographic systems
Comparação entre métodos subjetivos e quantitativos na medida da resolução limite de sistemas radiográficos
Matheus Alvarez, Marcela de Oliveira, Diana R. Pina and José R. A. Miranda
Associação Brasileira de Física Médica®
Editorial
Revista Brasileira de Física Médica.2012;6(1):1-2.
Patient safety and the medical physicist
O
ver the past 18 months several articles have appeared in the “New York Times” and other newspapers describing
overexposures of patients to radiation used for medical purposes1-4. These articles have revealed problems in the
medical use of radiation that must be addressed by medical physicists working with physicians and technologists.
Overexposures in computed tomography
In several institutions, overexposures have occurred during use of x-ray computed tomography (CT) for brain perfusion
studies to identify the neurological consequences of strokes and other events. In some cases, patients received exposures
that were several times greater than necessary. The overexposures were caused by use of inappropriate CT protocols for
brain perfusion studies, and by the desire to achieve appealing low-noise images rather than images acquired at the lowest
dose consistent with adequate diagnostic information. Another contributing factor was the cacophony of terms used to
describe CT parameters across makes and models of CT scanners.
To resolve these problems, the AAPM hosted a meeting in April, 2010 entitled “CT Dose Summit: Optimization of
Protocols”. One outcome of the meeting was establishment of a working group with two charges. The first charge was
to standardize parameter terminology across different makes and models of CT scanners. The second charge was to
develop consensus protocols for CT procedures, beginning with brain perfusion studies, and make these protocols available wherever CT procedures are performed. Consensus protocols for adult brain perfusion studies are now posted on the
AAPM website5, and protocols for other conditions are under development. Discussions are underway with industry about
terminology standardization, and guidelines for use of the NEMA XR-25 CT dose-check standard are also posted on the
AAPM website6.
Although recent media attention has targeted computed tomography, other areas of medical imaging also require
constant vigilance. In particular, interventional, cardiovascular and neurointerventional imaging procedures use prolonged
fluoroscopy together with digital spot acquisitions, resulting often in relatively high radiation dose to patients. As facilities
transition to new, more sophisticated imaging equipment, traditional imaging protocols may become obsolete and cause
suboptimal images and unnecessary patient exposures if used.
Major campaigns to reduce exposures in medical imaging have been launched by professional organizations, including the AAPM. The Image Gently campaign7 addresses exposures to pediatric patients, and the Image Wisely campaign8
focuses on adult patients.
Overexposures in radiation therapy
The “New York Times” also reported patient overexposures caused by mistakes in the calibration and application of therapeutic x ray beams from linear accelerators. Two patients died from overexposures caused by mistakes during radiation
delivery, and several other cases have been cited where calibration errors caused patient overexposures.
Stimulated in part by the “New York Times” articles, the AAPM convened a meeting in Miami in June, 2010 entitled
“Safety in Radiation Therapy: A Call to Action”. The purpose of the meeting was to identify the causes of radiation therapy
errors, establish approaches to reducing these errors, and protect patients from disastrous consequences if errors do
occur. Twenty recommendations from the meeting were described in an article published simultaneously in the January
2011 issues of “Medical Physics and Practical Radiation Oncology”9. Follow-up to the recommendations is currently under
discussion within the AAPM, and will in part be the responsibility of the Institute for the Assessment of Medical Devices, a
collaboration between the AAPM and the Morgridge Institute of Research based in Madison WI10.
Some of the recommendations from the Miami meeting can be highlighted. They include (1) reduce distractions and
traffic at the accelerator console so that the operator can focus exclusively on patient treatment; (2) simplify the treatment
console so that the operator has fewer computer screens to monitor and fewer parameters to track; (3) reduce reliance on
1
Hendee WR
computer-control of the treatment and return control of the treatment to the operator; (4) provide early warning systems to
indicate when a treatment exceeds defined parameters, or an equipment malfunction or operator mistake occurs; (5) use
checklists and implement a double-check verification process to ensure before treatment that patient and machine set-ups
are proper; (6) apply statistical tools to the treatment process to identify potential problems and to analyze the cause of
problems when they occur; (7) establish a national reporting system of errors and malfunctions so that everyone can learn
from problems at other institutions; (8) encourage external audits and accreditation of treatment facilities to ensure periodic
peer-review; (9) reinforce reliance on written policies and procedures to guide the treatment process with individual patients; and (10) empower all members of the treatment team to call “time out” when a treatment design seems inadequate
or a treatment process encounters a problem.
Conclusion
Recent reports of overexposures have prompted several initiatives to improve the use of medical radiation so that patient
risks are minimized. These initiatives should be led by medical physicists working collaboratively with physicians, technologists, regulators and industrial representatives.
Acknowledgements
The author thanks Drs. Andrew Karellas, David Rogers and Anthony Wolbarst for their helpful comments.
William R. Hendee
Editor Medical Physics
(Publishing in Med Phys. 2011;38(6):i-ii — Authorized by personal communication)
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2
Bogdanich W. Radiation offers new cures, and ways to do harm. NY Times, January 24, 2010.
Bogdanich W, Rebelo K. A pinpoint beam strays invisibly, harming instead of healing. NY Times, December 29, 2010.
Bogdanich W. After stroke scans, patients face serious health risks. NY Times, August 1, 2010.
Bogdanich W. West Virginia hospital overirradiated brain scan patients, records show. NY Times, March 6, 2011.
The American Association of Physicists in Medicine. CT scan protocols. [cited 2011 Mar 28]. Available from: www.aapm.org/pubs/CTprotocols
The American Association of Physicists in Medicine. NEMA Issues New Standards Publication XR 25-2010: Computed Tomography Dose Check. [cited 2011
Apr 21]. Available from: www.aapm.org/announcements/NEMAXR25.asp
Image Gently. The Alliance for Radiation Safety in Pediatric Imaging. [cited 2011 Mar 28]. Available from: http://www.pedrad.org/associations/5364/ig/
Image Wisely. Radiation Safety in Adult Medical Imaging. http://www.imagewisely.org/ (accessed March 28, 2011)
Hendee W, Herman M. Improving safety in radiation oncology. Med Phys. 2011;38(1):78-82.
Wisconsin Institute for Discovery. Morgridge Institute for Research. [cited 2011 Mar 28]. Available from: http://discovery.wisc.edu/morgridge.
Artigo Original
Primary and scattering contributions to
beta scaled dose point kernels by means of
Monte Carlo simulations
Contribuições primária e espalhada para dosimetria
beta calculadas pelo dose point kernels empregando
simulações pelo Método Monte Carlo
Mauro Valente1, Francesca Botta2, Pedro Pérez3 and Guido Pedroli2
1
CONICET – Buenos Aires, Argentina; FaMAF, Universidad Nacional de Córdoba – Córdoba, Argentina.
2
Medical Physics Department, European Institute of Oncology – Milan, Italy.
3
FaMAF, Universidad Nacional de Córdoba – Córdoba, Argentina; ANPCyT – Buenos Aires, Argentina.
Abstract
Beta-emitters have proved to be appropriate for radioimmunotherapy. The dosimetric characterization of each radionuclide has to be carefully
investigated. One usual and practical dosimetric approach is the calculation of dose distribution from a unit point source emitting particles according
to any radionuclide of interest, which is known as dose point kernel. Absorbed dose distributions are due to primary and radiation scattering
contributions. This work presented a method capable of performing dose distributions for nuclear medicine dosimetry by means of Monte Carlo
methods. Dedicated subroutines have been developed in order to separately compute primary and scattering contributions to the total absorbed
dose, performing particle transport up to 1 keV or least. Preliminarily, the suitability of the calculation method has been satisfactory, being tested
for monoenergetic sources, and it was further applied to the characterization of different beta-minus radionuclides of nuclear medicine interests for
radioimmunotherapy.
Keywords: nuclear medicine, beta-emitter, dose point kernel, Monte Carlo simulation.
Resumo
Fontes de radiação que emitem partículas beta são comprovadamente apropriadas para radioimunoterapia. Para tanto, a caracterização dosimétrica
do respectivo radionuclídeo tem de ser realizada cuidadosamente. Uma abordagem dosimétrica prática e usual é o cálculo da distribuição de dose
de uma fonte pontual unitária emitindo partículas de acordo com o radionuclídeo de interesse, a qual é conhecida como dose point kernel. As
distribuições de doses absorvidas são devidas às contribuições das radiações primária e espalhada. Este estudo apresenta um método capaz de
verificar as distribuições de dose para dosimetria em medicina nuclear empregando o método Monte Carlo. Subrotinas têm sido desenvolvidas para
permitir calcular separadamente as contribuições primária e espalhada da dose absorvida total, utilizando o transporte de partículas até 1keV ou
menos. Preliminarmente, a adequação do método de cálculo foi testada de forma satisfatória para fontes monoenergéticas, e foi ainda aplicada à
caracterização de diferentes radionuclídeos beta emissores de interesse em medicina nuclear para radioimunoterapia.
Palavras-chave: medicina nuclear, beta emissor, dose point kernel, simulação Monte Carlo.
Introduction
The interest from the nuclear medicine community in developing novel radiopharmaceuticals for radioimmunotherapy motivates active investigations devoted to the study and application of radiolabeled molecules with the capability for selectively
distinguish treatment target and further tumor cells irradiation.
The utilization of this kind of pharmaceuticals results in spatial
activity distributions with extremely non-uniform characteristics
within the patient. Actually, this feature constitutes precisely
the main advantage of these methods in view of maximizing
the discrimination between affected and healthy tissue1.
Activity distribution may be determined by means of different modalities. Nowadays, it is mainly measured using modern
imaging techniques but it is also possible to infer it by semi-emprical methods. The information about the activity distribution is
then incorporated in the treatment planning system in order to
obtain an estimation of the corresponding dose distribution. In
Corresponding author: Mauro Valente – CONICET & FaMAF University of Cordoba – Medina Allende y Haya de la Torre, Ciudad Universitaria – Cordoba –
Argentina – E-mail: [email protected]
3
Valente M, Botta F, Pérez P, Pedroli G
this sense, patient-specific dose distribution may be attained by
suitable calculations starting from activity distribution by means
of either Monte Carlo simulation or direct analytical methods1,2.
The dose distribution about a unit point source of any radionuclide of interest — known as dose point kernel (DPK) — has
proven to be a particularly useful tool for dosimetric calculation
by means of analytical methods3,4. Analytical procedures, however, can be straightforwardly performed only when considering homogeneous media. Therefore, analytical procedures
may show non-negligible limitations for practical situations.
This work presented a method capable of calculating
DPK for nuclear medicine dosimetry by means of Monte Carlo
methods. In addition, dedicated subroutines have been developed in order to compute primary and scattering contributions
to the total absorbed dose. The developed calculation method
has been applied to the characterization of different beta-minus
radionuclides of interest for nuclear medicine therapy.
Materials and methods
Theoretical background
The starting point for the proposed method is to consider a
simple situation of an isotropic point source emitting electrons
moving radially outward. Boltzmann radiation transport equation along with the continuous slowing down approximation
(CSDA) for charged particles predict that emitted electrons
shall continuously slow down according to the stopping power
function S(E), which depends on the electron kinetic energy
and, of course, physical properties of the irradiated material.
For a monoenergetic source, which energy is E0, it can be
calculated the remaining energy E(s) at a distance s from the
source location by means of:
E0
dE
=s
(
)
S
E
E (s )
(1)
where S(E) is the stopping power.
For practical reasons, it is usually convenient to introduce
the scaled DPK for beta particles (F) by means of the following
definition:
F ( s / RCSDA) =
δE ( s) / E 0
δs / RCSDA
(2)
where δs stands for the shell thickness, RCSDA is the particle
range in the CSDA, δE(s) is energy delivered in the shell between s and s + δs.
In order to avoid a singularity at the origin, it is assumed
by convention that F(s=0) equals RCSDA/40, where RCSDA represents the CSDA range defined by:
E0
RCSDA= ∫
0
4
dE
S (E )
(3)
Analytical approaches for solving the presented model
need to assume implicitly some approximations. Specifically,
straight-line motion along with continuous energy loss have
been taken as valid for electron interaction mechanism.
However, it is actually known that departures from continuous
slowing down arise from multiple scattering and energy loss
fluctuations, like delta-ray and Bremsstrahlung production.
Contrary to analytical techniques, Monte Carlo calculations
of DPK are capable of more realistic approaches, mainly due
to the possibility of handling multiple scattering as well as radiative energy losses. In this framework, it becomes possible to
consider the fact that some part of the energy loss straggling
may be carried out to positions far away, even at distances
larger than RCSDA.
When considering non monoenergetic sources, like radionuclides, it is necessary to calculate scaled DPK obtained by
weighting the corresponding associated spectra, This aim is
usually attained decomposing the spectrum into M groups according to the branching probability bi and end-point energy
Ei, as follows:
M
N ( E ) = ∑ pi N ( E )
i
(4)
i=1
where N indicates the channel intensity.
Implemented calculation method
Specific subroutine has been developed based on the
PENELOPE v. 2008 main code5 to calculate scaled DPK. The
subroutine has been specifically developed for assessing primary and scattering contributions. The primary component is
considered as dose contributions from primary particles, which
are actually emitted by the point source. On the other hand,
the scattering component is due to all kind of dose contributions that carry out when scattered (secondaries etc.) particles
deposit energy within the shell. When considering electrons as
primary particles, the implemented interaction mechanisms
that may change particle phase state and/or generate secondary radiation were soft event (energy and angle variations lower
than specific threshold values), elastic collision, hard inelastic
collision, Bremsstrahlung emission, inner-shell (K, L and M) impact ionization and delta interaction.
Scaled DPK were simulated considering a 10 cm radius
water-equivalent spherical phantom and energy deposition
was tallied in concentric shells having thickness of RCSDA/40,
where the RCSDA electron ranges have been extracted from the
ESTAR database6, as indicated in Figure 1.
PENELOPE v. 2008 main code databases provide a
large list of different materials along with the corresponding
radiation-matter interaction properties. As mentioned above,
scaled DPK have been calculated in water-equivalent spherical phantoms which physical and geometrical properties have
been introduced by means of the MATERIAL and PENGEOM
packages, respectively.
Primary and scattering contributions to beta scaled dose point kernels by means of Monte Carlo simulations
Results and discussion
After preliminary consistency tests, the dedicated Monte Carlo
subroutine has been used for the calculation of in-water energy
deposition of monoenergetic sources. A set of isotropic point
sources emitting 10 keV, 50 keV, 100 keV, 500 keV, 1 MeV and
3 MeV electrons has been considered with the aim of covering
the energy range of interests for typical beta-minus radionuclides used in nuclear medicine treatments. A typical result for
energy deposition distribution is reported in Figure 2.
From such results for the energy deposition within concentric shells, it becomes straightforward to obtain the
scaled DPK by means of Eq. 3 using shell radius as travelled path s.
As example of the capability of the developed calculation
system to attain primary and scattering contributions separation, Figures 3 to 6 show the scaled DPK results obtained for
a monoenergetic case along with three typical radionuclides
used in nuclear medicine treatments.
In the case of radionuclides, the traveled path s has
been normalized to the corresponding spectrum weighted
CSDA range (<RCSDA>). Similarly, the energy value E0 used for
deposited energy normalization within shells has been calculated according to the spectrum weighted mean value.
As reported in Figures 4 to 6, the relative contribution from
scattering radiation to total scaled DPK depends strongly on
radionuclide emission properties.
According to the obtained results (Figures 3 to 6) it can
be established that each investigated radionuclide presents different relative distribution between the primary and scattering
contributions to the total scaled DPK.
However, it was found in all cases that there is a non uniform relative scattering contribution among distance to point
source, therefore meaning that scattering to primary ratio
needs to be calculated at any distance from point source.
The calculations performed with the dedicated subroutine
used absorption energy at 1 keV as fixed threshold value, except for the 10 keV source for which an absorption value of 0.1
keV was considered. This criterion allowed to ensure that simulated showers have been appropriately transported until kinetic
energy reduced to values, at least, hundred times lower than
the initial one. The absorption energy represents the lower limit
for the particle kinetic energy that has to be simulated. Once a
particle reduces its kinetic energy to this threshold value, it is
Dose Point Kernel F (s, RCSDA)
Water, Liquid
Range (g/cm2)
102
100
10-2
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
Total
Primary
0
0.25
0.5
0.75
1
1.25
1.5
s/RCSDA
10-4 -2
10
10-1
100
101
102
103
Energy (MeV)
CSDA Range
Figure 3. Separation of primary contribution (solid red triangles)
from total (solid blue circles) scaled DPK for 1 MeV electron
source.
Figure 1. ESTAR RCSDA for liquid water.
x104
Deposited Energy [eV]
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Distance [cm]
Figure 2. Energy deposition mean value for 1 MeV electron
source as function of distance to the point source.
1.6
1.2
0.8
Primary
Total
Scattering
0.4
0.2
0.1
0
0.25
0.5
0.75
1
1.25
1.5
s/RCSDA
Figure 4. Separation of primary (solid blue triangles) and scattering (solid red squares) contributions from total (solid black circles) scaled DPK for 90Y source, using RCSDA = 0.432 cm in water.
5
Valente M, Botta F, Pérez P, Pedroli G
1.2
0.8
0.4
0.2
0.1
Total
Primary
Scattering
0
0.25
0.5
0.75
1.0
1.25
1.5
s/RCSDA
Dose Point Kernel F (s/RCSDA)
Figure 5. Separation of primary (solid blue triangles) and scattering (solid red squares) contributions from total (solid black circles)
scaled DPK for 177Lu source, using RCSDA = 0.025 cm in water.
1.2
0.8
0.4
0.2
0.1
0
Total
Primary
Scattering
0.25
0.5
0.75
s/RCSDA
1.0
1.25
1.5
Figure 6. Separation of primary (solid blue triangles) and scattering (solid red squares) contributions from total (solid black circles)
scaled DPK for 131I source, using RCSDA = 0.040 cm in water.
“locally absorbed”, which means that the residual energy (less
than the user defined absorption energy) is locally deposited
and the particle tracking is considered to be finished.
Actually, disregarding the radionuclide type, greater relative
scattering contributions have been found at short scaled distances, i.e. concentrated quite around the isotropically emitting
point source. In addition, contrary to the case of monoenegetic
sources for which maximum of relative scattering contribution
correspond to deeper penetration distances, the obtained results show that, in the case of radionuclides, the maximum of
relative contribution from scattering to total scaled DPK happened for scaled distances close to 0.2, which means 20% of
the actual effective CSDA range (<RCSDA>). This fact may arise
from the combination of different energy channels each one
having its own penetration capacity until particle thermalization.
In addition, both monoenergetic sources and radionuclides
have shown the same behavior regarding the decreasing tendency for the relative scattering contribution at large distances,
as expected.
Conclusion
A novel calculation system along with corresponding Monte
Carlo subroutine has been developed. The first consistency
6
tests regarding monoenergetic electron sources have preliminary shown the viability of the proposed calculation method.
Moreover, it has been satisfactory benchmarked when applied some radionuclides typically used in nuclear medicine
treatment. At the moment, efforts are devoted for extending
the proposed method to other radionuclides appropriate for
nuclear medicine, like 89Sr, 153Sm, 186Re and 188Re. In base on
the preliminary tests and the obtained results, the purposed
method seems to be a suitable and promising tool for assessing primary and scattering contributions to total energy deposition for calculating scaled dose point kernels in nuclear medicine. Furthermore, the proposed method can be improved in
order to distinguish even between the different components of
the scattering contribution to total DPK, according to the corresponding interaction mechanism.
It has been found, as it is well-known, that primary and
scattering energy fluences are significantly different at any location within the irradiated phantom, therefore it may be expected that the corresponding differences in linear energy transfer
(LET) and ionization properties would affect the net energy deposition. In addition, due to intrinsic physical properties, suitable distinction between primary and scattering contributions
may be particularly useful for clinical dosimetric purposes because this information may be used for improving radiobiological calculations, like tumor control probability (TCP) and normal
tissue complication probability (NTCP).
Acknowledgment
This work has been partially supported by grants from research
Projects PIP 11420090100398, PICT 2008-243 (CONICET
and ANPCyT) along with PFDT fellowship from ANPCyT of
Argentina.
References
1. Prestwich W, Nunes J, Kwok C. Beta dose point kernels for radionucides of
potential use in radioimmuno-therapy. J Nucl Med. 1989;30(6):1036-46. Erratum
in: J Nucl Med. 1989;30(10):1739-40.
2. Prestwich W, Chan L, Kwok C, Wilson B. Dose point kernels for beta-emitting
radioisotopes. In: Proceedings of the Fourth International Radiopharmaceutical
Dosimetry Symposium in Oak Ridge. Tennessee, USA, November 5-8, 1985. p.
545-61.
3. Botta F, Cremonesi M, Di Dia A, Ferrari M, Valente M, De Cicco C, et al.
90Y, 177Lu, and 131I therapy optimization: Monte Carlo calculation of
dose distribution and radiobiological evaluations. J Nucl Med (Reston, USA).
2009;50(2):1859-60.
4. Uusijärvi H, Chouin N, Bernhardt P, Ferrer L, Bardiès M, Forssell-Aronsson E.
Comparison of electron Dose Point Kernels in water generated by the Monte Carlo
codes, PENELOPE, GEANT4, MCNPX and ETRAN. Cancer Biother Radiopharm.
2009;24(4):461-7.
5. Salvat F, Fernández-Varea JM, Sempau J. PENELOPE-2008: a code system for
Monte Carlo simulation of electron and photon transport. Barcelona: Nuclear
Energy Agency; 2008.
6. National Institute of Standards and Technology [homepage on the Internet]. ESTAR
database [http://www.nist.gov/index.html]. 2007. Available from: http://physics.
nist.gov/PhysRefData/Star/Text/ESTAR.html
Artigo Original
Intrinsic spatial resolution limitations due
to differences between positron emission
position and annihilation detection localization
Limitações da resolução espacial intrínseca devido às
diferenças entre a posição da emissão do pósitron e a
detecção da localização de aniquilação
Pedro Pérez1, Francisco Malano2 and Mauro Valente2
Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Córdoba (UNC) – Córdoba, Argentina;
Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT) – Buenos Aires, Argentina.
2
Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Córdoba (UNC) – Córdoba, Argentina;
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) – Buenos Aires, Argentina.
1
Abstract
Since its successful implementation for clinical diagnostic, positron emission tomography (PET) represents the most promising medical imaging
technique. The recent major growth of PET imaging is mainly due to its ability to trace the biologic pathways of different compounds in the patient’s
body, assuming the patient can be labeled with some PET isotope. Regardless of the type of isotope, the PET imaging method is based on the
detection of two 511-keV gamma photons being emitted in opposite directions, with almost 180o between them, as a consequence of electronpositron annihilation. Therefore, this imaging method is intrinsically limited by random uncertainties in spatial resolutions, related with differences
between the actual position of positron emission and the location of the detected annihilation. This study presents an approach with the Monte Carlo
method to analyze the influence of this effect on different isotopes of potential implementation in PET.
Keywords: nuclear medicine imaging, PET, Monte Carlo simulation.
Resumo
Desde sua implementação bem sucedida, a tomografia por emissão de pósitrons (PET) representa uma das técnicas de imagem mais promissoras
para diagnóstico clínico. O grande crescimento recente da imagem por PET é principalmente devido à sua capacidade de rastrear o caminho
biológico de diferentes compostos no corpo do paciente, assumindo que o paciente possa ser marcado com algum isótopo PET. Desconsiderando o
tipo de isótopo, o método de imagem por PET é baseado na detecção de dois fótons gama de 511 keV, sendo emitidos em direções opostas, com
quase 180° entre eles, como consequência da aniquilação do par elétron-pósitron. Desta forma, este método de imagem é intrinsicamente limitado
pelas incertezas aleatórias na resolução espacial relacionada às diferenças entre a posição real de emissão do pósitron e a localização da aniquilação
detectada. Este estudo apresenta uma abordagem pelo método Monte Carlo para estudar a influência deste efeito para diferentes isótopos com
potencial implementação em PET.
Palavras-chave: imagem em medicina nuclear, PET, simulação Monte Carlo.
Introduction
Positron emission tomography (PET) is one of the more
important nuclear medicine imaging techniques being currently used. It is actually considered to have the capability
to change the whole impact role of nuclear medicine; not
because it does everything better than conventional single photon emission imaging like SPECT, but because it
has the impact and public relations of the fastest growing
diagnostic specialty1. Nowadays, PET is a powerful imaging technique which utilizes almost exclusively 18F tracer
agents, like fluorodeoxyglucose (FDG) to infuse patient in
order to produce three-dimensional (3D) images of functional processes in the body. The imaging system is based on the detection of the pairs of gamma rays emitted
indirectly by a positron-emitting radionuclide tracer, which
Corresponding author: Mauro Valente – CONICET & FaMAF University of Cordoba – Medina Allende y Haya de la Torre – Ciudad Universitaria – Córdoba –
Argentina – E-mail: [email protected]
7
Pérez P, Malano F, Valente M
is introduced into the body on a biologically active molecule1,2. Tracer concentration images can be acquired in
three-dimensional spaceat different times, therefore constituting a four-dimensional technique. Images are acquired within the body and they are further reconstructed
by computer analysis. Modern scanners accomplish dual
single-photon emission computed tomography/computed
tomography (SPECT-CT) or PET/computed tomography
(PET-CT) acquisition in the same procedure.
The most significant fraction of electron-positron
decays result in two 511-keV gamma photons being
emitted at almost 180o to each other; hence becoming
possible to localize their source along a straight line of
coincidence (LOR). In practice, the LOR has a finite width, as the emitted photons are not exactly 180o apart.
Therefore, employing detectors having high enough time
resolution, it becomes possible to localize the event to
a segment of a chord, whose length is determined by
the detector timing resolution. In this sense, improving
time resolution may obtain better signal-to-noise ratio
(SNR); and therefore requiring fewer events to achieve
the same image quality1.
Different radionuclides may be appropriate for PET
scanning. However, isotopes having short half-life are typically used1, as reported in Table 1.
One of the most relevant features of PET imaging techniques is its capability to trace the biologic pathway of
different compounds within patient, provided it can be radiolabeled with some PET isotope. Therefore allowing to
perform almost any kind of specific processes1,3. Actually,
great efforts are devoted to research and characterization
of radiotracers for new target molecules.
The potentiality of new radiotracers is determined by
many different factors, including costs and complexity for
its production as well as efficiency performance for specific target imaging. Therefore, as a consequence of the
imaging mechanism based on the detection of the pair
of annihilation gamma rays, it results in intrinsic spatial
resolution uncertainties associated with the annihilation
localization, which may differ from the actual positron
emission position. This effect should be added to others,
like detection system, electronic noise and image reconstruction algorithms and eventually patient motion, in order
to quantify all the components contributing to the total
spatial uncertainty.
The impact of the positron flight on spatial resolution
has been recently analyzed by different authors. Studies
have been conducted experimentally4,5, through theoretical calculations6 or by Monte Carlo methods7,8. Actually,
Table 1. PET radionuclides half-life.
Isotope
11
C
13
N
15
O
18
F
8
Approximate half-life [minutes]
20
10
2
110
Sánchez-Crespo et al.7 investigated the influence of
positron distance of flight in various human tissues on
the spatial resolution in PET for positrons from different
radioisotopes.
However, it can be demonstrated that almost all cases can be approximately described by positrons travelling in water.
This work presented investigations about the cloud of
annihilation points around different positron sources in water performed with the aim of studying and characterizing
the intrinsic spatial resolution limitations due to uncertainties arising from differences between positron emission position and actual annihilation localization. Different isotopes
of potential use in PET (Table 1) have been investigated,
disregarding other properties, like production reliability and
practical reasons for utilization convenience.
Materials and methods
A full stochastic Monte Carlo technique has been developed in order to be the start point for the study of the
influence to spatial resolution arising from uncertainties
due to differences between positron emission position
and annihilation localization. Specific subroutine has been
developed, based on the PENELOPE v. 2008 main code
in order to simulate a point source isotropically emitting
positrons with energy distribution, according to the actual emission properties of each radioisotope. The computer code system PENELOPE v. 20089 performs Monte
Carlo simulation of coupled electron, positron and photon
transport in arbitrary materials, with energy ranging within
102 to 109 eV. Charged particles (electrons and positrons)
are simulated by means of a mixed procedure consisting of dividing detailed simulation for “hard” events, while
implementing a condensed approach for “soft” events.
The distinction between soft and hard events is determined by user-defined thresholds regarding angular deflection and energy loss in the interaction. The PENELOPE
code has been largely applied or different applications on
nuclear medicine, including imaging as well as therapy
techniques10,11.
The PENELOPE v. 2008 distribution includes specific packages dedicated to material file creation by means of physical properties included in internal database
along with suitable analytical models. In addition, there
is the PENGEOM package exclusively devoted to handle user-defined simulation geometry in base on quadric
surface approach.
With the aim of performing suitable characterization
of positron transport within aqueous media a specific
and dedicated simulation code has been developed. This
subroutine package allows computing complete full stochastic positron transport, taking into account all radiation interaction mechanisms by means of mixed particle
tracking approach. The considered interaction events are
soft events, hard elastic collisions, hard inelastic collisions,
Intrinsic spatial resolution limitations due to differences between positron emission position and annihilation detection localization
Elast
Inelast
Bremss
Annih.
Total
Ioniz.
1E-15
1E-16
1E-17
1E-18
1E-19
1E-20
1E-21
1E-22
1E-23
1E-24
1E-25
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
In this work, different PET radioisotopes (11C, 13N,
O and 18F) have been considered to investigate the
effect of annihilation localization uncertainties. The considered radioisotopes emission spectra have been extracted from validated database3 and they are reported
in Figures 3 and 4.
The simulation geometry used to perform these investigations considered an isotropic homogeneous medium
of water equivalent material extended within a 100-mm
radius sphere.
In order to assess mean traveled distance before positron annihilation, it is not necessary to consider the whole
imaging system. However if a complete description about
15
Probability
Cross Section [cm 2 ]
Bremsstrahlung emission, inner-shell impact ionization,
annihilations and delta ray interactions. The corresponding
water cross-sections extracted from PENELOPE databases are reported in Figure 1.
Therefore, once positron cross-sections are already
established, it becomes necessary to study the corresponding penetration distances, which are strongly correlated with particle range and, of course, the mean travelled
distance between consecutive collisions, defined as mean
free path (MFP), usually called l.
Figure 2 presents the corresponded ranges and MFP
obtained from PENELOPE cross-sections database as a
function of positron kinetic energy.
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
C
N
11
13
0
2
4
6
8
10
12
x105
Energy [eV]
9
Energy [eV]
100
10
1
0.1
0.01
1E-3
1E-4
1E-5
1E-6
1E-7
1E-8
1E-9
Figure 3. 11C and 13N positron emission spectra used for Monte
Carlo simulations. Emission spectra are reported as normalized
emission intensity probability per energy channel.
MFP
Range
Probability
g cm -2
Figure 1. Water cross-sections for positrons: elastic (green),
Inelastic (red), Bremsstrahlung (blue), annihilation (yellow), inner-shell ionization (magenta) and total (black) extracted from
PENELOPE database, according to the Bethe formalism in the
Born approximation.
10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9
Energy [eV]
Figure 2. In water ranges (red circle) and mean free path
(MFP – black triangle) calculated using PENELOPE crosssection database.
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
15
O
F
18
0
2
4
6
8
10
Energy [eV]
12
14
16
18
x105
Figure 4. 15O and 18F positron emission spectra used for Monte
Carlo simulations. Emission spectra are reported as normalized
emission intensity probability per energy channel.
9
Pérez P, Malano F, Valente M
PET imaging spatial resolution would be the goal of the
study, it would be mandatory to consider the complete
imaging system including specific phantom/patient geometry, mass distribution, isotope activity and distribution
and of course collimation and detection devices.
Results and discussion
It is noticeably that even when positron range increases
continuously with energy, there is a remarkable plateau for
positron MFP at energies greater than 1 MeV (Figure 2),
approximately. This threshold is in correspondence with
the stabilization plateau for the total cross-section, as
expected.
As mentioned, isotropic point source has been placed at the origin of Cartesian coordinates and the developed program allowed to determine the annihilation
A
position for different monoenergetic positron sources or
emission spectra.
Figures 5A and 6A show examples of the 3D representation of annihilation positions for 106 primary showers per
run obtained considering a typical PET radioisotopes (15O
and 18F). Once, annihilation localizations have been already determined, it becomes straightforward to calculate the
travelled path distribution as the distance from origin to
annihilation localization, as shown in Figures 5B and 6B.
This study has been performed for different radioisotopes
and for a wide range of monoenergetic sources - some of
the obtained results are reported in Table 2.
The obtained results show reasonable trends when
comparing with the corresponding emission spectra.
As expected, the behavior of the obtained results as a
function of the energy seems to be in good agreement with
the corresponding mean ranges weighted according to the
emission spectra, which may be calculated from analytical
A
1
0.5
Z [cm]
Z [cm]
0.5
0
0
-0.5
-0.5
0.5
-1
1
0.5
0
-0.5
Y [cm]
-1
-1
-0.5
0.5
0
0
Y [cm]
X [cm]
0
-0.5 -0.5
X [cm]
0.01
0.15
Annihilation distance [cm]
0.2
B
2.5
x 104
x 104
Frequency over 106 showers
Frequency over 106 showers
B
2
1.5
1
0.5
0
0
0.2
0.4
0.6
0.8
Annihilation distance [cm]
1
Figure 5. Three-dimensional representation of in-water annihilation localization for 106 primary 15O positrons isotropically
emitted from a point source at the origin (A) and the histogram
of the corresponding traveled path distribution of annihilation
localization (B).
10
0.5
1
3
2
1
0
0
0.05
0.25
Figure 6. Three-dimensional representation of in-water
annihilation localization for 106 primary 18F positrons isotropically emitted from a point source at the origin (A) and
its corresponding travelled path distribution of annihilation
localization (B).
Intrinsic spatial resolution limitations due to differences between positron emission position and annihilation detection localization
Table 2. Monoenergetic e+ source and PET radionuclides
in-water mean path.
Experimental
Data (cm)4
Isotope
Mean value (cm)
SD (cm)
50 keV
0.0029
0.0008
100 keV
0.0097
0.0024
0.30
0.06
C
0. 097
0.06
0.111
N
0.14
0.09
0.142
O
0.22
0.14
0.149
F
0.52
0.038
1 MeV
11
13
15
18
SD: standard deviation.
methods or obtained from standard databases9,10. Greater
differences between emission and annihilation positions
correspond to higher energies or harder spectra. Along
with practical features, like product costs and reliability, this
intrinsic limitation may be pointed out and eventually taken
into account when evaluating the potentiality and relative
convenience of the different radioisotopes.
As reported in Figures 5 and 6, it is clear that the MFP
distribution of emitted positrons does not exhibit Gaussian
trend. The obtained Poisson distribution may be main reason for contributing to differences between positron emission position and annihilation localization. In this sense it
results convenient to employ stochastic approaches unlike
deterministic analytical models.
Conclusions
A suitable method for investigating the intrinsic limitations to PET spatial resolution due to differences between emission and annihilation positions has been
proposed. A dedicated Monte Carlo subroutine has
been developed for this purpose. As reported in the
presented results for static emission sources, intrinsic
uncertainties due to differences between emission and
annihilation positions may actually arise to non-negligible limitations for the spatial resolution. However, this
effect may be even more significant when considering
dynamic emission sources, as may be the case of organ
motion within patients. Actually, efforts are being dedicated to the development of time-dependent analogue
algorithm, for the simulation of moving sources, in order
to assess the influence of this effect in a more realistic
clinical configuration.
Acknowledgment
This work has been partially supported by grants from research Projects PIP 11420090100398, PICT 2008-243 along
Secretaría de Ciencia y Tecnológia (SeCyT) from Consejo
Nacional de Investigaciones Científicas y Técnica (CONICET),
Agencia Nacional de Promoción Científica y Tecnológica
(ANPCyT) and Universidad Nacional de Córdoba (UNC)
along with a Programa de Formacion de Doctores en areas
Prioritarias de Tecnologia (PFDT) PhD. fellowship of Argentina.
References
1. Bailey D, Townsend W, Valk P, Maisey M. Positron emission tomography.
London: Springer-Verlag; 2005.
2. Dietlein M, Weber K, Gandjour A, Moka D, Theissen P, Lauterbach K, et al.
Cost-effectiveness of FDG-PET for the management of solitary pulmonary
nodules: a decision analysis based on cost reimbursement in Germany. Eur
J Nucl Med. 2000;27(10):1441-56.
3. Cherry SR, Sorenson J, Phelps M. Physics in nuclear medicine. 3rd ed.
Philadelphia: Saunders; 2003.
4. Derenzo SE. Precision measurement of annihilation point spread
distributions for medically important positron emitters. In: Positron
Annihilation. Lake Yamaka, Japan; 1979:1-5.
5. Cho ZH, Chan JK, Ericksson L, Singh M, Graham S, MacDonald MS, et
al. Positron ranges obtained from biomedically important positron-emitting
radionuclides. J Nucl Med. 1975;16(12):1174-16.
6. Palmer MR, Brownell GL. Annihilation density distribution calculations
for medically important positron emitters. IEEE Transactions on Medical
Imaging. 1992;11(3):373-8.
7. Sánchez-Crespo A, Andreo P, Larsson SA. Positron flight in human tissues
and its influence on PET image spatial resolution. Eur J Nucl Med Mol
Imaging. 2004;31(1):44-51.
8. Levin CS, Hoffman EJ. Calculation of positron range and its effect on
the fundamental limit of positron emission tomography system spatial
resolution. Phys Med Biol. 1999;44:781-799.
9. Salvat F, Fernández-Varea JM, Sempau J. PENELOPE-2008: A Code
System for Monte Carlo Simulation of Electron and Photon Transport.
Barcelona: Nuclear Energy Agency; 2008.
10. Botta F, Cremonesi M, Di Dia A, Ferrari M, Valente M, De Cicco C, et al.
90Y, 177Lu, and 131I therapy optimization: Monte Carlo calculation of dose
distribution and radiobiological evaluations. J Nucl Med. 2009; 50(2):1859-60.
11. Uusijarvi H, Chouin N, Bernhardt P. Comparison of electron Dose Point
Kernels in water generated by the Monte Carlo codes, PENELOPE, GEANT4,
MCNPX and ETRAN. Cancer Biother Radiopharm. 2009;24(4):461-7.
11
Artigo Original
Comparison between subjective and
quantitative methods for assessing the
resolution limit of radiographic systems
Comparação entre métodos subjetivos e quantitativos na
medida da resolução limite de sistemas radiográficos
Matheus Alvarez1, Marcela de Oliveira1, Diana R. Pina2 and José R. A. Miranda1
Instituto de Biociências de Botucatu, Universidade Estadual Paulista “Júlio de Mesquita Filho” (UNESP) – Botucatu
(SP), Brazil.
2
Departamento de Doenças Tropicais e Diagnóstico por Imagem, Hospital das Clínicas da Faculdade de Medicina de
Botucatu da UNESP – Botucatu (SP), Brazil.
1
Abstract
The aim of this study was to compare two ways of measuring the resolution limit of radiographic systems, one subjective and one quantitative.
To this end, nine images were acquired with different radiographic techniques using a pattern of bars and aluminum plates. With these images
were acquired modulation transfer function (MTF) through the edge image obtained by the aluminum plate — the MTF 10% was measured on
all images — and the variation of these points, which was faced with the evaluation obtained by the resolution limit of the standard bar. Although
we have observed a greater variation between measurements obtained using the bar-pattern, the simplicity of this measuring technique favors the
common use of the same. We concluded that, to optimize the quality control of radiographic equipment, it is suggested to measure the MTF at least
in periods of time while the annual pattern of bars to be used in shorter time periods to measure changes in resolution of the system.
Keywords: optimization, quality control, radiography.
Resumo
O objetivo deste estudo foi comparar duas formas de aferição da resolução limite de sistemas radiográficos, uma subjetiva e outra quantitativa. Para
tal, foram adquiridas nove imagens com diferentes técnicas radiográficas utilizando um padrão de barras e placas de alumínio. Com estas imagens,
foram adquiridas a função de transferência modulada (FTM) através da imagem da borda obtida pela placa de alumínio — a FTM foi aferida 10%
em todas as imagens — e a variação destes pontos — que foi confrontada com a avaliação da resolução limite obtida através do padrão de
barras. Apesar de termos observado uma maior variação entre as medidas obtidas com a utilização do padrão de barras, a simplicidade de medição
desta técnica favorece o uso corriqueiro da mesma. Concluí-se que, visando a otimização do controle de qualidade de equipamentos radiográficos,
sugere-se fazer a medição da FTM pelo menos em períodos de tempo anuais, enquanto que o padrão de barras seja utilizado em períodos de tempo
menores para a aferição de mudanças na resolução do sistema.
Palavras-chave: otimização, controle de qualidade, radiografia.
Introduction
In an x-ray imaging system, the detector properties are
determinant for the apparent resolution in the radiological
images1. Spatial resolution is one of the parameters that are
routinely checked during acceptance procedures and regular quality control measurements methods1. The spatial resolution of a radiographic imaging device is most appropriately expressed in terms of its modulation transfer function
(MTF), which indicates the decline of detector spatial resolution with spatial frequency2,3. Traditionally used methods
of MTF measurement involve imaging either a narrow slit
or a sharp edge to obtain the detector line spread function
(LSF), whose frequency transform leads to the MTF3-11. Over
the last few decades, robust techniques for slit4,5,10,11 and
edge6-9 measurements have been developed and used in
imaging research. These methods provide the advantage of
good accuracy over a near-continuous frequency domain.
However, this accuracy is dependent on the alignment of
the slit or edge targets with the radiation beam that typically requires a complex and time-consuming experimental
setup. As a result, slit and edge measurements are difficult
Corresponding author: Matheus Alvarez – Departamento de Física e Biofísica, Instituto de Biociências de Botucatu, Universidade Estadual Paulista “Júlio de
Mesquita Filho” (UNESP) – Distrito de Rubião Júnior, s/n – CEP: 18608-970 – Botucatu (SP), Brasil – E-mail: [email protected]
13
Alvarez M, Oliveira M, Pina DR, Miranda JRA
to perform and not suitable where spatial resolution has to
be monitored routinely and quickly, as is typically the case
in quality assurance (QA) measurements. To estimate the
limiting spatial resolution of the system, the frequencies at
which the MTF has fallen to 10% is commonly measured12.
An alternative procedure to estimate the limiting spatial
resolution of a radiographic device is to perform an exposition of a line-pair bar-pattern covering at least the range
1-5 line pairs (lp)/mm. The acquired image is examined according to the number of line pair that can be observed clearly, starting with the most easily resolved. The acceptable
tolerance value of this test is the same used for the MTF2-12.
In this work is presented a simulation study of the parameters involved in the MTF measurement followed by
a study of the relationship presented between the measurement of the limiting spatial resolution using the MTF
method and the line-pair bar-pattern method. Our aim was
to compare the bar-pattern method with the MTF method
and then to evaluate which method is better for the dairy
quality control tests and when is appropriate to perform
one test or other.
developed by Samei, Flynn and Reimann9 and Carton
et al.1. Basically, this algorithm requires an image of an
edge and the signal images must be linear with detector
dose. As illustrated in Figure 2, the process to calculate the
MTF includes six steps, following.
Step 1: A region of interest (ROI) centered on the edge
is selected. This ROI is defined by a width W and a length
A
B
Figure 1. Edge images. (A) Real image obtained from the aluminum sheet. (B) Simulated edge image.
Digital edge image
Material and methods
Data acquisition
Radiographies of a line-pair bar-pattern and an aluminum
target were obtained with entrance surface expositions in
the range of 0.9-200.9 uGy. An x-ray equipment Siemens
844002 and an AGFA CR-85X were used to obtain the
images. The line-pair bar-pattern images were evaluated
by three experienced medical physicists and the aluminum
radiographies were used to obtain the MTF of the system
and to measure data to simulate images with the same
pattern. The aluminum images were obtained using a
4.5 cm sheet of polimetilmetacrilate (PMMA) with a 2.0 mm
Aluminum foil placed above it.
Simulated images
The simulated images were within 512 x 512 pixel array,
the edge transition was defined by a 0º straight line passing through the center of the image dividing it into two regions with different average pixel values. The values of these two regions were generated by a Gaussian distribution
with mean and standard deviations obtained experimentally with values of 2,200+100 for the aluminum + PMMA
region and 3,000+100 for the PMMA region. Finally, a
low-pass median filter with dimensions of 2 x 2 was used
to better simulate the visual aspect of the simulated edge.
In Figure 1A is depicted the real edge image in comparison with a simulated edge image, which is depicted in
Figure 1B.
Modulation transfer function measumerents
Described in the following is the algorithm used to compute the MTF. This algorithm is based on the algorithms
14
Step 1
Linearization of
the image
Place the ROI in
the edge image
Apply Sobel operator
to detect the edge
Double Hough trasformation.
Finding the angle with 0.1
degree precision
Step 2
Correction of the
edge angle
Step 3
Step 4
Generation the Supersampled Edge
Spread Function (SESF)
Differentiation
Step 5
Fast Fourier transformation
Step 6
Third-order low-pass filtering
Presampled MTF
Figure 2. The processing steps applied in the digital edge image
to calculate the modulation transfer function of the radiologic
system.
Comparison between subjective and quantitative methods for assessing the resolution limit of radiographic systems
Measurement using line-pair bar-pattern
In Figure 4 is shown a radiograph of the line-pair bar
pattern used in this paper to measure the limiting resolution of the system by the medical physicists. The line-pair
bar-pattern used has line pairs/milimeter (lp/mm) in the range
of 0.6–5.0. The test is performed in the following way: the radiograph of the line-pair bar-pattern is viewed on the monitor
of the available workstation with at least a 1:1 zoom factor
and the number of line pairs that can be observed clearly is
taken as the limiting spatial resolution of the system. This test
was performed by three medical physicists to evaluate the
differences encountered in the visualization of them.
0.04
2
0.035
0
-2
0.03
0
5
10
15
20
25
30
Distance (mm)
Figure 3. Real supersampled Edge Spread Function (ESF) and
line spread function (LSF) obtained from one of the radiographs
used in this work.
Figure 4. Radiography of the line-pair bar-pattern tool used in
this study.
120
200sd
50sd
5sd
100
Results
80
MTF (%)
Simulated images
Noise and angulation were added in the simulated images
in order to test the algorithm performance and to better
understand some errors given in the development of the
program. The results are shown below.
Line Spread Function (LSF)
x 10-6
4
ESF
LSF
0.045
Edge Spread Function (ESP)
L. W is the total number of rows used for the determination
of the MTF. L is the length of the edge profiles.
Step 2: Sobel operator is applied to the image to detect
the position of the edge and a double Hough transform is applied to the resulting matrix to estimate the angle of the edge.
Then, the image is rotated to obtain and edge angle of 0°.
Step 3: A supersampled Edge Spread Function (ESF) is
generated by using the pixel values of N consecutive rows
across the edge: the value of the first pixel in the first row
gives the first data point in the supersampled ESF; the first
pixel in the second row gives the second data point, etc.;
and the first pixel in the Nth row gives the Nth data point.
Step 4: The line spread function (LSF) is calculated by
finite-element differentiation of the SESF using a convolution filter with a [-1 1] kernel.
Step 5: The modulus of the Fourier transform of the
LSF is calculated, the result is normalized to its zero-frequency value [MTF(0)=1].
Step 6: A third-order low-pass filter is applied to the
MTF. To avoid distortion of the MTF, the filter is applied
twice. A copy of the raw MTF data is made. On one array
the filter is applied from the first point to the end. On the
second array, the filter is applied in the reverse from the last
point to the first point of the MTF.
In Figure 3 are plotted a super sampled ESF and a LSF
obtained from real images using the algorithm above. The
limiting resolution of the system was measured at 10% of
the MTF in the images obtained.
60
40
20
Noise
Noise was added to the edge image by improving the
standard deviation of the Gaussian distribution that was
used to fill the areas of the simulated radiographs. In the
Figure 5 is depicted the MTF obtained for a standard deviation (in pixel values) of 5, 50 and 200.
0
0
0.5
1
1.5 2
2.5 3
3.5
Spatial Frequency (mm-1)
4
4.5
5
Figure 5. Three modulation transfer functions obtained by addition of the noise to the input image.
15
MTF (%)
Alvarez M, Oliveira M, Pina DR, Miranda JRA
100
90
80
70
60
50
40
30
20
10
Angulation
The angulation in the input image was proven to be one
of the most important factors in the MTF acquisition.
In Figure 6 is shown three MTF obtained with the angulation of the input image in 0°, 0.5° and 1°.
0 degree
1 degree
0.5 degree
0
0.5
1
1.5 2 2.5 3 3.5
Spatial Frequencyl (mm-1)
4
4.5
5
Figure 6. Three modulation transfer functions obtained by rotation of the input image by 0°,0.5° and 1°.
100
MTF (%)
80
Comparison between the resolution limit measured by
the modulation transfer function and the bar-pattern
In Figure 8 is plotted the resolution limit evaluated by three
medical physicists and the resolution limit obtained by
10% of the MTF.
Discussion and conclusions
60
40
20
0
Real images
MTF obtained from the real images were measured in the
points of 50, 20 and 10%. The points measured in 10%
were used to compare the limiting resolution of the system
while the others measured points were used to evaluate
the performance of our algorithm/x-ray system. In Figure 7
is shown an example of a MTF obtained using our algorithm while in the Table 1 is depicted the measured points
and the medical physicist readers’ maximum resolution.
0
1
2
3
Spatial Frequencyl (mm-1)
4
5
Figure 7. Modulation transfer function calculated from a
real image.
This paper evaluated the performance of the resolution limit obtained by a quantitative and a subjective way. The
first was performed calculating the MTF of the system and
demonstrating that it can give a better understanding of the
system spatial resolution than the subjective test. The subjective test was performed by the evaluation of the visibility
of a radiography of a line-pairs bar-pattern. It has been shown that the quantitative way, although it presents a contrast
response curve all over the frequency range, can be replaced by the subjective test in order to assess the maximum
resolution of the radiologic system. Figures 5 and 6 present
the effect of the noise and the angulation when assessing
Table 1. Reference points measured to each modulation transfer function calculated and the physicist readers’ evaluation of
the resolution limit.
16
50%
20%
10%
200.9
2.2±0.2
1.22
1.96
2.30
191.2
2.1±0.4
1.32
1.95
2.50
145.8
2.2±0.2
1.43
1.92
2.10
113.4
2.2±0.2
1.25
1.80
2.25
81.0
2.2±0.2
1.25
1.92
2.30
48.6
2.1±0.4
1.30
1.82
2.35
19.8
2.1±0.4
1.28
1.99
2.20
1.9
2.2±0.6
1.30
1.95
2.20
0.9
2.1±0.4
1.32
1.86
2.55
Mean±2SD
2.2±0.4
1.30±0.12
1.91±0.13
2.31±0.29
Spatial Frequency
(lp/mm)
Reader
(lp/mm)
10% MTF
Medical Physicists
2.6
MTF
Dose
(uGy)
MTF: modulation transfer function; SD: standard deviation
2.8
2.4
2.2
2
1.8
1.6
0
50
100
Dose (uGy)
150
200
Figure 8. Comparison between the resolution limit measured by
three medical physicists’ evaluation and 10% of the modulation
transfer function. The triangle indicates the measure of 10% of
the modulation transfer function while the squares represented
the medical physicists’ opinion.
Comparison between subjective and quantitative methods for assessing the resolution limit of radiographic systems
the MTF of the system. In agreement with Samei, Flynn and
Reimann9, extra caution with the dose and the angle of the
edge is needed when assessing the ESF in order to obtain
the maximum MTF with less noise as possible.
Although the results obtained by the quantitative method showed fewer variations than the obtained by the
subjective way, the caution need when placing the edge,
the need of the linearization of the image and the need of
digital image processing knowledge contributes to the difficulty of the calculation of the MTF. These factors favored
the realization of the subjective test.
In this way, we conclude that it is advisable to perform
the MTF test for an in-depth study of the contrast response
of the system all over the frequency range. To check the
resolution limit of the system, the bar-pattern imaging test
should be sufficient.
References
1. Carton AK, Vandenbroucke D, Struye L, Maidment AD, Kao YH, Albert M,
et al. Validation of MTF measurement for digital mammography quality
control. Med Phys. 2005;32(6):1684-95.
2. Gopal A, Samant SS. Validity of the line-pair bar-pattern method in the
measurement of the modulation transfer function (MTF) in megavoltage
imaging. Med Phys. 2008;35(1):270-9.
3. Metz CE, Doi K. Transfer function analysis of radiographic imaging systems.
Phys Med Biol. 1979;24(6):1079-106.
4. Rossman K. Measurement of the line spread function of radiographic
systems containing fluorescent screens. Phys Med Biol. 1964;
18:551-7.
5. Dobbins 3rd JT, Ergun DL, Rutz L, Hinshaw DA, Blume H, Clark DC. DQE(f)
of four generations of computed radiography acquisiton devices. Med
Phys.1995;22(10):1581-93.
6. Judy PF. The line spread function and modulation transfer function of a
computed tomographic scanner. Med Phys. 1976;3(4):, 233-236
7. Cunningham IA, Fenster A. A method for modulation transfer function
determination from edge profiles with correction for finite element
differentiation. Med Phys; 1987; 14; 533-537.
8. Moy JP, Signal-to-noise ratio and spatial resolution in x-ray e;ectronic
imagers: Is the MTF a revelant parameter?. Med Phys, 2000;27(1),
86-93.
9. Samei E, Flynn MJ, Reimann DA, A method for measuring the presampled
MTF of digital radiographic systems using an edge test device. Med Phys,
1998;25(1), 102-113.
10. Fujita H, Morishita J, Ueda K, Tsai D Y, Ohtsuka A and Fujikawa T. Resolution
Properties of a computed radiographic systems. SPIE Med Imaging, 1989;
1090;263-275
11. Fujita H, Tsay DY, Itoh T, Doi K, Morishita J, Ueda K and Ohtsuka A, A
simple method for determining the modulation transfer function in digital
radiography IEEE Trans Med Imaging. 1992;11(1):34-9.
12. International Atomic Energy Agency (IAEA). Human health series nº 17:
Quality Assurance Programme for Digital Mammography. Vienna: IAEA
Press; 2011. 177 p.
17
Instruções aos autores
Informações gerais
A Revista Brasileira de Física Médica (Rev Bras Fis Med. ISSN
1984 9001 - versão eletrônica; ISSN 2176-8978 - versão impressa) é uma publicação da Associação Brasileira de Física
Médica (ABFM). Criada em 2005, tem como objetivo publicar trabalhos originais nas áreas de Radioterapia, Medicina
Nuclear, Radiologia Diagnóstica, Proteção Radiológica e
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O Conselho Editorial da RBFM é composto por especialistas reconhecidos de origem nacional e internacional, atuantes em instituições de ensino e pesquisa, bem como em
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Manuscritos contendo resultados de pesquisa básica
II
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nih.gov); Abstract e keywords correspondentes ao Resumo
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A(t) = A0e-lt(1)
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Referências
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listadas nesta mesma ordem na última seção do artigo.
As abreviaturas utilizadas para os periódicos citados nas
referências devem seguir o padrão da base de dados
PubMed. Para referências com dois ou mais autores, citar
até seis nomes (seguidos da expressão et al. se o trabalho
possuir mais de 6 autores)2. Para citar artigos de periódicos1,2, livros3, eventos4, relatórios técnicos5, dissertações e
teses6, página na internet7, consulte o artigo8.
1. Heshmati HM, Hofbauer LC. Multiple endocrine neoplasia type 2. Eur J Endocrinol. 1997;137(6):572-8.
2. Krummer SC, Giulkiani ER, Susin LO, Folleto JL, Lermen
NR, Wu VY, et al. Evolução do padrão de aleitamento
materno. Rev Saúde Pública. 2000;34(2):143-8.
3. Naisman HA, Kerr GR. Fetal growth and development.
New York: Mc Graw-Hill; 1970.
4.Kimura J, Shibasaki H, editors. Recent advances in clinical neurophysiology. Proceedings of the
10th International Congress of EMG and Clinical
Neurophysiology; 1995; Kyoto; Japan. Amsterdam:
Elsevier; 1996.
5. Instituto da Criança. Hospital das Clínicas. Faculdade
de Medicina da Universidade de São Paulo. Relatório
Anual de atividades, 1993. São Paulo; 1994.
6. Carneiro MS. A imunidade mediada pelo linfócito T
na asma brônquica. [Tese de Doutorado]. São Paulo:
Faculdade de Medicina da Universidade de São Paulo;
1978.
7.Cancer-Pain.org [homepage on the Internet]. New
York: Association of Cancer Online Resources, Inc.;
c2000-01 [cited 2002 Jul 9]. Available from: http://
www.cancer-pain.org/
8. International Committee of Medical Journal Editors.
Uniform requirements for manuscripts submitted to
biomedical journals. N Engl J Med. 1997;336:309-16.
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a seguir:
• Artigos de Revisão e Tutoriais;
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O recebimento do trabalho será prontamente confirmado por comunicação eletrônica. A partir daí, todas as
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devolvidos aos autores.
III

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