Thomas L. Szabo

Time domain wave equations for lossy media obeying a frequency power law

For attenuation described by a slowly varying power law function of frequency, α=α0‖ω‖y, classical lossy time domain wave equations exist only for the restricted cases where y=0 or y=2. For the frequently occurring practical situation in which attenuation is much smaller than the wave number, a lossy dispersion characteristic is derived that has the desired attenuation general power law dependence. In order to obtain the corresponding time domain lossy wave equation, time domain loss operators similar in function to existing derivative operators are developed through the use of generalized functions. Three forms of lossy wave equations are found, depending on whether y is an even or odd integer or a noninteger. A time domain expression of causality analogous in function to the Kramers–Kronig relations in the frequency domain is used to derive the causal wave equations. Final causal versions of the time domain wave equations are obtained even for the cases where y≥1, which, according to the Paley–Wiener th...

Causal theories and data for acoustic attenuation obeying a frequency power law

This study compares causal theories, based on Kramers–Kronig relations, fractional calculus, and on those derived from new time domain causal relationships, to diverse data. All these theories are based on the assumptions that the functional form of the attenuation persists beyond the measurement range and that attenuation is much smaller than the wave number. The data, for lossy media with attenuation having a power‐law frequency dependence with an exponent y, include cases for both liquids and solids, ranging from acoustic to ultrasound frequencies. Data are in closer correspondence with the new theory which predicts decreasing dispersion as the power exponent y approaches zero or an even integer. Experimental results and supporting evidence show that the classical case of frequency‐squared attenuation is dispersionless. An approximate nearly local Kramers–Kronig theory is in agreement with the time causal theory when the exponent is close to one, but deviates for other values. The comprehensive time ca...

A model for longitudinal and shear wave propagation in viscoelastic media

Relaxation models fail to predict and explain loss characteristics of many viscoelastic materials which follow a frequency power law. A model based on a time-domain statement of causality is presented that describes observed power-law behavior of many viscoelastic materials. A Hookes law is derived from power-law loss characteristics; it reduces to the Hookes law for the Voigt model for the specific case of quadratic frequency loss. Broadband loss and velocity data for both longitudinal and shear elastic types of waves agree well with predictions. These acoustic loss models are compared to theories for loss mechanisms in dielectrics based on isolated polar molecules and cooperative interactions.

Tidal stretches do not modulate responsiveness of intact airways in vitro

Studies on isolated tracheal airway smooth muscle (ASM) strips have shown that length/force fluctuations, similar to those likely occurring during breathing, will mitigate ASM contractility. These studies conjecture that, solely by reducing length oscillations on a healthy, intact airway, one can create airway hyperresponsiveness, but this has never been explicitly tested. The intact airway has additional complexities of geometry and structure that may impact its relevance to isolated ASM strips. We examined the role of transmural pressure (Ptm) fluctuations of physiological amplitudes on the responsiveness of an intact airway. We developed an integrated system utilizing ultrasound imaging to provide real-time measurements of luminal radius and wall thickness over the full length of an intact airway (generation 10 and below) during Ptm oscillations. First, airway constriction dynamics to cumulative acetylcholine (ACh) doses (10(-7) to 10(-3) M) were measured during static and dynamic Ptm protocols. Regardless of the breathing pattern, the Ptm oscillation protocols were ineffective in reducing the net level of constriction for any ACh dose, compared with the static control (P = 0.225-0.793). Next, Ptm oscillations of increasing peak-to-peak amplitude were applied subsequent to constricting intact airways under static conditions (5.0-cmH(2)O Ptm) with a moderate ACh dose (10(-5) M). Peak-to-peak Ptm oscillations < or = 5.0 cmH(2)O resulted in no statistically significant bronchodilatory response (P = 0.429 and 0.490). Larger oscillations (10 cmH(2)O, peak to peak) produced modest dilation of 4.3% (P = 0.009). The lack of modulation of airway responsiveness by Ptm oscillations in intact, healthy airways suggests that ASM level mechanisms alone may not be the sole determinant of airway responsiveness.

Effects on nonlinearity on the estimation of in situ values of acoustic output parameters.

Water can generate extreme waveform distortion compared to tissue, as indicated by the Goldberg number for water, which is 20 times larger than that of tissue at typical diagnostic ultrasound levels. This result was demonstrated by using tofu as a tissue mimicking material. By adjusting transducer voltage drive levels in water to match the peak rarefactional pressures in water to those of waveforms in tofu, a close correspondence was obtained for the peak compressional pressure and time average intensity with depth. A poorer correspondence was found by comparing tofu waveforms with water waveforms that were compensated for broadband attenuation and driven at the same voltage level as tofu. A simplified broadband derating factor, allowing for band‐width adjustment, was shown to be more accurate than the standard monochromatic derating. Several new indicators for quantifying the degree of observed nonlinearity are suggested: a field based nonlinearity parameter, a peak pressure ratio pc/pr, and a second harmonic to fundamental frequency spectral ratio. These indicators may have the potential for more consistent characterization of nonlinear relationships among output parameters and drive levels.

An inertial-optical tracking system for portable, quantitative, 3D ultrasound

Freehand 3D ultrasound imaging has been growing in popularity. However, the unavoidable reconstruction errors introduced by freehand motion have limited its usefulness. To overcome this, freehand ultrasound systems have been augmented with external tracking sensors to produce accurate 3D images in mainly experimental settings, but these systems have yet to be accepted for general clinical use. In addition, the use of external tracking sensors limits the portability of the system. This paper presents a 5 degree of freedom, low cost, integrated tracking device for quantitative, freehand, 3D ultrasound. It uses a combination of optical and inertial sensors to track the position and orientation of the ultrasound probe during a 3D scan. These sensors can be attached to or contained completely within the ultrasound transducer. Stradwin 3D ultrasound software acquires 2D image frames from the ultrasound system and position and orientation data from the tracking system to generate 3D ultrasound images in real-time. 3D reconstruction performance was evaluated by freehand scanning cylindrical inclusions in a tissue mimicking ultrasound phantom. Different scan patterns were tested to provide performance data for errors introduced in individual degrees of freedom. 3D images were formed from the data with and without the use of the tracking information, and then manually segmented. The volume and surface accuracy of the segmented regions were then compared to the ground truth. The mean volume error was 3.84% with the position information and 18.57% without. The mean RMS surface error was .381 mm with the position information and .843 mm without.

Generalized Fourier transform diffraction theory for parabolically anisotropic media

A convenient diffraction formalism is presented for a planar ultrasonic source of arbitrary shape radiating into a medium which is parabolically anisotropic (or isotropic). Under the Fresnel approximation, the field amplitude is shown to be a Fourier transform of the aperture source function for both the nearfield and farfield. For the two‐dimensional (surface‐wave) case, closed‐form field expressions were obtained for the following source shapes: rectangular, Gaussian, truncated cosine, and truncated Gaussian. Diffraction loss and phase advance curves for equal and unequal apertures show that the nearly ideal characteristics of a Gaussian source can be approximated well by truncated source shapes.

Conditionally Increased Acoustic Pressures in Nonfetal Diagnostic Ultrasound Examinations Without Contrast Agents: A Preliminary Assessment

The mechanical index (MI) has been used by the US Food and Drug Administration (FDA) since 1992 for regulatory decisions regarding the acoustic output of diagnostic ultrasound equipment. Its formula is based on predictions of acoustic cavitation under specific conditions. Since its implementation over 2 decades ago, new imaging modes have been developed that employ unique beam sequences exploiting higher‐order acoustic phenomena, and, concurrently, studies of the bioeffects of ultrasound under a range of imaging scenarios have been conducted. In 2012, the American Institute of Ultrasound in Medicine Technical Standards Committee convened a working group of its Output Standards Subcommittee to examine and report on the potential risks and benefits of the use of conditionally increased acoustic pressures (CIP) under specific diagnostic imaging scenarios. The term “conditionally” is included to indicate that CIP would be considered on a per‐patient basis for the duration required to obtain the necessary diagnostic information. This document is a result of that effort. In summary, a fundamental assumption in the MI calculation is the presence of a preexisting gas body. For tissues not known to contain preexisting gas bodies, based on theoretical predications and experimentally reported cavitation thresholds, we find this assumption to be invalid. We thus conclude that exceeding the recommended maximum MI level given in the FDA guidance could be warranted without concern for increased risk of cavitation in these tissues. However, there is limited literature assessing the potential clinical benefit of exceeding the MI guidelines in these tissues. The report proposes a 3‐tiered approach for CIP that follows the model for employing elevated output in magnetic resonance imaging and concludes with summary recommendations to facilitate Institutional Review Board (IRB)‐monitored clinical studies investigating CIP in specific tissues.

Determining the pulse-echo electromechanical characteristic of a transducer using flat plates and point targets

A common technique to determine the electromechanical response of a spherically focusing transducer is to use a reference pulse echo from a flat plate in the focal plane of the transducer. We show that when the pressure focusing gain of the transducer is much greater than unity, the focal plane reflection is a valid approximation of the desired electromechanical response. An alternative calibration target is a point scatterer and we show theoretically and experimentally that this waveform is the double time differential of the flat-plate response. The use of calibration to describe general scatterers through a Born approximation (Jensen, J. A. (1991), J. Acoust. Soc. Am. 89, 182–190) is discussed.

Ultrasound Transducer Selection in Clinical Imaging Practice

Many types of medical ultrasound transducers are used in clinical practice. They operate at different center frequencies, have different physical dimensions, footprints, and shapes, and provide different image formats. However, little information is available about which transducers are most appropriate for a given application, and the purpose of this article is to address this deficiency. Specifically, the relationship between the transducer, imaging format, and clinical applications is discussed, and systematic selection criteria that allow matching of transducers to specific clinical needs are presented. These criteria include access to and coverage of the region of interest, maximum scan depth, and coverage of essential diagnostic modes required to optimize a patients diagnosis. Three comprehensive figures organize and summarize the imaging planes, scanning modes, and types of diagnostic transducers to facilitate their selection in clinical diagnosis.