HEAVY ion therapy is an advantageous modality over the

Measurement of electron density and effective atomic number using dual-energy x-ray CT T. Tsunoo, M. Torikoshi, Y. Ohno, M. Endo, M. Natsuhori, T. Kakizaki, N. Yamada, N. Ito, N. Yagi, and K. Uesugi Abstract The information on the electron densities of bodies is important for the treatment planning of radiotherapy. In order to obtain the electron densities directly, we have developed dual-energy x-ray computed tomography(ct) using synchrotron radiation. It was experimentally proved that the electron density was deduced with about 1 % accuracy from two linear attenuation coefficient. However, the linear attenuation coefficient were measured by a few percent lower than the theoretical ones. We assumed that the less accurate linear attenuation coefficients were caused by the influence of scattered radiation and the non-linearity in the response of the detector. In comparison of the scattered radiation to the simulation results, the scattered radiation contributed at the most 0.5 % to the linear attenuation coefficients. Correcting the non-linearity in the detector response functions, the values of linear attenuation coefficient were improved drastically. I. INTRODUCTION HEAVY ion therapy is an advantageous modality over the other radiotherapy in terms of safety delivering high doses together with high cell-killing ability.[1] One of the most important factor in the treatment planning is to estimate the range of heavy ion in the body accurately. The range of heavy ion is approximately proportional to electron density of an object. At present, the electron densities distribution in a patient are deduced from CT numbers which are obtained from a conventional x-ray CT due to a one-to-one correspondence is postulated between the electron density and CT number. [2][3][4] However, the CT number could have uncertainty due to the beam hardening effect and the approximation of linear correction between electron density and CT number. In the treatment planning, the target volume is defined in consideration of the uncertainty. In 1970s, dual-kv x-ray CT and Compton x-ray CT were studied and developed to measure the electron density.[5][6][7] However, no practical technique has been realized for the methods except for densitometry. We suppose that there were difficulties in obtaining high accuracy and good quality of images We have proposed dual-energy x-ray CT to directly acquire the information on the electron density using synchrotron radiation(sr) to improve the accuracy of the measurement.[8][9] The electron density is derived from linear T. Tsunoo, M. Torikoshi, Y. Ohno, and M. Endo are with National Institute of Radiological Sciences, Chiba 263-8555, Japan M. Natsuhori, T. Kakizaki, N. Yamada, and N. Itoh are with Kitazato University, Aomori 034-8628, Japan N. Yagi and K. Uesugi are with Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, Japan attenuation coefficients measured at two energies in the dualenergy x-ray CT. The mono-energy x-rays are obtained by monochromatizing SR. This method is in principle free of the beam hardening effect. We carried out the experiments of the dual-energy x-ray CT using SR at SPring-8. In this paper, we introduce the dual-energy x-ray CT briefly and present the problems on the quantitative measuremnet. II. CONCEPT OF DUAL-ENERGY X-RAY CT A linear attenuation coefficient µ of a material can be distinguished from photoelectric absorption, coherent scattering, and incoherent scattering in the diagnostic range of energy from 30 to 150 kev. Jackson and Hawkes proposed a convenient formula for calculation of the linear attenuation coefficient which is valid for from light elements to medium elements at less than a few hundred KeV [10]. Employing the formula, it is simplified as follows, µ(e) =ρ e (Z 4 F (Z, E)+G(Z, E)), (1) where ρ e is the electron density, Z is the atomic number, ρ e Z 4 F (Z, E) and ρ e G(Z, E) are the photoelectric absorption term and the scattering term, respectively. The simultaneous equations are formed using the linear attenuation coefficients for two energies E 1 and E 2. Solving the simultaneous equations, Z and ρ e can be obtained as follows, Z 4 = µ(e 2)G(Z, E 1 ) µ(e 1 )G(Z, E 2 ) µ(e 1 )F (Z, E 2 ) µ(e 2 )F (Z, E 1 ) (2) and ρ e = µ(e 1 )F (Z, E 2 ) µ(e 2 )F (Z, E 1 ) F (Z, E 2 )G(Z, E 1 ) F (Z, E 1 )G(Z, E 2 ). (3) Eq.(2) can be solved iteratively. Once Z is obtained, then the electron density can be derived from Eq.(3). We call this Z an effective atomic number. III. PURPOSE It was experimentally proved that the accuracy of electron density measured in the dual-energy x-ray CT achieved about ±1 % or less.[8] Examples of the electron densities measured with a two dimensional(2d) detector are shown in Fig.1. The samples were water, ethanol, and solution of K 2 HPO 4 with concentration of 1 to 5 %. It shows that all values agreed with the theoretical values within ±1 %.[11] However, in the case of water, the linear attenuation coefficients from which the electron density is derived as shown in the previous section

[ 10 +23 ] 40 m 210 m the distance between an object and the detector Measured electron density (/cm 3 ) 3.5 3.0 C 2 H 5 OH H 2 O K 2 HPO 4 1% K 2 HPO 4 2% K 2 HPO 4 3% K 2 HPO 4 4% K 2 HPO 4 5% +1 % line 1 % line Si(311) 2 monochromator Si(311) 2 monochromator ionization chamber Ar 1 atm hutch 1 (a)the CT scanning geometry. ionization chamber Ar 1 atm 500 mm hutch 1 Al absorber t 0~93 mm rotation table object (b)the linearity measurement of the 2D detector. hutch 3 hutch 3 2D detector 2D detector 3.0 3.5 [ 10 +23 ] Theoretical electron density (/cm 3 ) Fig. 1. The comparison between the measured electron density and theoretical one. Ethanol, water, K 2 HPO 4 solutionof1%,2%,3%,4%,and5%are displayed. Each error bars are standard devision in the ROI(144 pixels). have been measured lower than the theoretical values by about 1 to 3 %. To obtain highly accurate electron density, it is essential to make more accurate measurement of the linear attenuation coefficients. Generally, the most likely cause for degrading the accuracy of linear attenuation coefficient is the influence of scattered radiation.[12] In a conventional CT, the CT number deteriorate due to the scattered radiation such as the cupping effect. Another candidate of the cause to lower the accuracy is nonlinearity such as saturation in a response of the detector. The transmitted intensity I and the intensity of incident photon I 0 are necessary for the CT reconstruction. The projection data p is expressed as follow: p = ln I I 0 = ln exp ( ) µ(t)dt = µ(t)dt (4) where µ is a linear attenuation coefficient, and t is the length passed through an object. If the response of the detector is not linear, the proportionality between I and I 0 is not guaranteed. It might give rise to incorrect linear attenuation coefficients. We carried out two kinds of experiments to verify the causes of less accurate linear attenuation coefficients and to search the way for improvement. IV. EXPERIMENTS A. Experiment for influence of scattered radiation The experimental setup for monochromatic x-ray CT scanning is shown in Fig.2(a). Experiment was carried out at the bending magnet beamline of BL20B2 in SPring-8. The SR was monochromatized with a double crystal monochromator of Si(311). The dimension of the beam at about 210 m downstream from the light source was horizontally about 220 mm and vertically about 5 mm. The monochromatic x-rays of 40 and 70 kev were used for the low energy scanning and the Fig. 2. system in the beamline BL20B2 at SPring-8. high energy scanning, respectively. The monochromator was detuned in order to exclude the higher order harmonic waves. The ionization chamber was set to measure the number of incident photons in the first experimental hutch at 40 m from the light source. The 2D detector was set in the third experimental hutch. The element of 2D detector consist of agd 2 O 2 S:Pr scintillator and a photodiode. The number of elements are 256 96, and each size is 0.894 1.024 mm 2. The object-detector distances were 385, 1286, 2099, and 3005 mm. The sampling angle was 0.8 and the number of total views was 450 in 180 scanning. Two sets of 50 images without an object(i 0 -image) were acquired before and after the scanning respectively. All pixel values of each image were divided by the ionization chamber s counts. The water phantom of φ 100 mmwasusedasthesample. B. Measurement of response of 2D detector Fig.2(b) shows the setup for the measurement of the response of the 2D detector. The I 0 images were taken at the various beam intensities adjusted by the thickness of the absorber located about 500 mm downstream of the ionization chamber in the first hutch. Alminium(Al) plates with the purity of 96 to 98 %(JIS-A5000) were used as the absorbers. Since the distance between the absorber and the 2D detector was about 150 m, we neglected the influence of scattered radiation from the absorber. The precision of the thickness were about ±0.02 mm. The thickness of the absorbers was selected from 3 to 93 mm in the unit of 3 mm. The absorber was perpendicular to the beam direction. At each absorber thickness the 50 images were acquired. V. RESULT A. Measurement of influence of scattered radiation The linear attenuation coefficients of water were plotted against the object-detector distance in Fig.3. The linear attenuation coefficients were averaged over all pixels in a rectangular region of interest(roi) indicated in Fig.4. Each error bar is standard devision of all pixels in the ROI.

Linear attenuation coefficient (/cm) Linear attenuation coefficient (/cm) 0.27 H 2 O 40 kev: 0.268 /cm line 0.265 0.26 fan beam reconstruction parallel beam reconstruction simulation results 0.255 0 1000 2000 3000 The object detector distance (mm) 0.195 0.190 (a)the result as 40 kev. H 2 O 70 kev: 0.193 /cm line fan beam reconstruction parallel beam reconstruction simulation results 0.185 0 1000 2000 3000 The object detector distance (mm) (b)the result as 70 kev. Fig. 3. The relationship between the object-detector distance and measured linear attenuation coefficient. Each error bars are standard devision in the ROI. The closed circles were the results reconstructed by using a parallel beam reconstruction algorithm with the Shepp-Logan filter function. We anticipated that the resultant attenuation coefficient increasing and approaching to the theoretical value with the object-detector distance increasing, because it was predicted that the contribution of scattered radiation became smaller as the distance became longer. However, they decreased as the object-detector distance became longer. This showed that in the long distance cases, divergence of the SR beam was not negligible in reconstructing the images. The projection image of the water phantom was lightly expanded as the object-detector distance became longer. The fan beam reconstruction algorithm was applied to the projections. The results were shown with open circles in Fig.3. The parameters of the source-object distance and the objectdetector distance are necessary for the fan beam algorithm to adjust the expansion of the projection image in additional the ROI 44x44 Fig. 4. The CT image which the object is φ 100 mm water phantom, energy is 40 kev, and the object-detector distance is 1280 mm. The ROI is 44 44 pixels which each size is 0.893 0.893 mm 2. parameters of the parallel beam algorithm. The source-object distance of 210 m was used. The object-detector distance was as mentioned above. The results using the fan beam algorithm showed increment in the linear attenuation coefficients with the object-detector distance. The difference between the attenuation coefficients measured at the shortest distance and the longest distance is about 0.5 % for 40 kev and about 0.3 % for 70 kev. B. Measurement of response of 2D detector As shown in Fig.5, the beam intensity N at the 2D detector is expressed as following, N = N 0 exp( t µ Al (E)), (5) where N 0 is the beam intensity before the absorber, t is the thickness of the absorber, µ Al is the linear attenuation coefficient of the absorber, and E is beam energy. Since the ionization chamber counts are proportional to the beam intensity, we can use the counts as N 0. In Fig.5, 16-bit AD values of several detector elements are plotted against the beam intensity estimated by Eq.(5). Each AD values was averaged over those measured 50 times sequentially. The error bars of each data is standard devision. The results of three detector elements for 40 kev x-ray are indicated in Fig.5(a), and those for 70 kev x-ray are in Fig.5(b). The dotted lines are the best fitted linear function to the data, and the solid lines are the best fitted power function in a type of ai α +b mentioned in the next section. The power terms α of the function for 40 kev x-ray results range from 0.965 to 0.988, and those for 70 kev x-ray range from 0.979 to 0.990. VI. DISCUSSION A. Influence of scattered radiation Using the fan beam reconstruction algorithm, the measured linear attenuation coefficient(µ) of water for 40 kev x-ray was 2.1 % smaller than the theoretical value at the objectdetector distance of 385 mm and was 1.8 % smaller than that at 3005 mm. It seemed that the 0.5 % difference between both values measured at 385 mm and at 3005 mm was due to the influence of scattered radiation. To reveal the influence of the scattered radiation on µ at various object-detector distances, scattered radiation were simulated and superimposed on simulated CT data. The µ s were reconstructed in a parallel beam

2D detector output 2D detector output 10 4 10 3 40 kev x:250,y:49 x:126,y:49 x:42,y:49 linear function power function 243.8+2.687x 195.3+3.395x 0.9725 248.4+5.824x 189.4+7.516x 0.9654 117.1+7.018x 131.9+7.561x 0.9881 10 2 10 1 10 2 10 3 Relative beam intensity (arb.units) 10 4 10 3 10 2 70 kev x:84,y:47 x:168,y:47 x:64,y:47 (a)the result as 40 kev. linear function power function 31.47+7.359x 7.958x 0.9901 51.70+6.636x 7.326x 0.9883 33.65+2.444x 2.914x 0.9790 10 1 10 2 10 3 Relative beam intensity (arb.units) (b)the result as 70 kev. Fig. 5. The relationship between beam intensity and linearity of 2D detector. Each error bar is standard devision of 50 images. B. Non-linearity in the response of 2D detector The detector response function is mostly believed to be linear with respect to intensity of incident x-ray in a certain intensity region. Out of the region, the output might saturate to a certain degree due to too intense input or an offset bias. We assumed that the response of the 2D detector used for these experiments was expressed approximately by a function in a type of ai α + b, where α<1and b indicates the offset bias that is assumed to be much smaller than I. Then, the projection data, which is a line integral of µ is expressed as follows: p = ln I I 0 = ln aiα + b ai α 0 + b αln I = α p, (6) I 0 where I is the true transmitted photon number and I 0 is the true incident photon number without an object. The equation shows that the resultant µ is multiplied by α. The solid lines present the best fitted response function in Fig.5 as typical cases as mentioned in the section V-B. In the high intensity region, the values seem to be linear to the ionization chamber count, while they gradually deviate from the linear line in the low intensity region. The functions are better fitted to the experimental data than the linear curve. In these cases, the offset bias b was also dealt with as a free parameter. The numerical values of the resultant a s, b s, and α s are shown in the Fig.5. The α values are less than one as we expected, but it is very closed to one. The projection images were corrected using the resultant response functions. However, the offset bias b s were assumed to be a constant 200 for 40 kev x-ray that estimated from the bias term b of the fitted power function in Fig.5(a). For 70 kev x-ray, the b s were assumed to be zero. In the 40 kev measurement, the average µ of 0.263±0.002 /cm was improved to be 0.268±0.003 /cm agreed with theoretical value of 0.268. The ethanol s µ of 0.187±0.002 /cm was improved to be 0.191±0.006 /cm. That was only 0.5 % less than theoretical value of 0.192. However, the image quality deteriorated strongly under the correction using the response function correction. When obtaining the response functions, the offset biases b for all pixels were assumed to be zero commonly as mentioned above. algorithm for simplification. They are plotted by close squares in Fig.3 comparing to the experimental results. The simulated µ s behaved in the similar manner as the experimental data reconstructed in the fan beam algorithm. This shows that the fan beam reconstruction algorithm is at least necessary for reconstructing projection data acquired at the distance between the object and the detector more than about 1 m. The simulation resulted that the scattering affected the µ measurement about 0.5 % or less even at the distance of 0.4 m, and it is negligibly small at the distance of 3 m. There is still 1.8 % difference between the measured µ in 40 kev and the theoretical value even if the contribution of scattered radiation is negligibly small. In the case of 70 kev, it is about 0.9 %. VII. SUMMARY The accuracy of measurement of linear attenuation coefficients was experimentally investigated. In comparison of the scattered radiation to the simulation results, it was found that the scattered radiation lowered the linear attenuation coefficients at the most 0.5 %, and its contribution was negligibly small when the object-detector distance was more than 1 m. Correcting the non-linearity in the experimental data using the response functions, the linear attenuation coefficients were improved drastically. Quality of the reconstructed images, however, deteriorated. It seemed that the offset bias in the response function of the individual element must be dealt with correctly otherwise the correction degrades the image quality. We concluded that the two dimensional detector was not able to provide quantitative data unless the data were corrected

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