A discrete-scatterer model for ultrasonic images of rough surfaces

Minimum variance beamforming applied to ultrasound imaging with a partially shaded aperture

Shadowing of an imaging aperture occurs when ultrasound beams are partially obstructed by an acoustically hard tissue, e.g., bone tissue. This effect leads to reduced resolution and, in some cases, geometrical distortion. In this paper, we initially introduce a binary apodization model to simulate effects of the shadowing on the point scatterers located close to a bone structure. Further, in a simulation study and an in vitro experiment, the minimum variance (MV) beamforming method is employed to image scatterers partly located in the shadow of bone. We show that the MV beamformer can result in a distorted image when the imaging aperture is highly obstructed by the bone structure. This distortion can be seen as an apparent lateral shift of the point spread function and a decrease in the sensitivity. Based on the signal power across the aperture, we adaptively determine the shadowed elements and discard their corresponding data from the covariance matrix to improve the MV beamformer performance. This modified MV beamformer can retain the resolution and compensate for the apparent lateral shifting and signal attenuation for the shadowed point scatterers.

3-D in vitro estimation of temperature using the change in backscattered ultrasonic energy

Temperature imaging with a non-invasive modality to monitor the heating of tumors during hyperthermia treatment is an attractive alternative to sparse invasive measurement. Previously, we predicted monotonic changes in backscattered energy (CBE) of ultrasound with temperature for certain sub-wavelength scatterers. We also measured CBE values similar to our predictions in bovine liver, turkey breast muscle, and pork rib muscle in 2-D in vitro studies and in nude mice during 2-D in vivo studies. To extend these studies to three dimensions, we compensated for motion and measured CBE in turkey breast muscle. 3-D data sets were assembled from images formed by a phased-array imager with a 7.5-MHz linear probe moved in 0.6-mm steps in elevation during uniform heating from 37 to 45 degrees C in 0.5 degrees C increments. We used cross-correlation as a similarity measure in RF signals to automatically track feature displacement as a function of temperature. Feature displacement was non-rigid. Envelopes of image regions, compensated for non-rigid motion, were found with the Hilbert transform then smoothed with a 3 x 3 running average filter before forming the backscattered energy at each pixel. CBE in 3-D motion-compensated images was nearly linear with an average sensitivity of 0.30 dB/ degrees C. 3-D estimation of temperature in separate tissue regions had errors with a maximum standard deviation of about 0.5 degrees C over 1-cm(3) volumes. Success of CBE temperature estimation based on 3-D non-rigid tracking and compensation for real and apparent motion of image features could serve as the foundation for the eventual generation of 3-D temperature maps in soft tissue in a non-invasive, convenient, and low-cost way in clinical hyperthermia.

A simulation model for ultrasonic temperature imaging using change in backscattered energy

Ultrasound backscattered from tissue has previously been shown theoretically and experimentally to change predictably with temperature in the hyperthermia range, i.e., 37 degrees C to 45 degrees C, motivating use of the change in backscattered ultrasonic energy (CBE) for ultrasonic thermometry. Our earlier theoretical model predicts that CBE from an individual scatterer will be monotonic with temperature, with, e.g., positive change for lipid-based scatterers and negative for aqueous-based scatterers. Experimental results have previously confirmed the presence of these positive and negative changes in one-dimensional ultrasonic signals and in two-dimensional images acquired from in vitro bovine, porcine and turkey tissues. In order to investigate CBE for populations of scatterers, we have developed an ultrasonic image simulation model, including temperature dependence for individual scatterers based on predictions from our theoretical model. CBE computed from images simulated for populations of randomly distributed scatterers behaves similarly to experimental results, with monotonic variation for individual pixel measurements and for image regions. Effects on CBE of scatterer type and distribution, size of the image region and signal-to-noise ratio have been examined. This model also provides the basis for future work regarding significant issues relevant to temperature imaging based on ultrasonic CBE such as effects of motion on CBE, limitations of motion-compensation techniques and accuracy of temperature estimation, including tradeoffs between temperature accuracy and available spatial resolution.

Estimation of surface pose with a physically-based ultrasonic image model

State-of-the-art approaches to shape analysis in medical images use a variety of sophisticated models for object shape. We have developed an image model that permits the application of these approaches to ultrasonic images, with detailed methods for representing rough surfaces. Our physically-based, probabilistic image model incorporates the combined effects of the system point-spread function (PSF), the tissue microstructure, and the gross tissue shape. At each image pixel, the amplitude mean and variance are computed directly from the model, characterizing the combined influence of shape, microstructure, and system PSF. Calculation of the SNR0 is used to further classify each pixel as Rayleigh- or non-Rayleigh-distributed. This characterization was used here to generate a data likelihood representing any set of images of a given surface by a probability density conditioned on the surface pose, or rotation and translation. The utility of this likelihood was demonstrated by applying maximum likelihood estimation to infer the pose of a cadaveric vertebra from simulated images of its surface. Successful results were achieved using derivative-based optimization algorithms for a data set of only three images. With a quasi-Newton BFGS algorithm, error in 15 of 20 trials was less than 0.4 degrees in rotation and 0.2 mm in translation. Estimation was inaccurate in only 1 of 20 trials. These results illustrate the potential of a physically-based image model in a rigorous approach to image analysis and also serve as an example of quantitative assessment of the model via performance in a specific application.

A physically based, probabilistic model for ultrasonic images incorporating shape, microstructure, and system characteristics

Recent successes with Bayesian methods for analysis of shape in medical images have motivated our development of a shape-based data likelihood for ultrasound, the foundation of which is a computationally feasible, pixel-based, probabilistic image model. Previous probabilistic models for ultrasound generally assume an analytic form, e.g., Rayleigh, Rician, K, Generalized K, etc., then attempt to fit data to the model. Assumptions and intensive computation inherent in such an approach make it unsuitable for our purposes. In the pursuit of a new model, we have described previously a physical model for image formation that incorporates the imaging system characteristics, the surface shape, and the surface microstructure. That physical model was validated via a visual comparison of simulated and actual images of a cadaveric vertebra. In this work, a random phasor sum representation of the physical model provides the basis for a probabilistic form. In contrast to existing probabilistic models, we compute the amplitude mean and variance directly from the physical model. These statistics can be displayed as images to characterize the tissue, but, more importantly, they permit the subsequent assignment of a suitable density function to each pixel for the purposes of constructing a data likelihood. The order of these steps, i.e., first computing the statistics and then assigning a density function, permits the inclusion of the local surface shape, the surface microstructure, and the system characteristics at every image pixel without violating the physical model. Currently, the value of the SNR0, the ratio of the mean to the standard deviation, is used to estimate whether a pixel is Rayleigh- or non-Rayleigh-distributed. This assessment forms the basis for a data likelihood constructed as a product of Rayleigh and Gaussian density functions describing the individual image pixels.