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 α_v β₃ -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 α_v β₃ integrins in primordial neovasculature, particularly in acoustically unfavorable environments.