**6.1 Theory of K edge filters**

There is another method of generating small energy bandwidth X-ray radiation. It is known that in addition to the Brehmstrahlung radiation, materials bombarded with electrons produce characteristic radiation which increases the intensity of the X-ray radiation at energy levels specific to each material. For instance, a typical X-ray radiation spectrum for a Tungsten (W) anode using 100 kV anode-cathode potential and a 2 mm Al window is shown in Figure 4. As before, the lowest energy X-rays are absorbed by the Al output window. The sharp peeks in the X-ray spectrum are characteristic for the anode material. These peeks are the result of the electron structure of a given material and they show the energy differences between electron shells of the atomic structure.

For example, W has 3 electron shells that play a role in its use as a K edge filter. The 3 innermost electron shells are designated "K", "L", "M", where K is the innermost shell, and M the outermost. For W, K has an energy of 70keV, L has an energy of 11keV, and M has an energy of 3keV. The characteristic peaks for W will occur at "L minus K" and "M minus K" or at 59keV (designated the K peak) and 67keV (designated the K peak). W also has a second electron in its K shell with a slightly different binding energy which explains the doublets in Figure 4.

The same phenomenon works in the opposite way; materials absorb X-ray photons which are above their binding energy. This is the basis of the K edge filters. Generally at these (energy) levels the X-ray absorption of the material jumps (increases) when the material is used as an X-ray filter. Figure 5 shows the X-ray spectrum for the same W anode and the same X-ray tube voltage as in Figure 4 but with an added 0.2 mm W sheet as a filter. This

Fig. 4. W anode spectra with low energy filter of 2 mm Al.

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 141

relevant energy range, the decomposition (4) has to be extended by the energy dependent attenuation function of this particular element as a third component (Sukovic and Clinthorne 1999). The decomposition for a high Z element with K edge in the diagnostic

��

where the values a = 1*,* 2*,* 3 represent the photoelectric, Compton and the K edge components, respectively. In the above formula, aK(x��) and fK(E) denote the local density and the mass attenuation coefficient of the K edge material. The latter includes the photoelectric

Table 1 provides a list of some K edge filters whose K edge energies (except for Al and Cu filters) fall into the region where they are or could be applied to X-ray imaging. From the

K edge filtering has been used for mammography for some time where different Rhodium (Rh) and Molybdenum (Mo) anode and filter combinations are used to generate energy

**Material** Aluminum Copper Molybdenum Rhodium Silver Tin Iodine **Chemical sign** Al Cu Mo Rh Ag Sn I **Atomic number** 13 29 42 45 47 50 53 **K edge energy in keV** 1.6 8.98 20 23.22 25.51 29.2 33.16

**Material** Barium Cerium Neodimium Europium Gadolinium Holmium **Chemical sign** Ba Ce Nd Eu Gd Ho **Atomic number** 56 58 60 63 64 67 **K edge energy in keV** 37.45 40.44 43.56 48.5 50.2 55.6

**Material** Erbium Ytterbium Tantalum Tungsten Gold Bismuth Uranium **Chemical sign** Er Yb Ta W Au Bi U **Atomic number** 68 70 73 74 79 83 92 **K edge energy in keV** 57.5 61.3 67.41 69.5 80.72 90.53 115.6

Table 1. K edge energies for different materials already used or that can be used in K-edge

As shown in Figure 6, at an anode voltage of 28 kV, a Mo anode – Mo filter combination gives a lower mean energy of 17.6 keV better suited for thinner, lower density breasts, while the Rh anode – Rh filter combination has a mean energy of 18.3 keV, which is better for thicker and denser breast imaging. Different Mo and Rh anode and filter combinations are used in some specialized mammography imagers and various anode voltages to fine tune the optimum energy spectrum to obtain maximum contrast at minimum dose for different breast types. Tungsten (W) anodes with higher anode voltages (40kV) and Silver (Ag) filters

table it is clear that the K edge energy increases with increasing atomic number.

�+ a�(x��)f�(E) = ∑ a� �

��� (x��)f�(E) (8)

�� + a��(x��)f�� � �

effect, Compton effect and K edge contributions of the material.

**6.2 K edge materials, energies, and applications** 

energy range becomes:

μ(E, x��) = a��(x��) �

peaks in the 15- 23 keV energy range.

X-ray imaging.

added tungsten sheet filters out not only the low energy X-rays but the X-ray spectrum also shows a huge drop in intensity (the absorption increases dramatically) above the tungsten K edge. Please note that the total intensity decreased as well. The scale of Figure 5 is different from that of Figure 4 for better visibility. The total intensity after K edge filtering is always lower than without it for the same energy range but the characteristic K edge radiation peaks are still present. This example shows that material K edge absorption can be used to suppress both low and high energy portions of the original X-ray spectrum to produce narrow bandwidth X-ray radiation or so called quasi-monochromatic X-rays.

Fig. 5. Tungsten (W) anode with 0.2 mm W (K edge) filter.

The absorption spectra of K edge filters can be calculated. If there are no K-edge discontinuities, then the energy dependence of the linear attenuation coefficient μ(E, x��) of materials can be described by a linear combination of the photo-electric and the Compton cross-sections ���(E) and ���(E)(Alvarez and Macovski 1976)

$$\mu(\mathbf{E}, \widehat{\mathbf{x}}) = \mathbf{a}\_{\text{ph}}(\widehat{\mathbf{x}}) \frac{1}{\mathbf{E}^3} + \mathbf{a}\_{\text{Co}}(\widehat{\mathbf{x}}) \mathbf{f}\_{\text{KN}}(\mathbf{E}/\mathbf{E}\_{\text{e}}) \tag{4}$$

Here Ee = 510.975 keV denotes the rest mass energy of the electron, and the vector x�� describes the space dependence of the attenuation and 1/E3 approximates the energy dependence of the photoelectric interaction. The energy dependence of the Klein–Nishina cross-section (Compton scattering) is given by:

$$f\_{\rm KN}(\mathbf{a}) = \frac{1+a}{a^2} \left[ \frac{2(1+a)}{1+2a} - \frac{1}{a} \ln(1+2a) \right] + \frac{1}{2a} \ln(1+2a) - \frac{1+3a}{(1+2a)^2} \tag{5}$$

Where 510.975 keV, and aph and FKN are given as:

$$\mathbf{a\_{ph}} \approx \mathbf{K\_1} \times \frac{\rho}{\mathbf{A}} \times \mathbf{Z^n} \qquad \quad \mathbf{n} \approx 4 \tag{6}$$

$$\mathbf{a}\_{\rm Co} \approx \mathbf{K}\_2 \times \frac{\rho}{\mathbf{A}} \times \mathbf{Z} \tag{7}$$

where K1 and K2 are constants, ρ is mass density, A is atomic weight and Z is atomic number. When a material with high atomic number Z is present, the above description of the attenuation properties of the matter has to be modified. To correctly describe the attenuation of a sample containing a single element with K edge discontinuity inside the relevant energy range, the decomposition (4) has to be extended by the energy dependent attenuation function of this particular element as a third component (Sukovic and Clinthorne 1999). The decomposition for a high Z element with K edge in the diagnostic energy range becomes:

$$\mu\text{(E,\'{x})} = \mathbf{a\_{ph}}\left(\mathbf{\widetilde{x}}\right)\frac{1}{\mathbf{E}^3} + \mathbf{a\_{Co}}\left(\mathbf{\widetilde{x}}\right)\mathbf{f\_{KN}}\left(\frac{\mathbf{E}}{\mathbf{E}\_6}\right) + \mathbf{a\_K}\left(\mathbf{\widetilde{x}}\right)\mathbf{f\_K}\left(\mathbf{E}\right) = \boldsymbol{\Sigma}\_{\mathbf{a=1}}^3 \mathbf{a\_a}\left(\mathbf{\widetilde{x}}\right)\mathbf{f\_a}\left(\mathbf{E}\right) \tag{8}$$

where the values a = 1*,* 2*,* 3 represent the photoelectric, Compton and the K edge components, respectively. In the above formula, aK(x��) and fK(E) denote the local density and the mass attenuation coefficient of the K edge material. The latter includes the photoelectric effect, Compton effect and K edge contributions of the material.

#### **6.2 K edge materials, energies, and applications**

140 Imaging of the Breast – Technical Aspects and Clinical Implication

added tungsten sheet filters out not only the low energy X-rays but the X-ray spectrum also shows a huge drop in intensity (the absorption increases dramatically) above the tungsten K edge. Please note that the total intensity decreased as well. The scale of Figure 5 is different from that of Figure 4 for better visibility. The total intensity after K edge filtering is always lower than without it for the same energy range but the characteristic K edge radiation peaks are still present. This example shows that material K edge absorption can be used to suppress both low and high energy portions of the original X-ray spectrum to produce

The absorption spectra of K edge filters can be calculated. If there are no K-edge discontinuities, then the energy dependence of the linear attenuation coefficient μ(E, x��) of materials can be described by a linear combination of the photo-electric and the Compton

Here Ee = 510.975 keV denotes the rest mass energy of the electron, and the vector x�� describes the space dependence of the attenuation and 1/E3 approximates the energy dependence of the photoelectric interaction. The energy dependence of the Klein–Nishina

� ln(1 + 2α)� + �

�

�� + a��(x��)f��(E/E�) (4)

�� ln(1 + 2α) − � � ��

× Z� n ≈ 4 (6)

× Z (7)

(� � ��)� (5)

narrow bandwidth X-ray radiation or so called quasi-monochromatic X-rays.

Fig. 5. Tungsten (W) anode with 0.2 mm W (K edge) filter.

cross-sections ���(E) and ���(E)(Alvarez and Macovski 1976)

�� ��(� � �) � � �� <sup>−</sup> �

Where 510.975 keV, and aph and FKN are given as:

cross-section (Compton scattering) is given by:

f��(α) = � � �

μ(E, x��) = a��(x��) �

a�� ≈ K� <sup>×</sup> �

�

a�� ≈ K� <sup>×</sup> �

where K1 and K2 are constants, ρ is mass density, A is atomic weight and Z is atomic number. When a material with high atomic number Z is present, the above description of the attenuation properties of the matter has to be modified. To correctly describe the attenuation of a sample containing a single element with K edge discontinuity inside the Table 1 provides a list of some K edge filters whose K edge energies (except for Al and Cu filters) fall into the region where they are or could be applied to X-ray imaging. From the table it is clear that the K edge energy increases with increasing atomic number.

K edge filtering has been used for mammography for some time where different Rhodium (Rh) and Molybdenum (Mo) anode and filter combinations are used to generate energy peaks in the 15- 23 keV energy range.




Table 1. K edge energies for different materials already used or that can be used in K-edge X-ray imaging.

As shown in Figure 6, at an anode voltage of 28 kV, a Mo anode – Mo filter combination gives a lower mean energy of 17.6 keV better suited for thinner, lower density breasts, while the Rh anode – Rh filter combination has a mean energy of 18.3 keV, which is better for thicker and denser breast imaging. Different Mo and Rh anode and filter combinations are used in some specialized mammography imagers and various anode voltages to fine tune the optimum energy spectrum to obtain maximum contrast at minimum dose for different breast types. Tungsten (W) anodes with higher anode voltages (40kV) and Silver (Ag) filters

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 143

We know that Iodine has a K edge energy of 33.16 keV. To enhance the contrast of the iodine we have to use K edge filters which have K edges somewhat above the Iodine K edge. These materials are Cerium (Ce) Neodymium (Nd) And Europium (Eu). Figure 7 provides a comparison of the x-ray spectra using these different K edge filters for Iodine contrast

Fig. 7. Iodine (I) as a contrast agent and a few possible K edge filters: Cerium (Ce)

(Er), Ytterbium (Yb) and Tantalum (Ta) or even Tungsten (W).

Cerium and Samarium anodes (Sato, Tanaka et al. 2007).

(see also in Section 7).

higher K edge energy than Ta so it cuts off the spectra at higher keV.

Another contrast material, Gadolinium (Gd) has been extensively used in MRI due to its special magnetic properties. In the bloodstream it behaves similar to the Iodine; it also accumulates in the tumor region when injected in the blood and clears out slower from tumors than it clears from the bloodstream. However, it also has a K edge energy for X-rays at 50.2 keV versus the 33.16 keV K edge of Iodine. This makes Gd a contrast material candidate not so much for X-ray mammography but rather for general radiographic applications. To improve the visibility of Gd absorption, K edge filters with K edge energies slightly over that of the Gd can be used. Possible candidates are Holmium (Ho), Erbium

Figure 8 gives a comparison of the X-ray spectrum of some K edge materials for Gd. It shows the spectra of Gd in red and a few possible K edge filters in other colors. Ta and W spectra have very similar shapes, both showing the W anode K edge spectra, but W has a

An interesting approach for K edge filtering is to use an X-ray tube target material made of K edge filter materials, as was demonstrated by Sato et al (Sato, Tanaka et al. 2004) with

A further possibility is to combine dual energy imaging with K edge filters. Taking an image with a filter which has a K edge over the K edge of the contrast agent and one which has a K edge below and then using weighted subtraction can further improve the contrast. This is also seen from Table 4 in section 6.4.2. The Ce filter enhances the contrast while the Iodine filter decreases the Iodine contrast. So further contrast improvement can be obtained by weighted subtraction of the two spectra rather than by just using the Ce filter image alone

enhancement.

Neodymium (ND) and Europium (Eu).

could also be used. This combination would be especially useful for imaging very large and dense breasts.

Evaluation of different x-ray sources with varying anode voltages is given by Jennings et al. (Jennings, Quinn et al. 1993) and Venkatakrishnan (Venkatakrishnan, Yavuz et al. 1999). Optimization of spectral shape for digital mammography is given by Fahrig and Yaffe (Fahrig and Yaffe 1994). Dose versus image quality was also experimentally studied on a CsI flat panel mammo imaging system using Mo/Mo anode/filter combination. (Huda W Fau - Sajewicz, Sajewicz Am Fau - Ogden et al.) Optimization of the anode-filter combination is provided by Varjonen et al. (Varjonen and Strommer 2008) and a very good Monte Carlo analysis of different combinations is provided by Dance et al. (Dance, Thilander et al. 2000) for both film and digital imaging. Fahrig et al. (Fahrig, Rowlands et al. 1996) investigated the a-Se based digital imagers and found that the optimal x-ray spectra is similar to the indirect (scintillator + photodiode) based imagers.

An X-ray tube at 30 kVp anode-cathode voltage does not provide enough flux for fast three dimensional breast imaging (breast CT). Generally higher tube voltage (60-80kVp) is applied (Boone, Nelson et al. 2001) to keep the imaging time within reasonable limits (breath withholding during the CT scan). However, it is known that the X-ray contrast decreases with increasing X-ray energies. However, in the following we will investigate how we can improve the visualization of tumors in X-ray CT images utilizing K edge filtering.

Fig. 6. X-ray applications with K edge filtering.

It is known that iodine has a high Z number which provides reasonable X-ray absorption. It dissolves in water and it has been used for intravenous injection to check blood flow in the body. It is common knowledge that most tumors have generally leaky blood vessels. Blood leaks from the vessels near tumors into the intercellular tissues and it generally takes a longer time to be re-circulated than blood that has not leaked out. So if we inject iodine into the blood stream, this iodine will also leak out in the tumor region and it will stay there for a period of time while the iodine in the rest of the vessels clears up more quickly. The presence of the iodine at the tumor will enhance the contrast of the image for several minutes following the iodine injection.

could also be used. This combination would be especially useful for imaging very large and

Evaluation of different x-ray sources with varying anode voltages is given by Jennings et al. (Jennings, Quinn et al. 1993) and Venkatakrishnan (Venkatakrishnan, Yavuz et al. 1999). Optimization of spectral shape for digital mammography is given by Fahrig and Yaffe (Fahrig and Yaffe 1994). Dose versus image quality was also experimentally studied on a CsI flat panel mammo imaging system using Mo/Mo anode/filter combination. (Huda W Fau - Sajewicz, Sajewicz Am Fau - Ogden et al.) Optimization of the anode-filter combination is provided by Varjonen et al. (Varjonen and Strommer 2008) and a very good Monte Carlo analysis of different combinations is provided by Dance et al. (Dance, Thilander et al. 2000) for both film and digital imaging. Fahrig et al. (Fahrig, Rowlands et al. 1996) investigated the a-Se based digital imagers and found that the optimal x-ray spectra is similar to the

An X-ray tube at 30 kVp anode-cathode voltage does not provide enough flux for fast three dimensional breast imaging (breast CT). Generally higher tube voltage (60-80kVp) is applied (Boone, Nelson et al. 2001) to keep the imaging time within reasonable limits (breath withholding during the CT scan). However, it is known that the X-ray contrast decreases with increasing X-ray energies. However, in the following we will investigate how we can

It is known that iodine has a high Z number which provides reasonable X-ray absorption. It dissolves in water and it has been used for intravenous injection to check blood flow in the body. It is common knowledge that most tumors have generally leaky blood vessels. Blood leaks from the vessels near tumors into the intercellular tissues and it generally takes a longer time to be re-circulated than blood that has not leaked out. So if we inject iodine into the blood stream, this iodine will also leak out in the tumor region and it will stay there for a period of time while the iodine in the rest of the vessels clears up more quickly. The presence of the iodine at the tumor will enhance the contrast of the image for several

improve the visualization of tumors in X-ray CT images utilizing K edge filtering.

dense breasts.

indirect (scintillator + photodiode) based imagers.

Fig. 6. X-ray applications with K edge filtering.

minutes following the iodine injection.

We know that Iodine has a K edge energy of 33.16 keV. To enhance the contrast of the iodine we have to use K edge filters which have K edges somewhat above the Iodine K edge. These materials are Cerium (Ce) Neodymium (Nd) And Europium (Eu). Figure 7 provides a comparison of the x-ray spectra using these different K edge filters for Iodine contrast enhancement.

Fig. 7. Iodine (I) as a contrast agent and a few possible K edge filters: Cerium (Ce) Neodymium (ND) and Europium (Eu).

Another contrast material, Gadolinium (Gd) has been extensively used in MRI due to its special magnetic properties. In the bloodstream it behaves similar to the Iodine; it also accumulates in the tumor region when injected in the blood and clears out slower from tumors than it clears from the bloodstream. However, it also has a K edge energy for X-rays at 50.2 keV versus the 33.16 keV K edge of Iodine. This makes Gd a contrast material candidate not so much for X-ray mammography but rather for general radiographic applications. To improve the visibility of Gd absorption, K edge filters with K edge energies slightly over that of the Gd can be used. Possible candidates are Holmium (Ho), Erbium (Er), Ytterbium (Yb) and Tantalum (Ta) or even Tungsten (W).

Figure 8 gives a comparison of the X-ray spectrum of some K edge materials for Gd. It shows the spectra of Gd in red and a few possible K edge filters in other colors. Ta and W spectra have very similar shapes, both showing the W anode K edge spectra, but W has a higher K edge energy than Ta so it cuts off the spectra at higher keV.

An interesting approach for K edge filtering is to use an X-ray tube target material made of K edge filter materials, as was demonstrated by Sato et al (Sato, Tanaka et al. 2004) with Cerium and Samarium anodes (Sato, Tanaka et al. 2007).

A further possibility is to combine dual energy imaging with K edge filters. Taking an image with a filter which has a K edge over the K edge of the contrast agent and one which has a K edge below and then using weighted subtraction can further improve the contrast. This is also seen from Table 4 in section 6.4.2. The Ce filter enhances the contrast while the Iodine filter decreases the Iodine contrast. So further contrast improvement can be obtained by weighted subtraction of the two spectra rather than by just using the Ce filter image alone (see also in Section 7).

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 145

A rotational table was used to rotate the phantoms during CT image sequences. First it was verified that the center (focal spot) of the X-ray radiation was lined up with the center of the X-ray imager and that the imaginary line between these two points crossed the pivot-line of the rotation. This alignment was done with the help of a so called Isocal phantom. This phantom consists of a graphite cylinder with BBs, which are arranged in a spiral pattern alongside the perimeter. A detailed description of this method and the phantom is given by A. Jeung et al (Jeung, Sloutsky et al. 2005). We also processed a norm factor calibration when we used a cylindrical object of the same size and material as the bulk of the CT phantoms but without any holes in it. This calibration method is described in more details by Matsinos

The rotational table was driven by a stepper motor for precision rotational speed. 625 images were taken during one 360o rotation. The rotational speed and the imaging speed were synchronized. From these values the angles were calculated for each transmission

Fig. 9. Hounsfield unit CT phantoms.

Fig. 10. Iodine solution phantoms.

et al (Matsinos 2005).

Fig. 8. Gd spectrum is in red. To enhance the contrast, Er, Ta or W can serve as K edge filters, which have higher K edges as Gd.

#### **6.3 Experimental work with K edge filters**

This section describes some of the author's own work on different K edge filters used for mammographic CT applications (Zentai 2011).

For the CT tests, so called HU (Hounsfield Unit) Phantoms were prepared. One set was made for HU calibration. This set consisted of small bottles filled with different water and alcohol solutions for densities less than water and also with water and glycerin mixtures for densities higher than water. The bottles were pushed into holes in a large polyethylene cylinder as shown in Figure 9. Polyethylene plugs were used for keeping the bottles in place and also for having the same material densities below and above the bottles. However, small holes were drilled in the center of the plugs for letting the extra air out when pushing the plugs in place. These holes contained air, so HU numbers for the air could also be evaluated by using the air pocket images of these holes. We found that for alcohol-water and glycerinwater solutions the X-ray absorption is proportional to the density. So the numbers written over the bottles of Figure 9 represent the relative densities of the solutions in g/cm3.

As we know, HU numbers are proportional to the absorption (densities) of these liquids; water has HU=0 and air has HU=-1000. HU from 0 to 2000 represent liquids and solids denser than water. For instance, the density of pure alcohol is 0.782 and the approximate Hounsfield number for alcohol can be calculated (-1000 × 0.782) = -782. Similarly, the density of pure glycerin is 1.14 and the Hounsfield number is then 114. So a set of five different solutions and air were used for calibrating the HU numbers for different X-ray tube voltages and different filters.

To compare the HU numbers of different iodine solutions another fixture was designed as shown in Figure 10. The numbers in the figure give the relative density of the iodine solutions in mg/ml.

Fig. 9. Hounsfield unit CT phantoms.

Fig. 8. Gd spectrum is in red. To enhance the contrast, Er, Ta or W can serve as K edge

This section describes some of the author's own work on different K edge filters used for

For the CT tests, so called HU (Hounsfield Unit) Phantoms were prepared. One set was made for HU calibration. This set consisted of small bottles filled with different water and alcohol solutions for densities less than water and also with water and glycerin mixtures for densities higher than water. The bottles were pushed into holes in a large polyethylene cylinder as shown in Figure 9. Polyethylene plugs were used for keeping the bottles in place and also for having the same material densities below and above the bottles. However, small holes were drilled in the center of the plugs for letting the extra air out when pushing the plugs in place. These holes contained air, so HU numbers for the air could also be evaluated by using the air pocket images of these holes. We found that for alcohol-water and glycerinwater solutions the X-ray absorption is proportional to the density. So the numbers written

over the bottles of Figure 9 represent the relative densities of the solutions in g/cm3.

As we know, HU numbers are proportional to the absorption (densities) of these liquids; water has HU=0 and air has HU=-1000. HU from 0 to 2000 represent liquids and solids denser than water. For instance, the density of pure alcohol is 0.782 and the approximate Hounsfield number for alcohol can be calculated (-1000 × 0.782) = -782. Similarly, the density of pure glycerin is 1.14 and the Hounsfield number is then 114. So a set of five different solutions and air were used for calibrating the HU numbers for different X-ray

To compare the HU numbers of different iodine solutions another fixture was designed as shown in Figure 10. The numbers in the figure give the relative density of the iodine

filters, which have higher K edges as Gd.

tube voltages and different filters.

solutions in mg/ml.

**6.3 Experimental work with K edge filters** 

mammographic CT applications (Zentai 2011).

Fig. 10. Iodine solution phantoms.

A rotational table was used to rotate the phantoms during CT image sequences. First it was verified that the center (focal spot) of the X-ray radiation was lined up with the center of the X-ray imager and that the imaginary line between these two points crossed the pivot-line of the rotation. This alignment was done with the help of a so called Isocal phantom. This phantom consists of a graphite cylinder with BBs, which are arranged in a spiral pattern alongside the perimeter. A detailed description of this method and the phantom is given by A. Jeung et al (Jeung, Sloutsky et al. 2005). We also processed a norm factor calibration when we used a cylindrical object of the same size and material as the bulk of the CT phantoms but without any holes in it. This calibration method is described in more details by Matsinos et al (Matsinos 2005).

The rotational table was driven by a stepper motor for precision rotational speed. 625 images were taken during one 360o rotation. The rotational speed and the imaging speed were synchronized. From these values the angles were calculated for each transmission

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 147

Fig. 11. Calculated 60kVp X-ray spectra with 0.4mm Iodine and 0.4 mm CsI filter.

Fig. 12. 60 kVp spectra without any external filter and with 0.4 mm I filter are compared

From Figure 12 it is clear that while Al effects only the low energy X-rays, copper shifts the mean energy to higher values and K edge filters (Figure 13) significantly decrease the total

The calculated and measured spectra of the K edge filter materials were compared. Figure 14 contrasts measured and calculated spectra of 0.71mm thick Ce filter. Very good agreement is shown in the 20 - 69 keV energy range. The flux drop of the measured spectra over 69 keV is attributed to the so called heel effect, which was simulated by Monte Carlo method and also measured by Bhat et al (Bhat, Pattison et al. 1999). This effect refers to a falloff of intensity in the X-ray radiation when the electron beam from the cathode hits the anode at a small angle. Because of the thick anode material, part of the X-ray generated deeper in the anode is also absorbed in the anode (in our case tungsten). This is practically the same filtering effect which is shown in Figure 5. It is especially significant above the 69.5 keV K edge of the tungsten anode where this absorption sharply increases causing a sharp

with 100 kVp spectra of 2.24 mm Al and 0.4 mm Cu filters.

flux having only single transmission peaks about the K edge energy.

image required for the CT reconstruction. A modified Feldkamp back-projection (Feldkamp, Davis et al. 1984) algorithm was used for cone beam CT reconstruction developed by John Pavkovich at Varian (Pavkovich 1979; Pavkovich).

Imaging was done on a Varian 4030CB CsI/photodiode flat panel imager. The readout ASICs of the imager were set to dynamic gain mode. In this mode the readout ASICs can automatically switch from a high to a low gain mode during the integration time when the signal level exceeds a given limit. This mode provides about 16.5 bit resolution even when the A/D converter has only a 14 bit range. A detailed description of the functions of this readout ASIC is given in (Roos, Colbeth et al. 2004). Imager calibrations were also performed to assure areas of the image where the gain is in transition still appear smooth and continuous.

Different filters were used to evaluate the effect of filtering on the S/N (Signal to Noise) value of the reconstructed CT images and also for the contrast ratio in comparison to CT images without any beam filtering. Lists of the filters and their thicknesses and the corresponding K edges are given in Table 2.


Table 2. Filters applied during the experiments and their consecutive K edge energies.

The entrance doses for each imaging case were measured with a Radcal dose meter, which was placed in the center of the rotational table, where the geometrical center of the object was during the imaging data collection using the exact same conditions.

It is clear that Al and Cu have K edges at very low energies and in this experiment these materials were used as beam hardening filters, filtering out the low energy X-rays. Cerium, Europium and Neodymium all have K edges slightly over the K edge of iodine so they could provide narrow bandwidth filtering for iodine imaging. For comparison we also used a 0.4 mm equivalent thickness iodine solution as a filter. For the K edge filter and no filter experiments we used 60 and 70 kVp X-ray tube anode voltage and 100 kVp for the Cu and Al filters for higher X-ray flux.

#### **6.4 Measurements, results and discussions**

#### **6.4.1 Calculation and measurement of X-ray spectra**

Spectra of some K edge materials with the given thicknesses were calculated. The calculation was based on the Report 78 Spectrum Processor Program IPEM 1997 (Cranley, Gilmore et al. 1997). The original program contained only absorption spectra of a few materials so additional absorption spectra were obtained from the NIST XCOM website (NIST 2009). Some calculated spectra are given in Figure 11, Figure 12, and in Figure 13.

Figure 11 shows that the CsI scintillator used in the 4030CB flat panel detector has some filtering effects because of the K edge of Iodine contained in the CsI.

image required for the CT reconstruction. A modified Feldkamp back-projection (Feldkamp, Davis et al. 1984) algorithm was used for cone beam CT reconstruction developed by John

Imaging was done on a Varian 4030CB CsI/photodiode flat panel imager. The readout ASICs of the imager were set to dynamic gain mode. In this mode the readout ASICs can automatically switch from a high to a low gain mode during the integration time when the signal level exceeds a given limit. This mode provides about 16.5 bit resolution even when the A/D converter has only a 14 bit range. A detailed description of the functions of this readout ASIC is given in (Roos, Colbeth et al. 2004). Imager calibrations were also performed to assure areas of the image where the gain is in transition still appear smooth

Different filters were used to evaluate the effect of filtering on the S/N (Signal to Noise) value of the reconstructed CT images and also for the contrast ratio in comparison to CT images without any beam filtering. Lists of the filters and their thicknesses and the

> **Neodymium (Nd)**

**thickness 0.4 mm 0.71 mm 0.7 mm 1.0 mm 2.24 mm 0.5 mm** 

**KeV) 33.16 40.44 43.56 48.50 1.56 8.98**

**Europium (Eu)**

**Aluminum (Al)**

**Copper (Cu)**

Table 2. Filters applied during the experiments and their consecutive K edge energies.

was during the imaging data collection using the exact same conditions.

 **Cerium (Ce)**

The entrance doses for each imaging case were measured with a Radcal dose meter, which was placed in the center of the rotational table, where the geometrical center of the object

It is clear that Al and Cu have K edges at very low energies and in this experiment these materials were used as beam hardening filters, filtering out the low energy X-rays. Cerium, Europium and Neodymium all have K edges slightly over the K edge of iodine so they could provide narrow bandwidth filtering for iodine imaging. For comparison we also used a 0.4 mm equivalent thickness iodine solution as a filter. For the K edge filter and no filter experiments we used 60 and 70 kVp X-ray tube anode voltage and 100 kVp for the Cu and

Spectra of some K edge materials with the given thicknesses were calculated. The calculation was based on the Report 78 Spectrum Processor Program IPEM 1997 (Cranley, Gilmore et al. 1997). The original program contained only absorption spectra of a few materials so additional absorption spectra were obtained from the NIST XCOM website (NIST 2009). Some calculated spectra are given in Figure 11, Figure 12, and in Figure 13.

Figure 11 shows that the CsI scintillator used in the 4030CB flat panel detector has some

Pavkovich at Varian (Pavkovich 1979; Pavkovich).

corresponding K edges are given in Table 2.

**Filter parameters** 

**Effective** 

**K edge (in** 

 **Iodine (I)**

Al filters for higher X-ray flux.

**6.4 Measurements, results and discussions** 

**6.4.1 Calculation and measurement of X-ray spectra** 

filtering effects because of the K edge of Iodine contained in the CsI.

and continuous.

Fig. 11. Calculated 60kVp X-ray spectra with 0.4mm Iodine and 0.4 mm CsI filter.

Fig. 12. 60 kVp spectra without any external filter and with 0.4 mm I filter are compared with 100 kVp spectra of 2.24 mm Al and 0.4 mm Cu filters.

From Figure 12 it is clear that while Al effects only the low energy X-rays, copper shifts the mean energy to higher values and K edge filters (Figure 13) significantly decrease the total flux having only single transmission peaks about the K edge energy.

The calculated and measured spectra of the K edge filter materials were compared. Figure 14 contrasts measured and calculated spectra of 0.71mm thick Ce filter. Very good agreement is shown in the 20 - 69 keV energy range. The flux drop of the measured spectra over 69 keV is attributed to the so called heel effect, which was simulated by Monte Carlo method and also measured by Bhat et al (Bhat, Pattison et al. 1999). This effect refers to a falloff of intensity in the X-ray radiation when the electron beam from the cathode hits the anode at a small angle. Because of the thick anode material, part of the X-ray generated deeper in the anode is also absorbed in the anode (in our case tungsten). This is practically the same filtering effect which is shown in Figure 5. It is especially significant above the 69.5 keV K edge of the tungsten anode where this absorption sharply increases causing a sharp

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 149

After good agreement between the measured and calculated spectra was demonstrated, CT scans were carried out. It is noted that the K edge filtered X-ray scans require much longer exposure time per frame than scans with the non-filtered or Al and Cu filtered beams in

CT scans were taken first with the HU phantoms (Figure 9). For each filter and at each kVp, CT reconstructions were carried out and the HU numbers were normalized with the help of the known densities of the HU phantoms. During the normalization an offset and a slope value had to be adjusted at the reconstructed numbers for the best match with the

Next, CT scans were taken of the iodine samples of Figure 10 and the offset and slope calibration numbers from the HU phantom results were applied. A typical CT reconstructed axial view image of the iodine samples with Eu filter is shown in Figure 15. The iodine

It is known that HU numbers depend on the energy and spectrum of the X-ray beam and that is why HU calibrations are always performed using the HU phantoms at each X-ray energy and with each filter. Furthermore, some comparisons were made of how much the HU numbers were different if the calibration values from the no filter case were applied

Fig. 15. A CT reconstructed axial image slice of iodine bottles. Image sequence was taken at 2 fr/s with 1.0 mm Eu filter at 70 kVp\_20 mA continuous X-ray exposure. From top right to

Using the calibrated offset and gain numbers for the iodine samples, HU numbers were obtained for the same iodine filtering as shown in Figure 10. To double check the numbers the air and water (0.00 mg/ml) values were used, which should be close to the nominal - 1000 and 0 HU numbers. In this case the largest error is for the air, where the difference

clockwise the iodine content of the bottles is 0, 0.5, 1.0, 4.0 and 16.0 mg/ml.

between the nominal and reconstructed values was about 20 HU.

instead of applying the calibration values for the proper energy and filter.

**6.4.2 Cone beam measurements** 

order to get comparable dose results.

content increases from top right clockwise.

theoretical values.

decrease above this X-ray energy as can be seen in the measured spectra. However, this decrease would not affect the filter materials K edge behavior since those energies are much lower than the tungsten K edge as shown in Figure 13. Furthermore, most of the measurements with K edge filters were taken only at 60 or 70 kVp X-ray energies, the heel effect does not even show up at these low energies (below the tungsten K edge).

Fig. 13. Simulated spectra for 70 kVp X-ray source and 0.71 mm Ce, 0.7 mm Nd, 1 mm Eu and 0.4 mm I filtering.

Similarly, good agreement between the calculated and measured spectra for the Nd, I and Eu filters was found. Furthermore, our Ce, Nd and Eu spectra calculations and measurements are also very consistent with similar measurements taken by Crotty et al. (Crotty, McKinley et al. 2006).

Fig. 14. Comparison of calculated and measured X-ray spectra after 0.71 mm Ce filter. Both the measured and the calculated spectra were normalized for the maximum flux value.

#### **6.4.2 Cone beam measurements**

148 Imaging of the Breast – Technical Aspects and Clinical Implication

decrease above this X-ray energy as can be seen in the measured spectra. However, this decrease would not affect the filter materials K edge behavior since those energies are much lower than the tungsten K edge as shown in Figure 13. Furthermore, most of the measurements with K edge filters were taken only at 60 or 70 kVp X-ray energies, the heel

Fig. 13. Simulated spectra for 70 kVp X-ray source and 0.71 mm Ce, 0.7 mm Nd, 1 mm Eu

Similarly, good agreement between the calculated and measured spectra for the Nd, I and Eu filters was found. Furthermore, our Ce, Nd and Eu spectra calculations and measurements are also very consistent with similar measurements taken by Crotty et al.

Fig. 14. Comparison of calculated and measured X-ray spectra after 0.71 mm Ce filter. Both the measured and the calculated spectra were normalized for the maximum flux value.

and 0.4 mm I filtering.

(Crotty, McKinley et al. 2006).

effect does not even show up at these low energies (below the tungsten K edge).

After good agreement between the measured and calculated spectra was demonstrated, CT scans were carried out. It is noted that the K edge filtered X-ray scans require much longer exposure time per frame than scans with the non-filtered or Al and Cu filtered beams in order to get comparable dose results.

CT scans were taken first with the HU phantoms (Figure 9). For each filter and at each kVp, CT reconstructions were carried out and the HU numbers were normalized with the help of the known densities of the HU phantoms. During the normalization an offset and a slope value had to be adjusted at the reconstructed numbers for the best match with the theoretical values.

Next, CT scans were taken of the iodine samples of Figure 10 and the offset and slope calibration numbers from the HU phantom results were applied. A typical CT reconstructed axial view image of the iodine samples with Eu filter is shown in Figure 15. The iodine content increases from top right clockwise.

It is known that HU numbers depend on the energy and spectrum of the X-ray beam and that is why HU calibrations are always performed using the HU phantoms at each X-ray energy and with each filter. Furthermore, some comparisons were made of how much the HU numbers were different if the calibration values from the no filter case were applied instead of applying the calibration values for the proper energy and filter.

Fig. 15. A CT reconstructed axial image slice of iodine bottles. Image sequence was taken at 2 fr/s with 1.0 mm Eu filter at 70 kVp\_20 mA continuous X-ray exposure. From top right to clockwise the iodine content of the bottles is 0, 0.5, 1.0, 4.0 and 16.0 mg/ml.

Using the calibrated offset and gain numbers for the iodine samples, HU numbers were obtained for the same iodine filtering as shown in Figure 10. To double check the numbers the air and water (0.00 mg/ml) values were used, which should be close to the nominal - 1000 and 0 HU numbers. In this case the largest error is for the air, where the difference between the nominal and reconstructed values was about 20 HU.

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 151

It is quite obvious that the Cerium filter at 60kVp energy significantly increased the HU number (increased the contrast) of iodine. It shows a 26% improvement. Eu and Nd filters also improved the contrast by 16 and 17% respectively. The Al and Cu filters made the X-ray beam harder, so the iodine contrast considerably decreased when these filters and higher X-ray energies were used. However, it is interesting to note that the iodine contrast enhancement with K edge filters drastically depends on the X-ray tube voltage. When the X- ray energies were increased from 60 kVp to 70 kVp, the Ce filter contrast enhancement effect had nearly gone and it gave about the same contrast as the no filter case (see Table 4). This means that to obtain the maximum HU (contrast) improvement with iodine, the right X-ray tube voltage has to be set for each filter material. Furthermore, the material of the imaged object also has an

effect on beam hardening, which needs to be considered in the optimization process.

**HU(0 mg/ml)**

No filter (60kVp) 866 1.00 Cu filter (100kVp) 501 0.58 Al filter (100kVp) 599 0.69 I filter (60kVp) 718 0.83 Ce filter (60kVp) 1093 1.26 Ce filter (70kVp) 874 1.01 Eu filter (70kVp)) 1007 1.16 Nd filter (70kVp) 1015 1.17

**[HU(16)-HU(0)] filter / [HU(16)-HU(0)] nofilter**

**Filter HU(16 mg/ml)-**

Table 4. HU number difference comparison between the 16 mg/ml iodine and 0 mg/ml (pure water) solutions and the relative HU change for different filters and X-ray energies.

case was still about 2-3 times lower.

After the iodine contrast improvement, S/N (Signal–to-Noise) ratio was optimized. Dose per frame was varied to find the highest S/N. Generally the X-ray flux, after the filters were applied, was an order of magnitude lower than the flux in the no filter case or when the Al or Cu filters were used. To compensate for this effect the exposure time was increased by decreasing the framerate. However, the maximum exposure time per frame was also limited by the heat load limit of the X-ray tube because 625 frames had to be taken for CT reconstruction. Finally, the dose per frame numbers for the filter cases versus the no filter

The S/N ratios were measured at all sample positions and also inside the bulk polyethylene far from the samples. Finally these numbers were averaged for a given measurement to find the (S/N)filter. It is known that for the ideal case, when the electronics noise is negligible, the signal to noise (S/N) value is proportional to the square root of the number of incoming photons (flux). For equivalent image quality the S/N values have to be the same and so we

> ≈ � � �� ��������� �

� � �� ������

� (9)

calculated the filtered dose values corresponding to equivalent S/N (Zentai 2011).

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Table 3. CT reconstruction (HU) values for iodine samples with iodine filter.

Table 3 shows that the HU number increases with increasing iodine content, as expected. The HU slopes for iodine with different filters are plotted in Figure 16. It is shown that higher HU numbers were obtained (better iodine contrast) with Ce, Nd and Eu filters than without using any filter (No-filter case). The K edges all of these materials are above the K edge of iodine as shown in Figure 13. Furthermore, good HU linearity with iodine content was also observed for all cases.

However, if an Iodine filter is used for the iodine samples, lower contrast is obtained than in the no filter case. It is also noticeable that using higher energy X-rays with Al and Cu filters, which filter out the low energy part of the X-ray spectra, the contrast (HU number) further drops. Table 4 summarizes the HU differences with different filters and X-ray energies.

Fig. 16. HU slope with different filters.

Nominal (HU) values

Air -1000 -980.00 0.00 0 20.20 0.50 52.00 1.00 73.76 4.00 219.64 16.00 738.37

Table 3 shows that the HU number increases with increasing iodine content, as expected. The HU slopes for iodine with different filters are plotted in Figure 16. It is shown that higher HU numbers were obtained (better iodine contrast) with Ce, Nd and Eu filters than without using any filter (No-filter case). The K edges all of these materials are above the K edge of iodine as shown in Figure 13. Furthermore, good HU linearity with iodine content

However, if an Iodine filter is used for the iodine samples, lower contrast is obtained than in the no filter case. It is also noticeable that using higher energy X-rays with Al and Cu filters, which filter out the low energy part of the X-ray spectra, the contrast (HU number) further drops. Table 4 summarizes the HU differences with different filters and X-ray energies.

Table 3. CT reconstruction (HU) values for iodine samples with iodine filter.

Reconstructed (HU) values

Iodine content in water mg/ml

was also observed for all cases.

Fig. 16. HU slope with different filters.

It is quite obvious that the Cerium filter at 60kVp energy significantly increased the HU number (increased the contrast) of iodine. It shows a 26% improvement. Eu and Nd filters also improved the contrast by 16 and 17% respectively. The Al and Cu filters made the X-ray beam harder, so the iodine contrast considerably decreased when these filters and higher X-ray energies were used. However, it is interesting to note that the iodine contrast enhancement with K edge filters drastically depends on the X-ray tube voltage. When the X- ray energies were increased from 60 kVp to 70 kVp, the Ce filter contrast enhancement effect had nearly gone and it gave about the same contrast as the no filter case (see Table 4). This means that to obtain the maximum HU (contrast) improvement with iodine, the right X-ray tube voltage has to be set for each filter material. Furthermore, the material of the imaged object also has an effect on beam hardening, which needs to be considered in the optimization process.


Table 4. HU number difference comparison between the 16 mg/ml iodine and 0 mg/ml (pure water) solutions and the relative HU change for different filters and X-ray energies.

After the iodine contrast improvement, S/N (Signal–to-Noise) ratio was optimized. Dose per frame was varied to find the highest S/N. Generally the X-ray flux, after the filters were applied, was an order of magnitude lower than the flux in the no filter case or when the Al or Cu filters were used. To compensate for this effect the exposure time was increased by decreasing the framerate. However, the maximum exposure time per frame was also limited by the heat load limit of the X-ray tube because 625 frames had to be taken for CT reconstruction. Finally, the dose per frame numbers for the filter cases versus the no filter case was still about 2-3 times lower.

The S/N ratios were measured at all sample positions and also inside the bulk polyethylene far from the samples. Finally these numbers were averaged for a given measurement to find the (S/N)filter. It is known that for the ideal case, when the electronics noise is negligible, the signal to noise (S/N) value is proportional to the square root of the number of incoming photons (flux). For equivalent image quality the S/N values have to be the same and so we calculated the filtered dose values corresponding to equivalent S/N (Zentai 2011).

$$\frac{\text{Dose}\_{\text{eq:utilment}}}{\text{Dose}\_{\text{filter}}} \approx \frac{\left(\frac{\text{S}}{\text{N}}\right)^2\_{\text{no:filter}}}{\left(\frac{\text{S}}{\text{N}}\right)^2\_{\text{filter}}}\tag{9}$$

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 153

A further enhancement of K edge filters involves using these filers in combination with counting mode energy resolution detectors mostly in CT applications (Alvarez and Macovski 1976; Roessl, Brendel et al. 2008; Schlomka and et al. 2008; Watanabe, Sato et al.

It is interesting to note that K edge imaging is also used in NDT (non Destructive Testing) applications by Jensen et al (Technology ; Jensen, Aljundi et al. 1997), when they measure the total uranium content in reactor fuel plates using the K edge technique. A further interesting application of K edge imaging is in the analysis of paintings where researchers

This chapter presented different methods used in mammography to improve the contrast between adipose and glandular tissues but especially to find cancerous cells and regions.

First of all the right energy range has to be determined for minimum patient dose with maximum contrast. Dual energy imaging, which uses two images taken at different energies, further enhances the contrast between different tissues and especially when

Monochromatic X-ray beams are ideal for getting high quality images with optimal dose level and avoiding beam hardening artifacts. Moreover, monochromatic imaging can provide phase contrast images with excellent soft tissue contrast. The major drawbacks are that the synchrotrons, which can provide monochromatic beams with enough flux for

Quasi monochromatic X-rays can be obtained by diffraction of X-rays emitted by an X-ray tube onto a mosaic crystal. The output beam has a limited bandwidth, low output flux, and

Another method of generating quasi monochromatic beams uses K edge filters. These filter materials have K edge electrons with bonding energies in the diagnostic X-ray energy range. The material can absorb an X-ray photon, whose energy is equivalent to or slightly higher than the K edge energy, by releasing an electron. The material's X-ray absorption level dramatically increases at or above this energy. As a result, x-rays higher than the K edge energy are suddenly cut off. Using these materials as X-ray filters, a narrow x-ray transmission energy range below the K edge energy can be obtained. One advantage of the K edge filters is that they provide cone beam shaped X-ray radiation rather than fan beam

Iodine and Gadolinium are contrast agents injected into the blood flow. They absorb the x-rays better than body tissues providing an x-ray shadow. They accumulate in the cancerous cells and remain there longer than they remain in the blood stream. This enhanced x-ray absorption provides extra contrast for better visibility of tumors. Using K edge filters X-ray image contrast of the I or Gd absorption can be further increased. I and Gd are frequently used as contrast agents for CT imaging. The experimental part of this paper describes evaluation of a few K edge filter materials using Iodine contrast material. These filters were compared to the non filtered case and also to Al and Cu filters, which provided only X-ray beam hardening. CT scans were performed and the HU numbers

has a fan beam shape. This limits its application only for scanning type imagers.

medical imaging, are very large and expensive sources of X-rays.

verify authenticity and hunt for paintings that have been painted over (Dik 2004).

2008).

**7. Conclusion** 

contrast material is used.

shaped radiation.

Where Doseequivalent is the dose for the filter, which gives the same S/N ratio as the no filter case, and Dosefilter is the dose measured when a given filter was applied. (S/N)nofilter is the signal to noise ratio for the no filter case while (S/N)filter is for the filtered case. The dose per frame difference during the measurement was only 2-3 times lower for the filtered cases so we thought that the above approximation would not introduce significant error. This approximation was double checked with measurements and S/N evaluation at two different dose-rates and for 8 times dose difference the error using the above approximation was less than 10%.

The equivalent dose from equation (9):

$$\text{Dose}\_{\text{equivalent}} \approx \frac{\left(\frac{\text{s}}{\text{N}}\right)^2\_{\text{noffliter}}}{\left(\frac{\text{s}}{\text{N}}\right)^2\_{\text{filter}}} \times \text{Dose}\_{\text{filter}}\tag{1}$$

After calculating the equivalent doses for each filter, these dose values were divided by the no filter case dose and dose equivalent S/N dose ratios were obtained. Both the equivalent doses and dose ratios are reported in Table 5. These numbers tell how much absolute and relative dose is needed when using these filters to get the same S/N value as the no filter case.

Table 5 tells that practically all of the filter materials used in these experiments provide the same S/N ratio at lower dose as the no filter case. From the dose point of view a Cu filter gives nearly the same very low dose as a Eu filter. However, it is important not just to get lower dose but at the same time to provide better contrast resolution and therefore higher HU numbers for iodine as explained previously.


Table 5. Equivalent dose and dose rates.

#### **6.4.3 Some other applications of K edge filters**

In addition to mammography, Iodine and K edge filters are used for other medical x-ray imaging applications, such as lung tumor imaging and, frequently, angiography. (Nyman U Fau - Elmstahl, Elmstahl B Fau - Leander et al.), (Sato, Tanaka et al. 2004; Sato, Tanaka et al. 2007), (Sato, Hayasi et al. 2006).

A further enhancement of K edge filters involves using these filers in combination with counting mode energy resolution detectors mostly in CT applications (Alvarez and Macovski 1976; Roessl, Brendel et al. 2008; Schlomka and et al. 2008; Watanabe, Sato et al. 2008).

It is interesting to note that K edge imaging is also used in NDT (non Destructive Testing) applications by Jensen et al (Technology ; Jensen, Aljundi et al. 1997), when they measure the total uranium content in reactor fuel plates using the K edge technique. A further interesting application of K edge imaging is in the analysis of paintings where researchers verify authenticity and hunt for paintings that have been painted over (Dik 2004).
