Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Background The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell-to-cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell-to-cell adhesion, despite the fact that cell-to-cell adhesion is thought to play an important role. Results We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, ?, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and ?. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell-to-cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D = 161 - 243 ?m2 hour-1, q = 0.3 - 0.5 (low to moderate strength) and ? = 0.0305 - 0.0398 hour-1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony. Conclusions Our systematic approach to identify the cell diffusivity, cell-to-cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

Development of a computer based 1D-2D dynamic flood model. Case study of the Pagsangaan river basin in Leyte, the Philippines

Floods are among the most devastating events that affect primarily tropical, archipelagic countries such as the Philippines. With the current predictions of climate change set to include rising sea levels, intensification of typhoon strength and a general increase in the mean annual precipitation throughout the Philippines, it has become paramount to prepare for the future so that the increased risk of floods on the country does not translate into more economic and human loss. Field work and data gathering was done within the framework of an internship at the former German Technical Cooperation (GTZ) in cooperation with the Local Government Unit of Ormoc City, Leyte, The Philippines, in order to develop a dynamic computer based flood model for the basin of the Pagsangaan River. To this end, different geo-spatial analysis tools such as PCRaster and ArcGIS, hydrological analysis packages and basic engineering techniques were assessed and implemented. The aim was to develop a dynamic flood model and use the development process to determine the required data, availability and impact on the results as case study for flood early warning systems in the Philippines. The hope is that such projects can help to reduce flood risk by including the results of worst case scenario analyses and current climate change predictions into city planning for municipal development, monitoring strategies and early warning systems. The project was developed using a 1D-2D coupled model in SOBEK (Deltares Hydrological modelling software package) and was also used as a case study to analyze and understand the influence of different factors such as land use, schematization, time step size and tidal variation on the flood characteristics. Several sources of relevant satellite data were compared, such as Digital Elevation Models (DEMs) from ASTER and SRTM data, as well as satellite rainfall data from the GIOVANNI server (NASA) and field gauge data. Different methods were used in the attempt to partially calibrate and validate the model to finally simulate and study two Climate Change scenarios based on scenario A1B predictions. It was observed that large areas currently considered not prone to floods will become low flood risk (0.1-1 m water depth). Furthermore, larger sections of the floodplains upstream of the Lilo- an’s Bridge will become moderate flood risk areas (1 - 2 m water depth). The flood hazard maps created for the development of the present project will be presented to the LGU and the model will be used to create a larger set of possible flood prone areas related to rainfall intensity by GTZ’s Local Disaster Risk Management Department and to study possible improvements to the current early warning system and monitoring of the basin section belonging to Ormoc City; recommendations about further enhancement of the geo-hydro-meteorological data to improve the model’s accuracy mainly on areas of interest will also be presented at the LGU.

Spatial Patterns of Malaria Reported Deaths in Yunnan Province, China

Malaria has been a heavy social and health burden in the remote and poor areas in southern China. Analyses of malaria epidemic patterns can uncover important features of malaria transmission. This study identified spatial clusters, seasonal patterns, and geographic variations of malaria deaths at a county level in Yunnan, China, during 1991–2010. A discrete Poisson model was used to identify purely spatial clusters of malaria deaths. Logistic regression analysis was performed to detect changes in geographic patterns. The results show that malaria mortality had declined in Yunnan over the study period and the most likely spatial clusters (relative risk [RR] = 23.03–32.06, P < 0.001) of malaria deaths were identified in western Yunnan along the China–Myanmar border. The highest risk of malaria deaths occurred in autumn (RR = 58.91, P < 0.001) and summer (RR = 31.91, P < 0.001). The results suggested that the geographic distribution of malaria deaths was significantly changed with longitude, which indicated there was decreased mortality of malaria in eastern areas over the last two decades, although there was no significant change in latitude during the same period. Public health interventions should target populations in western Yunnan along border areas, especially focusing on floating populations crossing international borders.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

An additive model for spatio-temporal smoothing of cancer mortality rates

In this paper, a Bayesian hierarchical model is used to anaylze the female breast cancer mortality rates for the State of Missouri from 1969 through 2001. The logit transformations of the mortality rates are assumed to be linear over the time with additive spatial and age effects as intercepts and slopes. Objective priors of the hierarchical model are explored. The Bayesian estimates are quite robustness in terms change of the hyperparamaters. The spatial correlations are appeared in both intercepts and slopes.

Spatial metaphor as spatial technique in the work of Michel Foucault

This essay argues that the deployment of spatial metaphor in the writing of Michel Foucault is indivisible from his spatial politics. Beginning with his 1967 essay "Of Other Spaces," the development of Foucault's spatial politics and his growing awareness of the importance to his work of spatial (particularly geographic) metaphors can be charted. The focus here is not the concretisation of Foucault's early spatial obsessions—particularly with regard to the concept of "heterotopia"—into a theory or model. Rather, I am concerned with the way in which those obsessions inform Foucault's major works, in particular The Archaeology of Knowledge and Discipline and Punish. These works, I argue, do not develop a theory of space, but instead perform, through their rhetoric, a kind of spatial praxis. In this sense, Foucault's metaphors become "spatial techniques" for the practice and production of power–knowledge.

Spatially-explicit modelling of grassland classes - an improved method of integrating a climate-based classification model with interpolated climate surfaces

Spatially-explicit modelling of grassland classes is important to site-specific planning for improving grassland and environmental management over large areas. In this study, a climate-based grassland classification model, the Comprehensive and Sequential Classification System (CSCS) was integrated with spatially interpolated climate data to classify grassland in Gansu province, China. The study area is characterized by complex topographic features imposed by plateaus, high mountains, basins and deserts. To improve the quality of the interpolated climate data and the quality of the spatial classification over this complex topography, three linear regression methods, namely an analytic method based on multiple regression and residues (AMMRR), a modification of the AMMRR method through adding the effect of slope and aspect to the interpolation analysis (M-AMMRR) and a method which replaces the IDW approach for residue interpolation in M-AMMRR with an ordinary kriging approach (I-AMMRR), for interpolating climate variables were evaluated. The interpolation outcomes from the best interpolation method were then used in the CSCS model to classify the grassland in the study area. Climate variables interpolated included the annual cumulative temperature and annual total precipitation. The results indicated that the AMMRR and M-AMMRR methods generated acceptable climate surfaces but the best model fit and cross validation result were achieved by the I-AMMRR method. Twenty-six grassland classes were classified for the study area. The four grassland vegetation classes that covered more than half of the total study area were "cool temperate-arid temperate zonal semi-desert", "cool temperate-humid forest steppe and deciduous broad-leaved forest", "temperate-extra-arid temperate zonal desert", and "frigid per-humid rain tundra and alpine meadow". The vegetation classification map generated in this study provides spatial information on the locations and extents of the different grassland classes. This information can be used to facilitate government agencies' decision-making in land-use planning and environmental management, and for vegetation and biodiversity conservation. The information can also be used to assist land managers in the estimation of safe carrying capacities which will help to prevent overgrazing and land degradation.

Spatial prediction on a river network

This article develops methods for spatially predicting daily change of dissolved oxygen (Dochange) at both sampled locations (134 freshwater sites in 2002 and 2003) and other locations of interest throughout a river network in South East Queensland, Australia. In order to deal with the relative sparseness of the monitoring locations in comparison to the number of locations where one might want to make predictions, we make a classification of the river and stream locations. We then implement optimal spatial prediction (ordinary and constrained kriging) from geostatistics. Because of their directed-tree structure, rivers and streams offer special challenges. A complete approach to spatial prediction on a river network is given, with special attention paid to environmental exceedances. The methodology is used to produce a map of Dochange predictions for 2003. Dochange is one of the variables measured as part of the Ecosystem Health Monitoring Program conducted within the Moreton Bay Waterways and Catchments Partnership.

Identifying the spatial scale of land use that most strongly influences overall river ecosystem health score

Catchment and riparian degradation has resulted in declining ecosystem health of streams worldwide. With restoration a priority in many regions, there is an increasing interest in the scale at which land use influences stream ecosystem health. Our goal was to use a substantial data set collected as part of a monitoring program (the Southeast Queensland, Australia, Ecological Health Monitoring Program data set, collected at 116 sites over six years) to identify the spatial scale of land use, or the combination of spatial scales, that most strongly influences overall ecosystem health. In addition, we aimed to determine whether the most influential scale differed for different aspects of ecosystem health. We used linear-mixed models and a Bayesian model-averaging approach to generate models for the overall aggregated ecosystem health score and for each of the five component indicators (fish, macroinvertebrates, water quality, nutrients, and ecosystem processes) that make up the score. Dense forest close to the survey site, mid-dense forest in the hydrologically active nearstream areas of the catchment, urbanization in the riparian buffer, and tree cover at the reach scale were all significant in explaining ecosystem health, suggesting an overriding influence of forest cover, particularly close to the stream. Season and antecedent rainfall were also important explanatory variables, with some land-use variables showing significant seasonal interactions. There were also differential influences of land use for each of the component indicators. Our approach is useful given that restoring general ecosystem health is the focus of many stream restoration projects; it allowed us to predict the scale and catchment position of restoration that would result in the greatest improvement of ecosystem health in the regions streams and rivers. The models we generated suggested that good ecosystem health can be maintained in catchments where 80% of hydrologically active areas in close proximity to the stream have mid-dense forest cover and moderate health can be obtained with 60% cover.

A model of a large-area planar plasma producer based on surface wave propagation in a plasma-metal structure with a dielectric sheath

A theoretical model of a large-area planar plasma producer based on surface wave (SW) propagation in a plasma-metal structure with a dielectric sheath is presented. The SW which produces and sustains the microwave gas discharge in the planar structure propagates along an external magnetic field and possesses an eigenfrequency within the range between electron cyclotron and electron plasma frequencies. The spatial distributions of the produced plasma density, electromagnetic fields, energy flow density, phase velocity and reverse skin depth of the SW are obtained analytically and numerically.

A kinetic model for an argon plasma containing dust grains

A complex low-pressure argon discharge plasma containing dust grains is studied using a Boltzmann equation for the electrons and fluid equations for the ions. Local effects, such as the spatial distribution of the dust density and external electric field, are included, and their effect on the electron energy distribution, the electron and ion number densities, the electron temperature, and the dust charge are investigated. It is found that dust particles can strongly affect the plasma parameters by modifying the electron energy distribution, the electron temperature, the creation and loss of plasma particles, as well as the spatial distributions of the electrons and ions. In particular, for sufficiently high grain density and/or size, in a low-pressure argon glow discharge, the Druyvesteyn-like electron distribution in pristine plasmas can become nearly Maxwellian. Electron collection by the dust grains is the main cause for the change in the electron distribution function.

A hierarchical model of goal directed navigation selects trajectories in a visual environment

We have developed a Hierarchical Look-Ahead Trajectory Model (HiLAM) that incorporates the firing pattern of medial entorhinal grid cells in a planning circuit that includes interactions with hippocampus and prefrontal cortex. We show the model’s flexibility in representing large real world environments using odometry information obtained from challenging video sequences. We acquire the visual data from a camera mounted on a small tele-operated vehicle. The camera has a panoramic field of view with its focal point approximately 5 cm above the ground level, similar to what would be expected from a rat’s point of view. Using established algorithms for calculating perceptual speed from the apparent rate of visual change over time, we generate raw dead reckoning information which loses spatial fidelity over time due to error accumulation. We rectify the loss of fidelity by exploiting the loop-closure detection ability of a biologically inspired, robot navigation model termed RatSLAM. The rectified motion information serves as a velocity input to the HiLAM to encode the environment in the form of grid cell and place cell maps. Finally, we show goal directed path planning results of HiLAM in two different environments, an indoor square maze used in rodent experiments and an outdoor arena more than two orders of magnitude larger than the indoor maze. Together these results bridge for the first time the gap between higher fidelity bio-inspired navigation models (HiLAM) and more abstracted but highly functional bio-inspired robotic mapping systems (RatSLAM), and move from simulated environments into real-world studies in rodent-sized arenas and beyond.

An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach -- the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the SLA-based and grid-based approaches perform equally well for spatially dense data.

The choice of spatial scales and spatial smoothness priors for various spatial patterns

Given the drawbacks for using geo-political areas in mapping outcomes unrelated to geo-politics, a compromise is to aggregate and analyse data at the grid level. This has the advantage of allowing spatial smoothing and modelling at a biologically or physically relevant scale. This article addresses two consequent issues: the choice of the spatial smoothness prior and the scale of the grid. Firstly, we describe several spatial smoothness priors applicable for grid data and discuss the contexts in which these priors can be employed based on different aims. Two such aims are considered, i.e., to identify regions with clustering and to model spatial dependence in the data. Secondly, the choice of the grid size is shown to depend largely on the spatial patterns. We present a guide on the selection of spatial scales and smoothness priors for various point patterns based on the two aims for spatial smoothing.