Identification alone versus intraoperative neuromonitoring of the recurrent laryngeal nerve during thyroid surgery: experience of 2034 consecutive patients

Background: The aim of this study was to evaluate the ability of intraoperative neuromonitoring in reducing the postoperative recurrent laryngeal nerve palsy rate by a comparison between patients submitted to thyroidectomy with intraoperative neuromonitoring and with routine identification alone. Methods: Between June 2007 and December 2012, 2034 consecutive patients underwent thyroidectomy by a single surgical team. We compared patients who have had neuromonitoring and patients who have undergone surgery with nerve visualization alone. Patients in which neuromonitoring was not utilized (Group A) were 993, patients in which was utilized (group B) were 1041. Results: In group A 28 recurrent laryngeal nerve injuries were observed (2.82%), 21 (2.11%) transient and 7 (0.7%) permanent. In group B 23 recurrent laryngeal nerve injuries were observed (2.21%), in 17 cases (1.63%) transient and in 6 (0.58%) permanent. Differences were not statistically significative. Conclusions: Visual nerve identification remains the gold standard of recurrent laryngeal nerve management in thyroid surgery. Neuromonitoring helps to identify the nerve, in particular in difficult cases, but it did not decrease nerve injuries compared with visualization alone. Future studies are warranted to evaluate the benefit of intraoperative neuromonitoring in thyroidectomy, especially in conditions in which the recurrent nerve is at high risk of injury. Keywords: Neuromonitoring, Recurrent laryngeal nerve, Thyroidectom

Exact solutions to the focusing nonlinear Schrodinger equation

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form in terms of matrix exponentials. Such exact solutions can alternatively be written explicitly as algebraic combinations of exponential, trigonometric, and polynomial functions of the spatial and temporal coordinates.Comment: 60 pages, 18 figure

Diffusion in tight confinement: a lattice-gas cellular automaton approach. I. Structural equilibrium properties

The thermodynamic and transport properties of diffusing species in microporous materials are strongly influenced by their interactions with the confining framework, which provide the energy landscape for the transport process. The simple topology and the cellular nature of the α cages of a ZK4 zeolite suggest that it is appropriate to apply to the study of the problem of diffusion in tight confinement a time-space discrete model such as a lattice-gas cellular automaton (LGCA). In this paper we investigate the properties of an equilibrium LGCA constituted by a constant number of noninteracting identical particles, distributed among a fixed number of identical cells arranged in a three-dimensional cubic network and performing a synchronous random walk at constant temperature. Each cell of this network is characterized by a finite number of two types of adsorption sites: the exit sites available to particle transfer and the inner sites not available to such transfers. We represent the particle-framework interactions by assuming a differentiation in binding energy of the two types of sites. This leads to a strong dependence of equilibrium and transport properties on loading and temperature. The evolution rule of our LGCA model is constituted by two operations (randomization, in which the number of particles which will be able to try a jump to neighboring cells is determined, and propagation, in which the allowed jumps are performed), each one applied synchronously to all of the cells. The authors study the equilibrium distribution of states and the adsorption isotherm of the model under various conditions of loading and temperature. In connection with the differentiation in energy between exit and inner sites, the adsorption isotherm is described by a conventional Langmuir isotherm at high temperature and by a dual-site Langmuir isotherm at low temperature, while a first order diffuse phase transition takes place at very low temperature

Exact Solutions to the Sine-Gordon Equation

A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the temporal variable $t,$ and they are exponentially asymptotic to integer multiples of $2\pi$ as $x\to\pm\infty.$ The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method presented is generalizable to other integrable evolution equations where the inverse scattering transform is applied via the use of a Marchenko integral equation. By expressing the kernel of that Marchenko equation as a matrix exponential in terms of the matrix triplet and by exploiting the separability of that kernel, an exact solution formula to the Marchenko equation is derived, yielding various equivalent exact solution formulas for the sine-Gordon equation.Comment: 43 page

Rogue wave formation scenarios for the focusing nonlinear Schr\"odinger equation with parabolic-profile initial data on a compact support

We study the (1+1) focusing nonlinear Schroedinger (NLS) equation for an initial condition with concave parabolic profile on a compact support and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions of the resulting elliptic system, we generalise a result by Talanov, Guervich and Shvartsburg, finding a criterion on the chirp and modulus coefficients at time equal zero to determine whether the dispersionless solution features asymptotic relaxation or a blow-up at fine time, providing an explicit formula for the time of catastrophe. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semi-classical regime, whether the solution relaxes or develops a higher order rogue wave, whose amplitude can be several multiples of the height of the initial parabola. In the latter case, for small dispersion, the time of catastrophe for the corresponding dispersionless solution predicts almost exactly the onset time of the rogue wave. In our numerical experiments, the sign of the chirp appears to determine the prevailing scenario, among two competing mechanisms leading to the formation of a rogue wave. For negative values, the simulations are suggestive of the dispersive regularisation of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seem to result from the interaction of counter-propagating dispersive dam break flows, as described for the box problem by El, Khamis and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics.Comment: 17 pages, 5 figures, 1 tabl

Rogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support

We study the (1+1) focusing nonlinear Schrödinger equation for an initial condition with compactly supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blowup in finite time, generalizing a result by Talanov et al. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semiclassical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularization of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counterpropagating dispersive dam break flows, as in the box problem recently studied by El, Khamis, and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics