UltraFlex: Iterative Model-Based Ultrasonic Flexible-Array Shape Calibration

UltraFlex is an iterative model-based ultrasonic flexible-array shape calibration framework that uses automatic differentiation. This work evaluates array shape calibration model performance while examining multiple image quality metrics: speckle brightness, envelope entropy, coherence factor, lag-one coherence, common-midpoint correlation coefficient (CMCC), and common-midpoint phase error (CMPE). The accuracy of these image quality metrics was evaluated on simulated phantoms using a variety of array shapes. Experimental phantom and in vivo liver datasets were also investigated using transducers with known geometries. While speckle brightness, envelope entropy, and coherence factor enable model convergence under many conditions, lag-one coherence, CMCC, and CMPE enable more accurate element position estimations and improved visual ultrasound image focusing quality. Furthermore, the models based on the CMCC and phase-error quality metrics are the most robust against additive white noise while achieving median mean Euclidean errors (MEEs) of 3.7 μm for simulation, 29.7 μm for phantom, and 69.0 μm for in vivo liver data. These array shape calibration results show promise for future development of experimental flexible- and wearableultrasonic arrays.