## 2 Materials and Methods
### Stimulation Parameters  
In this set up we used a 15 MHz bandwidth linear power amplifier [11] and a hydrophone (0.25-20 MHz frequency range, sensitivity: 282 nV/Pa, HGL 0400 series by Onda Sonics Corp. Sunnyvale, CA, USA) was used to determine the trend of the probe pressure range and the US focus. Spheroids were treated at three different stimulation frequencies and then each well containing a treated spheroid was stained using Calcein AM/PI dye. Subsequently, spheroid images were acquired using a confocal fluorescence microscope, and cell vitality vs. mortality was assessed using the BioFilmAnalyzer software [14]. For \(f\) = 1 MHz stimulation, a value of F = 90 mm from the transducer was chosen as the focal distance since it is the first point on the interpolation curve (Figure 4). This point is located in the far field and with the chosen parameters the Rayleigh length (\(Z_{R}\)) results at 55 mm from the Ultrasound probe surface. The Rayleigh length is an important parameter because it represents the distance along the propagation direction of the beam from the waist to the place where the area of the cross section is doubled, and it is commonly use when beams are modeled as Gaussian beams:  
\[z_{R}=\frac{a^{2}}{\lambda}=\frac{a^{2}f}{c}=55\;\text{mm} \tag{1}\]  
where \(a\) is the radius of the piezoelectric and \(c\) is velocity of propagation in the medium. For 2 MHz stimulation (Figure 5), measurements were taken around the Rayleigh distance (110 mm). In fact, in the graph there are points that give an irregular trend and that come out of the interpolation curve (80, 90 and 100 mm). The point chosen for stimulation is at a distance of 120 mm from the translator. For 3 MHz stimulation (Figure 6), the points measured by the hydrophone are located in the near field, in fact \(Z_{R}=165\) mm. The only point that is positioned around the Rayleigh distance is 150 mm, chosen as the optimal stimulation point. Figure 4: Focal distance calculation. At 1 MHz stimulation frequency the selected stimulation point is at a distance of 90 mm from the transducer (green circumference), this point in fact results in the Far Field. This value results from a test made with the hydrophone and by a subsequent linear interpolation. \(Z_{R}\) indicates the distance of Rayleigh (dotted line in red). The orange line in the figure indicates the peak-to-peak pressure trend carried out by the Ultrasound and Non Destructive Testing (USCND) laboratory of the Dept. of Information Engineering of the University of Florence. Figure 5: Focal distance calculation. At 2 MHz stimulation frequency the selected stimulation point is at a distance of 120 mm from the transducer (green circumference). This value results from the test made with the hydrophone and by a subsequent linear interpolation. \(Z_{R}\) indicates the distance of Rayleigh (dotted line in red), in this case the \(Z_{R}\) is located right after the cut-off region where the precision is very uneven. The orange line in the figure indicates the peak-to-peak pressure trend made by the USCND laboratories. To calculate the intensity, the following aspects were considered:  
* The difference between the acoustic impedances of the water and the multiwell cover generate a reflection of the pressure wave, which can be assessed with the following formula [11]: \[\text{P}_{\text{i}}\;\text{P}_{\text{t}}=T=1-\text{Z}_{\text{p}}-\text{Z}_{ \text{a}}\;\text{Z}_{\text{p}}+\text{Z}_{\text{a}}=0.62\] (2) where \(\text{p}_{\text{i}}\) and \(\text{p}_{\text{t}}\) are the pressure incident on the cover of the multiwell and the pressure transmitted through the cover, respectively. \(T\) is the transmission coefficient. \(\text{Z}_{\text{p}}\) and \(\text{Z}_{\text{a}}\) are respectively the acoustic impedance of the PMMA cover (3.23 MRayls) and of the water (1.48 MRayls).