## 2 Materials and Methods
### Models Equations and Conditions  
The ultrasound transmission under experimental conditions was modeled to determine the effect of the culture dish and its relative inclination in both the radiation pattern and the total delivered energy. The heat in the system produced by ultrasound absorption was also analyzed. Both models were developed with the finite element method (FEM) using COMSOL Multiphysics 5.5 (COMSOL AB, Stockholm, Sweden) in a PC-workstation with 8-core 3 GHz microprocessor and 64 RAM (Dell, Round Rock, TX, USA). When required, modeling results were post-processed using MATLAB 2018a (MathWorks, Natick, MA, USA). The ultrasound transmitted pattern and the heat produced in the dish were modeled assuming a 2D axisymmetric geometry (Figure 1b) based on the symmetry of the culture dish and the measured field [21]. The transducer radiation was set on boundary 1; boundaries 2 and 3 were configured to have the same acoustic impedance of water to reduce wave reflections at the walls; boundaries 4, 5, 10, 11 and 12 were set as hard boundaries (zero particle velocity) to represent the large differences of the acoustic impedances between the respective media (water or polystyrene) and the air; interior boundaries had a continuity condition. The pressure radiating at boundary 1 had a radial pattern of a simple supported Bessel function [21] given by  
\[p(r)=P_{0}\Big{[}C_{1}J_{0}\Big{(}\beta_{2N-1}\frac{r}{a}\Big{)}+C_{2}\Big{]} \cdot\sum_{m=1}^{4}\Big{[}1-\Big{(}\frac{r}{a}\Big{)}^{2m}\Big{]} \tag{1}\]where \(r\) is the radial coordinate, \(a\) is the transducer radius (m), \(J_{0}\) is a Bessel function of the first kind of order zero, and \(P_{0}\) is the spatial-averaged pressure amplitude at the transducer surface (Pa), which depends on the acoustic intensity [22]; \(C_{1}=C_{2}=0.5\), \(\beta=33.776\), \(m=4\) and \(N=6\), which are detailed in [21]. Under harmonic conditions, standing waves can be produced at distances that are multiples of half-wavelength of the ultrasound in the transmitting media [12]. For studying these resonances, an additional 2D geometry (no-axisymmetric) was created (Figure 1c); this second geometry was based on Figure 1b with the addition of an identical mirrored section. Boundary conditions are those mentioned for Figure 1b, since the boundaries are correspondent; the radiating boundary was also set using (1) by substituting \(r\) with \(|x|\). Using this second geometry, parametric sweeps at variable transducer-to-dish (\(TD\)) distances and depths of culture medium (\(CM\)) were carried out; the latter distance was varied from 9.0 to 12.0 mm while the former from 1.0 to 3.5 mm, both with steps of 0.1 mm. Additionally, it was studied the suppression of the standing waves produced by relative inclinations between the transducer and the dish during experiments; for this, we hypothesized that small inclinations could improve the repeatability of the results. The dish subdomain and the transducer boundary were rotated as shown in Figure 1c (sketched inclinations are not scaled). Therefore, an additional parametric sweep, combined with the two previously described sets, was computed by varying both angles, \(\xi\) and \(\varphi\), from \(-2^{\circ}\) to \(2^{\circ}\) at steps of 0.5\({}^{\circ}\). The amplitude of the acoustic pressure at the surface of the culture medium was averaged to determine the acoustic pressure transmitted at each parameter combination. The mesh in both geometries consisted of 15 quadrangular elements per wavelength, which represents 85,000 elements for the 2D model. Mesh convergence was verified by increasing the mesh resolution with less than 0.019% of the variation of the pressure amplitude. The radiating pattern at the dish was modeled with a time-dependent simulation using the 2D axisymmetric geometry and a tone-burst of ten sine-cycles with the radial distribution of (1). The peak-to-peak pressure at the water surface was obtained.