Effect of transducer position on ultrasonic backscatter measurements of cancellous bone.

Ultrasonic backscatter techniques are being developed to detect changes in bone caused by osteoporosis and other diseases. Backscatter measurements performed at peripheral skeletal sites such as the heel may place the interrogated region of bone tissue in the acoustic near field of the transducer. The purpose of this study is to investigate how measurements in the near field affect backscatter parameters used for ultrasonic bone assessment. Ultrasonic measurements were performed in a water tank using a planar 2.25 MHz transducer. Signals were acquired for five transducer-specimen distances: N/4, N/2, 3 N/4, N, and 5 N/4, where N is the near-field distance, a location that represents the transition from the near field to far field. Five backscatter parameters previously identified as potentially useful for ultrasonic bone assessment purposes were measured: apparent integrated backscatter, frequency slope of apparent backscatter (FSAB), frequency intercept of apparent backscatter, normalized mean of the backscatter difference, and backscatter amplitude decay constant. All five parameters depended on transducer-specimen distance to varying degrees with FSAB exhibiting the greatest dependence on distance. These results suggest that laboratory studies of bone should evaluate the performance of backscatter parameters using transducer-specimen distances that may be encountered clinically including distances where the ultrasonically interrogated region is in the near field of the transducer.

Characterization of sphere-plane contact loss nonlinearity inside a cylindrical container using nonlinear ultrasound resonance spectroscopy.

Cylindrical containers, such as liquid tanks and pressure vessels, are ubiquitous in storage applications. Traditional lines of non-destructive evaluation (NDE) are mostly focused on the integrity of containers, but studies on solid contents within using external sensors are lacking. In previous work, metrics were developed to estimate the structural integrity of mock-up fuel assemblies inside a lab-scale nuclear dry storage cask. Linear acoustic resonance techniques were shown to be sensitive down to single assembly level. In this work, this problem is further examined by studying contact nonlinearity in a simplified system using Nonlinear Ultrasound Resonance Spectroscopy (NRUS). This system consists of a single layer of identical spheres with varying composition and size evenly distributed at the bottom of a cylindrical aluminum container. The resonance frequency shifts due to varying amplitudes were mostly affected by the total mass of spheres inside, while diameter and composition of spheres played minor roles. A phenomenological model was developed based on the resulting shifts and was studied numerically using finite element simulations. The agreement between simulations and experiments suggests that the contact nonlinearity is predominated by a contact loss mechanism. This NRUS technique may complement linear acoustic techniques for solid cargo NDE inside sealed vessels.

Broadband wave packet dynamics of minimally diffractive ultrasonic fields from axicon and stepped fraxicon lenses.

A fraxicon is a stepped phase plate lens designed to be a discrete approximation of the axicon, a refractive cone-shaped lens. Both lenses generate minimally diffractive Bessel beams with long depths of focus. Here the characteristics of broadband pulses modified by these lenses to compare and contrast the dynamics of the propagating wave packets were examined. Pulses from a spherically focused Fresnel lens are also examined to provide the context of a conventional design. The wave packets generated through the fraxicon exhibit many of the same characteristics of those from the axicon such as lateral compactness and axial integrity, although the fraxicon packets do exhibit noticeable dispersion in comparison. Both the fraxicon and axicon wave packets have a much tighter lateral extent than those of the Fresnel throughout the propagation region. The most significant difference between the fraxicon and axicon is with the group speeds of the packets with the fraxicon group subsonic and the axicon supersonic across a 50 mm path. Supplemental movies are provided for direct visualization of the propagation (for movies of the waveforms and energy profiles of the wave packet propagation that was experimentally obtained). To assess the conformity of the low profile lenses to their design parameters, frequency domain comparisons of measurements with simulations are also presented and are in good agreement.

Spatial filters suppress ripple artifacts in the computation of acoustic fields with the angular spectrum method.

The angular spectrum method (ASM) is an effective tool for propagating wave fields between parallel planes through decomposition of the field into a series of independent plane waves. One source of error is interference from mirror sources introduced through the inherent periodicity of the fast Fourier transform (FFT) used to implement this method numerically. Here, spatial filters attenuate waves propagating at large angles, which are sensitive to mirror sources. Simulations show that this suppresses the ripple artifact whilst preserving the accuracy of the ASM-computed fields. To achieve comparable performance without filtering requires up to a 13.5-fold increase in computation time.

The effect of static pressure on the strength of inertial cavitation events.

Recent investigations of cavitation in fluids pressurized up to 30 MPa found that the intensity of light emissions increased by 1000-fold over that measured for single bubble sonoluminescence. A series of measurements is reported here to extend this original work by resolving the static pressure dependence of the shock wave and light emissions from the first and the most energetic collapses, along with the total shock wave energy and light emissions for the event. Each of these parameters was found to increase with the static pressure of the fluid. Furthermore, the energy of these shock wave and light emissions was found to increase in proportion to the stored acoustic energy in the system. These findings were corroborated using the Gilmore equation to numerically compute the work done by the liquid during the bubble collapse. The overall findings suggest that the increased collapse strength at high static pressure is due to the increased tension required to generate inertial cavitation, and not an increased pressure gradient between the interior of the vaporous bubble and the surrounding liquid.

The effect of static pressure on the inertial cavitation threshold.

The amplitude of the acoustic pressure required to nucleate a gas or vapor bubble in a fluid, and to have that bubble undergo an inertial collapse, is termed the inertial cavitation threshold. The magnitude of the inertial cavitation threshold is typically limited by mechanisms other than homogeneous nucleation such that the theoretical maximum is never achieved. However, the onset of inertial cavitation can be suppressed by increasing the static pressure of the fluid. The inertial cavitation threshold was measured in ultrapure water at static pressures up to 30 MPa (300 bars) by exciting a radially symmetric standing wave field in a spherical resonator driven at a resonant frequency of 25.5 kHz. The threshold was found to increase linearly with the static pressure; an exponentially decaying temperature dependence was also found. The nature and properties of the nucleating mechanisms were investigated by comparing the measured thresholds to an independent analysis of the particulate content and available models for nucleation.

Suppression of an acoustic mode by an elastic mode of a liquid-filled spherical shell resonator.

The purpose of this paper is to report on the suppression of an approximately radial (radially symmetric) acoustic mode by an elastic mode of a water-filled, spherical shell resonator. The resonator, which has a 1-in. wall thickness and a 9.5-in. outer diameter, was externally driven by a small transducer bolted to the external wall. Experiments showed that for the range of drive frequencies (19.7-20.6 kHz) and sound speeds in water (1520-1570 m/s) considered in this paper, a nonradial (radially nonsymmetric) mode was also excited, in addition to the radial mode. Furthermore, as the sound speed in the liquid was changed, the resonance frequency of the nonradial mode crossed with that of the radial one and the amplitude of the latter was greatly reduced near the crossing point. The crossing of the eigenfrequency curves of these two modes was also predicted theoretically. Further calculations demonstrated that while the radial mode is an acoustic one associated with the interior fluid, the nonradial mode is an elastic one associated with the shell. Thus, the suppression of the radial acoustic mode is apparently caused by the overlapping with the nonradial elastic mode near the crossing point.

Simplified expressions of the subtracted Kramers-Kronig relations using the expanded forms applied to ultrasonic power-law systems.

The Kramers-Kronig (KK) relations are a large class of integral transformations that exploit the broad principle of simple causality in order to link the physical properties of matter and materials. In applications to the complex-valued wavenumber for acoustic propagation, the method of subtractions is used to form convergent integral relations between the phase velocity and the attenuation coefficient. When the method of subtractions is applied in the usual manner, the integrands in the relations become unnecessarily complicated. In this work, an expanded form of the subtracted relations is presented, which is essentially a truncated Taylor series expansion of the Hilbert transforms. The implementation of the relations only requires the explicit evaluation of two simply expressed integrals involving the Hilbert transform kernel. These two integrals determine the values of the other terms in the subtracted relations, demonstrating the computational efficiency of the technique. The method is illustrated analytically through its application to power-law attenuation coefficients and its associated dispersion, which are observed in a wide variety of materials. This approach explicitly shows the central role of the Hilbert transform kernel in the KK relations, which can become obscured in other formulations.

Determination of power-law attenuation coefficient and dispersion spectra in multi-wall carbon nanotube composites using Kramers-Kronig relations.

Using a broadband through-transmission technique, the attenuation coefficient and phase velocity spectra have been measured for a set of multi-wall carbon nanotube (MWCNT)-nylon composites (from pure nylon to 20% MWCNT by weight) in the ultrasonic frequency band from 4 to 14 MHz. The samples were found to be effectively homogeneous on spatial scales from the low end of ultrasonic wavelengths investigated and up (>0.2 mm). Using Kramers-Kronig relations, the attenuation and dispersion data were found to be consistent with a power-law attenuation model with a range of exponents from y=1.12 to y=1.19 over the measurement bandwidth. The attenuation coefficients of the respective samples are found to decrease with increasing MWCNT content and a similar trend holds also for the dispersion. In contrast, the mean phase velocities for the samples rise with increasing MWCNT content indicating an increase in the mechanical moduli.

Intensified biochip system using chemiluminescence for the detection of Bacillus globigii spores.

This paper reports the first intensified biochip system for chemiluminescence detection and the feasibility of using this system for the analysis of biological warfare agents is demonstrated. An enzyme-linked immunosorbent assay targeting Bacillus globigii spores, a surrogate species for Bacillus anthracis, using a chemiluminescent alkaline phosphatase substrate is combined with a compact intensified biochip detection system. The enzymatic amplification was found to be an attractive method for detection of low spore concentrations when combined with the intensified biochip device. This system was capable of detecting approximately 1 x 10(5) Bacillus globigii spores. Moreover, the chemiluminescence method, combined with the self-contained biochip design, allows for a simple, compact system that does not require laser excitation and is readily adaptable to field use.

Development of a Tissue-Mimicking Phantom of the Brain for Ultrasonic Studies.

Constructing tissue-mimicking phantoms of the brain for ultrasonic studies is complicated by the low backscatter coefficient of brain tissue, causing difficulties in simultaneously matching the backscatter and attenuation properties. In this work, we report on the development of a polyvinyl alcohol-based tissue-mimicking phantom with properties approaching those of human brain tissue. Polyvinyl alcohol was selected as the base material for the phantom as its properties can be varied by freeze-thaw cycling, variations in concentration and the addition of scattering inclusions, allowing some independent control of backscatter and attenuation. The ultrasonic properties (including speed of sound, attenuation and backscatter) were optimized using these methods with talc powder as an additive. It was determined that the ultrasonic properties of the phantom produced in this study are best matched to brain tissue in the frequency range 1-3 MHz, indicating its utility for laboratory ultrasonic studies in this frequency range.

The time-domain signature of negative acoustic group velocity in microsphere suspensions.

In the wake of recent reports of superluminal acoustic group velocities in sonic and ultrasonic regions of the acoustic spectrum, this paper describes the time-domain manifestation of such group velocities through simulations of the linear propagation of ultrasonic wave packets in a suspension of elastic microspheres. Conditions under which arbitrarily large and negative group velocities can be observed as the speed of a peak in the envelope of an acoustic pulse are described. Propagation simulations demonstrate the physical signature of negative group velocities, as well as the causal compliance of the superluminal acoustic pulses examined in this work.

Causal determination of acoustic group velocity and frequency derivative of attenuation with finite-bandwidth Kramers-Kronig relations.

Kramers-Kronig (KK) analyses of experimental data are complicated by the extrapolation problem, that is, how the unexamined spectral bands impact KK calculations. This work demonstrates the causal linkages in resonant-type data provided by acoustic KK relations for the group velocity (c(g)) and the derivative of the attenuation coefficient (alpha') (components of the derivative of the acoustic complex wave number) without extrapolation or unmeasured parameters. These relations provide stricter tests of causal consistency relative to previously established KK relations for the phase velocity (c(p)) and attenuation coefficient (alpha) (components of the undifferentiated acoustic wave number) due to their shape invariance with respect to subtraction constants. For both the group velocity and attenuation derivative, three forms of the relations are derived. These relations are equivalent for bandwidths covering the entire infinite spectrum, but differ when restricted to bandlimited spectra. Using experimental data from suspensions of elastic spheres in saline, the accuracy of finite-bandwidth KK predictions for c(g) and alpha' is demonstrated. Of the multiple methods, the most accurate were found to be those whose integrals were expressed only in terms of the phase velocity and attenuation coefficient themselves, requiring no differentiated quantities.

Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion.

Causality imposes restrictions on both the time-domain and frequency-domain responses of a system. The Kramers-Kronig (K-K) relations relate the real and imaginary parts of the frequency-domain response. In ultrasonics, K-K relations often are used to link attenuation and dispersion. We review both integral and differential forms of the frequency-domain K-K relations that are relevant to theoretical models and laboratory measurements. We consider two methods for implementing integral K-K relations for the case of finite-bandwidth data, namely, extrapolation of data and restriction of integration limits. For the latter approach, we discuss the accuracy of K-K predictions for specific classes of system behavior and how the truncation of the integrals affects this accuracy. We demonstrate the accurate prediction of attenuation and dispersion using several forms of the K-K relations relevant to experimental measurements of media with attenuation coefficients obeying a frequency power law and media consisting of resonant scatterers. We also review the time-causal relations that describe the time-domain consequences of causality in the wave equation. These relations can be thought of as time-domain analogs of the (frequency-domain) K-K relations. Causality-imposed relations, such as the K-K and time-causal relations, provide useful tools for the analysis of measurements and models of acoustic systems.

Detection of bacterial pathogen DNA using an integrated complementary metal oxide semiconductor microchip system with capillary array electrophoresis.

In this paper, we show an integrated complementary metal oxide semiconductor (CMOS)-based microchip system with capillary array electrophoresis (CAE) for the detection of bacterial pathogen amplified by polymerase chain reaction (PCR). In order to demonstrate the efficacy of PCR reaction for the heat-labile toxin producing enterotoxigenic Escherichia coli (E. coli), which causes cholera-like diarrhea, 100 bp DNA ladders were injected along with the PCR product. Poly(vinylpyrrolidone) (PVP) was used as the separation medium and provided separation resolution which was adequate for the identification of PCR product. The miniaturized integrated CMOS microchip system with CAE has excellent advantages over conventional instrumental systems for analysis of bacterial pathogens such as compactness, low cost, high speed, and multiplex capability. Furthermore, the miniaturized integrated CMOS microchip system should be compatible with a variety of microfabricated devices that aim at more rapid and high-throughput analysis.

Differential forms of the Kramers-Krönig dispersion relations.

Differential forms of the Kramers-Krönig dispersion relations provide an alternative to the integral Kramers-Krönig dispersion relations for comparison with finite-bandwidth experimental data. The differential forms of the Kramers-Krönig relations are developed in the context of tempered distributions. Results are illustrated for media with attenuation obeying an arbitrary frequency power law (alpha(omega) = alpha0 + alpha1(absolute value of omega)y). Dispersion predictions using the differential dispersion relations are compared to the measured dispersion for a series of specimens (two polymers, an egg yolk, and two liquids) exhibiting attenuation obeying a frequency power law (1.00 < or = y < or = 1.99), with very good agreement found. For this form of ultrasonic attenuation, the differential Kramers-Krönig dispersion prediction is found to be identical to the (integral) Kramers-Krönig dispersion prediction.

Finite-bandwidth Kramers-Kronig relations for acoustic group velocity and attenuation derivative applied to encapsulated microbubble suspensions.

Kramers-Kronig (KK) analyses of experimental data are complicated by the conflict between the inherently bandlimited data and the requirement of KK integrals for a complete infinite spectrum of input information. For data exhibiting localized extrema, KK relations can provide accurate transforms over finite bandwidths due to the local-weighting properties of the KK kernel. Recently, acoustic KK relations have been derived for the determination of the group velocity (cg) and the derivative of the attenuation coefficient (alpha') (components of the derivative of the acoustic complex wave number). These relations are applicable to bandlimited data exhibiting resonant features without extrapolation or unmeasured parameters. In contrast to twice-subtracted finite-bandwidth KK predictions for phase velocity and attenuation coefficient (components of the undifferentiated wave number), these more recently derived relations for cg and alpha' provide stricter tests of causal consistency because the resulting shapes are invariant with respect to subtraction constants. The integrals in these relations can be formulated so that they only require the phase velocity and attenuation coefficient data without differentiation. Using experimental data from suspensions of encapsulated microbubbles, the finite-bandwidth KK predictions for cg and alpha' are found to provide an accurate mapping of the primary wave number quantities onto their derivatives.

Ultrasonic properties of a suspension of microspheres supporting negative group velocities.

The ultrasonic attenuation coefficient, phase velocity, and group velocity spectra are reported for a suspension that supports negative group velocities. The suspension consists of plastic microspheres with an average radius of 80 microm in an aqueous medium at a volume fraction of 3%. The spectra are measured using a broadband method covering a range from 2 to 20 MHz. The suspension exhibits negative group delays over a band near 4.5 MHz, with the group velocity magnitude exceeding 4.3 x 10(8) m/s at one point. The causal consistency of these results is confirmed using Kramers-Kronig relations.

Finite-bandwidth effects on the causal prediction of ultrasonic attenuation of the power-law form.

Kramers-Kronig (K-K) relations exist as a consequence of causality, placing nonlocal constraints on the relationship between dispersion and absorption. The finite-bandwidth method of applying these relations is examined where the K-K integrals are restricted to the spectrum of the experimental data. These finite-bandwidth K-K relations are known to work with resonant-type data and here are applied to dispersion data consistent with a power-law attenuation coefficient (exponent from 1 to 2). Bandwidth-restricted forms of the zero and once-subtracted K-K relations are used to determine the attenuation coefficient from phase velocity. Analytically, it is shown that these transforms produce the proper power-law form of the attenuation coefficient as a stand-alone term summed with artifacts that are dependent on the integration limits. Calculations are performed to demonstrate how these finite-bandwidth artifacts affect the K-K predictions under a variety of conditions. The predictions are studied in a local context as a function of subtraction frequency, bandwidth, and power-law exponent. The K-K predictions of the power-law exponent within various decades of the spectrum are also examined. In general, the agreement between finite-bandwidth K-K predictions and exact values grows as the power-law exponent approaches 1 and with increasing bandwidth.

A miniature biochip system for detection of aerosolized Bacillus globigii spores.

The feasibility of using a novel detection scheme for the analysis of biological warfare agents is demonstrated using Bacillus globigii spores, a surrogate species for Bacillus anthracis. In this paper, a sensitive and selective enzyme-linked immunosorbent assay using a novel fluorogenic alkaline phosphatase substrate (dimethylacridinone phosphate) is combined with a compact biochip detection system, which includes a miniature diode laser for excitation. Detection of aerosolized spores was achieved by coupling the miniature system to a portable bioaerosol sampler, and the performance of the antibody-based recognition and enzyme amplification method was evaluated. The bioassay performance was found to be compatible with the air sampling device, and the enzymatic amplification was found to be an attractive amplification method for detection of low spore concentrations. The combined portable bioaerosol sampler and miniature biochip system detected 100 B. globigii spores, corresponding to 17 aerosolized spores/L of air. Moreover, the incorporation of the miniature diode laser with the self-contained biochip design allows for a compact system that is readily adaptable to field use. In addition, these studies have included investigations into the tradeoff between assay time and sensitivity.