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

Abstract

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.

Multiparameter identification of a lossy fluid-like object from its transient acoustic response

“…The ultimate goal of the majority of the applications of inverse scattering is to obtain a quantitative image [1] of a corrupted (such as by a crack: [2][3][4][5]), diseased (such as affected by a tumor: [6][7][8][9][10][11]) or otherwise inhomogeneous ( [12][13][14][15][16]) body. To do this in an oft-employed manner (e.g.…”

An ultrasound tomography system with polyvinyl alcohol (PVA) moldings for coupling: in vivo results for 3-D pulse-echo imaging of the female breast

“…It is well known that for breast fatty tissue, values are in the range of 1400 to 1450 m/s, whereas breast parenchyma has sos values of about 1470 to 1540 m/s [39]- [41]. These values vary strongly between individuals, e.g., the ratio of fatty breast tissue typically increases with age, so ideally the sos distribution within the object must be reconstructed in 3-d utilizing beamline-based transmission concepts or more sophisticated diffraction or inverse techniques [13], [14], [19], [42], [43]. based on these sos maps, numerical ray tracing (nrT) algorithms can be applied to correct pulse-echo beamlines for refraction and ToF in a continuously varying sos distribution (bent ray theory) [44]- [46].…”

“…In contrast to aUs, UsT data are processed with multi-directional algorithms for pulse-echo imaging, such as full-angle spatial compounding (Fasc) [10] or the synthetic aperture focusing technique (saFT) [11], [12], to reduce speckle pattern and to achieve an increased and isotropic resolution. Furthermore, with UsT systems, histological tissue parameters such as the speed of sound (sos) or attenuation distribution can be reconstructed with beamline-based transmission techniques from X-ray computed tomography (cT), such as the algebraic reconstruction technique (arT) [10] or diffraction/inverse methods [13], [14]. development in aUs and UsT has made promising progress in recent years and the results encourage clinical introduction of such systems, especially for breast cancer imaging in terms of tumor detection and differentiation.…”

Quantitative volumetric breast imaging with 3D inverse scatter computed tomography

“…The third stage of development is the introduction of true wave equation based methods (not linear perturbation approximations) as models of ultrasound wave propagation [19,20]. The wave equation approach provides a non-linear model of considerable accuracy, compensates for multiple scattering and provides constant resolution throughout the image volume.…”

“…The method does not account for density variations but for scatter in the forward direction this approximation has proven reasonable. Detailed description of the IST algorithm is published elsewhere [20,24,25].…”