From nonlinear reaction-diffusion processes to permanent microscale structures.

Biomorphs are polycrystalline aggregates that self-assemble during inorganic precipitation reactions. The shape repertoire of these microstructures include hemispherical objects with complicated internal features such as radial spikes and cones as well as folded sheets reminiscent of corals. We propose that at the microscale, some of these patterns are caused by nonlinear reaction-diffusion processes and present a simple model for this unconventional type of precipitation. The model consists of three reaction steps that convert a reactant species autocatalytically into an intermediate and eventually into a solid, immobile product. Numerical simulations of the model in three space dimensions reveal product structures that are similar to the experimentally observed biomorphs.

Directed adaptation of synchronization levels in oscillator communities.

We present an adaptive control scheme that realizes desired dynamics of an oscillator network with a given number of communities by adjusting the coupling weights between oscillators accordingly. The scheme allows, for example, to simultaneously establish different pregiven synchronization levels in the particular communities as well as phase relationships between them. We apply the method in numerical simulations with all-to-all and randomly coupled networks. Moreover, we provide an experimental proof of concept validating our numerical findings in a network of optically coupled photosensitive chemical micro-oscillators.

A novel technique to initiate and investigate scroll waves in thin layers of the photosensitive Belousov-Zhabotinsky reaction.

While free scroll rings are non-stationary objects that either grow or contract with time, spatial confinement can have a large impact on their evolution reaching from significant lifetime extension (J.F. Totz, H. Engel, O. Steinbock, New J. Phys. 17, 093043 (2015)) up to formation of stable stationary and breathing pacemakers (A. Azhand, J.F. Totz, H. Engel, EPL 108, 10004 (2014)). Here, we explore the parameter range in which the interaction between an axis-symmetric scroll ring and a confining planar no-flux boundary can be studied experimentally in transparent gel layers supporting chemical wave propagation in the photosensitive variant of the Belousov-Zhabotinsky medium. Based on full three-dimensional simulations of the underlying modified complete Oregonator model for experimentally realistic parameters, we determine the conditions for successful initiation of scroll rings in a phase diagram spanned by the layer thickness and the applied light intensity. Furthermore, we discuss whether the illumination-induced excitability gradient due to Lambert-Beer's law as well as a possible inclination of the filament plane with respect to the no-flux boundary can destabilize the scroll ring.

Controlling the position of traveling waves in reaction-diffusion systems.

We present a method to control the position as a function of time of one-dimensional traveling wave solutions to reaction-diffusion systems according to a prespecified protocol of motion. Given this protocol, the control function is found as the solution of a perturbatively derived integral equation. Two cases are considered. First, we derive an analytical expression for the space (x) and time (t) dependent control function f(x,t) that is valid for arbitrary protocols and many reaction-diffusion systems. These results are close to numerically computed optimal controls. Second, for stationary control of traveling waves in one-component systems, the integral equation reduces to a Fredholm integral equation of the first kind. In both cases, the control can be expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed knowledge of the reaction kinetics unnecessary.

Intracellular mechanochemical waves in an active poroelastic model.

Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. We incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as an interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing, and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.

Analytical approximations for spiral waves.

We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R(0). For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R(+)) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R(+) with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.

A case of Flavonifractor plautii blood stream infection in a severe burn patient and a review of the literature.

BACKGROUND: Flavonifractor plautii is a strictly anaerobic rod shaped bacterium belonging to the family of Clostridiales. It is a commensal of the human intestinal microbiota which was seldom isolated from clinical samples, therefore clinical data are scarce. To date, only four cases of F. plautii infections were described, all occurring in immunosuppressed patients. CASE PRESENTATION: We report a case where F. plautii was isolated from the blood culture of a severe burn victim and identified by matrix-assisted laser desorption ionization time-of-flight mass spectrometry. DISCUSSION: To the best of our knowledge, this is the first case of F. plautii blood stream infection described in a burn patient.

First-order synchronization transition in a large population of strongly coupled relaxation oscillators.

Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting first-order transition is robust with respect to changes in network connectivity and natural frequency distribution. This allows us to identify the relaxation character of the oscillators as the essential parameter that determines the nature of the synchronization transition. We further support this hypothesis by revealing the mechanism of the transition, which cannot be accounted for by standard phase reduction techniques.

Transition from spiral wave chimeras to phase cluster states.

Photochemically coupled Belousov-Zhabotinsky micro-oscillators are studied in experiments and simulations. Generally good agreement between the experimental and simulated dynamical behavior is found, with spiral wave chimeras exhibited at small values of the time delay in the coupling between the oscillators, spiral wave core splitting at higher values, and phase cluster states replacing the spiral wave dynamics at the highest values of the time delay. Spiral wave chimera dynamics is exhibited experimentally for much of the time delay range, while spiral wave phase cluster states are exhibited more in the model simulations. In addition to comparing the experimental and simulation behavior, we explore the novel spiral wave phase cluster states and develop a mechanism for this new and unusual dynamical behavior.

Active poroelastic two-phase model for the motion of physarum microplasmodia.

The onset of self-organized motion is studied in a poroelastic two-phase model with free boundaries for Physarum microplasmodia (MP). In the model, an active gel phase is assumed to be interpenetrated by a passive fluid phase on small length scales. A feedback loop between calcium kinetics, mechanical deformations, and induced fluid flow gives rise to pattern formation and the establishment of an axis of polarity. Altogether, we find that the calcium kinetics that breaks the conservation of the total calcium concentration in the model and a nonlinear friction between MP and substrate are both necessary ingredients to obtain an oscillatory movement with net motion of the MP. By numerical simulations in one spatial dimension, we find two different types of oscillations with net motion as well as modes with time-periodic or irregular switching of the axis of polarity. The more frequent type of net motion is characterized by mechano-chemical waves traveling from the front towards the rear. The second type is characterized by mechano-chemical waves that appear alternating from the front and the back. While both types exhibit oscillatory forward and backward movement with net motion in each cycle, the trajectory and gel flow pattern of the second type are also similar to recent experimental measurements of peristaltic MP motion. We found moving MPs in extended regions of experimentally accessible parameters, such as length, period and substrate friction strength. Simulations of the model show that the net speed increases with the length, provided that MPs are longer than a critical length of ≈ 120 µm. Both predictions are in line with recent experimental observations.

Anomalous pulse interaction in dissipative media.

We review a number of phenomena occurring in one-dimensional excitable media due to modified decay behind propagating pulses. Those phenomena can be grouped in two categories depending on whether the wake of a solitary pulse is oscillatory or not. Oscillatory decay leads to nonannihilative head-on collision of pulses and oscillatory dispersion relation of periodic pulse trains. Stronger wake oscillations can even result in a bistable dispersion relation. Those effects are illustrated with the help of the Oregonator and FitzHugh-Nagumo models for excitable media. For a monotonic wake, we show that it is possible to induce bound states of solitary pulses and anomalous dispersion of periodic pulse trains by introducing nonlocal spatial coupling to the excitable medium.

Wave trains in an excitable FitzHugh-Nagumo model: bistable dispersion relation and formation of isolas.

We investigate the dispersion relations of nonlinear periodic wave trains in excitable systems which describe the dependence of the propagation velocity on the wavelength. Pulse interaction by oscillating pulse tails within a wave train leads to bistable wavelength bands, in which two stable and one unstable wave train coexist for the same wavelength. The essential spectra of the unstable wave trains exhibit a circle of eigenvalues with positive real parts which is detached from the imaginary axis. We describe the destruction of the bistable dispersion curve and the formation of isolas of wave trains in a sequence of transcritical bifurcations unfolding into pairs of saddle-node bifurcations. It turns out that additional dispersion curves of unstable wave trains play an important role in the destruction of the bistable dispersion curve.

Creating bound states in excitable media by means of nonlocal coupling.

We consider pulses of excitation in reaction-diffusion systems subjected to nonlocal coupling. This coupling represents long-range connections between the elements of the medium; the connection strength decays exponentially with the distance. Without coupling, pulses interact only repulsively and bound states with two or more pulses propagating at the same velocity are impossible. Upon switching on nonlocal coupling, pulses begin to interact attractively and form bound states. First we present numerical results on the emergence of bound states in the excitable Oregonator model for the photosensitive Belousov-Zhabotinsky reaction with nonlocal coupling. Then we show that the appearance of bound states is provided solely by the exponential decay of nonlocal coupling and thus can be found in a wide class of excitable systems, regardless of the particular kinetics. The theoretical explanation of the emergence of bound states is based on the bifurcation analysis of the profile equations that describe the spatial shape of pulses. The central object is a codimension-4 homoclinic orbit which exists for zero coupling strength. The emergence of bound states is described by the bifurcation to 2-homoclinic solutions from the codimension-4 homoclinic orbit upon switching on nonlocal coupling. We stress that the high codimension of the bifurcation to bound states is generic, provided that the coupling range is sufficiently large.

Wave instability induced by nonlocal spatial coupling in a model of the light-sensitive Belousov-Zhabotinsky reaction.

We study spatiotemporal patterns resulting from instabilities induced by nonlocal spatial coupling in the Oregonator model of the light-sensitive Belousov-Zhabotinsky reaction. In this system, nonlocal coupling can be externally imposed by means of an optical feedback loop which links the intensity of locally applied illumination with the activity in a certain vicinity of a particular point weighted by a given coupling function. This effect is included in the three-variable Oregonator model by an additional integral term in the photochemically induced bromide flow. A linear stability analysis of this modified Oregonator model predicts that wave and Turing instabilities of the homogeneous steady state can be induced for experimentally realistic parameter values. In particular, we find that a long-range inhibition in the optical feedback leads to a Turing instability, while a long-range activation induces wave patterns. Using a weakly nonlinear analysis, we derive amplitude equations for the wave instability which are valid close to the instability threshold. Therein, we find that the wave instability occurs supercritically or subcritically and that traveling waves are preferred over standing waves. The results of the theoretical analysis are in good agreement with numerical simulations of the model near the wave instability threshold. For larger distances from threshold, a secondary breathing instability is found for traveling waves.

Hysteresis and drift of spiral waves near heterogeneities: From chemical experiments to cardiac simulations.

Dissipative patterns in excitable reaction-diffusion systems can be strongly affected by spatial heterogeneities. Using the photosensitive Belousov-Zhabotinsky reaction, we show a hysteresis effect in the transition between free and pinned spiral rotation. The latter state involves the rotation around a disk-shaped obstacle with an impermeable and inert boundary. The transition is controlled by changes in light intensity. For permeable heterogeneities of higher excitability, we observe spiral drift along both linear and circular boundaries. Our results confirm recent theoretical predictions and, in the case of spiral drift, are further reproduced by numerical simulations with a modified Oregonator model. Additional simulations with a cardiac model show that orbital motion can also exist in anisotropic and three-dimensional systems.

Use of the neutrophil-to-lymphocyte ratio as a component of a score to predict postoperative mortality after surgery for hip fracture in elderly subjects.

BACKGROUND: Hip fracture precedes death in 12-37 % of elderly people. Identification of high risk patients may contribute to target those in whom optimal management, resource allocation and trials efficiency are needed. The aim of this study is to evaluate a predictive score of mortality after hip fracture in older persons on the basis of the objective prognostic factors easily available: age, sex and neutrophil-to-lymphocyte ratio (NLR) and C-reactive protein (CRP). PATIENTS AND METHODS: After the ethical committee approval, we analyzed our prospective database including 286 consecutive older patients (>64 years) with hip fracture. A score [range 0-4] was constructed, based on a previous analysis, combining age (1 point per decade above 74 years), sex (1 point for male gender) and NLR at postoperative day +5 (1 point if > 5). A receiver-operating curve (ROC) analysis was performed. Similar analyses were performed with CRP (1 point if > 7.65 mg/dL). RESULTS: In the 286 patients (male 31 %), the median age was 84 (65-102) years, and the mean NLR values were 6.47 ± 6.07. At 1 year, 82/286 patients died (28.7 %). In the 235 patients with complete data, significant differences in term of mortality risk are observed (P < 0.001). Performance analysis shows an AUC of 0.72[95 % CI 0.65-0.79]. CRP performed less than NLR (AUC for CRP alone: 0.53[95 % CI 0.45-0.61], P = 0.42, with a sensitivity of 58.5 % and a specificity of 57.1 % for a cut-off value of 7.65 mg/dL; and for NLR alone: 0.59 [95 % CI 0.51-0.66]; P = 0.02, with a sensitivity of 55 % and a specificity of 65 % for a cut-off value of 4.9). CONCLUSION: A discrete 0-4 scoring systems based on age, sex and the NLR was shown to be predictive of mortality in elderly patients during the first postoperative year following surgery for hip fracture repair.

The neutrophil-to-lymphocyte ratio (NLR) after surgery for hip fracture (HF).

BACKGROUND: The NLR is a prognostic factor for outcome and survival in cardiology, oncology and digestive surgery. NLR has not yet been studied in HF. METHODS: Retrospective analysis of a prospective cohort of 247 consecutive patients, older than 65 years, operated for HF. Mortality at 12 months was registered, as the perioperative NLR values. RESULTS: After hip surgery in the 247 patients (women 71%, median age 85 years, range: 66-102), the mortality was 27.2% [95%confidence interval (CI): 21.4-33.0] at 12 months. Univariate analysis detected four risk factors for mortality: age (Hazard Ratio (HR)--by 10 year-increments: 2.08 [95%CI: 1.37-3.17], P<0.001), male gender (HR: 1.92 [95%CI: 1.17-3.14], P=0.009, MCM (≥3) (HR: 1.71 [95%CI: 1.006-2.92], P=0.047 and NLR>5 at day 5 (HR: 1.8 [95%CI: 1.11-2.94], P=0.002). In multivariate analysis, two factors remained significantly associated with mortality: age (HR: 2.28 [95%CI: 1.49-3.47], P<0.001) and male gender (HR: 2.26 [95%CI: 1.38-3.72], P=0.001). Two independent risk factors of postoperative cardiovascular complications were identified: NLR>5 at day 5 (Odds Ratio (OR): 3.34 [95%CI: 2.33-4.80], P=0.001) and MCM (OR: 3.04 [95%CI: 2.16-4.29], P=0.006). A higher risk of infection was independently associated with a NLR>5 at day 5 (OR: 2.12 [95%CI: 1.44-3.11], P=0.02). CONCLUSIONS: The NLR at fifth postoperative day is a risk factor of postoperative mortality and cardiovascular complications.

Phase-lag synchronization in networks of coupled chemical oscillators.

Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively "fire," with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.

Dynamics of spiral waves under global feedback in excitable domains of different shapes.

It is found that the dynamics of spiral waves subjected to global feedback is extremely sensitive to the domain shape. Bifurcations in the velocity field which specifies the resonant drift of the spiral wave core induced by global feedback are analyzed. It is shown, for example, that smooth variation of the eccentricity of an elliptical domain induces a cascade of bifurcations that can dramatically change the spiral wave evolution. In a square domain a set of point attractors appears instead of the circular resonance attractor typical of a circular domain. These predictions are in good quantitative agreement with numerical integrations of an excitable reaction-diffusion system performed under global feedback.