Exploiting harmonic signature of gas vesicles in amplitude-modulated singular value decomposition for ultrafast ultrasound molecular imaging

<i>Objective.</i>Ultrafast nonlinear ultrasound imaging of gas vesicles (GVs) promises high-sensitivity biomolecular visualization for applications such as targeted molecular imaging and real-time tracking of gene expression. However, separating GV-specific signals from tissue remains challenging due to tissue clutter and limitations of current methods, which require complex transmit schemes and suffer from incomplete tissue suppression. This study aims to develop and validate harmonic amplitude-modulated singular value decomposition (HAM-SVD), a novel technique that represents a shift from current GV imaging methods by exploiting the unique nonlinear pressure-dependence of the GV harmonic signature.<i>Approach.</i>HAM-SVD employs single-cycle plane waves transmitted at 9.6 MHz across five tilted angles at a pulse repetition frequency of 2500 Hz, under four duty cycles (DCs) with alternating polarity. Beamformed data are reshaped into a space-pressure Casorati matrix and decomposed via SVD. Tissue background is suppressed by discarding the first (weakly nonlinear tissue) and lowest (noise) singular modes, yielding images comprised solely of pressure-dependent second-harmonic GV signals. The method was validated through numerical simulations,<i>in vitro</i>phantom experiments, and<i>in vivo</i>rat lower limb imaging.<i>Main results.</i>HAM-SVD achieved a signal-to-background ratio of 19.16 ± 1.63 dB<i>in vivo</i>, significantly outperforming pulse inversion (14.19 ± 1.41 dB) and amplitude modulation (AM-SVD) (15.79 ± 1.38 dB). Simulation and phantom studies demonstrated superior spatial coherence in singular vector decomposition and reduced nonlinear artifacts compared to AM-SVD. HAM-SVD enables wide-field, ultrafast imaging without complex transmit sequences while maintaining robust tissue clutter suppression across varying pressure levels.<i>Significance.</i>By combining harmonic imaging with AM-SVD's adaptive clutter filtering, HAM-SVD overcomes limitations of conventional nonlinear techniques, including depth restrictions in xAM and incomplete tissue cancellation in pulse inversion. This approach enhances molecular imaging specificity for GVs and holds translational potential for ultrasound localization microscopy of slow-flowing contrast agents and preclinical disease-targeted molecular imaging.