Surprise waves in fluids are recognized to trigger spherical gas bubbles to rapidly collapse and form solid re-entrant jets in direction of the propagating surprise. reasonable collection of a single efficiency parameter, this model is able to reproduce observations of an apparent 1000-shock threshold before wide-spread tissue injury occurs in targeted kidneys and the approximate extent of this injury after a typical clinical dose of 2000 shock waves. INTRODUCTION We consider a small gas-filled bubble being compressed rapidly by a shock wave (observe Fig. ?Fig.1)1) and its subsequent jetting toward a viscous material. This configuration is usually motivated by medical procedures such as shock-wave lithotripsy, during which shock waves are directed toward kidney stones in the hope of fracturing them into passable pieces. At clinical shock-wave doses, there appears to be significant collateral injury to the kidney,1, 2 which is usually implicated in certain short- and long-term complications.3 The action of cavitation bubbles is implicated in this injury.4, 5 Open in a separate window Physique 1 Configuration schematic (see text). Bubble growth, caused by the negative-pressure phase of the lithotripter wave,6 has been suggested as a potential mechanism of the injury,7 but the bubble collapse is also potentially damaging. It is known that a bubble can collapse asymmetrically leading to the formation of SYN-115 novel inhibtior a so-called re-entrant jet,8, 9 which starts from where the shock SYN-115 novel inhibtior first encounters the bubble and is able to penetrate the bubbles much side with sufficient velocity to damage nearby material. This is one of the mechanisms thought to cause cavitational damage in designed systems in cases where the flows dynamic pressure causes the cavitation and subsequent collapse.8 The shock sensitivity of explosives also appears to depend on this jetting mechanism. In this case, the formation of local hot spots in the material by the dissipation associated with this jetting seems to increase the overall explosive sensitivity of energetic materials to shock-like mechanical impacts.10, 11 In tissues, this jetting has been hypothesized to be the mechanism of mechanical injury during lithotripsy (e.g., see the recent conversation of Klaseboer et al.12), and it is potentially the mechanism by which bubbles subjected to bursts of high-intensity focused ultrasound (HIFU) can erode tissue SYN-115 novel inhibtior (e.g., Ref. 13). HIFU is also well known to cause thermal injury to tissue, but our concern is with mechanical effects at energy deposition rates that preclude significant heating. Thermal injury is not expected in lithotripsy.14 Simulations of collapsing bubbles typically neglect viscosity,12, 15, 16, 17, 18, 19, 20, 21 which is indeed justified based on the Reynolds numbers of the jets expected under typical conditions,20 though for very small bubbles viscous effects have been identified for non-shock-induced (so-called Rayleigh) collapse near a wall.22 The re-entrant jets for lithotripter shocks appear to have speeds of around 1000 mMs,12 so for any 1 mm diameter bubble in water the jet Reynolds number is about 106. Even if we presume that the re-entrant jet diameter is only 1% of the bubble diameter, this Reynolds number is still 104. However, the significantly smaller bubbles that might form in microvessels in the kidney Rabbit Polyclonal to Synaptophysin (say, 20 m diameter) and the significantly higher viscosities of tissue (at least hundreds of occasions that of water) can lead to re-entrant jets with Reynolds numbers of around unity. This suggests that tissue viscosity might play a significant role in suppressing the jetting and any injury it might cause. Recent experiments including laser-induced bubble growth and collapse in viscous fluids suggest that higher viscosity fluids both suppress the strength of the jetting and slow the time level of the collapse.23 Viscosity has also recently been proposed to be important for the confinement of bubble expansion when subjected to model lithotripter shock profiles.24 Assuming spherical symmetry, we recently generalized the well-known RayleighCPlesset bubble dynamics model to account for confinement by an elastic membrane and an extensive Voigt visco-elastic material.24 Results suggest that even the highest estimates of tissue elasticity fail to suppress bubble growth significantly, but because of the small scales and nature of the expansion, even moderate estimates of tissue viscosity were able to play a substantive role is suppressing bubble.