Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background: Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model. Results: The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF. Conclusions: Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

Sustainable and profitable grazing management in a highly variable environment-evidence and insights from a long term grazing trial in northern Australia.

Rainfall variability is a major challenge to sustainable management in semi-arid rangelands. We present empirical evidence from a large, long-term grazing trial in northern Australia on the relative performance of constant heavy stocking, moderate stocking at long-term carrying capacity and variable stocking in coping with climate variability over a range of rainfall years. Moderate stocking gave good economic returns, maintained pasture condition and minimised soil loss and runoff. Heavy stocking was neither sustainable nor profitable in the long term. Variable stocking generally performed well but suffered economic loss and some decline in pasture condition in the transition from good to poor years. Importantly, our results show that sustainable and profitable management are compatible in semi-arid rangelands.

Tree growth relationships and silvicultural tools to assist stand management in private native spotted gum dominant forests in Queensland and northern New South Wales.

Spotted gum dominant forests occur from Cooktown in northern Queensland (Qld) to Orbost in Victoria (Boland et al. 2006) and these forests are commercially very important with spotted gum the most commonly harvested hardwood timber in Qld and one of the most important in New South Wales (NSW). Spotted gum has a wide range of end uses from solid wood products through to power transmission poles and generally has excellent sawing and timber qualities (Hopewell 2004). The private native forest resource in southern Qld and northern NSW is a critical component of the hardwood timber industry (Anon 2005, Timber Qld 2006) and currently half or more of the native forest timber resource harvested in northern NSW and Qld is sourced from private land. However, in many cases productivity on private lands is well below what could be achieved with appropriate silvicultural management. This project provides silvicultural management tools to assist extension staff, land owners and managers in the south east Qld and north eastern NSW regions. The intent was that this would lead to improvement of the productivity of the private estate through implementation of appropriate management. The other intention of this project was to implement a number of silvicultural experiments and demonstration sites to provide data on growth rates of managed and unmanaged forests so that landholders can make informed decisions on the future management of their forests. To assist forest managers and improve the ability to predict forest productivity in the private resource, the project has developed: • A set of spotted gum specific silvicultural guidelines for timber production on private land that cover both silvicultural treatment and harvesting. The guidelines were developed for extension officers and property owners. • A simple decision support tool, referred to as the spotted gum productivity assessment tool (SPAT), that allows an estimation of: 1. Tree growth productivity on specific sites. Estimation is based on the analysis of site and growth data collected from a large number of yield and experimental plots on Crown land across a wide range of spotted gum forest types. Growth algorithms were developed using tree growth and site data and the algorithms were used to formulate basic economic predictors. 2. Pasture development under a range of tree stockings and the expected livestock carrying capacity at nominated tree stockings for a particular area. 3. Above-ground tree biomass and carbon stored in trees. •A series of experiments in spotted gum forests on private lands across the study area to quantify growth and to provide measures of the effect of silvicultural thinning and different agro-forestry regimes. The adoption and use of these tools by farm forestry extension officers and private land holders in both field operations and in training exercises will, over time, improve the commercial management of spotted gum forests for both timber and grazing. Future measurement of the experimental sites at ages five, 10 and 15 years will provide longer term data on the effects of various stocking rates and thinning regimes and facilitate modification and improvement of these silvicultural prescriptions.

Objective `Safe' Grazing Capacities for South-West Queensland Australia: Model Application and Evaluation

This paper describes the employment of two experienced graziers as consultants to apply and evaluate a model for calculating 'safe' long-term grazing capacities of individual properties. The model was based on ecological principles and entailed estimates of average annual forage grown (kglha) on the different land systems on each property and the calculation of the number of livestock (dry sheep equivalents, DSE) required to 'safely' utilise this forage. The grazier consultants applied and evaluated the 'safe' grazing capacity model on 20 properties of their choosing. For evaluation, model results were compared with; (a) the Department of Lands rated carrying capacities for those properties and (b) the grazing capacity assessed independently by the owners of those properties. For the 20 properties, the average 'safe' grazing capacity calculated by the model (21.0 DSE/kmZ) was 8% lighter than the average of the owner assessed capacities (22.7 DSE/kmZ), which in tum was 37% lighter than the average of the pre-1989 Department of Lands rated carrying capacity (31.0 DSE/kmZ). The grazing land management and administrative implications of these results and the role graziers played as consultants are discussed.

Wet season resting - economic insights from scenario modelling

Pasture degradation, particularly that attributable to overgrazing, is a significant problem across the northern Australian rangelands. Although grazing studies have identified the scope for wet season resting strategies to be used to rehabilitate degraded pastures, the economic outcome of these strategies has not been extensively demonstrated. An exploratory study of the prospective economic value of wet season resting is presented using an economic simulation model of a 28000 ha beef enterprise located in the Charters Towers region of north-eastern Australia to explore seven hypothetical scenarios centred on the projected performance of a wet season resting strategy. A series of 20-year simulations for a range of pasture recovery profiles, stocking capacity, animal productivity responses, beef prices and agistment options are compared with a baseline scenario of taking no action. Estimates of the net present value of the 20-year difference in total enterprise gross margins between the various resting options and the 'do nothing' option identify that wet season resting can offer a positive economic return for the range of scenarios examined, although this is contingent on the assumptions that are made concerning the trajectories of change in carrying capacity and animal productivity. Some implications for management and policy making to support the practical implementation of wet season resting strategies are discussed.

Enhancing pasture stability and profitability for producers in Poplar Box and Silver-leaved Ironbark woodlands.

Over 7 years, this project collected data about the pasture, tree and soil surface dynamics of two major Aristida/Bothriochloa pasture types within the eucalypt woodlands of central Queensland. Six different grazing management scenarios were compared ecologically and economically, along with the effects of spring burns and tree killing. Heavy stocking (3-4 ha per adult equivalent) produced the greatest short-term financial return from healthy pastures but was not a sustainable practice and long-term cash returns were no better than those from moderate stocking. The environmental benefits of moderate grazing over heavy grazing were very clear. Light stocking produced better environmental outcomes compared to moderate stocking but was clearly inferior with respect to economic returns. Killing silver-leaved ironbark trees near Rubyvale produced no measurable improvement in pasture growth or quality for at least 6 years whereas at Injune the same treatment of poplar box trees resulted in an immediate and large enhancement in pasture production and carrying capacity. The gritty red duplex soil at Rubyvale was much more erodible than the grey solodic at Injune although the latter becomes very erodible if the stable surface soil is breached. Good seasonal rainfall produced faster changes in pasture composition than extremes of grazing management. The perennial grasses were easier to recruit than to eliminate by grazing management changes.

Sustainable management for rangelands in a variable climate: evidence and insights from northern Australia

Inter-annual rainfall variability is a major challenge to sustainable and productive grazing management on rangelands. In Australia, rainfall variability is particularly pronounced and failure to manage appropriately leads to major economic loss and environmental degradation. Recommended strategies to manage sustainably include stocking at long-term carrying capacity (LTCC) or varying stock numbers with forage availability. These strategies are conceptually simple but difficult to implement, given the scale and spatial heterogeneity of grazing properties and the uncertainty of the climate. This paper presents learnings and insights from northern Australia gained from research and modelling on managing for rainfall variability. A method to objectively estimate LTCC in large, heterogeneous paddocks is discussed, and guidelines and tools to tactically adjust stocking rates are presented. The possible use of seasonal climate forecasts (SCF) in management is also considered. Results from a 13-year grazing trial in Queensland show that constant stocking at LTCC was far more profitable and largely maintained land condition compared with heavy stocking (HSR). Variable stocking (VAR) with or without the use of SCF was marginally more profitable, but income variability was greater and land condition poorer than constant stocking at LTCC. Two commercial scale trials in the Northern Territory with breeder cows highlighted the practical difficulties of variable stocking and provided evidence that heavier pasture utilisation rates depress reproductive performance. Simulation modelling across a range of regions in northern Australia also showed a decline in resource condition and profitability under heavy stocking rates. Modelling further suggested that the relative value of variable v. constant stocking depends on stocking rate and land condition. Importantly, variable stocking may possibly allow slightly higher stocking rates without pasture degradation. Enterprise-level simulations run for breeder herds nevertheless show that poor economic performance can occur under constant stocking and even under variable stocking in some circumstances. Modelling and research results both suggest that a form of constrained flexible stocking should be applied to manage for climate variability. Active adaptive management and research will be required as future climate changes make managing for rainfall variability increasingly challenging.

Sustainable grazing management for temporal and spatial variability in north Australian rangelands – a synthesis of the latest evidence and recommendations

Rainfall variability is a major challenge to sustainable grazing management in northern Australia, with management often complicated further by large, spatially-heterogeneous paddocks. This paper presents the latest grazing research and associated bio-economic modelling from northern Australia and assesses the extent to which current recommendations to manage for these issues are supported. Overall, stocking around the safe long-term carrying capacity will maintain land condition and maximise long-term profitability. However, stocking rates should be varied in a risk-averse manner as pasture availability varies between years. Periodic wet-season spelling is also essential to maintain pasture condition and allow recovery of overgrazed areas. Uneven grazing distributions can be partially managed through fencing, providing additional water-points and in some cases patch-burning, although the economics of infrastructure development are extremely context-dependent. Overall, complex multi-paddock grazing systems do not appear justified in northern Australia. Provided the key management principles outlined above are applied in an active, adaptive manner, acceptable economic and environmental outcomes will be achieved irrespective of the grazing system applied.

Managing cattle grazing intensity: effects on soil organic matter and soil nitrogen

Extensive cattle grazing is the dominant land use in northern Australia. It has been suggested that grazing intensity and rainfall have profound effects on the dynamics of soil nutrients in northern Australia’s semi-arid rangelands. Previous studies have found positive, neutral and negative effects of grazing pressure on soil nutrients. These inconsistencies could be due to short-term experiments that do not capture the slow dynamics of some soil nutrients and the effects of interannual variability in rainfall. In a long-term cattle grazing trial in northern Australia on Brown Sodosol–Yellow Kandosol complex, we analysed soil organic matter and mineral nitrogen in surface soils (0–10 cm depth) 11, 12 and 16 years after trial establishment on experimental plots representing moderate stocking (stocked at the long-term carrying capacity for the region) and heavy stocking (stocked at twice the long-term carrying capacity). Higher soil organic matter was found under heavy stocking, although grazing treatment had little effect on mineral and total soil nitrogen. Interannual variability had a large effect on soil mineral nitrogen, but not on soil organic matter, suggesting that soil nitrogen levels observed in this soil complex may be affected by other indirect pathways, such as climate. The effect of interannual variability in rainfall and the effects of other soil types need to be explored further.

Effect of membrane action on the plastic collapse load of circular orthotropic slabs with fixed edges

In the case of reinforced concrete slabs fixed at the boundaries, considerable enhancement in the load carrying capacity takes place due to compressive membrane action. In this paper a method is presented to analyse the effects of membrane action in fixed orthotropic circular slabs, carrying uniformly distributed loads. Depending on the radial moment capacity being greater or less than the circumferential moment capacity, two cases of orthotropy have been considered. Numerical results are worked out for certain assumed physical parameters and for different coefficients of orthotropy. Variations of load and bending moments with the central deflection are presented.

Prediction of fatigue strength in plain and reinforced concrete beams

A fatigue crack propagation model for concrete is proposed based on the concepts of fracture mechanics. This model takes into account the loading history, frequency of applied load, and size, effect parameters. Using this model, a method is described based on linear elastic fracture mechanics to assess the residual strength of cracked plain and reinforced concrete (RC) beams. This could be used to predict the residual strength (load carrying capacity) of cracked or damaged plain and reinforced concrete beams at a given level of damage. It has been seen that the fatigue crack propagation rate increases as. the size of plain concrete, beam increases indicating an increase in brittleness. In reinforced concrete (RC) beams, the fracture process becomes stable only when the beam is sufficiently reinforced.

Limit analysis of rectangular R.C. slabs on ground

A method is presented for obtaining lower bound on the carrying capacity of reinforced concrete foundation slab-structures subject to non-uniform contact pressure distributions. Functional approach suggested by Vallance for simply supported square slabs subject to uniform pressure distribution has been extended to simply supported rectangular slabs subject to symmetrical non-uniform pressure distributions. Radial solutions, ideally suited for rotationally symmetric problems, are shown to be adoptable for regular polygonal slabs subject to contact pressure paraboloids with constant edge pressures. The functional approach has been shown to be well suited even when the pressure is varying along the edges.

Fracture behavior of concrete–concrete interface using acoustic emission technique

The fracture behavior of concrete–concrete interface is characterized using acoustic emission (AE). Beams of different sizes having jointed interface between two different strengths of concrete are tested. The results of load, displacement, CMOD, AE-events and AE-energy are analyzed. The width of fracture process zone and damage zone are computed using AE-data and are found to be independent of size. It is observed that, as the difference in compressive strength of concrete on either side of interface increases, the load carrying capacity, number of AE-events, AE-energy, width of fracture process zone and damage zone decreases.

3-D Warping in Four-Bar Laminated Linkages

This paper deals with the evaluation of the component-laminate load-carrying capacity, i.e., to calculate the loads that cause the failure of the individual layers and the component-laminate as a whole in four-bar mechanism. The component-laminate load-carrying capacity is evaluated using the Tsai-Wu-Hahn failure criterion for various layups. The reserve factor of each ply in the component-laminate is calculated by using the maximum resultant force and the maximum resultant moment occurring at different time steps at the joints of the mechanism. Here, all component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict more quickly and accurately than would otherwise be possible. Local 3-D stress, strain and displacement fields for representative sections in the component-bars are recovered, based on the stress resultants from the 1-D global beam analysis. A numerical example is presented which illustrates the failure of each component-laminate and the mechanism as a whole.

Graphical method to determine the parameters of the two-parameter fracture model for concrete

To evaluate the parameters in the two-parameter fracture model, i.e. the critical stress intensity factor and critical crack tip opening displacement for the fracture of plain concrete in Mode 1 for the given test configuration and geometry, considerable computational effort is necessary. A simple graphical method has been proposed using normalized fracture parameters for the three-point bend (3PB) notched specimen and the double-edged notched (DEN) specimen. A similar graphical method is proposed to compute the maximum load carrying capacity of a specimen, using the critical fracture parameters both for 3PB and DEN configurations.