Temperature increase in a two-layer obstetric model of tissues in the case of linear and nonlinear propagation of a continuous ultrasonic wave

The object of the present study was the analysis of temperature effects which arise in a two-layer tissue model applied in obstetrics, from the point of view of continuous wave radiation of a focussed Gaussian ultrasound beam. In particular, the authors considered nonlinear propagation using the weak shock theory and compared the results of the analysis with those obtained assuming linear propagation. It was demonstrated that for 3 MHz, 10 cm focal length of the beam, the transducer diameter of 1 cm and the intensity of 0.1 W/cm$^2$ the schock parameter does ot then exceed 1.66 cm. For a radiated intensity equal to 1 W/cm$^2$ the shock coefficient is higher than unity, causing losses related to nonlinear propagation. The temperature distributions were determined along the beam axis using both the weak shock theory and the linear propagation procedure.