[Postoperative outcomes in patients with closed patellar fractures]

OBJECTIVE

To improve postoperative outcomes in patients with closed patellar fractures using a new method of surgical treatment.

MATERIAL AND METHODS

The authors proposed a new method of patellar osteosynthesis. Technique of osteosynthesis is described, and surgical scheme is presented. Treatment outcomes were analyzed in 68 patients with closed patellar fractures. The control group consisted of 34 patients who underwent Weber osteosynthesis. The authors assessed clinical and radiological data. Moreover, clinical example of a patient with traumatic closed patellar fracture and illustrations of surgical treatment are presented.

RESULTS

Clinical data indicate the advantage of treatment in the main group.

Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion

In systems with cyclic dynamics, invasions often generate periodic spatiotemporal oscillations, which undergo a subsequent transition to chaos. The periodic oscillations have the form of a wavetrain and occur in a band of constant width. In applications, a key question is whether one expects spatiotemporal data to be dominated by regular or irregular oscillations or to involve a significant proportion of both. This depends on the width of the wavetrain band. Here, we present mathematical theory that enables the direct calculation of this width. Our method synthesizes recent developments in stability theory and computation. It is developed for only 1 equation system, but because this is a normal form close to a Hopf bifurcation, the results can be applied directly to a wide range of models. We illustrate this by considering a classic example from ecology: wavetrains in the wake of the invasion of a prey population by predators.