SVD-Based Separation of Stable and Inertial Cavitation Signals Applied to Passive Cavitation Mapping During HIFU

Detection of inertial and stable cavitation is important for guiding high-intensity focused ultrasound (HIFU). Acoustic transducers can passively detect broadband noise from inertial cavitation and the scattering of HIFU harmonics from stable cavitation bubbles. Conventional approaches to cavitation noise diagnostics typically involve computing the Fourier transform of the time-domain noise signal, applying a custom comb filter to isolate the frequency components of interest, followed by an inverse Fourier transform. We present an alternative technique based on singular value decomposition (SVD) that efficiently separates the broadband emissions and HIFU harmonics. Spatiotemporally resolved cavitation detection was achieved using a 128-element, 5-MHz linear-array ultrasound imaging system operating in the receive mode at 15 frames/s. A 1.1-MHz transducer delivered HIFU to tissue-mimicking phantoms and excised liver tissue for a duration of 5 s. Beamformed radio frequency signals corresponding to each scan line in a frame were assembled into a matrix, and SVD was performed. Spectra of the singular vectors obtained from a tissue-mimicking gel phantom were analyzed by computing the peak ratio (R), defined as the ratio of the peak of its fifth-order polynomial fit and the maximum spectral peak. Singular vectors that produced an R <; 0.048 were classified as those representing stable cavitation, i.e., predominantly containing harmonics of HIFU. The projection of data onto this singular base reproduced stable cavitation signals. Similarly, singular vectors that produced an R > 0.2 were classified as those predominantly containing broadband noise associated with inertial cavitation. These singular vectors were used to isolate the inertial cavitation signal. The R-value thresholds determined using gel data were then employed to analyze cavitation data obtained from bovine liver ex vivo. The SVD-based method faithfully reproduced the structural details in the spatiotemporal cavitation maps produced using the more cumbersome comb-filter approach with a maximum root-meansquared error of 10%.