# Pencil Beam Spectral Measurements of Ce, Ho, Yb, and Ba Powders for Potential Use in Medical Applications

Authors: N. Martini; V. Koukou; C. Michail; P. Sotiropoulou; N. Kalyvas; I. Kandarakis; G. Nikiforidis; G. Fountos
Journal: Journal of Spectroscopy
 (2015)

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## Abstract

The aim of the present study was to obtain modified X-ray spectra, by using appropriate filter materials for use in applications such as dual energy X-ray imaging. K-edge filtering technique was implemented in order to obtain narrow energy bands for both dual- and single-kVp techniques. Three lanthanide filters (cerium, holmium, and ytterbium) and a filter outside lanthanides (barium), with low K-edge, were used to modify the X-ray spectra. The X-ray energies that were used in this work ranged from 60 to 100 kVp. Relative root mean square error (RMSE) and the coefficient of variation were used for filter selection. The increasing filter thicknesses led to narrower energy bands. For the dual-kVp technique, 0.7916 g/cm2 Ho, 0.9422 g/cm2 Yb, and 1.0095 g/cm2 Yb were selected for 70, 80, and 90 kVp, respectively. For the single-kVp technique 0.5991 g/cm2 Ce, 0.8750 g/cm2 Ba, and 0.8654 g/cm2 Ce were selected for 80, 90, and 100 kVp, respectively. The filtered X-ray spectra of this work, after appropriate modification, could be used in various X-ray applications, such as dual-energy mammography, bone absorptiometry, and digital tomosynthesis.


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## Body

## 1. Introduction

The photon spectrum from a conventional X-ray tube consists of a broadband of energies [1]. In dual energy medical applications, a low- and a high-energy band are required [2–6]. In order to resolve the broadband spectrum into low- and high-energy bands, the following three methods can be used: (i) K-edge filtering [7, 8], (ii) kVp switching [9, 10], and (iii) the combination of both [8, 11].In single-kVp techniques, only a single exposure is required with K-edge filtering for both energies to be present simultaneously in the radiation beam. Selective attenuation of photons, just above the absorption edge, creates a transmitted spectrum consisting of two relatively narrow energy bands after heavy filtration [12]. Single-kVp techniques are used in quantitative measurements such as bone densitometry.Dual-kVp techniques employ two sequential measurements at different kilovoltages, typically with different filters between exposures. In this technique, K-edge filtering is used to remove selectively energy photons, above the K-edge, from the spectra, while lower-energy photons are also diminished due to their low penetrability. When K-edge filters are applied, narrower spectra are obtained compared with the spectra filtered with conventional filters. The use of K-edge lanthanide filtering in dual-kVp technique for the narrowing of the low-energy peak was suggested initially by Rutt [8]. The narrowing of the low kV-spectrum results in greater separability between the two peaks in spectra as well as decrease of beam hardening effects. Gustafsson et al. [11] suggested the use of K-edge lanthanide filter for both the low- and high-energy exposures to narrow both the low- and high-keV peaks in spectra. Simulation studies indicated that K-edge filtered spectra could be used to various X-ray applications, such as dual energy mammography, X-ray computed mammotomography (dual-kVp), and bone densitometry (single-kVp) [4–6, 13–15]. Several semiconductor detectors have been proposed for X-ray spectra measurements under clinical conditions [16–22].In this paper, X-ray spectra filtered with several different powder filter materials were measured. A pencil beam was used, as the cone beam depends on the size and the position of the filter, as well as the broadening of the beam. In addition, when pencil beam is used, the divergence of the linear attenuation coefficient is minimized. A cadmium telluride (CdTe) energy discriminating and counting detector was used. K-edge filtering technique was implemented in order to obtain narrow energy bands, for both dual- and single-kVp techniques. The spectra presented here for the dual-kVp technique can be used in imaging techniques such as X-ray mammography, computed mammotomography, and angiography, while the spectra for the single-kVp technique can be used in bone densitometry for bone characterization.


## 2. Materials and Methods

X-ray spectroscopy was performed by measuring spectra from a tungsten (W) anode Norland XR-46 (Norland Medical Systems Inc., Fort Atkinson, WI). The tube voltage ranges from 60 to 100 kV. Five separate X-ray tube operating voltages, from 60 to 100 kVp, in 10 kV increments were investigated. The collimation applied was the standard collimation employed by Norland for dual energy X-ray absorptiometry (DEXA) applications. The divergence at a distance of 20.5 cm was 4 mm. The samarium (Sm) filter employed by Norland was extracted and replaced with the filters used in this study. Figure1 shows the set-up used for the measurement of the spectra.Figure 1
The set-up used for the spectra measurement.For the K-edge technique, barium (Ba), cerium (Ce), holmium (Ho), and ytterbium (Yb) were used, with their K-edge energies ranging from 37.44 to 61.33 keV. The Ce, Ho, and Yb filters were selected since they cover almost the whole atomic number (Z) range of lanthanides. The Ba filter material was, also, selected as an element outside lanthanides due to its lower K-edge. Elements with lower K-edge than Ba were not selected since they are eliminating the number of total counts in the low-energy peak in X-ray spectra. For the filtration with Ba, Ce, Ho, and Yb, barium chloride dihydrate (BaCl2(H2O)2) (Mallinckrodt, 10326-17-9), cerium(IV) oxide (CeO2) (Alfa Aesar, 44656, 99% purity), holmium(III) oxide (Ho2O3) (Sigma-Aldrich, H9750-10G, 99.9% purity), and ytterbium(III) oxide (Yb2O3) (Sigma-Aldrich, 246999-50G, 99% purity) powders were used, respectively. The areal densities of the substances ranged from 0.0818 to 2.0443 g/cm2 corresponding to element (Ba, Ce, Ho, and Yb) thicknesses from 100 to 2500 μm, respectively (Table 1). The powders were prepared, by a mixture with pure carbon (7%) powder, in the form of 13 mm diameter discs (Figure 1), using an infrared spectroscopy hydraulic pellet press, by applying compression of 14 tons for 10 min. The mixture of the powders with the carbon was accomplished in order for the materials to be consistent. The acquisition parameters are summarized in Table 2. All the measurements had 5 min acquisition time. In the dual-kVp technique, Ce was used for the low energy and Ho and Yb were used for the high energy, while Ba and Ce filters were used for the single-kVp technique.Table 1
Areal density ranges of the used substances and the corresponding elements.
Substance
Substance areal density
Element areal density
Element density
Element thickness
Value layers
(g/cm2)
(g/cm2)
(g/cm3)
(μm)
BaCl2(H2O)2
0.6224–1.5561
0.3500–0.8750
3.500
1000–2500
162–793
CeO2
0.0818–2.0443
0.0665–1.6643
6.657
100–2500
67–238
Ho2O3
0.5037–1.5112
0.4398–1.3193
8.795
500–1500
75–399
Yb2O3
0.3832–1.1495
0.3365–1.0095
6.730
500–1500
76–178Table 2
Substances, kVp range, and exposure techniques used.
Substance
kVp
Technique
BaCl2(H2O)2
80–100
Single-kVp
CeO2
60–100
Dual- and single-kVp
Ho2O3
70–90
Dual-kVp
Yb2O3
70–90
Dual-kVpThe X-ray energy discriminating and counting detector system that was used for the spectroscopy measurements was a portable cadmium telluride (CdTe) detector (AMPTEK XR-100T) [23–26]. The CdTe detector was connected to a digital processor (PX4 Digital Pulse Processor), including three major components: (i) a high performance shaping amplifier, (ii) a multichannel analyzer (MCA), and (iii) power supplies. The detector was calibrated for energy scales, linearity checks, and energy resolution, by using 125I (35 keV) and 99
mTC γ-ray (140.6 keV) calibration sources. The source to detector distance (SDD) was 47.5 cm.The measured spectra were corrected for both efficiency and dead time of the PX4 multichannel analyzer in order to determine the incident photons on the detector surface. The efficiency of the XR-100CdTe results from the product of the probability of transmission through beryllium (Be) window and the probability of the photon interactions within the active area of the CdTe detector. The data provided by the manufacturer were used for the detector efficiency corrections [27].For all corrected measured spectra, relative root mean square error (RMSE
rel
⁡) was calculated as an indicative parameter of spectral energy bandwidth. The RMSE
rel
⁡ was used as a metric of the narrowing of the spectrum, since it calculates the divergence between values and in this case each energy, of the spectrum, from the corresponding mean energy [28]. RMSE
rel
⁡ can be expressed as
(1)
RMS
E
rel
⁡
=
∑
E
min
⁡
E
max
⁡
Φ
E
i
E
i
-
E
¯
2
∑
E
min
⁡
E
max
⁡
Φ
E
i
E
i
,
where Φ
E
i are the photons at each energy, E
i is the energy (keV), and E
¯ is the mean energy of the spectrum (keV).The filters and the thickness range were chosen in order to fulfill both of the following criteria: (a) the narrowing of the energy band of the spectrum quantitated byRMSE
rel
⁡ and (b) the total number of photons in spectrum to exceed 106. When the total number of photons exceeds 106, the coefficient of variation (CV(%)) in this measurement will be less than 0.1% since the photon detection considers Poisson distribution and CV(%) was calculated from the following equation:
(2)
CV
(
%
)
=
∑
Φ
E
i
∑
Φ
E
i
·
100
,
where Φ
E
i are the photons at each energy E
i.


## 3. Results and Discussion

The results are presented as functions of the areal density of the corresponding element. Figure2 shows measured spectra for 60 kVp, Ce filtered X-ray beam with areal densities of 0.4659 and 0.9319 g/cm2, respectively. The 0.4659 g/cm2 Ce filtered spectrum is plotted with continuous line, whereas the corresponding 0.9319 g/cm2 is plotted with dashed lines. As it can be seen from Figure 2, the spectrum shape is not changing significantly, when increasing areal density, while the number of photons decreased to about 40%. Thicker filters reduce the number of lower-energy photons, while the high-energy photons are eliminated by the K-edge absorption [4–6]. Consequently, the mean energy of the filtered beam is concentrated around the K-edge of the filter material [12, 13].Figure 2
Low-energy spectrum at 60 kVp filtered with 0.4659 and 0.9319 g/cm2 Ce (700 and 1400 μm Ce, resp.).Table3 shows the RMSE
rel
⁡ and the CV(%) for the Ho and Yb filters used in 70, 80, and 90 kVp. At 70 kVp, 0.7916 g/cm2 Ho and 0.8076 g/cm2 Yb resulted in CV(%) approximately 0.1%. The Ho filter was selected as it had lower RMSE
rel
⁡ compared with Yb (7.14%). At 80 kVp, 0.7916 g/cm2 Ho and 0.9422 g/cm2 Yb fulfilled the limitation of CV(%). The Yb filter was selected as it resulted in 14.41% lower RMSE
rel
⁡. Finally, at 90 kVp, 0.8795 g/cm2 Ho and 1.0095 g/cm2 Yb resulted in CV(%) approximately 0.1%. However, the Yb had 37.74% lower RMSE
rel
⁡ compared with the Ho. Figures 3, 4, and 5 show the corresponding Ho and Yb filtered spectra at 70, 80, and 90 kVp, respectively. In Figures 3, 4, and 5, a small number of counts at energies over the K-edge were measured which are not visible in these plots. However, at 90 kVp Ho filtered spectrum (Figure 5), a number of counts at energies over the K-edge are noticeable, since the K absorption edge of Ho is lower than that of Yb. In Table 4, the selected filters for dual-kVp technique at 70, 80, and 90 kVp are shown. The mean energies, ME, were calculated as ME
=
∑
Φ
E
i
E
i
/
∑
Φ
E
i, where Φ
E
i are the photons at each energy E
i, for energies from 30 to 65 keV.Table 3
Filters used in dual-kVp technique.
kVp (keV)
Areal density(g/cm2)
RMSErel
CV (%)
Ho
Yb
Ho
Yb
Ho
Yb
70
0.7619
0.8076
0.0112
0.0120
0.1018
0.0980
80
0.7619
0.9422
0.0118
0.0101
0.0931
0.1035
90
0.8795
1.0095
0.0159
0.0099
0.1067
0.1035Table 4
Mean and maximum energies for the selected dual-kVp filters.
kVp (keV)
Element
Areal density
Mean energy
Maximum energy
(g/cm2)
(keV)
(keV)
70
Ho
0.7619
50.31
55
80
Yb
0.9422
56.13
61
90
Yb
1.0095
56.89
61Figure 3
High-energy spectrum at 70 kVp filtered with 0.7916 g/cm2 Ho and 0.8076 g/cm2 Yb (900 μm Ho and 1200 μm Yb).Figure 4
High-energy spectrum at 80 kVp filtered with 0.7916 g/cm2 Ho and 0.9422 g/cm2 Yb (900 μm Ho and 1400 μm Yb).Figure 5
High-energy spectrum at 90 kVp filtered with 0.8795 g/cm2 Ho and 1.0095 g/cm2 Yb (1000 μm Ho and 1500 μm Yb).Figure6 shows an 80 kVp X-ray spectrum filtered with 0.5991 g/cm2 Ce for the single-kVp technique. A comparison of the filtered beams, at 60 kVp (Figure 2) and 80 kVp (Figure 6), shows that the high-energy photons result in a bimodal shape of the spectrum, by allowing higher-energy photon to pass through [12–14].Figure 6
High-energy spectrum at 80 kVp filtered with 0.5991 g/cm2 Ce (900 μm Ce).Figure7 shows a 90 kVp spectrum filtered with 0.8750 g/cm2 Ba. A sharp cutoff is evident in the detected photons at energies higher than the K-edge, leading to a spectrum with narrower energy bands. This spectrum, compared with a 0.8400 g/cm2 Ba filtered spectrum, resulted in 2.47% and 3.19% decreased RMSE
rel
⁡ in the low and the high peak, respectively.Figure 7
High-energy spectrum at 90 kVp filtered with 0.8750 g/cm2 Ba (2500 μm Ba).Figure8 shows 100 kVp spectra filtered with 0.8654 g/cm2 Ce and 0.7700 g/cm2 Ba. The low peak of Ba is narrower than the low peak of Ce, while the total number of counts in CeO2 filtration was 9.46 times higher in the low peak.Figure 8
High-energy spectra at 100 kVp filtered with 0.8654 g/cm2 Ce and 0.7700 g/cm2 Ba (1300 μm Ce and 2200 μm Ba).Table5 summarizes the ranges of mean energies of the substances used in each technique (dual- or single-kVp) and the kVps. In dual-kVp technique, the mean energies of the low- and high-energy band ranged from 35.05 to 37.65 keV and 48.16 to 56.89 keV, respectively, while for the single-kVp technique they ranged from 34.01 to 39.13 keV and 63.93 to 88.16 keV for the low- and high-energy band, respectively. This wide range, especially in high energy, indicates that these spectra could be used in several X-ray applications that are of interest in these energies, such as dual energy mammography and dual energy X-ray absorptiometry or even the mass calcium to phosphorus ratio determination in biological hydroxyapatite [4–6, 29].Table 5
Summarized mean energy values for both exposure techniques.
Technique
Substance
kVp
Thickness(μm)
Mean energy range
(keV)
Low energy
High energy
Dual-kVp
CeO2
60
100–1000
35.05–37.65
—
Ho2O3
70
—
48.16–51.92
80
500–1500
—
49.12–52.10
90
—
50.91–52.46
Yb2O3
70
—
50.39–55.56
80
500–1500
—
52.15–56.38
90
—
53.87–56.89
Single-kVp
CeO2
80
37.72–39.12
68.39–73.27
90
1000–2500
37.75–39.12
74.69–81.02
100
37.75–39.13
80.74–88.36
BaCl2(H2O)2
80
34.01–35.49
63.93–69.54
90
1000–2500
34.05–35.51
68.82–70.06
100
34.08–35.52
73.43–82.34RMSE
rel
⁡ values are plotted as a function of areal density for all filters used in the dual-kVp technique and are shown in Figures 9, 10, and 11 corresponding to 70, 80, and 90 kVp. It can be seen that, at 70 and 80 kVp, both filters had the same impact on the spectral width, over all areal density ranges. On the contrary, at 90 kVp, Yb minimizes the RMSE
rel
⁡ over all areal density ranges, since the K-edge absorption energy of Yb is higher than the K-edge of Ho filter.Figure 9
RMSE
rel
⁡ values as a function of areal density for all filters used in the dual-kVp technique at 70 kVp.Figure 10
RMSE
rel
⁡ values as a function of areal density for all filters used in the dual-kVp technique at 80 kVp.Figure 11
RMSE
rel
⁡ values as a function of areal density for all filters used in the dual-kVp technique at 90 kVp.Furthermore, for the single-kVp technique, theRMSE
rel
⁡ values are plotted as a function of areal density for all filters tested shown in Figures 12, 13, and 14, corresponding to 80, 90, and 100 kVp. As the areal density increases, lower RMSE
rel
⁡ values of the high-energy peak indicate that narrower beams can be obtained by using either Ce or Ba filter materials. Similar results were observed in previous studies [12, 14].Figure 12
RMSE
rel
⁡ values as a function of areal density for all filters used in the single-kVp technique at 80 kVp (subscript 1 referred to Ba and 2 to Ce).Figure 13
RMSE
rel
⁡ values as a function of areal density for all filters used in the single-kVp technique at 90 kVp (subscript 1 referred to Ba and 2 to Ce).Figure 14
RMSE
rel
⁡ values as a function of areal density for all filters used in the single-kVp technique at 100 kVp (subscript 1 referred to Ba and 2 to Ce).Using narrow energy X-ray beams, instead of wide energy X-rays, has several advantages in medical applications. Generally, in X-ray tubes inherent and added filtration is used to suppress the low-energy portion of the spectra. Low energies contribute to radiation dose, which increases the probability of cancer. Therefore, dose reduction at X-ray applications, that is, X-ray mammography, computed mammotomography, and computed tomography, would benefit the patients. Furthermore, using narrow beams, in dual energy techniques, is expected to improve separation of tissues with very small differences in attenuation coefficients or possibly the ability of noninvasive tissue characterization [3, 12–14, 29]. Also, imaging with narrow energy spectra provides lower scatter noise and as a result beneficial influence on image contrast and signal-to-noise ratio [2, 13, 14]. Heavy K-edge filtering used in this study indicated that elimination of low-energy photons was accomplished for both dual- and single-kVp techniques, leading to narrow energy bands. However, this technique reduces photon influence, (value layers in Table 1), and thus higher output X-ray tubes are required.The spectra presented here for the dual-kVp technique can be used in imaging techniques, while the spectra for the single-kVp technique can be used in quantitative bone densitometry measurements and imaging using silicon strip photon counting detectors [30].Mean energy range of the spectra was in the diagnostic X-ray energy range indicating that these spectra could be useful in various medical applications such as mammography, computed mammotomography, angiography, and DEXA.


## 4. Conclusions

In the present study, pencil X-ray beams were measured and filtered with different filter materials. K-edge filtering was implemented in order to obtain narrow energy bands for both dual- and single-kVp techniques. The increasing filter thickness resulted in narrowing of the spectral energy band, while on the contrary the total number of photons decreased. The X-ray tube voltages used in this work ranged from 60 to 100 kVp providing higher mean beam energies. The resulting mean energies, after filtration, indicate that these X-ray spectra could be used in various X-ray applications, such as dual energy mammography and absorptiometry and digital tomosynthesis improving their efficiency.



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