# Dual-Energy X-ray Medical Imaging with Inverse Compton Sources: A Simulation Study

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## Abstract

**:**

## 1. Introduction

## 2. K-Edge Subtraction Imaging

## 3. X-ray Imaging with Inverse Compton Scattering Sources

#### 3.1. Inverse Compton Scattering

#### 3.2. Inverse Compton Scattering Sources

#### Dual-Energy Imaging Implementation with Inverse Compton Scattering Sources

#### 3.3. K-Edge Subtraction Imaging with Inverse Compton Sources

## 4. Materials and Methods

#### 4.1. Phantoms

#### 4.2. X-Ray Beams

#### 4.3. Figures of Merit

## 5. Results

#### 5.1. Contrast-Enhanced Dual-Energy Mammography (CEDEM)

#### 5.2. Coronary Angiography

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ICS | Inverse Compton Scattering |

KES | K-Edge Subtraction |

IP | Interaction Point |

BW | Bandwidth |

RMS | Root Mean Square |

CEDEM | Contrast Enhanced Dual Energy Mammography |

SNR | Signal to Noise Ratio |

ROI | Region Of Interest |

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**Figure 2.**Simulation of the X-ray emission of BriXS source. (

**a**) Distribution of scattered photons as a function of the photon energy E and the scattering angle $\theta $, (

**b**) Energy spectrum for three different values of the collimation angle ${\theta}_{max}$.

**Figure 3.**ICS spectra used for our calculation in the mammography case. The features of these spectra, which are normalized to the integral, are reported in Table 3. The mass attenuation coefficient of iodine is also reported as a reference.

**Figure 4.**(

**a**) Mammography case (${t}_{T}$ = 5 cm): signal of the reconstructed detail as a function of the separation $\Delta E$ and bandwidth BW of two Gaussian beams bracketing the iodine K-edge. The peak separation is symmetric with respect to the K-edge. The expected signal was 1 $\times {10}^{-3}$ g cm${}^{-2}$. (

**b**) Noise per pixel ${\sigma}_{p}$ as a function of the peak energy separation $\Delta E$.

**Figure 5.**Signal-to-noise ratio per pixel calculated, in the mammography case, as a function of peak values of the two ICS spectra bracketing the iodine K-edge. The spectra featured an energy bandwidth of 3% RMS. A detail with a thickness of 5 mm and a contrast medium concentration of 2 mg mL${}^{-1}$ embedded in a bulk composed of 5 cm was considered. The number of impinging photons was 4.5 $\times {10}^{5}$ for both the spectra.

**Figure 6.**Simulated images of the phantom considered in our mammography case study. The details are the regions of interest (ROIs) labelled in red in the contrast image.

**Figure 7.**Coronary angiography case: detail mass thickness reconstructed, as a function of the peak values of the two ICS spectra bracketing the iodine K-edge. The spectra featured an energy bandwidth of 3% RMS. A detail with a thickness of 5 mm and a contrast medium concentration of 10 mg mL${}^{-1}$, embedded in a bulk composed of 19 cm of soft tissue and 1 cm of bone, was considered.

**Figure 9.**Comparison of the contrast images obtained with two different couples of ICS beams in the coronary angiography case. (

**a**) ${E}^{-}$ = 32.5 keV and ${E}^{+}$ = 34.5 keV. (

**b**) ${E}^{-}$ = 32 keV and ${E}^{+}$ = 36 keV. In both cases, the energy bandwidth and the beam intensity were assumed to vary as a function of the pixel position (emission angle) according to Equations (9) and (10), respectively.

Source | Energy | Bandwidth | Intensity (ph/s) | Brilliance (ph s${}^{-1}$mm${}^{-2}$mrad${}^{-2}$ (0.1%BW)${}^{-1}$) |
---|---|---|---|---|

MuCLS [33] | 15–35 keV | 3–5% | (1.5–4.5) $\times {10}^{10}$ | 1.2 $\times {10}^{10}$ |

ThomX [36] | 45–90 keV | 1–10% | ${10}^{13}$ (10% BW) | ${10}^{11}$ |

STAR [30] | 20–100 keV | 1–10% | ${10}^{10}$ (10% BW) | ${10}^{9}$ |

BriXS [35] | 20–180 keV | 1–10% | ${10}^{11}$–${10}^{13}$ | ${10}^{13}$–${10}^{14}$ |

**Table 2.**Features of the phantoms used in our case studies. The densities of the bone and the soft tissues were ${\rho}_{T}$ = 1.04 g cm${}^{-3}$ and ${\rho}_{B}$ = 1.41 g cm${}^{-3}$, respectively. The contrast medium concentration ${c}_{CM}$ was 2 mg mL${}^{-1}$ and 10 mg mL${}^{-1}$ for the CEDEM and coronary angiography case, respectively.

Phantom | ${\mathit{L}}_{\mathit{x}}\times {\mathit{L}}_{\mathit{y}}$ | ${\mathit{t}}_{\mathit{T}}$ | ${\mathit{t}}_{\mathit{D}}$ | ${\mathit{D}}_{\mathit{x}}\times {\mathit{D}}_{\mathit{y}}$ | ${\mathit{t}}_{\mathit{B}}$ | ${\mathit{D}}_{\mathit{x}}\times {\mathit{D}}_{\mathit{y}}$ |
---|---|---|---|---|---|---|

(cm × cm) | (cm) | (cm) | (cm × cm) | (cm) | (cm × cm) | |

mammography (CEDEM) | 8.0 × 8.0 | 5.0 ± 0.1 | 0.25, 0.5, 0.75 | 0.25${}^{2}$, 0.5${}^{2}$, 0.75${}^{2}$ | - | - |

coronary angiography | 3.5 × 3.5 | 20.0 ± 0.2 | 0.3, 0.5, 0.7 | ${L}_{x}\times {t}_{D}$ | 1.0 | $1.0\times {L}_{y}$ |

**Table 3.**Features of some X-ray energy spectra used in our case studies. Overlap of the two beams bracketing the iodine K-edge is 3.5% and 18.5% for the mammography and coronary angiography case, respectively. ${E}_{m}$ and ${E}_{max}$ are the mean and the maximum energy of the spectra, respectively. ${L}_{f}$ is the ratio between the integral of the part of spectrum approximated by a logistic function and the total area, while ${B}_{f}$ is the portion of spectrum below the iodine K-edge. The other symbols have the meaning already specified.

Case | Beam | ${\mathit{p}}_{\mathit{L}}$ | ${\mathit{p}}_{\mathit{R}}$ | ${\mathit{E}}_{\mathit{p}}$ | ${\mathit{E}}_{\mathit{m}}$ | ${\mathit{E}}_{\mathbf{max}}$ | BW (RMS) | ${\mathit{L}}_{\mathit{f}}$ | ${\mathit{B}}_{\mathit{f}}$ |
---|---|---|---|---|---|---|---|---|---|

(keV) | (keV) | (keV) | (%) | (%) | (%) | ||||

mammography (CEDEM) | LE | 0.8012 | 0.012 | 32.0 | 31.4 | 34.1 | 3.00 | 70.5 | 99.9 |

mammography (CEDEM) | HE | 0.9212 | 0.012 | 36.0 | 35.3 | 38.1 | 3.05 | 70.3 | 4.6 |

coronary angiography | LE | 0.8162 | 0.012 | 32.5 | 31.9 | 34.5 | 3.00 | 71.0 | 97.4 |

coronary angiography | HE | 0.8762 | 0.012 | 34.5 | 33.9 | 36.7 | 3.04 | 71.0 | 20.1 |

**Table 4.**Analysis of the contrast image of the mammography phantom. For each ROI, m is the mean value of the mass thickness, ${\mathrm{m}}_{\mathrm{BG}}$ and ${\mathbf{\sigma}}_{\mathrm{BG}}$ are the mean value and the standard deviation of the mass thickness (sampled in the background part of the image close to the detail). The other symbols have the meaning already specified.

ROI | n | m | ${\mathbf{m}}_{\mathbf{BG}}$ | ${\mathit{\sigma}}_{\mathbf{BG}}$ | S | ${\left(\mathit{\rho}\mathit{t}\right)}_{\mathit{X}}^{\mathbf{true}}$ | $\mathit{SNR}$ |
---|---|---|---|---|---|---|---|

(mg/cm${}^{2}$) | (mg/cm${}^{2}$) | (mg/cm${}^{2}$) | (mg/cm${}^{2}$) | (mg/cm${}^{2}$) | |||

1 | 81 | 1.001 | −0.580 | 0.029 | 1.58 | 1.50 | 55 |

2 | 81 | 0.719 | −0.351 | 0.029 | 1.07 | 1.00 | 37 |

3 | 81 | −0.052 | −0.594 | 0.029 | 0.54 | 0.50 | 19 |

4 | 289 | 1.235 | −0.374 | 0.016 | 1.61 | 1.50 | 103 |

5 | 289 | 1.000 | −0.079 | 0.016 | 1.08 | 1.00 | 69 |

6 | 289 | 0.157 | −0.375 | 0.016 | 0.53 | 0.50 | 34 |

7 | 676 | 0.985 | −0.631 | 0.010 | 1.62 | 1.50 | 158 |

8 | 676 | 0.682 | −0.397 | 0.010 | 1.08 | 1.00 | 106 |

9 | 676 | −0.094 | −0.631 | 0.010 | 0.54 | 0.50 | 53 |

**Table 5.**Analysis of the contrast image of the phantom for coronary angiography. For each ROI, m is the mean value of the mass thickness, ${\mathrm{m}}_{\mathrm{BG}}$ and ${\mathbf{\sigma}}_{\mathrm{BG}}$ are the mean value and the standard deviation of the mass thickness sampled in the background part of the image close to the detail. The other symbols have the meaning already specified.

ROI | n | m | ${\mathbf{m}}_{\mathbf{BG}}$ | ${\mathit{\sigma}}_{\mathbf{BG}}$ | S | ${\left(\mathit{\rho}\mathit{t}\right)}_{\mathit{X}}^{\mathbf{true}}$ | $\mathit{SNR}$ |
---|---|---|---|---|---|---|---|

(mg/cm${}^{2}$) | (mg/cm${}^{2}$) | (mg/cm${}^{2}$) | (mg/cm${}^{2}$) | (mg/cm${}^{2}$) | |||

top vessel | 144 | 4.92 | −0.603 | 0.163 | 5.53 | 7.00 | 34 |

top vessel (bone) | 144 | 3.54 | −2.46 | 0.228 | 6.00 | 7.00 | 26 |

central vessel | 64 | 4.04 | −0.624 | 0.239 | 4.66 | 5.00 | 20 |

central vessel (bone) | 64 | 2.21 | −2.47 | 0.324 | 4.68 | 5.00 | 14 |

bottom vessel | 16 | 1.90 | −0.644 | 0.507 | 2.55 | 3.00 | 5.0 |

bottom vessel (bone) | 16 | 0.051 | −2.74 | 0.869 | 2.79 | 3.00 | 3.2 |

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**MDPI and ACS Style**

Paternò, G.; Cardarelli, P.; Gambaccini, M.; Taibi, A.
Dual-Energy X-ray Medical Imaging with Inverse Compton Sources: A Simulation Study. *Crystals* **2020**, *10*, 834.
https://doi.org/10.3390/cryst10090834

**AMA Style**

Paternò G, Cardarelli P, Gambaccini M, Taibi A.
Dual-Energy X-ray Medical Imaging with Inverse Compton Sources: A Simulation Study. *Crystals*. 2020; 10(9):834.
https://doi.org/10.3390/cryst10090834

**Chicago/Turabian Style**

Paternò, Gianfranco, Paolo Cardarelli, Mauro Gambaccini, and Angelo Taibi.
2020. "Dual-Energy X-ray Medical Imaging with Inverse Compton Sources: A Simulation Study" *Crystals* 10, no. 9: 834.
https://doi.org/10.3390/cryst10090834