PVCP phantom acoustic properties were characterized using a broadband through-transmission technique.47,48 Briefly, PVCP disks of various compositions were placed in a water bath at the shared focus of a pair of coaxially aligned broadband transducers (V320, Panametrics, Waltham, Massachusetts), with one transducer acting as an emitter and the other as a detector. Both transducers had 7.5 MHz center frequencies, 1.27 cm diameters, and 3.81 cm focal lengths. Transducers were connected to a pulser/receiver (Model 5800PR, Panametrics), and received US signals were digitized (8 bit, 50 MHz) using a 400-MHz oscilloscope (9310C, Teledyne LeCroy, Chestnut Ridge, New York). Speed of sound in liquid plasticizers was also measured using this technique by replacing the solid sample mount with a liquid sample housing with thin plastic membranes. Because the membranes were thick enough to cause reverberation artifacts at higher acoustic frequencies, liquids were measured using a pair of lower-frequency transducers with 1 MHz center frequencies, 1.91 cm diameters, and 3.81 cm focal lengths (V314, Panametrics). The use of lower frequencies is valid because speed of sound is expected to have weak dependence on frequency (i.e., dispersion).43 Additionally, attenuation of liquid plasticizers was not calculated, as attenuation was expected to be low and to not correspond to that of PVCP gels. Speed of sound in the sample, , was calculated as48Display Formula
(1)where is the speed of sound in water, is the pulse delay between sample measurement and a water-only path reference measurement, and is the sample thickness. The acoustic attenuation coefficient versus frequency, , was calculated over 4 to 9 MHz as47Display Formula
(2)where is the acoustic power spectrum measured through a water path, and is the power spectrum measured through the sample. The range of 4 to 9 MHz was selected based on transducer frequency response and correlates to acoustic frequencies used in many reported PAT systems. Sample power spectra were acquired at three spatial positions in the sample, averaging 60 measurements at each position. Acoustic attenuation spectra are often assumed to follow a power-law form;14 for each of the three locations, the averaged attenuation spectrum was calculated and then fitted to the power-law relationship , where and are fitting parameters. Mean and standard deviation were calculated for the set of three fitted attenuation spectra per sample, from which coefficient of variation was computed and expressed as a percentage.