Nakagami-m parametric characterization of contrast-enhanced ultrasound: In vivo validations

Background, Motivation and Objectives: The distribution of echoes from simulated and in vitro nonlinear scattering microbubbles obeys the Nakagami (NK) model, of which shape parameter ( $m$ ) has the potential to suppress the artifacts from systems and operators in echo amplitude-coding contrast-enhanced ultrasound (CEUS) (Med. Phys. 2019, 46: 5467–5477). However, the feasibility of $m$ estimation in in vivo CEUS is still controversial and its sensitivity and discriminability are limited, since raw envelopes are regulated by complex radiofrequency (RF) and video-frequency (VF) processing. This study aimed to illustrate this regulation mechanism and overcome these limitations. Statement of Contribution/Methods: The regulation mechanism of eight harmonic detection techniques and logarithmic compression on NK distributions was investigated in both B and pulse-inversion (PI) modes. A window-modulated compounding moment estimator (WMCME) was developed to estimate the CEUS $m$ values. Sensitivity and discriminability of $m$ -coding CEUS were respectively quantified by m-contrast-to-tissue ratio (mCTR), m-contrast-to-noise ratio (mCNR), and −2 dB half-lengths of axial and lateral autocorrelation functions, which were validated via in vivo perfusion experiments of rabbit kidneys. Results, Discussion and Conclusions: Regulated by the RF&VF processing, the distributions of CEUS also obeyed the NK model, of which NK-fitted correlation coefficient was $.99\pm 0.01\ (p in t-test and $p in Kolmogorov-Smirnov test). In all m-coding CEUS methods, logarithmic m-coding PI scheme well-characterized the ring-like perfusion features and details within the renal cortex. The $m$ CTR, $m$ CNR, −2 dB axial and lateral half-lengths were up to $7.9\pm 1.5\ \mathrm{dB},\ 34.4\pm 1.7\ \mathrm{dB},\ 1.02\pm 0.02$ and $.91\pm 0.02\ \mathrm{mm}$ , respectively, which were higher than or comparable with amplitude-coding CEUS. The NK model can characterize CEUS even if the envelope distributions were regulated by the RF & VF processing. The logarithmic $m$ -coding PI scheme significantly improved the sensitivity, discriminability, and robustness of $m$ estimation in CEUS. This scheme provided an option to remove those artifacts in echo amplitude-coding CEUS and more distinctly characterize the inherent microvasculature marked by microbubbles, which could provide a valuable technique to improve precise diagnoses and therapy.