Temperature elevations computed for three-layer and four-layer obstetrical tissue models in nonlinear and linear...

The authors computed temperature elevations in a three-layer and a four-layer tissue model, assuming the crucial obstetrical case when the ultrasonic pulse propagating through the abdominal wall and the fluid-filled bladder penetrates into soft fetal tissues. To consider nonlinear propagation, the authors applied a new theory of nonlinear increase of absorption recently developed by the first author. Computations were carried out for pulses with a carrier frequency of 3 MHz, duration time of 1.33 micros, and pulse repetition frequency of 3.3 kHz. Similar computations were carried out for a four-layer tissue model corresponding to the third trimester of gestation. The ceramic piezoelectric transducer 2 cm in diameter radiated the ultrasonic beam focused at a distance of 6.5 cm. The intensities at the radiating transducer (at the source) were I(SAPA) = 10 and 5 W/cm2. Temperature elevations and distributions were determined numerically for various values of low-amplitude absorption coefficients assumed to be the same as attenuation coefficients. It was shown in the three-layer tissue model that the maximum temperature elevation can be about 50% higher for nonlinear than for linear propagation. The maximum fetal temperature elevation in this case was 2.36 degrees C for nonlinear and 1.84 degrees C for linear propagation. The temperature elevation in the abdominal wall was lower than those temperatures when the attenuation of the abdominal wall was assumed to be a low value of 0.05 Np/cm.MHz (0.45 dB/cm.MHz). However, when it was increased to 0.16 Np/cm.MHz (1.4 dB/cm.MHz), the temperature elevation of the abdominal wall reached 3.2 degrees C and the maximum fetal elevation was 1.65 degrees C. In such cases, the abdominal wall became the principal source of heat production. In this case, the difference between fetal temperature elevations for nonlinear and linear propagation was only about 10%. The results obtained in the four-layer tissue model, in which the uterus tissue also was represented, show that temperature elevations in this case are about 3.6 times lower than in the three-layer tissue model, with comparable attenuation of the abdominal wall. Differences between nonlinear and linear propagation in the four-layer tissue model are negligible. The temperature elevations obtained were proportional to the pulse repetition frequency, without changing temperature distributions in the ultrasonic beam. In this manner, fetal temperature elevations can be reduced by reducing the repetition frequency.