Attenuation Coefficient Estimation of Tissue-Mimicking Phantoms

The reference phantom method^{13 (link)} was used to estimate the attenuation coefficient of a sample from RF echo signals obtained from a clinical scanner. The reference phantom method accounts for system-dependent parameters (transducer and pulser-receiver transfer functions) using power spectral density estimates from a reference material (with speed of sound equal to that of the sample), generated at the same depths as estimates from the sample. The sample consisted of a homogeneous tissue-mimicking phantom composed of water-based gel containing graphite powder (50mg/cm³ of agar) to control the attenuation and 3000E glass beads (Potters Industries, Inc., Valley Forge, PA; 5 to 40μm diameter, 4mg/cm³ of agar) to provide scattering.^{45 (link)} The reference phantom was a similar homogeneous material, consisting of an emulsion of 70% safflower oil in gelatin and also containing 3000E glass-bead scatterers (4mg/cm³ of emulsion). Both the sample and the reference phantoms were in acrylic boxes that had 25μm thick Saran wrap® (Dow Chemical, Midland, MI) scanning windows.
During phantom fabrication, 2.5cm-thick test samples were prepared to measure the sound speed and attenuation of the phantom materials. Laboratory estimates of α(f) and the speed of sound of these materials were performed using a narrowband substitution technique^{46 (link)} at frequencies from 2.25 to 10MHz. The attenuation coefficient was modeled as a power of frequency f, using: $$\alpha \left(f\right)={\alpha }_0{f}^{\beta }.$$
Table I shows the resultant α₀ and β (and the corresponding R² of the power-law fit), and the estimated speed of sound c ± one standard deviation for both phantoms. The speed of sound of the sample and the reference materials agreed within 0.4%. This difference is not expected to be a significant source of bias in the attenuation estimates.^{47 (link)} The laboratory-estimated parameters of the power-law fit were used as the expected values to which the α₀ and β estimates from scanner derived backscatter signals were compared.