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Angiogenesis has been postulated as an important marker for the early detection of cancer. The proteins associated with new vessels are sub-resolution for ultrasonic imaging, necessitating the use of contrast agents. In this work we use a liquid, perfluorocarbon nanoparticle previously shown to enhance specific targets in in vitro and in situ settings. Previous studies focused on the use of conventional signal analysis techniques including signal amplitude, signal energy, and spectral analysis. To explore the possibility of further increasing contrast between targeted bio-markers and untargeted tissue, we applied concepts from measure-theoretic (e.g., information theory, thermodynamics) and topological dynamics. Specifically, Shannon entropy, HS, its continuous limit, HC, and three quantities obtained using analogies with thermodynamics: Cv, Eth, which have been described elsewhere. We describe the outcome of employing these types of dynamical quantities to ultrasonic data acquired in vivo using New Zealand white rabbits implanted with VX2-tumors and then exposed over the course of two hours to αvβ3 integrin-targeted liquid perfluorocarbon nanoparticles.