5. Quantitative Computed Tomography Using Dual-Energy Monochromatic X-rays

Masami Torikoshi, Takanori Tsunoo, Makoto Sasaki, Masahiro Endo, Yutaka Noda, Kentaro Uesugi¹, Maoto Yagi¹ and Kazuyuki Hyodo² (¹Japan Synchrotron Radiation Research Institute, Hyogo, Japan; ²High Energy Accelerator Research Organization, Tsukuba, Japan)

Keywords: CT, electron density, synchrotron radiation, monochromatic x-rays

Monochromatic x-ray computed tomography (CT) at two different energies provides information about electron density of human tissue without ambiguity due to the beam hardening effect. This information makes the treatment planning for heavyion radiotherapy more accurate. We have started a feasibility study on the dual energy x-ray CT by using synchrotron radiation. The first goal of this study was measurement of the electron density with precision of less than one percent. A translate-rotate scanning mode CT system was developed for quantitative measurement in order to clarify what precision in the measurement was achieved in the dual energy x-ray CT.

A photon attenuation coefficient is approximately described by the following equation:

where the first term denotes a photoelectric effect, the second term denotes a scattering effect and _e denotes the electron density of an object. Solving simultaneous equations with respect to µ(k₁) and µ(k₂) with the aid of an iterative calculation gives an atomic number Z (we call it an effective atomic number) and the electron density _e.

Experiments were carried out at BL20B2 of SPring-8 by using high intensity x-rays of 40 keV and 70 keV that were obtained by monochromatizing synchrotron radiation. The translate-rotate scanning mode CT system consisted of an x-ray detector with a plastic scintillator, a rotating table and a sliding stage. An ionization chamber, upstream from the rotating table, counted the number of the incident photons. The plastic scintillator was connected with a photo-multiplier (Hamamatsu Photonics R3550). The output current of the detector was proved to be proportional to the x-ray intensity from 10⁴ ph/s to about 10⁹ ph/s. The rotating table on which a sample was set was moved horizontally in a step of 1 mm. Data were taken every step by being exposed to the x-rays for a few hundred ms. At the end of the stroke, the object was rotated by 0.8°. This motion was repeated until the rotation angle became 180°.

Several samples were used: phantoms equivalent to human tissue produced by Kyoto-kagaku Co. (1) soft tissue (SZ207), (2) adipose tissue (SZ49), (3) cartilage bone (SZ160) and (4) compact bone (BE-T), and aqueous solutions of dipotassium hydrophosphate K₂HPO₄. An ellipsoidal vessel with the dimensions of 16 cm × 12 cm filled with water that contained smaller vessels filled with the solutions was used for simulation of a human head.

In order to verify the electron densities measured with the dual energy x-ray CT, (i) we compared them with the theoretical values for the solutions of the head phantom, and (ii) we measured the electron densities of the tissue phantoms by a different method using carbon ions for a second comparison. The carbon ions entered a water column after they penetrated a sample, they have a range in water. The range was measured, both with and without the sample in the front of the water column. The difference of the ranges gave information on the stopping power of the sample for carbon ions. Therefore, the electron density of the sample can be derived from the difference of the range using the Bethe-Bloch formula. The mean excitation energy for water was 75 eV quoted from ICRU 37, and it was used for the tissue phantoms except for BE-T. The mean excitation energy for BE-T was calculated from values listed in the catalogue of Kyoto-kagaku Co. and was 108 eV. In addition, aluminum samples were used to evaluate the precision of this method. Comparison of the aluminum electron density with the theoretical one suggests that the precision of this method is less than 0.5%.

The images of the head phantom reconstructed based on the electron density and the effective atomic number are shown in Figs. 5(a) and 5(b), respectively. There are noticeable differences between these images. The acrylic plastic of the vessel wall has a high electron density, but its effective atomic number is relatively small. This shows that the acrylic plastic has the highest density among materials of the head phantom, and it consists of relatively light elements. The K₂HPO₄ solutions have less electron density than the acrylic plastic but their effective atomic numbers are higher due to the existence of heavier elements such as potassium and phosphate. For the K₂HPO₄ solutions, the average ratio of the difference between the electron density and the theoretical value to the theoretical value is 0.25 %. In the case of the tissue phantoms, the ratio is 0.97 %. The results of the comparison are summarized in Fig. 6.

We conclude that:

(1) the first goal of this study has been almost achieved: electron density measurement with the precision of less than 1 %;

(2) the image of electron density and the image of effective atomic number describe different features of the material.

The information on the electron density and on the effective atomic number of a human tissue may open an avenue for new medical diagnoses.

Publications:
Torikoshi M., Tsunoo T., Endo M., Noda K., Kumada M., Yamada S., Soga F. and Hyodo K.: J. Biomed. Opt. 6, 371-377, 2001.

Fig.5(a). The image of the head phantom based on the electron density. As the color becomes lighter, the electron density becomes higher.

Fig.5(b). The image of the head phantom based on the effective atomic number. As the color becomes lighter, the atomic number becomes larger.

Fig.6. Comparison of the electron densities with the theoretical values for the K2HPO4 solutions and with the values measured in the method of stopping powers for the tissue phantoms.