Three-dimensional model of elastic wave propagation in kidney stones with application to shock wave lithotripsy

Shock wave lithotripsy (SWL) has been used to treat kidney stones for decades. However, there is growing recognition that shock waves induced trauma to kidney tissues. The poor understanding of kidney stone comminution by SWL has led to the design of new lithotripters that do not appear to have better clinical outcomes. A three-dimensional time-domain finite-difference solution to the linear elastic equations was applied to investigate the stress and velocity fields of kidney stones subject to lithotripsy shock waves. Simulations with cylindrical and spherical shapes indicated the importance of shear waves in generating high tension in the stones. The kidney stone models were scanned from micro-computed tomography and had diameters from 2 mm to 5 mm. It was found for these shapes too that shear waves induced by interference of the shock wave with stone boundaries dominated the high stress in the stones. The traditional belief of stone comminution mechanism by spell mechanism does not play an important role due to the irregular proximal and distal stone surfaces. It was found for natural stones that stone orientation had an impact on the generation of high stress with a smooth convex surface producing the highest internal stresses. The conclusion of this work is that lithotripters with a focal width larger than a stone should be able to break the stone more efficiently since the large focal width shock waves result in stronger interaction with stone circumferences and produce larger shear waves.