Biomedical subjects

Kendall R Waters

Publications and source records attributed to Kendall R Waters.

6 recordsLinked to original sources

PubMed2005

Causal determination of acoustic group velocity and frequency derivative of attenuation with finite-bandwidth Kramers-Kronig relations.

Kramers-Kronig (KK) analyses of experimental data are complicated by the extrapolation problem, that is, how the unexamined spectral bands impact KK calculations. This work demonstrates the causal linkages in resonant-type data provided by acoustic KK relations for the group velocity (c(g)) and the derivative of the attenuation coefficient (alpha') (components of the derivative of the acoustic complex wave number) without extrapolation or unmeasured parameters. These relations provide stricter tests of causal consistency relative to previously established KK relations for the phase velocity (c(p)) and attenuation coefficient (alpha) (components of the undifferentiated acoustic wave number) due to their shape invariance with respect to subtraction constants. For both the group velocity and attenuation derivative, three forms of the relations are derived. These relations are equivalent for bandwidths covering the entire infinite spectrum, but differ when restricted to bandlimited spectra. Using experimental data from suspensions of elastic spheres in saline, the accuracy of finite-bandwidth KK predictions for c(g) and alpha' is demonstrated. Of the multiple methods, the most accurate were found to be those whose integrals were expressed only in terms of the phase velocity and attenuation coefficient themselves, requiring no differentiated quantities.

Acoustics↗

PubMed2005

Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion.

Causality imposes restrictions on both the time-domain and frequency-domain responses of a system. The Kramers-Kronig (K-K) relations relate the real and imaginary parts of the frequency-domain response. In ultrasonics, K-K relations often are used to link attenuation and dispersion. We review both integral and differential forms of the frequency-domain K-K relations that are relevant to theoretical models and laboratory measurements. We consider two methods for implementing integral K-K relations for the case of finite-bandwidth data, namely, extrapolation of data and restriction of integration limits. For the latter approach, we discuss the accuracy of K-K predictions for specific classes of system behavior and how the truncation of the integrals affects this accuracy. We demonstrate the accurate prediction of attenuation and dispersion using several forms of the K-K relations relevant to experimental measurements of media with attenuation coefficients obeying a frequency power law and media consisting of resonant scatterers. We also review the time-causal relations that describe the time-domain consequences of causality in the wave equation. These relations can be thought of as time-domain analogs of the (frequency-domain) K-K relations. Causality-imposed relations, such as the K-K and time-causal relations, provide useful tools for the analysis of measurements and models of acoustic systems.

Journal Article↗

PubMed2004

Temperature estimation using ultrasonic spatial compound imaging.

The feasibility of temperature estimation during high-intensity focused ultrasound therapy using pulse-echo diagnostic ultrasound data has been demonstrated. This method is based upon the measurement of thermally-induced modifications in backscattered RF echoes due to thermal expansion and local changes in the speed of sound. It has been shown that strong ripple artifacts due to the thermo-acoustic lens effect severely corrupt the temperature estimates behind the heated region. We propose here a new imaging technique that improves the temperature estimation behind the heated region and reduces the variance of the temperature estimates in the entire image. We replaced the conventional beamforming on transmit with multiple steered plane wave insonifications using several subapertures. A two-dimensional temperature map is estimated from axial displacement maps between consecutive RF images of identically steered plane wave insonifications. Temperature estimation is then improved by averaging the two-dimensional maps from the multiple steered plane wave insonifications. Experiments were conducted in a tissue-mimicking gelatin-based phantom and in fresh bovine liver.

Animals↗

PubMed2003

Parametric analysis of carotid plaque using a clinical ultrasound imaging system.

We evaluated quantitative ultrasonic methods for assessment of carotid plaque content. In vitro measurements of fixed, carotid plaque specimens obtained by surgical endarterectomy were performed using a clinical Philips HDI 5000 imaging system connected to a radiofrequency (RF) signal-acquisition system. We acquired RF signals and grey-scale images from carotid specimens (n = 17) and a tissue-mimicking reference phantom. Imaged plaque sections were then classified according to histology. Parametric images were constructed from the integrated backscatter (IBS), and the midband, slope and intercept values of a straight-line fit to the apparent backscatter transfer function. Analysis was performed on 82 regions-of-interest (ROIs). The IBS values for collagen, lipid and hemorrhage plaques were 5.8 +/- 5.4, 3.9 +/- 3.7, 2.8 +/- 2.2 dB, respectively. Midband and IBS parameter images exhibited good agreement in morphology with histology, whereas the slope and intercept parameter images were noisy. Mean IBS, midband, and grey-scale values of complex plaques were found to be statistically different (p < 0.05) from lipid, hemorrhage and fibrolipid plaques. The bias and limits of agreement (1.3 +/- 4.9 dB) between the grey-scale and IBS methods, however, indicated that the two methods were not interchangeable. Results indicate necessary improvements, such as reduction of large measurement variances and identification of robust parameters, that will permit multiparametric characterization of carotid plaque under in vivo conditions.

Carotid Arteries↗

PubMed2003

Differential forms of the Kramers-Krönig dispersion relations.

Differential forms of the Kramers-Krönig dispersion relations provide an alternative to the integral Kramers-Krönig dispersion relations for comparison with finite-bandwidth experimental data. The differential forms of the Kramers-Krönig relations are developed in the context of tempered distributions. Results are illustrated for media with attenuation obeying an arbitrary frequency power law (alpha(omega) = alpha0 + alpha1(absolute value of omega)y). Dispersion predictions using the differential dispersion relations are compared to the measured dispersion for a series of specimens (two polymers, an egg yolk, and two liquids) exhibiting attenuation obeying a frequency power law (1.00 < or = y < or = 1.99), with very good agreement found. For this form of ultrasonic attenuation, the differential Kramers-Krönig dispersion prediction is found to be identical to the (integral) Kramers-Krönig dispersion prediction.

Algorithms↗

PubMed2003

Finite-bandwidth effects on the causal prediction of ultrasonic attenuation of the power-law form.

Kramers-Kronig (K-K) relations exist as a consequence of causality, placing nonlocal constraints on the relationship between dispersion and absorption. The finite-bandwidth method of applying these relations is examined where the K-K integrals are restricted to the spectrum of the experimental data. These finite-bandwidth K-K relations are known to work with resonant-type data and here are applied to dispersion data consistent with a power-law attenuation coefficient (exponent from 1 to 2). Bandwidth-restricted forms of the zero and once-subtracted K-K relations are used to determine the attenuation coefficient from phase velocity. Analytically, it is shown that these transforms produce the proper power-law form of the attenuation coefficient as a stand-alone term summed with artifacts that are dependent on the integration limits. Calculations are performed to demonstrate how these finite-bandwidth artifacts affect the K-K predictions under a variety of conditions. The predictions are studied in a local context as a function of subtraction frequency, bandwidth, and power-law exponent. The K-K predictions of the power-law exponent within various decades of the spectrum are also examined. In general, the agreement between finite-bandwidth K-K predictions and exact values grows as the power-law exponent approaches 1 and with increasing bandwidth.

Models, Theoretical↗