Estimating concentration of ultrasound contrast agents with backscatter coefficients: experimental and theoretical aspects

Ultrasound contrast agents (UCAs) have been explored as a means to enhance therapeutic techniques. Because the effectiveness of these techniques relies on the UCA concentration at a target site, it would be beneficial to estimate UCA concentration noninvasively. In this study, a noninvasive method for estimating UCA concentration was developed in vitro. Backscatter coefficients (BSCs) estimated from measurements of Definity(?) UCAs were fitted to a theoretical scattering model in the 15-25 MHz range using a Levenberg-Marquardt regression technique. The model was defined by the UCA size distribution and concentration, and therefore concentration estimates were extracted directly from the fit. Calculation of the BSC was accomplished using planar reference measurements from the back wall of a Plexiglas(?) chamber and an average of 500 snapshots of ultrasonic backscatter from UCAs flowing through the chamber. In order to verify the ultrasonically derived UCA concentration estimates, a sample of the UCAs was extracted from the flow path and the concentration was estimated with a hemacytometer. UCA concentrations of 1, 2, and 5 times the dose recommended by the manufacturer were used in experiments. All BSC-based estimates were within one standard deviation of hemacytometer based estimates for peak rarefactional pressures of 100-400 kPa.     

Ultrasonic backscatter coefficient quantitative estimates from high-concentration Chinese Hamster Ovary cell pellet biophantoms

Previous work estimated the ultrasonic backscatter coefficient (BSC) from low-concentration (volume density <3%) Chinese Hamster Ovary (CHO, 6.7-μm cell radius) cell pellets. This study extends the work to higher cell concentrations (volume densities: 9.6% to 63%). At low concentration, BSC magnitude is proportional to the cell concentration and BSC frequency dependency is independent of cell concentration. At high cell concentration, BSC magnitude is not proportional to cell concentration and BSC frequency dependency is dependent on cell concentration. This transition occurs when the volume density reaches between 10% and 30%. Under high cell concentration conditions, the BSC magnitude increases slower than proportionally with the number density at low frequencies (ka<1), as observed by others. However, what is new is that the BSC magnitude can increase either slower or faster than proportionally with number density at high frequencies (ka>1). The concentric sphere model least squares estimates show a decrease in estimated cell radius with number density, suggesting that the concentric spheres model is becoming less applicable as concentration increases because the estimated cell radius becomes smaller than that measured. The critical volume density, starting from when the model becomes less applicable, is estimated to be between 10% and 30% cell volume density.     

Describing small-scale structure in random media using pulse-echo ultrasound

A method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J.J. Faran, J. Acoust. Soc. Am. 23, 405-418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere-in-agar and polystyrene sphere-in-agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.     

Carrier frequency offset and impulse noise estimation for underwater acoustic orthogonal frequency division multiplexing

The carrier frequency offset（CFO）and impulse noise always affect the performance of underwater acoustic communication_systems.The CFO and impulse noise could be estimated by using the null subcarriers to cancel the effects of the two types of interference.The null subcarriers estimation methods include optimal separate estimation and joint estimation.The separate estimation firstly estimates the CFO value and then estimates the impulse noise value.However,the CFO and impulse noise always affect each other when either of them is estimated separately.The performance could be improved by using the joint estimation.The results of simulations and experiments have showed that these two optimization methods have good performance and the joint estimation has better performance than the separate estimation method.There is 3 dB performance gain at the BER value of 10~（-2）when using the joint estimation method.Thus these methods could improve the system robustness by using the CFO compensation and impulse noise suppression.     

Underwater implosion of glass spheres

Underwater implosion experiments were conducted with thin-wall glass spheres to determine the influence that structural failure has on the pressure pulse. Four experiments were conducted with glass spheres having an outside diameter of 7.62 cm, thickness of 0.762 mm, and an estimated buckling pressure of 7.57 MPa. The experiments were performed in a pressure vessel at a hydrostatic pressure of 6.996 MPa. The average peak pressure of the implosion pressure pulse was 26.1 MPa, measured at a radial distance of 10.16 cm from the sphere center. A computational fluid structure interaction model was developed to assess how the failure rate of the glass structure influences the pressure time history. The model employed a specified glass failure sequence that is uniform in time and space. It was found that for the conditions of the test, a glass failure rate of 275 m/s provided a reasonable representation of the test data. The test data and the model results show that the failure time history of the structure has a significant influence on an implosion pressure pulse. Computational prediction of an implosion pressure pulse needs to include the failure time history of the structure; otherwise it will overpredict the pressure time history.     

Deformation and strength of silica fibers in three-point bending in consideration of nonlinear elasticity of glass

We consider the problem of asymmetric strain and stress distribution in silica fiber under threepoint bending. The parameters of nonlinear elasticity of silica glass under tension and compression are estimated using available data from the literature. It has been found that consideration of the nonlinear elasticity of silica glass leads to a slight increase in the calculated values of strength compared to the data obtained from estimates based on the linear theory of elasticity.     

Photoakustische Messung der Absorption an einem Ensemble dichtgepackter kugelförmiger Absorber

Photoacoustic Measurement of Absorption in an Ensemble of Close-Packed Absorbing Spheres Using the Rosencwaig-Gersho-model the photoacoustic absorption signal from an ensemble of tightly packed absorbing spheres was calculated taking into account the light scattering of the sample. Theoretical results were compared with experimental data, obtained from high refracting glass beads (so called Ballotini).     

Perturbation expansions and series acceleration procedures. Part I. ε-convergence and critical parameters

A simple acceleration of convergence technique known as the ‘ε-convergence algorithm’ (ea) is applied to determine the critical temperatures and exponents. Several illustrations involving well-known series expansions appropriate to two- and three-dimensional Ising models, three-dimensional Heisenberg models, etc., are given. Apart from this, a few recently studied ferrimagnetic systems have also been analysed to emphasise the generality of the approach. Where exact solutions are available, our estimates obtained from this procedure are in excellent agreement. In the case of other models, the critical parameters we have obtained are consistent with other estimates such as those of the Padé approximants and group theoretic methods. The same procedure is applied to the partial virial series for hard spheres and hard discs and it is demonstrated that the divergence of pressure occurs when the close-packing density is reached. The asymptotic form for the virial equation of state is found to beP/ρkT ∼ (1 −ρ/ρ _c ⁻¹ for hard spheres and hard discs. Apart from the estimation of ‘critical parameters’, we have applied theea and the parametrised Euler transformation to sum the partial, truncated virial series for hard spheres and hard discs. The resulting values of pressure so obtained, compare favourably with the molecular dynamics results.     

Calculation of the Stokes and Aerodynamic Equivalent Diameters of a short reinforcing fiber

A concern about all reinforcing fibers is the extent to which they are respirable. The degree of respirability of a particle is frequently estimated in terms of its aerodynamic equivalent diameter being less than a certain value (typically 3.5 to 7 μ). However, the aerodynamic equivalent diameter, like the Stokes diameter, is only defined exactly for spheres, which is far from the shape of acicular fibers. Thus, it is useful to be able to calculate, based on actual fiber diameter and aspect ratio, the effective Stokes and aerodynamic equivalent diameters of various fibers. The present paper derives simple expression for relating the two effective diameters to actual fiber dimensions. Calculated results are compared with experimental data for glass fiber and three fractions of phosphate fiber [1], which is a short, reinforcing inorganic fiber. Agreement is seen to be good. Phosphate fiber was fractionated using a sedimentation technique described in the paper. The resulting fractions were characterized by semi-manual measurements of micrographic dimensions and compared with results obtained from particle size instruments based on sedimentation principles. Based on these results, a large weight fraction of phosphate fiber is predicted not to be respirable.     

Estimation of surface area concentration of workplace incidental nanoparticles based on number and mass concentrations

Surface area was estimated by three different methods using number and/or mass concentrations obtained from either two or three instruments that are commonly used in the field. The estimated surface area concentrations were compared with reference surface area concentrations (SA_REF) calculated from the particle size distributions obtained from a scanning mobility particle sizer and an optical particle counter (OPC). The first estimation method (SA_PSD) used particle size distribution measured by a condensation particle counter (CPC) and an OPC. The second method (SA_INV1) used an inversion routine based on PM1.0, PM2.5, and number concentrations to reconstruct assumed lognormal size distributions by minimizing the difference between measurements and calculated values. The third method (SA_INV2) utilized a simpler inversion method that used PM1.0 and number concentrations to construct a lognormal size distribution with an assumed value of geometric standard deviation. All estimated surface area concentrations were calculated from the reconstructed size distributions. These methods were evaluated using particle measurements obtained in a restaurant, an aluminum die-casting factory, and a diesel engine laboratory. SA_PSD was 0.7–1.8 times higher and SA_INV1 and SA_INV2 were 2.2–8 times higher than SA_REF in the restaurant and diesel engine laboratory. In the die casting facility, all estimated surface area concentrations were lower than SA_REF. However, the estimated surface area concentration using all three methods had qualitatively similar exposure trends and rankings to those using SA_REF within a workplace. This study suggests that surface area concentration estimation based on particle size distribution (SA_PSD) is a more accurate and convenient method to estimate surface area concentrations than estimation methods using inversion routines and may be feasible to use for classifying exposure groups and identifying exposure trends.     

Improved scatterer size estimation using backscatter coefficient measurements with coded excitation and pulse compression

Scatterer size estimates from ultrasonic backscatter coefficient measurements have been used to differentiate diseased tissue from normal. A low echo signal-to-noise ratio (eSNR) leads to increased bias and variance in scatterer size estimates. One way to improve the eSNR is to use coded excitation (CE). The normalized backscatter coefficient was measured from three tissue-mimicking phantoms by using CE and conventional pulsing (CP) techniques. The three phantoms contained randomly spaced glass beads with median diameters of 30, 45, and 82 mum, respectively. Measurements were made with two weakly focused, single-element transducers (f(0)=5 MHz and f(0)=10 MHz). For CE, a linear frequency modulated chirp with a time bandwidth product of 40 was used and pulse compression was accomplished by the use of a Wiener filter. Preliminary results indicated that improved estimation bias versus penetration depth was obtained by using CE compared to CP. The depth of penetration, where the accuracy of scatterer diameter estimates (absolute divergence <25%) were obtained with the 10 MHz transducer, was increased up to 50% by using CE versus CP techniques. In addition, for a majority of the phantoms, the increase in eSNR from CE resulted in a modest reduction in estimate variance versus depth of penetration.     

Vibrational modes of free nanoparticles: from atomic to continuum scales

Vibration analysis of free standing silicon nanoparticles, with sizes ranging from 0.732 to 4.223 nm, are calculated using two different methods: molecular mechanics and classical continuum elasticity. Three different geometries are studied: cubes, spheres, and tetrahedrons. Continuum mechanics methods provide good estimates of the lowest natural frequency of particles having at least 836 (R>1.5 nm) and 800 (R>1.28 nm) atoms for cube- and tetrahedron-shaped nanostructures, respectively. Equations for vibrational frequencies of smaller particles as a function of size are proposed. The vibrational modes obtained from both methods were practically the same for the sphere- and tetrahedron-shaped particles with a large number of atoms. However, for the cube geometry only the shape of the modes corresponding to the lowest couple of frequencies occur in the same order. In general, vibrational modes shapes obtained using both methods are the same although the order in which they appear may be shifted.     

Achievable accuracy of parameter estimation for multidimensional NMR experiments

A fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer-Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer-Rao lower bound can be calculated for data obtained from multidimensional NMR experiments. The Cramer-Rao lower bound is compared to the variance of parameter estimates for simulated data using a least-squares estimation procedure. It is also shown how our results on the Cramer-Rao lower bound can be used to analyze whether an experimental design can be improved to provide experimental data which can result in parameter estimates with higher accuracy. The concept of nonuniform averaging in the indirect dimension is introduced and studied in connection with nonuniform sampling of the data.     

Perturbation expansions and series acceleration procedures: Part-II. Extrapolation techniques

Three new procedures for the extrapolation of series coefficients from a given power series expansion are proposed. They are based on (i) a novel resummation identity, (ii) parametrised Euler transformation (pet) and (iii) a modifiedpet. Several examples taken from the Ising model series expansions, ferrimagnetic systems, etc., are illustrated. Apart from these applications, the higher order virial coefficients for hard spheres and hard discs have also been evaluated using the new techniques and these are compared with the estimates obtained by other methods. A satisfactory agreement is revealed between the two.     

静电探针测量强流电子束电离气体产生的等离子体密度

 用电离理论和核物理学中讨论电子束通过介质后的能量损耗方法分别估算了强流电子束电离中性气体产生的等离子体的密度。在实验中将静电探针应用于测量强流电子束电离氮气产生的等离子体的密度,得出等离子体密度随气压变化的曲线。实验结果表明在1～15帕气压范围内,等离子体密度在量级,与理论结果相符,证明静电探针用于诊断强流相对论电子束电离中性气体产生的等离子体的密度是可行的。     

Adjoint and defect error bounding and correction for functional estimates

We present two error estimation approaches for bounding or correcting the error in functional estimates such as lift or drag. Adjoint methods quantify the error in a particular output functional that results from residual errors in approximating the solution to the partial differential equation. Defect methods can be used to bound or reduce the error in the entire solution, with corresponding improvements to functional estimates. Both approaches rely on smooth solution reconstructions and may be used separately or in combination to obtain highly accurate solutions with asymptotically sharp error bounds. The adjoint theory is presented for both smooth and shocked problems; numerical experiments confirm fourth-order error estimates for a pressure integral of shocked quasi-1D Euler flow. By employing defect and adjoint methods together and accounting for errors in approximating the geometry, it is possible to obtain functional estimates that exceed the order of accuracy of the discretization process and the reconstruction approach. Superconvergent drag estimates are obtained for subsonic Euler flow over a lifting airfoil.     

Suitability of laser Doppler velocimetry for the calibration of pressure microphones

The details of a new approach for absolute calibration of microphones, based on the direct measurement of acoustic particle velocity using laser Doppler velocimetry (LDV), are presented and discussed. The calibration technique is carried out inside a tube in which plane waves propagate and closed by a rigid termination. The method developed proposes to estimate the acoustic pressure with two velocity measurements and a physical model. Minimum theoretical uncertainties on the estimated pressure and minimum measurable pressure are calculated from the Cramer Rao bounds on the estimated acoustic velocity amplitude and phase. These uncertainties and the minimum measurable pressure help to optimize the experimental set up. Acoustic pressure estimations performed with LDV are compared with acoustic pressures obtained with a reference microphone. Measurements lead to a minimum bias of 0.006 dB and a minimum uncertainty of 0.013 dB on the acoustic pressure estimation for frequencies 1360 Hz and 680 Hz.     

New group contribution method for the prediction of normal melting points

The melting point of organic compounds was estimated using a simple group contribution method. The optimum parameters of this new method were obtained using particle swarm optimization in a multivariate linear regression. The melting temperatures of 250 pure compounds were predicted, and the results were compared with experimental data and other models available in the literature. Compared to the currently used group contribution methods, the new method makes significant improvements in accuracy and applicability of this important property. The study shows that the proposed method presents an excellent alternative for the estimation of the melting temperature of organic compounds (AARD of 10%) from the knowledge of the molecular structure.     

Efficient and accurate estimation of relative order tensors from λ-maps

The rapid increase in the availability of RDC data from multiple alignment media in recent years has necessitated the development of more sophisticated analyses that extract the RDC data’s full information content. This article presents an analysis of the distribution of RDCs from two media (2D-RDC data), using the information obtained from a λ-map. This article also introduces an efficient algorithm, which leverages these findings to extract the order tensors for each alignment medium using unassigned RDC data in the absence of any structural information. The results of applying this 2D-RDC analysis method to synthetic and experimental data are reported in this article. The relative order tensor estimates obtained from the 2D-RDC analysis are compared to order tensors obtained from the program REDCAT after using assignment and structural information. The final comparisons indicate that the relative order tensors estimated from the unassigned 2D-RDC method very closely match the results from methods that require assignment and structural information. The presented method is successful even in cases with small datasets. The results of analyzing experimental RDC data for the protein 1P7E are presented to demonstrate the potential of the presented work in accurately estimating the principal order parameters from RDC data that incompletely sample the RDC space. In addition to the new algorithm, a discussion of the uniqueness of the solutions is presented; no more than two clusters of distinct solutions have been shown to satisfy each λ-map.     

Ultrasonic backscatter coefficient quantitative estimates from Chinese hamster ovary cell pellet biophantoms

A cell pellet biophantom technique is introduced, and applied to the ultrasonic backscatter coefficient (BSC) estimate using Chinese hamster ovary (CHO) cells. Also introduced is a concentric sphere scattering model because of its geometrical similarities to cells with a nucleus. BSC comparisons were made between the concentric sphere model and other well-understood models for mathematical verification purposes. BSC estimates from CHO cell pellet biophantoms of known number density were performed with 40 and 80 MHz focused transducers (overall bandwidth: 26-105 MHz). These biophantoms were histologically processed and then evaluated for cell viability. Cell pellet BSC estimates were in agreement with the concentric sphere model. Fitting the model to the BSC data yielded quantitative values for the outer sphere and inner sphere. The radius of the cell model was 6.8 ± 0.7 μm; the impedance of the cytoplasm model was 1.63 ± 0.03 Mrayl and the impedance of the nuclear model was 1.55 ± 0.09 Mrayl. The concentric sphere model appears as a new tool for providing quantitative information on cell structures and will tend to have a fundamental role in the classification of biological tissues.