Nonattenuating Media Research Articles

Energy partitioning among compressional and shear waves in three-dimensional attenuating elastic media.

In strongly scattering elastic media without attenuation and dispersion, the wavefield is dominated by shear waves, and in three dimensions, the ratio of the S to P energy is given by ES/EP=2(vP/vS)3. This study investigates how this ratio is influenced by attenuation. Both the case of the ringdown mode, where the energy evolves from initial values, and the case of energy equilibrium, where the attenuation is balanced by energy injection sources, are treated. It is shown that in ringdown mode, the energy ratio ES/EP satisfies a Ricatti equation in time: hence, the energy ratio is not an exponential function of time. It is also shown that the long-time energy ratio differs from the value in non-attenuating media when the attenuation coefficients for P and S waves are different. In the case of energy equilibrium, the energy ratio only is equal to the value in non-attenuating media when (1) the time scale of P- and S-wave equilibration is much smaller than the attenuation time or (2) the energy injection rate for each wave type is balanced by the dissipation for that wave type. The latter situation happens when the wavefield is excited by thermal fluctuations in thermal equilibrium.

Reduced order model approach for imaging with waves

We introduce a novel, computationally inexpensive approach for imaging with an active array of sensors, which probe an unknown medium with a pulse and measure the resulting waves. The imaging function is based on the principle of time reversal in non-attenuating media and uses a data driven estimate of the ‘internal wave’ originating from the vicinity of the imaging point and propagating to the sensors through the unknown medium. We explain how this estimate can be obtained using a reduced order model (ROM) for the wave propagation. We analyze the imaging function, connect it to the time reversal process and describe how its resolution depends on the aperture of the array, the bandwidth of the probing pulse and the medium through which the waves propagate. We also show how the internal wave can be used for selective focusing of waves at points in the imaging region. This can be implemented experimentally and can be used for pixel scanning imaging. We assess the performance of the imaging methods with numerical simulations and compare them to the conventional reverse-time migration method and the ‘backprojection’ method introduced recently as an application of the same ROM.

Radiant fluxes from on- and off-axis point sources irradiating a circular disc through two different homogeneous isotropic media

The multidomain integral equation method is used to calculate fluxes of radiation from various on- and off-axis point sources passing through two different homogeneous isotropic media and striking a surface of a circular disc perpendicular to the optical axes of these sources. This method is dedicated to radiation passing through attenuating or nonattenuating media with a Fresnel interface and is applicable for arbitrary radiation patterns of point sources. The paper presents, firstly, the generalized multidomain integral equation method, expressed by double iterated integrals, for calculating radiant fluxes from arbitrary emitting point sources. This generalized method is simplified then to the form of multidomain single integral equation method applicable for rotationally symmetrical radiation patterns with optical axes perpendicular to the disc. Next, the simplified method is used for computer simulation of radiant fluxes incident on the disc from small Lambertian and Gaussian sources represented by point source models. All numerical results obtained from this simulation have shown high accuracy and efficiency of the presented method. Selected results are illustrated graphically and validated by Optical Software for Layout and Optimization (OSLO) from Lambda Research Corporation. Potential applications of the presented method include optical sensing and metrology, optical coupling, immersion microscopes, light-extraction problems and creative lighting design.

Time-reverse modelling of acoustic wave propagation in attenuating media

SUMMARY Time-reverse modelling (TRM) of acoustic wave propagation has been widely implemented in seismic migration and time-reversal source imaging. The basic assumption of this modelling is that the wave equation is time-invariant in non-attenuating media. In the Earth, attenuation often invalidates this assumption of time-invariance. To overcome this problem, I propose a TRM approach that compensates for attenuation and dispersion effects during the wave propagation in attenuating media. This approach is based on a viscoacoustic wave equation which explicitly separates attenuation and dispersion following a constant-Q model. Compensating for attenuation and dispersion during TRM is achieved by reversing the sign of the attenuation operator coefficient while leaving the counterpart dispersion parameter unchanged in this viscoacoustic wave equation. A low-pass filter is included to avoid amplifying high-frequency noise during TRM. I demonstrate the effects of the filter on the attenuation and the phase velocity by comparing with theoretical solutions in a 1-D Pierre shale homogeneous medium. Three synthetic examples are used to demonstrate the feasibility of attenuation compensation during TRM. The first example uses a 1-D homogeneous model to demonstrate the accuracy of the numerical implementation of the methodology. The second example shows the applicability of source location using a 2-D layering model. The last example uses a 2-D cross-well synthetic experiment to show that the methodology can also be implemented in conjunction with reverse-time migration to image subsurface reflectors. When attenuation compensation is included, I find improved estimation of the source location, the excitation timing of the point source, the magnitude of the focused source wavelet and the reflectivity image of reflectors, particularly for deep structures underneath strongly attenuating zones.

Design and performance of Huffman sequences in medical ultrasound coded excitation

This paper deals with coded-excitation techniques for ultrasound medical echography. Specifically, linear Huffman coding is proposed as an alternative approach to other widely established techniques, such as complementary Golay coding and linear frequency modulation. The code design is guided by an optimization procedure that boosts the signal-to-noise ratio gain (GSNR) and, interestingly, also makes the code robust in pulsed-Doppler applications. The paper capitalizes on a thorough analytical model that can be used to design any linear coded-excitation system. This model highlights that the performance in frequency-dependent attenuating media mostly depends on the pulse-shaping waveform when the codes are characterized by almost ideal (i.e., Kronecker delta) autocorrelation. In this framework, different pulse shapers and different code lengths are considered to identify coded signals that optimize the contrast resolution at the output of the receiver pulse compression. Computer simulations confirm that the proposed Huffman codes are particularly effective, and that there are scenarios in which they may be preferable to the other established approaches, both in attenuating and non-attenuating media. Specifically, for a single scatterer at 150 mm in a 0.7-dB/(MHz·cm) attenuating medium, the proposed Huffman design achieves a main-to-side lobe ratio (MSR) equal to 65 dB, whereas tapered linear frequency modulation and classical complementary Golay codes achieve 35 and 45 dB, respectively.

Evaluation of the angular spectrum approach for simulations of near-field pressures.

The implementation of the angular spectrum approach based on the two-dimensional fast Fourier transform is evaluated for near-field pressure simulations of square ultrasound transducers, where the three-dimensional pressure field is calculated from the normal velocity distribution on the transducer surface. The pressure field is propagated in the spatial frequency domain with the spatial propagator or the spectral propagator. The spatial propagator yields accurate results in the central portion of the computational grid while significant errors are produced near the edge due to the finite extent of the window applied to the spatial propagator. Likewise, the spectral propagator is inherently undersampled in the spatial frequency domain, and this causes high frequency errors in the computed pressure field. This aliasing problem is alleviated with angular restriction. The results show that, in nonattenuating media, the spatial propagator achieves smaller errors than the spectral propagator after the region of interest is truncated to exclude the windowing error. For pressure calculations in attenuating media or with apodized pistons as sources, the spatial and spectral propagator achieve similar accuracies. In all simulations, the angular spectrum calculations with the spatial propagator take more time than calculations with the spectral propagator.

Design of focused ultrasound surgery transducers

High-intensity focused ultrasound surgery (FUS) has been developed for the extracorporeal treatment of various benign and malignant soft tissue tumors. The system developed at the Institute of Cancer Research/Royal Marsden (ICR/RM) National Health Service (NHS) Trust incorporates a 150 mm focal length focused bowl transducer operated at 1.7 MHz, and is currently undergoing Phase 1 clinical trials for the treatment of benign prostatic hyperplasia and superficial bladder cancer. However, the application of this transducer is limited by its focal length to a maximum depth of 100 mm, and by power absorption in the skin to a minimum depth of 40 mm. A computer model of acoustic fields, which assumes uniform excitation of the transducer over its entire surface, has previously been published. This has been used both to calculate the intensity in nonattenuating media, and to estimate the absorbed power per unit volume in homogeneous tissues in order to allow determination of the transducer configurations (frequency, focal length, and diameter) necessary for the treatment of both deep (/spl sim/150 mm) and shallow (/spl sim/20 mm) soft tissue tumors. These depths encompass the typical range for human tissues which are likely to be treated. Calculations cover the frequency range 0.5-4.5 MHz, focal lengths from 70 to 200 mm, and transducer diameters from 30 to 190 mm. The results show that appropriate transducers can be designed for the noninvasive treatment of tumors in specific organs.

Experimental point spread function of fm pulse imaging scheme.

In this paper, we have examined the possibility of incorporating pulse compression techniques into a conventional medical B-scan imaging scheme. Linear frequency modulation fm, one form of pulse coding among many others, has been used in this study. With this approach, one can overcome current peak intensity limitations. A theoretical framework that includes medium propagation effects, transducer bandwidth and diffraction effects is presented, which could be used to examine the system point spread function under this imaging scheme. A prototype experimental set-up and signal processing are described and used for simple imaging tasks in attenuating and nonattenuating media. Analysis of the experimental point spread functions shows that resolution similar to conventional short pulse imaging can be achieved. However, the existence of large range side lobe levels usually associated with pulse compression processing can degrade contrast resolution in medical ultrasound. We have considered various different factors that can affect the range side lobe levels and examined their effect either experimentally or through simulations. The technique has the potential for improving signal-to-noise ratio (SNR), maximum penetration depth and resolution without exceeding peak intensity limitations. Some possible applications are discussed that merit further evaluation. Our work demonstrates the feasibility of this technique and presents a theoretical framework that can be used in future studies aimed at evaluating image quality, system performance, and possible artifacts under such an imaging scheme.

Experimental Point Spread Function of FM Pulse Imaging Scheme

In this paper, we have examined the possibility of incorporating pulse compression techniques into a conventional medical B-scan imaging scheme. Linear frequency modulation fm, one form of pulse coding among many others, has been used in this study. With this approach, one can overcome current peak intensity limitations. A theoretical framework that includes medium propagation effects, transducer bandwidth and diffraction effects is presented, which could be used to examine the system point spread function under this imaging scheme. A prototype experimental set-up and signal processing are described and used for simple imaging tasks in attenuating and nonattenuating media. Analysis of the experimental point spread functions shows that resolution similar to conventional short pulse imaging can be achieved. However, the existence of large range side lobe levels usually associated with pulse compression processing can degrade contrast resolution in medical ultrasound. We have considered various different factors that can affect the range side lobe levels and examined their effect either experimentally or through simulations. The technique has the potential for improving signal-to-noise ratio (SNR), maximum penetration depth and resolution without exceeding peak intensity limitations. Some possible applications are discussed that merit further evaluation. Our work demonstrates the feasibility of this technique and presents a theoretical framework that can be used in future studies aimed at evaluating image quality, system performance, and possible artifacts under such an imaging scheme.

Frequency domain method for the prediction of the ultrasonic field patterns of pulsed, focused radiators

A theoretical model is presented which can be used to calculate the pressure field patterns of pulsed, focused ultrasonic radiators in attenuating and nonattenuating media. Pressure pulses are calculated by superimposing continuous wave solutions at discrete frequencies. Due to the speed of the method, time signals can be calculated at many positions in the transducer beam in a reasonable amount of time. To test the model, theoretical predictions for the pressure signals are compared to hydrophone measurements for a conventional diagnostic transducer. In addition, signal envelopes are studied in order to determine the effects of attenuation and dispersion on the imaging characteristics of a focused radiator. This work may have significant application to the design of transducers for specific imaging purposes or to the analysis of the imaging process.

Field patterns of pulsed, focused radiators in attenuating and non-attenuating media

Field patterns of pulsed, focused radiators in attenuating and non-attenuating media

Field patterns of pulsed, focused, ultrasonic radiators in attenuating and nonattenuating media

A theoretical method which can be used to calculate the pressure field patterns of pulsed, focused, ultrasonic radiators in attenuating and nonattenuating media is discussed in this paper. The underlying principle involved is the superposition of continuous wave beams to form pressure pulses. The method is adapted to the circumstances associated with using a hydrophone to measure field patterns. Experimentally obtained hydrophone signals are then compared to theoretical predictions. The field patterns of four transducer-pulser combinations are investigated. A medium with tissue-mimicking acoustical properties is used to attenuate the ultrasonic beam in these studies. The theory compares favorably with experiment whether an attenuating medium is present or not. However, the theory fails at positions very close to the transducer face (∠1 cm) and when significant nonlinear effects occur during the transmission of the pulse through the medium. This work may have significant applications in research devoted to designing ultrasonic transducers for particular studies, determining dose profiles of medical ultrasonic machines, and analyzing the ultrasonic signals backscattered from within patients.

Pressure field patterns of a pulsed focused transducer in attenuating and nonattenuating media

Pressure field patterns of a pulsed focused transducer in attenuating and nonattenuating media