Spatial Response Identification for Flexible and Accurate Ultrasound Transducer Calibration and its Application to Brain Imaging

Accurate wave-equation modeling 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 characterization of the ultrasound transducers, the physical devices that are responsible for generating and recording ultrasound energy. However, existing methods fail to characterize 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 modeling: spatial response identification (SRI). This method introduces a parameterization 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 discretization 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 honoring the full wave equation. SRI generates a model that can accommodate the complex, heterogeneous spatial response seen experimentally for ultrasound transducers. Experimental results show that SRI outperforms standard methods both in transmission and reception modes. Finally, numerical experiments using full-waveform inversion demonstrate that existing transducer-modeling approaches are insufficient to produce successful reconstructions of the human brain, whereas errors in our SRI algorithm are sufficiently small to allow accurate image reconstructions.