Characterisation and optimisation of foams for varicose vein sclerotherapy.

BACKGROUND: Foam sclerotherapy is the process of using an aqueous foam to deliver surfactant to a varicose vein to damage vein wall endothelial cells, causing the vein to spasm, collapse and ultimately be re-absorbed into the body. Aqueous foams are complex fluids that can exhibit a significant yield stress and high effective viscosity which depend on their composition, particularly the bubble size and liquid fraction. OBJECTIVE: To characterise the properties of foams used for varicose vein sclerotherapy and determine their effectiveness in the displacement of blood during sclerotherapy. METHODS: Foams are modelled as yield stress fluids and their flow profiles in a model vein are predicted. Values of the yield stress are determined from experimental data for three different foams using the Sauter mean of the bubble size distribution. Along with the measured liquid fraction of the foams, this information is collected into a Bingham number which entirely characterises the process of sclerotherapy. RESULTS: Polydispersity in bubble size has a strong effect on the yield stress of a foam and the Sauter mean of the size distribution better captures the effects of a few large bubbles. Reducing the polydispersity increases the yield stress, and a higher yield stress results in a larger plug region moving along the vein, which is more effective in displacing blood. The width of the plug region is proportional to the Bingham number, which also has a quadratic dependence on the liquid fraction of the foam. Assuming typical values for the rate of injection of a foam, we predict that for a vein of diameter 5 mm, the most effective foams have low liquid fraction, a narrow size distribution, and a Bingham number B ≈ 4.5. CONCLUSIONS: The Sauter mean radius provides the most appropriate measure of the bubble size for sclerotherapy and the Bingham number then provides a simple measure of the efficacy of foam sclerotherapy in a vein of a given size, and explains the ability of different foams to remove varicose veins. Foams containing small bubbles, with a narrow size distribution, and a low liquid fraction are beneficial for sclerotherapy.

Simulation of surfactant transport during the rheological relaxation of two-dimensional dry foams.

We describe a numerical model to predict the rheology of two-dimensional dry foams. The model accurately describes soap film curvature and viscous friction with the walls, and includes the transport of surfactant within the films and across the vertices where films meet. It accommodates the changes in foam topology that occur when a foam flows and, in particular, accurately represents the relaxation of the foam following a topological change. The model is validated against experimental data, allowing the prediction of elastic and viscous parameters associated with different surfactant solutions.

Ideal wet two-dimensional foams and emulsions with finite contact angle.

We present simulations that show that the equilibrium structure of an ideal two-dimensional foam with a finite contact angle develops an inhomogeneity for high liquid fraction φ. In liquid-liquid emulsions this inhomogeneity is known as flocculation. In the case of an ordered foam this requires a perturbation, but in a disordered foam inhomogeneity grows steadily and spontaneously with φ, as demonstrated in our simulations performed with the Surface Evolver.

Curvature driven motion of a bubble in a toroidal Hele-Shaw cell.

We investigate the equilibrium properties of a single area-minimizing bubble trapped between two narrowly separated parallel curved plates. We begin with the case of a bubble trapped between concentric spherical plates. We develop a model which shows that the surface energy of the bubble is lower when confined between spherical plates than between flat plates. We confirm our findings by comparing against Surface Evolver simulations. We then derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the model, we consider a bubble trapped between concentric tori. In the toroidal case, we find that the sensitivity of the bubble's energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature.

Quasicrystalline three-dimensional foams.

We present a numerical study of quasiperiodic foams, in which the bubbles are generated as duals of quasiperiodic Frank-Kasper phases. These foams are investigated as potential candidates to the celebrated Kelvin problem for the partition of three-dimensional space with equal volume bubbles and minimal surface area. Interestingly, one of the computed structures falls close to (but still slightly above) the best known Weaire-Phelan periodic candidate. In addition we find a correlation between the normalized bubble surface area and the root mean squared deviation of the number of faces, giving an additional clue to understanding the main geometrical ingredients driving the Kelvin problem.

Cooperation and punishment in community-structured populations with migration.

The stable presence of punishing strategies in various cooperative species is a persistent puzzle in the study of the evolution of cooperation. To investigate the effect of group competition, we study the evolutionary dynamics of the Public Goods Game with punishment in a metapopulation that consists of separate communities. In addition to (a) well-mixed non-interacting communities, we model three distinct types of interaction between communities, (b) Migration independent of fitness; (c) Competition between whole communities, where entire communities replace each other depending on average fitness; (d) Migration where the probability of an offspring replacing an individual in another community depends on fitness. We use stochastic simulations to study the long-run frequencies of strategies with these interactions, subject to high mutation and migration rates. In cases (a) and (b), the transition between cooperation/punishment and defection regimes occurs for similar parameter values; with migration (b), the transitions are steeper due to higher total mixing. Fitness-based migration (d) by contrast can help support cooperation, changing the locations of transitions, but while group selection (c) does stabilise cooperation over much of the parameter space, fitness-based migration (d) acts as a proxy for group selection only in a smaller region.

Nonequivalence of updating rules in evolutionary games under high mutation rates.

Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model.

Comparative study of non-invasive force and stress inference methods in tissue.

In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. For that purpose, a possible new approach is force inference (up to a single prefactor) from cell shapes and connectivity. It is non-invasive and can provide space-time maps of stress in a whole tissue, unlike existing methods. To validate this approach, three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were compared. Tests using two artificial and two experimental data sets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in different systems of interest is discussed.

The transition from three-dimensional to two-dimensional foam structures.

A two-dimensional foam consists of a monolayer of bubbles. It can be created by squeezing the more familiar three-dimensional foam between two parallel glass plates. We describe and explain the minimum plate separation H which must be reached to fully effect the transition from three- to two- dimensional foam. We find that H/V(1/3) is close to one, where V is the average bubble volume, and increases slightly when the side-walls of the container are taken into account.

Elastoplastic flow of a foam around an obstacle.

We simulate quasistatic flows of an ideal two-dimensional monodisperse foam around different obstacles, both symmetric and asymmetric, in a channel. We record both pressure and network contributions to the drag and lift forces and study them as a function of obstacle geometry. We show that the drag force increases linearly with the cross section of an obstacles. The lift on an asymmetric aerofoil-like shape is negative and increases with its arc length, mainly due to the pressure contribution.

Free-energy-based method for step size detection of processive molecular motors.

We report a free-energy-based algorithm to estimate the step size of processive molecular motors from noisy, experimental time position traces. In our approach, the problem of estimating step sizes reduces to the evaluation of the free energy of directed lattice polymers in a random potential. The present approach is Bayesian in spirit as we do not aim to determine the most likely underlying time trace but rather to determine the step size and stepping frequency that are most likely to yield the observed data. We test this method on synthetic data for the simple case of noisy traces with fixed underlying step size and Poissonian stepping statistics. We find that the present scheme can work at signal-to-noise levels that are about 40% worse than those where the best existing step detection methods fail. More importantly, the present approach yields a much more accurate estimate of the step size. Although we focus on the case of non-reversing walks with a single step size, we show that we can detect if this assumption is violated. In principle, the method can be extended to more complex stepping scenarios but we find that for noisy data, multi-parameter fits are not reliable.

Discrete rearranging disordered patterns: prediction of elastic and plastic behavior, and application to two-dimensional foams.

We study the elasto-plastic behavior of materials made of individual (discrete) objects such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities such as the elastic strain of the structure, the yield strain, and the yield function. The past history of the sample plays no explicit role except through its effect on these statistical quantities. They suffice to relate the discrete scale with the collective global scale. At this global scale, the material behaves as a continuous medium; it is described with tensors such as elastic strain, stress, and velocity gradient. We write the differential equations which predict their elastic and plastic behavior in both the general case and the case of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3. We suggest practical applications including the following: when to choose a scalar formalism rather than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a high, yield strain.

Simulation of defects in bubble clusters.

Topological defects in a foam, either isolated (disclinations and dislocations) or in pairs, affect the energy and stress, and play an important role in foam deformation. Surface evolver simulations were performed on large finite clusters of bubbles. These allow us to evaluate the effect of the topology of the defects, and the distance between defects, on the energy and pressure of foam clusters of different sizes. The energy of such defects follows trends similar to known analytical results for a continuous medium.

The effect of vaccination on undetected persistence of foot-and-mouth disease virus in cattle herds and sheep flocks.

The importance of carrier animals (those in whom virus persists after recovery from disease or acute infection) and their potential role in the spread of disease remain open questions within foot-and-mouth disease epidemiology. Using simple probabilistic models we attempt to quantify the effect of emergency vaccination--and especially the time of application--on the likely number of such animals, using data from challenge experiments on both cattle and sheep to determine the probability of persistence in diseased and subclinically infected animals. We show that the number of persistently infected animals in a group is predominantly determined by the number of animals initially infected on premises--the high variability of which ultimately limits the accuracy of any predictions of carrier numbers based upon transmission models. Furthermore, results suggest that, within a cattle herd, carrier numbers may be increased if challenge occurs shortly after vaccination. We show that the quality of inspection is the principal factor influencing whether or not carrier herds occur and that, by reducing clinical signs, the application of vaccination in regularly checked stock also results in an increase in undetected persistently infected animals. Where clinical detection would be poor regardless of the use of vaccination (i.e. particularly in sheep), vaccination will result in a reduction in the probability of a group containing undetected carriers: otherwise there is a benefit only if vaccination is applied sufficiently far in advance of any challenge. The implications of the results for serosurveillance are discussed, including the requisite test sensitivity and practices for successful implementation.

Theory of surface-potential-mediated photorefractivelike effects in liquid crystals.

We make a phenomenological model of optical two-beam interaction in a model planar liquid crystal cell. The liquid crystal is subject to homeotropic anchoring at the cell walls, is surrounded by thin photosensitive layers, and is subject to a variable potential across the cell. These systems are often known as liquid crystal photorefractive systems. The interference between the two obliquely incident beams causes a time-independent periodic modulation in electric field intensity in the direction transverse to the cell normal. Our model includes this field phenomenologically by supposing an effect on the electric potential at the cell walls. The transverse periodic surface potential causes spatially periodic departures from a pure homeotropic texture. The texture modulation acts as a grating for the incident light. The incident light is both directly transmitted and also subject to diffraction. The lowest order diffracted beams correspond to energy exchange between the beams. We find that the degree of energy exchange can be strongly sensitive to the mean angle of incidence, the angle between the beams, and the imposed potential across the cell. We use the model to speculate about what factors optimize nonlinear optical interaction in liquid crystalline photorefractive systems.

Relationship between job strain and smoking cessation: the Finnish Public Sector Study.

AIMS: To examine whether job strain (ie, excessive demands combined with low control) is related to smoking cessation. METHODS: Prospective cohort study of 4928 Finnish employees who were baseline smokers. In addition to individual scores, coworker-assessed work unit level scores were calculated. A multilevel logistic regression analysis, with work units at the second level, was performed. RESULTS: At follow-up, 21% of baseline smokers had quit smoking. After adjustment for sex, age, employer and marital status, elevated odds ratios (ORs) for smoking cessation were found for the lowest vs the highest quartile of work unit level job strain (OR 1.43, 95% CI 1.17 to 1.75) and for the highest vs the lowest quartile of work unit level job control (OR 1.61, 95% CI 1.31 to 1.96). After additional adjustment for health behaviours and trait anxiety, similar results were observed. Further adjustment for socioeconomic position slightly attenuated these associations, but an additional adjustment for individual strain/control had little effect on the results. The association between job strain and smoking cessation was slightly stronger in light than in moderate/heavy smokers. The results for individual job strain and job control were in the same direction as the work unit models, although these relationships became insignificant after adjustment for socioeconomic position. Job demands were not associated with smoking cessation. CONCLUSIONS: Smoking cessation may be less likely in workplaces with high strain and low control. Policies and programs addressing employee job strain and control might also contribute to the effectiveness of smoking cessation interventions.

Thermographic measurement of the emittance plot of a single positive ion beamlet.

Measurements have been made of the emittance plot of a partly neutralized positive ion beamlet, using a slit, a polymer target, and an infrared camera. This thermographic approach is intrinsically linear and absolute (since the properties of the target are known and approximately independent of temperature). It is sufficiently sensitive that only one short pulse is required to capture the entire range of the angular coordinate y('). Ions and neutral atoms are both detected with equal sensitivity. The measurement is unaffected by secondary electrons emitted by the target and by electrons traveling with the positive ion beam, as both types of electron carry very little energy. No specialized electronics or beam deflection devices are required. Providing the region downstream of the mask is free of fields, the target can be several meters away from the mask, allowing good resolution in the y(') axis. The target can be as large as required.

Simulations of two-dimensional foam rheology: localization in linear Couette flow and the interaction of settling discs.

Surface Evolver simulations of flowing two-dimensional foams are described. These are used for two purposes. Firstly, to extract the location of the T 1s, the changes in bubble topology that occur during plastic flow. It is shown that in linear Couette flow the T1 s are localized in space, becoming more so as the polydispersity of the foam decreases. Secondly, the sedimentation of two circular discs through a foam under gravity is studied. If the discs are sufficiently close, they begin to interact and one moves behind the other during their descent.

Democratization in a passive dendritic tree: an analytical investigation.

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as "dendritic democracy". Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green's representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius.

Modelling studies to estimate the prevalence of foot-and-mouth disease carriers after reactive vaccination.

Foot-and-mouth disease (FMD) is a highly contagious and economically significant viral disease of cloven-hoofed animals. Vaccination can be used to help restrict the spread of the infection, but evidence must be provided to show that the infection has been eradicated in order to regain the FMD-free status. While serological tests have been developed, which can identify animals that have been infected regardless of vaccination status, it is vital to know the probable prevalence of herds with FMD carriers and the within-herd prevalence of those carriers in order to design efficient post-epidemic surveillance strategies that establish freedom from disease. Here, we present the results of a study to model the expected prevalence of carriers after application of emergency vaccination and the impact of this on the sensitivity of test systems for their detection. Results showed that the expected prevalence of carrier-containing herds after reactive vaccination is likely to be very low, approximately 0.2%, and there will only be a small number of carriers, most likely one, in the positive herds. Therefore, sensitivity for carrier detection can be optimized by adopting an individual-based testing regime in which all animals in all vaccinated herds are tested and positive animals rather than herds are culled.