1st International Conference on Experiments/Process/System Modelling /Simulation/Optimization
1st IC-EpsMsO
Athens, 6-9 July, 2005
©IC-EpsMsO
THE EFFECT OF NON-IDEAL DETECTORS ON ENERGY WEIGHTED SPECRTA
USED IN X-RAY MEDICAL IMAGING
George D. Patatoukas1, Panayiotis .Liaparinos1, Anastasios .Gaitanis2, Ioannis .Kandarakis2, Georgios
.Panayiotakis1
1. Department of Medical Physics, Medical School, University of Patras, 265 00
Patras, Greece
2.Depatrment of Medical Instrumentation Technology, Technological Educational Institution of Athens, Agiou
Spyridonos street, Aigaleo, 122 10 Athens, Greece
Abstract. The present study investigates the effect that a recently introduced energy weighting technique
appears to have on the quality of signal to noise ratio (SNR) in x-ray medical imaging under the assumption that
the detector considered is non-ideal. Recent developments show that under stringent assumptions an energy
weighted spectrum can lead to SNR enhancement, as well as in dose reduction. So far in the literature all
scintillation detector characteristics have been ignored. For this reason, in this work the scintillation detectors
have been considered to be non-ideal. This way the effect that the intrinsic scintillation detector properties
potentially have on energy weighted spectra is presented. Moreover, a theoretical evaluation of the SNR under
these conditions is carried out. Results show that SNR enhancement is achievable with this method and the
enhancement factor values can be as high as 30. Such concept could prove useful, especially if energy-sensitive
pixel detectors are developed, in all fields of digital medical imaging.
INTRODUCTION
The idea of signal enhancement with the use of an energy-dependent function that operates upon the
signal has been already applied to medical imaging as a technique 1,2 . Such method could give rise to the
creation of new pixel detectors that are energy-sensitive and if embodied to a medical imaging system, could
define each photon not only spatially but also in terms of its energy. This way, the signal to noise ratio (SNR)
and other parameters (DQE, contrast etc) could see an improvement that could help the diagnostic procedure.
Such concept has been previously reported in the literature in two cases (Cahn et al (1), Griesch et al
(2)). In both these cases all noise sources have been assumed to be zero except for quantum fluctuations. Monte
Carlo simulation methods have shown that energy weighting resulted in SNR enhancement by a factor of 1.9 (2).
In addition such a SNR enhancement is more obvious when using Molybdenum anode rather that Tungsten
anode. Finally, it has been reported that DQE results, for weighted signals, were similar for microcalcifications
and tumours.
The present study investigates how an energy-dependent weighting function affects the SNR in the
presence of a non-ideal scintillation detector under mammographic conditions. The scintillator considered
was Gd 2 O2 S : Tb , a typical scintillation screen used in mammography (3). An algorithm was produced to study
the variation of the weighting factor in terms of anode material (Mo or W), of energy (25 ->40 KV) and in terms
of tumour or microcalcification thickness.
MATERIALS AND METHODS
Definition of energy weighting
Let us consider a typical x-ray situation as seen in figure 1; A parallel photon flux Φ (E) is incident on a
phantom, which includes two different regions (breast and microcalcification or breast and tumour) with
different attenuation coefficients μ1 and μ2 . Once the x-ray flux exits the phantom region, it enters the
scintillator and the final optical signal is produced and emitted.
Under these conditions the energy weighting factor is defined in the following way similarly to Giersch
et al (2).
W=
S1  S 2
S1  S 2
1st International Conference on Experiments/Process/System Modelling /Simulation/Optimization
1st IC-EpsMsO
Athens, 6-9 July, 2005
©IC-EpsMsO
where:
S 1 is the optical signal through the breast tissue, and
S 2 is the optical signal through breast and microcalcification (or tumour).
Φ (E)
Breast region
μ1
microcalcification
(or tumour region)
μ2
 ' ' E 
 ' E 
Gd 2 O2 S : Tb
S1
S2
Figure 1. Typical x ray imaging situation using a phantom with two different regions (breast and
microcalcification, or, breast and tumour).
Simulation parameters
To simulate the complete imaging situation, different anode materials (Molybdenum and Tungsten)
were used for a variety of different energies from 25 to 40 kV. All spectra were downloaded from the SIMENS©
website () and were created according to the Boone (4) algorithm.
The phantom designed was 1-dimensional and can be seen in figure 1. It included breast tissue of
thickness 4.5 cm and tumour (or microcalcification) of varying thickness.
Attenuation coefficient values for breast, microocalcification and tumour were calculated according to
the following formulae according to Chan et al (1):
The cross section has been previously expressed by the following equation:
 ( E )  24.15Z 4.2 E 3  0.56Z
where Z is the atomic number, E is the x-ray photon energy. This way, the attenuation coefficient for any
substance can be calculated using equation 3:
 E  
 ( E )  0
A
where ρ is the material density, A is the atomic mass and N 0 is the Avogadro’s number. Values for these
parameters are given in table 1 ().
Tissue
Breast
Microcalcification
Effective
Z
Effective
A
14.76
6.56
26.88
11.48
Density
 g 
3 
 cm 

2.2
0.98
1st International Conference on Experiments/Process/System Modelling /Simulation/Optimization
1st IC-EpsMsO
Athens, 6-9 July, 2005
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Tumour
7.64
14.53
1.04
Table 1: Parameters used for the calculation of cross section and attenuation coefficients for different materials,
in equations 2 &3.
Scintillator characteristics
In contrast to previous works, this study examines the effect of energy weighting under mammographic
conditions in the presence of non-ideal detector. The scintillator considered was Gd 2 O2 S : Tb , and its thickness
was 32 mgcm
Tb
3
2
, typically used for mammographic examinations (3). The emission for this material results from
forbidden 4f to 4f transitions, and the highest intensity line is at 545 nm, in the green region of the
3
spectrum. Its density is 7.3 gcm , it is not hydroscopic and its decay time is of order of ms ().
A very important parameter that characterises a scintillation screen is the function G  . This parameter
represents the fraction of spatial frequency dependent light flux generated in the phosphor material at depth t and
transmitted to the screen output, giving the final signal. The full expression for G  is given by equation 4,
according to Ludwig 1971 (5), Swank 1973 (6), Beutel et al 1993(7), Kandarakis et al 1997(8).
Gλ  u,t  
σρ  qβ  σ  eqT   qβ  σ  e qT 
 qβ  σ  qβ  σρ  eqT   qβ  σ  qβ  σρ  e qT
The variable q can then be calculated by the following formula:
1
2

 u  2
q   σ 2  4π 2   

 d  

Where u is the spatial frequency, d is the packing density. Since in this study detector characteristics
were analysed in the spatial domain, spatial frequency u was set equal to 0, giving q=σ. The G  (u, t) function
depends on the optical parameters σ, β and packing density ρ. For
3
assigned to the three parameters: σ=30, β=0.03, ρ=3.65 gcm
Gd 2 O2 S :Tb, the following values were
(Using packing density 50%) ().
Signal and Noise definitions
For the calculation of the signal the following formulae were used:(9).
c
E
G( 0, Δt )dEdT
Eλ
S2    Φ0''  E  QDE( E )ηc
E
G( 0, Δt )dEdT
Eλ
S1  
T
 Φ  E  QDE( E )η
'
0
E
T E
In the above expressions S 1 denotes the signal exiting the scintillator that has passed only from the
breast region, and S 2 denotes the signal that has passed from two different regions. In addition c was set equal
to 0.19 and
 was set equal to 0.002274 keV (10).
In a similar way, noise for both signals was defined by the following expressions according to … (11).
1st International Conference on Experiments/Process/System Modelling /Simulation/Optimization
1st IC-EpsMsO
Athens, 6-9 July, 2005
©IC-EpsMsO
 E

N1   Φ0' eiμΔt μΔt  ηc
G 0,Δt 
i
 Eλ

2
 E

N 2   Φ0'' eiμΔt μΔt ηc
G 0,Δt 
i
 Eλ

2
Using equations 6, 7, 8 &9 the signal to noise ratio can be defined as:
S1  S 2
SNR 
1
( N1  N 2 )2
Finally, the weighted SNR is defined by equation 11 using equations 10 & 1.
SNRweighted 
[  S1  S2 W 2 ]
1
[( N1  N 2 )W 2 ] 2
Concluding, a new variable can be defined using equations 10 & 11, namely the SNR ratio .
SNRratio 
SNRweighted
SNR
Results and discussion
Results of the simulation can be seen in figures 2 and 3. In both cases the SNR enhancement is obvious,
especially in the case that a microcalcification is present. In this case the larger the size of the microcalcification,
the bigger the SNR ratio is, with values that start from 6.3 for a 0.02 cm calcification and reach 30.9 when the
microcalcification size is 0.2 cm. It is wroth noting that when using Mo anode instead of W, under the same
conditions (E, microcalcification size), the enhancement effect is bigger
In the case that a tumour is present, again the SNR in enhanced by a factor that varies from 1.1 and can
reach values up to 9.07 for tumour sizes of 0.2 and 1.4 cm respectively. As in the previous case the weighting is
bigger for Mo than for W. The reason for this is that the Mo spectrum shows stronger variation with respect to
energy, leading to larger weighting factor and SNR enhancement, as it has been previously reported by other
studies(1).
SNR ratio for Mo 30 KV
SNR ratio for W 30 KV
35
30
SNR ratio
25
20
15
10
5
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
Microcalcification thickness (cm)
Figure 2. SNR ratio variation with microcalcification thickness at 30KV using two different anode materials Mo
and W. The SNR enhancement is clearly larger when using Molybdenum.
1st International Conference on Experiments/Process/System Modelling /Simulation/Optimization
1st IC-EpsMsO
Athens, 6-9 July, 2005
©IC-EpsMsO
10
SNR ratio for Mo 30 KV
SNR ratio for W 30 KV
SNR ratio
8
6
4
2
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Tumour thickness (cm)
Figure 3. SNR ratio variation with tumour thickness at 30KV using two different anode materials Molybdenum
and Tungsten. The SNR enhancement is again larger when using Molybdenum, but overall is less that when
microcalcification is present.
It is obvious that the factor of enhancement is much greater when microcalification is present, even at
the same conditions (size, anode material or energy). This is mainly due to the difference in the attenuation
coefficients of the two regions, as clearly seen in figure 4. In the same energy interval (3.5 to 10.5 keV), the
microcalcification attenuation coefficient μ is many orders of magnitude greater than that of the tumour. This
effect can be verified by figure 5 which shows the completely different behaviour of the weighting function
under the same conditions.
2500
Microcalcification miu
Tumor miu
Attenuation coefficient
2000
1500
1000
500
0
3
4
5
6
7
8
9
10
11
Energy (keV)
Figure 4. Attenuation coefficients μ for microcalcification and tumor in the low-energy regions (up to 10.5 keV)
Weighing factor for 0.2 cm microcalcification using Mo
Weighing factor for 0.2 cm tumor using Mo
1.0
Weighting factor
0.8
0.6
0.4
0.2
0.0
0
5
10
15
20
25
30
35
40
Energy (keV)
Figure 5. Weighting factor variation with energy for Mo at 36 KV for microcalcification and tumour lesions both
with size 0.2 cm
1st International Conference on Experiments/Process/System Modelling /Simulation/Optimization
1st IC-EpsMsO
Athens, 6-9 July, 2005
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Finally, an overall evaluation of this technique can be seen in the following. It is clearly shown how
microcalcification provides the strongest weighting in comparison to tumour, and that Molybdenum as an anode
material is more efficient for this technique than Tungsten.
22
20
SNR ratio
18
16
SNR
SNR
SNR
SNR
14
12
ratio
ratio
ratio
ratio
for
for
for
for
microcalcification thickness 0.08 cm using Mo
microcalcification thickness 0.08 cm using W
tumor thickness 0.9 cm using Mo
tumor thickness 0.9 cm using W
10
8
6
24
26
28
30
32
34
36
38
40
42
Energy (keV)
Figure 6. Variation of SNR ratio with energy for microcalcification and for tumour using different anode
materials
Conclusions
The purpose of this study was to investigate how energy weighted based technique could influence the
quality of SNR in typical mammographic conditions. A theoretical model was developed using MatLab©
software to simulate the x ray imaging conditions. Results showed that SNR enhancement is achievable under
such conditions. The SNR ratio of the weighted signal to the original signal can reach values up to 30 under
specific conditions. Larger enhancement is achieved when using Molybdenum than Tungsten spectra, due to
the strong variations of the Mo spectra. In addition microcalcification regions can lead to bigger SNR ratios than
tumour regions because the weighting factor shows a dependency on the difference in the emitted signal from
different regions (equation 1). Such difference does exist and is particularly large in the low energy regions (up
to 9 keV). Future developments in digital medical imaging with energy-sensitive pixel detectors could bring in
use this theoretical concept, leading to many advantages in diagnostics.
References
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)