A structural model for the in vivo human cornea including collagen-swelling interaction

A structural model of the in vivo cornea, which accounts for tissue swelling behaviour, for the three-dimensional organization of stromal fibres and for collagen-swelling interaction, is proposed. Modelled as a binary electrolyte gel in thermodynamic equilibrium, the stromal electrostatic free energy is based on the mean-field approximation. To account for active endothelial ionic transport in the in vivo cornea, which modulates osmotic pressure and hydration, stromal mobile ions are shown to satisfy a modified Boltzmann distribution. The elasticity of the stromal collagen network is modelled based on three-dimensional collagen orientation probability distributions for every point in the stroma obtained by synthesizing X-ray diffraction data for azimuthal angle distributions and second harmonic-generated image processing for inclination angle distributions. The model is implemented in a finite-element framework and employed to predict free and confined swelling of stroma in an ionic bath. For the in vivo cornea, the model is used to predict corneal swelling due to increasing intraocular pressure (IOP) and is adapted to model swelling in Fuchs'' corneal dystrophy. The biomechanical response of the in vivo cornea to a typical LASIK surgery for myopia is analysed, including tissue fluid pressure and swelling responses. The model provides a new interpretation of the corneal active hydration control (pump-leak) mechanism based on osmotic pressure modulation. The results also illustrate the structural necessity of fibre inclination in stabilizing the corneal refractive surface with respect to changes in tissue hydration and IOP.     

Characterization of age-related variation in corneal biomechanical properties

An experimental study has been conducted to determine the stress–strain behaviour of human corneal tissue and how the behaviour varies with age. Fifty-seven well-preserved ex vivo donor corneas aged between 30 and 99 years were subjected to cycles of posterior pressure up to 60 mm Hg while monitoring their behaviour. The corneas were mechanically clamped along their ring of scleral tissue and kept in physiological conditions of temperature and hydration. The tissue demonstrated hyper-elastic pressure-deformation and stress–strain behaviour that closely matched an exponential trend. Clear stiffening (increased resistance to deformation) with age was observed in all loading cycles, and the rate of stiffness growth was nonlinear with bias towards older specimens. With a strong statistical association between stiffness and age (p < 0.05), it was possible to develop generic stress–strain equations that were suitable for all ages between 30 and 99 years. These equations, which closely matched the experimental results, depicted corneal stiffening with age in a form suitable for implementation in numerical simulations of ocular biomechanical behaviour.     

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke.     

Modelling cholera epidemics: the role of waterways,human mobility and sanitation

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000–2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.     

Time and dose-dependent risk of pneumococcal pneumonia following influenza: a model for within-host interaction between influenza and Streptococcus pneumoniae

A significant fraction of seasonal and in particular pandemic influenza deaths are attributed to secondary bacterial infections. In animal models, influenza virus predisposes hosts to severe infection with both Streptococcus pneumoniae and Staphylococcus aureus. Despite its importance, the mechanistic nature of the interaction between influenza and pneumococci, its dependence on the timing and sequence of infections as well as the clinical and epidemiological consequences remain unclear. We explore an immune-mediated model of the viral–bacterial interaction that quantifies the timing and the intensity of the interaction. Taking advantage of the wealth of knowledge gained from animal models, and the quantitative understanding of the kinetics of pathogen-specific immunological dynamics, we formulate a mathematical model for immune-mediated interaction between influenza virus and S. pneumoniae in the lungs. We use the model to examine the pathogenic effect of inoculum size and timing of pneumococcal invasion relative to influenza infection, as well as the efficacy of antivirals in preventing severe pneumococcal disease. We find that our model is able to capture the key features of the interaction observed in animal experiments. The model predicts that introduction of pneumococcal bacteria during a 4–6 day window following influenza infection results in invasive pneumonia at significantly lower inoculum size than in hosts not infected with influenza. Furthermore, we find that antiviral treatment administered later than 4 days after influenza infection was not able to prevent invasive pneumococcal disease. This work provides a quantitative framework to study interactions between influenza and pneumococci and has the potential to accurately quantify the interactions. Such quantitative understanding can form a basis for effective clinical care, public health policies and pandemic preparedness.     

Analysis of self-overlap reveals trade-offs in plankton swimming trajectories

Movement is a fundamental behaviour of organisms that not only brings about beneficial encounters with resources and mates, but also at the same time exposes the organism to dangerous encounters with predators. The movement patterns adopted by organisms should reflect a balance between these contrasting processes. This trade-off can be hypothesized as being evident in the behaviour of plankton, which inhabit a dilute three-dimensional environment with few refuges or orienting landmarks. We present an analysis of the swimming path geometries based on a volumetric Monte Carlo sampling approach, which is particularly adept at revealing such trade-offs by measuring the self-overlap of the trajectories. Application of this method to experimentally measured trajectories reveals that swimming patterns in copepods are shaped to efficiently explore volumes at small scales, while achieving a large overlap at larger scales. Regularities in the observed trajectories make the transition between these two regimes always sharper than in randomized trajectories or as predicted by random walk theory. Thus, real trajectories present a stronger separation between exploration for food and exposure to predators. The specific scale and features of this transition depend on species, gender and local environmental conditions, pointing at adaptation to state and stage-dependent evolutionary trade-offs.     

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological ‘four-fibre family’ constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.     

Modelling the emergence of polarity patterns for the intercellular transport of auxin in plants

The hormone auxin is actively transported throughout plants via protein machineries including the dedicated transporter known as PIN. The associated transport is ordered with nearby cells driving auxin flux in similar directions. Here, we provide a model of both the auxin transport and of the dynamics of cellular polarization based on flux sensing. Our main findings are: (i) spontaneous intracellular PIN polarization arises if PIN recycling dynamics are sufficiently nonlinear, (ii) there is no need for an auxin concentration gradient and (iii) ordered multi-cellular patterns of PIN polarization are favoured by molecular noise.     

Modelling the dynamics of viral suppressors of RNA silencing

Virus infection in plants is limited by RNA silencing. In turn, viruses can counter RNA silencing with silencing suppressors. Viral suppressors of RNA silencing have been shown to play a role in symptom development in plants. We here study four different strategies employed by silencing suppressors: small interfering RNA (siRNA) binding, double-strand RNA (dsRNA) binding and degrading or inactivating Argonaute. We study the effect of the suppressors on viral accumulation within the cell as well as its spread on a tissue with mathematical and computational models. We find that suppressors which target Argonaute are very effective in a single cell, but that targeting dsRNA or siRNA is much more effective at the tissue level. Although targeting Argonaute can be beneficial for viral spread, it can also cause hindrance in some cases owing to raised levels of siRNAs that can spread to other cells.     

Alkoxide-based precursors for direct drawing of metal oxide micro- and nanofibres

The invention of electrospinning has solved the problem of producing micro- and nanoscaled metal oxide fibres in bulk quantities. However, until now no methods have been available for preparing a single nanofibre of a metal oxide. In this work, the direct drawing method was successfully applied to produce metal oxide (SnO₂, TiO₂, ZrO₂, HfO₂ and CeO₂) fibres with a high aspect ratio (up to 10 000) and a diameter as small as 200 nm. The sol–gel processing includes consumption of precursors obtained from alkoxides by aqueous or non-aqueous polymerization. Shear thinning of the precursors enables pulling a material into a fibre. This rheological behaviour can be explained by sliding of particles owing to external forces. Transmission (propagation) of light along microscaled fibres and their excellent surface morphology suggest that metal oxide nanofibres can be directly drawn from sol precursors for use in integrated photonic systems.     

Spatial heterogeneity enhances and modulates excitability in a mathematical model of the myometrium

The muscular layer of the uterus (myometrium) undergoes profound changes in global excitability prior to parturition. Here, a mathematical model of the myocyte network is developed to investigate the hypothesis that spatial heterogeneity is essential to the transition from local to global excitation which the myometrium undergoes just prior to birth. Each myometrial smooth muscle cell is represented by an element with FitzHugh–Nagumo dynamics. The cells are coupled through resistors that represent gap junctions. Spatial heterogeneity is introduced by means of stochastic variation in coupling strengths, with parameters derived from physiological data. Numerical simulations indicate that even modest increases in the heterogeneity of the system can amplify the ability of locally applied stimuli to elicit global excitation. Moreover, in networks driven by a pacemaker cell, global oscillations of excitation are impeded in fully connected and strongly coupled networks. The ability of a locally stimulated cell or pacemaker cell to excite the network is shown to be strongly dependent on the local spatial correlation structure of the couplings. In summary, spatial heterogeneity is a key factor in enhancing and modulating global excitability.     

A novel in vivo method for quantifying the interfacial biochemical bond strength of bone implants

Quantifying the in vivo interfacial biochemical bond strength of bone implants is a biological challenge. We have developed a new and novel in vivo method to identify an interfacial biochemical bond in bone implants and to measure its bonding strength. This method, named biochemical bond measurement (BBM), involves a combination of the implant devices to measure true interfacial bond strength and surface property controls, and thus enables the contributions of mechanical interlocking and biochemical bonding to be distinguished from the measured strength values. We applied the BBM method to a rabbit model, and observed great differences in bone integration between the oxygen (control group) and magnesium (test group) plasma immersion ion-implanted titanium implants (0.046 versus 0.086 MPa, n=10, p=0.005). The biochemical bond in the test implants resulted in superior interfacial behaviour of the implants to bone: (i) close contact to approximately 2 μm thin amorphous interfacial tissue, (ii) pronounced mineralization of the interfacial tissue, (iii) rapid bone healing in contact, and (iv) strong integration to bone. The BBM method can be applied to in vivo experimental models not only to validate the presence of a biochemical bond at the bone–implant interface but also to measure the relative quantity of biochemical bond strength. The present study may provide new avenues for better understanding the role of a biochemical bond involved in the integration of bone implants.     

Is there the potential for an epidemic of variant Creutzfeldt–Jakob disease via blood transfusion in the UK?

The discovery of three individuals suspected to have contracted variant Creutzfeldt-Jakob disease (vCJD) through blood transfusions has heightened concerns that a secondary epidemic via human-to-human transmission could occur in the UK. The Department of Health responded immediately to this threat by banning those who had received blood transfusions since 1980 from donating blood. In this paper, we conduct a sensitivity analysis to explore the potential size of a blood-borne vCJD epidemic and investigate the effectiveness of public health interventions. A mathematical model was developed together with an expression for the basic reproduction number (R0). The sensitivity of model predictions to unknown parameters determining the transmission of vCJD via infected blood was assessed under pessimistic modelling assumptions. We found that the size of the epidemic (up until 2080) was bounded above by 900 cases, with self-sustaining epidemics (R0>1) also possible; but the scenarios under which such epidemics could arise were found to be biologically implausible. Under optimistic assumptions, public health interventions reduced the upper bound to 250 and further still when only biologically plausible scenarios were considered. Our results support the belief that scenarios leading to large or self-sustaining epidemics are possible but unlikely, and that public health interventions were effective.     

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.     

Cerebrospinal fluid dynamics in the human cranial subarachnoid space: an overlooked mediator of cerebral disease. I. Computational model

Abnormal cerebrospinal fluid (CSF) flow is suspected to be a contributor to the pathogenesis of neurodegenerative diseases such as Alzheimer''s through the accumulation of toxic metabolites, and to the malfunction of intracranial pressure regulation, possibly through disruption of neuroendocrine communication. For the understanding of transport processes involved in either, knowledge of in vivo CSF dynamics is important. We present a three-dimensional, transient, subject-specific computational analysis of CSF flow in the human cranial subarachnoid space (SAS) based on in vivo magnetic resonance imaging. We observed large variations in the spatial distribution of flow velocities with a temporal peak of 5 cm s⁻¹ in the anterior SAS and less than 4 mm s⁻¹ in the superior part. This could reflect dissimilar flushing requirements of brain areas that may show differences in susceptibility to pathological CSF flow. Our methods can be used to compare the transport of metabolites and neuroendocrine substances in healthy and diseased brains.     

Two Coils Resonant Ramsey’s Method for the Measurement of Time Reversal Invariance Violation in Neutron Transmission

It is proposed within the framework of Ramsey’s method to register two-dimensional spectra, depending on the neutron phase and neutron energy, for measuring parity (P) and time (T) violating amplitudes of the interaction of polarized neutrons with polarized ¹³⁹La nuclei in region of the p-wave resonance. The form of the phase spectrum and corresponding expressions for the asymmetries are obtained on the basis of a formalism of a spin density matrix. It is shown that the ratio of the P,T,-violating to P-violating imaginary amplitudes can be obtained from the measurements of the neutron phase spectrum with polarized and unpolarized ¹³⁹La target.     

Cerebrospinal fluid dynamics in the human cranial subarachnoid space: an overlooked mediator of cerebral disease. II. In vitro arachnoid outflow model

The arachnoid membrane (AM) and granulations (AGs) are important in cerebrospinal fluid (CSF) homeostasis, regulating intracranial pressure in health and disease. We offer a functional perspective of the human AM''s transport mechanism to clarify the role of AM in the movement of CSF and metabolites. Using cultures of human AG cells and a specialized perfusion system, we have shown that this in vitro model mimics the in vivo characteristics of unidirectional fluid transport and we present the first report of serum-free permeability values (92.5 µl min⁻¹ mm Hg⁻¹ cm⁻²), which in turn are in agreement with the CSF outflow rates derived from a dynamic, in vivo magnetic resonance imaging-based computational model of the subarachnoid cranial space (130.9 µl min⁻¹ mm Hg⁻¹ cm⁻²). Lucifer yellow permeability experiments have verified the maintenance of tight junctions by the arachnoidal cells with a peak occurring around 21 days post-seeding, which is when all perfusion experiments were conducted. Addition of ruthenium red to the perfusate, and subsequent analysis of its distribution post-perfusion, has verified the passage of perfusate via both paracellular and transcellular mechanisms with intracellular vacuoles of approximately 1 µm in diameter being the predominant transport mechanism. The comparison of the computational and in vitro models is the first report to measure human CSF dynamics functionally and structurally, enabling the development of innovative approaches to modify CSF outflow and will change concepts and management of neurodegenerative diseases resulting from CSF stagnation.