# 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

- Conceição, R.C.; Mohr, J.J.; O’Halloran, M. An Introduction to Microwave Imaging for Breast Cancer Detection; Springer: Berlin/Heidelberg, Germany, 2016. [Google Scholar]
- Nikolova, N.K. Microwave imaging for breast cancer. IEEE Microw. Mag.
**2011**, 12, 78–94. [Google Scholar] [CrossRef] - Omer, M.; Mojabi, P.; Kurrant, D.; LoVetri, J.; Fear, E. Proof-of-concept of the incorporation of ultrasound-derived structural information into microwave radar imaging. IEEE J. Multiscale Multiphys. Comput. Tech.
**2018**, 3, 129–139. [Google Scholar] [CrossRef] - Neira, L.M.; Van Veen, B.D.; Hagness, S.C. High-resolution microwave breast imaging using a 3-D inverse scattering algorithm with a variable-strength spatial prior constraint. IEEE Trans. Antennas Propag.
**2017**, 65, 6002–6014. [Google Scholar] [CrossRef] - Poplack, S.P.; Tosteson, T.D.; Wells, W.A.; Pogue, B.W.; Meaney, P.M.; Hartov, A.; Kogel, C.A.; Soho, S.K.; Gibson, J.J.; Paulsen, K.D. Electromagnetic breast imaging: Results of a pilot study in women with abnormal mammograms. Radiology
**2007**, 243, 350–359. [Google Scholar] [CrossRef] [Green Version] - Catapano, I.; Di Donato, L.; Crocco, L.; Bucci, O.M.; Morabito, A.F.; Isernia, T.; Massa, R. On quantitative microwave tomography of female breast. Prog. Electromagn. Res.
**2009**, 97, 75–93. [Google Scholar] [CrossRef] [Green Version] - Abdollahi, N.; Kurrant, D.; Mojabi, P.; Omer, M.; Fear, E.; LoVetri, J. Incorporation of ultrasonic prior information for improving quantitative microwave imaging of breast. IEEE J. Multiscale Multiphys. Comput. Tech.
**2019**, 4, 98–110. [Google Scholar] [CrossRef] - Ambrosanio, M.; Kosmas, P.; Pascazio, V. A Multithreshold Iterative DBIM-Based Algorithm for the Imaging of Heterogeneous Breast Tissues. IEEE Trans. Biomed. Eng.
**2019**, 66, 509–520. [Google Scholar] [CrossRef] - Benny, R.; Anjit, T.A.; Mythili, P. An overview of microwave imaging for breast tumor detection. Prog. Electromagn. Res.
**2020**, 87, 61–91. [Google Scholar] [CrossRef] - Lazebnik, M.; Popovic, D.; McCartney, L.; Watkins, C.B.; Lindstrom, M.J.; Harter, J.; Sewall, S.; Ogilvie, T.; Magliocco, A.; Breslin, T.M.; et al. A large-scale study of the ultrawideband microwave dielectric properties of normal, benign and malignant breast tissues obtained from cancer surgeries. Phys. Med. Biol.
**2007**, 52, 6093. [Google Scholar] [CrossRef] - Shea, J.D.; Kosmas, P.; Hagness, S.C.; Van Veen, B.D. Three-dimensional microwave imaging of realistic numerical breast phantoms via a multiple-frequency inverse scattering technique. Med. Phys. (Lancaster)
**2010**, 37, 4210–4226. [Google Scholar] [CrossRef] - Brown, K.G.; Geddert, N.; Asefi, M.; LoVetri, J.; Jeffrey, I. Hybridizable discontinuous Galerkin method contrast source inversion of 2-D and 3-D dielectric and magnetic targets. IEEE Trans. Microw. Theory Tech.
**2019**, 67, 1766–1777. [Google Scholar] [CrossRef] - Asefi, M.; Baran, A.; LoVetri, J. An Experimental Phantom Study for Air-Based Quasi-Resonant Microwave Breast Imaging. IEEE Trans. Microw. Theory Tech.
**2019**, 67, 3946–3954. [Google Scholar] [CrossRef] - Zakaria, A.; Jeffrey, I.; LoVetri, J.; Zakaria, A. Full-vectorial parallel finite-element contrast source inversion method. Prog. Electromagn. Res.
**2013**, 142, 463–483. [Google Scholar] [CrossRef] [Green Version] - Tournier, P.H.; Bonazzoli, M.; Dolean, V.; Rapetti, F.; Hecht, F.; Nataf, F.; Aliferis, I.; El Kanfoud, I.; Migliaccio, C.; De Buhan, M.; et al. Numerical Modeling and High-Speed Parallel Computing: New Perspectives on Tomographic Microwave Imaging for Brain Stroke Detection and Monitoring. IEEE Antennas Propag. Mag.
**2017**, 59, 98–110. [Google Scholar] [CrossRef] [Green Version] - Kurrant, D.; Baran, A.; LoVetri, J.; Fear, E. Integrating prior information into microwave tomography Part 1: Impact of detail on image quality. Med. Phys.
**2017**, 44, 6461–6481. [Google Scholar] [CrossRef] - Kurrant, D.; Fear, E.; Baran, A.; LoVetri, J. Integrating prior information into microwave tomography part 2: Impact of errors in prior information on microwave tomography image quality. Med. Phys. (Lancaster)
**2017**, 44, 6482–6503. [Google Scholar] [CrossRef] - Golnabi, A.H.; Meaney, P.M.; Paulsen, K.D. Tomographic microwave imaging with incorporated prior spatial information. IEEE Trans. Microw. Theory Tech.
**2013**, 61, 2129–2136. [Google Scholar] [CrossRef] - Bevacqua, M.T.; Bellizzi, G.G.; Isernia, T.; Crocco, L. A method for effective permittivity and conductivity mapping of biological scenarios via segmented contrast source inversion. Prog. Electromagn. Res.
**2019**, 164, 1–15. [Google Scholar] [CrossRef] [Green Version] - Abdollahi, N.; Jeffrey, I.; LoVetri, J. Improved Tumor Detection via Quantitative Microwave Breast Imaging Using Eigenfunction-Based Prior. IEEE Trans. Comput. Imaging
**2020**, 6, 1194–1202. [Google Scholar] [CrossRef] - Hughson, M.; Jeffrey, I.; LoVetri, J. Ultrasound and Microwave Imaging with Prior Property Dependencies. In Proceedings of the 2019 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), Boston, MA, USA, 29–31 May 2019; pp. 1–4. [Google Scholar]
- Obermeier, R.; Martinez-Lorenzo, J.A. Compressive sensing unmixing algorithm for breast cancer detection. IET Microw. Antennas Propag.
**2018**, 12, 533–541. [Google Scholar] [CrossRef] - Chen, X. Computational Methods for Electromagnetic Inverse Scattering; John Wiley & Sons Pte. Ltd.: Singapore, 2018. [Google Scholar]
- Wei, Z.; Chen, X. Deep-learning schemes for full-wave nonlinear inverse scattering problems. IEEE Trans. Geosci. Remote Sens.
**2018**, 57, 1849–1860. [Google Scholar] [CrossRef] - Li, L.; Wang, L.; Teixeira, F.; Che, L.; Cui, T. DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering. IEEE Trans. Antennas Propag.
**2018**. [Google Scholar] [CrossRef] [Green Version] - Guo, R.; Song, X.; Li, M.; Yang, F.; Xu, S.; Abubakar, A. Supervised descent learning technique for 2-D microwave imaging. IEEE Trans. Antennas Propag.
**2019**, 67, 3550–3554. [Google Scholar] [CrossRef] - Oktay, O.; Ferrante, E.; Kamnitsas, K.; Heinrich, M.P.; Bai, W.; Caballero, J.; Guerrero, R.; Cook, S.A.; de Marvao, A.; Dawes, T.; et al. Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and Segmentation. IEEE Trans. Med. Imaging
**2017**, 37, 384–395. [Google Scholar] [CrossRef] [Green Version] - Shao, W.; Du, Y. Microwave Imaging by Deep Learning Network: Feasibility and Training Method. IEEE Trans. Antennas Propag.
**2020**, 68, 5626–5635. [Google Scholar] [CrossRef] - Chen, X.; Wei, Z.; Li, M.; Rocca, P. A Review of Deep Learning Approaches for Inverse Scattering Problems (Invited Review). Prog. Electromagn. Res.
**2020**, 167, 67–81. [Google Scholar] [CrossRef] - Khoshdel, V.; Ashraf, A.; LoVetri, J. Enhancement of Multimodal Microwave-Ultrasound Breast Imaging Using a Deep-Learning Technique. Sensors
**2019**, 19, 4050. [Google Scholar] [CrossRef] [Green Version] - Mojabi, P.; Khoshdel, V.; LoVetri, J. Tissue-Type Classification With Uncertainty Quantification of Microwave and Ultrasound Breast Imaging: A Deep Learning Approach. IEEE Access
**2020**, 8, 182092–182104. [Google Scholar] [CrossRef] - Khoshdel, V.; Asefi, M.; Ashraf, A.; LoVetri, J. Full 3D Microwave Breast Imaging Using a Deep-Learning Technique. J. Imaging
**2020**, 6, 80. [Google Scholar] [CrossRef] - Gilmore, C.; Jeffrey, I.; Asefi, M.; Geddert, N.T.; Brown, K.G.; LoVetri, J. Phaseless Parametric Inversion for System Calibration and Obtaining Prior Information. IEEE Access
**2019**, 7, 128735–128745. [Google Scholar] [CrossRef] - Edwards, K.; Krakalovich, K.; Kruk, R.; Khoshdel, V.; LoVetri, J.; Gilmore, C.; Jeffrey, I. The implementation of neural networks for phaseless parametric inversion. In Proceedings of the 2020 XXXIIIrd General Assembly and Scientific Symposium of the International Union of Radio Science, Rome, Italy, 29 August–5 September 2020; pp. 1–3. [Google Scholar]
- Edwards, K.; Geddert, N.; Krakalovich, K.; Kruk, R.; Asefi, M.; Lovetri, J.; Gilmore, C.; Jeffrey, I. Stored Grain Inventory Management Using Neural-Network-Based Parametric Electromagnetic Inversion. IEEE Access
**2020**, 8, 207182–207192. [Google Scholar] [CrossRef] - Nemez, K.; Asefi, M.; Baran, A.; LoVetri, J. A faceted magnetic field probe resonant chamber for 3D breast MWI: A synthetic study. In Proceedings of the 2016 17th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM), Montreal, QC, Canada, 10–13 July 2016; pp. 1–3. [Google Scholar]
- Nemez, K.; Baran, A.; Asefi, M.; LoVetri, J. Modeling error and calibration techniques for a faceted metallic chamber for magnetic field microwave imaging. IEEE Trans. Microw. Theory Tech.
**2017**, 65, 4347–4356. [Google Scholar] [CrossRef] - Geddert, N. An electromagnetic hybridizable discontinuous Galerkin method forward solver with high-order geometry for inverse problems. Master’s Thesis, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada, 2020. [Google Scholar]
- Gilmore, C.; Zakaria, A.; Pistorius, S.; LoVetri, J. Microwave imaging of human forearms: Pilot study and image enhancement. Int. J. Biomed. Imaging
**2013**, 2013, 673027. [Google Scholar] [CrossRef] - Van Den Berg, P.M.; Kleinman, R.E. A contrast source inversion method. Inverse Probl.
**1997**, 13, 1607. [Google Scholar] [CrossRef] - Zakaria, A.; Gilmore, C.; LoVetri, J. Finite-element contrast source inversion method for microwave imaging. Inverse Probl.
**2010**, 26, 115010. [Google Scholar] [CrossRef] [Green Version]

**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