Debye Parameters Research Articles

Microwave dielectric properties of normal, fibroelastotic, and malignant human lung tissue

Technological development of microwave treatment and detection techniques for lung cancer requires accurate and comprehensive knowledge of the microwave dielectric properties of human lung tissue. We characterize the dielectric properties of room temperature human lung tissue from 0.5 to 10 GHz for three lung tissue groups: normal, fibroelastotic, and malignant. We fit a two-pole Debye model to the measured frequency-dependent complex permittivity and calculate the median Debye parameters for the three groups. We find that malignant lung tissue is approximately 10% higher in relative permittivity and conductivity compared to normal lung tissue; this trend matches previously reported normal versus malignant data for other biological tissues. There is little contrast between benign lung tissue with fibroelastosis and malignant lung tissue. We extrapolate our data from room temperature to 37 °C using a temperature-dependence model for animal lung tissue and use the Maxwell-Garnett dielectric mixing model to predict the dielectric properties of inflation-dynamic human lung tissue; both approximations correspond with previously reported dielectric data of bovine and porcine lung tissue.

Terahertz relaxation polarization modeling of micro-water inside nano-modified dielectrics and imaging distribution of free/bound water

The additional moisture can be easily introduced into dielectric materials with the nano-doping, which could have adverse impacts on the insulating properties. Herein, samples with different moisture absorption are tested using Terahertz (THz) waves. The relaxation resonance integrated polarization model is developed to illustrate the water absorption effect by the nano-filler on the THz spectrum, which is related to the hydrogen bond (HB) state of water molecular clusters. Detection of moisture content is realized by the polarized resonance intensity in the proposed model. The different HB states of free water and bound water are effectively distinguished using the Debye parameters in the model, and the formation process of water involved in the HB network is analyzed. Meanwhile, the proposed model is verified by molecular simulation. This work provides an application-worthy method to distinguish nuances in moisture contents and distribution in nano-dielectrics, with advantages of non-destructiveness, rapidity and 2D visualization.

Triage of in vivo burn injuries and prediction of wound healing outcome using neural networks and modeling of the terahertz permittivity based on the double Debye dielectric parameters.

The initial assessment of the depth of a burn injury during triage forms the basis for determination of the course of the clinical treatment plan. However, severe skin burns are highly dynamic and hard to predict. This results in a low accuracy rate of about 60 - 75% in the diagnosis of partial-thickness burns in the acute post-burn period. Terahertz time-domain spectroscopy (THz-TDS) has demonstrated a significant potential for non-invasive and timely estimation of the burn severity. Here, we describe a methodology for the measurement and numerical modeling of the dielectric permittivity of the in vivo porcine skin burns. We use the double Debye dielectric relaxation theory to model the permittivity of the burned tissue. We further investigate the origins of dielectric contrast between the burns of various severity, as determined histologically based on the percentage of the burned dermis, using the empirical Debye parameters. We demonstrate that the five parameters of the double Debye model can form an artificial neural network classification algorithm capable of automatic diagnosis of the severity of the burn injuries, and predicting its ultimate wound healing outcome by forecasting its re-epithelialization status in 28 days. Our results demonstrate that the Debye dielectric parameters provide a physics-based approach for the extraction of the biomedical diagnostic markers from the broadband THz pulses. This method can significantly boost dimensionality reduction of THz training data in artificial intelligence models and streamline machine learning algorithms.

Maximum Likelihood Estimation of Debye Relaxation Parameters With Open-Ended Coaxial Probes

In this paper, we present a new method to measure the complex dielectric permittivity of materials-under-test with an open-ended coaxial probe. The method, which explicitly takes measurement noise into account to enhance the stability of the measurements, is formulated based on the maximum likelihood estimation of the Debye parameters from calibrated reflection measurements performed at the aperture of the probe. In particular, the measurement noises at different frequencies are approximated with independent Gaussian distributions. To estimate the mean and the standard deviation of the mentioned probability distributions at each frequency, the differences among repetitive measurements of a reference sample are analyzed. Later, these statistical distributions are enforced into a cost functional to derive an optimization scheme based on the maximum likelihood estimation. Finally, the cost functional is iteratively minimized with a second-order Newton-based technique to retrieve the Debye relaxation parameters of a material. We further experimentally verified the method with various liquid samples and the accuracy of the obtained results is compared with the previous works.

A Method for Extracting Debye Parameters as a Tool for Monitoring Watered and Contaminated Soils.

Soil monitoring is a key topic from several perspectives, such as moisture level control for irrigation management and anti-contamination purposes. Monitoring the latter is becoming even more important due to increasing environmental pollution. As a direct consequence, there is a strong demand for innovative monitoring systems that are low cost, provide for quasi-real time and in situ monitoring, high sensitivity, and adequate accuracy. Starting from these considerations, this paper addresses the implementation of a microwave reflectometry based-system utilizing a customized bifilar probe and a miniaturized Vector Network Analyzer (m-VNA). The main objective is to relate frequency-domain (FD) measurements to the features of interest, such as the water content and/or the percentage of some polluting substances, through an innovative automatable procedure to retrieve the Debye dielectric parameters of the soil under different conditions. The results from this study confirm the potential of microwave reflectometry for moisture monitoring and contamination detection.

Glucose level detection using millimetre-wave metamaterial-inspired resonator.

Millimetre-wave frequencies are promising for sensitive detection of glucose levels in the blood, where the temperature effect is insignificant. All these features provide the feasibility of continuous, portable, and accurate monitoring of glucose levels. This paper presents a metamaterial-inspired resonator comprising five split-rings to detect glucose levels at 24.9 GHz. The plexiglass case containing blood is modelled on the sensor’s surface and the structure is simulated for the glucose levels in blood from 50 mg/dl to 120 mg/dl. The novelty of the sensor is demonstrated by the capability to sense the normal glucose levels at millimetre-wave frequencies. The dielectric characteristics of the blood are modelled by using the Debye parameters. The proposed design can detect small changes in the dielectric properties of blood caused by varying glucose levels. The variation in the transmission coefficient for each glucose level tested in this study is determined by the quality factor and resonant frequency. The sensor presented can detect the change in the quality factor of transmission response up to 2.71/mg/dl. The sensor’s performance has also been tested to detect diabetic hyperosmolar syndrome. The sensor showed a linear shift in resonant frequency with the change in glucose levels, and an R2 of 0.9976 was obtained by applying regression analysis. Thus, the sensor can be used to monitor glucose in a normal range as well as at extreme levels.

Microwave Dielectric Property Retrieval From Open-Ended Coaxial Probe Response With Deep Learning

This work presents a technique for dielectric property retrieval through Debye parameter reconstruction from open-ended coaxial probe (OECP) response. Debye parameters were obtained with the application of a deep learning (DL) model to the reflection coefficient response of the OECP when terminated with a material under test. The OECP was modelled with the well-known admittance technique from 0.5 to 6 GHz with 20 MHz resolution. A dataset was generated using the admittance technique and obtained data was utilized to design the DL model. As part of the standard procedure, the dataset was separated to train, validate, and test parts by allocating the 80%, 10%, and 10% of the dataset to each section, respectively. Obtained percent relative error for Debye parameters were 1.86±3.01%, 3.33±9.52%, and 2.07±7.42% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon _{s}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon _\infty $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> , respectively. To further test the constructed DL model, OECP responses were measured at the same frequency band when it was terminated with five different standard liquids, four mixtures, and a gel-like material. Reconstructed Debye parameters from the DL model were used to retrieve the complex dielectric properties and obtained results were compared with the literature data. Obtained mean percent relative error was ranging from 1.21±0.06 to 10.89±0.08 within the frequency band of interest.

A Method to Measure Complex Dielectric Permittivity With Open-Ended Coaxial Probes

This work presents a new method to measure the complex dielectric permittivity (CDP) variation of materials under test (MUTs) with open-ended coaxial probes. The CDP variation of an MUT is a continuous function of frequency as modeled with various dielectric relaxation models. Hence, the accuracy and the repeatability of CDP measurements can be improved by enforcing such spectral continuity. Here, we derive a new formulation that explicitly enforces the spectral continuity via the Debye relaxation model. In particular, we construct a cost functional based on an admittance integral at the tip of an open-ended coaxial probe. The Debye model parameters are substituted into the admittance integral to form a set of nonlinear equations. Later, these equations are iteratively minimized by a Gauss–Newton-based minimization scheme, for measured reflection coefficients when the tip of the probe is in contact with the MUT. The presented method differs from the conventional CDP measurement techniques in two aspects. First, the method looks for a global solution across the investigated frequency spectrum instead of solving CDP values individually at each frequency step. Second, the Debye parameters are directly retrieved without any data-fitting. The presented method is experimentally verified with various liquid samples, and the accuracy of obtained results is compared against the literature.

Parameter Optimization of Frequency Selective Surfaces Made of Composite Materials

Debye model is used for approximating the frequency dependent complex effective permittivity of the composite structures in filter and shielding applications at microwave frequencies. In debye model, desired shielding effectiveness (SE) is obtained by determining the Debye parameters using trial and error method. But this may result in wasting time or not converging to an optimum solution. In this work to overcome this problem Debye parameters were optimized by using Differential Evolution (DE) algorithm. A Maxwell Garnett (MG) mixing rule was applied to these optimized parameters to obtain frequency selective surface (FSS) parameters. 12dB shielding threshold was chosen between 0.05 – 5GHz frequency range. In accordance with the obtained parameters of FSS, a structure was designed in CST simulation software and simulations had been conducted to obtain SE results. It was seen that the results obtained from analytical computations agree with those obtained from simulations.

Microwave Heat-Treated Electronic Waste Constituted X-Band Radar Absorbing Structure Using Electromagnetic Mixing Model Assisted Optimization Strategy

Potential radar absorbing material (RAM) for suppressing electromagnetic (EM) wave over a range of oblique angles of incidence are needed in many applications. In this article, an attempt is being made to build cost-effective and efficient RAM using the EM characterization of microwave heat-treated (MHT) electronic waste followed by an EM mixing model-assisted analytical approach. The robust and facile top-down fabrication technique is employed for the development of heterogeneous composites, which are further subjected to microwave heat treatment at distinct power wattages. The magneto-dielectric spectrographic analysis of samples is carried out in the range of 8.2 to 12.4 GHz. The Debye parameters are optimized and succeeded to obey EM property of the synthesized samples. Jaya's algorithm is adopted for the optimal design of single and dual-layer RAMs at normal and oblique angle incidence based on the constitutive EM parameters under certain restrictive conditions. The embraced MHT method prompts an improvement in microstructure coherency that further increases absorption bandwidth (BW). As a result, a 2.1 mm thick single layer RAM achieves a minimum reflection coefficient (RC) of -17.1 dB at 10.3 GHz with a 100% BW below -10 dB threshold. The groundbreaking findings are obtained by performing a three-fold study of dual-layer RAMs, culminating a minimum RC of -47.8 dB at 11.8 GHz with a layer thickness of 1.8 mm. This article shows that the microwave heat-treated composites have enormous potential in the development of lightweight and broadband RAMs for stealth applications.

Permittivity Characterization of Dispersive Materials Using Power Measurements

This article presents an inexpensive transmission line (TL) approach to reconstruct the dielectric properties of dispersive and non-dispersive materials, with low or high loss. This method uses amplitude-only transmission measurements, namely power measurements, thereby removing the need for phase measurements. The proposed method only requires a signal generator and a power sensor for complex permittivity characterization without the need for either a scalar or a vector network analyzer. In the proposed method, a Debye model for the frequency dispersion of the material under test (MUT) is used; however, the applicability extends to other models. A coaxial line is considered as an ideal TL, and by using the inverse solution of the forward scattering equation in different frequencies, which requires numerically solving a system of nonlinear equations, the Debye parameters are extracted. For experimental validation, a suspended coaxial line was designed and fabricated. The permittivities of several liquid chemicals were measured within a frequency band of 0.3-3 GHz to demonstrate the validity of the technique.

Microwave Bone Imaging: A Preliminary Investigation on Numerical Bone Phantoms for Bone Health Monitoring.

Microwave tomography (MWT) can be used as an alternative modality for monitoring human bone health. Studies have found a significant dielectric contrast between healthy and diseased human trabecular bones. A set of diverse bone phantoms were developed based on single-pole Debye parameters of osteoporotic and osteoarthritis human trabecular bones. The bone phantoms were designed as a two-layered circular structure, where the outer layer mimics the dielectric properties of the cortical bone and the inner layer mimics the dielectric properties of the trabecular bone. The electromagnetic (EM) inverse scattering problem was solved using a distorted Born iterative method (DBIM). A compressed sensing-based linear inversion approach referred to as iterative method with adaptive thresholding for compressed sensing (IMATCS) has been employed for solving the underdetermined set of linear equations at each DBIM iteration. To overcome the challenges posed by the ill-posedness of the EM inverse scattering problem, the-based regularization approach was adopted in the amalgamation of the IMATCS approach. The simulation results showed that osteoporotic and osteoarthritis bones can be differentiated based on the reconstructed dielectric properties even for low values of the signal-to-noise ratio. These results show that the adopted approach can be used to monitor bone health based on the reconstructed dielectric properties.

Debye Parameters of Humidity-Varying Soils for Induction Logging Techniques

This paper focuses on the tabulation of calculated Debye coefficients for a wide range of soils for source waves ranging from 300 MHz to 2 GHz. Debye coefficients of different soils will produce accurate FDTD dispersive simulations for wireline logging purposes. The FDTD dispersion analysis is based on an Auxiliary Differential Equation (ADE) method which depends on the Debye coefficients. A complex set of soil data is acquired and used in a twostep numerical solver to calculate the Debye coefficients. For a wide range of soils, Debye coefficients were developed for one, two, and three pole expansions. Most fits for one pole fits were highly inaccurate, so the coefficients generated were disregarded. Coefficients for two and three term expansions were accurate and were generated and tabulated here.

Patient-Specific Debye Parameters for Human Blood.

This paper develops a patient-specific model for the Debye parameters of human blood based on hemoglobin content. Blood samples were collected from 176 patients visiting the University Hospital, with both permittivity measurements and standard hematological analysis performed on each blood draw. The complete blood count of each sample provided information on the hemoglobin concentration of each sample; in total there were 73 distinct hemoglobin concentrations reported. An iterative process was used to find patient-specific, based on hemoglobin content, Debye parameters. First, a two-stage genetic algorithm was used to solve for the parameters of a two-pole Debye model based on the mean-blood properties. Then, a modified two-pole Debye model incorporating hemoglobin information was developed, and those parameters were solved for using the same two-stage genetic algorithm. This paper presents the parameters for both the mean-blood model and the patient-specific model. The patient-specific model has a mean-fractional error across all 73 samples of 3.41% compared to 7.64% when using the mean-blood model to represent the entire population. This work demonstrates the range in the dielectric properties of human blood samples and highlights the need for incorporating patient-specific information when using the Debye parameters to model the dielectric properties of human blood.

A Novel Two-Peak Analysis for Dielectric Spectroscopy

This paper describes a method for estimating model parameters $\varepsilon _{s}$ and $\Delta \varepsilon = \varepsilon _{s} - \varepsilon _{\infty }$ from the peaks in the imaginary permittivity and loss-tangent spectra. The analysis describes how measured parameters obtained from an impedance spectrometer, the magnitude of the impedance, and phase angle, are directly converted into complex permittivity and loss tangent. As an application, the method is used to detect and quantify the crystallization of skim-milk powder, which shows a dramatic change in the Debye parameters as it converts from the amorphous to crystalline state.

Dielectric and Double Debye Parameters of Artificial Normal Skin and Melanoma

The aim of this study is to characterise the artificial normal skin and melanoma by testing samples with different fibroblast and metastatic melanoma cell densities using terahertz (THz) time-domain spectroscopy (TDS) attenuated total reflection (ATR) technique. Results show that melanoma samples have higher refractive index and absorption coefficient than artificial normal skin with the same fibroblast density in the frequency range between 0.4 and 1.6 THz, and this contrast increases with frequency. It is primarily because that the melanoma samples have higher water content than artificial normal skin, and the main reason to melanoma containing more water is that tumour cells degrade the contraction of the collagen lattice. In addition, complex refractive index and permittivity of the melanoma samples have larger variations than that of normal skin samples. For example, the refractive index of artificial normal skin at 0.5 THz increases 4.3% while that of melanoma samples increases 8.7% when the cell density rises from 0.1 to 1 M/ml. It indicates that cellular response of fibroblast and melanoma cells to THz radiation is significantly different. Furthermore, the extracted double Debye (DD) model parameters demonstrate that the static permittivity at low frequency and slow relaxation time can be reliable classifiers to differentiate melanoma from healthy skin regardless of the cell density. This study helps understand the complex response of skin tissues to THz radiation and the origin of the contrast between normal skin and cancerous tissues.

Novel concept of detecting basal cell carcinoma in skin tissue using a continuous-wave millimeter-wave rectangular glass filled probe.

PurposeThis article presents the study and simulation results of a millimeter (mm)-wave device for cancerous tissue detection. mm-Wave approach ensures cheaper equipment instead of the traditional terahertz (THz) frequency approach. A probe that could be implemented using inexpensive silicon technology is proposed, and it also permits integration of entire measuring tool for easy deployment. Skin cancer was chosen as it representŝ80% of all newly diagnosed cases and is the most common form of cancer in Australia. For an initial development and validation, due to data availability consideration in the open literature, basal cell carcinoma (BCC) was used for simulations.Methods and resultsA probe, using high-frequency signals in the upper mm-wave frequency spectrum (90–300 GHz) to maximize the lateral resolution (mm precision) and allows the detection of tumors located at up to 0.5 mm deep in the skin, is proposed. A frequency-dependent relativity permittivity and an equivalent conductivity of skins were calculated based on the double Debye parameters. For the first time, electromagnetic (EM) models were generated and used along with a high-frequency EM simulator, ANSYS HFSS, to demonstrate the sensitivity of the concept. The following two scenarios were studied: in scenario one, a BCC layer of different thicknesses (10–3000 μm) was located on the top of the normal skin and, in scenario two, the BCC was embedded in normal skin at depths from 10 to 3000 μm. Variability using ±10% of the corresponding dielectric property was also considered.ConclusionThis study showed that the reflection coefficients vs frequency could capture useful information indicating the possible presence of BCC at mm-wave frequencies. Both magnitude and phase of the reflection coefficient were quantified, with two scenarios analyzed. It was found that a dual-band approach, 100–150 and 200–250 GHz, has the ability to highlight deviations from the normal skin.

Concentration analysis of breast tissue phantoms with terahertz spectroscopy.

Terahertz imaging has been previously shown to be capable of distinguishing normal breast tissue from its cancerous form, indicating its applicability to breast conserving surgery. The heterogeneous composition of breast tissue is among the main challenges to progressing this potential research towards a practical application. In this paper, two concentration analysis methods are proposed for analyzing phantoms mimicking breast tissue. The dielectric properties and the double Debye parameters were used to determine the phantom composition. The first method is wholly based on the conventional effective medium theory while the second one combines this theoretical model with empirical polynomial models. Through assessing the accuracy of these methods, their potential for application to quantifying breast tissue pathology was confirmed.

Extended Jaya's Algorithm for Optimal Design of Broadband Layered Microwave Absorbing Structures

Layered microwave absorbing structures (MASs) for the suppression of electromagnetic signals are important due to their broadband frequency response. However, optimization of such structures is difficult because several design variables are involved. A method for the efficient design of broadband, layered, magneto-dielectric MASs is based on analytical modeling of the frequency-dependent complex dielectric permittivity ( ${\mathbf \varepsilon_{r}}$ ) and magnetic permeability ( ${\mu} _{r}$ ). The use of an efficient, extended Jaya's algorithm for optimization results in highly feasible values of ${\mathbf \varepsilon_{r}}$ and ${\mu} _{r}$ based on optimal Debye parameters for a specific reflection loss (RL) and a −10 dB absorption bandwidth. The optimization is carried out in the X-band for both single- and dual-layer MASs. Deeper insight is obtained by optimizing RL with and without constraints on absorber layer coating thickness. The results show the effectiveness of the optimization for the design of MASs for practical applications.

Microwave measurement system for dispersive dielectric properties of densely packed pellets

We present a microwave measurement system that is intended for the estimation of the dispersive dielectric properties for densely packed pellets. In particular, we estimate the Debye parameters for the effective permittivity of a mixture of air and densely packed moist microcrystalline cellulose pellets for the frequency band 2.7–5.1GHz. The Debye parameters are estimated by means of minimizing the misfit between the measured scattering parameters and the corresponding computed response given a model of the measurement system. This minimization is performed by means of a nonlinear iterative optimization procedure, which is supported by continuum sensitivities, and the optimum is found in 10–60 iterations for the cases presented in this article. We find that increasing moisture content yields an increase in the static permittivity and a decrease in the relaxation time.