Infrapatellar branch of the saphenous nerve lesion following tibial nailing: it is possible to avoid it?

BACKGROUND: Iatrogenic injury to the infrapatellar branches of saphenous nerve is a common complication following tibial nailing. This lesion seems to be directly related to the surgical approach adopted for nail insertion. The aim of the present study was to systematically review the current literature in order to assess the eventual superiority of one surgical approach for tibial nailing over the others in limiting the neurological impairment related to infrapatellar branch injury. MATERIALS AND METHODS: The available literature was systematically screened searching papers dealing with iatrogenic injury to the infrapatellar branch of saphenous nerve after intramedullary tibial nailing. The terms "Saphenous" and "Infrapatellar branch" were used in combination with "intramedullary nailing" and "tibial fractures", supplying no limits regarding the publication year. Only publications in English were considered. Case reports, technical notes, instructional course, literature reviews, biomechanical and/ or in vitro studies were all excluded. Coleman methodological score was performed in all the retained articles. RESULTS: Four articles matched the inclusion criteria. There were one original article and three retrospective study. Hypoesthesia and a larger extension of the area of sensory-loss were more frequently observed after vertical incision approach in three out of four articles. A trend towards a lower rate of iatrogenic nerve damage using a transverse incision was found in the remaining one, without any statistical significance. CONCLUSIONS: In order to avoid infrapatellar nerve lesion, horizontal or oblique incisions or percutaneous approaches should be favored, although in some cases a longitudinal incision is required. Limited-extension incisions could minimize the risk and the incidence of this complication.

Effect of a small loss or gain in the periodic nonlinear Schrödinger anomalous wave dynamics.

The focusing nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability of quasimonochromatic waves in weakly nonlinear media, the main physical mechanism for the appearance of anomalous (rogue) waves (AWs) in nature. In this paper, concentrating on the simplest case of a single unstable mode, we study the special Cauchy problem for the NLS equation perturbed by a linear loss or gain term, corresponding to periodic initial perturbations of the unstable background solution of the NLS. Using the finite gap method and the theory of perturbations of soliton partial differential equations, we construct the proper analytic model describing quantitatively how the solution evolves after a suitable transient into slowly varying lower dimensional patterns (attractors) on the (x,t) plane, characterized by ΔX=L/2 in the case of loss and by ΔX=0 in the case of gain, where ΔX is the x shift of the position of the AW during the recurrence, and L is the period. This process is described, to leading order, in terms of elementary functions of the initial data. Since dissipation can hardly be avoided in all natural phenomena involving AWs, and since a small dissipation induces O(1) effects on the periodic AW dynamics, generating the slowly varying loss or gain attractors analytically described in this paper, we expect that these attractors together with their generalizations corresponding to more unstable modes will play a basic role in the theory of periodic AWs in nature.

Fermi-Pasta-Ulam-Tsingou recurrence of periodic anomalous waves in the complex Ginzburg-Landau and in the Lugiato-Lefever equations.

The complex Ginzburg-Landau (CGL) equation, an envelope model relevant in the description of several natural phenomena like binary-fluid convection and second-order phase transitions, and the Lugiato-Lefever (LL) equation, describing the dynamics of optical fields in pumped lossy cavities, can be viewed as nonintegrable generalizations of the nonlinear Schrödinger (NLS) equation, including diffusion, linear and nonlinear loss or gain terms, and external forcing. In this paper we treat the nonintegrable terms of both equations as small perturbations of the integrable focusing NLS equation, and we study the Cauchy problem of the CGL and LL equations corresponding to periodic initial perturbations of the unstable NLS background solution, in the simplest case of a single unstable mode. Using the approach developed in a recent paper by the authors with P. G. Grinevich [Phys. Rev. E 101, 032204 (2020)10.1103/PhysRevE.101.032204], based on the finite gap method and the theory of perturbations of soliton PDEs, we construct the proper analytic models describing quantitatively how the solution evolves, after a suitable transient, into a Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence of anomalous waves (AWs) described by slowly varying lower dimensional patterns (attractors) in the (x,t) plane, characterized by Δx=L/2 or Δx=0 in the case in which loss or gain, respectively, effects prevail, where Δx is the x-shift of the position of the AW during the recurrence and L is the period. We also obtain, in the CGL case, the analytic condition for which loss and gain exactly balance, stabilizing the ideal FPUT recurrence of periodic NLS AWs; such a stabilization is not possible in the LL case due to the external forcing. These processes are described, to leading order, in terms of elementary functions of the initial data in the CGL case, and in terms of elementary and special functions of the initial data in the LL case.