Spatial response identification for flexible and accurate ultrasound transducer calibration and its application to brain imaging

Accurate wave-equation modelling is becoming increasingly important in modern imaging and therapeutic ultrasound methodologies such as ultrasound computed tomography, optoacoustic tomography or high-intensity focused ultrasound. All of them rely on the ability to accurately model the physics of wave propagation, including accurate characterisation of the ultrasound transducers, the physical devices that are responsible for generating and recording ultrasound energy. However, existing methods fail to characterise the transducer response with the accuracy required to fully exploit the capabilities of these emerging imaging and therapeutic techniques. Consequently, we have designed a new algorithm for ultrasound transducer calibration and modelling: spatial response identification. This method introduces a parametrisation of the ultrasound transducer and provides a method to calibrate the transducer model using experimental data, based on a formulation of the problem that is completely independent of the discretisation chosen for the transducer or the number of parameters used. The proposed technique models the transducer as a linear time-invariant system that is spatially heterogeneous, and identifies the model parameters that are best at explaining the experimental data while honouring the full wave equation. Spatial response identification generates a model that can accommodate the complex, heterogeneous spatial response seen experimentally for ultrasound transducers. Experimental results show that spatial response identification outperforms standard methods both in transmission and reception mode. Finally, numerical experiments using full-waveform inversion demonstrate that existing transducer-modelling approaches are insufficient to produce successful reconstructions of the human brain, whereas errors in our spatial response identification algorithm are sufficiently small to allow accurate image reconstructions.