Temperature dependence of harmonics generated by nonlinear ultrasound beam propagation in water: A simulation study

Nonlinear ultrasound beam propagation is exploited in various biomedical applications of ultrasound. In this work, the feasibility of using harmonic pressure amplitudes generated by nonlinear ultrasound propagation in noninvasive temperature estimation has been studied. The nonlinear propagation of a 30-cycle Gaussian-envelop sinusoidal pulse in water was simulated. The ultrasound source had a pressure amplitude of 0.35 MP from a flat circular transducer of 22 mm diameter with three different center frequencies of 1 MHz, 2.5 MHz and 5 MHz. The simulations were performed using a numerical solution of Khoklov-Zabolotskaya-Kuznetsov (KZK) nonlinear wave equation with temperature dependent medium parameters. The water temperature was assumed to increase from 20°C to 60°C in the simulations. Using empirical published data, the medium´s parameters including sound speed, density, absorption coefficient and nonlinearity parameter (B/A) were modeled as a function of temperature in the simulations. The harmonic amplitudes were analyzed at axial distances from the transducer where the last pressure maximum occurs for each temperature. The pressure amplitudes of the fundamental frequency, the second and the third harmonics changed by 0.2% and 9.1%, -6.1% and 17.5%, -11.8% and 30.3% for pulses with transmit frequencies of 1 MHz and 5 MHz, respectively, due to the temperature change. The harmonics were weakly affected by temperature for the transmit pulse with a center frequency of 2.5 MHz. It is concluded that temperature estimation based on changes in the nonlinear harmonics is feasible with transmit frequencies higher than 3 MHz. The large changes in the harmonics as a function of temperature show that this could potentially be a basis for an ultrasound-based thermometry method.