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.

4-chlorophenol removal from water using graphite and graphene oxides as photocatalysts.

Graphite and graphene oxides have been studied amply in the last decade, due to their diverse properties and possible applications. Recently, their functionality as photocatalytic materials in water splitting was reported. Research in these materials is increasing due to their band gap values around 1.8-4 eV, and therefore, these are comparable with other photocatalysts currently used in heterogeneous photocatalytic processes. Thus, this research reports the photocatalytic effectiveness of graphite oxide (GO) and graphene oxide (GEO) in the degradation of 4-chlorophenol (4-CP) in water. Under the conditions defined for this research, 92 and 97% of 4-CP were degraded with GO and GEO respectively, also 97% of total organic carbon was removed. In addition, by-products of 4-CP that produce a yellow solution obtained only using photolysis are eliminated by photocatalyst process with GO and GEO. The degradation of 4-CP was monitored by UV-Vis spectroscopy, High Performance Liquid Chromatography (HPLC) and Chemical Oxygen Demand (COD). Thus, photocatalytic activity to remove 4-CP from water employing GO and GEO without doping is successfully showed, and therefore, a new gate in research for these materials is opened.

Combined short and long-delay tandem shock waves to improve shock wave lithotripsy according to the Gilmore-Akulichev theory.

Extracorporeal shock wave lithotripsy is a common non-invasive treatment for urinary stones whose fragmentation is achieved mainly by acoustic cavitation and mechanical stress. A few years ago, in vitro and in vivo experimentation demonstrated that such fragmentation can be improved, without increasing tissue damage, by sending a second shock wave hundreds of microseconds after the previous wave. Later, numerical simulations revealed that if the second pulse had a longer full width at half maximum than a standard shock wave, cavitation could be enhanced significantly. On the other side, a theoretical study showed that stress inside the stone can be increased if two lithotripter shock waves hit the stone with a delay of only 20 µs. We used the Gilmore-Akulichev formulation to show that, in principle, both effects can be combined, that is, stress and cavitation could be increased using a pressure pulse with long full width at half maximum, which reaches the stone within hundreds of microseconds after two 20 µs-delayed initial shock waves. Implementing the suggested pressure profile into clinical devices could be feasible, especially with piezoelectric shock wave sources.

Modified shock waves for extracorporeal shock wave lithotripsy: a simulation based on the Gilmore formulation.

Extracorporeal shock wave lithotripsy (SWL) is a reliable therapy for the treatment of urolithiasis. Nevertheless, improvements to enhance stone fragmentation and reduce tissue damage are still needed. During SWL, cavitation is one of the most important stone fragmentation mechanisms. Bubbles with a diameter between about 7 and 55µm have been reported to expand and collapse after shock wave passage, forming liquid microjets at velocities of up to 400m/s that contribute to the pulverization of renal calculi. Several authors have reported that the fragmentation efficiency may be improved by using tandem shock waves. Tandem SWL is based on the fact that the collapse of a bubble can be intensified if a second shock wave arrives tenths or even a few hundredths of microseconds before its collapse. The object of this study is to determine if tandem pulses consisting of a conventional shock wave (estimated rise time between 1 and 20ns), followed by a slower second pressure profile (0.8µs rise time), have advantages over conventional tandem SWL. The Gilmore equation was used to simulate the influence of the modified pressure field on the dynamics of a single bubble immersed in water and compare the results with the behavior of the same bubble subjected to tandem shock waves. The influence of the delay between pulses on the dynamics of the collapsing bubble was also studied for both conventional and modified tandem waves. For a bubble of 0.07mm, our results indicate that the modified pressure profile enhances cavitation compared to conventional tandem waves at a wide range of delays (10-280µs). According to this, the proposed pressure profile could be more efficient for SWL than conventional tandem shock waves. Similar results were obtained for a ten times smaller bubble.