Lithotripter shock wave interaction with a bubble near various biomaterials.

Following previous work on the dynamics of an oscillating bubble near a bio-material (Ohl et al 2009 Phys. Med. Biol. 54 6313-36) and the interaction of a bubble with a shockwave (Klaseboer et al 2007 J. Fluid Mech. 593 33-56), the present work concerns the interaction of a gas bubble with a traveling shock wave (such as from a lithotripter) in the vicinity of bio-materials such as fat, skin, muscle, cornea, cartilage, and bone. The bubble is situated in water (to represent a water-like biofluid). The bubble collapses are not spherically symmetric, but tend to feature a high speed jet. A few simulations are performed and compared with available experimental observations from Sankin and Zhong (2006 Phys. Rev. E 74 046304). The collapses of cavitation bubbles (created by laser in the experiment) near an elastic membrane when hit by a lithotripter shock wave are correctly captured by the simulation. This is followed by a more systematic study of the effects involved concerning shockwave bubble biomaterial interactions. If a subsequent rarefaction wave hits the collapsed bubble, it will re-expand to a very large size straining the bio-materials nearby before collapsing once again. It is noted that, for hard bio-material like bone, reflection of the shock wave at the bone-water interface can affect the bubble dynamics. Also the initial size of the bubble has a significant effect. Large bubbles (∼1 mm) will split into smaller bubbles, while small bubbles collapse with a high speed jet in the travel direction of the shock wave. The numerical model offers a computationally efficient way of understanding the complex phenomena involving the interplay of a bubble, a shock wave, and a nearby bio-material.

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.

Measures of linear and nonlinear interdependence of electrocortigram time series from evoked-response potential experiments.

In this brief discussion, we consider various coupling measures applied to electrocortigram (ECoG) data. The analysis consists of both linear and nonlinear measures of coupling - or interdependence - between two ensembles of measurements collected at two electrodes in an evoked-response potential (ERP) experiment. The interdependence measures are applied to simulated time series data and experimental ECoG data. The algorithms discussed here are implemented in the interactive data language (IDL) and available for download from the authors.