Abstract
The effects of stone size on the process and comminution efficiency of shock wave lithotripsy (SWL) were investigated in experiments, numerical simulations and scale analysis. Cylindrical BegoStone phantoms with approximately equal height and diameter of either 4, 7 or 10 mm, in a total aggregated mass of about 1.5 g, were treated in an electromagnetic shock wave lithotripter field. The resultant stone comminution was found to correlate closely with the average peak pressure, P(+(avg)), incident on the stones. The P(+(avg)) threshold necessary to initiate stone fragmentation in water increased from 7.9 to 8.8 to 12.7 MPa, respectively, as stone size decreased from 10 to 7 to 4 mm. Similar changes in the P(+(avg)) threshold were observed for the 7- and 10-mm stones treated in 1,3-butanediol, in which cavitation is suppressed, suggesting that the observed size dependency is due to changes in stress distribution within stones of different size. Moreover, the slope of the correlation curve between stone comminution and ln(P¯(+(avg))) in water increased with decreasing stone size, whereas the opposite trend was observed in 1,3-butanediol. The progression of stone comminution in SWL exhibited size-dependence: the 7- and 10-mm stones fragmented into progressively smaller pieces, whereas a significant portion (>30%) of the 4-mm stones reached a stalemate within the size range of 2.8 ∼ 4 mm, even after 1000 shocks. Analytical scaling considerations suggest size-dependent fragmentation behavior, a hypothesis further supported by numerical model calculations that reveal changing patterns of constructive and destructive wave interference and, thus, variations in the maximum tensile stress or stress integral produced in cylindrical and spherical stone of different sizes.