Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Simplified method for including spatial correlations in mean-field approximations

Biological systems involving proliferation, migration and death are observed across all scales. For example, they govern cellular processes such as wound-healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behaviour. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pair-wise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplication, in the form of a partial differential equation description for the evolution of pair-wise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behaviour in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before, and our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Final report : offsite manufacture in Australia Final report off-site manufacture in Australia

Off-site Manufacture (OSM) has long been recognised, both in Australia and internationally, as offering numerous benefits to all parties in the construction process. More importantly, it is recognised as a key vehicle for driving improvement within the construction industry. The uptake of OSM in construction is however limited, despite well documented benefits. The research aims to determine the ‘state-of-the-art’ of OSM in Australia. It confirms the benefits and identifies the real and perceived barriers to the widespread adoption of OSM. Further the project identifies opportunities for future investment and research. Although numerous reports have been produced in the UK on the state of OSM adoption within that region, no prominent studies exist for the Australian context. This scoping study is an essential component upon which to build any initiatives that can take advantage of the benefits of OSM in construction. The Construction 2020 report predicted that OSM is set to increase in use over the next 5-15 years, further justifying the need for such a study. The long-term goal of this study is to contribute to the improvement of the Australian construction industry through a realisation of the potential benefits of OSM.

Off-site Manufacture in Australia : Current State and Future Directions

Off-site manufacture (OSM) offers numerous benefits to all parties in the construction process. The uptake of OSM in Australia has, however, been limited. This limited uptake corresponds to similar trends in the UK and US, although the level of OSM there appears to be increasing. This project undertook three workshops — one each in Victoria, Queensland and Western Australia — and 18 interviews with key stakeholders to assist in identifying the general benefits and barriers to OSM uptake in the Australian construction industry. Seven case studies were also undertaken, involving construction projects that used OSM, ranging from civil projects through to residential. Each of these case studies has been analysed to identify what worked and what didn’t, and suggest the lessons to be learned from each project.

Drivers constraints and the future of off-site manufacture in Australia.

Much has been written on Off-site Manufacture (OSM) in construction, particularly regarding the perceived benefits and barriers to implementation. However, very little understanding of the state of OSM in the Australian construction industry exists. A ‘scoping study' has recently been undertaken to determine the ‘state-of-the-art’ of OSM in Australia. This involved several industry workshops, interviews and case studies across four major states of Australia. The study surveyed a range of suppliers across the construction supply-chain, incorporating the civil, commercial and housing segments of the market. This revealed that skills shortages and lack of adequate OSM knowledge are generally the greatest issues facing OSM in Australia. The drivers and constraints that emerged from the research were, in large measure, consistent with those found in the US and UK, although some Australian anomalies are evident, such as the geographical disparity of markets. A comparative analysis with similar studies in the UK and US is reported, illustrating both the drivers and constraints confronting the industry in Australia. OSM uptake into the future is however dependent on many factors, not least of which is a better understanding of the construction process and its associated costs.

Site survey and analysis of highway trucks overloading status quo in Anhui

In 2004, with the increasing overloading restriction requirements of society in Anhui, a provincial comprehensive overloading transportation survey has been developed to take evaluations on overloading actuality and enforcement efficiency with the support of the World Bank. A total of six site surveys were conducted at Hefei, Fuyang, Luan, Wuhu, Huainan and Huangshan Areas with four main contents respectively: traffic volume, axle load, freight information and registration information. Via statistical analysis on the survey data, conclusions were gained that: vehicle overloading are very universal and serious problems at arterial highways in Anhui now. The traffic loads have far exceeded the designed endure capacity of highways and have caused prevalent premature pavement damage, especially for rigid pavement. The overloading trucks are unimpeded engaged in highway freight transportation actually due to the disordered overloading enforcement strategies and the deficient inspecting technologies.

The role of sensation seeking and need for cognition on web-site evaluations : a resource-matching perspective

The Internet theoretically enables marketers to personalize a Website to an individual consumer. This article examines optimal Website design from the perspective of personality trait theory and resource-matching theory. The influence of two traits relevant to Internet Web-site processing—sensation seeking and need for cognition— were studied in the context of resource matching and different levels of Web-site complexity. Data were collected at two points of time: personality-trait data and a laboratory experiment using constructed Web sites. Results reveal that (a) subjects prefer Web sites of a medium level of complexity, rather than high or low complexity; (b)high sensation seekers prefer complex visual designs, and low sensation seekers simple visual designs, both in Web sites of medium complexity; and (c) high need-for-cognition subjects evaluated Web sites with high verbal and low visual complexity more favourably.

Spectrometric and voltammetric studies of the interaction between quercetin and bovine serum albumin using warfarin as site marker with the aid of chemometrics

The interaction of quercetin, which is a bioflavonoid, with bovine serum albumin (BSA) was investigated under pseudo-physiological conditions by the application of UV–vis spectrometry, spectrofluorimetry and cyclic voltammetry (CV). These studies indicated a cooperative interaction between the quercetin–BSA complex and warfarin, which produced a ternary complex, quercetin–BSA–warfarin. It was found that both quercetin and warfarin were located in site I. However, the spectra of these three components overlapped and the chemometrics method – multivariate curve resolution-alternating least squares (MCR-ALS) was applied to resolve the spectra. The resolved spectra of quercetin–BSA and warfarin agreed well with their measured spectra, and importantly, the spectrum of the quercetin–BSA–warfarin complex was extracted. These results allowed the rationalization of the behaviour of the overlapping spectra. At lower concentrations ([warfarin] < 1 × 10−5 mol L−1), most of the site marker reacted with the quercetin–BSA, but free warfarin was present at higher concentrations. Interestingly, the ratio between quercetin–BSA and warfarin was found to be 1:2, suggesting a quercetin–BSA–(warfarin)2 complex, and the estimated equilibrium constant was 1.4 × 1011 M−2. The results suggest that at low concentrations, warfarin binds at the high-affinity sites (HAS), while low-affinity binding sites (LAS) are occupied at higher concentrations.