## Fig xA Three dimensional figure of interactive

The independent variable, b, in the RSM-derived equations had been transformed before model-building. The rationale for doing so was due to the underlying assumption of RSM modeling, which suggests that the response, Yi, must be linearly related to the independent variables (a, b, c). However, poor performance of the initial models built from the raw data (without transformation) proved otherwise. The independent variable representing ultrasound processing duration (i.e. time) was therefore transformed to b = e(2 × Time). This TAK-901 indicates that the amount of MRPs formed was not directly dependent on the duration of exposure to ultrasound, but instead strongly depended on e(2 × Time). Such a transformation can be supported by the theory of reaction kinetics, which utilizes integrated rate law equations to relate the final concentrations of products to the initial reactant concentration and reaction time. From first-order integrated rate law equation, it is possible to deduce that the quantity of reactants in a first-order non-reversible reaction declines exponentially with time. Similarly, the production of MRPs was not increasing linearly with processing time, but instead would show a strong dependence on e(k × Time), where k is a rate constant-like parameter. The value of k was determined to be 2, through a trial and error procedure, which improved the model quality the most.