Three-dimensional echo decorrelation monitoring of radiofrequency ablation in ex vivo bovine liver.

Three-dimensional (3D) echo decorrelation imaging was investigated for monitoring radiofrequency ablation (RFA) in ex vivo bovine liver. RFA experiments (N = 14) were imaged by 3D ultrasound using a matrix array, with in-phase and quadrature complex echo volumes acquired about every 11 s. Tissue specimens were then frozen at -80 °C, sectioned, and semi-automatically segmented. Receiver operating characteristic (ROC) curves were constructed for assessing ablation prediction performance of 3D echo decorrelation with three potential normalization approaches, as well as 3D integrated backscatter (IBS). ROC analysis indicated that 3D echo decorrelation imaging is potentially a good predictor of local RFA, with the best prediction performance observed for globally normalized decorrelation. Tissue temperatures, recorded by four thermocouples integrated into the RFA probe, showed good correspondence with spatially averaged decorrelation and statistically significant but weak correlation with measured echo decorrelation at the same spatial locations. In tests predicting ablation zones using a weighted K-means clustering approach, echo decorrelation performed better than IBS, with smaller root mean square volume errors and higher Dice coefficients relative to measured ablation zones. These results suggest that 3D echo decorrelation and IBS imaging are capable of real-time monitoring of thermal ablation, with potential application to clinical treatment of liver tumors.

2pBAb5. Validation of three-dimensional strain tracking by volumetric ultrasound image correlation in a pubovisceral muscle model.

Little is understood about the biomechanical changes leading to pelvic floor disorders such as stress urinary incontinence. In order to measure regional biomechanical properties of the pelvic floor muscles in vivo, a three dimensional (3D) strain tracking technique employing correlation of volumetric ultrasound images has been implemented. In this technique, local 3D displacements are determined as a function of applied stress and then converted to strain maps. To validate this approach, an in vitro model of the pubovisceral muscle, with a hemispherical indenter emulating the downward stress caused by intra-abdominal pressure, was constructed. Volumetric B-scan images were recorded as a function of indenter displacement while muscle strain was measured independently by a sonomicrometry system (Sonometrics). Local strains were computed by ultrasound image correlation and compared with sonomicrometry-measured strains to assess strain tracking accuracy. Image correlation by maximizing an exponential likelihood function was found more reliable than the Pearson correlation coefficient. Strain accuracy was dependent on sizes of the subvolumes used for image correlation, relative to characteristic speckle length scales of the images. Decorrelation of echo signals was mapped as a function of indenter displacement and local tissue orientation. Strain measurement accuracy was weakly related to local echo decorrelation.

Spatial specificity and sensitivity of passive cavitation imaging for monitoring high-intensity focused ultrasound thermal ablation in ex vivo bovine liver.

Passive cavitation images (PCIs) generated from scattered acoustic waves are a potential technique for monitoring lesion formation during high-intensity focused ultrasound (HIFU) thermal ablation. HIFU lesion prediction by PCIs was assessed in ex vivo bovine liver samples (N=14) during 30-s sonications with 1.1-MHz continuous-wave ultrasound (1989 W/cm^2 estimated spatial-peak intensity). Treated samples were sectioned, optically scanned, and the HIFU lesions segmented based on tissue discoloration. During each insonation, a 192-element, 7-MHz linear array (L7/Iris 2, Ardent Sound) passively recorded emissions from a plane containing the HIFU propagation axis oriented parallel to the image azimuth direction. PCIs were formed from beamformed A-lines filtered into fundamental, harmonic, ultraharmonic, and inharmonic frequency bands. Lesion prediction was tested using binary classification of local tissue ablation based on thresholded PCIs, with spatial specificity and sensitivity of lesion prediction quantified by the area under receiver operating characteristic curves (AUROC). Tadpole-shaped lesions were best predicted by harmonic emissions (AUROC=0.76), prefocal lesions were best predicted by harmonic or ultraharmonic emissions (AUROC=0.86), and cigar-type focal lesions were best predicted by fundamental and harmonic emissions (AUROC=0.65). These results demonstrate spatial specificity and sensitivity when predicting HIFU lesions with PCIs.

A k-space method for large-scale models of wave propagation in tissue.

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths; most current two-dimensional methods, such as finite-difference and finite-element methods, are unable to compute propagation on this scale with the efficiency needed for imaging studies. Furthermore, for most available methods of simulating ultrasonic propagation, large-scale, three-dimensional computations of ultrasonic scattering are infeasible. Some of these difficulties have been overcome by previous pseudospectral and k-space methods, which allow substantial portions of the necessary computations to be executed using fast Fourier transforms. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x) < or = c0) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.

Quantitative flaw reconstruction from ultrasonic surface wavefields measured by electronic speckle pattern interferometry.

A new method for imaging flaws in plate and shell structures is presented. The method employs two-dimensional ultrasonic surface wave data obtained by optical electronic speckle pattern interferometry (ESPI) techniques. In the imaging method, the measured out-of-plane displacement field associated with an externally excited ultrasonic Lamb wave is processed to obtain the spatial frequency domain spectrum of the wavefield. A free space Green's function is then deconvolved from the wavefield to obtain quantitative images of effective scattering sources. Because the strength of these effective sources is directly dependent on local variations in sample thickness and material properties, these images provide a direct map of internal inhomogeneities. Simulation results show that the method accurately images flaws for a wide range of sizes and material contrast ratios. These results also demonstrate that flaw features much smaller than an acoustic wavelength can be imaged, consistent with the theoretical capability of the imaging method to employ scattered evanescent waves. Reconstructions are also obtained from ultrasonic Lamb wave displacement fields recorded by ESPI in a flawed aluminum plate. These reconstructions indicate that the present method has potential for imaging flaws in complex structures for which ESPI wavefield measurements cannot be straightforwardly interpreted.

Simulation of ultrasonic pulse propagation, distortion, and attenuation in the human chest wall.

A finite-difference time-domain model for ultrasonic pulse propagation through soft tissue has been extended to incorporate absorption effects as well as longitudinal-wave propagation in cartilage and bone. This extended model has been used to simulate ultrasonic propagation through anatomically detailed representations of chest wall structure. The inhomogeneous chest wall tissue is represented by two-dimensional maps determined by staining chest wall cross sections to distinguish between tissue types, digitally scanning the stained cross sections, and mapping each pixel of the scanned images to fat, muscle, connective tissue, cartilage, or bone. Each pixel of the tissue map is then assigned a sound speed, density, and absorption value determined from published measurements and assumed to be representative of the local tissue type. Computational results for energy level fluctuations and arrival time fluctuations show qualitative agreement with measurements performed on the same specimens, but show significantly less waveform distortion than measurements. Visualization of simulated tissue-ultrasound interactions in the chest wall shows possible mechanisms for image aberration in echocardiography, including effects associated with reflection and diffraction caused by rib structures. A comparison of distortion effects for varying pulse center frequencies shows that, for soft tissue paths through the chest wall, energy level and waveform distortion increase markedly with rising ultrasonic frequency and that arrival-time fluctuations increase to a lesser degree.

The effect of abdominal wall morphology on ultrasonic pulse distortion. Part I. Measurements.

The relative importance of the fat and muscle layers of the human abdominal wall in producing ultrasonic wavefront distortion was assessed by means of direct measurements. Specimens employed included six whole abdominal wall specimens and twelve partial specimens obtained by dividing each whole specimen into a fat and a muscle layer. In the measurement technique employed, a hemispheric transducer transmitted a 3.75-MHz ultrasonic pulse through a tissue section. The received wavefront was measured by a linear array translated in the elevation direction to synthesize a two-dimensional aperture. Insertion loss was also measured at various locations on each specimen. Differences in arrival time and energy level between the measured waveforms and computed references that account for geometric delay and spreading were calculated. After correction for the effects of geometry, the received waveforms were synthetically focused. The characteristics of the distortion produced by each specimen and the quality of the resulting focus were analyzed and compared. The measurements show that muscle produces greater arrival time distortion than fat while fat produces greater energy level distortion than muscle, but that the distortion produced by the entire abdominal wall is not equivalent to a simple combination of distortion effects produced by the layers. The results also indicate that both fat and muscle layers contribute significantly to the distortion of ultrasonic beams by the abdominal wall. However, the spatial characteristics of the distortion produced by fat and muscle layers differ substantially. Distortion produced by muscle layers, as well as focal images aberrated by muscle layers, show considerable anisotropy associated with muscle fiber orientation. Distortion produced by fat layers shows smaller-scale, granular structure associated with scattering from the septa surrounding individual fat lobules. Thick layers of fat may be expected to cause poor image quality due to both scattering and bulk absorption effects, while thick muscle layers may be expected to cause focus aberration due to large arrival time fluctuations. Correction of aberrated focuses using time-shift compensation shows more complete correction for muscle sections than for fat sections, so that correction methods based on phase screen models may be more appropriate for muscle layers than for fat layers.

The effect of abdominal wall morphology on ultrasonic pulse distortion. Part II. Simulations.

Wavefront propagation through the abdominal wall was simulated using a finite-difference time-domain implementation of the linearized wave propagation equations for a lossless, inhomogeneous, two-dimensional fluid as well as a simplified straight-ray model for a two-dimensional absorbing medium. Scanned images of six human abdominal wall cross sections provided the data for the propagation media in the simulations. The images were mapped into regions of fat, muscle, and connective tissue, each of which was assigned uniform sound speed, density, and absorption values. Propagation was simulated through each whole specimen as well as through each fat layer and muscle layer individually. Wavefronts computed by the finite-difference method contained arrival time, energy level, and wave shape distortion similar to that in measurements. Straight-ray simulations produced arrival time fluctuations similar to measurements but produced much smaller energy level fluctuations. These simulations confirm that both fat and muscle produce significant wavefront distortion and that distortion produced by fat sections differs from that produced by muscle sections. Spatial correlation of distortion with tissue composition suggests that most major arrival time fluctuations are caused by propagation through large-scale inhomogeneities such as fatty regions within muscle layers, while most amplitude and waveform variations are the result of scattering from smaller inhomogeneities such as septa within the subcutaneous fat. Additional finite-difference simulations performed using uniform-layer models of the abdominal wall indicate that wavefront distortion is primarily caused by tissue structures and inhomogeneities rather than by refraction at layer interfaces or by variations in layer thicknesses.

Measurements of differential scattering cross section using a ring transducer.

A procedure for the measurement of intrinsic scattering object properties is presented and used to obtain illustrative results. The procedure is based on the measurement of the scattered acoustic field as a function of scattering angle and frequency. Measurements are normalized using analytically determined expressions for emitter and detector beams resulting from a combination of unfocused linear elements arranged in a circular configuration. The spatial effects of finite emitter pulse length and detector gate length are represented by a convolution formula valid for narrow-band transmitted signals and long receiver gates. The normalization includes correction for target absorption as well as measurement of the directly transmitted acoustic power in the free field and yields the average differential scattering cross section per unit volume. Under the Born approximation, this quantity is directly proportional to the spatial-frequency spectrum of the scattering medium inhomogeneities. Measured results are reported for two phantoms consisting of glass microspheres embedded in a weakly absorbing agar background medium. For the phantoms employed, scattering effects, rather than increased absorption, are shown to account for most of the difference in transmission loss between pure agar and agar with glass spheres. The measured differential scattering cross sections are compared with theoretical cross sections for distributions of glass spheres measured experimentally. The measured values show good relative agreement with theory for varying angle, frequency, and phantom properties. The results are interpreted in terms of wave space resolution and the potential for tissue characterization using similar fixed transducer configurations.

Focusing and imaging using eigenfunctions of the scattering operator.

An inverse scattering method that uses eigenfunctions of the scattering operator is presented. This approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media. Scattered acoustic fields are described using a compact, normal operator. The eigenfunctions of this operator are shown to correspond to the far-field patterns of source distributions that are directly proportional to the position-dependent contrast of a scattering object. Conversely, the eigenfunctions of the scattering operator specify incident-wave patterns that focus on these effective source distributions. These focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions. A regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products, so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities. The corresponding linearized problem is solved analytically, resulting in a simple formula for the low-pass-filtered scattering potential. The linear formula is analytically equivalent to known filtered-backpropagation formulas for Born inversion, and, at least in the case of small scattering objects, has advantages of computational simplicity and efficiency. A similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium. Computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media, quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions, inverse scattering in an inhomogeneous background medium, and reconstructions for data corrupted by noise.

Simulation of ultrasonic pulse propagation through the abdominal wall.

Ultrasonic pulse propagation through the abdominal wall has been simulated using a model for two-dimensional propagation through anatomically realistic tissue cross sections. The time-domain equations for wave propagation in a medium of variable sound speed and density were discretized to obtain a set of coupled finite-difference equations. These difference equations were solved numerically using a two-step MacCormack scheme that is fourth-order accurate in space and second-order accurate in time. The inhomogeneous tissue of the abdominal wall was represented by two-dimensional matrices of sound speed and density values. These values were determined by processing scanned images of abdominal wall cross sections stained to identify connective tissue, muscle, and fat, each of which was assumed to have a constant sound speed and density. The computational configuration was chosen to simulate that of wavefront distortion measurements performed on the same specimens. Qualitative agreement was found between those measurements and the results of the present computations, indicating that the computational model correctly depicts the salient characteristics of ultrasonic wavefront distortion in vivo. However, quantitative agreement was limited by the two-dimensionality of the computation and the absence of detailed tissue microstructure. Calculations performed using an asymptotic straight-ray approximation showed good agreement with time-shift aberrations predicted by the full-wave method, but did not explain the amplitude fluctuations and waveform distortion found in the experiments and the full-wave calculations. Visualization of computed wave propagation within tissue cross sections suggests that amplitude fluctuations and waveform distortion observed in ultrasonic propagation through the abdominal wall are associated with scattering from internal inhomogeneities such as septa within the subcutaneous fat. These observations, as well as statistical analysis of computed and observed amplitude fluctuations, suggest that weak fluctuation models do not fully describe ultrasonic wavefront distortion caused by the abdominal wall.

Wave space resolution in ultrasonic scattering measurements.

The spatial-frequency spectra of the spatial properties of a scattering medium can be determined from measurements of scattering over a number of angles or frequencies. In such measurements, the spatial localization associated with transducer beam patterns and time gates causes an uncertainty in the measured spatial-frequency domain properties of the scatterer. This uncertainty is analyzed using an analytic and computational model in which system effects are represented by a spatial-frequency domain function. Wave space resolution in a particular direction is shown to be inversely proportional to the spatial-frequency spread of the system function in that direction. In the backscatter case, wave space resolution is limited in the direction of the scattering vector by a convolution of the emitted pulse and the detector time gate, and resolution in the lateral direction depends mainly on the transducer aperture, increasing approximately in proportion to the aperture diameter. In the case of backscatter measurements, smooth aperture apodization improves lateral resolution somewhat but has little effect on resolution in the direction of the scattering vector. For angular scattering measurements, resolution in all directions depends on both the aperture size and (for sufficiently short time gates) on the time gates employed. Illustration of the practical importance of wave space resolution is provided using analysis of two previously published tissue characterization experiments.

A theory of aneurysm sounds.

Narrow-band sounds are known to be associated with some intracranial aneurysms. Previously proposed theories for the mechanism of aneurysm sounds do not satisfactorily explain the small spectral widths of the sounds. A simple theory is proposed here which gives quantitatively correct predictions of the spectral widths and which also explains other salient features of aneurysm sounds. The physical features of the aneurysm are described in terms of lumped mechanical elements, and the interaction between the aneurysm vibration and the blood flow is recognized as having the characteristic features of a nonlinear feedback system. The resulting model, with the application of the method of describing function analysis commonly used in nonlinear control theory, yields predictions of steady oscillation frequencies and predictions of the ranges of arterial flow velocities for which substantial oscillations can be excited. An analysis of radiation losses associated with peristaltic waves indicates that aneurysms, in the absence of any nonlinearity, behave as low-quality factor resonators with resonator quality factors on the order of 1-10, much lower than those that would be inferred from the observed spectral widths of aneurysm sounds. Aneurysm sounds are predicted by the present nonlinear theory to have center frequencies on the order of 400 Hz and bandwidths corresponding to quality factors on the order of 40, in good agreement with in vivo observations. It is concluded that linear resonance theories are incapable of fully describing aneurysm sounds.(ABSTRACT TRUNCATED AT 250 WORDS)