Subharmonic Response of Polymer Contrast Agents Based on the Empirical Mode Decomposition

Abstract

The subharmonic threshold for ultrasound contrast agents has been defined as a 20-25 dB difference between the fundamental and subharmonic (2/1) spectral components of the backscatter signal. However, this Fourier-based criterion assumes a linear time-invariant signal. A more appropriate criterion for short cycle and frequency-modulated waveforms is proposed with an adaptive signal-processing approach based on the empirical mode decomposition (EMD) method. The signal is decomposed into an orthogonal basis known as intrinsic mode functions (IMFs) and a subharmonic threshold is defined with respect to the energy ratio of the subharmonic IMF component to that of the incident signal. The method is applied to backscatter data acquired from two polymer-shelled contrast agents, Philips (#38, mean diameter 2.0 [Formula: see text]) and Point Biomedical (#12027, mean diameter 3.9 [Formula: see text]). The acoustic backscatter signals are investigated for a single contrast agent subjected to monofrequency (20 MHz, 20 cycles) and chirp (15-25 MHz, 20 cycles) forcing for incident pressures ranging from 0.5 to 2.4 MPa. In comparison to the spectral peak difference (20 dB) criterion, the EMD method is more sensitive in determining subharmonic signals.

An Improved Empirical Mode Decomposition Based on Local Integral Mean and Its Application in Signal Processing

“…Among them, EMD has been criticized by signal processing experts because of the lack of orthogonal decomposition theory, which has become a major problem restricting the application of EMD [12,13]. Various research studies based on the orthogonal or approximate orthogonal decomposition methods of EMD [12,[14][15][16][17] are not convincing. References [18,19] use Schmidtʼs formula to make IMFs strictly orthogonal, but it cannot guarantee that the IMF is obtained from the orthogonal decomposition of the signal.…”