Steerable ultrasonic propulsion of rigid objects based on circular pressure modulation of a focused sectorial transducer array.

• A circular pressure modulation approach for steerable ultrasonic propulsion of rigid objects is developed based on the simplified sector-array of focused transducers. • The general theory of ARF exerting on on-axis rigid spheres is derived in explicit formula for traditional and inclined focused fields based on acoustic scattering. • The ARF acting on on-axis spheres by focused fields exhibits an axial distribution of increasing followed by decreasing with the peak slightly beyond the focus. • Inclined propulsion is realized by adjusting the angle of power-on sources, with the maximum deflection angle determined by the F-number and element number of the sector-array. • This study provides an applicable technique for steerable propulsion of calculi using an ultrasonic power supply without the complex control in amplitude and phase for the sector-array. As a common disease of human urinary system, the high prevalence and incidence rate of renal calculus have brought heavy burden to society. Traditional ultrasonic lithotripsy struggles with the comprehensive elimination of residual fragments and may inadvertently inflict renal damage. Although focused ultrasound can propel stones by the acoustic radiation force (ARF) with minimal tissue damage and enhanced passage rate, it is still lack of the accurate control for calculi at different locations. A circular pressure modulation approach for steerable ultrasonic propulsion of rigid objects is developed based on a sector-array of focused transducers. The ARF exerted on on-axis rigid spheres (stones) is derived based on acoustic scattering. It is proved that the ARF of focused fields exhibits an axial distribution of increasing followed by decreasing with the peak slightly beyond the focus. As the sphere radius increases, the ARF exerted on spheres at the focus increases accordingly with a decreasing growth rate. Inclined propulsion can be realized by the circular binary pressure modulation with the deflection increased by expanding the angle of power-off sector sources. The maximum deflection angle approaching 60° is determined by the F-number and element number of the sector-array. Experimental propulsions of steel balls are conducted using an 8-element sector-array with motion trajectories captured by a high-speed camera. Distributions of the motion speed and acceleration for steel balls of different radii are calculated through image processing. The ARF of mN level and the deflection angle of 12° are demonstrated by the successful propulsion of steel balls. This research provides an effective and flexible approach of steerable stone propulsion using an ultrasonic power supply without the complex control in amplitude or phase and the high-precision motion of the sector-array, hence promoting the practical application in non-invasive treatment of stones. [ABSTRACT FROM AUTHOR]