Biomedical subjects

A C Fowler

Publications and source records attributed to A C Fowler.

13 recordsLinked to original sources

PubMed2006

High frequency spikes in long period blood cell oscillations.

Several hematological diseases are characterised by oscillations of various blood cell populations. Two of these are a variant of chronic myelogenous leukemia (CML) and cyclical neutropenia (CN). These oscillations typically have long periods ranging from 20 to 60 days, despite the fact that the stem cell cycling time is thought to be of the order of 2-3 days. Clinical data from humans and laboratory data from the grey collie animal model of CN is suggestive of the idea that these long period oscillations may also contain higher frequency spiky oscillations. We show how such oscillations can be understood in the context of slow periodic stem cell oscillations, by analysing a two component differential-delay equation model of stem cell and neutrophil populations.

Algorithms↗

PubMed2006

Subglacial floods beneath ice sheets.

Subglacial floods (jökulhlaups) are well documented as occurring beneath present day glaciers and ice caps. In addition, it is known that massive floods have occurred from ice-dammed lakes proximal to the Laurentide ice sheet during the last ice age, and it has been suggested that at least one such flood below the waning ice sheet was responsible for a dramatic cooling event some 8000 years ago. We propose that drainage of lakes from beneath ice sheets will generally occur in a time-periodic fashion, and that such floods can be of severe magnitude. Such hydraulic eruptions are likely to have caused severe climatic disturbances in the past, and may well do so in the future.

Journal Article↗

PubMed2005

A delay recruitment model of the cardiovascular control system.

We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and allows us to compare the baroreflex influence on heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.

Baroreflex↗

PubMed2004

A model for water uptake by plant roots.

We present a model for water uptake by plant roots from unsaturated soil. The model includes the simultaneous flow of water inside the root network and in the soil. It is constructed by considering first the water uptake by a single root, and then using the parameterized results thereby obtained to build a model for water uptake by the developing root network. We focus our model on annual plants, in particular the model will be applicable to commercial monocultures like maize, wheat, etc. The model is solved numerically, and the results are compared with approximate analytic solutions. The model predicts that as a result of water uptake by plant roots, dry and wet zones will develop in the soil. The wet zone is located near the surface of the soil and the depth of it is determined by a balance between rainfall and the rate of water uptake. The dry zone develops directly beneath the wet zone because the influence of the rainfall at the soil surface does not reach this region, due to the nonlinear nature of the water flow in the partially saturated soil. We develop approximate analytic expressions for the depth of the wet zone and discuss briefly its ecological significance for the plant. Using this model we also address the question of where water uptake sites are concentrated in the root system. The model indicates that the regions near the base of the root system (i.e. close to the ground surface) and near the root tips will take up more water than the middle region of the root system, again due to the highly nonlinear nature of water flow in the soil.

Models, Biological↗

PubMed2004

A mathematical model for water and nutrient uptake by plant root systems.

This article deals with modelling the simultaneous uptake of water and highly buffered nutrient, such as phosphate, by root branching structures from partially saturated soil. We use the simultaneous water and nutrient uptake model to investigate the effect that water movement has on nutrient uptake. With the aid of this model we are also able to show that the previous models by Barber and Tinker and Nye systematically underestimated the phosphate uptake, due to the oversimplified approach in dealing with root branching structure. In this article we show how this discrepancy can be remedied and the root branching structure included in the models of plant nutrient uptake. We will also discuss the differences in the results for continuous and spot fertilization combined with variable rainfall.

Models, Biological↗

PubMed2001

A mathematical model of plant nutrient uptake.

The classical model of plant root nutrient uptake due to Nye. Tinker and Barber is developed and extended. We provide an explicit closed formula for the uptake by a single cylindrical root for all cases of practical interest by solving the absorption-diffusion equation for the soil nutrient concentration asymptotically in the limit of large time. We then use this single root model as a building block to construct a model which allows for root size distribution in a more realistic plant root system, and we include the effects of root branching and growth. The results are compared with previous theoretical and experimental studies.

Mathematical Computing↗

PubMed2000

The effect of incubation time distribution on the extinction characteristics of a rabies epizootic.

The continuous model of Anderson et al. (1981), Nature 289, 765-771, is successful in describing certain characteristics of rabies epizootics, in particular, the secondary recurrences which follow the initial outbreak; however, it also predicts the occurrence of exponentially small minima in the infected population, which would realistically imply extinction of the virus. Here we show that inclusion of a more realistic distribution of incubation times in the model can explain why extinction will not occur, and we give explicit parametric estimates for the minimum infected fox density which will occur in the model, in terms of the incubation time distribution.

Animals↗

PubMed2000

The role of the central chemoreceptor in causing periodic breathing.

In a previous publication (Fowler et al., 1993), we reduced the classical cardiorespiratory control model of (Grodins et al., 1967) to a much simpler form, which we then used to study the phenomenon of periodic breathing. In particular, cardiac output was assumed constant, and a single (constant) delay representing arterial blood transport time between lung and brain was included in the model. In this paper we extend this earlier work, both by allowing for the variability in transport delays, due to the dependence of cardiac output on blood gas concentrations, and also by including further delays in the system. In addition, we extensively discuss the physiological implications of parameter variations in the model; several novel mechanisms for periodic breathing in clinical situations are proposed. The results are discussed in the light of recent observational studies.

Carbon Dioxide↗

PubMed1995

Ecological chaos in the wake of invasion.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos.

Animals↗

PubMed1994

A method for filtering respiratory oscillations.

We present a method based on dynamical systems theory which can be used to filter time series in a way which is superior to classical Fourier decomposition. This method is applied to three data-sets, taken from respiratory measurements of two children in quiet and REM sleep. Our purpose is to filter the several different oscillatory mechanisms which operate, in order to provide clearer signals on which further analysis and diagnosis can be based.

Humans↗

PubMed1993

A mathematical analysis of the Grodins model of respiratory control.

The classical Grodins model of chemical respiratory control is analysed. Scaling and asymptotic analysis are used to reduce the model drastically to a much simplified form. In essence, the model consists of two separate controllers due to oxygen and carbon dioxide. The authors focus on the carbon dioxide controller, and show that it can be considered as two coupled delay recruitment equations. While, in normal circumstances, steady ventilation is stable, it is shown that, by varying controlling parameters, periodic and chaotic solutions may be obtained.

Brain↗

PubMed1984

A mathematical model of exoprotein production in bacteria.

We present a simple mathematical model for the synthesis of extracellular proteins by a class of bacteria which secrete significant quantities of this exoprotein in late-exponential and stationary phases. This model is the simplest generalization of Michaelis-Menten kinetics (the Monod model) and agrees well with laboratory experiments in batch culture. The model may serve as a simple prototype for the analysis of certain virulent bacterial infections in vivo, particularly that of Pseudomonas aeruginosa in burn wounds.

Bacteria↗

PubMed1981

Approximate solution of a model of biological immune responses incorporating delay.

A model of the humoral immune response, proposed by Dibrov, Livshits and Volkenstein (1977b), in which the antibody production by a constant target cell population depends on the antigenic stimulation at earlier times, is considered from an analytic standpoint. A method of approximation based on a consideration of the asymptotic limit of "large" delay in the antibody response is shown to be applicable, and to give results similar to those obtained numerically by the above authors. The relevance of this type of approximation to other systems exhibiting "outbreak" phenomena is discussed.

Animals↗