Biomedical subjects
Publications and source records attributed to Erik Mosekilde.
The article makes use of three different examples (sensory information processing in the rat trigeminal complex, intracellular interaction in snail neurons and multimodal dynamics in nephron autoregulation) to demonstrate how modern approaches to time-series analysis based on the wavelet-transform can provide information about the underlying complex biological processes.
Numerical studies of higher-dimensional piecewise-smooth systems have recently shown how a torus can arise from a periodic cycle through a special type of border-collision bifurcation. The present article investigates this new route to quasiperiodicity in the two-dimensional piecewise-linear normal form map. We have obtained the chart of the dynamical modes for this map and showed that border-collision bifurcations can lead to the birth of a stable closed invariant curve associated with quasiperiodic or periodic dynamics. In the parameter regions leading to the existence of an invariant closed curve, there may be transitions between an ergodic torus and a resonance torus, but the mechanism of creation for the resonance tongues is distinctly different from that observed in smooth maps. The transition from a stable focus point to a resonance torus may lead directly to a new focus of higher periodicity, e.g., a period-5 focus. This article also contains a discussion of torus destruction via a homoclinic bifurcation in the piecewise-linear normal map. Using a dc-dc converter with two-level control as an example, we report the first experimental verification of the direct transition to quasiperiodicity through a border-collision bifurcation.
Using a relatively simple model we examine how variations of the extracellular potassium concentration can give rise to synchronization of two nearby pacemaker cells. With the volume of the extracellular space and the rate of potassium diffusion as control parameters, the dual nature of this resource-mediated coupling is found to be responsible for the coexistence of competing patterns of in- and anti-phase synchronization between identical cells. Cell heterogeneity produces significant modifications of the dynamical regimes in the control parameter plane. By comparison with conventional gap junctional coupling, potassium signaling gives rise to considerable changes of the cellular response to external stimuli.
The paper investigates the special clustering phenomena that one can observe in systems of nonlinear oscillators that are coupled via a shared flow of primary resources (or a common power supply). This type of coupling, which appears to be quite frequent in nature, implies that one can no longer separate the inherent dynamics of the individual oscillator from the properties of the coupling network. Illustrated by examples from microbiological population dynamics, renal physiology, and electronic oscillator theory, we show how competition for primary resources in a resource distribution chain leads to a number of new generic phenomena, including partial synchronization, sliding of the synchronization region with the resource supply, and coupling-induced inhomogeneity.
Mechanism-based modeling is an approach in which the physiological, pathological and pharmacological processes of relevance to a given problem are represented as directly as possible. This approach allows us (i) to test whether assumed hypotheses are consistent with observed behaviour, (ii) to examine the sensitivity of a system to parameter variation, (iii) to learn about processes not directly amenable to experimentation, and (iv) to predict system behavior under conditions not previously experienced. The paper illustrates different aspects of the application of mechanism-based modeling through three different examples of relevance to the treatment of diabetes and hypertension: subcutaneous absorption of insulin, pulsatile insulin secretion in normal young persons, and synchronization of the pressure and flow regulation in neighbouring nephrons. The underlying ideas are that each regulatory mechanism represents the target for intervention and that the development of new and more effective drugs must be based on a deeper understanding of the biological processes.
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Large populations of globally coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that, for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.
A stochastic model of the electrophysiological behavior of the pancreatic beta cell is studied, as a paradigmatic example of a bursting biological cell embedded in a noisy environment. The analysis is focused on the distortion that a growing noise causes to the basic properties of the membrane potential signals, such as their periodic or chaotic nature, and their bursting or spiking behavior. We present effective computational tools to obtain as much information as possible from these signals, and we suggest that the methods could be applied to real time series. Finally, a universal dependence of the main characteristics of the membrane potential on the size of the considered cell cluster is presented.
This Letter presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to populations of any size and functional form in the region of coherence. It requires linear variation or a narrow distribution for the dispersed parameter. Although an approximation, the method allows us to quantitatively study the transitions among the collective regimes as bifurcations of the effective macroscopic degrees of freedom. To illustrate, the phenomenon of oscillator death and the route to full locking are examined for chaotic oscillators with time scale mismatch.
Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded in the fully synchronized state lose their transverse stability, and the appearance of globally and locally riddled basins of attraction is discussed, respectively, in terms of the subcritical, supercritical nature of the riddling bifurcations. We show how the introduction of a small parameter mismatch between the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled Rössler oscillators.
Experimental data for tubular pressure oscillations in rat kidneys are analyzed in order to examine the different types of synchronization that can arise between neighboring functional units. For rats with normal blood pressure, the individual unit (the nephron) typically exhibits regular oscillations in its tubular pressure and flow variations. For such rats, both in-phase and antiphase synchronization can be demonstrated in the experimental data. For spontaneously hypertensive rats, where the pressure variations in the individual nephrons are highly irregular, signs of chaotic phase and frequency synchronization can be observed. Accounting for a hemodynamic as well as for a vascular coupling between nephrons that share a common interlobular artery, we develop a mathematical model of the pressure and flow regulation in a pair of adjacent nephrons. We show that this model, for appropriate values of the parameters, can reproduce the different types of experimentally observed synchronization. (c) 2001 American Institute of Physics.
One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period-doubling cascades. Similar phenomena arise in response to increasing blood pressure. The numerical analyses are supported by existing experimental results on anesthetized rats. (c) 1996 American Institute of Physics.
We present a detailed numerical investigation of the phase-locking regions in a forced model of slow oscillations in human insulin secretion and blood glucose concentration. The bifurcation structures of period 2pi and 4pi tongues are mapped out and found to be qualitatively identical to those of several other periodically forced self-oscillating systems operating across a Hopf-bifurcation point. The numerical analyses are supplemented by clinical experiments. (c) 1995 American Institute of Physics.