In photon and particle radiation therapy treatment planning, single-energy computed tomography (CT) image is commonly used to distinguish materials inside a patient body and to calculate absorbed doses. A CT image is a distribution of linear attenuation coefficient (LAC) of each pixel. To calculate the dose in the patient body, LACs are converted to corresponding mass densities using a conversion table. However, estimated LACs for each pixel can be different from true LACs due to the beam-hardening effect: when polychromatic X-rays pass through a subject, the effective energy of X-rays increases because of the absorption of low energy X-rays. Also, estimated LACs of different materials would be similar and hard to distinguish in single-energy CT image. Thus, a mis-assignment of mass density may occur in single-energy CT measurement.

To make the dose calculation accurately, a Monte Carlo method has been implemented [1] . If the mis-assignment of mass density due to the beam-hardening effect happened, it can lead to significant dose errors: up to 10% error for 6 - 15 megavoltage (MV) photons [2] . Recently, an effective atomic number (Z_eff) attracts attention as an alternative value to LAC.

Commonly, Z_eff measurement is performed by the use of LACs measured by X-rays with two different energies. Thus, the use of synchrotron facilities where can generate monochromatic X-ray is one of the best methods for Z_eff measurement [3] . However, synchrotrons are too large to install in general hospitals. Alternative methods are a photon-counting CT or a fast kVp switching dual-energy CT. Photon-counting CT uses X-ray detectors which can measure the energy of X-ray. However, photon-counting CT has a limitation in counting rate which is less than 0.5 × 10⁶ s⁻¹ in general [4] . Typical number of X-rays coming into a detector in clinical practice is 10⁹ mm⁻²・s⁻¹ when they pass the air only and 10⁶ mm⁻²・s⁻¹ when they pass a thick body [5] . In this stage, photon-counting CT is not practical in view of counting rate problem. Fast kVp switching dual-energy CT requires two projection data on each measurement direction with switching high and low voltages within 10 ms [6] . Two transmission measurements are performed by X-rays with two different averaged energies. The difference between the two averaged energies is, however, not very large: with 80 and 140 kVp, the typical averaged energies at the exit of X-ray tube are 41.4 and 58.9 keV, respectively. According to the transmission direction of a human body, the averaged energy changes and results in beam-hardening artifact in CT image.

To overcome the problems associated with photon-counting CT and dual- energy CT, we have proposed a novel energy-resolved CT by using a transXend detector [7] . The schematic drawing of the transXend detector is shown in Figure 1 of [7] . The transXend detector consists of several segmented detectors aligned in the X-ray incident direction and measures X-rays as electric currents. The X-ray energy distribution is given after analysis using pre-estimated response function (RF). The transXend detector gives photon numbers in arbitrary energy ranges. Since X-rays are measured as electric currents by the transXend detector, there are no problems associated with the counting rate. This transXend detector collects transmission data of an object under study by repeating rotation and transverse movements. Thus, we called this detector the one-dimensional (1D) transXend detector. Yamashita et al. reported that Z_eff of aluminum was measured within 1% error, where the error was defined as (Z_eff − Z)/Z [8] . Kanno et al. also reported that relative error of measured Z_effs of water and acrylic were within 3% [9] . Both studies were performed by the 1D transXend detector.

For the application of two-dimensional (2D) transXend detector for clinical practice in the future, the authors invented stripe absorbers which are placed in front of a flat panel detector (FPD) [10] . The stripe absorbers consist of two kinds of metal ribbons and provides four different X-ray energy spectra. Kanno et al. reported the possibility of 2D transXend detector using a thermo-lumine- scent plate [11] .

As mentioned above, Z_eff measurements for aluminum, acrylic, and water using the 1D transXend detector were conducted previously. In this study, we performed Z_eff measurements for eleven human tissue-equivalent materials by the energy-resolved CT using the 2D transXend detector with a FPD. The eleven materials were grouped into four material categories: LUNG, SOFT TISSUE,

SOFT BONE, and BONE. Z_effs were measured by using the RFs estimated under two different scenarios: With RFs estimated for the same materials with the one used for CT measurements, or with RFs estimated for different materials in each material category.

Spiers et al. proposed the definition of Z_eff for considering the X-ray absorption by human tissue [12] :

Z eff = ∑ k α k Z k 2.94 2.94 , (1)

where α_k is the electron number fraction, and Z_k is the atomic number of element k.

Torikoshi et al. showed the measurement of Z_eff with two different monochromatic X-ray energies using a synchrotron facility [3] . In the energy range for X-ray CT, 80 - 140 keV, the X-ray LAC of element Z for monochromatic energy E can be written as

μ ( E ) = ρ e { Z 4 F ( E , Z ) + G ( E , Z ) } . (2)

Here ρ_e is the electron density, ρ_eZ⁴F(E,Z) is the photoelectric term, and ρ_eG(E,Z) is the scattering term. Thus, atomic number Z can be described by the ratio of LAC:

f ( Z ) = μ ( E a ) / μ ( E b ) . (3)

Since the LAC of elements are summarized as a function of X-ray energy in the table of the National Institute of Standards and Technology (NIST), the term f(Z) can be drawn by plotting the value of μ(E_a)/μ(E_b) as a function of Z [13] . Therefore, the Z_eff can be obtained by using the Equation (3) with measuring LACs at two different X-ray energies E_a and E_b. Since a CT image is the distribution of LAC, the ratio can be obtained by dividing two CT images which were acquired by two different monochromatic X-ray energies E_a and E_b.

When the transXend detector is used for X-ray transmission measurement, the relationship between the measured electric currents and the X-ray energy distribution is expressed in terms of following matrix equation [7] :

( I 1 I 2 ⋮ I m ) = ( R 1 , 1 R 1 , 2 ⋯ R 1 , n R 2 , 1 R 2 , 2 ⋮ ⋮ ⋱ R m , 1 ⋯ R m , n ) ( Y 1 Y 2 ⋮ Y n ) . (4)

Here I_i (i = 1, m) is the electric current value measured by i-th segmented detector, Y_j (j = 1, n) is the number of X-rays in the energy range E_j , and R_i,j is the RF of the i-th segment detector in the energy range E_j. The X-ray energy distribution is obtained by solving Equation (4) using an unfolding code, such as SAND II [14] . In the unfolding process, the number of energy ranges and the widths of energy ranges can be assigned according to the materials of interest. More detailed information is described in elsewhere [15] .

For the clinical application of the transXend detector, a 2D transXend detector should be developed. To make the transXend detector system two-dimensional, we used a FPD and stripe absorbers which consist of two different absorbers A and B in a lattice shape, as shown in Figure 1 [9] . With the stripe absorbers placed in front of the FPD, four different regions, (a)-(d), can be made, as shown in Figure 1. In region (a), X-rays enter to the FPD without passing two absorbers. Subsequently, in region (b), (c), and (d), X-rays passed through the absorber A, B, and A + B, respectively. We used 1 mm-wide and 0.1-mm-thick tin and copper for absorber A and B, respectively. Calculated X-ray spectra arriving at FPD pixels in each region are shown in Figure 2. Considering the four regions as one pixel, each region has the role of segmented detectors. X-ray energy distribution can be acquired for the 2D position on the FPD by unfolding electric currents measured by the four regions. The employed FPD was Remote RadEye2 (Teledyne Rad-icon Imaging, Sunnydale, CA, USA) with pixel matrix of 1024 × 1024 pixel² (active area 49.3 × 49.2 mm²). The pixel size of photodiode was 48 × 48 μm². Incident X-ray photons are absorbed by a Gd₂O₂S scintillator plate and scintillation photons are detected by a 2D CMOS photodiode array.

Eleven RMI rods (Gammex, Middleton, WI, US) were used in this study, as summarized in Table 1. Diameter and height of each rod was 28 mm and 70 mm, respectively. RMI rods were often used as the calibration materials of CT

number―mass density conversion table for the dose distribution calculation in radiotherapy treatment planning. In such calibration, each rod was inserted to a 330-mm-diameter and 50-mm-height RMI phantom and all rods were scanned simultaneously. In this study, however, each rod was scanned individually to measure its Z_eff for avoiding the fan-beam effect.

Experimental set up was shown in Figure 3. As described in the previous paper, RF measurement for the phantom material was necessary prior to CT measurement [7] . Used materials for RF measurement were the same ones with the phantom for CT measurement: slabs of different thicknesses were prepared for each material in the phantom. We, however, transmission data for the RF estimation by a numerical calculation using Lambert-Beer’s law since each rod was uniform:

I = I 0 exp ( − μ t ) . (5)

Here I is photon number transmitted through a material with LAC, μ, with thickness t, I₀ is incident photon number. Transmission data was calculated for each rod material with thicknesses ranging from 0 to 30 mm at intervals of 5 mm. I₀ was normalized to the measured current induced by X-rays which passed the air only. In transXend analysis, RF data was interpolated by 1 mm interval. Scatter X-rays were not considered in the calculation.

After calculating transmission data for the RF estimation, each rod was scanned from one direction by the X-rays. Employed X-ray tube was ERESCO MF4 (GE Sensing & Inspection Technologies, Ahrensburg, Germany) with a tungsten target and built-in filters made from 0.8-mm-thick beryllium and 2-mm-thick aluminum. The X-ray tube was placed 1000 mm away from the FPD. The X-ray tube operating conditions were 120 kV for tube voltage, 2.3 mA

for tube current, and 1 s for exposure time. Since each rod was axial symmetry, projection data for each rod was duplicated 359 times to make 1˚ step data. Source-to-axis of the phantom distance was 850 mm.

Six energy ranges were defined for obtaining X-ray energy distribution, as shown in Table 2. Since almost no X-rays with the energy under 15.0 keV entered into the FPD, those X-rays were excluded from the analysis. The X-rays in the energy range E₂: 35.0 - 36.0 keV and E₅: 65.0 - 66.0 keV were used as pseudo-monochromatic X-rays. Measured currents in the center column of the FPD were unfolded by SAND II code to obtain energy distributions. Number of X-rays in each energy ranges were estimated for each projection. With Y₂ and Y₅, CT images were reconstructed by maximum likelihood-expectation maximization method [16] . Iterative number was 30 times which was optimized prior to the measurements. With the LAC data table of NIST, Z-μ(E₂)/μ(E₅) relationship can be drawn as Figure 4. CT images of μ(E₂) and μ(E₅) for each rod were converted to a Z_eff image using Figure 4.

In previous studies [7] [8] , the RF was estimated by using the same material with the one of phantom for CT measurement. In this study, we demonstrated two different analysis scenarios. In the first scenario, we employed the RF estimated for the same material as the one of the phantom for CT measurement (self-RF scenario). In the second scenario, we employed the RF estimated for the different material than the one of the phantom for CT measurement (cross-RF scenario). The purpose of the cross-RF scenario was to determine the representative rod materials in each material category. Reduction of the number of materials for RF estimation would widen the application of energy-resolved CT using 2D transXend detector. Mean and standard deviation (SD) of Z_eff for each rod material was calculated in 10 × 10 mm² region-of-interest on Z_eff image.