Deconvolution approaches for energy-preserving spatiotemporal cavitation dosimetry using passive acoustic mapping

The ability to quantify and compare different cavitational treatments is essential given their accelerating clinical adoption. Passive acoustic mapping (PAM) can reconstruct quantitative maps of cavitational radiated energy density (CRED) in real time, providing a powerful platform for cavitation dosimetry. However, significant imaging artefacts caused by a large and variable point spread function (PSF) limit the spatial resolvability of PAM-derived cavitation doses. The Lucy-Richardson deconvolution (LRD) can significantly reduce imaging artefacts, correct for gross overestimates of CRED values, and reduce setup-dependence of CRED estimates when applied to PAM images. However, the LRD condenses source energy densities into the central axis of the image, obscuring the underlying source distribution. Typically, a single central PSF is used to perform deconvolution, which additionally preserves biases in energy estimation due to PSF variation. This work investigates the underlying causes of these errors and presents four deconvolution approaches designed to preserve source localisation and improve spatial accuracy of PAM images. Each algorithm is tested using numerical simulations and experimental cavitational data monitoring cavitation in vitro as well as in normothermically perfused porcine liver, and show varied accuracy, robustness, and computational load. Modelling PSF variations over space to enable a shift-variant implementation of the LRD (svLRD-PAM) improves the spatial accuracy of cavitation doses and reduces imaging artefacts by 4-5 fold with a modest and parallelisable 36% increase in computation time relative to the standard delay-sum-integrate beamformer. svLRD-PAM shows great promise as the next step towards accurate, spatially resolvable cavitation dosimetry.