Kriging model to study the dynamics of a bubble subjected to tandem shock waves as used in biomedical applications

The purpose of this work was to develop a metamodel (Kriging model) to identify the most important input parameters of shock wave pressure profiles as used in biomedical applications without solving a large number of differential equations. Shock wave-induced cavitation is involved in several biological effects. During bubble collapse, secondary shock waves and microjets are formed. For some applications, it is desirable to enhance this phenomenon by applying a second shock wave before bubble collapse; however, the delay between the leading shock wave and the second pressure pulse has yet to be optimized. This optimization can be done using numerical analysis. A metamodel that predicts the most convenient ranges for the input variables and provides information on the joint effects between the input variables was tested. Because the metamodel is an analytical expression, running it fifty thousand times and analyzing variables, such as the pressure amplitude, delay between pulses, and pressure rise time, was fast and easy. Furthermore, this method can be a helpful tool to study the joint effect between the input variables and reduce the computation time. The metamodel can also be adapted to analyze simulations based on equations different from the Gilmore-Akulichev formulation, which was used in this study.