186 research outputs found
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
Pattern formation in a generalised chemotactic model
Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development
Macrophage anti-inflammatory behaviour in a multiphase model of atherosclerotic plaque development
Atherosclerosis is an inflammatory disease characterised by the formation of plaques, which are deposits of lipids and cholesterol-laden macrophages that form in the artery wall. The inflammation is often non-resolving, due in large part to changes in normal macrophage anti-inflammatory behaviour that are induced by the toxic plaque microenvironment. These changes include higher death rates, defective efferocytic uptake of dead cells, and reduced rates of emigration. We develop a free boundary multiphase model for early atherosclerotic plaques, and we use it to investigate the effects of impaired macrophage anti-inflammatory behaviour on plaque structure and growth. We find that high rates of cell death relative to efferocytic uptake results in a plaque populated mostly by dead cells. We also find that emigration can potentially slow or halt plaque growth by allowing material to exit the plaque, but this is contingent on the availability of live macrophage foam cells in the deep plaque. Finally, we introduce an additional bead species to model macrophage tagging via microspheres, and we use the extended model to explore how high rates of cell death and low rates of efferocytosis and emigration prevent the clearance of macrophages from the plaque
Sport in the city: measuring economic significance at the local level
In many cities throughout Europe, sport is increasingly being used as a tool for economic revitalisation. While there has been a growth in literature relating to the specific economic impacts of sports-led development, including professional sport facilities, teams, and sport events, limited research has been undertaken on the contribution of the whole sport sector to output and employment. In the United Kingdom (UK), studies have focused on evaluating sport-related economic activity at the national level, yet despite the increasing use of sport for local economic development little research has been undertaken at the city level. To address this situation, this article uses the National Income Accounting framework to measure the economic importance of sport in Sheffield, UK. It shows that the value-added in 1996/97 was 165.61m or 4.11% of Gross Domestic Product (GDP), approximately twice the amount predicted from current national estimates. It is argued that this can primarily be explained by previous studies under-estimating the economic importance of sport, largely due to methodological differences. It goes on to suggest that future research on the significance of sport should be undertaken at the local level to provide policymakers with information at the spatial level where regeneration programmes are being implemented.</p
A Two-Phase Model of Early Fibrous Cap Formation in Atherosclerosis
Atherosclerotic plaque growth is characterised by chronic inflammation that
promotes accumulation of cellular debris and extracellular fat in the inner
artery wall. This material is highly thrombogenic, and plaque rupture can lead
to the formation of blood clots that occlude major arteries and cause
myocardial infarction or stroke. In advanced plaques, vascular smooth muscle
cells (SMCs) migrate from deeper in the artery wall to synthesise a cap of
fibrous tissue that stabilises the plaque and sequesters the thrombogenic
plaque content from the bloodstream. The fibrous cap provides crucial
protection against the clinical consequences of atherosclerosis, but the
mechanisms of cap formation are poorly understood. In particular, it is unclear
why certain plaques become stable and robust while others become fragile and
vulnerable to rupture.
We develop a multiphase model with non-standard boundary conditions to
investigate early fibrous cap formation in the atherosclerotic plaque. The
model is parameterised using a range of in vitro and in vivo data, and includes
highly nonlinear mechanisms of SMC proliferation and migration in response to
an endothelium-derived chemical signal. We demonstrate that the model SMC
population naturally evolves towards a steady-state, and predict a rate of cap
formation and a final plaque SMC content consistent with experimental
observations in mice. Parameter sensitivity simulations show that SMC
proliferation makes a limited contribution to cap formation, and highlight that
stable cap formation relies on a critical balance between SMC recruitment to
the plaque, SMC migration within the plaque and SMC loss by apoptosis. The
model represents the first detailed in silico study of fibrous cap formation in
atherosclerosis, and establishes a multiphase modelling framework that can be
readily extended to investigate many other aspects of plaque development
A Multiphase Model of Growth Factor-Regulated Atherosclerotic Cap Formation
Atherosclerosis is characterised by the growth of fatty plaques in the inner
(intimal) layer of the artery wall. In mature plaques, vascular smooth muscle
cells (SMCs) are recruited from the adjacent medial layer to deposit a cap of
fibrous collagen over the fatty plaque core. The fibrous cap isolates the
thrombogenic content of the plaque from the bloodstream and prevents the
formation of blood clots that cause myocardial infarction or stroke. Despite
the important protective role of the cap, the mechanisms that regulate cap
formation and maintenance are not well understood. It remains unclear why
certain caps become stable, while others become vulnerable to rupture. We
develop a multiphase PDE model with non-standard boundary conditions to
investigate collagen cap formation by SMCs in response to growth factor signals
from the endothelium. Diffusible platelet-derived growth factor (PDGF)
stimulates SMC migration, proliferation and collagen degradation, while
diffusible transforming growth factor (TGF)- stimulates SMC collagen
synthesis and inhibits collagen degradation. The model SMCs respond
haptotactically to gradients in the collagen phase and have reduced rates of
migration and proliferation in dense collagenous tissue. The model, which is
parameterised using a range of in vivo and in vitro experimental data,
reproduces several observations from studies of plaque growth in
atherosclerosis-prone mice. Numerical simulations and model analysis
demonstrate that a stable cap can be formed by a relatively small SMC
population and emphasise the critical role of TGF- in effective cap
formation and maintenance. These findings provide unique insight into the
cellular and biochemical mechanisms that may lead to plaque destabilisation and
rupture. This work represents an important step towards the development of a
comprehensive in silico plaque
Bifurcating spatial patterns in a cell-chemotaxis model
Spatial pattern formation is a key issue in early embroynic development. Embroynic cells divide, migrate, and differentiate to form the various structures, markings and organs of the body. Perhaps the most spectacular manifestation of this process is animal coat markings. These patterns are formed by melanin-secreting cells which migrate from the neural crest to the epidermal and dermal layers of the skin
Modeling the spectrum of V4334 Sgr (Sakurai's Object)
Theoretical spectral energy distributions were computed for a grid of
hydrogen-deficient and carbon-rich model atmospheres of T(eff) in the range of
5000-6250 K and log g = 1.0 - 0.0 by the technique of opacity sampling, taking
into account continuous, molecular band and atomic line absorption. These
energy distributions were compared with the spectrum of V4334 Sgr (Sakurai's
object) of April, 1997 in the wavelength interval 300-1000 nm. We show that (1)
the shape of the theoretical spectra depends strongly on T(eff) but only very
weakly on the hydrogen abundance; (2) the comparison of the observed and
computed spectra permits to estimate T(eff) approximately 5500 K for V4334 Sgr
in April, 1997, and its interstellar reddening (plus a possible circumstellar
contribution) E(B-V) approximately 0.70.Comment: 7 pages, 8 figures, LaTeX, accepted by Astronomy and Astrophysic
Partial differential equations for self-organization in cellular and developmental biology
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field
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