Two dimensional pattern formation in a chemotactic system

Chemotaxis is known to be important in cell aggregation in a variety of contexts. We propose a simple partial differential equation model for a chemotactic system of two species, a population of cells and a chemoattractant to which cells respond. Linear analysis shows that there exists the possibility of spatially inhomogeneous solutions to the model equations for suitable choices of parameters. We solve the full nonlinear steady state equations numerically on a two dimensional rectangular domain. By using mode selection from the linear analysis we produce simple pattern elements such as stripes and regular spots. More complex patterns evolve from these simple solutions as parameter values or domain shape change continuously. An example bifurcation diagram is calculated using the chemotactic response of the cells as the bifurcation parameter. These numerical solutions suggest that a chemotactic mechanism can produce a rich variety of complex patterns

Natural resources inventory and monitoring in Oregon with ERTS imagery

Multidiscipline team interpretation of ERTS satellite and highflight imagery is providing resource and land use information needed for land use planning in Oregon. A coordinated inventory of geology, soil-landscapes, forest and range vegetation, and land use for Crook County, illustrates the value of this approach for broad area and state planning. Other applications include mapping fault zones, inventory of forest clearcut areas, location of forest insect damage, and monitoring irrigation development. Computer classification is being developed for use in conjunction with visual interpretation

Limit cycles in the presence of convection, a travelling wave analysis

We consider a diffusion model with limit cycle reaction functions, in the presence of convection. We select a set of functions derived from a realistic reaction model: the Schnakenberg equations. This resultant form is unsymmetrical. We find a transformation which maps the irregular equations into model form. Next we transform the dependent variables into polar form. From here, a travelling wave analysis is performed on the radial variable. Results are complex, but we make some simple estimates. We carry out numerical experiments to test our analysis. An initial `knock' starts the propagation of pattern. The speed of the travelling wave is not quite as expected. We investigate further. The system demonstrates distinctly different behaviour to the left and the right. We explain how this phenomenon occurs by examining the underlying behaviour.Comment: 20 pages, 5 figure

Modelling spatially regulated B-catenin dynamics & invasion in intestinal crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt

The comparative evaluation of ERTS-1 imagery for resource inventory in land use planning

The author has identified the following significant results. Multidiscipline team interpretation and mapping of resources for Crook County is nearly complete on 1:250,000 scale enlargements of ERTS-1 imagery. Maps of geology, landforms, soils and vegetation-land use are being interpreted to show limitations, suitabilities and geologic hazards for land use planning. Mapping of lineaments and structures from ERTS-1 imagery has shown a number of features not previously mapped in Oregon. A timber inventory of Ochoco National Forest has been made. Inventory of forest clear-cutting practices has been successfully demonstrated with ERTS-1 color composites. Soil tonal differences in fallow fields shown on ERTS-1 correspond with major soil boundaries in loess-mantled terrain. A digital classification system used for discriminating natural vegetation and geologic materials classes has been successful in separation of most major classes around Newberry Cauldera, Mt. Washington and Big Summit Prairie. Computer routines are available for correction of scanner data variations; and for matching scales and coordinates between digital and photographic imagery. Methods of Diazo film color printing of computer classifications and elevation-slope perspective plots with computer are being developed

High resolution nighttime cloud-cover radiometer Quarterly report XVII, 1 Oct. 1965 - 1 Jan. 1966

Electronic, optical, mechanical, and electron packaging component and system design reviews for high resolution cloud cover infrared radiomete

The comparative evaluation of ERTS-1 imagery for resource inventory in land use planning

The author has identified the following significant results. Multidiscipline team interpretation and mapping of resources for Crook County is complete on 1:250,000 scale enlargements of ERTS imagery and 1:120,000 hi-flight photography. Maps of geology, soils, vegetation-land use and land resources units were interpreted to show limitations, suitabilities, and geologic hazards for land use planning. Mapping of lineaments and structures from ERTS imagery has shown a number of features not previously mapped in Oregon. A multistage timber inventory of Ochoco National Forest was made, using ERTS images as the first stage. Inventory of forest clear-cutting practices was successfully demonstrated with color composites. Soil tonal differences in fallow fields correspond with major soil boundaries in loess-mantled terrain. A digital classification system used for discriminating natural vegetation and geologic material classes was successful in separating most major classes around Newberry Caldera, Mt. Washington, and Big Summit Prairie

A mathematical model for fibro-proliferative wound healing disorders

The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsenet al., J. theor. Biol. 177, 113–128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states—a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders

Formation of regular spatial patterns in ratio-dependent predator-prey model driven by spatial colored-noise

Results are reported concerning the formation of spatial patterns in the two-species ratio-dependent predator-prey model driven by spatial colored-noise. The results show that there is a critical value with respect to the intensity of spatial noise for this system when the parameters are in the Turing space, above which the regular spatial patterns appear in two dimensions, but under which there are not regular spatial patterns produced. In particular, we investigate in two-dimensional space the formation of regular spatial patterns with the spatial noise added in the side and the center of the simulation domain, respectively.Comment: 4 pages and 3 figure