Flexible array curvature and sound speed estimations with a maximum spatial lag-one coherence metric

Flexible transducer arrays have the potential to conform to various organ shapes and sizes during photoacoustic image-guided interventions. However, incorrect sound speeds and array shapes can interfere with photoacoustic target localization and degrade image quality. We propose a metric to estimate the sound speed surrounding a target and the radii of curvature of flexible arrays with approximately concave shapes. The metric is defined as the maximum lag-one spatial coherence of the time-delayed, zero-mean channel data received from a region of interest surrounding a photoacoustic target (which we abbreviate as mLOC). Performance is demonstrated with simulated and experimental phantom data. Three photoacoustic targets were simulated in k-Wave with 1540 m/s medium sound speed, and photoacoustic signals were received by a transducer with a flat shape and an 81.3 mm radius of curvature. To acquire experimental photoacoustic data with the flexible array placed on flat and curved surfaces, an optical fiber paired with a hollow metal needle was inserted into an 83-mm-radius hemispherical plastisol phantom at three locations. When implementing beamforming time delays to calculate mLOC, the associated sound speed and radii of curvature ranged 1080-2000 m/s and 60-120 mm, respectively. The sound speed and array curvature estimated by the maximized mLOC were 1540 m/s and 81 mm, respectively, in simulation, resulting in accuracies of 100% and 99.63%, respectively. The sound speed in the phantom was empirically estimated by the maximum of mLOC as 1543 m/s, which led to the array curvature estimation of 85 mm and the corresponding accuracy of 97.59%. Results demonstrate the potential of mLOC to approximate sound speeds and array radii when these variables are unknown in future flexible array imaging scenarios