## Abstract

### Background and Purpose

### Materials and Methods

### Results

### Conclusions

## Keywords

## 1. Introduction

## 2. Methods and materials

### 2.1 SPR estimation methods

### 2.2 Virtual patient

^{3}, represented an average female subject structured with 140 organs made of 53 standard human tissues. The mass density and elemental weights of each tissue were provided in the ICRP Publication 110 [

### 2.3 Calculation of reference SPR

*I*-values given in Tables 2.8 and 2.11 in the ICRU49 report [

### 2.4 CT imaging and CT reconstruction

*Fixed Forced Detection Actor*. This module deterministically computes digitally reconstructed radiographs using the reconstruction toolkit (RTK) v1.3.0 [

^{2}were acquired. The thickness of the detector row was 1 mm for the Gammex acquisitions and 2 mm for the ICRP phantom. The source-to-isocenter distance was 626 mm and the source-to-detector distance was 1026 mm. For the simulations of the CT projections, the measured dual-energy spectra (low energy (LE): 100 kVp, high energy (HE): 150 kVp + 0.6 mm Sn) and the measured detector response for the SOMATOM Force dual-source CT scanner were used, kindly provided by Siemens Healthcare (Forchheim, Germany). To have a fair comparison between the projection-based and the image-based methods, energy spectra with high mean energies were chosen to reduce the beam-hardening for the image-based methods. To represent a realistic scenario, Poisson distributed noise was applied to the projections. For each slice, a total central dose of 20 mGy was delivered, with an equal dose split between the two energy spectra, thus a central dose of 10 mGy per energy spectrum; the calculation of the number of photons needed to deliver a given dose is described in Appendix C. No bowtie-filter was simulated.

^{2}and for the Gammex the pixel dimension of 1 × 1 mm

^{2}.

### 2.5 SPR comparison

## 3. Results

Per slice | Head | Sternum | Breast | Pelvis | |
---|---|---|---|---|---|

PB (AMK) | Mean | 0.28% | 0.32% | 0.29% | −0.45% |

Uns. mean | 0.28% | 0.32% | 0.64% | 0.66% | |

IB (SPP) | Mean | −0.06% | 0.03% | 0.17% | −0.99% |

Uns. mean | 0.46% | 0.30% | 0.29% | 0.99% | |

IB (SK) | Mean | −0.17% | −0.06% | −0.09% | −0.85% |

Uns. mean | 0.20% | 0.20% | 0.40% | 0.85% | |

IB (Han) | Mean | 0.01% | 0.26% | 0.79% | −0.60% |

Uns. mean | 0.34% | 0.26% | 0.79% | 0.86% | |

All slices | RMSE | Mean | Uns. mean | $\sigma $ | |

PB (AMK) | 0.54% | 0.07% | 0.49% | 0.56% | |

IB (SPP) | 0.68% | −0.27% | 0.55% | 0.65% | |

IB (SK) | 0.61% | −0.33% | 0.44% | 0.53% | |

IB (Han) | 0.70% | 0.06% | 0.59% | 0.73% |

Head (122.8 mm) | Sternum (162.5 mm) | Breast (162.1 mm) | Pelvis (181.7 mm) | |||||
---|---|---|---|---|---|---|---|---|

Method | $\mu \pm \sigma $ (%) | RMSE (%) | $\mu \pm \sigma $ (%) | RMSE (%) | $\mu \pm \sigma $ (%) | RMSE (%) | $\mu \pm \sigma $ (%) | RMSE (%) |

PB (AMK) | −0.24 ± 0.81 | 0.84 | −0.01 ± 0.64 | 0.64 | −0.04 ± 0.58 | 0.58 | −0.14 ± 0.80 | 0.82 |

IB (SPP) | −0.41 ± 0.86 | 0.95 | 0.01 ± 0.81 | 0.81 | 0.04 ± 0.72 | 0.72 | 0.03 ± 1.10 | 1.10 |

IB (SK) | −0.51 ± 0.80 | 0.95 | −0.28 ± 0.63 | 0.69 | −0.33 ± 0.57 | 0.66 | −0.44 ± 0.80 | 0.91 |

IB (Han) | −0.10 ± 0.82 | 0.82 | 0.36 ± 0.75 | 0.83 | 0.35 ± 0.65 | 0.74 | 0.47 ± 1.19 | 1.28 |

## 4. Discussion

## 5. Conclusion

## Disclosure of conflicts of interest

## Acknowledgments

## Appendix A. SPR estimation methods

### A.1 Projection-based method (AMK)

P. Linstrom, W. Mallard, NIST Standard Reference Database Number 69, [Online] Available:http://webbook.nist.gov, National Institute of Standards and Technology, Gaithersburg, MD. (retrieved December 6, 2016).

where $(\mu /\rho )$ represented the mass attenuation coefficient of ST and CB, and

*a*is the mass fraction of ST and CB in the volume at location $\mathit{x}$ – in this BMD these mass fractions represented the energy-independent coefficients.

where $\ell \in L(u\text{,}\theta )$ was the line-segment between the source and a detector pixel located at position $u$ for a given projection angle $\theta $.

where ${I}_{\text{LE}}$ and ${I}_{\text{HE}}$ were the measured intensities for the LE and the HE spectrum, respectively, for a given projection angle; ${S}_{\text{LE}}$ and ${S}_{\text{HE}}$ were the normalized energy spectra weighted by the detector response.

where ${Z}_{i}$ was the atomic number, ${A}_{i}$ was the atomic mass and ${w}_{i}$ was the elemental weight fraction for element

*i*of the tabulated compounds ST, CB and water (represented with the index W) [

P. Linstrom, W. Mallard, NIST Standard Reference Database Number 69, [Online] Available:http://webbook.nist.gov, National Institute of Standards and Technology, Gaithersburg, MD. (retrieved December 6, 2016).

### A.2 Image-based method – SPR parametrization (SPP)

Here, subscript

*j*refers to the energy spectrum $(j=\text{LE,HE})$, and

*A*and

*B*are fitting parameters. The linear attenuation coefficients, $\mu (E)$, for the Gammex inserts were calculated based on XCOM data [

Berger MJ, Hubbell JH, Seltzer SM, Chang J, Coursey JS, Sukumar R, et al., XCOM: photon cross section database (version 1.5), [Online] Available: http://physics.nist.gov/xcom, National Institute of Standards and Technology, Gaithersburg, MD; 2010.

*j*. In this study we used a separation point between the tissue groups set to ${\mathcal{H}}_{\text{LE}}=150$ HU.

*u*, for the 92 reference human tissues [

where the ${x}_{i}$’s are fitting parameters. The fitting parameters used in this study can be found in Table A.1. When these expressions were used to estimate the SPR for the AF phantom, the attenuation ratios were calculated using the fitting parameters found together with the effective energies, ${u}_{j}^{t}={\mathcal{H}}_{j}/{A}_{j}^{t}+{B}_{j}^{t}$. The same separation between soft and bone tissue was used for the SPR estimation as for the calculation of the attenuation ratios.

Energy spectra characterization | SPR fitting parameters | |||||
---|---|---|---|---|---|---|

LE (64 keV) | HE (96 keV) | Soft tissues | Bone tissues | |||

${A}^{\text{soft}}$ | 988.8 | 991.3 | ${x}_{1}$ | 3.161 | ${x}_{5}$ | 0.8251 |

${A}^{\text{bone}}$ | 971.8 | 984.8 | ${x}_{2}$ | 1.176 | ${x}_{6}$ | 0.03853 |

${B}^{\text{soft}}$ | 1.006 | 1.007 | ${x}_{3}$ | −1.136 | ${x}_{7}$ | 0.1150 |

${B}^{\text{bone}}$ | 0.9803 | 1.004 | ${x}_{4}$ | −0.01883 | ${x}_{8}$ | −0.008910 |

### A.3 Image-based method – Saito and Kanematsu’s (SK) method

*a*,

*b*and $\alpha $ were found by making calibration fits to the theoretical ${\rho}_{e}$ values for the 92 reference human tissues and their CT numbers calculated from Eqs. ((A.7), (A.8)). To take the low RED values for lung tissue into account the constants were found by minimizing the relative deviations $\left({\text{RED}}^{\mathtt{theo}}-{\text{RED}}^{\mathtt{est}}\right)/{\text{RED}}^{\mathtt{theo}}$. The parameters used in this study can be seen in Table A.2. The CT numbers for the 92 reference human tissues used in the calibration were calculated from Eq. (A.8) and the effective energies given in Table A.1.

a | b | $\alpha $ |
---|---|---|

1.0085 | 1.0091 | 0.5202 |

### A.4 Image-based method – Han’s (Han) method

_{2}23% aqueous solution. An unknown material was assigned to one of the two basis material sets according to its ratio of reduced CT numbers, $\xi ={u}_{\text{HE}}/{u}_{\text{LE}}$; materials with $\xi \u2a7e0.97$ were categorized as soft tissues and assigned to the water-polystyrene group, while materials with $\xi <0.97$ were categorized as bone tissues and assigned to the water-CaCl

_{2}-group.

${E}_{\text{eff}}$ (keV) | ${A}_{j}$ | ${B}_{j}$ | |
---|---|---|---|

100 kVp | 64 | 992.1 | 1.003 |

Sn150 kVp | 96 | 990.2 | 1.007 |

where the subscripts 1 and 2 denotes the two basis materials.

and

where ED is the electron density. The RED is then be found by dividing by the electron density of water. ${f}_{I}$ is a correction factor for the

*I*values. It was found as a linear fit between the parameter $\frac{{c}_{1}}{{c}_{1}+{c}_{2}}$ and the ratio $\frac{{I}_{\text{theo}}}{{I}_{\text{BVM}}}$, ${f}_{I}=a\phantom{\rule{0.12em}{0ex}}\frac{{I}_{\text{theo}}}{{I}_{\text{BVM}}}+b$. Here ${I}_{\text{theo}}$ is the theoretical

*I*-value for the reference human tissue calculated based on the Bragg additivity rule. There is a fit for each of the two tissue groups, and the calibration parameters are listed in Table A.4. If the correction factor, ${f}_{I}$, was negative, when estimating for an unknown material, it was set to 1 to avoid complex numbers when calculating the SPR estimates.

*a*and

*b*) for the correction factor ${f}_{I}=a\phantom{\rule{0.12em}{0ex}}\frac{{I}_{\text{theo}}}{{I}_{\text{BVM}}}+b$ used in Han’s method, see Eq. A.14.

Soft tissues | Bone tissues | ||
---|---|---|---|

${a}_{\text{soft}}=0.0837$ | ${b}_{\text{soft}}=0.8996$ | ${a}_{\text{bone}}=-0.0599$ | ${b}_{\text{bone}}=1.021$ |

## Appendix B. SPR reference values for the thirteen ROIs

*N*is the number of pixels in the ROI.

ROI name | AF Material-ID | Tissue type | ${\text{SPR}}_{\text{ref}}$ | N | |
---|---|---|---|---|---|

Head | 1a | 49 | Adipose tissue | 0.972 | 75 |

1b | 32 | Brain | 1.051 | 111 | |

1c | 8 | Cranium, spongiosa | 1.203 | 27 | |

Sternum | 2a | 3 | Humeri, upper half, spongiosa | 1.157 | 195 |

2b | 29 | Muscle tissue | 1.046 | 147 | |

2c | 29 | Muscle tissue | 1.046 | 75 | |

Breast | 3a | 50 | Lung tissue (compressed lungs) | 0.384 | 195 |

3b | 28 | Blood | 1.055 | 195 | |

3c | 48 | Breast (mammary gland) | 1.040 | 47 | |

Pelvis | 4a | 29 | Muscle tissue | 1.046 | 111 |

4b | 49 | Adipose tissue | 0.972 | 147 | |

4c | 14 | Pelvis, spongiosa | 1.100 | 47 | |

4d | 9 | Femora, upper half, spongiosa | 1.053 | 75 |

## Appendix C. Calculation of CT dose

where ${A}_{\text{beam}}$ is the area covered by the beam at the isocenter,

*S*is the detected energy spectrum with unity area: ${\int}_{E}S(E)\mathit{dE}=1$. $\left({\mu}_{\text{en,W}}(E)/{\rho}_{\text{W}}\right)$ and ${\mu}_{\text{W}}$ are the energy-dependent mass energy absorption coefficient and the linear attenuation coefficient of water, respectively, both taken from the NIST database [

Hubbell JH, Seltzer SM. Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients (version 1.4), [Online] Available: http://physics.nist.gov/xaamdi. National Institute of Standards and Technology, Gaithersburg, MD; 2004.

*r*is the radius of the phantom.

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☆Dr. Ludvig Muren, a co-author of this paper, is Editor-in-Chief of Physics & Imaging in Radiation Oncology. A member of the Editorial Board managed the editorial process for this manuscript independently from Dr. Muren and the manuscript was subject to the Journal’s usual peer-review process.

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