# Dielectric Characterization of Ex-Vivo Breast Tissues: Differentiation of Tumor Types through Permittivity Measurements

^{1}

^{2}

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## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Classification

#### 2.2. Measurement System

- A rotating circular table
- The DAK 3.5(TL2) probe
- A vector network analyzer (VNA) (i.e., Copper Mountain S5085)
- Computer software for the DAK 3.5

_{dak}radius flat platform surrounding the open-ended coaxial probe with an inner radius (r

_{1}= 2 mm) and an outer radius (r

_{2}= 3 mm). The sensing fundamental is based on the variation of the ending capacity of the probe. The capacity per unit length is given by

_{t}will be the result of the shunted connection of the forward capacitance of the probe, c

_{f}, and the subsequent shunted capacitances, c

_{1}and c

_{2}, formed between the probe and the corresponding tissue layers. This is represented as follows:

#### 2.3. Protocol

- Preliminary review: This stage involves assessing various prior monitoring results, including ultrasound, mammography, and medical diagnoses. The exact location of the tumor is identified and documented thanks to the surgeon’s help. The tumor size is determined and noted.
- Instrument preparation: The vector network analyzer (VNA) is turned on 30 min before the measurement to stabilize thermal effects. This ensures the equipment is stabilized and ready for use. Calibration of the Speag DAK equipment is carried out using a standard open-short and water method. This step is vital to guarantee accurate measurements.
- Ex vivo procedure: The pressure is verified, ensuring a measure of 22 kPa calculated based on the measuring instrument that will be in contact with the tissue. This ensures the tissue retains its shape characteristics while maintaining sufficient contact for measurement. Ambient temperature is recorded, noting specific values between 22° and 27 °C for correct estimation of the electrical characteristics of the tumor. The exact time from tissue removal to measurement is determined to be a maximum of 5 min. Data are collected from three different points on the same sample to ensure accuracy and provide a comprehensive view.
- Data analysis: With the collected data, specific values for permittivity and conductivity are computed. These metrics are vital for understanding the electrical properties of tumor tissue.
- Pathological diagnosis: Finally, with the measurement data in hand, they are cross-referenced with the pathology results.

## 3. Experiment Design

## 4. Result and Discussion

_{i}denotes the current measurement. Additionally, the index i, ranging from 1 to n, indicates the number of repetitions conducted at the same frequency point.

^{∗}(f) as a function of frequency (f):

- ${\epsilon}^{\ast}\left(f\right)$ is the complex permittivity as a function of frequency.
- ε′ is the real part of permittivity.
- ε″(f) is the imaginary part of permittivity as a function of frequency.
- ${\epsilon}_{0}$ is the permittivity of free space.
- j is the imaginary unit.
- ${\epsilon}_{r}^{\ast}\left(\omega \right)o\epsilon \left(\omega \right)$ is the relative complex permittivity as a function of angular frequency ω.
- ${\epsilon}_{\infty}$ is the permittivity at infinite frequency.
- ${\epsilon}_{s}$ is the static permittivity in the low frequency limit, representing the maximum polarization of the material.
- $\u2206\epsilon $ and $\u2206{\epsilon}_{m}$ are the increments of permittivity.
- $\tau $ and ${\tau}_{m}$ are the relaxation times.
- α and ${\alpha}_{m}$ are the dispersion parameters.
- σ and ${\sigma}_{s}$ are the conductivities.
- M is the number of terms in the summation (for the Double Debye model).
- $\u2206{\epsilon}_{1}$, $\u2206{\epsilon}_{2}$, ${\tau}_{1}$, ${\tau}_{2}$, ${\alpha}_{1}$, ${\alpha}_{2}$ are changes in permittivity, relaxation times, and dispersion parameters for two different relaxation processes.
- j is the imaginary unit j2 = −1.
- ${\epsilon}_{0}$ is the permittivity of free space.

- N is the total number of data points.
- The average of average of ε′(ω) and average of average of σ(ω) are the average values of the real permittivity and the conductivity over all measured frequencies.

## 5. Discussion

**ε**

_{r}= 45.6; mucinous,

**ε**

_{r}= 59.5; lobular,

**ε**

_{r}= 35.1)- or benign (

**ε**

_{r}= 27.6) tumors. This achievement highlights the importance of this technique in fast and accurate identification of diagnosis, overcoming previous limitations of dielectric spectroscopy thanks to improved control over measurement variables.

## 6. Conclusions

_{r}= 45.6; mucinous, ε

_{r}= 59.5; lobular, ε

_{r}= 35.1) or benign (ε

_{r}= 27.6) tumors. Furthermore, clinically identifying permittivity differences opens up new avenues for breast cancer diagnosis and treatment without having to wait for histological analysis.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Dielectric characterization parameters extracted from permittivity: (

**a**) conductivity and (

**b**) loss tangent.

Tumor Type | Histological Type | N Patients | N Samples | N Measurements |
---|---|---|---|---|

Malignant | Ductal carcinoma | 30 | 40 | 120 |

Lobular carcinoma | 10 | 13 | 39 | |

Mucinous carcinoma | 10 | 13 | 39 | |

Benign | Fibroadenoma | 20 | 27 | 81 |

Tumor Type | Histological Type | N Measurements | Permittivity | |
---|---|---|---|---|

2 GHz | 4 GHz | |||

Malignant | Ductal carcinoma | 120 | 45.6 $\pm \text{}6$ | 39.9$\text{}\pm \text{}6$ |

Lobular carcinoma | 39 | 35.1$\text{}\pm \text{}4$ | 31.7$\text{}\pm \text{}4$ | |

Mucinous carcinoma | 39 | 59.4$\text{}\pm \text{}5$ | 55.6$\text{}\pm \text{}5$ | |

Benign | Fibroadenoma | 81 | 27.6$\text{}\pm \text{}4$ | 24.6$\text{}\pm \text{}4$ |

Model | Mucinous | Lobular | Ductal | Fibroadenoma |
---|---|---|---|---|

Debye | 26.589 | 13.395 | 13.542 | 27.392 |

Double Debye | 0.074 | 0.432 | 0.192 | 27.393 |

Simple Cole–Cole | 7.684 | 2.285 | 2.060 | 26.618 |

Double Cole–Cole | 0.042 | 0.410 | 2.145 | 2.083 |

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**MDPI and ACS Style**

Fernández-Aranzamendi, E.G.; Castillo-Araníbar, P.R.; San Román Castillo, E.G.; Oller, B.S.; Ventura-Zaa, L.; Eguiluz-Rodriguez, G.; González-Posadas, V.; Segovia-Vargas, D.
Dielectric Characterization of Ex-Vivo Breast Tissues: Differentiation of Tumor Types through Permittivity Measurements. *Cancers* **2024**, *16*, 793.
https://doi.org/10.3390/cancers16040793

**AMA Style**

Fernández-Aranzamendi EG, Castillo-Araníbar PR, San Román Castillo EG, Oller BS, Ventura-Zaa L, Eguiluz-Rodriguez G, González-Posadas V, Segovia-Vargas D.
Dielectric Characterization of Ex-Vivo Breast Tissues: Differentiation of Tumor Types through Permittivity Measurements. *Cancers*. 2024; 16(4):793.
https://doi.org/10.3390/cancers16040793

**Chicago/Turabian Style**

Fernández-Aranzamendi, Elizabeth G., Patricia R. Castillo-Araníbar, Ebert G. San Román Castillo, Belén S. Oller, Luz Ventura-Zaa, Gelber Eguiluz-Rodriguez, Vicente González-Posadas, and Daniel Segovia-Vargas.
2024. "Dielectric Characterization of Ex-Vivo Breast Tissues: Differentiation of Tumor Types through Permittivity Measurements" *Cancers* 16, no. 4: 793.
https://doi.org/10.3390/cancers16040793