Low-Frequency Ultrasonic Tomography: Mathematical Methods and Experimental Results

Abstract

This paper describes investigation of the possibilities of low-frequency ultrasonic tomography in medicine. The main application is the development of tomographic methods for differential diagnosis of breast cancer. To solve the inverse problem, a mathematical model is used that describes both the phenomena of diffraction and refraction and the absorption of ultrasound in an inhomogeneous medium. The algorithms developed for reconstructing the velocity structure were evaluated using the test bench for experimental studies. Broadband ultrasonic sources in the 50–600 kHz range were used for sounding. A Teledyne Reson TC4038 hydrophone with a sensitivity of approximately 4 µV/Pa and a frequency range of 10–800 kHz was used as a receiver. A Teledyne Reson VP1000 preamplifier was used to amplify the signals. The studies were carried out on phantoms with acoustic parameters close to the properties of human soft tissues. A layerwise model was used to reconstruct the three-dimensional velocity structure. The sound speed cross-sections reconstructed from the experimental data have a resolution of approximately 2 mm, while the central wavelength is approximately 4 mm. An important result of the work is an experimental confirmation of the correspondence of the model to physical processes.