## 5 Discussion  
This study used EMD as a strategy to develop a gain-independent index for describing the echogenicity of a scattering medium. An ideal echo model was used to concord with the EMD properties to demonstrate theoretically the feasibility of the proposed hypothesis. The current experimental results obtained from the phantoms demonstrated that the proposed IER maybe less affected by the gain setting. EMD has been widely applied in resolving several engineering and scientific problems [18]. Increasingly, more studies have investigated EMD applications in the field of medical ultrasound imaging, including tissue harmonic imaging [17], signal filtering [19], improvements in tissue characterization by using statistical parameters [20; 21], image contrast enhancement [22; 23], and elastography construction [24].This study is the first to explain how EMD eliminates the effects of the system gain from echogenicity measurement. In this study, the IER was defined using the \(C_{1}\) and \(C_{2}\) of the backscattered signals. Thecurrent findings and explanations are summarized below to support the proposed method: (i) referring to the schematic of an ultrasound imaging system (Figure 2), ultrasound echo signals are received by a transducer with a specific bandwidth. The received signals are subsequently amplified using the same amplifier stage with a passband that is typically designed to overlap with the transducer bandwidth for amplifying the signals with the same gain; (ii) the results showed that the \(C_{1}\) and \(C_{2}\) account for up to 90% of the amplitude of the backscattered signals, demonstrating that the first and second IMFs are the primary components of the original signals; and (iii) the summation of each IMF multiplied by the gain factor equals the signal multiplied using the same gain. For these reasons, it is convincing to define the IER using the first and second IMFs based on the proposed Equations (12) and (13). It is interesting to discuss the physical meanings of the IER. As indicated in Figure 7, the \(C_{1}\) and \(C_{2}\) intensities decreased as the lipid concentrations were increased. This is because when the lipid emulsion concentration increases, the phantom increases the attenuation effects to reduce the echo  
Figure 10: The image intensities of \(C_{1}\) (**a**) and \(C_{2}\) (**b**) modes and the IER (**c**) as a function of ultrasound frequency. Whenincreasing the frequency, the IER had a mean decreasing rate of \(-8.67\%\) per MHz, which was lower than those of the \(C_{1}\) and \(C_{2}\) intensities. intensity [15]. It should be noted that the IER also decreased as the lipid concentrations were increased. Comparing the results in Figure 7 suggests a considerable difference in the sensitivities of \(C_{1}\) and \(C_{2}\) intensities to respond to variations in the lipid concentrations. The first \(C_{1}\) IMF adequately follows the form of the original ultrasound signal and is the highest-frequency component [17]. Because the attenuation effect is proportional to the signal frequency, the \(C_{1}\) signal intensity may be more sensitive to the attenuation effect and may thus weaken in a high-attenuation scattering medium. Although the \(C_{2}\) intensity decreases as the attenuation effect increases, the influence of attenuation on the signal intensity is relatively weaker because the \(C_{2}\) IMF is a relatively low-frequency signal. In other words, the IER not only depends on the backscattered intensity but also correlates with the effect of ultrasound frequency. As mentioned in Introduction, the factors \(G\), \(h(t)\), and \(z(t)\) are functions of frequency. In modern ultrasound systems, the frequency effect of the system gain \(G\) may be ignored because wideband electronic amplifiers are typically used in circuits to ensure that the frequency-independent passbands in the Bode Plots of the amplifiers can cover the bandwidth of the transducer. However, the transfer function of the transducer \(h(t)\) is frequency-dependent.