Active bundles of polar and bipolar filaments.

Bundles of actin filaments and molecular motors of the myosin family are a common subcellular organizational motif. Typically, such bundles are under contractile stress resulting from interactions between the filaments and the motors. This holds in particular for contractile rings that appear in the late stages of cell division in animal cells and that cleave the mother into two daughter cells. It was recently shown that myosin organizes into regularly spaced clusters along rings in mammalian cells, whereas myosin clusters in fission yeast travel along the perimeter of actomyosin rings [Wollrab et al., Nat. Commun. 7, 11860 (2016)2041-172310.1038/ncomms11860]. A mechanism based on the association of the structurally polar actin filaments into bipolar structures was shown to provide a common explanation for both observations. Here, we analyze the dynamics of this mechanism in detail. We find a rich phase diagram depending on the actomyosin interaction strength and the stability of the bipolar structures. The system can notably organize into traveling waves. Furthermore, we identify the nature of the bifurcations connecting the various patterns as parameters are changed. Finally, we report experimental patterns observed in cytokinetic rings in fission yeast and link them to solutions of our dynamic equations. Our analysis highlights the possible role played by local polarity sorting of actin filaments for the dynamics and functionality of actomyosin networks.

[Indications for Surgical Correction of Degenerative Spondylolisthesis]. / Indikationen zur Korrekturspondylodese bei degenerativer Spondylolisthesis.

There is no general consensus about indications for surgical treatment of degenerative spondylolisthesis. This is--in part--due to a paucity of knowledge of its natural history and outcomes of conservative treatment, as well as a relatively small number of sufficiently powered outcome studies for surgical treatment. We aim to provide an overview of current surgical techniques and deduce indications based on two simple principles: presence of neurological deficits and instability. Today, decompression and instrumented fusion is the standard of care. However, the complete armamentarium of possible treatment options should be carefully considered, and the adequate procedures and instruments used should be chosen individually, when a decision to operate is made.

Elongational flow effects on the vortex growth out of Couette flow in ferrofluids.

The growth behavior of stationary axisymmetric vortices and of oscillatory, nonaxisymmetric spiral vortices in Taylor-Couette flow of a ferrofluid in between differentially rotating cylinders is analyzed using a numerical linear stability analysis. The investigation is done as a function of the inner and outer cylinder's rotation rates, the axial wave number of the vortex flows, and the magnitude of an applied homogeneous axial magnetic field. In particular, the consequences of incorporating elongational flow effects in the magnetization balance equation on the marginal control parameters that separate growth from decay behavior are determined. That is done for several values of the transport coefficient that measures the strength of these effects.

[Cervical disc herniation]. / Der zervikale Bandscheibenvorfall.

The cervical disc herniation is characterized by prolapsed nucleus pulposus material through the annulus into the spinal canal. The local mechanical or chemical irritation of neural structures typically leads to symptoms of radiculopathy, cervicocephalgia or myelopathy. Pronounced sensorimotor deficits or intractable pain constitute surgical treatment. In all other cases conservative treatment is indicated, including pain medication, active and passive physiotherapy, and local injections, respectively. Anterior cervical discectomy and interbody fusion (ACDF) is still the surgical treatment of choice. Predominantly, cages with or without plates are in use to obtain solid fusion. The implantation of a total disc replacement is a viable alternative, if no contraindications exist. Other surgical techniques may be performed in proper selected cases. The overall clinical and radiological results of both surgical and conservative treatment are good.

Islands of instability for growth of spiral vortices in the Taylor-Couette system with and without axial through flow.

We present numerical calculations of the linearized Navier-Stokes equations for axially extended and axially localized spiral structures in the Taylor-Couette system. The eigenvalue surface for spiral vortices with azimuthal wave number M=2 shows significantly more structure than that for vortices with M=0 and 1. Islands are found in parameter space where axially periodic vortex perturbations can grow. Bicriticality of different axial wave numbers is observed. Furthermore, parameter islands of absolute instability are found where wave packets consisting of near-critical extended perturbations can grow and expand via oppositely moving fronts. Some results are compared with those of the Ginzburg-Landau approximation.

End wall effects on the transitions between Taylor vortices and spiral vortices.

We present numerical simulations as well as experimental results concerning transitions between Taylor vortices and spiral vortices in the Taylor-Couette system with rigid, nonrotating lids at the cylinder ends. These transitions are performed by wavy structures appearing via a secondary bifurcation out of Taylor vortices and spirals, respectively. In the presence of these axial end walls, pure spiral solutions do not occur as for axially periodic boundary conditions but are substituted by primary bifurcating, stable wavy spiral structures. Similarly to the periodic system, we found a transition from Taylor vortices to wavy spirals mediated by so-called wavy Taylor vortices and, on the other hand, a transition from wavy spirals to Taylor vortices triggered by a propagating defect. We furthermore observed and investigated the primary bifurcation of wavy spirals out of the basic circular Couette flow with Ekman vortices at the cylinder ends.

Influence of homogeneous magnetic fields on the flow of a ferrofluid in the Taylor-Couette system.

We investigate numerically the influence of a homogeneous magnetic field on a ferrofluid in the gap between two concentric, independently rotating cylinders. The full Navier-Stokes equations are solved with a combination of a finite difference method and a Galerkin method. Structure, dynamics, symmetry properties, bifurcation, and stability behavior of different vortex structures are investigated for axial and transversal magnetic fields, as well as combinations of them. We show that a transversal magnetic field modulates the Taylor vortex flow and the spiral vortex flow. Thus, a transversal magnetic field induces wavy structures: wavy Taylor vortex flow (wTVF) and wavy spiral vortex flow. In contrast to the classic wTVF, which is a secondarily bifurcating structure, these magnetically generated wavy Taylor vortices are pinned by the magnetic field, i.e., they are stationary and they appear via a primary forward bifurcation out of the basic state of circular Couette flow.

Nonlinear defects separating spiral waves in Taylor-Couette flow.

Stable domain walls which are realized by a defect between oppositely traveling spiral waves in a pattern-forming hydrodynamic system, i.e., Taylor-Couette flow, are studied numerically as well as experimentally. A nonlinear mode coupling resulting from the nonlinearities in the underlying momentum balance is found to be essential for the stability of the defects. These nonlinearly driven defects separate spiral domains and act either as a phase generating or annihilating defect. Specific phase differences of either 0 or pi between the participating traveling waves are a characteristic feature of this defect. The influence of a symmetry breaking externally imposed flow on the spiral domains and the defects is studied. The numerical and experimental results are in excellent agreement.

Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction.

A flow state consisting of two oppositely traveling waves (TWs) with oscillating amplitudes has been found in the counter-rotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing waves that are nonlinear superpositions of left- and right-handed spiral vortex waves with equal time-independent amplitudes. Beyond a critical driving, the two spiral TW modes start to oscillate in counterphase due to a Hopf bifurcation. The trigger for this bifurcation is provided by a nonlinearly excited mode of different symmetry than the spiral TWs. A three-mode coupled amplitude equation model is presented that captures this bifurcation scenario. The mode-coupling between two symmetry degenerate critical modes and a nonlinearly excited one that is contained in the model can be expected to occur in other structure-forming systems as well.

Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system.

Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counter-rotating Taylor-Couette system that were done for fixed axial wavelengths are supplemented by exploring the dependence of the vortex phenomena waves on their wavelength. This yields information about the experimental and numerical accessibility of the various bifurcation scenarios. Also backward bifurcating standing waves with oscillating amplitudes of the constituent traveling waves are found.

Localized spirals in Taylor-Couette flow.

We present a type of spiral vortex state that appears from a supercritical Hopf bifurcation below the linear instability of circular Couette flow in a Taylor-Couette system with rigid end plates. These spirals have been found experimentally as well as numerically as "pure" states but also coexist with "classical" spirals (or axially standing waves for smaller systems) which typically appear from linear instability in counterrotating Taylor-Couette flow. These spiral states have an axial distribution of the strongly localized amplitude in the vicinity of the rigid end plates that confine the system in the axial direction. Furthermore, they show significantly different oscillation frequencies compared to the critical spiral frequencies. Despite the localization of the amplitude near the ends, the states appear as global states with spirals that propagate either toward the middle from each end of the system or vice versa. In contrast to classical spirals, these states exhibit a spatial or a spatiotemporal reflection symmetry.

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

Controlling the stability transfer between oppositely traveling waves and standing waves by inversion-symmetry-breaking perturbations.

The effect of an externally applied flow on symmetry degenerated waves propagating into opposite directions and standing waves that exchange stability with the traveling waves via mixed states is analyzed. Wave structures that consist of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and explained quantitatively by amplitude equations containing quintic coupling terms. The latter are appropriate to describe the influence of inversion-symmetry-breaking perturbations on many oscillatory instabilities with O(2) symmetry.

Free vascularized fibular grafting for reconstruction after tumor resection in the upper extremity.

BACKGROUND: Limb salvage is viable in the majority of patients with malignant bone tumors, but especially in case of extensive tumors and bad soft tissue conditions, it is challenging in upper extremity. OBJECTIVES/METHOD: The clinical and radiological results of 21 patients, who had free vascularized fibular grafts (VFG), for diaphyseal (14), and epipyseal (7) defect reconstruction of the upper extremity, are presented. The indications for VFG were resection after osteosarcoma (9 cases), Ewings sarcoma (9 cases), chondrosarcoma (1 case), rhabdomyosarcoma (1 case), and 1 case of fibrous dysplasia. The 20 malignant tumors were staged as follows: 2a (1), 2b (18), 3 (1). The mean follow-up was 43.6 months (min 6.0-max 131.9). Functional results were described and graded quantitatively according to the MSTS-score. RESULTS: Results were satisfactory with regard to pain, emotional acceptance, manual dexterity, and function. Lifting ability was decreased in two patients. Hypertrophy index was 31% (min 13%-max 71%). Main complications were fracture (5), pseudoarthrosis (4), prolonged wound healing (4), temporary nerve irritation (2), and deep infection (1). Re-operation was required in eight patients (12 operations). CONCLUSION: VFG offers a good possibility for biological reconstruction of large skeletal defects, with an acceptable complication and re-operation rate. When conservative treatment of complications was not successful, further surgery led to recovery in the majority of cases.

Competition between traveling fluid waves of left and right spiral vortices and their different amplitude combinations.

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counterrotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude-equation approximations. Stable cross-spiral structures with continuously varying content of left- and right-spiral modes are found. They provide a stability transferring connection between the initially stable, axially counterpropagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly farther away from the onset of vortex flow.

Spiral vortices traveling between two rotating defects in the Taylor-Couette system.

Numerical calculations of vortex flows in Taylor-Couette systems with counter rotating cylinders are presented. The full, time-dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method. Annular gaps of radius ratio eta=0.5 and of several heights are simulated. They are closed by nonrotating lids that produce localized Ekman vortices in their vicinity and that prevent axial phase propagation of spiral vortices. The existence and spatiotemporal properties of rotating defects, modulated Ekman vortices, and the spiral vortex structures in the bulk are elucidated in quantitative detail.

Spiral vortices and Taylor vortices in the annulus between rotating cylinders and the effect of an axial flow.

We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter rotating as well as with corotating cylinders. The full, time dependent Navier Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation, and stability behavior between spiral vortices with azimuthal wave numbers M=+/-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1, 0, and 1 vortex structures are changed by an externally imposed axial through flow with Reynolds numbers in the range -40< or =Re< or =40. Among other things we investigate when left handed or right handed spirals or toroidally closed vortices are preferred.

Spiral and Taylor vortex fronts and pulses in axial through flow.

The influence of an axial through flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio eta=0.5 is determined. The Navier-Stokes equations (NSE) linearized around the basic Couette-Poiseuille flow are solved numerically with a shooting method in a wide range of through flow strengths Re and different rates of co-rotating and counter-rotating cylinders for toroidally closed vortices with azimuthal wave number m=0 and for spiral vortex flow with m=+/-1. For each of these three different vortex varieties we have investigated (i) axially extended vortex structures, (ii) axially localized vortex pulses, and (iii) vortex fronts. The complex dispersion relations of the linearized NSE for vortex modes with the three different m are evaluated for real axial wave numbers for (i) and over the plane of complex axial wave numbers for (ii) and (iii). We have also determined the Ginzburg-Landau amplitude equation (GLE) approximation in order to analyze its predictions for the vortex structures (ii) and (iii). Critical bifurcation thresholds for extended vortex structures are evaluated. The boundaries between absolute and convective instability of the basic state for vortex pulses are determined with a saddle-point analysis of the dispersion relations. Fit parameters for power-law expansions of the boundaries up to Re4 are listed in two tables. Finally, the linearly selected front behavior of growing vortex structures is investigated using saddle-point analyses of the dispersion relations of NSE and GLE. For the two front intensity profiles (increasing in positive or negative axial direction) we have determined front velocities, axial growth rates, and the wave numbers and frequencies of the unfolding vortex patterns with azimuthal wave numbers m=0,+/-1, respectively.