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Research Papers

Influence of Microstructure on the High-Frequency Ultrasound Measurement of Peak Density

[+] Author and Article Information
Jeremy Stromer

Department of Mechanical Engineering,
University of Connecticut Storrs,
191 Auditorium Road, Unit 3139,
Storrs, CT 06269
e-mail: jeremy.stromer@uconn.edu

Leila Ladani

Mechanical and Aerospace Engineering,
Institute for Predictive Performance
Methodologies,
University of Texas at
Arlington Research Institute,
7300 Jack Newell Boulevard South,
Fort Worth, TX 76118
e-mail: Leila.Ladani@uta.edu

1Corresponding author.

Manuscript received October 27, 2017; final manuscript received July 30, 2018; published online August 31, 2018. Assoc. Editor: Yuris Dzenis.

ASME J Nondestructive Evaluation 1(4), 041008 (Aug 31, 2018) (10 pages) Paper No: NDE-17-1102; doi: 10.1115/1.4041067 History: Received October 27, 2017; Revised July 30, 2018

Peak density is an ultrasound measurement, which has been found to vary according to microstructure, and is defined as the number of local extrema within the resulting power spectrum of an ultrasound measurement. However, the physical factors which influence peak density are not fully understood. This work studies the microstructural characteristics which affect peak density through experimental, computationa,l and analytical means for high-frequency ultrasound of 22–41 MHz. Experiments are conducted using gelatin-based phantoms with glass microsphere scatterers with diameters of 5, 9, 34, and 69 μm and number densities of 1, 25, 50, 75, and 100 mm−3. The experiments show the peak density to vary according to the configuration. For example, for phantoms with a number density of 50 mm−3, the peak density has values of 3, 5, 9, and 12 for each sphere diameter. Finite element simulations are developed and analytical methods are discussed to investigate the underlying physics. Simulated results showed similar trends in the response to microstructure as the experiment. When comparing scattering cross section, peak density was found to vary similarly, implying a correlation between the total scattering and the peak density. Peak density and total scattering increased predominately with increased particle size but increased with scatterer number as well. Simulations comparing glass and polystyrene scatterers showed dependence on the material properties. Twenty-four of the 56 test cases showed peak density to be statistically different between the materials. These values behaved analogously to the scattering cross section.

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Figures

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Fig. 3

Flowchart for the experimental determination of peak density

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Fig. 2

The pulse received through a small amount of coupling gel (a). The resulting frequency spectrum (b). This was the calibration spectrum used in our experiments. The bandwidth of the transducer is 22–41 MHz.

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Fig. 1

Photographs of phantoms used in this study: 9 μm size microspheres with 1 mm−3 density (a); 34 μm size microspheres with 25 mm−3 density (b); and 69 μm size microspheres with 50 mm−3 density (c). Due to some difficulty imaging the 5 μm phantoms, we do not have any images of these phantoms.

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Fig. 10

Forward scattering according to Faran for each modeled sphere diameter: (a) 5 μm, (b) 9 μm, (c) 34 μm, and (d) 69 μm. Note that these may vary from the spectra in Fig. 6 because the previous figure sums the intensity of the pressure field across the transducer face. The graphs here show the scattered field in the pure forward direction only.

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Fig. 9

Comparison of measurements taken for experimental phantoms: peak density (a) and pulse amplitude (b)

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Fig. 7

Bar graphs showing the measured peak densities for the experiment and finite element model

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Fig. 8

Peak densities for the expanded model including larger and additional scatterers added to the simulation domain

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Fig. 11

Calculation of the total scattering using analytical techniques. Note that z-axis uses a logarithmic scale in order to show the full range of σs,total.

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Fig. 12

Simulated peak densities for glass (a) and polystyrene (b). Comparison of σs,total and peak density for glass (c) and polystyrene scatterers (d). Note the logarithmic scale for σs,total.

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Fig. 4

Geometry used in the finite element model. Modeling domains are shown in (a). The four sets of randomly distributed microspheres are given in (a)–(d).

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Fig. 5

Flowchart for determination of simulated peak density. This process is completed for each scatterer diameter as well as the different numbers of scatterers.

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Fig. 6

Examples of the simulated frequency spectra for a single scatter of diameter : (a) 5 μm, (b) 9 μm, (c) 34 μm, and (d) 69 μm. This is the magnitude of the scattered pressure field on the entire face of the simulated transducer.

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Fig. 13

Main effects' plots for the simulated peak density (a) and the analytical cross section (b). Error bars in (a) correspond to the standard deviation.

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