  Attenuation of ultrasound waves varies with tissue composition, hence its
estimation offers great potential for tissue characterization and diagnosis and
staging of pathology. We recently proposed a method that allows to spatially
reconstruct the distribution of the overall ultrasound attenuation in tissue
based on computed tomography, using reflections from a passive acoustic
reflector. This requires a standard ultrasound transducer operating in
pulse-echo mode and a calibration protocol using water measurements, thus it
can be implemented on conventional ultrasound systems with minor adaptations.
Herein, we extend this method by additionally estimating and imaging the
frequency-dependent nature of local ultrasound attenuation for the first time.
Spatial distributions of attenuation coefficient and exponent are
reconstructed, enabling an elaborate and expressive tissue-specific
characterization. With simulations, we demonstrate that our proposed method
yields a low reconstruction error of 0.04dB/cm at 1MHz for attenuation
coefficient and 0.08 for the frequency exponent. With tissue-mimicking phantoms
and ex-vivo bovine muscle samples, a high reconstruction contrast as well as
reproducibility are demonstrated. Attenuation exponents of a gelatin-cellulose
mixture and an ex-vivo bovine muscle sample were found to be, respectively, 1.4
and 0.5 on average, consistently from different images of their heterogeneous
compositions. Such frequency-dependent parametrization could enable novel
imaging and diagnostic techniques, as well as facilitate attenuation
compensation of other ultrasound-based imaging techniques.
