Introduction and limitation of dual-energy imaging method

1.3.1 Energy subtraction

In DR imaging, energy subtraction, equivalent thickness, and synthetic method were used for enhancement of bone and tissue. The linear attenuation coefficient

)

(E can be represented as a function of energy (E) that is a combination of photoelectric absorption and Compton scattering within the diagnostic energy ranges [21]. Hence, above the K-edge of a material for diagnostic radiography, the linear attenuation coefficient can again be described by a set of basis functions [22, 23].

These basis functions are used to produce an energy-selective image such as bone and tissue with a dual-energy technique in accordance with an empirical model due to the characteristics of the bremsstrahlung x-ray spectrum [22]. Based on the previously mentioned energy subtraction method, a dual-energy subtraction image was derived from the difference between logarithmic intensity images utilizing low and high energy.

In case of a monoenergetic source, no beam hardening can occur because the X-ray have only one energy. Therefore, the X-ray intensity can be measured at the detector and described as:

e

x

I

I 

₀ ^ , (1.1)

where I₀ depicts the incident X-ray intensity,  is the value of a linear attenuation coefficient over the material thickness x [24]. If an object includes the soft-tissue thickness t_s and bone thickness t_b, with the low- and the high-energy beams (energy level for i = 1 is 70 kVp and for i = 2 is 140 kVp), the log transmission measurements

) can be given by the ratio of low- and high-energy linear attenuation coefficients:

),

Therefore, the equations for the energy subtraction of bone and tissue images are:

),

In the case of polychromatic X-rays,  is calculated as the spectrum. We generated the spectrum from the tungsten anode spectral model using interpolating polynomials (TASMIP) code to calculate the weighting factors w_s and

wb [26, 28]. The ratios of linear attenuation coefficients (i.e., weighting factors) in equations (1.4) and (1.5) can be determined by the exposed dual energy spectra. The mass attenuation functions of bone and soft tissue were computed from the NIST data [27] within the diagnostic energy range.

1.3.2 Equivalent thickness and synthetic methods

According to the previous work, photoelectric effect and Compton scattering are dominant at a diagnostic x-ray range. These two effects can be represented by two set of basis functions f₁

(

E

)

and f₂

(

E

)

:

In projection radiography, the relative detected X-ray photon flux is defined by



^

^



 a x y z ds

A

_{i i}

( , , )

i  1 , 2 .

(1.12)

Because aluminum is close to bone whereas PMMA behaves like soft tissue, the two basis functions f₁

(

E

)

and f₂

(

E

)

can be replaced with energy dependence of these two materials.

Thus equation (1.11) is rewritten as

al (1.13) can be expressed as following

,

2

,

0.4, 0.5, and 0.6 cm. Thus we construct the matrix equation for aluminum and PMMA thickness from equation (1.18) and (1.19). Then the a coefficients can be calculated by using inverse matrix from the equations. The synthesized monochromatic image can be formed from the equivalent thickness information, which is plotted on the basis

projection plane with characteristic angles. The equation with the two vectors is aluminum to a unique equivalent thickness of a material having a characteristic angle

. The angle  was determined by the equation of Lehmann et al. [23] as following

From this equation (1.21), it is possible to cancel any given material from the image and fill the resulting cavity with any other given material. It is called with material look-alike, which is within the synthesized monochromatic region and able to achieve material cancellation.

The phantom images are displayed in Figure 1.7 for the three methods and two materials. The comparisons of profiles of the phantom images are plotted in Figure 1.8.

When the results acquired with the cylindrical phantom were compared, the relative intensity of aluminum with the equivalent thickness and the synthetic methods was 2.17 times higher than that obtained with the energy subtraction method in terms of the

profiles in Figure 1.8. The relative intensity of PMMA achieved with the synthetic method was 5.69 times better than that achieved with the energy subtraction method, as shown in figure 1.9. Although using the equivalent thickness method improved the relative intensity of the PMMA, the method resulted in aluminum shadows in the PMMA image. In contrast, the synthetic method can effectively remove the aluminum hole shadows and enhance the PMMA intensity, as shown in Figure 1.9.

However, theses method for DE imaging such as energy subtraction, equivalent thickness, and synthetic method were limitation in projection error in case of superimposed three materials. Since the energy subtraction and the equivalent thickness are assuming that the two basis materials for separating bone and tissue image, the methods are limited for discriminating three materials. Synthetic method produces a certain material by synthesize with characteristic angle two basis materials such as aluminum and PMMA. However, the synthetic method was also generated from two basis materials similar to equivalent thickness, and the method need complex imaging process due to the polychromatic X-ray energy. Therefore, the monochromatic triple-energy (TE) beam is needed to reduce projection error, maximize image contrast, and minimize radiation dose.

Figure 1.7 Phantom images acquired with energy subtraction, equivalent thickness, and synthetic methods. (a) and (b) were obtained with 70 and 140 kV, respectively.

Aluminum images were acquired with the energy subtraction (c), equivalent thickness (e), and synthetic methods (g). PMMA images were acquired by the energy subtraction (d), equivalent thickness (f), and synthetic methods (h). The arrow in (a) indicates the profile detailed in Figure 1.8 and 1.9.

Figure 1.8 Comparison of the profiles in the aluminum image acquired with the energy subtraction, equivalent thickness, and synthetic methods.

Figure 1.9 Profiles of the PMMA image acquired with the energy subtraction, equivalent thickness, and synthetic methods.

문서에서 Design and characterization of the multi-energy monochromatic X-ray beam in X-ray imaging systems (페이지 24-34)