Proportional Insulin Infusion in Closed-Loop Control of Blood Glucose.

A differential equation model is formulated that describes the dynamics of glucose concentration in blood circulation. The model accounts for the intake of food, expenditure of calories and the control of glucose levels by insulin and glucagon. These and other hormones affect the blood glucose level in various ways. In this study only main effects are taken into consideration. Moreover, by making a quasi-steady state approximation the model is reduced to a single nonlinear differential equation of which parameters are fit to data from healthy subjects. Feedback provided by insulin plays a key role in the control of the blood glucose level. Reduced ß-cell function and insulin resistance may hamper this process. With the present model it is shown how by closed-loop control these defects, in an organic way, can be compensated with continuous infusion of exogenous insulin.

The Dynamics of Addiction: Craving versus Self-Control.

This study deals with addictive acts that exhibit a stable pattern not intervening with the normal routine of daily life. Nevertheless, in the long term such behaviour may result in health damage. Alcohol consumption is an example of such addictive habit. The aim is to describe the process of addiction as a dynamical system in the way this is done in the natural and technological sciences. The dynamics of the addictive behaviour is described by a mathematical model consisting of two coupled difference equations. They determine the change in time of two state variables, craving and self-control. The model equations contain terms that represent external forces such as societal rules, peer influences and cues. The latter are formulated as events that are Poisson distributed in time. With the model it is shown how a person can get addicted when changing lifestyle. Although craving is the dominant variable in the process of addiction, the moment of getting dependent is clearly marked by a switch in a variable that fits the definition of addiction vulnerability in the literature. Furthermore, the way chance affects a therapeutic addiction intervention is analysed by carrying out a Monte Carlo simulation. Essential in the dynamical model is a nonlinear component which determines the configuration of the two stable states of the system: being dependent or not dependent. Under identical external conditions both may be stable (hysteresis). With the dynamical systems approach possible switches between the two states are explored (repeated relapses).

Reconstruction of the drive underlying food intake and its control by leptin and dieting.

The intake of food and the expenditure of calories is modelled by a system of differential equations. The state variables are the amount of calories stored in adipose tissue and the level of plasma leptin. The model has as input a drive that controls the intake of food. This drive consists of a collective of physiological and psychological incentives to eat or to stop eating. An individual based approach is presented by which the parameters of the system can be set using data of a subject. The method of analysis is fully worked out using weight data of two persons. The model is prone to extensions by transferring incentives being part of the input to the collection of state variables.

Transitions in smoking behaviour and the design of cessation schemes.

The intake of nicotine by smoking cigarettes is modelled by a dynamical system of differential equations. The variables are the internal level of nicotine and the level of craving. The model is based on the dynamics of neural receptors and the way they enhance craving. Lighting of a cigarette is parametrised by a time-dependent Poisson process. The nicotine intake rate is assumed to be proportional with the parameter of this stochastic process. The effect of craving is damped by a control mechanism in which awareness of the risks of smoking and societal measures play a role. Fluctuations in this damping may cause transitions from smoking to non-smoking and vice versa. With the use of Monte Carlo simulation the effect of abrupt and gradual cessation therapies are evaluated. Combination of the two in a mixed scheme yields a therapy with a duration that can be set at wish.

Estimation of parameters in a Bertalanffy type of temperature dependent growth model using data on juvenile stone loach (Barbatula barbatula).

Parameters of a Bertalanffy type of temperature dependent growth model are fitted using data from a population of stone loach (Barbatula barbatula). Over two periods respectively in 1990 and 2010 length data of this population has been collected at a lowland stream in the central part of the Netherlands. The estimation of the maximum length of a fully grown individual is given special attention because it is in fact found as the result of an extrapolation over a large interval of the entire lifetime. It is concluded that this parameter should not at forehand be set at one fixed value for the population at that location due to varying conditions over the years.

Limit-cycle oscillators subject to a delayed feedback.

The coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback. For the case of a weakly nonlinear oscillator, we discuss the validity of a previously determined phase equation. For the case of a strongly nonlinear oscillator, we derive a phase equation and analyze its bifurcation diagram. Our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback.