Ultrasonic properties of tissues

Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.

Section: Compliance Relaxation Function For Frequency Power Law Lossesmentioning

confidence: 99%

“…A functionvðsÞ that for s ¼ jx provides the power law attenuation coefficient a(x) ¼ a 1 |x| b as observed in many measurements, 7,8,29 iŝ…”

Section: Compliance Relaxation Function For Frequency Power Law Lossesmentioning

confidence: 99%

A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation

Demi

Dongen

Verweij

2011

“…The relaxation function formulation enables the modeling of many types of attenuation, among which the frequency power law losses that are exhibited by many biological tissues. 28,30,31,[48][49][50] The coefficient of nonlinearity b indicates the degree of nonlinear behavior of the considered medium, and may be written as…”

Section: Theory a Wave Equationmentioning

confidence: 99%

Computation of nonlinear ultrasound fields using a linearized contrast source method

Verweij

Demi

Dongen

2013

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

“…The forward problem is well-known: Given some distribution of speed of sound and attenuation, c(x), a(x), respectively, determine the pressure field f(x) produced by the impinging of a known incident pressure field f inc x ð Þ [often a plane wave, f inc x ð Þ e ik 0 Áx ], k 0 k 0û Áx,û 2 S 1 (2D case), the unit circle, gives the direction of the incoming plane wave, and k 0 2pf c 0 is the wavenumber associated with frequency f, and background speed of sound c 0 -background attenuation is assumed negligible for water (Bamber, 1998)). The incident field is modeled using the Rayleigh Integral, this need only be done once, and then stored, so accuracy is more important than efficiency here.…”

Section: Theory a Backgroundmentioning

confidence: 99%

Non-linear inverse scattering: High resolution quantitative breast tissue tomography

Wiskin¹,

Borup

Johnson

et al. 2012

138

126

Recent published results in inverse scattering generally show the difficulty in dealing with moderate to high contrast inhomogeneities when employing linearized or iteratively linearized algorithms (e.g., distorted Born iterative method). This paper presents a fully nonlinear algorithm utilizing full wave field data, that results in ultrasound computed tomographic images from a laboratory breast scanner, and shows several such unique images from volunteer subjects. The forward problem, data collection process and inverse scattering algorithm used are discussed. A functional that represents the "best fit" between predicted and measured data is minimized, and therefore requires a very fast forward problem solver, Jacobian calculation, and gradient estimation, all of which are described. The data collection device is described. The algorithm and device yield quantitative estimates of human breast tissue in vivo. Several high resolution images, measuring $150 by 150 wavelengths, obtained from the 2D inverse scattering algorithms, using data collected from a first prototype, are shown and discussed. The quantitative values are compared with previous published work.