CIENCIAS NUCLEARES
Pet-Compton system. Comparative evaluation with PET system using Monte Carlo simulation
Sistema Pet-compton. Evaluación comparativa con el sistema PET usando la simulación por Monte Carlo
Angelina Díaz García1*, Juan A. Rubio Rodríguez2, José M. Pérez Morales2, Pedro Arce Dubois2, Oscar Vela Morales2, Eduardo Arista Romeu1, Carlos Willmott Zappacosta2, Yamiel Abreu Alfonso1, Antonio Leyva Fabelo1, Ibrahin Piñera Hernández1, Lourdes Bolaños Pérez1
1Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cuba
2Centro de Investigaciones Energéticas, Mediombientales y Tecnológicas
(CIEMAT), España
ABSTRACT
Positron Emission Tomography (PET) in small animals has actually achieved spatial resolution round about 1 mm and currently there are under study different approaches to improve this spatial resolution. One of them combines PET technology with Compton Cameras. This paper presents the idea of the so called "PET-Compton" systems and has included comparative evaluation of spatial resolution and global efficiency in both PET and PET-Compton system by means of Monte Carlo simulations using Geant4 code. Simulation was done on a PET-Compton system made-up of LYSO-LuYAP scintillating detectors of particular small animal PET scanner named "Clear-PET"
and for Compton
detectors based on CdZnTe semiconductor. A group of radionuclides that emits
a positron ()
and
quantum almost simultaneously
and fulfills some selection criteria for their possible use in PET-Compton systems
for medical and biological applications were studied under simulation conditions.
By means of analytical reconstruction using SSRB (Single Slide Rebinning)
method were obtained superior spatial resolution in PET-Compton system for all
tested radionuclides (reaching sub-millimeter values of for
source). However this analysis done by simulation have shown limited global
efficiency values in "PET-Compton" system (in the order of
%)
instead of values around
% that have been achieved in PET system.
Palabras claves: compton effect, computerized simulation, Monte Carlo method, positron computed tomography, spatial resolution, G codes
RESUMEN
En la actualidad
la tomografía por emisión de positrones (PET en pequeños
animales ha alcanzado valores de resolución espacial cercanos a mm y
en estos momentos se encuentran bajo estudio diferentes aproximaciones para
mejorar dicha resolución espacial. Una de ellas combina la tecnología
PET con las cámaras Compton. Este trabajo presenta la idea del denominado
Sistema "PET-Compton" e incluye una evaluación comparativa
de la resolución espacial y la eficiencia global de los sistemas PET
y PET-Compton por medio de la simulación por Monte Carlo, utilizando
el código Geant4. La simulación fue realizada en un sistema PET-Compton
compuesto por detectores centellantes de LYSO-LUYAP de un específico
y pequeño escáner PET denominado "Clear-PET" y para
detectores Compton en base al semiconductor CdZnTe. Se estudiaron bajo las condiciones
de simulación un grupo de radionúclidos que emiten un positrón
() y un cuanto
gamma casi simultáneamente y cumplen ciertos criterios de selección
para su posible utilización en aplicaciones médicas y biomédicas
de los sistemas PET-Compton. Por medio de la reconstrucción analítica,
empleando el método de reordenamiento de cortes simples (SSRB)
se obtuvo una resolución espacial superior para el sistema PET-Compton
en todos los radionúclidos de prueba, que alcanzó valores por
debajo del milímetro para la fuente de
.
Sin embargo, el análisis realizado por medio de la simulación
demostró valores limitados de eficiencia global para el sistema PET-Compton
(del orden de
) en contraposición
a los valores cercanos a
que se alcanzaron para el sistema PET.
Key words: efecto compton, simulación computarizada, método de Monte Carlo, tomografía computarizada con positrón, resolución espacial, código G
INTRODUCTION
In order to improve
spatial resolution in medical imaging systems preserving its sensitivity, it
was consider the possibility of modifying PET scanner in a way that it
will be capable not only to detect two quanta from the annihilation
of a
in coincidence,
but also at least one additional
quantum [1]. If it is possibly to determine the direction of
quantum that has not come from positron annihilation just one point in the space
could be obtained. Moreover, knowledge of the direction of non-positron annihilation
generated
quantum may
be relevant for the reconstruction process presumably improving PET's spatial
resolution. The aim of this work is to assess, via Monte Carlo simulation, the
possibility of obtaining better spatial resolution than that which actually
characterizes small animals PET scanners (close to 1 mm) by means of more precise
location of the radionuclide emission point and at the same time simplifying
reconstruction process. Technology setup that supports this idea is a
combination of two imaging techniques that benefit from the superiority of electronic
collimation in terms of better sensitivity: Positron Emission Tomography [2]
and detection system that use Compton scattering (Compton cameras) [3]. Both
systems will be used as a single imaging system, hereinafter "PET-Compton".
PET operation principle
is based on the detection in coincidence of two quanta of 511 keV emitted simultaneously in the opposite directions (at angle
180°); because of the annihilation of
when it interact
with the electrons of the medium. You can then locate the positron-emitting
tracer at some point on the line joining the detectors that record these simultaneous
events. The line is called line of response (LoR). It is important to emphasize
the necessity for accumulating a large number of LoRs to know more accurately
the emitting source position using image reconstruction algorithms.
Imaging systems using the Compton scattering can also determine the position
and the source activity. Events can be selected by energy through the sum of
the energies deposited in two detectors placed at some distance in the -emitting
radionuclide field of view. First detector can measure the kinetic energy deposited
by the incident
quantum
, its position and interaction time. A resulted
quantum suffers Compton scattering and hits second detector where its energy
is absorbed and recorded time of interaction and position of incidence. Having
time information from both detectors coincidence is registered. Measurements
of the position of interaction in each detector determine the direction of scattered
quantum and having the
magnitude of the energy deposited in the first detector the scattering angle
is calculated using formula from Compton kinematics.
For each event
the emission is confined to the surface of a known cone angle (), whose
apex is determined by the interaction point in the first detector and its axis
is defined by the line joining points of interaction in both detectors. The
sum of the kinetic energy of the electron and the scattered
quantum is equal to the incident
quantum energy. The surface of each cone is a measure of the location of the
activity and is obtained through online registration. Three-dimensional distribution
of activity is obtained by reconstruction from a large number of cones using
appropriate algorithms.
Both PET and Compton systems allow reaching more sensitivity than mechanically collimated Single Photon Emission Tomography systems, but still have limitations to achieve sub millimeter spatial resolution. Also, the complex process of image reconstruction requires a large number of lines of response (LoRs) in the case of PET and cone of response (CoRs) in Compton scattering.
As explained above
the idea is to add a Compton imaging detector to a PET system with the
intention that not only have to be detected two 511 keV
quanta in coincidence from the annihilation of positron but at least as well
another additional
quantum
with energy close to 1 MeV. The principle of calculating the emission
area is based on the estimation of the intersection of the LoR-PET with CoR-Compton
as shown in figure 1.
The proposal is that using the coincidences
obtained with specific radionuclides that emit a positron and a
quantum practically at the same time the location of the emitter source could
be measured “in three dimensions”.
Simulated "PET-Compton" system consists of two detector rings: smaller inner diameter ring as first (front) Compton scattering detector and an external ring with dual function, second (rear) Compton detector and PET detector. To achieve optimum performance of this system detectors placed in both rings must have the best possible parameters in terms of spatial, temporal and energy resolution. In theory each ring can separately form LoR-PET but here just the LoRs formed in the outer ring will be considered.
In the absence of errors is analytically possible to reconstruct the emission point P (figure 2) using the points of interaction in PET , the interaction points of the Compton events
and the Compton angle
.
The searched point P is located in a straight line connecting ,
and is defined by the parameter
,
Based on geometrical considerations the following expression is obtained:
And substituing (2) in (3):
Introducing the following definitions:
Making and rising to square both expressions:
Thus developing the square binomial:
The above expression is a quadratic equation in :
The solutions to this equation can be:
Described algorithm has been incorporated into the simulation program. Thus the position of the emitting source is directly reconstructed in three dimensions, event by event, allowing further examinations at low count rate and to monitor kinetics of the injected radiopharmaceutical.
The suggested PET-Compton system assumes the finding of a positron-emitting radionuclide with additional gamma radiation . Besides, herein selection was based on two more criteria:
Taking into account
also detection properties of the current systems selection has been finally
limited to those radionuclides with the following properties: 1) Energy of
decay as low as possible, to avoid uncertainty product of the distance traveled
by the
before
annihilation 2) non-positron
quantum have to be issued with high emission rate almost simultaneously with
the
so that
the coincidence time is within the typical detector time resolution which is
in the order of 500 psec, 2)
quantum should preferably be emitted alone to avoid background noise due to
spurious signals in the detector and 3) its energy should be greater than energy
of
quanta from the positron
annihilation and around 1 MeV, this fact will allow better Compton scattering
angular resolution and consequently superior "PET-Compton" spatial
resolution at the emission point 4) Radionuclide half-life have to be short
to avoid excessive exposure to radiation but long enough to ensure the quality
of the image. 5) Daughter radionuclide must be stable, to prevent further emissions.
From a detailed
analysis of the radionuclides that meet these parameters and including also
the interest on their current or previous use in biomedical research or medical
applications for present simulation of "PET-Compton" system were selected
[4] ,
[5] and
[6] radionuclide.
has been included despite
its long half-life (2.6 years), which not allow it use in diagnostic imaging,
because it has similar
and
quantum energy emission range to other two selected radionuclides and also
patterns available sources can be used in further experimental studies. Main
characteristics of these radioactive sources are shown in table 1 and 2.
MATERIALS AND METHODS
For assessing “PET-Compton” possibility of obtaining better spatial resolution than PET there were simulated both systems Geant4 code by means of GAMOS framework [7].
For physical processes GAMOS uses the extension to low energies (up to 250 eV)
of electromagnetic interactions. In the case of includes the process
of annihilation with the electrons of the medium, according to their energy.
For electrons and
quanta
takes into account the relevant electromagnetic processes in the energy interval
of interest, in this case, Photoelectric, Compton scattering and Raleigh effects
for
quanta
and bremsstrahlung and ionization for electrons [8].
Detailed analysis of data was made incorporating to GAMOS the mathematical algorithm of LoR-PET CoR-Compton intersection described in section 2.1. "PET-Compton" results were compared with the results obtained in PET system for the same activity and volume of radiation sources. For reconstruction in PET Single Slice ReBinning (SSRB) analytical method was used.
Simulated "PET-Compton"
system consists in two concentric detector rings. The outer ring is a PET for
small animals named "ClearPET" with high spatial resolution (1.25
mm nominal) that uses scintillators detectors of LYSO-LuYAP [9]. This detector
ring operates as positron annihilation detector and also as a second Compton
scattering detector. The inner ring covers the entire "ClearPET" field
of view and it is formed from an array of CdZnTe (CZT) pixelated semiconductor
detectors as a front Compton scattering detector. Because it is very important
to know as accurate as possible the position of incidence and energy deposited
by quantum in Compton
scattering it has pixels size 300 X 300 µm and high energy resolution
(~1,5%). Two implemented in practice "Clear-PET" detector
ring diameters (295 and 135 mm) were evaluated. Perspective
view of the simulated geometries is shown in figure 3.
Real "ClearPET" parameters obtained from the producer engineering drawings were introduced in the simulation. They are the following:
Also the axial
modules displacement of 7 mm has been introduced in the simulation and only
active radiation detectors and
reflectors were considered.
CZT detectors parameters used for simulations were the following:
Details of CZT geometry is shown in figure 4. and detection system characteristics introduced in the simulation are shown in table 3.
For the simulation
there were used points and spherical (1 mm) ,
and
sources placed in a 4 cm diameter water phantom. In order to visualize the spatial
resolution limit simulation was done also for the case of two radioactive sources
located at a distance between them slightly larger than positron average range
(
-2,5 mm,
-1,7
mm,
-0,7 mm). We selected
a value of source activity of 10 mCi (370 MBq) and the total number of decays
analyzed is 370x
, i.e.
the output values correspond to 1 second measurement. The selection of the number
of decays analyzed was determined by high consumption of time and computing
resources.
RESULTS
Comparison was made for two of the basic parameters that characterize medical imaging systems: spatial resolution (FWHM) and global efficiency. Spatial resolution was determined as the full width half maximum of the Point Spread Function (PSF) peak of radionuclide emission. For "PET-Compton" was obtained by the statistical accumulation of points from LoR-PET CoR-Compton intersection and from the reconstructed events in PET. Global efficiency was determined as the ratio between the number of "PET-Compton" or PET events produced by simulation and the number of total events launched. Figure 5 shows one and two spherical sources placed in water phantom inside the CZT detector ring.
Figure 6 shows the magnified view of positron tracking (dashed blue), PET positron annihilation lines (green) and electron scattering (red lines) in water phantom for two point sources of a) , b)
and c)
. The difference of the positron range for each radionuclide is simply recognized.
Spatial resolution (FWHM)
Spatial resolution values were calculated using AMIDE (Medical Image Data Examiner) [10] software, a tool for the analysis of multidimensional medical data. PET and PET-Compton FWHM values for both ClearPET diameters are plotted in figure 7.
For better interpretation the obtained results are shown in table 4 where we can corroborate that in all cases PET-Compton spatial resolution is improved in comparison with spatial resolution obtained for PET only systems using the same radionuclides and simulations parameters.
Best values of
spatial resolution are obtained in PET-Compton settings with greater distance
between the ClearPET and CZT rings (maximum "ClearPET" diameter) and
it went below 1 mm for
due to its lower
range.
In order to see
the difference, figure 8 shows the obtained results
in AMIDE's visualization screens for PET-Compton (top) and PET (bottom), under
the same conditions for simulated and
radionuclides.
In fact for PET-Compton system there is a background of less intense spots corresponding to the second point of intersection LoR-PET CoR-Compton (see equation 8). However, because its position is random while the accumulation in the real point of emission is high the effect on the screen has been removed rising the lower visualization threshold.
Rendering view
of two point sources
in PET-Compton system with better performance (maximum "PET" diameter)
placed at 0,7 mm is shown in Figure 9a). For comparison,
in Figure 9b) is shown the same view of these two sources
in PET system with better resolution (minimum "ClearPET" diameter).
Just in the first case two point sources separation can be insinuated.
FWHM simulation analysis indicates that this "PET-Compton" configuration evidences a possible area of radionuclide emissions much narrower and thus, improved spatial resolution than PET.
Efficiency analysis
In order to estimate global efficiency in "PET-Compton" system and compare it with the efficiency obtained in PET the ratio among simulated events (PET, "PET-Compton") and total launched events under the same simulation conditions was calculated.
Graphics of global system efficiency for the events of each type are shown in Figure 10. For better identification of the results in graphics b) and c) global efficiency values in % of the three radionuclides have been joined in dotted lines (maximum "ClearPET" diameter) and solid lines (minimum "ClearPET" diameter).
The events called
are those in which
all
quanta
(2
-PET and 1
-Compton)
had come up from the same radioactive decay and in PET-Comptonvalid is added
the fact that LoR-PET CoR-Compton intersection point is close to the radionuclide
point of emission (
1
mm).
As can be seen
efficiency varies over a wide range depending on the type of interaction that
occurs within the field of view. Figure 10a) shows PET global efficiency
which is about 0.5% (4000-5000 coincidences in 1 million events). Figure 10b) shows total PET-Compton global efficiency that is of the order of for the minimum "ClearPET" diameter and
for the maximum "ClearPET" diameter. Figure 10c) shows
the global efficiency of "valid" PET-Compton events where all
quanta are from the same decay event and obtained by simulation intersection
point are close to the radionuclide emission point. PET-Compton "valid"
global efficiency is in the order of
for the "ClearPET" minimum diameter and
for the maximum diameter. Besides, it can be observed that in all analyzed cases
there is an increased efficiency for
radionuclide, because it has two non-positron
quanta in cascade that have been analyzed as one event. This is acceptable taking
into consideration that in current detector systems it is not possible practically
to separate this type of events occurring so close in time.
This "PET-Compton" system analysis done by simulation shows limited global efficiency values, particularly when the results are restricted to "valid".
However it is
necessary to consider also the fact that due to the large amount of computing
resources and time required by the simulation program total number of decays
analyzed for each configuration is just 370 x ,
hence the output values correspond to 1 second measurement while reasonable
measurement time in these techniques are from 15 minutes to 1 hour approximately.
The increase in the number of events detected in "valid" PET-Compton,
that is possible to achieve increasing simulation time should improve signal
to noise ratio and consequently spatial resolution of the system.
CONCLUSIONS
Mathematical modeling
has demonstrated that the image using "three
quanta" is expected sharper and could permit more accurate diagnosis.
However, the fact that it is necessary to register 4 coincidence events (two
corresponding to positron annihilation and two from Compton scattering) significantly
limits the global detection efficiency and can affect the spatial resolution
for the same statistical data. Thus further development of this method should
include the optimization of the factors that could increase global "PET-Compton"
efficiency, more specifically, geometric efficiency of the designed system (larger
distance between detectors rings and other detection configurations with more
efficiency for Compton scattering) is suggested.
Finally would
be interesting to note that the simulated system design also allows it use in
both, PET and "three
quanta" mode. They are complementary and the second mode could be used
as a higher resolution "lens" when it is required in PET image providing
an additional option, certainly for molecular imaging and quite possibly for
clinical diagnosis.
ACKNOWLEDGEMENTS
This work was done under the ITACA* project and we would like to thanks CIEMAT for the financial and technological support.
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Recibido: 18 de octubre de 2012-07
Aceptado: 10 de mayo de 2012