Estimation of blood velocity with high frequency ultrasound

In order to map blood velocity in small regions near the transducer, we evaluate the performance of the wideband maximum likelihood (WMLE) strategy and infinite impulse response (IIR) filters for blood velocity estimation with a transducer center frequency of 38 MHz. Using a short transmitted pulse and the narrow lateral beam width obtained using this frequency, we show that velocities smaller than 1 mm/s can be estimated reliably. In addition, using both changes in the location and magnitude of the peak of the RF correlation, vessels as small as 40 μm can be visualized in the RF signal and distinguished from stationary tissue. The experimental system also provides the opportunity to examine changes in flow and in the vessel wall over a cardiac cycle     

The correlation between coordination and bond angle distribution in network-forming liquids

The structure and diffusion in SiO₂ and Al₂O₃ liquids under pressure have been studied by molecular dynamics simulation. We show that although different states of considered liquids differ significantly in the number of TO_x units and OT_y linkages (T = Si, Al; x = 4, 5, 6; y = 2, 3, 4), their partial bond angle distributions (BAD) are identical. Furthermore, the total BADs are directly related to the partial BADs and coordination distribution. This result supports a technique to determine the fraction of TO_x and OT_y from the experimental bond angle distribution. The simulation also reveals the anomalous behavior of diffusion in silica liquid caused by the change in diffusion mechanisms occurring in low- and high-density models. The diffusion in alumina liquid also results from a similar mechanism like the one for high-density sample of silica liquid.     

A real-time ultrasound time-domain correlation blood flowmeter. I. Theory and design

A real-time ultrasound time-domain correlation (UTDC) blood flowmeter has been developed. Real-time performance has been achieved through the implementation of a custom-designed high-speed residue-number system (RNS) hardware correlator. The flowmeter is interfaced to a commercial ultrasound imager and can produce one-dimensional velocity versus range graphs at a rate of three per second. It has been validated in a blood flow phantom under a variety of conditions along with in vivo measurements in the human carotid artery. The theory of the time-domain correlation technique, design and implementation of flowmeter hardware, and the important correlation parameters which affect the performance of the flowmeter are described.     

On the angle ply higher order beam vibrations

Vibrations of angle ply laminated beams are studied using the higher order theory and isoparametric 1d finite element formulations through proper constitution of elasticity matrix. Subsequent to the validation of the formulation, deep sandwich and composite beams are critically analyzed for various boundary conditions. Frequencies classified based on their spectrum are presented along with those of first order theories for comparison.     

A real-time ultrasound time-domain correlation blood flowmeter. II. Performance and experimental verification

For Part I, see ibid., vol.40, no.6, p.768-775 (1993). The performance of a real-time ultrasound time-domain correlation (UTDC) flowmeter employing a high-speed residue number system correlator under various flow conditions for different correlation parameter settings is evaluated. Previous work has incorporated a weighted-averaging scheme to estimate the flow velocity over a wide number of echo signal spacings. The present evaluation indicates that a linear averaging of 50 adjacent echo signal pairs produces equivalent accuracy and precision at real-time processing speed as compared to previous non-real time systems incorporating weighted averaging.     

Study of the correlation between GaN material properties and the growth conditions of radio frequency plasma-assisted molecular beam epitaxy

The material properties of GaN thin films grown by radio frequency (RF) nitrogen plasma source molecular beam epitaxy (MBE) on (0001) Al₂O₃ substrates have been correlated to the V/III flux ratio during GaN growth and to the type and thickness of the buffer layer. The most remarkable observation is the change in the sign of the residual strain, from tensile to compressive as the V/III ratio alters from N-rich to stoichiometric (or slightly Ga-rich) conditions for GaN layers with a 17 nm AlN buffer layer. The residual strain was significantly reduced for a thinner 5 nm AlN buffer and it was zero for a 20 nm GaN buffer. A reduction of the rms surface roughness from 20 to 3 nm was achieved by decreasing the V/III ratio. Finally, stacking faults were observed only for significantly N-rich growth conditions.     

An illumination problem with tradeoff between coverage of a dataset and aperture angle of a conic light beam

Let \(\{a_i:i\in I\}\) be a finite set in \({\mathbb{R}}^n\). The illumination problem addressed in this work concerns the optimal location and orientation of a conic light beam

$$ R\big (z,y,s\big )= \left\{ x \in {\mathbb{R}}^n : s\,\Vert x-z\Vert - \langle y, x-z\rangle \le 0\right\} .$$

The aperture angle \(\vartheta = 2\arccos s\) of the conic light beam is a decreasing function of the sharpness coefficient \( s\in [0,1]\). The problem at hand is to select an apex z in a prescribed compact region \(Z\subseteq {\mathbb{R}}^n\) and a unit vector \(y\in {\mathbb{R}}^n\) so that the conic light beam R(z, y, s) fulfils two conflicting requirements: it captures as many points \(a_i\) as possible and, at the same time, it has a sharpness coefficient s as large as possible.

     

Quantum state diffusion and time correlation functions

Abstract

In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master equations. Quantum state diffusion (QSD) gives a useful method of solving these problems by unravelling the master equation into stochastic trajectories; but there is no generally accepted definition of a time correlation function for a single QSD trajectory. In this paper we show how QSD can be used to calculate these spectra directly; by formally solving the equations which arise, we arrive at a natural definition for a two-time correlation function in QSD, which depends explicitly on the stochastic noise of the particular trajectory, and which agrees in the mean with the ensemble average definition of correlation functions.     

Analytical far-field divergence angle of a truncated gaussian beam

Approximate, but accurate, analytical expressions for the far-field divergence angle of a Gaussian beam normally incident on a circular aperture are derived. A first equation is obtained based on the concept of Gaussian transform, in which the Bessel function present in the far-field diffraction integral is approximated by a Gaussian function. Refining this approach yields another simple, practical closed-form formula with such a level of accuracy that we propose that it can be used as an exact reference. All approximations hold for any combination of Gaussian beam width and aperture radius.     

FLASH correlation: a new method for 3-D ultrasound tissue motion tracking and blood velocity estimation

We report a new method for tracking tissue motion and blood flow in three dimensions (3-D) using successive volumetric ultrasound scans. The method is based on combining the concepts of feature tracking and 3-D correlation search to achieve a compromise between accuracy and computational efficiency. This paper introduces the new method and the experimental setup used for its evaluation in a tissue-mimicking material. Results are presented demonstrating that the new method has both satisfactory tracking performance and the potential for practical real-time implementation.     

Estimation of density functions and upcrossing-rates from samples

This paper assesses techniques for estimating univariate probability density functions, and highlights strengths and weaknesses of several methods. Applications are given for non-Gaussian distributions typical of the dynamic response of nonlinear systems. It is concluded that of the methods considered the maximum likelihood method is generally the most suitable when predicting extreme values. The moment and maximum likelihood methods are adapted for estimation of upcrossing-rate functions.     

Spectra and autocorrelation functions of a geometrically nonlinear beam

Abstract

The aim of this paper is to explore the Fourier spectra and autocorrelation functions of a geometrically nonlinear elastic beam with supports subjected to harmonic excitation. By using the large deformation theory and considering the deflection caused by both moment and shear as well as the inertia force induced by both displacement and rotation, the equation of motion is derived, which turns out to be a nonlinear fourth‐order partial differential equation. Because of the complexity of the partial differential equation, this paper first employs the Galerkin method to reduce it into a nonlinear second‐order ordinary differential equation. Then the Runge‐Kutta‐Verner numerical method is applied to find the solution. Due to the nonlinearity of the equation, chaotic motion is found to exist in this nonlinear elastic beam system. This paper draws time histories and Poincaré maps to show that chaotic motion indeed exists in the geometrically nonlinear elastic beam. For both regular and chaotic motions, Fourier spectra and autocorrelation functions are then plotted, which can be used as important criteria to diagnose whether the geometrically nonlinear beam will be chaotic in the future because of the significantly different results from those two kinds of motions.     

Deflection dynamics of rock beam caused by ultrasound

A new method for monitoring the time dependent dynamics of materials is proposed and implemented. By completely separating the conditioning (here ultrasound), the probing (here gravity), and the material state indicator (here deflection), the details of this dynamic process becomes apparent. The method allows both continuous monitoring of the material state without cross-interaction by the measuring process on the results, as well as complete freedom of conditioning and probing. It was successfully tested for sensitivity and repeatability when applied on a horizontally suspended beam of gabbro rock, which was observed to sag when subjected to ultrasound. These introductory tests have given new insights. The beam rises back, against the force of gravity, after the ultrasound is turned off. The deflection motions are fast both at the onset and at the termination of ultrasound, with the subsequent continuations being much slower. This new method is able to provide the higher accuracy needed for the advancement of the theoretical framework for material property time dependent dynamics.     

Spin-rotation invariance and the structure of correlation functions in magnetic systems

We analyze, in the framework of the functional approach to statistical mechanics, general properties of correlation functions in ordered magnetic systems. The aim of this paper is to investigate what consequences can be derived from the requirement of invariance of the theory under local infinitesimal spin rotation. The extension of the method that we introduce, to include anisotropic Hamiltonians, is discussed, and the case of the anisotropy described by an internal field is worked out. Our main results are a set of generalized Ward identities, a microscopic definition of the stiffness constant as a static limit of a local response function, and an exact asymptotic expression for the correlation functions of interest, for zero temperature and small wave length and frequency. Modifications to the hydrodynamic expression for correlation functions in the case where anisotropy is present are also discussed.     

Comparison between 2-D cross correlation with 2-D sub-sampling and 2-D tracking using beam steering

We have previously presented multi-dimensional sub-sample motion estimation techniques that use multi-dimensional polynomial fitting to the discrete cross-correlation function to jointly estimate the sub-sample motion in all three spatial directions. Previous simulation and experimental results showed that these estimators significantly improve the performance of the motion estimation in 2-D and 3-D. In this short communication, we present additional simulation results and compare these techniques to 2-D tracking using beam steering. The results show that beam steering technique performs better in estimating the motion vector especially the lateral component.     

The volume of ions and ion-solvent pair correlation functions

In this paper we summarize some of our recent work on the apparent molal volumes of transition metal salts in water. The densities of NiCl₂, Ni(ClO₄)₂, CoCl₂, Co(ClO₄)₂, and Mn(ClO₄)₂ solutions have been measured from 15 to 140°C. Solutions of FeCl₂, Fe(ClO₄)₂, CuCl₂, Cu(ClO₄)₂, ZnCl₂, and Zn(ClO₄)₂ were measured from 15 to 55°C. The apparent molal volumes at infinite dilution are reported and the effect of temperature is discussed. A new approach to the calculation of ionic volumes from salt volumes is presented. It is shown that the ionic volume is directly related to the direct ion-solvent correlation function. A large ligand field effect on transition metal volumes is noted.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Measuring optical power transmission near the critical angle for sensing beam deflection

We investigate an internal-transmission method for measuring microdeflections of an optical beam as a potential tool for the development of new compact and stable optical sensors. We calculate the detection limits of the internal-transmission method when an ideal coherent optical source and an ideal quasi-monochromatic thermallike source are used. The proposed method is compared with an internal-reflection method previously studied. It is found theoretically and verified experimentally that the transmission method may have better resolution than the reflection method. We also compare the calculated sensitivity as a function of the angle of incidence with experimental results for both methods.     

An in vitro study of the correlation between bubble distribution, acoustic emission, and cell damage by contrast ultrasound

The objective of this study was to investigate the influences of total exposure duration and pulse-to-pulse bubble distribution on contrast-mediated cell damage. Murine macrophage cells were grown as monolayers on thin polyester sheets. Contrast agent microbubbles were attached to these cells by incubation. Focused ultrasound exposures (P/sub r/= 2 MPa) were implemented at a frequency of 2.25 MHz with 46 cycle pulses and pulse repetition frequencies (PRF) of 1 kHz, 500 Hz, 100 Hz, and 10 Hz in a degassed water bath at 10 or 100 pulses. A 1 MHz receive transducer measured the scattered signal. The frequency spectrum was normalized to a control spectrum from linear scatterers. Photomicrographs were captured before, during, and after exposure at a frame rate of 2000 fps and a pixel resolution of 960 times 720. Results clearly show that cell death is increased, up to 60%, by increasing total exposure duration from 0 ms to 100 ms. There was an increasing difference in cell damage between a 10-pulse exposure and a 100-pulse exposure with increasing PRF. The greatest change in damage occurred at 1000 Hz PRF with a 53% increase between 10-pulse and 100-pulse exposures. For each pulse from 0 to 10, an overlay of the 2 mum bubble count with corresponding emission shows consistent behavior in its pulse-to-pulse changes, indicating a correlation between acoustic emission, bubble distribution, and cell damage.     

Fast ultrasound beam prediction for linear and regular two-dimensional arrays

Real-time beam predictions are highly desirable for the patient-specific computations required in ultrasound therapy guidance and treatment planning. To address the longstanding issue of the computational burden associated with calculating the acoustic field in large volumes, we use graphics processing unit (GPU) computing to accelerate the computation of monochromatic pressure fields for therapeutic ultrasound arrays. In our strategy, we start with acceleration of field computations for single rectangular pistons, and then we explore fast calculations for arrays of rectangular pistons. For single-piston calculations, we employ the fast near-field method (FNM) to accurately and efficiently estimate the complex near-field wave patterns for rectangular pistons in homogeneous media. The FNM is compared with the Rayleigh-Sommerfeld method (RSM) for the number of abscissas required in the respective numerical integrations to achieve 1%, 0.1%, and 0.01% accuracy in the field calculations. Next, algorithms are described for accelerated computation of beam patterns for two different ultrasound transducer arrays: regular 1-D linear arrays and regular 2-D linear arrays. For the array types considered, the algorithm is split into two parts: 1) the computation of the field from one piston, and 2) the computation of a piston-array beam pattern based on a pre-computed field from one piston. It is shown that the process of calculating an array beam pattern is equivalent to the convolution of the single-piston field with the complex weights associated with an array of pistons. Our results show that the algorithms for computing monochromatic fields from linear and regularly spaced arrays can benefit greatly from GPU computing hardware, exceeding the performance of an expensive CPU by more than 100 times using an inexpensive GPU board. For a single rectangular piston, the FNM method facilitates volumetric computations with 0.01% accuracy at rates better than 30 ns per field point. Furthermore, we demonstrate array calculation speeds of up to 11.5 X 10(9) field-points per piston per second (0.087 ns per field point per piston) for a 512-piston linear array. Beam volumes containing 256(3) field points are calculated within 1 s for 1-D and 2-D arrays containing 512 and 20(2) pistons, respectively, thus facilitating future real-time thermal dose predictions.