A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model

Guo, Bin; Li, Jian; Zmuda, Henry

doi:10.1109/lmwc.2006.885583

Cited by 60 publications

(30 citation statements)

References 9 publications

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“…Cole-Cole dispersion models are frequently used for biological media since they cab provide a better representation than Debye models for broad frequency ranges including frequencies below tens of MHz [106]- [108] and, as alluded before, involve fractional derivatives. These can be approximated in terms of a finite series and incorporated into the FDTD update by, for example, applying a conventional ADE approach for each term of the series [64] or by the -transform approach [109].…”

Section: Fdtd For Dispersive Media: Selected Examples 1) Microwavementioning

confidence: 99%

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

Teixeira

2008

IEEE Trans. Antennas Propagat.

197

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Section: Fdtd For Dispersive Media: Selected Examples 1) Microwavementioning

confidence: 99%

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

Teixeira

2008

IEEE Trans. Antennas Propagat.

197

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“…The finite-difference time-domain (FDTD) method [3] is commonly used for computational investigations of such modalities. The overall accuracy of FDTD simulations of wideband microwave interactions with breast tissue is prescribed in part by the accuracy of the model used to capture the relaxation-based Manuscript [3], [4] to the Cole-Cole model that is more computationally complex [5], [6].…”

mentioning

confidence: 99%

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

Lazebnik

Okoniewski

Booske

et al. 2007

IEEE Microw. Wireless Compon. Lett.

230

149

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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.Index Terms-Breast cancer detection and treatment, Cole-Cole model, Debye model, dielectric properties, finite-difference timedomain (FDTD).

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“…Consequently, 0,ti y(t i ) for t i ∈ [0. 5,10]. For this purpose, we apply the trapezoidal numerical integration method to approximate the integrals in (40) and (41) by considering the noisy observation y ϖ .…”

Section: Polynomial Signalmentioning

confidence: 99%

“…[5,6,7,8]) and in signal processing applications (see, e.g. [9,10,11,12]). The fractional order numerical differentiation is concerned with the estimation of the fractional order derivatives of an unknown signal from its discrete noisy observed data.…”

Section: Introductionmentioning

confidence: 99%

Robust fractional order differentiators using generalized modulating functions method

Liu

Laleg‐Kirati

2015

Signal Processing

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This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

show abstract

A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model

Cited by 60 publications

References 9 publications

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

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

Robust fractional order differentiators using generalized modulating functions method

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