A new computer automated radioactive particle tracking method has been developed by the Nuclear Engineering Institute. The method has adopted a physical model consisting of a punctual particle inside a cylindrical unit so that the space is formed by small cubic cells. Each cell is assigned a probability factor identifying a reconstruction matrix element as it has been made in image reconstruction applications. Particle’s instantaneous coordinates are estimated using a dedicated software to reconstruct the cell’s activity images so as to identify the unique cell with the greatest probability to contain the particle and, consequently, the fluctuating velocity fields of the phase under investigation. In order to quantify the precision of this method, a test was carried out to evaluate detection system’s performance indicators, resolution and sensitivity, from the experimental data collected during the circular movement of a 198Au particle. According to the results, the CARPT method already has a liable performance: a mean resolution equal to 1.3 mm and a mean sensitivity equal to 10.7% / mm

Brandão, Luís Eduardo

Vieira, Wilson S.

Carpe dIEN

2011 International Nuclear Atlantic Conference - INAC 2011 
Belo Horizonte,MG, Brazil, October 24-28, 2011 
ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN 
ISBN: 978-85-99141-04-5 
 
PERFORMANCE INDICATORS OF A NEW COMPUTER AUTOMATED 
RADIOACTIVE PARTICLE TRACKING (CARPT) METHOD  
 
Wilson S. Vieira 1 Luís E. Brandão2 
 
1 Serviço de Tecnologia e Engenharia de Reatores 
Instituto de Engenharia Nuclear 
Rua Hélio de Almeida, s/n 
28630-050 Rio de Janeiro, RJ 
wilson@ien.gov.br 
 
2 Divisão de Radiofármacos 
Instituto de Engenharia Nuclear 
Rua Hélio de Almeida, s/n 
28630-050 Rio de Janeiro, RJ 
brandao@ien.gov.br 
 
 
 
 
 
ABSTRACT 
 
A new computer automated radioactive particle tracking method has been developed by 
the Nuclear Engineering Institute. The method has adopted a physical model consisting 
of a punctual particle inside a cylindrical unit so that the space is formed by small cubic 
cells.  Each cell is assigned a probability factor identifying a reconstruction matrix 
element as it has been made in image reconstruction applications. Particle’s 
instantaneous coordinates are estimated using a dedicated software to reconstruct the 
cell’s activity images so as to identify the unique cell with the greatest probability to 
contain the particle and, consequently, the fluctuating velocity fields of the phase under 
investigation.  In order to quantify the precision of this method, a test was carried out to 
evaluate detection system’s performance indicators, resolution and sensitivity, from the 
experimental data collected during the circular movement of a 198Au particle.  
According to the results, the CARPT method already has a liable performance: a mean 
resolution equal to 1.3 mm and a mean sensitivity equal to 10.7% / mm. 
 
1. INTRODUCTION 
 
1.1 The CARPT Technique 
 
The Computer Automated Radioactive Particle Tracking is a non-invasive technique 
that uses a radioactive tracer inside a single microsphere which has physical properties 
that are similar in behavior of the solid or liquid phase under investigation. Also, this 
experimental technique is useful to acquire the velocity field or the mixing information 
in liquid-solid, gas-solid, gas-liquid, and gas-liquid-solid systems and is well suited to 
validate CFD codes or to develop a reactor model. In addition to the behavior of the 
phase’s displacement patterns, it is possible to prevent unwanted phenomena in 
industrial processes, the same as recirculation, or segregation [1]. 
The new method that has been developing at the Nuclear Engineering Institute to 
optimize the CARPT technique emphasizes a physical model for the industrial unit and 
it is supported by a special software to evaluate the particle's position at a given time 
[1]. 
To measure the effective capacity of a radioactive particle tracking method in a test, 
previous researchers have proposed two variables to optimize the setup of the detectors 
arrangement: resolution and sensitivity.  
The objective of this research is to measure the resolution and the sensitivity of the 
detection system as well as to track a circular trajectory of a radioactive particle moving 
in a fluid through the new CARPT technique [1]. Furthermore, a reduced scale test was 
carried out to evaluate those parameters under three different radioactive particle’s 
angular velocities.  
 
1.2 The Performance Indicators 
  
1.2.1 Resolution 
 
When a radioactive particle is moving in a fluid, it emits photons that are detected at a 
predetermined frequency by the radiation detection system.  Resolution is the parameter 
that measures how two neighboring particle positions along the trajectory r vary with 
the corresponding counts (N) in the detector.  It can be expressed as [2]: 
 
r(t)r ;)( == dN
drrR Nσ                                      (1)  
 
R(r) is the detector resolution that is, the rate of change of the reconstructed particle’s 
displacement with the corresponding measured photon counts. R(r) is a function of the 
particle’s position. 
 
1.2.2 Sensitivity 
 
The resolution should be complemented with another indicator named sensitivity.  It is a 
variable to determine how the detector’s counts (N) vary with a small particle’s 
displacement.  If this displacement occurs along r, sensitivity is defined as [2]: 
 
r(t)r ;)(ln)( == dr
NdrS                                          (2)  
 
S(r) is also a function of the particle’s position. 
2011 International Nuclear Atlantic Conference - INAC 2011 
Belo Horizonte,MG, Brazil, October 24-28, 2011 
ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN 
ISBN: 978-85-99141-04-5 
 
 
2. METHODOLOGY 
 
The new CARPT method has been employed by the authors in a test that has been 
conducted at the Radioactive Tracer Laboratory, inside the Nuclear Engineering 
Institute.  In this method, a gamma radiation detection system was used for measuring 
and recording the counts in the full energy peak from the gamma decay of the 198Au 
particle while it was moving in water. The detectors have been mounted to reproduce a 
specific geometry around the tank, as viewed in Figure 1. 
 
The optimized physical parameters of the test are described on Table 1 and the main 
variables that were controlled are listed on Table 2.  Detectors’ coordinates have been 
optimized for a punctual 198Au particle at rest around the tank [1]. 
 
The tank’s blades were moved by an electric motor whose power had been adjusted to 
achieve the rotation periods paired with the cases C1, C2 and C3. In all of them, the 
radioactive particle was attached on the extremity of a blade. The mean rotating periods 
were calculated from measurements using a chronograph and the corresponding mean 
angular velocities were calculated later dividing 2π by the mean rotating periods (values 
registered on the second line of the table 2).   
 
It has been employed a data acquisition frequency equal to 100 Hz (the time interval 
between two consecutive counts is 0.01 s).  Lately, the counts in the photo-peak have 
been recorded in ASCII files in order to feed the software as input data. Soon after 
running the software, it’s possible to extract vectors containing particle’s properties for 
each instant (position, velocity or concentration profile). 
 
 
Figure 1. The CARPT set up that was mounted around the cylinder. The total 
number of detectors is four. 
2011 International Nuclear Atlantic Conference - INAC 2011 
Belo Horizonte,MG, Brazil, October 24-28, 2011 
ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN 
ISBN: 978-85-99141-04-5 
 
 
Table 1 Test’s parameters 
 
Tank’s high (cm)/water level (cm) 60.0 ±0.05/32.0±0.05 
Cross-section’s diameter (cm) 40.0±0.05 
Isotope/source’s geometry/Activity 
(Bq) 
198Au/sphere/9.0 x106  
Linear attenuation coefficient- water 
(cm-1) 
0.1061  (NIST, 2002) 
Linear attenuation coefficient – air 
(cm-1) 
0.0001053  (NIST, 2002) 
Linear attenuation coefficient - 
wall(cm-1) 
0.20424  (NIST, 2002) 
Photo-peak energy (Mev) 0.412 (95.56%) (IAEA, 2003) 
Detector-tank’s wall  distance (cm) 10.0 ±0.05 
Detector’s front diameter  (cm) 5.08±0.005 
Collimator length (cm) 10.0±0.05 
Collimator aperture (cm) 5.09±0.005 
Detectors’ coordinates (cm) 1 (0,-30,16) 2 (30,0,21) 3 (0,30,16) 4  (-30,0,11) 
 
Table 2 Test’s specification 
 
Case C1 C2 C3 
Mean rotating period T(s) 5.5 2.3 1.8 
Mean angular velocity 
ω(rad/s) 
1.1 2.7 3.5 
 
2.1.   Resolution and Sensitivity’s Determination  
 
To determine the performance indicators of the detection system employing a real test, it has 
been considered an important factor that depends on the time interval between the counts. 
Particle’s trajectories have been reconstructed for the three cases choosing the minimum time 
interval (∆t) to distinguish two different neighboring positions along their path (the path 
tracked during one period) . The particle’s  coordinates X(t), Y(t) ,Z(t), X(t + ∆t), Y(t + ∆t), 
Z(t + ∆t),… were paired with their corresponding detector counts N1(t), N2(t), N3(t), 
N1(t+∆t),…and tabulated for the cases C1, C2 and C3. Next, the graphs σN(r(t) x N)  and  
(lnN) x r (t)  have been plotted from the tabulated data so that the equations 1 and 2 could be 
applied to calculate the individual values of resolution and sensitivity for each detector. Next, 
these four detector’s results were combined to calculate the system’s performance [2] [4]. 
2011 International Nuclear Atlantic Conference - INAC 2011 
Belo Horizonte,MG, Brazil, October 24-28, 2011 
ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN 
ISBN: 978-85-99141-04-5 
 
INAC 2011, Belo Horizonte, MG, Brazil. 
 
 
3.  RESULTS 
 
The test has been conducted successfully and the recorded counts have been saved in ASCII 
files.  These experimental data have been used in the CARPT software that had been 
developed specifically to reconstruct the particle’s positions that were occupied along its 
path. Next, the particle’s velocity profiles have been reconstructed as well as plotted in 
figures 2, 3 and 4 for all cases.   It can be noted that particle´s trajectories are approximately 
circular because of the radioactive particle’s constraint (the 198Au particle was attached to one 
of the blades). 
 
The tables 3, 4 and 5 contain the calculated values of resolution and sensitivity for all cases 
where the title “best resolution” refers to the minimum value of R(r) which has been 
calculated along the particle’s trajectory.  Otherwise, a “worst resolution” corresponds to the 
maximum value of R(r).  An inverse meaning should be considered to evaluate the sensitivity 
because of the nature of its definition. 
 
The CARPT software had been run several times to achieve the minimum time interval 
between two consecutive counts until this value (∆t) has been finally found.  Besides, it has 
been observed, as shown in the tables 3, 4 and 5, that the minimum time interval is inversely 
proportional to the particle’s angular velocity and, therefore, the number of data collected in 
the case C3 is the greatest (50).   
 
All results are similar in statistics for the three cases. It can be observed that the resolution 
and the sensitivity of the new CARPT method are not affected by the particle’s angular 
velocity since the minimum time interval isn’t less than the data acquisition time.  As a result, 
considering a constant CARPT set up and the method employed, the best resolution found is 
equal to 1.3 mm and the best value of the sensitivity is 10.7 % / mm. 
 
INAC 2011, Belo Horizonte, MG, Brazil. 
 
 
Figure 2. Velocity profiles of the 198Au particle during one period of  
its circular movement: case C1. 
 
 
 
Figure 3. Velocity profiles of the 198Au particle during one period of  
its circular movement: case C2. 
 
2011 International Nuclear Atlantic Conference - INAC 2011 
Belo Horizonte,MG, Brazil, October 24-28, 2011 
ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN 
ISBN: 978-85-99141-04-5 
 
INAC 2011, Belo Horizonte, MG, Brazil. 
 
 
 
Figure 4. Velocity profiles of the 198Au particle during one period of  
its circular movement: case C3. 
  
Table 3. Case C1:  detection system’s performance calculated on 30 198Au source’s 
positions 
 
1.1rad/s;∆t=0.20s Resolution (mm) Sensitivity(%/mm) 
Detector Best Worst Mean Best Worst Mean 
1 1.1 18.0 4.1 11.3 0.2 4.5 
2 0.9 11.7 3.3 18.4 0.4 5.1 
3 1.0 15.8 2.8 18.5 3.0 5.9 
4 0.8 12.6 3.7 19.9 0.6 5.2 
1+2+3+4 0.6 2.8 1.6 30.0 4.6 10.4 
 
Table 4. Case C2: detection system’s performance calculated on 20 198Au source’s 
positions 
 
2.7rad/s;∆t=0.15s Resolution (mm) Sensitivity(%/mm) 
Detector Best Worst Mean Best Worst Mean 
1 0.3 5.9 2.3 26.0 1.2 8.4 
2 0.6 7.4 2.9 16.7 0.5 6.4 
3 0.7 15.3 3.0 33.5 0.6 8.2 
4 0.5 19.4 5.7 23.2 0.6 6.5 
1+2+3+4 0.7 3.0 1.6 42.7 3.8 14.9 
 
INAC 2011, Belo Horizonte, MG, Brazil. 
 
Table 5. Case C3: detection system’s performance calculated on 50 198Au source’s 
positions 
 
3.5rad/s;t=0.04s Resolution (mm) Sensitivity(%/mm) 
Detector Best Worst Mean Best Worst Mean 
1 0.6 64.3 4.9 25.4 0.3 6.0 
2 0.6 39.1 5.7 31.9 0.2 5.9 
3 0.5 32.5 5.2 25.8 0.2 3.9 
4 0.2 76.0 5.0 38.5 0.04 5.3 
1+2+3+4 0.3 2.7 1.3 57.1 3.9 10.7 
 
4.  CONCLUSIONS  
 
In this research, we have verified that it is possible to evaluate the CARPT detection system’s 
performance using the experimental data of a particle’s tracking test because results are in 
accordance with those viewed in the literature [2].  Consequently, this can be an alternative 
procedure to check the resolution and the sensitivity of a detector arrangement.  In the future, 
the feasibility of this procedure to evaluate the CARPT performance as a function of source’s 
activity will be investigated. 
 
 
 
REFERENCES 
 
1. W. Vieira, Método para a Avaliação de Unidades Industriais utilizando a Técnica de 
Rastreamento de Partícula Radioativa. Tese de Doutorado, Universidade Federal do 
Rio de Janeiro, Rio de Janeiro, Brasil (2009). 
2. S. Roy, F. Larachi, M. Al-Dahhan, et al., “Resolution and Sensitivity in Computer 
Automated Radioactive Particle Tracking (CARPT),” ”Proceedings of SPIE” 
Vol.4188, pp. 122-133 (2001). 
3. Associação Brasileira de Normas Técnicas, Guide to the Expression of 
Measurement’s Uncertainties, second ed., ABNT, Rio de Janeiro, Brasil (1998). 
4. N. Tsoulfanidis, Measurement and Detection of Radiation, second ed. Taylor 
&Francis, Washington ,USA (1995) . 
 
 


Performance indicators of a new Computer Automated Radioactive Particle Tracking (CARPT) method

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Performance indicators of a new Computer Automated Radioactive Particle Tracking (CARPT) method

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