Biphasic behaviour in malignant invasion

Invasion is an important facet of malignant growth that enables tumour cells to colonise adjacent regions of normal tissue. Factors known to influence such invasion include the rate at which the tumour cells produce tissue-degrading molecules, or proteases, and the composition of the surrounding tissue matrix. A common feature of experimental studies is the biphasic dependence of the speed at which the tumour cells invade on properties such as protease production rates and the density of the normal tissue. For example, tumour cells may invade dense tissues at the same speed as they invade less dense tissue, with maximal invasion seen for intermediate tissue densities. In this paper, a theoretical model of malignant invasion is developed. The model consists of two coupled partial differential equations describing the behaviour of the tumour cells and the surrounding normal tissue. Numerical methods show that the model exhibits steady travelling wave solutions that are stable and may be smooth or discontinuous. Attention focuses on the more biologically relevant, discontinuous solutions which are characterised by a jump in the tumour cell concentration. The model also reproduces the biphasic dependence of the tumour cell invasion speed on the density of the surrounding normal tissue. We explain how this arises by seeking constant-form travelling wave solutions and applying non-standard phase plane methods to the resulting system of ordinary differential equations. In the phase plane, the system possesses a singular curve. Discontinuous solutions may be constructed by connecting trajectories that pass through particular points on the singular curve and recross it via a shock. For certain parameter values, there are two points at which trajectories may cross the singular curve and, as a result, two distinct discontinuous solutions may arise

Assessing regional variations in groundwater droughts

There is a need for a better understanding of the heterogeneous spatio-temporal response of aquifers to major meteorological droughts. Using a case study from Lincolnshire, UK, this poster describes a method to analyse groundwater level hydrographs and to assess variations in the spatio-temporal response of groundwater systems to meteorological droughts at the regional scale. The methods are equally applicable at larger scales

Evidence for change in the nature of groundwater drought in the UK since 1890

Groundwater is an important source of water for public supply, agricultural irrigation, and industry, as well as sustaining ecological flows to rivers, and it can be affected by drought. Groundwater droughts are characterised by lowered groundwater levels, reduced yields from boreholes, reduced baseflow and shortening of ephemeral streams. Episodes of historic drought are commonly used to benchmark and/or model future groundwater resources and for water resource management and drought planning purposes. Consequently, in order to prepare more effectively for future groundwater droughts, there is a need to better understand groundwater droughts from the recent past and to identify if and how features of groundwater droughts may have changed with time. Here we present the results of a preliminary analysis of the Standardised Groundwater level Index (SGI) for the UKs two longest groundwater level time series from Chilgrove House, Sussex, and Dalton Holme, Yorkshire (top right), to investigate if and how groundwater droughts have changed since the 1890s

Identify the opportunities provided by developments in earth observation and remote sensing for national scale monitoring of soil quality

Defra wish to establish to what extent national-scale soil monitoring (both state and change) of a series of soil indicators might be undertaken by the application of remote sensing methods. Current soil monitoring activities rely on the field-based collection and laboratory analysis of soil samples from across the landscape according to different sampling designs. The use of remote sensing offers the potential to encompass a larger proportion of the landscape, but the signal detected by the remote sensor has to be converted into a meaningful soil measurement which may have considerable uncertainty associated with it. The eleven soil indicators which were considered in this report are pH, organic carbon, bulk density, phosphorus (Olsen P), nitrogen (total N), magnesium (extractable), potassium (extractable), copper (aqua regia extractable), cadmium (aqua regia extractable), zinc (aqua regia extractable) and nickel (aqua regia extractable). However, we also comment on the potential use of remote sensing for monitoring of soil depth and (in particular) peat depth, plus soil erosion and compaction. In assessing the potential of remote sensing methods for soil monitoring of state and change, we addressed the following questions: 1. When will these be ready for use and what level of further development is required? 2. Could remote sensing of any of these indicators replace and/or complement traditional field based national scale soil monitoring? 3. Can meaningful measures of change be derived? 4. How could remote soil monitoring of individual indicators be incorporated into national scale soil monitoring schemes? To address these questions, we undertook a comprehensive literature and internet search and also wrote to a range of international experts in remote sensing. It is important to note that the monitoring of the status of soil indicators, and the monitoring of their change, are two quite different challenges; they are different variables and their variability is likely to differ. There are particular challenges to the application of remote sensing of soil in northern temperate regions (such as England and Wales), including the presence of year-round vegetation cover which means that soil spectral reflectance cannot be captured by airborne or satellite observations, and long-periods of cloud cover which limits the application of satellite-based spectroscopy. We summarise the potential for each of the indicators, grouped where appropriate. Unless otherwise stated, the remote sensing methods would need to be combined with ground-based sampling and analysis to make a contribution to detection of state or change in soil indicators. Soil metals (copper (Cu), cadmium (Cd), zinc (Zn), nickel (Ni)): there is no technical basis for applying current remote sensing approaches to monitor either state or change of these indicators and there are no published studies which have shown how this might be achieved. Soil nutrients: the most promising remote sensing technique to improve estimates of the status of extractable potassium (K) is the collection and application of airborne radiometric survey (detection of gamma radiation by low-flying aircraft) but this should be investigated further. This is unlikely to assist in monitoring change. Based on published literature, it may be possible to enhance mapping the state of extractable magnesium (Mg), but not to monitor change, using hyperspectral (satellite or airborne) remote sensing in cultivated areas. This needs to be investigated further. There are no current remote sensing methods for detecting state or change of Olsen (extractable) phosphorus (P). Organic carbon and total nitrogen: Based on published literature, it may be possible to enhance mapping the state of organic carbon and total nitrogen (but not to monitor change), using hyperspectral (satellite or airborne) remote sensing in cultivated areas only. In applying this approach the satellite data are applied using a statistical model which is trained using ground-based sampling and analysis of soil

Real-time inference of thermotolerant coliforms in groundwater

Enteric pathogens are typically inferred from the presence of cultured surrogate indicator organisms such as thermotolerant coliforms (TTCs). Their analysis requires suitable laboratories, specialist trained personnel, and is time-consuming, which can limit sampling resolution, particularly during critical pollution events. Tryptophan-like fluorescence has been demonstrated as a useful indicator of human influence on freshwater resources due to its association with sewage and farm waste. Following recent developments in field-deployable optical sensor technology, portable tryptophan-like fluorimeters are now commercially available. We demonstrate their real-time applicability at potable urban groundwater supplies in the developing world. We sampled over 100 supplies for TTCs, and traditional surrogates, such as turbidity and nutrients, as well as tryptophan-like fluorescence. The intensity of tryptophan-like fluorescence was the most effective predictor of the presence/absence and number of TTCs. These sensors have the potential to be included in real-time pollution alert systems for drinking water supplies throughout the world, as well as mapping enteric pathogen risks in developing regions

Boundary line models for soil nutrient concentrations and wheat yield in national-scale datasets

In boundary line analysis a biological response (e.g., crop yield) is assumed to be a function of a variable (e.g., soil nutrient concentration), which limits the response in only some subset of observations because other limiting factors also apply. The response function is therefore expressed by an upper boundary of the plot of the response against the variable. This model has been used in various branches of soil science. In this paper we apply it to the analysis of some large datasets, originating from commercial farms in England and Wales, on the recorded yield of wheat and measured concentrations of soil nutrients in within‐field soil management zones. We considered boundary line models for the effects of potassium (K), phosphorus (P) and magnesium (Mg) on yield, comparing the model with a simple bivariate normal distribution or a bivariate normal censored at a constant maximum yield. We were able to show, using likelihood‐based methods, that the boundary line model was preferable in most cases. The boundary line model suggested that the standard RB209 soil nutrient index values (Agriculture and Horticulture Development Board, nutrient management guide (RB209), 2017) are robust and apply at the within‐field scale. However, there was evidence that wheat yield could respond to additional Mg at concentrations above index 0, contrary to RB209 guidelines. Furthermore, there was evidence that the boundary line model for yield and P differs between soils at different pH and depth intervals, suggesting that shallow soils with larger pH require a larger target P index than others

Quantifying uncertainty in predictions of groundwater levels using formal likelihood methods

Informal and formal likelihood methods can be used to quantify uncertainty in modelled predictions of groundwater levels (GWLs). Informal methods use a relatively subjective criterion to identify sets of plausible or behavioural parameters of the GWL models. In contrast, formal methods specify a statistical model for the residuals or errors of the GWL model. The formal uncertainty estimates are only reliable when the assumptions of the statistical model are appropriate. We apply the formal approach to historical reconstructions of GWL hydrographs from four UK boreholes. We test whether a model which assumes Gaussian and independent errors is sufficient to represent the residuals or whether a model which includes temporal autocorrelation and a general non-Gaussian distribution is required. Groundwater level hydrographs are often observed at irregular time intervals so we use geostatistical methods to quantify the temporal autocorrelation rather than more standard time series methods such as autoregressive models. According to the Akaike Information Criterion, the more general statistical model better represents the residuals of the GWL model. However, no substantial difference between the accuracy of the GWL predictions and the estimates of their uncertainty is observed when the two statistical models are compared. When the general model is applied, significant temporal correlation over periods ranging from 3 to 20 months is evident for the different boreholes. When the GWL model parameters are sampled using a Markov Chain Monte Carlo approach the distributions based on the general statistical model differ from those of the Gaussian model, particularly for the boreholes with the most autocorrelation. These results suggest that the independent Gaussian model of residuals is sufficient to estimate the uncertainty of a GWL prediction on a single date. However, if realistically autocorrelated simulations of GWL hydrographs for multiple dates are required or if the distributions of the GWL model parameters are of interest, then the more general statistical model should be used

Assessment of the position accuracy of a single-frequency GPS receiver designed for electromagnetic induction surveys

In precision agriculture (PA), compact and lightweight electromagnetic induction (EMI) sensors have extensively been used to investigate the spatial variability of soil, to evaluate crop performance, and to identify management zones by mapping soil apparent electrical conductivity (ECa), a surrogate for primary and functional soil properties. As reported in the literature, differential global positioning systems (DGPS) with sub-metre to centimetre accuracy have been almost exclusively used to geo-reference these measurements. However, with the ongoing improvements in Global Navigation Satellite System (GNSS) technology, a single state-of-the-art DGPS receiver is likely to be more expensive than the geophysical sensor itself. In addition, survey costs quickly multiply if advanced real time kinematic correction or a base and rover configuration is used. However, the need for centimetre accuracy for surveys supporting PA is questionable as most PA applications are concerned with soil properties at scales above 1 m. The motivation for this study was to assess the position accuracy of a GNSS receiver especially designed for EMI surveys supporting PA applications. Results show that a robust, low-cost and single-frequency receiver is sufficient to geo-reference ECa measurements at the within-field scale. However, ECa data from a field characterized by a high spatial variability of subsurface properties compared to repeated ECa survey maps and remotely sensed leaf area index indicate that a lack of positioning accuracy can constrain the interpretability of such measurements. It is therefore demonstrated how relative and absolute positioning errors can be quantified and corrected. Finally, a summary of practical implications and considerations for the geo-referencing of ECa data using GNSS sensors are presented