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Updated: Jan 19, 2026
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Published on: May 9, 2021
Numerical and experimental investigation of impacts of nonlinear scattering encapsulated microbubbles on Nakagami
Diya Wang1,2, Yuchao Sang2, Xinyu Zhang2
1University of Montreal Hospital Research Center, Montreal, QC, H2X 0A9, Canada.
Purpose:
The Nakagami statistical model and Nakagami shape parameter m have been widely used in linear tissue characterization and preliminarily characterized the envelope distributions of nonlinear encapsulated microbubbles (EMBs). However, the Nakagami distribution of nonlinear scattering EMBs lacked a systematical investigation. Thus, this study aimed to investigate the Nakagami distribution of EMBs and illustrate the impact of EMBs' nonlinearity on the Nakagami model.
Method:
A group of simulated EMB phantoms and in vitro EMB dilutions with an increasing concentration distribution under various EMB nonlinearities, as regulated by acoustic parameters, were characterized by using the window-modulated compounding Greenwood-Durand estimator.
Results:
Raw envelope histograms of simulated and in vitro EMBs were well matched with the Nakagami distribution with a high correlation coefficient of 0.965 ± 0.021 (P < 0.005). The mean values and gradients of m parameters of simulated and in vitro EMBs were smaller than those of linear scatterers due to the stronger nonlinearity. These m values exhibited a quasi-linear improvement with the increase in second harmonic nonlinear-to-linear component ratio regulated by pulse lengths and excitation frequencies at low- and high-concentration conditions.
Conclusions:
The Nakagami distribution was suitable for the EMBs characterization but the corresponding m parameter was affected by the EMBs' nonlinearity. These validations provided support and nonlinear impact assessment for the EMBs' characterization using the Nakagami statistical model in the future.
