A Mathematical Model for Reverberations in Biomedical Ultrasound Transducers: a case study

Ultrasonography is a non-invasive diagnostic technique using ultrasound to produce images of internal body structures in real-time. It is a reliable, robust and reproducible diagnostic imaging modality commonly used in the clinical practice. Nevertheless, artifacts may occur in images, leading to misdiagnosis. This paper aims to characterize the reverberation artifacts that cause multiple copies of anatomic structures interfaces, degrading image quality and accuracy. Analyzing and optimizing the mechanical properties of the ultrasound probe play a crucial role in the reduction of reverberations. A simplified two-dimensional mathematical model was developed to simulate the response of an ultrasound transducer to a phantom specially designed to generate reverberations. Such model was verified by experiments using a dedicated water-tank set-up. The investigation of a linear array transducer showed that the model yields good results: R
²
=0.987 for the correlation between the arrival time of the echoes of simulated and experimental signals, and R
²
=0.945 for the correlation of their intensity, at the central frequency. These preliminary results show that the developed model allows for investigating whether changes in the constitutive characteristics of the individual transducer layers reduce reverberations and helps to predict transducer performance in terms of image quality.