Time-Domain Linear Model-based Framework for Passive Acoustic Mapping of Cavitation Activity

TL;DR

Experimental results show that the proposed framework achieves enhanced or competitive cavitation map quality while using only 20\% of the data typically required by frequency-domain methods, highlighting the substantial gain in data efficiency and the flexibility of spatiotemporal regularization to adapt to diverse passive cavitation scenarios, outperforming state-of-the-art techniques.

Abstract

Passive acoustic mapping enables the spatial mapping and temporal monitoring of cavitation activity, playing a crucial role in therapeutic ultrasound applications. Most conventional beamforming methods, whether implemented in the time or frequency domains, suffer from limited axial resolution due to the absence of a reference emission onset time. While frequency-domain methods, the most efficient of which are based on the cross-spectral matrix, require long signals for accurate estimation, time-domain methods typically achieve lower spatial resolution. To address these limitations, we propose a linear model-based beamforming framework fully formulated in the time domain. The linear forward model relates a discretized spatiotemporal distribution of cavitation activity to the temporal signals recorded by a probe, explicitly accounting for time-of-flight delays dictated by the acquisition geometry. This model is then inverted using regularization techniques that exploit prior knowledge of cavitation activity in both spatial and temporal domains. Experimental results show that the proposed framework achieves enhanced or competitive cavitation map quality while using only 20\% of the data typically required by frequency-domain methods. This highlights the substantial gain in data efficiency and the flexibility of our spatiotemporal regularization to adapt to diverse passive cavitation scenarios, outperforming state-of-the-art techniques.

Figures (8)

• Figure 1: Time-Domain Linear Model for Passive Acoustic Mapping (TD-LM-PAM) framework. (a) Cavitation monitoring, where a probe passively records acoustic emissions from clouds of microbubbles, followed by beamforming to display cavitation maps. (b) Forward model relying in a linear operator $\mathbf{A}$, linking the spatiotemporal distribution of cavitation activity, $\mathbf{x}$, to the recorded radio-frequency signals, $\mathbf{y}$. (c) General scheme of regularized inversion enabling the incorporation of prior knowledge, such as sparsity or smoothness.
• Figure 2: Mathematical notation scheme. $\mathbf{Y} \in \mathbb{R}^{N_m \times N_t}$ denotes the RF signals, and $\boldsymbol{\mathcal{X}} \in \mathbb{R}^{N_x \times N_z \times N_t }$ represents the cavitation spatiotemporal datacube.
• Figure 3: Linear forward operator toy example. The image plane consists of $N_x \times N_z = 3 \times 5$ pixels, observed over $N_t = 10$ time instants and recorded with a probe of $N_m = 3$ sensors. The structure of the operator $\mathbf{A}$ is determined by the sample delays stored in the matrix $\boldsymbol{\Delta}$. The zoomed-in figure shows the sub-blocks corresponding to the relationship between the third sensor and the lateral pixels for the second axial pixel.
• Figure 4: Estimated power maps of two laterally distributed inertial bubbles simulated at (-5,72) mm and (-3, 72) mm.
• Figure 5: Estimated power maps of two axially distributed inertial bubbles simulated at (-3, 64) mm and (-3, 72) mm.