A heuristic model of stone comminution in shock wave lithotripsy

Abstract

A heuristic model is presented to describe the overall progression of stone comminution in shock wave lithotripsy (SWL), accounting for the effects of shock wave dose and the average peak pressure, P þ(avg) , incident on the stone during the treatment. The model is developed through adaptation of the Weibull theory for brittle fracture, incorporating threshold values in dose and P þ(avg) that are required to initiate fragmentation. The model is validated against experimental data of stone comminution from two stone types (hard and soft BegoStone) obtained at various positions in lithotripter fields produced by two shock wave sources of different beam width and pulse profile both in water and in 1,3-butanediol (which suppresses cavitation). Subsequently, the model is used to assess the performance of a newly developed acoustic lens for electromagnetic lithotripters in comparison with its original counterpart both under static and simulated respiratory motion. The results have demonstrated the predictive value of this heuristic model in elucidating the physical basis for improved performance of the new lens. The model also provides a rationale for the selection of SWL treatment protocols to achieve effective stone comminution without elevating the risk of tissue injury.

Effects of Stone Size on the Comminution Process and Efficiency in Shock Wave Lithotripsy

“…Stone comminution (SC) is quantified by the ratio of weight of dried fragments smaller than 2 mm in diameter to the initial weight of the stones. Overall, the results confirm the general correlation between SC and P +(avg) or E eff observed previously using 10-mm spherical Begostone samples (Smith and Zhong 2012; Smith and Zhong 2013). The correlation between SC and P +(avg) , expressed in a linear-log relation of $SC=k_1\ln \left({\stackrel{false‒}{P}}_{+\left(avg\right)}\right)$ + b 1 where k 1 and b 1 are constants, and ${\stackrel{‒}{P}}_{+\left(avg\right)}=\frac{P_{+\left(avg\right)}}{P_0}$ with P 0 = 1 MPa, was used to determine the P +(avg) threshold [ calculated by using $P_{0}exp(-b_1∕k_1)$ and the slope of the correlation curve ( k 1 ) for different size groups in water and 1,3-butanediol, respectively.…”

“…A Weibull model (Smith and Zhong 2013) in the form of, $SC=1-\exp [-{true(\frac{dose-c}{d}true)}^e]$ where c, d and e represent the dose threshold, a normalization factor and the Weibull modulus, respectively, was used to fit the data ( R 2 = 0.97 to 1.00) from which the rate of SC was calculated for each size group. Although stones disintegrate progressively with increased shock number in all three groups, the efficiency of SC is significantly higher in the 7- and 10-mm groups than the 4-mm group beyond 500 shocks.…”

“…This study is motivated by the general observation that the rate of stone comminution during SWL is not uniform (Smith and Zhong 2013), but rather characterized by a rapid initial increase to a maximum within a few hundred shocks, followed by a slow progressive decay within a few thousand shocks towards the end of treatment (Zhong 2013). When a stone is disintegrated, the refraction of the incident lithotripter shock wave (LSW) into the resulting fragments and the interaction of different stress waves inside the stone material will change (Xi and Zhong 2001), leading to varied stone comminution rates (Xi and Zhong 2001; Zhong 2013).…”

Improving the lens design and performance of a contemporary electromagnetic shock wave lithotripter

“…These observations have been corroborated by recent findings that stone comminution in SWL is driven by the average (or local) peak pressure incident on the stone (as opposed to the global peak pressure in the lithotripter field) that exceeds a minimal pressure threshold to initiate fracture (14). Therefore, for the maximally allowable acoustic energy that can be safely delivered to the kidney, a lithotripter with a broad FW and lower peak pressure will have a larger fragmentation zone in the focal plane than its counterpart with narrow FW and high peak pressure (11,54). Results of our in vitro stone comminution experiments at r = 10 mm off-axis and in the membrane holder support this notion (Fig.…”

“…S3 A and B). The in vitro setup was further used to assess the effect of respiratory motion on stone comminution following a protocol described in SI Materials and Methods (54,63).…”