The nonlinearity has significant effect on the ultrasonic therapy using phased arrays.A numerical approach is developed to calculate the nonlinear sound field generated from a phased array based on the Gaussian superposition technique.The parameters of the phased array elements are first estimated from the focal parameters using the inverse matrix algorithm;Then the elements are expressed as a set of Gaussian functions;Finally,the nonlinear sound field can be calculated using the Gaussian superposition technique.In the numerical simulation,a 64×1 phased array is used as the transmitter.In the linear case,the difference between the results of the Gaussian superposition technique and the Fresnel integral is less than 0.5%,which verifies the feasibility of the approach.In the nonlinear case,the nonlinear fields of single-focus modes and double-focus modes are calculated.The results reveal that the nonlinear effects can improve the focusing performance,and the nonlinear effects are related with the source pressures and the excitation frequencies.
Lesions in porcine liver tissues created by continuous high intensity focused ultrasound(HIFU)exposures in vitro are theoretically and experimentally investigated,with the transmitter moving along a linear path at a fixed speed.Numerical simulations of the lesion formation are performed based on the Khokhlov-Zabolotskaya-Kuznetov equation and the bio-heat equation.In order to verify the theoretical predictions,experiments are performed in the one-dimensional scanning mode to measure the cross-sectional area of lesions created in the in vitro porcine liver exposed to 1.01-MHz HIFU pulses with the acoustic power of 70 W.The results indicate that,compared to the traditional discrete treatment protocol,the application of a continuous scanning model can create more uniform lesions in tissues and significantly reduces the total treatment time from 47 s to 30 s.
The extended two-mass model is adopted to analyze the nonlinear oscillation of pathological vocal folds during vocalization. Redundant tissue or area in laryngeal patients is modeled as a massless rigid connected to the upper mass of the vocal folds, and a parameter Q is introduced to represent the change of glottal configurations and tension imbalance between the left and right sides of vocal folds. Numerical simulations demonstrate that the pathological vocal-fold decreases the threshold of Q to generate nonlinear vocal oscillation, indicating the improvement of the sensitivity of vocal folds to asymmetries and enhancing the coupling between two sides. Furthermore, the pathological vocal-fold can lower the fundamental frequency and eliminate high-order harmonics, For example, the fundamental frequency decreases from 119.94 Hz to 84.95 Hz when Q=0.58 and the sub-glottal pressure 1450 Pa. However, there are no prominent effects on the amplitudes of sub-harmonic and low-order harmonics.
