The quadratic property of the human auditory sensation induced by focused amplitude-modulated ultrasound

Abstract

Three modes of low-intensity (≤100 mW/cm2) monotone amplitude-modulated (AM) ultrasound are focused on the region of the human cochlear and the human auditory response patterns are observed. The AM ultrasonic signal is defined as f(t) cos ωt, where f(t) is the monotone modulation signal and ω is the angular frequency of the ultrasonic carrier. The three modes of f(t) cos ωt are: (1) carrier-suppressed AM mode, cos Ωt cos ωt; (2) square-rooted AM mode, (1+cos Ωt)1/2 cos ωt; (3) standard AM mode, (1+cos Ωt) cos ωt, where Ω is the angular frequency of the monotone. They are applied in sequence to stimulate the subject. The pattern of auditory sensation of the subject to the ultrasonic stimulations follows the square of the modulation signal, f2(t), which are: (1) cos2 Ωt; (2) [(1+cos Ωt)1/2]2; (3) (1+cos Ωt)2. The subject senses the pure tone of 2Ω for the first mode of the ultrasonic stimulation, the pure tone of Ω for the second mode of the ultrasonic stimulation, and the mixed tones of Ω with relatively weaker intensity of 2Ω for the third mode of the ultrasonic stimulation. The response patterns reveal that the AM ultrasound induced human auditory sensation has the property of f2(t). This quadratic property is similar to the parametric demodulation of the focused AM ultrasound in water which has the form of d/dt[f2(t)], (B≫1) [Novikov, NonlinearUnderwaterAcoustics (Acoustical Society of America, Woodbury, NY, 1987), pp. 86–95]. [Work partially supported by Electro-Stim Corp.]