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Low-intensity pulsed ultrasound exposure has been shown clinically to shorten the fracture repair process and to induce healing of nonunions in humans, but its mechanism of action remains unclear. In this study we investigated the effect and mechanism of low-intensity pulsed ultrasound on nonunion fracture healing in rat tibias. A consistently reproducible nonunion was produced in rat tibias by muscle interposition without osteotomy. This model was produced by creating a closed tibial fracture with only the distal end of the tibialis anterior muscle interposed into the fracture site. One limb was noninvasively exposed to low-intensity pulsed ultrasound (a 200-millisecond burst of sine waves of 1.5 MHz, repeating at 1.0 kHz) for 20 minutes daily. The incident intensity was approximately 30 mW/cm2. Rats were killed at intervals between 2 and 6 weeks. The events were assessed by radiographs, microfocus X-ray computed tomograms, and histologic examination. After 6 weeks of exposure, 7 of 14 nonunion fractures showed healing on radiologic assessment. The results of three-dimensional microfocus X-ray computed tomographic reconstruction and histologic examination also supported this finding. On the other hand, all control tibias remained in a state of nonunion during the same period. These results indicate that low-intensity pulsed ultrasound promotes healing in the rat nonunion fracture model.

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The flow over a stationary golf ball has been numerically investigated by conducting large-eddy simulations in the subcritical, critical and supercritical regimes. A direct comparison of features of flow fields was made to a smooth sphere model. Particular attention was paid to the effect that the golf ball dimples have on the development of lateral force and wake structures. In the subcritical regime, the lateral force varies irregularly in time for both the golf ball and the smooth sphere, and the wake structures of these two models appear to be similar, indicating the limited effect of the surface roughness on the flow behaviors in this regime. In the critical regime, both the golf ball and the smooth sphere exhibit a larger magnitude lateral force oscillation compared to the subcritical cases, while the wavelengths of the flow structures show differences between the golf ball and the smooth sphere. In the Makoto Tsubokura Flow Turbulence Combust supercritical regime, both the golf ball and the smooth sphere are subjected to a nonzero lateral force during a long time interval. However, the magnitude of the lateral force acting on the golf ball is much smaller due to the relatively more concentrated and less asymmetric wake structures compared to the smooth sphere.