Electrical properties of frog skeletal muscle fibers interpreted with a mesh model of the tubular system.

This paper presents the construction, derivation, and test of a mesh model for the electrical properties of the transverse tubular system (T-system) in skeletal muscle. We model the irregular system of tubules as a random network of miniature transmission lines, using differential equations to describe the potential between the nodes and difference equations to describe the potential at the nodes. The solution to the equations can be accurately represented in several approximate forms with simple physical and graphical interpretations. All the parameters of the solution are specified by impedance and morphometric measurements. The effect of wide circumferential spacing between T-system openings is analyzed and the resulting restricted mesh model is shown to be approximated by a mesh with an access resistance. The continuous limit of the mesh model is shown to have the same form as the disk model of the T-system, but with a different expression for the tortuosity factor. The physical meaning of the tortuosity factor is examined, and a short derivation of the disk model is presented that gives results identical to the continuous limit of the mesh model. Both the mesh and restricted mesh models are compared with experimental data on the impedance of muscle fibers of the frog sartorius. The derived value for the resistivity of the lumen of the tubules is not too different from that of the bathing solution, the difference probably arising from the sensitivity of this value to errors in the morphometric measurements.     

Recurrent epidemics in small world networks

The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic susceptible-infective-recovered (SIR) model on complex networks. It was found that in addition to the reduction of the effective transmission rate, through the screening of infectives, spatial correlations have another major effect through the enhancement of stochastic fluctuations, which may become considerably larger than in the homogeneously mixed stochastic model. As a consequence, in finite spatially structured populations significant differences from the solutions of deterministic models are to be expected, since sizes even larger than those found for homogeneously mixed stochastic models are required for the effects of fluctuations to be negligible. Furthermore, time series of the (unforced) model provide patterns of recurrent epidemics with slightly irregular periods and realistic amplitudes, suggesting that stochastic models together with complex networks of contacts may be sufficient to describe the long-term dynamics of some diseases. The spatial effects were analysed quantitatively by modelling measles and pertussis, using a susceptible-exposed-infective-recovered (SEIR) model. Both the period and the spatial coherence of the epidemic peaks of pertussis are well described by the unforced model for realistic values of the parameters.     

Infectious disease modeling of social contagion in networks

Many behavioral phenomena have been found to spread interpersonally through social networks, in a manner similar to infectious diseases. An important difference between social contagion and traditional infectious diseases, however, is that behavioral phenomena can be acquired by non-social mechanisms as well as through social transmission. We introduce a novel theoretical framework for studying these phenomena (the SISa model) by adapting a classic disease model to include the possibility for 'automatic' (or 'spontaneous') non-social infection. We provide an example of the use of this framework by examining the spread of obesity in the Framingham Heart Study Network. The interaction assumptions of the model are validated using longitudinal network transmission data. We find that the current rate of becoming obese is 2 per year and increases by 0.5 percentage points for each obese social contact. The rate of recovering from obesity is 4 per year, and does not depend on the number of non-obese contacts. The model predicts a long-term obesity prevalence of approximately 42, and can be used to evaluate the effect of different interventions on steady-state obesity. Model predictions quantitatively reproduce the actual historical time course for the prevalence of obesity. We find that since the 1970s, the rate of recovery from obesity has remained relatively constant, while the rates of both spontaneous infection and transmission have steadily increased over time. This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, rather than by decreasing rates of losing weight. A key feature of the SISa model is its ability to characterize the relative importance of social transmission by quantitatively comparing rates of spontaneous versus contagious infection. It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs.     

Inhibition of bacterial conjugation by phage M13 and its protein g3p: quantitative analysis and model

Conjugation is the main mode of horizontal gene transfer that spreads antibiotic resistance among bacteria. Strategies for inhibiting conjugation may be useful for preserving the effectiveness of antibiotics and preventing the emergence of bacterial strains with multiple resistances. Filamentous bacteriophages were first observed to inhibit conjugation several decades ago. Here we investigate the mechanism of inhibition and find that the primary effect on conjugation is occlusion of the conjugative pilus by phage particles. This interaction is mediated primarily by phage coat protein g3p, and exogenous addition of the soluble fragment of g3p inhibited conjugation at low nanomolar concentrations. Our data are quantitatively consistent with a simple model in which association between the pili and phage particles or g3p prevents transmission of an F plasmid encoding tetracycline resistance. We also observe a decrease in the donor ability of infected cells, which is quantitatively consistent with a reduction in pili elaboration. Since many antibiotic-resistance factors confer susceptibility to phage infection through expression of conjugative pili (the receptor for filamentous phage), these results suggest that phage may be a source of soluble proteins that slow the spread of antibiotic resistance genes.     

Spreading disease: integro-differential equations old and new

We investigate an integro-differential equation for a disease spread by the dispersal of infectious individuals and compare this to Mollison's [Adv. Appl. Probab. 4 (1972) 233; D. Mollison, The rate of spatial propagation of simple epidemics, in: Proc. 6th Berkeley Symp. on Math. Statist. and Prob., vol. 3, University of California Press, Berkeley, 1972, p. 579; J. R. Statist. Soc. B 39 (3) (1977) 283] model of a disease spread by non-local contacts. For symmetric kernels with moment generating functions, spreading infectives leads to faster traveling waves for low rates of transmission, but to slower traveling waves for high rates of transmission. We approximate the shape of the traveling waves for the two models using both piecewise linearization and a regular-perturbation scheme.     

Modelling environmentally mediated spread of livestock-associated methicillin-resistant Staphylococcus aureus in a pig herd

Infectious disease models are a useful tool to support within-herd disease control strategies. This study presents a stochastic compartment model with environmentally mediated transmission to represent the spread of livestock-associated methicillin-resistant Staphylococcus aureus (LA-MRSA) in a farrow-to-finish pig herd. The aims of the study were to (1) construct a model of the spread of LA-MRSA that included spread of LA-MRSA through the environment; (2) parameterise the model to fit previously published observational data in order to obtain realistic LA-MRSA transmission rates; (3) and to investigate how changes in the mixing of animals in the farrowing and finishing units may affect the prevalence of LA-MRSA in a herd. The results showed that indirect transmission allowed LA-MRSA to persist in the herd without the assumption of persistently shedding individuals. Reducing the mixing of pigs upon entry to the finishing unit was also shown to lower the LA-MRSA prevalence in the unit if the initial LA-MRSA level in the unit was low, but at high prevalence, no effect of mixing was identified. In the farrowing unit, changing the proportion of piglets that were cross-fostered did not affect the within-herd LA-MRSA prevalence. The study demonstrates that there are several important knowledge gaps regarding the shedding and transmission of LA-MRSA in different animal age groups and further experimental studies are needed. This work also provides a new, robust and flexible model framework for the investigation of control and mitigation strategies for LA-MRSA and other infections in a pig herd.     

Mechanotransduction through the cytoskeleton

We constructed a model cytoskeleton to investigate the proposal that this interconnected filamentous structure can act as a mechano- and signal transducer. The model cytoskeleton is composed of rigid rods representing actin filaments, which are connected with springs representing cross-linker molecules. The entire mesh is placed in viscous cytoplasm. The model eukaryotic cell is submitted to either shock wave-like or periodic mechanical perturbations at its membrane. We calculated the efficiency of this network to transmit energy to the nuclear wall as a function of cross-linker stiffness, cytoplasmic viscosity, and external stimulation frequency. We found that the cytoskeleton behaves as a tunable band filter: for given linker molecules, energy transmission peaks in a narrow range of stimulation frequencies. Most of the normal modes of the network are spread over the same frequency range. Outside this range, signals are practically unable to reach their destination. Changing the cellular ratios of linker molecules with different elastic characteristics can control the allowable frequency range and, with it, the efficiency of mechanotransduction.     

Monitoring water reactions during the S-state cycle of the photosynthetic water-oxidizing center: detection of the DOD bending vibrations by means of Fourier transform infrared spectroscopy

Photosynthetic water oxidation takes place in the water-oxidizing center (WOC) of photosystem II (PSII). To clarify the mechanism of water oxidation, detecting water molecules in the WOC and monitoring their reactions at the molecular level are essential. In this study, we have for the first time detected the DOD bending vibrations of functional D 2O molecules during the S-state cycle of the WOC by means of Fourier transform infrared (FTIR) difference spectroscopy. Flash-induced FTIR difference spectra upon S-state transitions were measured using the PSII core complexes from Thermosynechococcus elongatus moderately deuterated with D 2 (16)O and D 2 (18)O. D 2 (16)O-minus-D 2 (18)O double difference spectra at individual S-state transitions exhibited six to eight peaks arising from the D (16)OD/D (18)OD bending vibrations in the 1250-1150 cm (-1) region. This observation indicates that at least two water molecules, not in any deprotonated forms, participate in the reaction at each S-state transition throughout the cycle. Most of the peaks exhibited clear counter peaks with opposite signs at different transitions, reflecting a series of reactions of water molecules at the catalytic site. In contrast, negative bands at approximately 1240 cm (-1) in the S 2 --> S 3, S 3 --> S 0, and possibly S 0 --> S 1 transitions, for which no clear counter peaks were found in other transitions, can be interpreted as insertion of substrate water into the WOC from a water cluster in the proteins. The characteristics of the weakly D-bonded OD stretching bands were consistent with the insertion of substrate from internal water molecules in the S 2 --> S 3 and S 3 --> S 0 transitions. The results of this study show that FTIR detection of the DOD bending vibrations is a powerful method for investigating the molecular mechanism of photosynthetic water oxidation as well as other enzymatic reactions involving functional water molecules.     

Quantitative assessment of the probability of bluetongue virus transmission by bovine semen and effectiveness of preventive measures

Given that bluetongue (BT) may potentially be transmitted by semen, that the disease has significantly expanded in recent years, and that millions of doses of cattle semen are annually traded throughout the world, the transmission of bluetongue virus (BTV) by semen could have severe consequences in the cattle industry. The hypothesis that infected bulls could excrete BTV in their semen led to restrictions on international trade of ruminant semen and the establishment of measures to prevent BTV transmission by semen. However, neither the risk of BTV transmission by semen nor the effectiveness of these measures was estimated quantitatively. The objective of the study was to assess, in case of introduction of BTV into a bovine semen collection centre (SCC), both the risk of BTV transmission by bovine semen and the risk reduction achieved by some of the preventive measures, by means of a stochastic risk assessment model. The model was applied to different scenarios, depending on for example the type of diagnostic test and the interval between the controls (testing) of donor bulls, or the rate of BTV spread within the SCC.Enzyme-linked immunosorbant assay (ELISA) controls of donor bulls every 60 days seemed to be an ineffective method for reducing the risk of BTV transmission in contrast to polymerase chain reaction (PCR) tests every 28 days. An increase in the rate of spread within the SCC resulted in a reduced risk of BTV transmission by semen. The storage of semen for 30 days prior to dispatch seemed to be an efficient way of reducing the risk of transmission by semen.The sensitivity analysis identified the probability of BTV shedding in semen as a crucial parameter in the probability of BTV transmission by semen. However, there is a great degree of uncertainty associated with this parameter, with significant differences depending on the BTV serotype.     

Gel observation chamber for rapid screening of root traits in cereal seedlings

A simple gel chamber is described for measurement of seedling root traits. Seedlings are located between two closely spaced flat layers of transparent gel, on plastic plates (at least one of which is transparent). Root system traits can be non-destructively recorded in two-dimensions using a flatbed scanner. Easily measured rooting traits include root length, elongation rate, longest root, deepest root, seminal root number, and angular spread of roots. Examples of wild, landrace, and cultivated barleys were grown in the gel chambers, between gel layers or in loosely packed soil. Root growth on the gel plates was similar to that in loose soil, with the cultivated barley having the most seminal axes (about 7), and widest angular spread of roots (about 120 °), and wild barley the fewest seminal axes (about 3), and narrowest angular spread of roots (about 40 °). Landrace barley lines tested were intermediate between wild barley and modern cultivars. Separate experiments were performed to study the effect of grain mass and grain size on these rooting traits. These experiments included parents of genetic mapping populations. Seminal root number was most strongly dependent on grain mass in the modern cultivar Chime. Grain size significantly influenced root number in the modern cultivar Derkado, the breeding line B83-12/21/5, and a selection from a landrace Tadmor, suggesting that grain size should be controlled in any screening exercise.     

The global transmission and control of influenza

New strains of influenza spread around the globe via the movement of infected individuals. The global dynamics of influenza are complicated by different patterns of influenza seasonality in different regions of the world. We have released an open-source stochastic mathematical model of the spread of influenza across 321 major, strategically located cities of the world. Influenza is transmitted between cities via infected airline passengers. Seasonality is simulated by increasing the transmissibility in each city at the times of the year when influenza has been observed to be most prevalent. The spatiotemporal spread of pandemic influenza can be understood through clusters of global transmission and links between them, which we identify using the epidemic percolation network (EPN) of the model. We use the model to explain the observed global pattern of spread for pandemic influenza A(H1N1) 2009-2010 (pandemic H1N1 2009) and to examine possible global patterns of spread for future pandemics depending on the origin of pandemic spread, time of year of emergence, and basic reproductive number (). We also use the model to investigate the effectiveness of a plausible global distribution of vaccine for various pandemic scenarios. For pandemic H1N1 2009, we show that the biggest impact of vaccination was in the temperate northern hemisphere. For pandemics starting in the temperate northern hemisphere in May or April, vaccination would have little effect in the temperate southern hemisphere and a small effect in the tropics. With the increasing interconnectedness of the world's population, we must take a global view of infectious disease transmission. Our open-source, computationally simple model can help public health officials plan for the next pandemic as well as deal with interpandemic influenza.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1-L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Alternative Feeding Strategies and Potential Disease Transmission in Wisconsin White-Tailed Deer

ABSTRACT We conducted experimental feeding using 3 feeding methods (pile, spread, trough) and 2 quantities (rationed, ad libitum) of shelled corn to compare deer activity and behavior with control sites and evaluate potential direct and indirect transmission of infectious disease in white-tailed deer (Odocoileus virginianus) in central Wisconsin, USA. Deer use was higher at 2 of the feeding sites than at natural feeding areas (P ≤ 0.02). Deer spent a higher proportion of time (P < 0.01) feeding at pile (49%) and spread (61%) treatments than at natural feeding areas (36%). We found higher deer use for rationed than ad libitum feeding quantities and feeding intensity was greatest at rationed piles and lowest at ad libitum spreads. We also observed closer pairwise distances (≤0.3 m) among deer when corn was provided in a trough relative to spread (P=0.03). Supplemental feeding poses risks for both direct and indirect disease transmission due to higher deer concentration and more intensive use relative to control areas. Concentrated feeding and contact among deer at feeding sites can also increase risk for disease transmission. Our results indicated that restrictions on feeding quantity would not mitigate the potential for disease transmission. None of the feeding strategies we evaluated substantially reduced the potential risk for disease transmission and banning supplemental feeding to reduce transmission is warranted.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

A network control theory approach to modeling and optimal control of zoonoses: case study of brucellosis transmission in sub-Saharan Africa

Background

Developing control policies for zoonotic diseases is challenging, both because of the complex spread dynamics exhibited by these diseases, and because of the need for implementing complex multi-species surveillance and control efforts using limited resources. Mathematical models, and in particular network models, of disease spread are promising as tools for control-policy design, because they can provide comprehensive quantitative representations of disease transmission.

Methodology/Principal Findings

A layered dynamical network model for the transmission and control of zoonotic diseases is introduced as a tool for analyzing disease spread and designing cost-effective surveillance and control. The model development is achieved using brucellosis transmission among wildlife, cattle herds, and human sub-populations in an agricultural system as a case study. Precisely, a model that tracks infection counts in interacting animal herds of multiple species (e.g., cattle herds and groups of wildlife for brucellosis) and in human subpopulations is introduced. The model is then abstracted to a form that permits comprehensive targeted design of multiple control capabilities as well as model identification from data. Next, techniques are developed for such quantitative design of control policies (that are directed to both the animal and human populations), and for model identification from snapshot and time-course data, by drawing on recent results in the network control community.

Conclusions/Significance

The modeling approach is shown to provide quantitative insight into comprehensive control policies for zoonotic diseases, and in turn to permit policy design for mitigation of these diseases. For the brucellosis-transmission example in particular, numerous insights are obtained regarding the optimal distribution of resources among available control capabilities (e.g., vaccination, surveillance and culling, pasteurization of milk) and points in the spread network (e.g., transhumance vs. sedentary herds). In addition, a preliminary identification of the network model for brucellosis is achieved using historical data, and the robustness of the obtained model is demonstrated. As a whole, our results indicate that network modeling can aid in designing control policies for zoonotic diseases.     

Chronic contamination decreases disease spread: a Daphnia-fungus-copper case study

Chemical contamination and disease outbreaks have increased in many ecosystems. However, connecting pollution to disease spread remains difficult, in part, because contaminants can simultaneously exert direct and multi-generational effects on several host and parasite traits. To address these challenges, we parametrized a model using a zooplankton-fungus-copper system. In individual-level assays, we considered three sublethal contamination scenarios: no contamination, single-generation contamination (hosts and parasites exposed only during the assays) and multi-generational contamination (hosts and parasites exposed for several generations prior to and during the assays). Contamination boosted transmission by increasing contact of hosts with parasites. However, it diminished parasite reproduction by reducing the size and lifespan of infected hosts. Multi-generational contamination further reduced parasite reproduction. The parametrized model predicted that a single generation of contamination would enhance disease spread (via enhanced transmission), whereas multi-generational contamination would inhibit epidemics relative to unpolluted conditions (through greatly depressed parasite reproduction). In a population-level experiment, multi-generational contamination reduced the size of experimental epidemics but did not affect Daphnia populations without disease. This result highlights the importance of multi-generational effects for disease dynamics. Such integration of models with experiments can provide predictive power for disease problems in contaminated environments.     

Orientation of mineral in bovine bone and the anisotropic mechanical properties of plexiform bone.

Angular dependent Young's modulus E phi presented by Bonfield and Grynpas [Nature 270, 453-454 (1977)] was simulated by using the distribution function of the orientation of mineral in plexiform bone introduced on the basis of an X-ray pole figure analysis (XPFA) and a small angle X-ray scattering (SAXS) results. Calculations were performed with the aid of a simple model which expresses well the geometrical characteristic of plexiform bone. Estimated angular dependent Young's modulus in terms of the distribution of mineral orientation reproduced the experimental results. The suitable aspect ratio of bone mineral for the reproduction of the empirical data was a reasonable value compared with the morphological study of bone mineral. It is concluded that the angular dependence of mechanical properties of plexiform bone is explained by the distribution of bone mineral orientation and its morphology.     

Impulse Propagation at the Septal and Commissural Junctions of Crayfish Lateral Giant Axons

Transmission across the septal junctions of the segmented giant axons of crayfish is accounted for quantitatively by a simple equivalent circuit. The septal membranes are passive, resistive components and transmission is ephaptic, by the electrotonic spread of the action current of the pre-septal spike. The electrotonic spread appears as a septal potential, considerably smaller than the pre-septal spike, but usually still large enough to initiate a new spike in the post-septal segments. The septal membranes do not exhibit rectification, at least over a range of ± 25 mv polarization and this accounts for their capacity for bidirectional transmission. The commissural branches, which are put forth by each lateral axon, make functional connections between the two axons. Transmission across these junctions can also be bidirectional and is probably also ephaptic. Under various conditions, the ladder-like network of cross-connections formed by the commissural junctions can give rise to circus propagation of impulses from one axon to the other. This can give rise to reverberatory activity of both axons at frequencies as high as 400/sec.     

The effects of different mesh generation methods on computational fluid dynamic analysis and power loss assessment in total cavopulmonary connection

The flow field and energetic efficiency of total cavopulmonary connection (TCPC) models have been studied by both in vitro experiment and computational fluid dynamics (CFD). All the previous CFD studies have employed the structured mesh generation method to create the TCPC simulation model. In this study, a realistic TCPC model with complete anatomical features was numerically simulated using both structured and unstructured mesh generation methods. The flow fields and energy losses were compared in these two meshes. Two different energy loss calculation methods, the control volume and viscous dissipation methods, were investigated. The energy losses were also compared to the in vitro experimental results. The results demonstrated that: (1) the flow fields in the structured model were qualitatively similar to the unstructured model; (2) more vortices were present in the structured model than in the unstructured model; (3) both models had the least energy loss when flow was equally distributed to the left and right pulmonary arteries, while high losses occurred for extreme pulmonary arterial flow splits; (4) the energy loss results calculated using the same method were significantly different for different meshes; and (5) the energy loss results calculated using different methods were significantly different for the same mesh.     

Subject specific finite elasticity simulations of the pelvic floor

An anatomically realistic computational model of the pelvic floor and anal canal regions was used in this study to examine the mechanics of normal defecatory function within the female pelvic floor. This subject specific, MRI-based model enabled mechanical simulations to be performed and quantitatively assessed against experimental data retrieved from the same volunteer. The levator ani muscle group mesh was used as the domain over which the governing equations of finite elasticity were solved using the finite element method with a Mooney-Rivlin material law. Deformation of the levator ani was simulated during a 'bear down' maneuver in order to visualize the way this muscle group functions in an asymptomatic subject. A pressure of 4 kPa was imposed on the mesh and the computed mesh displacements were compared to those obtained from dynamic MR images with an average, experimentally consistent, downwards displacement of 27.2 mm being achieved. The RMS error for this movement was 0.7 mm equating to a percentage error of 2.6% in the supero-inferior direction and 13.7 mm or 74.5% in the antero-posterior direction.