A Nonlinear Plane-Wave Algorithm for Diffractive Propagation Involving Shockwaves

Christopher, P. Ted

doi:10.1142/s0218396x93000202

Cited by 15 publications

(6 citation statements)

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“…Computational efficiency is improved to order N if nonlinearity is modelled in the time domain (Hamilton and Blackstock 1998). An algorithm of this type devised by Christopher (1993) is used here to model nonlinearity. The nonlinearity operator is defined as…”

Section: Computational Simulationsmentioning

confidence: 99%

“…Previous models valid for multilayer propagation have been described in the literature, as have models that offer excellent computational efficiency. Christopher andParker (1991a, 1991b) developed a phenomenological model that was used to investigate the axisymmetric acoustic field of a focused beam in layered fat and liver media, and included transmission and refraction at boundaries. Recently, Li and Zagzebski (2004) used a KZK implementation to simulate propagation in layered water-corn oil from an axisymmetric source; however, refraction effects were ignored in their model.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear ultrasound propagation through layered liquid and tissue-equivalent media: computational and experimental results at high frequency

et al. 2006

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Nonlinear propagation has been demonstrated to have a significant impact on ultrasound imaging. An efficient computational algorithm is presented to simulate nonlinear ultrasound propagation through layered liquid and tissue-equivalent media. Results are compared with hydrophone measurements. This study was undertaken to investigate the role of nonlinear propagation in high frequency ultrasound micro-imaging. The acoustic field of a focused transducer (20 MHz centre frequency, f-number 2.5) was simulated for layered media consisting of water and tissue-mimicking phantom, for several wide-bandwidth source pulses. The simulation model accounted for the effects of diffraction, attenuation and nonlinearity, with transmission and refraction at layer boundaries. The parameter of nonlinearity, B/A, of the water and tissue-mimicking phantom were assumed to be 5.2 and 7.4, respectively. The experimentally measured phantom B/A value found using a finite-amplitude insert-substitution method was shown to be 7.4 +/- 0.6. Relative amounts of measured second and third harmonic pressures as a function of the fundamental pressures at the focus were in good agreement with simulations. Agreement within 3% was found between measurements and simulations of the beam widths of the fundamental and second harmonic signals following propagation through the tissue phantom. The results demonstrate significant nonlinear propagation effects for high frequency imaging beams.

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Section: Computational Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear ultrasound propagation through layered liquid and tissue-equivalent media: computational and experimental results at high frequency

et al. 2006

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“…This approach makes the method free of the paraxial approximation which is inherent in other forward-wave methods based on the KZK equation. The nonlinear propagation is accounted for with a plane-wave time-domain algorithm employing first-order finite differences over time [9]. The method was provided as a Matlab code and it runs on a desktop PC.…”

Section: Methodsmentioning

confidence: 99%

P3B-3 Comparison of an Angular Spectrum Method and a Green's Function Method for Nonlinear Propagation of Pulsed Acoustic Fields from Medical Phased Array Transducers

Huijssen

Verweij

Jong

2007

2007 IEEE Ultrasonics Symposium Proceedings

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Predictions of nonlinear ultrasound beams of a medical phased array transducer, steered at 0, 22.5 and 45 degrees, and generated by a forward-wave and a full-wave numerical model are presented. The results from both models show a good agreement in the unsteered situation and in all fundamental field profiles, but they deviate significantly in the harmonic field profiles for the steered situations.

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Section: Introductionmentioning

confidence: 98%

“…This distortion manifests itself in frequency domain as the harmonics generation with multiple components of fundamental frequencies which did not exist in the spectrum of the emitted signal. This phenomenon is more significant when the intensity or the frequency of the wave are high [2].Linearity has an effect on all the methods of measurement and characterization of the mediums and ultrasounds equipment. For this reason, it is primordial to consider that in the definition, design and the development of the equipment using the ultrasonic waves.…”

mentioning

confidence: 99%

Theoretical study of harmonic generation sound beams in case of uniform, exponential and cosinusoidal apertures

Kourtiche¹,

Ali²,

Chitnalah³

et al.

2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Abstract-The non-linear propagation of ultrasound in medical imaging has recently been exploited to improve image resolution and remove near field artifacts generated by overlying tissue structures. The images are formed using the second harmonic energy generated by nonlinear propagation. Second harmonic beams have narrower beam width and lower side lobes than the fundamental. The second harmonic draws energy from the fundamental continuously along the propagation path. These characteristics contribute to improve the quality of medical ultrasound images.In this paper, our objective is to show that the choice source aperture has significant consequences on the quality of the field transmitted in term of directivity. We also studied the field generated by three apertures sources, in a nonlinear medium. Theoretical approach, based on the Khokhlov-ZabolotskayaKuznetsov (KZK) parabolic approximation is used in order to consider the diffraction effects related to the use of a focusing real source. The fundamental ultrasonic fields and the second harmonic are compared at three distances from the source. Width and side lobes were used when recording three distributions of the beam form. Keywords -Nonlinear, ultrasound, harmonic, KZK I. INTRODUCTIONIt has been shown since that several physical phenomena related to ultrasound propagation can not be explained by linear theory [1]. Among these phenomena one finds the nolinearity, the diffraction and the absorption. Indeed the local variations of velocity and density can not be neglected. Thus it is necessary to enhance these approximations and then obtain a non linear differential equations system. These variations result in a deformation of the temporal profile of the emitted ultrasonic wave. This distortion manifests itself in frequency domain as the harmonics generation with multiple components of fundamental frequencies which did not exist in the spectrum of the emitted signal. This phenomenon is more significant when the intensity or the frequency of the wave are high [2].Linearity has an effect on all the methods of measurement and characterization of the mediums and ultrasounds equipment. For this reason, it is primordial to consider that in the definition, design and the development of the equipment using the ultrasonic waves. A theoretical study is essential as a preliminary to demonstrate the distortion of the wave along the propagation in order to be able to simulate the experimental study. The general wave equation which is valid for no linearity, diffraction, and absorption in sound beams was derived by Kuznetsov [3] Zabolotskaya and Khokhlov [4]. This model was obtained starting from the physical basic laws by improving the approximations of the second order linear theory. It was validated by several researchers [5,6]. The objective of this work is the theoretical study of diffraction effects in the case of real sources [7,8]. We present, here particularly, the case of a focusing circular source. Three apertures: uniform, cosine and exponential were studied. ...

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A Nonlinear Plane-Wave Algorithm for Diffractive Propagation Involving Shockwaves

Cited by 15 publications

References 0 publications

Nonlinear ultrasound propagation through layered liquid and tissue-equivalent media: computational and experimental results at high frequency

Nonlinear ultrasound propagation through layered liquid and tissue-equivalent media: computational and experimental results at high frequency

P3B-3 Comparison of an Angular Spectrum Method and a Green's Function Method for Nonlinear Propagation of Pulsed Acoustic Fields from Medical Phased Array Transducers

Theoretical study of harmonic generation sound beams in case of uniform, exponential and cosinusoidal apertures

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