Figure 9.

Standing waves modulate ultrasonic neurostimulation. a, COMSOL simulation at 1.9 MHz and a nominal intensity of 56 W/cm² (focal intensity in free space) of a transducer with an ideal reflective surface, demonstrating a periodic modulation in acoustic intensity as a function of changing transducer distance to the MEA expressed in wavelengths. The intensity plotted is the on axis; average values in the retina. Zero distance indicates that the focal point of the transducer is coincident with the retina-MEA interface. Positive values of distance expressed in terms of wavelength indicate the transducer moving further away from the MEA. An ideal reflective transducer is shown to illustrate the periodicity of modulation with distance, and a transducer with lower reflectivity as we used would produce a smaller modulation at the same period. b, A 2.25 MHz transducer was operated with a carrier frequency of 2.9 MHz (λ = 517 μm). I_SP = 155 W/cm², and a 100 ms pulse was repeated every 15 s for 12 trials. Top, Raster plots and peristimulus time histograms of the response of one cell when the vertically oriented transducer was moved a distance of 0.5λ (blue) and 0.75λ (green). Bottom, Peak firing rate response from this cell when the transducer was vertical (0°, black), showing strong modulation with a period of λ/2 as the transducer was moved away from the MEA. Distance is measured in terms of wavelength relative to a starting position, which was chosen to maximize the population response. Also shown is the response when the transducer was tilted at an angle of 27° relative to vertical (red). c, Peak firing rate responses from 10 other cells when the transducer was vertical, demonstrating that many cells exhibit the same pattern of response with respect to transducer distance. d, Left, Normalized population response for vertical (0°, n = 37) and tilted (27°, n = 30) transducers. Middle, FFT of firing rate versus distance. The amplitude and phase are shown at a frequency of 2 cycles/λ for each cell that responds to ultrasound when the transducer is vertical (0°). In this plot, distance from the center represents the depth of modulation (normalized by the mean, linear scale) of the response by the transducer position at a period of λ/2. The angle is the phase of the 2 cycles/λ Fourier component, indicating the transducer distance at which the response was maximal. Blue cross represents the mean population response. Right, FFT of firing rate versus distance when transducer was tilted at 27°. e, Left, Same as in d, except the 2.25 MHz transducer was operated at a carrier frequency of 1.9 MHz (λ = 789 μm), and angle of the transducer when tilted was 21°; I_SP = 95 W/cm² (n = 90 for 0°, and n = 78 for 21°). Middle, The average phase differs from d because the transducer was not repositioned to set the peak response at the starting position. Right, For the tilted condition (21°), the distance traveled was only one full cycle (λ/2) with smaller step sizes.