Fovargue D. et al., 2019: An experimentally-calibrated damage mechanics model for stone fracture in shock wave lithotripsy
Daniel Fovargue, Sorin Mitran, Georgy Sankin, Ying Zhang, Pei Zhong
Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina.
Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina.
A damage model suggested by the Tuler–Butcher concept of dynamic accumulation of microscopic defects is obtained from experimental data on microcrack formation in synthetic kidney stones. Experimental data on appearance of microcracks is extracted from micro computed tomography images of BegoStone simulants obtained after subjecting the stone to successive pulses produced by an electromagnetic shock-wave lithotripter source. Image processing of the data is used to infer statistical distributions of crack length and width in representative transversal cross-sections of a cylindrical stone. A high-resolution finite volume computational model, capable of accurately modeling internal reflections due to local changes in material properties produced by material damage, is used to simulate the accumulation
of damage due to successive shocks. Comparison of statistical distributions of microcrack formation in computation and experiment allows calibration of the damage model. The model is subsequently used to compute fracture of a different aspect-ratio cylindrical stone predicting concurrent formation of two main fracture areas as observed experimentally.
Received: 7 November 2017 / Accepted: 5 April 2018 / Published online: 19 April 2018
© Springer Science+Business Media B.V., part of Springer Nature 2018. FREE ARTICLE
Almost 40 years after the first extracorporeal shock wave lithotripsy in humans, the fracture mechanism is still under debate. There is an enormous variety in size, form, mass, and chemical compound of kidney stones. Hardness, brittleness, mechanical structure etc. determine the destructibility of stones and are hard to calculate. To know the mechanism in detail may help to develop procedures to improve fragmentation and avoid side effects. The paper of Fovargue et al. investigates the formation of successive cracks due to repeated shock waves as common in routine lithotripsy procedures. The authors develop and calibrate a fracture model, which takes the interaction of previously generated cracks with succeeding shock waves into account. This approach matches with the common treatment regime of several hundred or thousand shock waves required for complete disintegration.
The results of some computational effort for a cylindrical stone model fixed by a rigid stone holder compare favourably with experimental data. A more complex configuration of realistic shock wave lithotripsy requires an increased computational effort, which may be worth if lithotripsy could gain safety and efficiency.
For further reading on mechanism of fragmentation, see: https://doi.org/10.1007/s00240-018-1102-6