Estimation of critical and viscous frequencies for Biot theory in cancellous bone

The use of Biot theory for modelling ultrasonic wave propagation in porous media involves the definition of a "critical frequency" above which both fast and slow compressional waves will, in principle, propagate. Critical frequencies have been evaluated for healthy and osteoporotic cancellous bone filled with water or marrow, using data from the literature. The range of pore sizes in bone gives rise to a critical frequency band rather than a single critical frequency, the mean of which is lower for osteoporotic bone than normal bone. However, the critical frequency is a theoretical concept and previous researchers considered a more realistic "viscous frequency" above which both fast and slow waves may be experimentally observed. Viscous frequencies in bone are found to be several orders of magnitude greater than calculated critical frequencies. Whereas two waves may well be observed at all ultrasonic frequencies for water-filled cancellous bone at 20 degrees C, it is probable megahertz frequencies would be needed for observation of two waves in vivo.     

Bonding Interface Imaging and Shear Strength Prediction by Ultrasound

The propagation of a longitudinal ultrasonic wave normally incident upon an adhesively bonded structure is studied. The structure consists of adherend and adhesive layers with finite thickness. Interfaces between adherend and adhesive are regarded as distributed springs. Theoretical and experimental results show that resonant frequencies of the bonded structure vary sensitively with the interface stiffness constants and adhesive thickness, and these interface characteristics are inversed by the simulation annealing (SA) method. Furthermore, the distribution image of interface stiffnesses is compared with the state of fracture interface, and quantitative prediction of shear strength is achieved based on the distribution of interface stiffnesses and adhesive thicknesses by using a back-propagation neutral network. The average relative error of the shear strength from prediction to real value is 10.7%.     

Analysis of ultrasonic attenuation in particle-reinforced plastics by a differential scheme

Attenuation of ultrasonic longitudinal waves in some particle-reinforced polymer composites is studied theoretically by a micromechanical model based on a differential (incremental) scheme. A set of differential equations is established by which the attenuation spectrum of the composite can be computed from the known properties of viscoelastic matrix and elastic particles. For a composite reinforced with glass particles with radius 0.15 mm, the proposed scheme is shown to predict the attenuation in better agreement with the foregoing experimental results than the previous simplistic independent scattering model. Based on this scheme, the dependence of the longitudinal attenuation spectrum of a particulate polymer composite on the wavelength-to-particle radius ratio and the particle volume fraction is examined in detail. It is then shown theoretically that the attenuation of the composite decreases monotonically with the particle volume fraction when the particle radius is sufficiently small compared to the incident wavelength, while it shows non-monotonic particle-fraction dependence when the ratio of the particle radius to the wavelength is larger. To examine this theoretical finding from an experimental point of view, the longitudinal attenuation in a glass-particle-reinforced polyester composite with particle radius 0.0225 mm is measured for different particle volume fractions. The measured attenuation characteristics are shown to support the qualitative features of the theoretical prediction.     

Parameter measurement of the cylindrically curved thin layer using low-frequency circumferential Lamb waves

The characteristic parameters of a cylindrically curved thin layer include its elastic constants, thickness and curved radius. A layer is considered thin if the echoes from the front and back surfaces of the layer cannot be separated in the time domain, and/or that the wave arrivals corresponding to longitudinal and shear wave part cannot be identified in the time or space domain. This paper describes a low-frequency circumferential Lamb wave method to characterize those parameters of a cylindrically curved thin layer. The technique is based on the measurement of circumferential Lamb wave phase velocity and the unknown parameter is estimated through minimizing the mean square error obtained by comparing theoretical and experimental phase velocities. The sensitivity and accuracy of the proposed technique to different parameters are analyzed. Using the present technique, a cylindrically curved thin layer with thickness down to ten percent of the longitudinal wavelength can be successfully measured with an average relative error less than two-percent in our experiment.     

Directing ultrasound at the cemento-enamel junction (CEJ) of human teeth: I. Asymmetry of ultrasonic path lengths

The diagnosis of degenerative changes in human teeth is of general interest because early detections can avoid greater health problems and further weakening effects. Since the wear of teeth determines their stability and lifetime in relation to the physiological load, an ultrasonic survey of any dimensional changes of the enamel layer and especially of the dentin wall thickness may be very helpful. However, an ultrasonographic diagnosis requires first to determine the anisotropic human tooth properties at clinically relevant locations and to simulate wave propagation phenomena in inhomogeneous tooth models with proper dimensions. The first article of a series that provides modular data of mineralized tissues in human teeth at the cemento-enamel junction (CEJ) deals with an ultrasonic method for measuring the asymmetry of dimensional characteristics of extracted human teeth and their ultrasonic path lengths (UPL). Heavily attenuating tooth halves were investigated with respect to the symmetry of normal and inclined oppositely directed radial ultrasonic paths. The measured UPLs ranged from 1.2 mm to 4.4 mm. The relative difference in inclined UPLs between the left and the right tooth halves reaches almost 30%. This reveals a large asymmetry. The mean difference of angles that represent fastest path lengths was 2.2+/-8.1 degrees, which indicates large asymmetry and anisotropy. Several aspects, which are required for a proper integration of asymmetric data into models designed for medical element engineering and simulation (MEES), are discussed.     

Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1-4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws.     

Ultrasound velocity in human muscle in vivo: perspective for edema studies

The present study examines the association of the changes in ultrasound velocity measured at 1 MHz using 1.5 micros duration tone burst in the human soleus muscle in vivo with several pathologies including patients with chronic renal failure (CRF) and disorders of the cardiovascular system. Total 127 subjects were investigated, with approximately equal number of male and female subjects uniformly distributed by age, from 15 to 70 years old. Since molecular composition of the tissue is thought to have greater effect on the bulk ultrasound velocity, potential contribution of both water and fat, two main variable components of a muscle, were taken into account. Observed negative correlation of ultrasound velocity with the body mass index was considered a result of an elevated fat content. Based on the obtained data, presence of leg edemas results in a measurably lower ultrasound velocity in the soleus muscle. Unless patients had visibly detected leg edema, no difference between healthy individuals, patients with chronic heart failure, or CRF was found. Despite relatively high individual variations in velocity, ranging from 1530 to 1615 m/s, a statistically significant gender correlated difference between average values of the velocity was observed. No dependence of velocity on subject age was detected. An indirect confirmation of the muscle fluid homeostasis was revealed in patients with CRF undergoing hemodialysis procedure. After hemodialysis, a significantly smaller increase (0.3% in average) of ultrasound velocity in the soleus muscle was observed than otherwise could be expected if a uniform relative loss of total body fluids was assumed (1-1.3%). In general, the study findings set a premise for using ultrasound velocity as a potential quantitative parameter for edema assessment.     

Effect of anisotropy on acoustoelastic birefringence in wood

The ultrasonic velocity of shear waves propagating through radial direction of a wood plate specimen, transversely to the loading direction, was measured. By rotating an ultrasonic sensor, the oscillation direction of the shear waves was varied with respect to the wood plate axis and loading direction. The relationship between shear wave velocity and oscillation direction was examined to discuss the effect of anisotropy on the acoustoelastic birefringence in wood. The results obtained were summarized as follows. When the oscillation direction of the shear wave corresponded to the tangential direction of the wood specimen regardless of the stress direction, shear wave velocity decreased markedly and the relationship between shear wave velocity and rotation angle tended to become discontinuous. That is, when the shear waves oscillated in the anisotropic axis of the wood, the shear wave velocity peaked unlike in the case of oscillation in the stress direction. In an isotropic material (acrylic, aluminum 5052), on the contrary, when the shear waves oscillated in the stress direction of the specimen, the shear wave velocity peaked regardless of the main-axis direction of the specimen. On the basis of the discussion of these results, the ultrasonic shear wave propagating in wood under stress is confirmed to be polarized in the anisotropic axis of the wood.     

Attenuation coefficient estimation using experimental diffraction corrections with multiple interface reflections

The ultrasonic attenuation coefficient of a fluid or solid is an acoustic parameter routinely estimated for the purpose of materials characterization and defect/disease detection. This paper describes a broadband attenuation coefficient estimation technique that combines two established estimation approaches. The key elements of these two approaches are: (1) the use of magnitude spectrum ratios of front surface, first back surface, and second back surface reflections from interfaces of materials with plate-like geometries, and (2) the use of an experimental diffraction correction approach to avoid diffraction losses. The combined estimation approach simplifies the attenuation coefficient estimation process by eliminating the need to explicitly make diffraction corrections or calculate reflection/transmission coefficients. The approach yields estimates of the attenuation coefficient, reflection coefficient, and material density. Models, experimental procedures, and signal analysis procedures, which support implementation of the approach, are presented. Attenuation coefficient and reflection coefficient estimates are presented for water and solid samples with estimates based on measurements made with multiple transducers.     

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh-Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the “compression-only” behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2-2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20 cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30 × 10⁻⁸ kg/s to 2.63 × 10⁻⁸ kg/s for the range of bubble radii, indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the “compression-only” behavior. As an example, the results of the simulation for a 2.03 μm radius bubble insonified with a 6 cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the “compression-only” behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653-656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius.     

Modeling of the acoustic response from contrast agent microbubbles near a rigid wall

In ultrasonic targeted imaging, specially designed encapsulated microbubbles are used, which are capable of selectively adhering to the target site in the body. A challenging problem is to distinguish the echoes from such adherent agents from echoes produced by freely circulating agents. In the present paper, an equation of radial oscillation for an encapsulated bubble near a plane rigid wall is derived. The equation is then used to simulate the echo from a layer of contrast agents localized on a wall. The echo spectrum of adherent microbubbles is compared to that of free, randomly distributed microbubbles inside a vessel, in order to examine differences between the acoustic responses of free and adherent agents. It is shown that the fundamental spectral component of adherent bubbles is perceptibly stronger than that of free bubbles. This increase is accounted for by a more coherent summation of echoes from adherent agents and the acoustic interaction between the agents and the wall. For cases tested, the increase of the fundamental component caused by the above two effects is on the order of 8-9 dB. Bubble aggregates, which are observed experimentally to form near a wall due to secondary Bjerknes forces, increase the intensity of the fundamental component only if they are formed by bubbles whose radii are well below the resonant radius. If the formation of aggregates contributes to the growth of the fundamental component, the increase can exceed 17 dB. Statistical analysis for the comparison between adhering and free bubbles, performed over random space bubble distributions, gives p-values much smaller than 0.05.     

Shock waves generated by confined XeCl excimer laser ablation of polyimide

We investigate shock waves generated by excimer laser ablation of sheet polyimide confined in water. The velocities of the ablation-induced pressure waves in the water are determined by an optical probe system. We measure supersonic velocities up to a few hundred microns away from the irradiated surface, indicating the formation of shock waves. We use these velocities to calculate the corresponding pressures. They are already in the kbar range at fluences comparable to the threshold of ablation. The shock pressure varies as the square root of the incident laser fluence, a behavior that is explained by the rapid heating of the confined gaseous products of ablation.The initially planar shock waves propagate, become spherical, and decay within a few hundred microns in the surrounding water to acoustic waves. During spherical expansion the shock pressure drops as the inverse of the square of the propagation distance.The shock waves generated may be relevant in explaining photoacoustic damage observed in biological tissue after excimer-ablation at corresponding irradiances. They may also be important in material processing applications of excimer laser ablation of polymers as they can lead to plastic deformation.     

Non-invasive determination of shock wave pressure generated by optical breakdown

Shock waves generated by a laser-induced plasma were investigated using a pump-and-probe technique. Both 7-ns and 40-ps laser pulses at 1.06 m were employed to initiate breakdown in water. Two He-Ne laser beams were used as a velocity probe, allowing the accurate measurement of the shock velocity around the plasma. The maximum shock pressure was determined from the measured shock velocities, the jump condition and the equation of state for water. The conservation of the total momentum of the shock front was used to derive expressions for the shock velocity, particle velocity and shock pressure vs. the distance (r) from the center of the plasma. For a shock wave of spherical symmetry, the shock pressure is proportional to 1/r ². Our work shows that the expanding plasma initially induces a shock wave; the shock wave dissipates rapidly becoming an acoustic wave within 300–500 m.     

Synthetic aperture focusing for defect reconstruction in anisotropic media

Ultrasonic inspection plays an important role in numerous industrial fields. One of the prominent tasks with respect to quantitative nondestructive evaluation is the determination of location, shape, size and orientation of defects. In this respect, the synthetic aperture focusing technique (SAFT) has been successfully applied to isotropic materials over the years. In anisotropic media, however, its application suffers from several phenomena, which are the direction dependence of the ultrasonic velocities, the beam skewing effect and the modified transducer radiation characteristics. In this article, a SAFT imaging algorithm is presented which fully accounts for the nature of wave radiation and propagation within anisotropic materials. For three-dimensional defect reconstruction, the spatial dependence of the ultrasonic group velocities as well as the radiation characteristics of the transducer are exploited--respective algorithms have been implemented for orthotropic material symmetry. Tests have been performed on unidirectional composite material.     

A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids

This paper presents a concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids. The formalism is capable of resolving completely the numerical instability problems associated with transfer matrix method, thereby obviating the extensive reformulation in its modified versions based on delta operator technique. In contrast to the earlier reflection matrix formalisms, all scattering matrices are obtained in a direct manner without invoking wave-propagator or scatterer operator concepts. Both local and global reflection and transmission matrices corresponding to scatterings in two and more layers are derived. The derivation of global scattering matrices in terms of the local ones is carried out concisely based on physical arguments to provide better insights into scattering mechanism. Another formulation which is even more succinct is also devised for obtaining the global scattering matrices directly from eigensolutions. The resultant expressions and algorithm are terse, efficient and convenient for implementation.     

Ultrasonic investigation of amorphous carbon in various frequencies at low temperatures from 2.1 to 300 K

Using pulse echo overlap measurement, the elastic behavior of amorphous carbon has been studied at ambient and low temperatures. The smaller ratio B/G of the bulk modulus to shear modulus and smaller Poisson's ratio σ at room temperature indicate that there is an intrinsic stiffening of transverse acoustic phonons in the amorphous carbon. The acoustic velocity and attenuation for longitudinal modes have been measured between 2.1 and 300 K at three frequencies of 7, 21 and 35 MHz, respectively. Their frequency and temperature dependence are observed. The elastic constant C₁₁ increases with decreasing temperature and show enhanced stiffening at low temperatures. In the 130-220 K region, the abnormal change and effect of longitudinal velocity and attenuation with temperature and frequency, and a phase transition associated with structure relaxations are discussed.     

Limited-diffraction wave generation by approaching theoretical X-wave electrical driving signals with rectangular pulses

The main interest of using limited diffracting waves is motivated by their potential applications in the enlargement of the field depth in acoustic imaging systems, under collimated conditions. In this work, an approach for simplifying the experimental arrangement, needed to generate limited diffracting waves, is proposed. The main idea is to approximate the theoretical X-wave electrical excitations by means of simple driving rectangular pulses. In order to optimize these driving signals in each array annulus, the L2 curve criterion is applied. The differences between theoretical X-wave signals and approximate driving pulses, related to their excitation effects, were minimized by using the time widths and amplitudes of the rectangular pulses as fitting parameters. The good agreement of the source vibration signals and resulting field distributions, provided by the drastic simplification presented here, with those obtained from the classical X-wave excitations, can be justified by the filtering effects induced by the transducer elements in frequency domain. These results suggest the possibility of achieving limited-diffraction waves with relatively simple driving waveforms, which can be implemented with a moderate cost in analogical electronics.     

Modelling the attenuation in the ATHENA finite elements code for the ultrasonic testing of austenitic stainless steel welds

Multipass welds made in austenitic stainless steel, in the primary circuit of nuclear power plants with pressurized water reactors, are characterized by an anisotropic and heterogeneous structure that disturbs the ultrasonic propagation and makes ultrasonic non-destructive testing difficult. The ATHENA 2D finite element simulation code was developed to help understand the various physical phenomena at play. In this paper, we shall describe the attenuation model implemented in this code to give an account of wave scattering phenomenon through polycrystalline materials. This model is in particular based on the optimization of two tensors that characterize this material on the basis of experimental values of ultrasonic velocities attenuation coefficients. Three experimental configurations, two of which are representative of the industrial welds assessment case, are studied in view of validating the model through comparison with the simulation results. We shall thus provide a quantitative proof that taking into account the attenuation in the ATHENA code dramatically improves the results in terms of the amplitude of the echoes. The association of the code and detailed characterization of a weld’s structure constitutes a remarkable breakthrough in the interpretation of the ultrasonic testing on this type of component.     

Spatially resolved ultrasonic attenuation in resistance spot welds: implications for nondestructive testing

Spatial variation of ultrasonic attenuation and velocity has been measured in plane parallel specimens extracted from resistance spot welds. In a strong weld, attenuation is larger in the nugget than in the parent material, and the region of increased attenuation is surrounded by a ring of decreased attenuation. In the center of a stick weld, attenuation is even larger than in a strong weld, and the low-attenuation ring is absent. These spatial variations are interpreted in terms of differences in grain size and martensite formation. Measured frequency dependences indicate the presence of an additional attenuation mechanism besides grain scattering. The observed attenuations do not vary as commonly presumed with weld quality, suggesting that the common practice of using ultrasonic attenuation to indicate weld quality is not a reliable methodology.