Metric quantification

In order to obtain MB sonodestruction rate MB concentration decay curves were approximated with exponential function⁷:

where A is the amplitude of the exponential function; B is the offset; α is the rate constant of the exponential function; t is time. α defines the rate of MB concentration decay and is termed MB sonodestruction rate. 1/ α results to time constant of the exponent function, τ, which implies the exposure duration necessary for MB concentration to decrease to 1/e times (37%) of the initial value.

In order to obtain inertial cavitation dose (ICD), the integral of scattering vs. exposure duration was calculated^20,38:

where ICD is inertial cavitation dose, t is time, 0 indicates 0 s (the beginning of the exposure duration), t_Final indicates the exposure duration at which the integration is finished.

The scattering values were cumulated during recorded exposure duration (1 s) at particular PNP as it was described previously^10,43.

With the aim to obtain attenuation rate, attenuation curves in exposure duration scale were approximated using sigmoidal function. Similarly, as described by Fan et al.⁷²:

where A₁ and A₂ are the initial and final attenuation values, respectively; k is the rate constant of the sigmoidal function; t is time; t_C is time at the sigmoidal center value.

The rate of the function, k, indicates the steepness of the attenuation curve and is defined as the attenuation rate.