Real-time calculation of a limiting form of the Renyi entropy applied to detection of subtle changes in scattering architecture.

Previously a new method for ultrasound signal characterization using entropy H(f) was reported, and it was demonstrated that in certain settings, further improvements in signal characterization could be obtained by generalizing to Renyi entropy-based signal characterization I(f)(r) with values of r near 2 (specifically r=1.99) [M. S. Hughes et al., J. Acoust. Soc. Am. 125, 3141-3145 (2009)]. It was speculated that further improvements in sensitivity might be realized at the limit r-->2. At that time, such investigation was not feasible due to excessive computational time required to calculate I(f)(r) near this limit. In this paper, an asymptotic expression for the limiting behavior of I(f)(r) as r-->2 is derived and used to present results analogous to those obtained with I(f)(1.99). Moreover, the limiting form I(f,infinity) is computable directly from the experimentally measured waveform f(t) by an algorithm that is suitable for real-time calculation and implementation.

Application of Renyi entropy for ultrasonic molecular imaging.

Previous work has demonstrated that a signal receiver based on a limiting form of the Shannon entropy is, in certain settings, more sensitive to subtle changes in scattering architecture than conventional energy-based signal receivers [M. S. Hughes et al., J. Acoust. Soc. Am. 121, 3542-3557 (2007)]. In this paper new results are presented demonstrating further improvements in sensitivity using a signal receiver based on the Renyi entropy.

Properties of an entropy-based signal receiver with an application to ultrasonic molecular imaging.

Qualitative and quantitative properties of the finite part, H(f), of the Shannon entropy of a continuous waveform f(t) in the continuum limit are derived in order to illuminate its use for waveform characterization. Simple upper and lower bounds on H(f), based on features of f(t), are defined. Quantitative criteria for a priori estimation of the average-case variation of H(f) and log E(f), where E(f) is the signal energy of f(t) are also derived. These provide relative sensitivity estimates that could be used to prospectively choose optimal imaging strategies in real-time ultrasonic imaging machines, where system bandwidth is often pushed to its limits. To demonstrate the utility of these sensitivity relations for this application, a study designed to assess the feasibility of identification of angiogenic neovasculature targeted with perfluorocarbon nanoparticles that specifically bind to alpha(v)beta3-integrin expression in tumors was performed. The outcome of this study agrees with the prospective sensitivity estimates that were used for the two receivers. Moreover, these data demonstrate the ability of entropy-based signal receivers when used in conjunction with targeted nanoparticles to elucidate the presence of alpha(v)beta3 integrins in primordial neovasculature, particularly in acoustically unfavorable environments.

Experimental determination of phase velocity of perfluorocarbons: applications to targeted contrast agents.

Targeted acoustic contrast agents are designed to enhance the sensitivity and specificity of ultrasonic diagnoses. We have previously developed a ligand targeted ultrasonic contrast system that is a lipid-encapsulated, liquid-perfluorocarbon emulsion. The emulsion particles are small (250 nm) and have inherently low echogenicity unless bound to a surface by a pretargeted ligand through avidin-biotin interactions. We have recently proposed a simple acoustic transmission line model that treats the emulsion particles as a thin layer over the targeted surface. In this model, the acoustic reflectivity of the sample increases for perfluorocarbons with smaller velocities of longitudinal sound or lower densities. In this study, we measure and report the velocity of longitudinal sound for 20 perfluorocarbons using a broadband phase spectroscopic approach for estimating phase velocities. Experimentally determined velocities ranged from 520+/-2 m/sec (perfluorohexane) to 705+/-5 m/s (perfluorodecalin). No measurable dispersion was observed over the useful bandwidth of 2 to 22 MHz. Increasing carbon backbone chain length and fluorine substitution with halogens of greater atomic weight increased the measured speed of sound. Our experimental data were consistent (R=0.87) with a published empirical model that predicts velocity as a function of molecular structure. These data provide a rational basis for optimizing targeted perfluorocarbon-based contrast agents and offer further insight into the physical mechanisms responsible for the observed enhancement of surface acoustic reflectivity.