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.

Characterisation of the tritrophic interactions between tobacco yellow dwarf virus, its vector and host-plants

Tobacco yellow dwarf virus (TbYDV, family Geminiviridae, genus Mastrevirus) is an economically important pathogen causing summer death and yellow dwarf disease in bean (Phaseolus vulgaris L.) and tobacco (Nicotiana tabacum L.), respectively. Prior to the commencement of this project, little was known about the epidemiology of TbYDV, its vector and host-plant range. As a result, disease control strategies have been restricted to regular poorly timed insecticide applications which are largely ineffective, environmentally hazardous and expensive. In an effort to address this problem, this PhD project was carried out in order to better understand the epidemiology of TbYDV, to identify its host-plant and vectors as well as to characterise the population dynamics and feeding physiology of the main insect vector and other possible vectors. The host-plants and possible leafhopper vectors of TbYDV were assessed over three consecutive growing seasons at seven field sites in the Ovens Valley, Northeastern Victoria, in commercial tobacco and bean growing properties. Leafhoppers and plants were collected and tested for the presence of TbYDV by PCR. Using sweep nets, twenty-three leafhopper species were identified at the seven sites with Orosius orientalis the predominant leafhopper. Of the 23 leafhopper species screened for TbYDV, only Orosius orientalis and Anzygina zealandica tested positive. Forty-two different plant species were also identified at the seven sites and tested. Of these, TbYDV was only detected in four dicotyledonous species, Amaranthus retroflexus, Phaseolus vulgaris, Nicotiana tabacum and Raphanus raphanistrum. Using a quadrat survey, the temporal distribution and diversity of vegetation at four of the field sites was monitored in order to assess the presence of, and changes in, potential host-plants for the leafhopper vector(s) and the virus. These surveys showed that plant composition and the climatic conditions at each site were the major influences on vector numbers, virus presence and the subsequent occurrence of tobacco yellow dwarf and bean summer death diseases. Forty-two plant species were identified from all sites and it was found that sites with the lowest incidence of disease had the highest proportion of monocotyledonous plants that are non hosts for both vector and the virus. In contrast, the sites with the highest disease incidence had more host-plant species for both vector and virus, and experienced higher temperatures and less rainfall. It is likely that these climatic conditions forced the leafhopper to move into the irrigated commercial tobacco and bean crop resulting in disease. In an attempt to understand leafhopper species diversity and abundance, in and around the field borders of commercially grown tobacco crops, leafhoppers were collected from four field sites using three different sampling techniques, namely pan trap, sticky trap and sweep net. Over 51000 leafhopper samples were collected, which comprised 57 species from 11 subfamilies and 19 tribes. Twentythree leafhopper species were recorded for the first time in Victoria in addition to several economically important pest species of crops other than tobacco and bean. The highest number and greatest diversity of leafhoppers were collected in yellow pan traps follow by sticky trap and sweep nets. Orosius orientalis was found to be the most abundant leafhopper collected from all sites with greatest numbers of this leafhopper also caught using the yellow pan trap. Using the three sampling methods mentioned above, the seasonal distribution and population dynamics of O. orientalis was studied at four field sites over three successive growing seasons. The population dynamics of the leafhopper was characterised by trimodal peaks of activity, occurring in the spring and summer months. Although O. orientalis was present in large numbers early in the growing season (September-October), TbYDV was only detected in these leafhoppers between late November and the end of January. The peak in the detection of TbYDV in O. orientalis correlated with the observation of disease symptoms in tobacco and bean and was also associated with warmer temperatures and lower rainfall. To understand the feeding requirements of Orosius orientalis and to enable screening of potential control agents, a chemically-defined artificial diet (designated PT-07) and feeding system was developed. This novel diet formulation allowed survival for O. orientalis for up to 46 days including complete development from first instar through to adulthood. The effect of three selected plant derived proteins, cowpea trypsin inhibitor (CpTi), Galanthus nivalis agglutinin (GNA) and wheat germ agglutinin (WGA), on leafhopper survival and development was assessed. Both GNA and WGA were shown to reduce leafhopper survival and development significantly when incorporated at a 0.1% (w/v) concentration. In contrast, CpTi at the same concentration did not exhibit significant antimetabolic properties. Based on these results, GNA and WGA are potentially useful antimetabolic agents for expression in genetically modified crops to improve the management of O. orientalis, TbYDV and the other pathogens it vectors. Finally, an electrical penetration graph (EPG) was used to study the feeding behaviour of O. orientalis to provide insights into TbYDV acquisition and transmission. Waveforms representing different feeding activity were acquired by EPG from adult O. orientalis feeding on two plant species, Phaseolus vulgaris and Nicotiana tabacum and a simple sucrose-based artificial diet. Five waveforms (designated O1-O5) were observed when O. orientalis fed on P. vulgaris, while only four (O1-O4) and three (O1-O3) waveforms were observed during feeding on N. tabacum and the artificial diet, respectively. The mean duration of each waveform and the waveform type differed markedly depending on the food source. This is the first detailed study on the tritrophic interactions between TbYDV, its leafhopper vector, O. orientalis, and host-plants. The results of this research have provided important fundamental information which can be used to develop more effective control strategies not only for O. orientalis, but also for TbYDV and other pathogens vectored by the leafhopper.

Broad Bean Mottle Virus: Identification, Serology, Host Range, and Occurrence on Faba Bean (Vicia Faba) in West Asia and Norm Africa

One of the faba bean viruses found in West Asia and North Africa was identified as broad bean mottle virus (BBMV) by host reactions, particle morphology and size, serology, and granular, often vesiculated cytoplasmic inclusions. Detailed research on four isolates, one each from Morocco, Tunisia, Sudan and Syria, provided new information on the virus. The isolates, though indistinguishable in ELISA or gel-diffusion tests, differed slightly in host range and symptoms. Twenty-one species (12 legumes and 9 non-legumes) out of 27 tested were systemically infected, and 14 of these by all four isolates. Infection in several species was symptomless, but major legumes such as chickpea, lentil and especially pea, suffered severely from infection. All 23 genotypes of faba bean, 2 of chickpea, 4 of lentil, 11 out of 21 of Phaseolus bean, and 16 out of 17 of pea were systemically sensitive to the virus. Twelve plant species were found to be new potential hosts and cucumber a new local-lesion test plant of the virus. BBMV particles occurred in faba bean plants in very high concentrations and seed transmission in this species (1.37%) was confirmed. An isolate from Syria was purified and two antisera were produced, one of which was used in ELISA to detect BBMV in faba bean field samples. Two hundred and three out of the 789 samples with symptoms suggestive of virus infection collected in 1985, 1986 and 1987, were found infected with BBMV: 4 out of 70 (4/70) tested samples from Egypt, 0/44 from Lebanon, 1/15 from Morocco, 46/254 from Sudan, 72/269 from Syria and 80/137 from Tunisia. This is the first report on its occurrence in Egypt, Syria and Tunisia. The virus is a potential threat to crop improvement in the region.

Digital processing of diffusion-tensor images of avascular tissues

Diffusion is the process that leads to the mixing of substances as a result of spontaneous and random thermal motion of individual atoms and molecules. It was first detected by the English botanist Robert Brown in 1827, and the phenomenon became known as ‘Brownian motion’. More specifically, the motion observed by Brown was translational diffusion – thermal motion resulting in random variations of the position of a molecule. This type of motion was given a correct theoretical interpretation in 1905 by Albert Einstein, who derived the relationship between temperature, the viscosity of the medium, the size of the diffusing molecule, and its diffusion coefficient. It is translational diffusion that is indirectly observed in MR diffusion-tensor imaging (DTI). The relationship obtained by Einstein provides the physical basis for using translational diffusion to probe the microscopic environment surrounding the molecule.

Diffusion of business improvement processes in manufacturing companies in India

Manufacturing organisations spend more on Business Process Improvement initiatives to make them more competitive in growing global market. This paper presents a Rapid Improvement Workshop (RIW) framework which companies can used to identify the critical factors regulating the diffusion of business process improvement in their company. The framework can then be used address how process improvement can be efficiently implemented. We use the results from case studies at Caterpillar India. The paper identifies the critical factors that contribute to the successful implementation of process improvement programs in manufacturing organisations. We further identify certain technological and cultural barriers to the implementation of process improvement programs and how Indian manufacturing companies can overcome these barriers to attain competitive advantage in the global markets.

Distinguishing forced versus discretionary replacements in new product diffusion models

In many product categories of durable goods such as TV, PC, and DVD player, the largest component of sales is generated by consumers replacing existing units. Aggregate sales models proposed by diffusion of innovation researchers for the replacement component of sales have incorporated several different replacement distributions such as Rayleigh, Weibull, Truncated Normal and Gamma. Although these alternative replacement distributions have been tested using both time series sales data and individual-level actuarial “life-tables” of replacement ages, there is no census on which distributions are more appropriate to model replacement behaviour. In the current study we are motivated to develop a new “modified gamma” distribution by two reasons. First we recognise that replacements have two fundamentally different drivers – those forced by failure and early, discretionary replacements. The replacement distribution for each of these drivers is expected to be quite different. Second, we observed a poor fit of other distributions to out empirical data. We conducted a survey of 8,077 households to empirically examine models of replacement sales for six electronic consumer durables – TVs, VCRs, DVD players, digital cameras, personal and notebook computers. This data allows us to construct individual-level “life-tables” for replacement ages. We demonstrate the new modified gamma model fits the empirical data better than existing models for all six products using both a primary and a hold-out sample.

Electron diffusion and back reaction in dye-sensitized solar cells : the effect of nonlinear recombination kinetics

The electron collection efficiency in dye-sensitized solar cells (DSCs) is usually related to the electron diffusion length, L = (Dτ)^1/2, where D is the diffusion coefficient of mobile electrons and τ is their lifetime, which is determined by electron transfer to the redox electrolyte. Analysis of incident photon-to-current efficiency (IPCE) spectra for front and rear illumination consistently gives smaller values of L than those derived from small amplitude methods. We show that the IPCE analysis is incorrect if recombination is not first-order in free electron concentration, and we demonstrate that the intensity dependence of the apparent L derived by first-order analysis of IPCE measurements and the voltage dependence of L derived from perturbation experiments can be fitted using the same reaction order, γ ≈ 0.8. The new analysis presented in this letter resolves the controversy over why L values derived from small amplitude methods are larger than those obtained from IPCE data.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Drug diffusion from polymeric delivery devices : a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy