Mathematics, medicine and microwaves

Albanese, Richard A.; Medina, Richard L.; Penn, John W.

doi:10.1088/0266-5611/10/5/001

Cited by 28 publications

(14 citation statements)

References 23 publications

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“…Introduction. The study of transient electromagnetic waves in lossy dispersive dielectrics is of great interest due to numerous applications [AMP94,APM89]. These include microwave imaging for medical applications in which one seeks to investigate the internal structure of an object (the human body) by means of electromagnetic fields at microwave frequencies (300 MHz -30 GHz).…”

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A computational and statistical framework for multidimensional domain acoustooptic material interrogation

Banks

Bokil

2005

Quart. Appl. Math.

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Abstract. We consider an electromagnetic interrogation technique in two and three dimensions for identifying the dielectric parameters (including the permittivity, the conductivity and the relaxation time) of a Debye medium. In this technique, a travelling acoustic pressure wave in the Debye medium is used as a virtual reflector for an interrogating microwave electromagnetic pulse that is generated in free space. The reflections of the microwave pulse from the air-Debye interface and from the acoustic pressure wave are recorded at a remote antenna. The data is used in an inverse problem to estimate the locally pressure dependent dielectric parameters of the Debye medium. We present a time domain formulation that is solved using finite differences (FDTD) in time and in space. Perfectly matched layer (PML) absorbing boundary conditions are used to absorb outgoing waves at the finite boundaries of the computational domain, preventing spurious reflections from reentering the domain.Using the method of least squares for the parameter identification problem, we compare two different algorithms (the gradient based Levenberg-Marquardt method and the gradient free, simplex based Nelder-Mead method) in solving an inverse problem to calculate estimates for two or more dielectric parameters. Finally we use statistical error analysis to construct confidence intervals for all the presented estimates, thereby providing a probabilistic statement about the computational procedure with uncertainty aspects of estimates.

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confidence: 99%

A computational and statistical framework for multidimensional domain acoustooptic material interrogation

Banks

Bokil

2005

Quart. Appl. Math.

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“…The study of transient electromagetic waves in lossy dispersive dielectrics is of great interest due to numerous applications [AMP94,APM89]. These include microwave imaging for medical applications in which one seeks to investigate the internal structure of an object (the human body) by means of electromagnetic fields at microwave frequencies (300 MHz -30 GHz).…”

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confidence: 99%

A Computational and Statistical Framework for Multidimensional Domain Acoustooptic Material Interrogation

Banks¹,

Bokil²

2005

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We consider an electromagnetic interrogation technique in two and three dimensions for identifying the dielectric parameters (including the permittivity, the conductivity and the relaxation time) of a Debye medium. In this technique a travelling acoustic pressure wave in the Debye medium is used as a virtual reflector for an interrogating microwave electromagnetic pulse that is generated in free space. The reflections of the microwave pulse from the air-Debye interface and from the acoustic pressure wave are recorded at a remote antenna. The data is used in an inverse problem to estimate the locally pressure dependent dielectric parameters of the Debye medium. We present a time domain formulation that is solved using finite differences (FDTD) in time and in space. Perfectly matched layer (PML) absorbing boundary conditions are used to absorb outgoing waves at the finite boundaries of the computational domain, preventing spurious reflections from reentering the domain.Using the method of least squares for the parameter identification problem, we compare two different algorithms (the gradient based Levenberg-Marquardt method, and the gradient free, simplex based Nelder-Mead method) in solving an inverse problem to calculate estimates for two or more dielectric parameters. Finally we use statistical error analysis to construct confidence intervals for all the presented estimates, thereby providing a probabilistic statement about the computational procedure with uncertainty aspects of estimates.Keywords: Electromagnetic-acoustic interaction, Debye dielectric materials, pulsed antenna source microwaves, inverse problems, FDTD, statistical inference. † email: htbanks@ncsu.edu ‡ email: vabokil@ncsu.edu 1 Report Documentation Page Form Approved OMB No. 0704-0188Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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“…Noninvasive interrogation of the interior of tissues and other materials by electromagnetic waves has important applications in various fields including medical imaging for the early detection of anomalies and nondestructive damage detection in aircraft [2,3]. For example, microwave imaging for breast cancer detection is expected to be safe for the patient and has the potential to detect very small cancerous tumors in the breast [16].…”

Section: Introductionmentioning

confidence: 99%

Analysis of stability and dispersion in a finite element method for Debye and Lorentz dispersive media

Banks

Bokil

Gibson

2008

Numerical Methods Partial

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Abstract:We study the stability properties of, and the phase error present in, a finite element scheme for Maxwell's equations coupled with Debye or Lorentz polarization. In one dimension we consider a second order formulation for the electric field with an ordinary differential equation for the polarization added as an auxiliary constraint. The finite element method uses linear finite elements in space for the electric field as well as the polarization, and a theta scheme for the time discretization. Numerical experiments suggest the method is unconditionally stable for both Debye and Lorentz models. We compare the stability and phase error properties of the method presented here with those of finite difference methods that have been analyzed in the literature. We also conduct numerical simulations that verify the stability and dispersion properties of the scheme. Keywords Report Documentation Page Form Approved OMB No. 0704-0188Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Mathematics, medicine and microwaves

Cited by 28 publications

References 23 publications

A computational and statistical framework for multidimensional domain acoustooptic material interrogation

A computational and statistical framework for multidimensional domain acoustooptic material interrogation

A Computational and Statistical Framework for Multidimensional Domain Acoustooptic Material Interrogation

Analysis of stability and dispersion in a finite element method for Debye and Lorentz dispersive media

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