Discussion

Filter designs and their results were validated in quantitative analysis by three quantitative indices: mean energy ratio, contrast variation ratio, and exposure efficiency by Monte Carlo simulation. The selection of filter materials, filter thickness, and tube potential is discussed below.

Filter materials are selected as Al (Z=13), Cu (Z=29), I (Z=53), Ba (Z=56), Ce (Z=58), Gd (Z=64), Er (Z=68), and W (Z=74) for obtaining the monochromatic X-ray beam. Al is widely used as an intrinsic filter in X-ray imaging system to minimize low energy X-ray photons, which cause the skin dose to the patient. Cu is used as an intermediate filter for the DE imaging operating sandwich detector system. I and Ba have been used in the previous work for the enhancement of I or Ba materials in the phantom due to the matching for K-edge energies of contrast medium. Ba, Ce, Gd, and Er are rare-earth materials, and the research of X-ray beam design included these due to their K-edge energy within the diagnostic range. W is used as a collimator in gamma camera system, which is used in this study for matching K-edge energy of tungsten target of the X-ray source. In monochromatic imaging, since beam energy is generally up to 70 keV, we used from Al to W (K-edge energy of 69.63 keV) material.

First, we found appropriate filter thickness for generating monochromatic X-ray beam. The tube loading is considered to prevent usage of a thicker filter. An effective thickness is 7 HVL, according to the results of mean energy evaluation. The calculated mean energy between 7 HVL and 8 HVL is similar for all filter materials. The mean

energy by using Al and Cu filters was increasing because their K-edge energies were 1.56 and 8.98 keV, respectively. Since X-ray source generates the photon energy more than 20 keV, K-edge energies of Al and Cu did not affect production of the monochromatic X-ray beam, alternatively, the mean energy increases with filter thickness increasing. Since the mean energies of I, Ba, Ce, Gd, Er, and W are close to the K-edge energies of their materials at 7 HVL thicknesses, filters except for Al and Cu for generating monochromatic beam are possible in 7 HVL thickness. Mean energy is related to the beam hardening effect. Therefore, the accuracy of measurement increases as mean energy approaches K-edge energy of filter.

The range of tube potential is decided from 40 to 90 kV. With increasing the tube potential, the energy spectrum of X-ray beam is a broad band window. Since the maximum K-edge energy of tungsten materials is 69.53 keV, high tube voltage is not sufficient in this study. In diagnostic X-ray spectrum, the dominant interaction is photoelelctric effect and Compton scattering [32–36]. The Compton scattering is expected with increasing tube potential within the range from 30 to 150 keV [34–36].

Therefore, we limited the tube potential to 90 kV.

At 7 HVL of Al, Cu, I, Ba, Ce, Gd, Er, and W and tube potentials ranging from 40 to 90 kV, we evaluated mean energy ratio, contrast variation ratio, and exposure efficiency. Mean energy ratio is the ratio of pre-mean energy to post-mean energy through the phantom. Overall results indicated that filtered X-ray beams performed better than in case of no filtration at equal tube potentials. Mean energy ratio of Al and Cu is almost constant over all tube potentials. This phenomenon is due to the low K-edge peak energy of Al and Cu. This means that the linear attenuation coefficients of

Al and Cu reduced exponentially at all tube voltages. The trend of alternations of I, Ba, Ce, and Gd is remarkable in mean energy ratio. Mean energy ratio of I is nearly 1 in a range from 40 to 50 kV. However, mean energy ratio of I is increasing from 50 to 70 kV, and then reducing from 70 to 90 kV. This effect is due to the increasing spectral tail over the edge energy of I filter with increasing tube potential. However, the K-edge effect of I filter was reduced when increasing the tube potential above 70 kV. The trend is similar to those for K-edge energies of Ba, Ce, and Gd filters.

With respect to contrast variation ratio, I, Ba, and Ce, outperformed other filters.

However, the appropriate tube potential to improve contrast is limited by filter materials. Contrast variation ratios of Al and Cu are reduced with increasing tube potential. The enhancement of image contrast by using monochromatic beam was assessed for this study with several filter materials at different tube potentials.

Therefore, it is expected that the monochromatic beam can improve the image contrast.

The trend of exposure efficiency of filter was reduced with increasing tube potential.

The exposure efficiency with changing tube potential illustrates that more filtration for a given tube potential yields better SNR²/exposure. In exposure efficiency, I, Ba, Ce, and Gd filters outperformed other filter materials. The exposure efficiency is maximized at 40 kV for all filter materials. The exposure efficiency of I, Ba, Ce, and Gd were maximized from 40 to 50 kV tube potentials. From the results of exposure efficiency, a dose reduction effect for patients is expected.

According to results of quantitative indices from the simulation study, appropriate filters for TE X-ray beam were I, Ba, Ce, and Gd filters, and resultant tube potentials were 50, 60, and 70 kV, respectively. Therefore, we selected I, Ba, and Gd filters and

50, 60, and 70 kV tube potentials, respectively for TE X-ray imaging. To investigate the spectrum of simulation results of the triple-energy beam, three spectra were measured with a photon-counting detector. The experimental results of three beams were matched to simulated spectra. The results indicated their peak energies is well matched for their K-edge peak energies. However, experimental data on low energy parts of the spectra were not matched to the simulation study. This effect is due to the charge-sharing of the photon-counting detector [37–41].

From the TE X-ray beam, three materials decomposition was performed for I, Al, and PMMA. Three materials can be decomposed by thickness density maps, which require the information of linear attenuation coefficients of I, Al, and PMMA.

Therefore, the linear attenuation coefficients were obtained with attenuation coefficient maps from simulation for the proposed method, and the results were compared to the results obtained with the photon-counting method. The results of linear attenuation coefficient were well matched to the known values for K-edge energy of the filter materials. The results of thickness density map for I, Al, and PMMA indicated that the decomposed image acquired with the proposed method was similar to the decomposed image obtained with the photon-counting method.

In this chapter, we investigated appropriate filter materials, filter thickness, and tube potentials. The quantitative evaluations were performed by the image metrics of mean energy ratio, contrast variation ratio, and exposure efficiency by using the filter materials, the filter thickness, and the tube potentials. Filter thickness of 7 HVL was used in this study for considering efficiency. For generating monochromatic X-ray beam, filters having K-edge energy within the tube potential range was effective for

enhancing contrast, shaping narrow beam, and reducing dose to patient. Therefore, the TE monochromatic X-ray beam was well validated with simulation study by verifying the quantitative image metric.

Chapter 4: Experiment with the designed