# A Machine Learning Workflow for Tumour Detection in Breasts Using 3D Microwave Imaging

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Faceted Air-Filled Chamber and Its Model for Microwave Breast Imaging

## 3. A Two-Stage Workflow for Prior Information Extraction and Data Inversion

#### 3.1. Stage 1: Bulk Parameter Inference using Neural Networks

#### 3.1.1. Labelled Data

#### 3.1.2. Stage 1 Network Architecture

#### 3.1.3. Sample Pre-Processing

#### 3.2. Stage 2: 3D Image Reconstruction and Tumour Detection

#### Contrast Source Inversion

#### 3.3. Calibration

## 4. Results

#### 4.1. Data Generation

#### 4.2. Tumor Detection Test Samples

#### 4.3. Parametric Inference of Fibroglandular Region Parameters

#### 4.4. CSI-Based Tumor Detection from Predicted Prior Information

#### 4.5. Monitoring Response to Tumor Treatment

#### 4.6. Preliminary Bulk Parameter Inference Results on Experimental Data

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Bulk parametric inversion of scattered-field data to recover prior information (our vector of parameters $\underline{\mathbf{p}}$), followed by data-to-image reconstruction using neural network recovered prior information.

**Figure 3.**Renderings of interior of faceted air-filled chamber (

**a**,

**b**) and cross-section (

**c**,

**d**) showing the three regions: air (grey), fat (dark blue), fibroglandular (light blue), for a medium (left) and small (right) fibroglandular region.

**Figure 4.**The Stage 1 bulk parameter inference network accepts breast-target data which may include a tumor, and outputs the bulk fibroglandular parameters.

**Figure 5.**Workflow stage 2 employing CSI, where $\underline{\mathbf{p}}$ is obtained from the bulk parameter inference network (first stage), and specifies the fibroglandular region in the imaging mesh.

**Figure 6.**True values (left) versus neural network predictions (right) for the fibroglandular region for the T1 test examples for the (

**a**) small fibroglandular case, (

**b**) medium fibroglandular case, and (

**c**) large fibroglandular case. The associated differences in the predicted complex-valued permittivity are provided in Table 3.

**Figure 7.**CSI reconstructions for two different tumor positions, when prior information has been generated by our neural network. +z projection (

**left**) and +x projection (

**right**) are shown. (

**a**,

**b**) show T1 and T2 for the small fibroglandular case; (

**c**–

**e**) show T1 (9 mm), T2, and the T1 (4.5 mm) for the medium fibroglandular case; (

**f**,

**g**) show T1 and T2 for the large fibroglandular case. Adipose (grey), fibroglandular (blue), and tumor (red) show the true geometry of the breast model tissues. The 85% thresholded contrast representing the reconstructed tumor is shown in black.

**Figure 8.**Point cloud representation of the CSI reconstruction of the real and imaginary parts of the complex contrast for the fibroglandular region for the T1 test examples with (

**a**,

**d**) a 9 mm tumor at position T1, (

**b**,

**e**) a 4.5 mm tumor at position T1, and (

**c**,

**f**) no tumor.

Radius Range [cm] | Height Range [cm] | ${\mathit{\epsilon}}^{\prime}$ Range | ${\mathit{\epsilon}}^{\prime \prime}$ Range |
---|---|---|---|

[2.85, 4.10] | [5.30, 9.80] | [15, 25] | [−25, −15] |

Metric | Error in | Error in | Error in | Error in |
---|---|---|---|---|

Radius [mm] | Height [mm] | ${\mathit{\epsilon}}^{\prime}$ | ${\mathit{\epsilon}}^{\prime \prime}$ | |

Average absolute error | 0.0280 | 0.0248 | 0.0866 | 0.0963 |

Average absolute error (%) | 0.97% | 0.83% | 0.58% | 0.39% |

Standard deviation | 0.0204 | 0.0194 | 0.0670 | 0.0765 |

Position | Tumor Radius | Radius | Height | ${\mathit{\epsilon}}^{\prime}$ | ${\mathit{\epsilon}}^{\prime \prime}$ |
---|---|---|---|---|---|

[mm] | [cm] | [cm] | |||

Small fibroglandular case: | |||||

True values: ${\underline{\mathbf{p}}}_{true}$ | 2.90 | 5.35 | 20.0 | −21.6 | |

No tumor | - | 3.06 | 6.04 | 16.02 | −21.85 |

T1 | 9 | 3.05 | 6.09 | 16.66 | −22.08 |

T2 | 9 | 3.06 | 6.13 | 16.03 | −22.07 |

Medium fibroglandular case: | |||||

True values: ${\underline{\mathbf{p}}}_{true}$ | 3.40 | 8.50 | 20.0 | −21.6 | |

No tumor | - | 3.39 | 8.46 | 19.90 | −21.60 |

T1 | 9 | 3.39 | 8.47 | 19.71 | −21.72 |

T1 | 4.5 | 3.40 | 8.44 | 20.03 | −21.57 |

T2 | 9 | 3.39 | 8.45 | 20.48 | −21.58 |

Large fibroglandular case: | |||||

True values: ${\underline{\mathbf{p}}}_{true}$ | 4.05 | 9.75 | 20.0 | −21.6 | |

No tumor | - | 4.07 | 9.71 | 19.81 | −21.55 |

T1 | 9 | 4.07 | 9.73 | 19.74 | −21.36 |

T2 | 9 | 4.06 | 9.72 | 19.79 | −21.58 |

Noise | Metric | Error in | Error in | Error in | Error in |
---|---|---|---|---|---|

Radius [mm] | Height [mm] | ${\mathit{\epsilon}}^{\prime}$ | ${\mathit{\epsilon}}^{\prime \prime}$ | ||

${10}^{-4}$ | Average | 0.0545 | 0.0251 | 1.28 | 0.167 |

(−80 dB) | Max | 0.161 | 0.775 | 3.98 | 0.478 |

${10}^{-3}$ | Average | 0.0549 | 0.0250 | 1.41 | 0.283 |

(−60 dB) | Max | 0.180 | 0.779 | 4.56 | 0.679 |

${10}^{-2}$ | Average | 0.115 | 0.444 | 4.06 | 2.92 |

(−40 dB) | Max | 0.233 | 1.31 | 7.47 | 10.1 |

**Table 5.**Summary of fibroglandular region parameter predictions for calibrated experimental examples.

Position | Tumor Radius | Radius | Height | ${\mathit{\epsilon}}^{\prime}$ | ${\mathit{\epsilon}}^{\prime \prime}$ |
---|---|---|---|---|---|

[mm] | [cm] | [cm] | |||

True values: ${\underline{\mathbf{p}}}_{true}$ | 3.40 | 8.50 | 20.0 | −21.6 | |

No tumor 1 | - | 3.50 | 8.39 | 13.37 | −14.24 |

No tumor 2 | - | 3.47 | 8.29 | 13.38 | −14.85 |

T1 | 9 | 3.56 | 8.56 | 11.83 | −15.38 |

T2 | 9 | 3.55 | 8.25 | 11.61 | −16.35 |

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**MDPI and ACS Style**

Edwards, K.; Khoshdel, V.; Asefi, M.; LoVetri, J.; Gilmore, C.; Jeffrey, I. A Machine Learning Workflow for Tumour Detection in Breasts Using 3D Microwave Imaging. *Electronics* **2021**, *10*, 674.
https://doi.org/10.3390/electronics10060674

**AMA Style**

Edwards K, Khoshdel V, Asefi M, LoVetri J, Gilmore C, Jeffrey I. A Machine Learning Workflow for Tumour Detection in Breasts Using 3D Microwave Imaging. *Electronics*. 2021; 10(6):674.
https://doi.org/10.3390/electronics10060674

**Chicago/Turabian Style**

Edwards, Keeley, Vahab Khoshdel, Mohammad Asefi, Joe LoVetri, Colin Gilmore, and Ian Jeffrey. 2021. "A Machine Learning Workflow for Tumour Detection in Breasts Using 3D Microwave Imaging" *Electronics* 10, no. 6: 674.
https://doi.org/10.3390/electronics10060674