Two-dimensional FDTD analysis of a pulsed microwave confocal systemfor breast cancer detection: fixed-focus and antenna-array sensors

A novel focused active microwave system is investigated for detecting tumors in the breast. In contrast to X-ray and ultrasound modalities, the method reviewed here exploits the breast-tissue physical properties unique to the microwave spectrum, namely, the translucent nature of normal breast tissues and the high dielectric contrast between malignant tumors and surrounding lesion-free normal breast tissues. The system uses a pulsed confocal technique and time-gating to enhance the detection of tumors while suppressing the effects of tissue heterogeneity and absorption. Using published data for the dielectric properties of normal breast tissues and malignant tumors, the authors have conducted a two-dimensional (2-D) finite-difference time-domain (FDTD) computational electromagnetics analysis of the system. The FDTD simulations showed that tumors as small as 2 mm in diameter could be robustly detected in the presence of the background clutter generated by the heterogeneity of the surrounding normal tissue. Lateral spatial resolution of the tumor location was found to be about 0.5 cm     

Effect of lesion morphology on microwave signature in 2-D ultra-wideband breast imaging

This paper studies the possibility of distinguishing between benign and malignant masses by exploiting the morphology-dependent temporal and spectral characteristics of their microwave backscatter response in ultra-wideband breast cancer detection. The spiculated border profiles of 2-D breast masses are generated by modifying the baseline elliptical rings based upon the irregularity of their peripheries. Furthermore, the single- and multilayer lesion models are used to characterize a distinct mass region followed by a sharp transition to background, and a blurred mass border exhibiting a gradual transition to background, respectively. Subsequently, the complex natural resonances (CNRs) of the backscatter microwave signature can be derived from the late-time target response and reveal diagnostically useful information. The fractional sequence CLEAN algorithm is proposed to estimate the lesions' delay intervals and identify the late-time responses. Finally, it is shown through numerical examples that the locations of dominant CNRs are dependent on the lesion morphologies, where 2-D computational breast phantoms with single and multiple lesions are investigated. The analysis is of potential use for discrimination between benign and malignant lesions, where the former usually possesses a better-defined, more compact shape as opposed to the latter.     

Study of optical and dielectric properties of annealed ZnO nanoparticles in the terahertz regime

The frequency-dependent optical and dielectric properties of annealed ZnO nanoparticles in the range of 0.1 to 0.9 THz are studied by using terahertz time-domain spectroscopy（THz-TDS）.The refractive index,power absorption and complex dielectric constants are obtained and the experimental results are well fit with a simple effective medium theory in conjunction with a pseudo-harmonic model.This study reveals that annealed ZnO nanoparticles exhibit the similar phonon response characteristics to the single ZnO crystal and other ZnO nanostructures,such as tetrapods and nanowires.     

Buried unexploded ordnance identification via complex naturalresonances

A classification technique focused on the identification of buried unexploded ordnance (UXO) using complex natural resonance (CNR) signature is considered. The total least square (TLS) Prony's (1795) method is used to extract CNRs from time-domain data, Full-scale UXO computational models and the body of revolution moment method (BORMM) code is used to obtain the backscattered fields, which are then used to give the theoretical free-space CNRs. Baum's (1993) transformation is used to relate a CNR in a lossy simple medium to the corresponding CNR in free space. A practical UXO classification yields an estimate of the UXO length from its CNR information. Successful UXO classification examples from actual measured data are presented     

Confocal microwave imaging for breast cancer detection: localization of tumors in three dimensions

The physical basis for breast tumor detection with microwave imaging is the contrast in dielectric properties of normal and malignant breast tissues. Confocal microwave imaging involves illuminating the breast with an ultra-wideband pulse from a number of antenna locations, then synthetically focusing reflections from the breast. The detection of malignant tumors is achieved by the coherent addition of returns from these strongly scattering objects. In this paper, we demonstrate the feasibility of detecting and localizing small (<1 cm) tumors in three dimensions with numerical models of two system configurations involving synthetic cylindrical and planar antenna arrays. Image formation algorithms are developed to enhance tumor responses and reduce early- and late-time clutter. The early-time clutter consists of the incident pulse and reflections from the skin, while the late-time clutter is primarily due to the heterogeneity of breast tissue. Successful detection of 6-mm-diameter spherical tumors is achieved with both planar and cylindrical systems, and similar performance measures are obtained. The influences of the synthetic array size and position relative to the tumor are also explored.     

DC power-bus design using FDTD modeling with dispersive media andsurface mount technology components

DC power-bus modeling in high-speed digital design using the finite-difference time-domain (FDTD) method is demonstrated herein. The dispersive character of the dielectric layers used in printed circuit board substrates is taken into account in this study. In particular, FR-4 is considered. The complex permittivity of the dielectric is approximated by a Debye model. A wide-band frequency response (100 MHz-5 GHz) is obtained through a single FDTD simulation. Good agreement is achieved between the modeled and measured results for a typical dc power-bus structure with multiple surface mount technology (SMT) decoupling capacitors placed on the printed circuit board (PCB). The FDTD method is then applied to investigate some general approaches of power-bus noise decoupling     

Dielectric properties of breast carcinoma and the surroundingtissues

Relative permittivity of infiltrating breast carcinoma and the surrounding tissue was measured. The experiments were performed at frequencies from 20 kHz to 100 MHz at 37°C using an automatic network analyzer and an end-of-the-line capacitive sensor. Cole-Cole dielectric parameters were calculated by curve fitting using a computer program. Three main categories of tissues were considered: the central part of the tumor, the tumor surrounding tissue, and the peripheral tissue. Within each category, the large spread of the dielectric data for different specimens suggests structural and cellular inhomogeneities of the tumor tissue. However, certain consistency has been found in the dielectric relaxation time and the coefficient of the distribution of the relaxation time within each category. The results seem to indicate that RF impedance imaging can potentially be used as a diagnostic modality for the detection of human breast carcinoma     

Highly Accurate Debye Models for Normal and Malignant Breast Tissue Dielectric Properties at Microwave Frequencies

The finite difference time domain (FDTD) method is widely used as a computational tool for development, validation, and optimization of emerging microwave breast cancer detection and treatment techniques. When expressed in terms of Debye parameters, dispersive breast tissue dielectric properties can be efficiently incorporated into FDTD codes. Previously, we experimentally characterized the dielectric properties of a large number of excised normal and malignant breast tissue samples from 0.5 to 20 GHz. We subdivided the large database of normal tissue data into three groups based on the percent adipose tissue present in a particular sample. In addition, we formed a group of all cancer samples that contained at least 30% malignant tissue. We summarized the data using one-pole Cole-Cole models that were rigorously fit to the median dielectric properties of the three normal tissue groups and one malignant tissue group. In this letter, we present computationally simpler one- and two-pole Debye models that retain the high accuracy of the Cole-Cole models. Model parameters are derived for two sets of frequency ranges: the entire measurement frequency range from 0.5 to 20 GHz, and the 3.1-10.6 GHz FCC band allocated for ultrawideband medical applications. The proposed Debye models provide a means for creating computationally efficient FDTD breast models with realistic wideband dielectric properties derived from the largest and most comprehensive experimental study conducted to date on human breast tissue.     

时域物理光学法分析均匀介质目标的瞬态散射

提出将时域物理光学法(TDPO)应用于计算电大均匀介质目标的时域散射场。将菲涅尔反射系数应用到频域物理光学近似中,由逆傅里叶变换推导出介质TDPO的表达式,从而使TDPO能够分析电大均匀介质目标的瞬态响应。同时给出了三角面片建模下入射波的遮挡消隐方法。计算了典型目标的瞬态散射响应和宽带雷达散射截面(RCS),与其他方法求得的结果吻合良好,验证了介质TDPO的正确性。     

Theory of the symmetrical super-condensed node for the TLM method

This paper describes a novel time-domain node for the TLM method. It has the unique feature of modeling arbitrary inhomogeneous media on a generally graded rectangular TLM mesh without using stubs. Variations in material properties and arbitrary aspect ratios of mesh cells are modeled by allowing different characteristic impedances in a cell, maintaining impulse synchronism throughout the mesh. The complete theory of the new node is given and its implementation on a general TLM mesh is discussed. Numerical results for a canonical resonator loaded with dielectric layers are presented for different grading cases. Substantial savings in computer storage and run-time as well as improved accuracy compared to the uniform mesh are achieved when an appropriate nonuniform grading of the TLM mesh is used     

氧化镁单晶在太赫兹波段的介电特性

利用太赫兹时域光谱系统,在0.5~9.5 THz范围内对氧化镁单晶基片的介电特性进行了研究,并获得折射率、吸收系数以及复介电函数信息。实验数据表明,在低频（ 2 THz）范围内,氧化镁单晶透过性较好,折射率在3.12~3.15之间。折射率和吸收系数均随频率增加而增大,且在3.16 THz和8.11 THz两处存在明显的吸收峰。通过经典的赝简谐振动理论很好地拟合了实验结果,分析了晶体中的横向光学声子振动模式,为氧化镁单晶在宽带太赫兹波段的应用提供了有益参考。     

Application of a finite-difference technique to the human radiofrequency dosimetry problem

A powerful finite-difference numerical technique has been applied to the human radiofrequency dosimetry problem. The method possesses inherent advantages over the method-of-moments approach in that its implementation requires much less computer memory. Consequently, it has the capability to calculate specific absorption rates (SARs) at higher frequencies and provides greater spatial resolution. The method is illustrated by the calculation of the time-domain and frequency-domain SAR responses at selected locations in the chest. The model for the human body is comprised of rectangular cells with dimensions of 4X4X6 cm and dielectric properties that simulate average tissue (2/3 muscle). Additionally, the upper torso (chest) is configured by both homogeneous and inhomogeneous models in which this region is subdivided into 20,736 cells with dimensions of 1X1X1 cm. The homogeneous model of the chest consists of cells with average tissue properties, and the calculated results are compared with measurements acquired from a homogeneous phantom model when the exposure frequency is 350 MHz. For the inhomogeneous chest model the lungs and surrounding region (ribs, spine, sternum, fat, and muscle) are modeled with as much spatial resolution as allowed by the 1X1X1 cm cells. Computed results from the inhomogeneous chest model are compared with the homogeneous model.     

The measurement of the dielectric and optical properties of nano thin films by THz differential time-domain spectroscopy

As feature sizes of circuits and devices approach 100 nm and chip frequencies climb into the upper GHz to THz range, it becomes increasingly important to have a convenient method of characterizing properties of thin dielectric films in the GHz to THz frequency range. THz time-domain spectroscopy provides a non-contact, non-destructive and highly sensitive optical tool to characterize the dielectric and optical properties of micron to nanometer scaled thin films at GHz and THz frequencies. The measurement of the dielectric and the optical properties of nanometer scaled dielectric films is performed using the THz differential time-domain spectroscopy. The real and imaginary parts of the complex dielectric constants and the optical constants of a variety of nano thin films are measured at GHz and THz frequencies.     

A novel systematic approach for equivalent model extraction of embedded high-speed interconnects in time domain

Based on time-domain scattered data, an efficient systematic approach in the time domain has been proposed to extract the SPICE-compatible models of embedded high-speed interconnects. The approach combines the layer-peeling technique and the generalized pencil-of-matrix method to obtain a pole-residue representation of the step response of the interconnects. An order-reduction procedure is implemented based on the bandwidth criterion to find the optimum pole-residue representation of the interconnects with minimum pole numbers. The SPICE-compatible lumped circuits are then systematically extracted from the pole-residue rational functions. The discontinuous microstrip lines and bonding wire structure are used to demonstrate the validity of the proposed approach. Good agreement is seen between the modeled and measured transient response. The advantages of this approach are the de-embedding ability for arbitrary nonuniform interconnects, systematically obtaining lower order and more accurate SPICE-compatible circuits, and broad-band performance of the extracted circuits.     

Rules for robust generation of accurate reduced-order models forhigh-speed coupled interconnections

Recently, robust algorithms have been established fur passive order reduction of electrical models of complex interconnection networks. However, very little is known about the way the order of the reduced model should be chosen to ensure accuracy in subsequent transient simulation studies, in this paper, a rule is derived for the selection of the order of the reduced model for interconnections modeled as transmission lines. It is shown that pulse rise time, interconnection length, and physical properties impact the order of the reduced model. The proposed rule is validated through numerical studies involving both analytic and numerical results from the frequency- and time-domain response of multiconductor transmission line circuits     

Terahertz attenuation and dispersion characteristics of coplanartransmission lines

Experimental verification of analytic formulas for the dispersion and the attenuation of electrical transient signals propagating on coplanar transmission lines is presented. The verification is done in the frequency domain over a terahertz range although the experiments are in the time domain. The analytic formulas are obtained from fits to the full-wave analysis results. It is quantitatively verified that the full-wave steady-state solutions can be directly applied to the transient time-domain propagation experiments. Subpicosecond electrical pulses and an external electrooptic sampling technique are used to obtain the time-domain propagation data. From the Fourier transforms of the time-domain data both the attenuation and the phase information as a function of frequency are extracted. The dispersion and the attenuation characteristics are investigated for both coplanar waveguide and coplanar strip transmission lines. The investigation is carried out on both semiinsulating semiconductor and dielectric substrate materials. No observable losses caused by the semiconductor material are indicated     

Tera Tool [terahertz time-domain spectroscopy]

The terahertz differential time-domain spectroscopic method is applied to characterize the dielectric and optical properties of a variety of thin films at terahertz frequency. The results of several samples including silicon dioxide, parylene-n polymer film, tantalum oxide film, and protein thin layer samples were presented. The dielectric property of silicon dioxide thin film is well fitted to that of a bulk. The dielectric properties of parylene-n thin films show good agreement with the result measured by the goniometric terahertz time-domain spectroscopy. The dielectric and optical properties of the tantalum oxide show reasonable data with previously available data. Some properties in thin films are slightly different from the bulk materials. The origin of this discrepancy is considered due to fine grain formation, mechanical stresses, formation of interfacial layers, or rough interfaces during thin-film deposition process. The terahertz differential time-domain spectroscopy may be applied to the measurement of the dielectric and optical properties of thin films (nanometer to micrometer) of several materials, which cannot be done by any other method.     

Dielectric Relaxation of HCl and NaCl Solutions Investigated by Terahertz Time-Domain Spectroscopy

We have used Terahertz time-domain spectroscopy (THz-TDS) to investigate the complex dielectric function of water solutions containing different ions. Using HCl and NaCl solutions with different concentrations we study the changes of the dielectric response introduced by the ions. We find a linear increase of the real and imaginary part of the dielectric function compared with pure water with increasing ion concentrations. We use an expanded model for fitting the dielectric function based on a combination of a Debye relation and damped harmonic oscillators for the anions and cations. A good agreement between the model and the experimental results is obtained.     

Modeling the visibility of breast malignancy by a microwave radiometer

A breast tumor is visible by a passive microwave radiometer if it changes the radiometric output of a healthy breast to an extent that overcomes the radiometric resolution for the given sensing antenna and integration time. We modeled breast temperature by the standard Pennes equation using thermal parameters found in the literature for normal and cancerous breast tissue. An apparent thermal volume and its dependence on blood perfusion have been estimated. The radiometric weighting function has been evaluated as a function of the size of a contacting antenna modeled as an aperture antenna. For comparison with the radiometric resolution, the difference signal between the outputs in the presence of a lesion and in its absence has been evaluated for different tumor sizes and depths. The results of the numerical analysis show that this difference signal depends on the average over-temperature in the lesion times the heating efficiency, given by the fraction of power delivered to the tumor when the antenna radiates onto the breast in active modality. A tumor of 6 mm (10 mm) diameter is visible by a 0.1 K radiometer and a 3 cm aperture antenna when it is not deeper than 1.2 cm (2.8 cm) under the assumption of ideal radiometer and antenna.