Electromagnetic Waves-Based Cancer Diagnosis and Therapy: Principles and Applications of Nanomaterials

Electromagnetic Waves-Based Cancer Diagnosis and Therapy: Principles and Applications of Nanomaterials is a reference solution for radiation-based methods in cancer therapy that benefit from nanosystems. The book gives foundational knowledge and the latest techniques across the electromagnetic wave spectrum. It assesses the advantages and limitations of nanosystems in therapy, providing researchers and specialists with the insight to leverage novel nanostructures for therapy and to improve the efficacy of existing methods. It presents a comprehensive reference on the use of nanosystems in radiation-based cancer therapy. What makes this book unique is its coverage of the electromagnetic wave spectrum.

Six chapters cover radio-wave-involved cancer therapy and imaging; cancer therapy by microwaves hypothermia; infra-red waves in cancer theranostics; the use of visible light in diagnosis; X-ray based treatments; and gamma ray-involved therapy and imaging. This book offers researchers and specialists a comprehensive overview of radiation-based methods using nanosystems. It will be of great use to researchers and specialists in cancer diagnosis who want to take advantage of novel nanostructures and to improve the performance of conventional methods in radiation-based cancer diagnosis and therapy.

• Provides a comprehensive reference of radiation-based methods in cancer therapy benefiting from nanosystems
• Presents advantages and limitations in the use of nanosystems for radiation-based methods in cancer therapy
• Helps researchers and specialists leverage the potential of novel nanostructures for therapy
• Offers ways to improve the performance of conventical methods using nanosystems, making this a one-stop solution to the use of nanosystems in radiation-based cancer therapy

• Language: English
• Publisher: Academic Press
• Release date: Apr 13, 2023
• ISBN: 9780323996297

Book preview

Electromagnetic Waves-Based Cancer Diagnosis and Therapy

Principles and Applications of Nanomaterials

Edited by

Mona Khafaji

Institute for Nanoscience and Nanotechnology, Sharif University of Technology, Tehran, Iran

Omid Bavi

Department of Mechanical Engineering, Shiraz University of Technology, Shiraz, Iran

Table of Contents

Cover image

Title page

Copyright

Dedication

List of contributors

Preface

Chapter 1. Radio wave/microwave-involved methods for cancer diagnosis

1. General aspects of microwave and dielectric

2. Mathematical model for dispersion

3. The permittivity of healthy and tumor tissue

4. Measuring the microwave response of tissues

5. Nanoparticle-enhanced microwave imaging

6. Conclusion and future remarks on microwave imaging

7. Introduction to magnetic resonance imaging

8. The behavior of nuclei in the presence of an external magnetic field

9. Resonance and excitation by RF pulse

10. Spin relaxation

11. Contrast agents for MRI

12. Nanocarriers for CAs

13. Conclusion and future remarks of MRI

Chapter 2. Cancer therapeutics methods based on microwaves/radio wave

1. Introduction

2. Radiofrequency and microwave heating

3. Ultrasound heating

4. Conclusion

Glossary

Chapter 3. Visible-NIR luminescent nanomaterials for cancer diagnostic applications

1. Introduction

2. Photoluminescence bioimaging

3. Endoscopy

4. Conclusion and perspectives

List of abbreviations

Chapter 4. Application of infrared waves in cancer therapy

1. An introduction to tumor phototherapy

2. Photodynamic therapy

3. Photothermal therapy

4. Combinatorial therapeutic approaches

5. Conclusion and future perspectives

Glossary

List of abbreviations

Chapter 5. X-ray-based cancer diagnosis and treatment methods

Introduction

Conclusion

Chapter 6. Gamma-ray involved in cancer therapy and imaging

1. Introduction

2. Radiolabeling of organic nanomaterials

3. Radiolabeling of inorganic nanomaterials

4. Conclusion

List of abbreviations

Index

Copyright

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Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

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Dedication

To the soul of my dearest aunt,

Dr. Suad,

and all the strong patients who struggle with cancer.

I hope to live to a day when no one loses their loved ones to cancer.

Mona Khafaji

To Zahra and Fatima,

My loves, my life, and my lights.

Omid Bavi

List of contributors

Mahnaz Ahmadi,     Department of Pharmaceutics, School of Pharmacy, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Elham Asadian

Department of Tissue Engineering and Applied Cell Sciences, School of Advanced Technologies in Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Medical Nanotechnology and Tissue Engineering Research Center, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Hossein Behnammanesh

Chronic Respiratory Diseases Research Center, National Research Institute of Tuberculosis and Lung Diseases (NRITLD), Shahid Beheshti University of Medical Sciences, Tehran, Iran

Department of Pharmaceutical Chemistry and Radiopharmacy, Faculty of Pharmacy, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Davood Beiki,     Research Center for Nuclear Medicine, Tehran University of Medical Sciences, Tehran, Iran

Maria Filomena Botelho

Institute of Biophysics and Institute for Clinical and Biomedical Research (iCBR), Area of Environment Genetics and Oncobiology (CIMAGO), Faculty of Medicine, University of Coimbra, Coimbra, Portugal

Center for Innovative Biomedicine and Biotechnology (CIBB), University of Coimbra, Coimbra, Portugal

Clinical and Academic Centre of Coimbra (CACC), Coimbra, Portugal

Somaiyeh Dadashi,     Faculty of Technical and Engineering, Tarbiat Modares University, Tehran, Iran

Hamid Delavari H.,     Department of Materials Engineering, Tarbiat Modares University, Tehran, Iran

Marjan Emzhik,     Department of Pharmaceutics, School of Pharmacy, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Maryam Sadat Ghorashi,     Laser and Plasma Research Institute, Shahid Beheshti University, Tehran, Iran

Maliheh Hajiramezanali,     Department of Radiopharmacy, Faculty of Pharmacy, Tehran University of Medical Sciences, Tehran, Iran

Neda Iranpour Anaraki,     Faculty of Science and Medicine, University of Fribourg, Fribourg, Switzerland

Marziyeh Jannesari

School of Chemical and Bioprocess Engineering, University College Dublin, Dublin, Ireland

Institute for Nanoscience and Nanotechnology (INST), Sharif University of Technology, Tehran, Iran

Safura Jokar

Department of Nuclear Pharmacy, Faculty of Pharmacy, Tehran University of Medical Sciences, Tehran, Iran

Institute of Biophysics and Institute for Clinical and Biomedical Research (iCBR), Area of Environment Genetics and Oncobiology (CIMAGO), Faculty of Medicine, University of Coimbra, Coimbra, Portugal

Saeedeh Khazaei,     Department of Pharmaceutical Biomaterials, Faculty of Pharmacy, Tehran University of Medical Sciences, Tehran, Iran

Mafalda Laranjo

Institute of Biophysics and Institute for Clinical and Biomedical Research (iCBR), Area of Environment Genetics and Oncobiology (CIMAGO), Faculty of Medicine, University of Coimbra, Coimbra, Portugal

Center for Innovative Biomedicine and Biotechnology (CIBB), University of Coimbra, Coimbra, Portugal

Clinical and Academic Centre of Coimbra (CACC), Coimbra, Portugal

Mahsa Madah,     Department of Materials Engineering, Tarbiat Modares University, Tehran, Iran

Mona Mosayebnia,     Department of Pharmaceutical Chemistry and Radiopharmacy, School of Pharmacy, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Marco Pedroni,     Università degli Studi di Verona, Verona, Italy

Negin Pournoori,     Bioengineering and Nanomedicine Group, Faculty of Medicine and Health Technology, Tampere University, Tampere, Finland

Mohammad-Ali Shahbazi

Department of Biomedical Engineering, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands

Department of Pharmaceutical Nanotechnology, School of Pharmacy, Zanjan University of Medical Sciences, Zanjan, Iran

Preface

In recent years, nanotechnology has gained great attention in resolving the limitations associated with conventional diagnostic and therapeutic methods. Using the capabilities of nanoscience has enabled researchers to present accurate designs and to control properties of nanostructures as theranostics agents.

The main idea of writing this book was to compose a reference solution for radiation-based methods in cancer diagnosis and therapy that benefit from nanosystems. The chapters and sections of the book have been designed in such a way that gives foundational knowledge and the latest techniques across the electromagnetic wave spectrum. It assesses the advantages and limitations of nanosystems in cancer diagnosis and therapy, providing researchers and specialists with the insight to leverage novel nanostructures for cancer treatment and to improve the efficacy of existing methods. It presents a comprehensive reference on the use of nanosystems in radiation-based cancer theranostics. What makes this book unique is its coverage of the electromagnetic wave spectrum.

Among the available scientific references on the subject of designing and developing nanosystems and their advantages in cancer treatment, this book creates an extensive collection of all the methods based on all kinds of radiation in the electromagnetic wave spectrum and, at the same time, discusses the role of nanoparticles (NPs) in these applications and how they have improved the efficiency of these methods as well. The book is mainly targeted at upper-level undergraduate and graduate students, researchers, and professionals. The readers will gain theoretical knowledge of basic physical and biologic processes associated with cancer, with an emphasis on the advances in diagnosis and therapy. This book will prepare the readership for further study to the Ph.D. level and is for all healthcare professionals caring for patients, researchers, and interested readers in healthcare industries.

In the first chapter, Pournoori and collaborators introduce some relevant knowledge about microwave radiation, dielectric, and polarization. The general aspects of AC relaxation, dispersion, and the mathematical model of dispersion are explained, and recent research on the application of nanomaterials as microwave contrast agents is discussed. In the next part of this chapter, the authors focus on the application of radio waves in diagnosis by introducing magnetic resonance imaging (MRI) principles, the mechanism of MRI image contrast, and finally, MRI contrast agents including paramagnetic and superparamagnetic NPs.

Thermal therapies, in combination with radiotherapy and chemotherapy, have been used for many years, with outstanding success in treating cancers. However, hyperthermia methods cannot thermally differentiate between the target tumor and the surrounding healthy tissues. Consequently, this nonselective tissue heating can provoke extreme side effects. Nanotechnology, i.e., employing NPs and nanocomposites, is predicted to have a significant possibility of revolutionizing hyperthermia methods. Therefore, an in-depth understanding of the hyperthermia processes and the rule of nanotechnology in improving these methods is necessary to achieve an efficient strategy in cancer treatments. So, in the second chapter, Iranpour et al. introduce the physics behind the thermal ablation and hyperthermia treatment in radio frequency, microwave, and ultrasound regions, and the various nanostructures and their specific properties that could improve the efficacy and accuracy of the thermal treatment are discussed.

Chapter 3 covers the usage of visible light/infrared waves in cancer diagnosis. Ghorashi et al. discuss the physics of photoluminescence phenomena, the prerequisites for selecting an appropriate nanoprobe, and the merits of photoluminescent probes based on nanomaterials. This chapter aids in profitable comprehension of the role of effective functional nanoprobes for photoluminescent diagnosis and will assist readers to acquire knowledge about the features, strengths, weaknesses, and diagnostic applications of luminescent nanoprobes, which will be helpful in designing and developing new nanoprobes intelligently.

In Chapter 4, Asadian et al. introduce photodynamic and photothermal therapy methods with a detailed discussion of their mechanisms of action. They then focus on the role of NP-based therapeutic approaches in overcoming the limitations of these two methods as well as in the development of more efficacious combinatorial cancer therapy strategies.

Jokar et al. provide a comprehensive overview of the basics of X-rays and the types of X-ray-based imaging modalities and radiotherapy in Chapter 5. They highlight the most recent advances and future perspectives in the application of nanotechnology in X-ray-based imaging methods and radiotherapy. And finally, Mosayebnia et al. explain the gamma-ray interactions with matter and the creation of images and γ-emitting radionuclides used in single-photon emission computerized tomography and positron emission tomography systems as well as the radiolabeling strategies applied for both organic and inorganic NPs and their advantages and disadvantages.

We did our best to make this book a useful educational resource for researchers and specialists in cancer theranostics to take advantage of the potential of novel nanostructures and improve the performance of conventional methods. We appreciate suggestions and comments for improvements and changes to the text. Correspondence can be sent directly to the editors/authors via e-mail.

Chapter 1: Radio wave/microwave-involved methods for cancer diagnosis

Negin Pournoori ¹ , Hamid Delavari H. ² , and Mahsa Madah ²       ¹ Bioengineering and Nanomedicine Group, Faculty of Medicine and Health Technology, Tampere University, Tampere, Finland      ² Department of Materials Engineering, Tarbiat Modares University, Tehran, Iran

Abstract

Microwave radiations are a section of the electromagnetic spectrum that ranges in frequency from 300 MHz to 300 GHz. The most common microwave applications are in households, communications, the military, industry, and medicine. In recent years, the microwave has been successfully used within medicine to treat and diagnose diseases such as cancer. Moreover, the microwave imaging (MWI) technique is cost-effective and uses nonionizing radiation for its application in medical diagnostics. MWI can be obtained directly from different dielectric characteristics of malignant tissue compared with those of normal tissue or indirectly revealed by hybrid techniques. This chapter will introduce some relevant knowledge about microwave radiation, dielectric, and polarization. Then, general aspects of AC relaxation, dispersion, and the mathematical model of dispersion are explained. In the next section, we will differentiate permittivity in healthy tissue from malignant tumor tissue, as well as the recent research on the application of nanomaterials as microwave contrast agents. In the next part of this chapter, we focus on the application of radio waves in diagnosis by introducing magnetic resonance imaging (MRI) principles, the mechanism of MRI image contrast, and finally, MRI contrast agents including paramagnetic and superparamagnetic nanoparticles.

Keywords

Cancer diagnoses; Contrast agents; Dielectric; Dispersion; Magnetic resonance imaging; Microwave imaging; Nanoparticles

1. General aspects of microwave and dielectric

1.1. Microwave range

According to the Institute of Electrical and Electronics Engineers (IEEE), radiofrequency (RF) radiation is normally defined as the lower frequency range (frequency from about 3 kHz to 300 GHz or wavelength from 100 km to 1 mm) of electromagnetic waves. RF is divided into radio waves and microwaves with different frequency magnitudes (or wavelengths). Microwave as one of the radiofrequency divisions refers to electromagnetic waves from 300 MHz to 300 GHz (wavelength 1 m to 1 mm) [1,2]. The equation that relates wavelength (λ) and frequency (f) is described simply by λ = c/f, where c stands for the speed of light propagating in a vacuum (2.99 × 10⁸ m/s). It is worth noting that the microwave frequency range covered here is called nonionizing radiation, whereas ultraviolet (UV) and X-rays are called ionizing radiation due to their ability to disrupt molecular structures.

1.2. Polarization

An electric field cannot penetrate and pass through the bulk of a conductor because the total charge (electrons) of a conductor lies at the outer surface of the conductor. A dielectric is known as a material where the electric field penetrates rather than having a free flow of electrons. Electric charges are not exchangeable between the dielectric and the metal electrode plates. A dielectric without free charges is known as an ideal dielectric, i.e., an insulator or a nonconductor. Moreover, a substance can be considered a dielectric if it can store energy capacitively.

It is noteworthy to mention that matter can demonstrate in a different manner in the alternating electric field. For example, at sufficiently high frequencies, even a metal can turn into a dielectric.

The tendency of matter to obtain an electric dipole moment when subjected to an electric field refers to polarizability. A material becomes polarized because that matter is made up of elementary particles such as protons and electrons that have an electric charge. Indeed, the electrons with negative charges and atomic nuclei with positive charges undergo charge separation, and then the creation or transformation of electric dipoles into the material will happen.

Electrical dipole moment ( ) of a dipole is represented as a vector

(1.1)

Where, is the vector distance from the negative to the positive charge. The direction of the electrical dipole moment is the same as . In SI, the unit of p is coulomb meter [Cm], and due to the small amount, it is also represented in the Debye unit (D = 3.37 × 10 −³⁰ [Cm]). Bound charges that can be replaced by a long-distance, L, contribute to a larger dipole moment. The dipole moment of a matter may be the consequence of the dipole moment of a molecule, various molecules, or an entire region. Therefore, the total dipole moment of a matter can be considered as all dipole moments of the individual dipoles. The dipole moment per unit volume is a quantity describing the degree of polarization of matter [3,4].

For an infinitesimal volume (dV) in the material, which carries an infinitesimal dipole moment (dp), we can define the polarization density or simply polarization (P) [Cm/m³ = C/m²]:

(1.2)

Polarization is therefore considered a macroscopic concept rather than the dipole moment of molecules or atoms. The polarization in biomaterials may be endogenic or exogenic.

A similar parameter relates the magnitude of the induced dipole moment (p) of an individual molecule to the local electric field (E L ) that induced the dipole. This parameter is called the molecular polarizability (α) [Cm²/V], and the dipole moment originating from the local electric field is given by the following:

(1.3)

This introduces complexity; however, there is a significant difference between the local and applied fields. If we have N molecules per unit volume leading to the polarization, the polarization density can be written as

(1.4)

The outer shell (membrane) of a living cell is endogenic polarized because of the negative charge of the cell interior concerning the extracellular fluid; indeed, this polarization is produced by the body itself. Whereas, applying an external electric field to polarize the tissue from the outside is exogenic polarization. The exogenic energy (electric field) may be stored or dissipated in the tissue.

The amount of the polarizability of matter is represented by permittivity (or absolute permittivity) and denoted by the Greek letter ε. In other words, permittivity measures the amount of dipole moment density produced (induced) by an electric field. In addition, the permittivity is often represented by the relative permittivity ε r , which is the ratio of the permittivity ε and the vacuum permittivity ε 0 (8.85 × 10 −¹² F/m).

In our notation, the complete expression of the permittivity ε is ε r ε 0. In addition, there exists a variety of subscripts for several cases such as ε 0, which is the permittivity of the vacuum and does not mean permittivity at zero frequency, or ε ∞ is the permittivity at very high frequencies (frequencies up in the optical range).

1.3. AC relaxation, dispersion, and mechanisms of polarization

As a dielectric material is polarized by applying an external electric field, the dipoles revert to a random orientation (a new equilibrium) state after the removal of the electric field; this process is called relaxation. This process happens in the time domain, after an enhancement or reduction of step in the electric field strength or direction. Indeed, a lag happens when there are changes in polarization and changes in the electric field. The time required for 63% of the dipoles to return to a disordered (a new equilibrium) state is defined as dielectric relaxation time (τ). The relaxation time depends on the polarization mechanism. As dielectric polarization is frequency dependent in an alternating electric field, this relaxation is often explained in terms of permittivity as a function of frequency, which is referred dispersion. In another word, a substance showing considerable permittivity changes in the interested frequency range is called a dispersive in that region.

Polarization in materials, in general, may be originated from distinctly diverse mechanisms that can be categorized as electronic, ionic (molecular), orientation (dipolar), and interfacial [4,5]. In electronic polarization, the applied electric field leads to a displacement of the electron cloud relevant to the nuclei in each atom and gives each atom (or molecule) a small dipole moment. The electronic polarization falls from visible light to ultraviolet (10⁵–10⁸ GHz). The ionic polarization is due to a relative change in the mean positions of the atomic nuclei within the molecules (or displacement of ions relevant to each other). In other words, ionic polarization is due to the displacement of positively charged ions (one nucleus) to negatively charged ions (another nucleus). The ionic polarization falls in the infrared range (300–10⁵ GHz). The third mechanism is orientation polarization, which occurs with molecules that have permanent dipole moments such as water. Indeed, orientation polarization of free water is considered the key mechanism of dispersion of tissues and biologic material at the microwave frequency range (MHz to GHz region) and is called γ-dispersion [6,7]. It is noteworthy to mention that in the radio wave range (about 100 MHz to low GHz), bound water into biologic material such as proteins demonstrates the main reason for dispersion, which is called δ-dispersion. However, this dispersion overlaps with polar subgroups of proteins and amino acids [5].

The key mechanism of the dispersion of biologic materials below the MHz range is called interfacial polarization (Maxwell–Wagner effect) [5,7]. This polarization is due to charge accumulation or forming electrical double layers at the interface of biologic media such as membranes of cells or around solvated macromolecules such as DNA. The charge species comes from free ions in electrolytes and biologic media. The charged membrane (Maxwell–Wagner) polarization is in the range of 10 kHz–100 MHz and is referred to as β-dispersion [5]. In addition, forming a charged double-layer polarization on the surface of the cell membrane can be responsible for another dispersion in the Hz to the kHz frequency range, which is called α-dispersion. In addition to the double layer, protein channels in the cell membrane can also be responsible for α-dispersion [5,6]. It should be noticed that α and β dispersions may not be as well separated. Fig. 1.1 shows a general illustration of the polarization region and the permittivity dispersion at various frequency ranges (real and imaginary parts of dielectric permittivity).

Figure 1.1  Illustration of dispersion as a function of frequency (real and imaginary parts of dielectric permittivity).

1.4. Electric flux density

In a dielectric material, the total electric field is calculated from the addition of the applied electric field to an induced electric field, resulting from the polarization of the material. The polarization a new vector field is then defined, known as the electric flux density or the displacement flux density [C/m²]:

(1.5)

This definition is generally applicable to all biologic materials.

For linear, isotropic, and nondispersive (lossless) materials, the electric flux density can be written as

(1.6)

By comparing the above equations, polarization can be written as

(1.7)

or

(1.8)

In other words, . The χ e is dimensionless electric susceptibility, indicating the degree of polarization of materials in response to an applied electric field. The great electric susceptibility means the great capability of a substance to polarize in reactance to the field, thereby resulting in a higher permittivity ( ). Long distances between charges for tissue components such as proteins result in a high permittivity due to greater polarization based on Eq. (1.1).

1.5. Complex conductivity and permittivity

It may be beneficial to treat σ and ε as complicated quantities. Complex conductivity σ is utilized when the material is a conductor with capacitive characteristics, and complex permittivity is applied when the material is an insulator (a dielectric).

(1.9)

(1.10)

By considering admittance Y (inverse of impedance) in the basic capacitor model with a complex capacitance (C) and a complex conductance (G) as:

(1.11)

it can be inferred that

(1.12)

(1.13)

It is noteworthy to mention that is sometimes called the loss factor. To simplify the confusing frequency-dependent relationships between complex components of the σ and ε, we can use the following equation:

(1.14)

When an AC voltage is employed over a capacitor, it will alternately charge and discharge. For an ideal (perfect) capacitive circuit, the alternating voltage lags the current by 90 degrees (π/2 radians). Indeed, the charging current is at maximum at 0 degrees and then decreases and reaches zero current flow at 90 degrees due to declining the rate of voltage change (dV). For a perfect capacitor, there is no power loss, but for a real capacitor, we can consider two types of losses dissipated by heat resistive and reactance losses. Resistive losses are caused by the resistance of leads, electrodes, connections, etc. Whereas, reactance losses are caused by capacitive reactance and inductive reactance. An ideal (perfect) capacitor with zero losses also has a loss angle of zero. Then, the loss angle (δ) of a capacitor can be defined as δ = π/2 − φ

(1.15)

(1.16)

Tan (δ) is also called the loss tangent or dissipation factor. Tan (δ) is defined as energy lost per cycle divided by energy stored per cycle [4].

2. Mathematical model for dispersion

2.1. Single relaxation time: Debye expression

So far, the permittivity dispersion at various frequency ranges has been discussed, and now we explain a prevalent mathematical model that is used to describe the frequency dependency of the permittivity of dielectrics, the so-called Debye expression [4,5].

The electric flux density or the displacement flux density [C/m²] is

(1.17)

Polarization can be written as , where χ e is dimensionless electric susceptibility.

As mentioned, polarization P(t) is a merger of electronic, atomic, orientation, and interfacial polarization. If we consider linear materials (the parameters are independent of the field level), the polarization response of the substance to a stimulating field (here, E(t) = E · δ(t), where δ(t) is the Dirac delta function) can be gained by the superposition of reactions of each mechanism. The atomic and electronic displacements respond immediately to the applied field, which means it is a faster process, and their superposition polarization (P 1) based on Eq. (1.8) in response to an electrical field can be written as follows:

(1.18)

Where, χ 1 is the steady-state susceptibility corresponding to the atomic and electronic polarization.

Whereas, the response of the interfacial effect and dipolar orientation to the electrical field is known to have exponential nature with a characterized relaxation time [5]. Based on the Debye theory assumption, if we consider only a single relaxation time (τ), the interfacial and dipolar superposition polarization (P 2) in response to an electrical field can be written as

(1.19)

Where χ 2 is the susceptibility corresponding to the interfacial and dipolar polarization. The corresponding equation for the displacement (the electric flux density) is then

(1.20)

The steady-state response, i.e., response to DC (static) field is as follows:

(1.21)

Where, ε s is called static permittivity.

At sufficiently high frequencies, the interfacial and dipolar orientation effects disappear; then one can consider the infinite (or optical) permittivity (ε ∞) as

(1.22)

Then,

(1.23)

If we rewrite the displacement Eq. (1.20) again,

(1.24)

by taking the Fourier transform of Eq. (1.23), and considering that

(1.25)

the real and imaginary parts of the complex permittivity can be simply derived by multiplying the complex part by its conjugate as follows:

(1.26)

(1.27)

Moreover, the conductivity based on Eq. (1.13) is

(1.28)

Fig. 1.2A shows the variation of ε′(ω) (Eq. 1.26) and ε″(ω) (Eq.1.27) versus ωτ. It shows a monotonous decrease of ε′ from ε s at zero frequency to ε ∞ at high frequency, and ε″ shows a peak value and zero value at low and high frequencies. For Debye relaxation, the characteristic frequency is defined as ωτ = 1 where ε″ is maximum, therefore, the values of ε′ and maximum value of ε″ are found as

(1.29)

(1.30)

It is beneficial to plot ε′ versus ε″, which is called the Cole–Cole diagram (Fig. 1.2B). It is shown as a semicircle within the first quadrant of ε complex plane with the center of :

(1.31)

Figure 1.2  Complex permittivity as Debye single dispersion relaxation (A), and as Cole–Cole diagram (B).

As mentioned earlier, the main contributor of biologic materials dispersion at microwave range is free water. The Debye parameters of water are well-established and can be found in the papers of Von Hippel [8,9], for example as ε ∞ = 5, ε s = 78.3, and τ = 8.3 ps at T = 25°C. Thus, the characteristic frequency of water is around 19 GHz at 25°C and is close to 20 GHz at room temperature 37°C.

2.2. Distributed relaxation time: Cole–Cole expression

In biologic materials, there is a distribution of relaxation time rather than a single relaxation time due to the electrical interaction between the biologic species [3–5]. The following relation can be considered for such distribution in biologic materials [1,5].

(1.32)

where σ I is ionic conductivity due to the free movement of ions in tissue electrolytes, and F(τ) is a function of the relaxation times distribution. It should be noticed that ionic conductivity has been considered in this relation.

Cole and Cole [10] suggested a distribution that was verified with experimental data, particularly for tissue dispersion. For the Cole–Cole distribution,

(1.33)

where β = 1 − α, 0 ≤ α ≤ 1, and s = ln(τ/τ 0). α is also called the Cole–Cole parameter that corresponds to four different (δ, α, β, and γ) dispersion regions. Larger α values correspond to broader imaginary permittivity peaks, which means wider distributions. τ 0 is the characteristic frequency (where F(τ) peaks) and is called the center of the dispersion.

The complex permittivity of a system with a distribution of relaxation time can be obtained by a combination of Eqs. (1.31) and (1.32), which is well-known as the Cole–Cole equation

(1.34)

It should be mentioned that for α = 0 and ignoring the ionic conductivity, this relation would decrease to those for the Debye single dispersion (Eq. 1.24).

It has been confirmed that at the microwave frequency range, the four-term Cole–Cole model contains unnecessarily redundant parameters. Indeed, ionic conductivity is the main mechanism of polarization in the lower frequency, and above a few hundred MHz, the predominant polarization mechanism is the dipolar relaxation of water, so a single-term relaxation would be adequate. Therefore, dipolar relaxations (γ dispersion) of bound and free water are chief parameters that contribute to the permittivity of tissues in the MHz to GHz region.

3. The permittivity of healthy and tumor tissue

Many articles provide the complex permittivity of many types of biologic tissues [11–19], however, the data on human tissues is inadequate due to the limited access to tumor tissue samples of human origin. Moreover, most measurements have been done on ex vivo (ex vivo refers to experiments or measurements in or on living tissues taken from an organism in a laboratory) samples that demonstrated differences with in vivo data. This variation may be due to loss of tissue water after cutting out, the missing blood perfusion in removed tissue, and the temperature variations. It has been proved that the amount of water in cancer lesions is more than that of normal tissue, and then a clear difference (contrast) in the permittivity can be observed between tumor and healthy tissue that helps us to identify or image them. Nevertheless, it is often impossible to consider a single permittivity value for any normal or cancer tissue because the tissues are heterogenous and show different properties among different patients.

The most comprehensive ex vivo study on breast tissue (healthy and malignant) in the microwave range (0.5 and 20 GHz) was published by Lazebnik et al. [20] in 2007. They fitted the measured data with a single-pole Cole–Cole for three groups of normal and malignant breast tissues (Table 1.1). They found that the adipose (fatty tissue) content has a significant impact on the dielectric characteristics of healthy tissue samples, while the dielectric properties of tumor tissue show minor influence with adipose content. Statistically, there was a major difference between normal and cancer samples without considering adipose content. Nevertheless, if adipose content is considered, the difference between normal and cancer samples for tissues with less than 10% adipose is statistically considerable; otherwise, no statistical major difference in the permittivity was detected by adjusting the adipose contents. Finally, it can be inferred that classification of one tissue type into healthy and malignant without considering the heterogenicity of tissue might be an oversimplification.

Table 1.1

Sugitani et al. [21] investigated 102 healthy and malignant breast tissues taken from 35 patients and distinguished a clear difference in the permittivity between adipose, glandular, and tumor tissue at 6 GHz for most of the individual patients. In this study, the complex permittivity of the samples was assessed in the frequency range of 0.5–20 GHz by applying a coaxial probe, and a two-pole Cole–Cole model was utilized to fit the data of each sample.

Realistic phantoms serve as a precious instrument to discover the feasibility of new prototype systems and improve design concepts related to microwave imaging (MWI). Laboratory phantoms allow examining system performance in terms of repeatability, stability, resolution, and the effect of experimental errors and noise. Indeed, these evaluations are necessary for preclinical use that provides an opportunity to examine