Studies revealed that navigation systems that provided intraoperative assistance might improve pedicle screw insertion accuracy, and also implied that different systems provided different pedicle screw insertion accuracy. A systematic review and meta-analysis was conducted to focus on the pedicle screw insertion accuracy with or without the assistance of image-guided system, and the variance among the different navigation systems. Comparative studies were searched on pedicle screw insertion accuracy between conventional and navigated method, and among different navigation systems. A total of 43 papers, including 28 clinical, 14 cadaveric and 1 model studies, were included in the current study. For clinical articles, there were 3 randomized clinical trials, 4 prospective comparative studies and 21 retrospective comparative studies. The incidence of pedicle violation among computer tomography-based navigation method group was statistically significantly less than that observed among the conventional group (OR 95% CI, in vivo: 0.32-0.60; in vitro: 0.24-0.75 P \ 0.01). Two-dimensional fluoroscopybased navigation system (OR 95% CI, in vivo: 0.27-0.48; in vitro: 0.43-0.88 P \ 0.01) and three-dimension fluoroscopy-based navigation system (OR 95% CI, in vivo: 0.09-0.38; in vitro: 0.09-0.36 P \ 0.01) also obtained significant reduced screw deviation rate over traditional methods. Between navigated approaches, statistically insignificant individual and pooled RR values were observed for all in vivo subgroups. Pooled estimate of in vitro studies show that computer tomography-based and three-dimension fluoroscopy-based navigation system provided more accurate pedicle screw insertion over two-dimension fluoroscopy-based navigation system. Our review showed that navigation provided a higher accuracy in the placement of pedicle screws compared with conventional methods. The superiority of navigation systems was obvious when they were applied to abnormal spinal structure. Although no strong in vivo evidence has detected significantly different pedicle screw placement accuracy among the three major navigation systems, meta-analysis revealed the variance in pedicle screw insertion accuracy with different navigation methods.

We investigate self-similar dynamical processes in an isothermal self-gravitational fluid with spherical symmetry. With reference to the earlier complementary solution results of Larson, Penston, Shu, Hunter and Whitworth & Summers, we further explore the 'semi-complete solution space' from an initial instant t → 0 + to a final stage t → +∞. These similarity solutions can describe and accommodate physical processes of radial inflow, core collapse, oscillations and envelope expansion (namely, outflow or wind) or contraction as well as shocks. In particular, we present new classes of self-similar solutions, referred to as 'envelope expansion with core collapse' (EECC) solutions, that feature concurrent interior core collapse and exterior envelope expansion. The interior collapse towards the central core approaches a free-fall state as the radius r → 0, while the exterior envelope expansion gradually approaches a constant radial flow speed as r → +∞. There exists at least one spherical stagnation surface of zero flow speed that separates the core collapse and the envelope outflow and that travels outward at constant speed, either subsonically or supersonically, in a self-similar manner. Without crossing the sonic critical line where the travel speed of non-linear disturbances relative to the radial flow is equal to the sound speed, there exists a continuous band of infinitely many EECC solutions with only one supersonic stagnation point as well as a continuous band of infinitely many similarity solutions for 'envelope contraction with core collapse' (ECCC) without stagnation point. Crossing the sonic critical line twice analytically, there are infinitely many discrete EECC solutions with one or more subsonic stagnation points. Such discrete EECC similarity solutions generally allow radial oscillations in the subsonic region between the central core collapse and the outer envelope expansion. In addition, we obtained complementary discrete ECCC similarity solutions that cross the sonic critical line twice with subsonic oscillations. In all these discrete solutions, subsonic spherical stagnation surfaces resulting from similarity oscillations travel outward at constant yet different speeds in a self-similar manner. With specified initial boundary or shock conditions, it is possible to construct an infinite number of such EECC similarity solutions, which are conceptually applicable to various astrophysical problems involving gravitational collapses and outflows. We mention potential applications of EECC similarity solutions to the formation process of protoplanetary nebulae connecting the asymptotic giant branch phase and the planetary nebula phase to H II clouds surrounding star formation regions, and to a certain evolution phase of galaxy clusters.