Fatigue of kidney stones with heterogeneous microstructure subjected to shock-wave lithotripsy.

In this article a theoretical framework is developed for the mechanics of kidney stones with an isotropic, random microstructure--such as those comprised of cystine or struvite. The approach is based on a micromechanical description of kidney stones comprised of crystals in a binding matrix. Stress concentration functions are developed to determine load sharing of the particle phase and the binding matrix phase. Measurements have shown the inclusions to be considerably harder than the binder; consequently, loading of a stone leads to higher stresses in the inclusions than in the binder. As an illustration of the theory, the fatigue of kidney stones subject to shock-wave lithotripsy is considered. Stress concentration functions are used to construct fatigue-life estimates for each phase, as a function of the volume fraction and of the mechanical properties of the constituents, as well as the loading from SWL. The failure of the binding matrix, or of the particulate phase, is determined explicitly in a model for the accumulation of distributed damage. The theory can be used to assess the importance of microscale heterogeneity on the comminution of renal calculi, and to estimate the number of cycles to failure in terms of measurable material properties.