# Low-Cost and Easily Fabricated Ultrasound-Guided Breast Phantom for Breast Biopsy Training
## 2 Materials and Methods
### Acoustic Property Characterization  
The acoustic testing system comprised a pulse receiver (Model 5072 PR; OLYMPUS), a three-axis motor stage, a data acquisition card (PXI-5152; National Instruments) and the programming environment LabView (Figure 3). A broadband immersion transducer with frequencies centered at 5 MHz was used in this system.  
The single transducer worked as both a transmitter and receiver (pulse-echo approach) to measure the speed of sound, attenuation coefficient, and relative backscatter power of the sample. The measurements were conducted in a degassed-water-filled tank, the glass bottom of which acted as a reflector plane. The three-axis motor stage accurately positioned the transducer in the tank to focus on the reflector. The ultrasonic pulse was transmitted through the water to the reflector. The transducer received the reflected pulse, and the data were saved and analyzed in MATLAB R2018b. For each measurement of a sample, two data sets were obtained by scanning the reflector with and without the sample placed between the transducer and reflector (reference data and sample data, respectively). Three measurements were performed on each sample. All acoustic measurements were performed in degassed water at room temperature of 24 \({}^{\circ}\)C.  
The time interval between the peaks of the radio frequency pulses was computed using MATLAB. A Perspex mold was placed inside the water tank, between the transducer and reflector, when the sample was not in place. The following equation was used to calculate the speed of sound of the sample [38]:  
\[c_{m}=\bigg{(}\frac{T_{w}-T_{m}}{t_{2}-t_{1}}+1\bigg{)}c_{w} \tag{2}\]  
where \(c_{w}\) is the speed of sound in water measured by scanning the reflector plane at 1 mm height differences, as illustrated in Figure 3; \(T_{m}\) and \(T_{w}\) are the travel times with and without the sample in the propagation path of the pulse signal obtained from the sample and reference data, respectively; and \(t_{1}\) and \(t_{2}\) are the travel times of the pulse signal from the transducer to the front and rear faces of the sample, respectively. The derivation of this equation can be referred to [38].  
The logarithmic difference between the spectra was used to calculate the attenuation coefficient, \(\alpha\) (dB/cm), as shown in Equation (3) [39], where \(d\) is the thickness of the sample  
Figure 3: Scanning acoustic macroscope (SAMa) system.  
and \(A(f)\) and \(A_{0}(f)\) are the magnitude spectrum of the sample and reference at frequency \(f\), respectively.  
\[\alpha(f)=-\frac{20}{2d}log_{10}\frac{A(f)}{A_{0}(f)} \tag{3}\]  
A backscattered radio frequency (RF) signal was captured between the front face of the sample and reflector plane for backscatter power measurement. [PERSON]'s method was used to estimate the spectral power density and obtain the normalized distribution of power per unit frequency to the total received power in the backscattered RF signal. The relative backscatter power of the sample at frequency \(f\), \(\mu(f)\), was calculated using the reference power spectrum, \(P_{0}(f)\), of the reference RF signal as follows [40]:  
\[\mu(f)=-10 log_{10}\frac{P(f)}{P_{0}(f)} \tag{4}\]