Biomedical subjects

E Mosekilde

Publications and source records attributed to E Mosekilde.

At least 19 recordsLinked to original sources

PubMed2005

Two-mode chaos and its synchronization properties.

Using a simple model with bimodal dynamics, we investigate the intra- and inter-system entrainment of the two different time scales involved in the chaotic oscillations. The transition between mode-locked and mode-unlocked chaos is analyzed for a single system. For coupled oscillators, we demonstrate full and partial synchronization patterns depending on the adjustment between the fast and slow time scales and reveal the embedded structure of the corresponding synchronization regions.

Journal Article↗

PubMed2005

Interference microscopy under double-wavelet analysis: a new approach to studying cell dynamics.

This Letter combines a novel experimental approach to the study of intracellular processes with a newly developed technique for multimode time-series analysis. Experiments are performed on isolated pond snail (Lymnaea stagnalis) neurons. Local variations in the cellular refractive index as detected by laser interference microscopy are related to the processes in the cell. A wavelet analysis shows the presence of several identifiable modes in the membrane and intracellular dynamics, and a double-wavelet analysis reveals nonlinear interactions between the regulatory processes in the form of mutual frequency and amplitude modulations.

Animals↗

PubMed2005

Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics.

On the basis of double-wavelet analysis, the paper proposes a method to study interactions in the form of frequency and amplitude modulation in nonstationary multimode data series. Special emphasis is given to the problem of quantifying the strength of modulation for a fast signal by a coexisting slower dynamics and to its physiological interpretation. Application of the approach is demonstrated for a number of model systems, including a model that generates chaotic dynamics. The approach is then applied to proximal tubular pressure data from rat nephrons in order to estimate the degree to which the myogenic dynamics of the afferent arteriole is modulated by the slower tubulo-glomerular dynamics. Our analysis reveals a significantly stronger interaction between the two mechanisms in spontaneously hypertensive rats than in normotensive rats.

Algorithms↗

PubMed2004

Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation.

Biological time series often display complex oscillations with several interacting rhythmic components. Renal autoregulation, for instance, involves at least two separate mechanisms both of which can produce oscillatory variations in the pressures and flows of the individual nephrons. Using double-wavelet analysis we propose a method to examine how the instantaneous frequency and amplitude of a fast mode is modulated by the presence of a slower mode. Our method is applied both to experimental data from normotensive and hypertensive rats showing different oscillatory patterns and to simulation results obtained from a physiologically based model of the nephron pressure and flow control. We reveal a nonlinear interaction between the two mechanisms that regulate the renal blood flow in the form of frequency and amplitude modulation of the myogenic oscillations.

Adaptation, Physiological↗

PubMed2003

Torus breakdown in noninvertible maps.

We propose a criterion for the destruction of a two-dimensional torus through the formation of an infinite set of cusp points on the closed invariant curves defining the resonance torus. This mechanism is specific to noninvertible maps. The cusp points arise when the tangent to the torus at the point of intersection with the critical curve L(0) coincides with the eigendirection corresponding to vanishing eigenvalue for the noninvertible map. Further parameter changes lead typically to the generation of loops (self-intersections of the invariant manifolds) followed by the transformation of the torus into a complex chaotic set.

Journal Article↗

PubMed2003

Complex phase dynamics in coupled bursters.

The phenomenon of phase multistability in the synchronization of two coupled oscillatory systems typically arises when the systems individually display complex wave forms associated, for instance, with the presence of subharmonic components. Alternatively, phase multistability can be caused by variations of the phase velocity along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns in the bursting behavior of a model of coupled pancreatic cells. In particular, we show how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes.

Journal Article↗

PubMed2002

Bimodal oscillations in nephron autoregulation.

The individual functional unit of the kidney (the nephron) displays oscillations in its pressure and flow regulation at two different time scales: fast oscillations associated with a myogenic dynamics of the afferent arteriole, and slower oscillations arising from a delay in the tubuloglomerular feedback. We investigate the intra- and internephron entrainment of the two time scales. In addition to full synchronization, both wavelet analyses of experimental data and numerical simulations reveal a partial entrainment in which neighboring nephrons attain a state of chaotic synchronization with respect to their slow dynamics, but the fast dynamics remain desynchronized.

Journal Article↗

PubMed2002

Transitions between beta and gamma rhythms in neural systems.

We study the coexistence of different rhythms in a local network of one inhibitory and two excitatory nerve cells for a wide range of the excitatory synapse strength and of the slow K+-channel conductance. The dynamic features of spike trains in the presence of noise are discussed. It is found that noise can both cause switching between different states and induce coherent firing events.

Animals↗

PubMed2002

Phase multistability of self-modulated oscillations.

The paper examines the type of multistability that one can observe in the synchronization of two oscillators when the systems individually display self-modulation or other types of multicrest wave forms. The investigation is based on a phase reduction method and on the calculation of phase maps for vanishing and finite coupling strengths, respectively. Various phase-locked patterns are observed. In the presence of a frequency mismatch, the two-parameter bifurcation analysis reveals a set of synchronization regions inserted one into the other. Numerical examples using a generator with inertial nonlinearity and a biologically motivated model of nephron autoregulation are presented.

Journal Article↗

PubMed2002

Quantitative effects of medium hardness and nutrient availability on the swarming motility of Serratia liquefaciens.

We report the first controlled measurements of expansion rates for swarming colonies of Serratia liquefaciens under different growth conditions, combined with qualitative observations of the organization of the colony into regions of differentiated cell types. Significantly, the results reveal that swarming colonies of S. liquefaciens can have an increasing expansion rate with time. We compare and contrast the expansion rate results with predictions from a recent mathematical model which coupled key hydrodynamical and biological mechanisms. Furthermore, we investigate whether the swarming colonies grow according to a power law or exponentially (for large times), as suggested by recent theoretical results.

Biofilms↗

PubMed2001

Scaling properties of bicritical dynamics in unidirectionally coupled period-doubling systems in the presence of noise.

We study scaling regularities associated with the effects of additive noise on the bicritical behavior of a system of two unidirectionally coupled quadratic maps. A renormalization group analysis of the effects of noise is developed. We outline the qualitative and quantitative differences between the response of the system to random perturbations added to the master subsystem or the slave subsystem. The universal constants determining the rescaling rules for the intensity of the noise sources in the master and slave subsystems are found to be gamma=6.619036... and nu=2.713708..., respectively. A number of computer graphical illustrations for the scaling regularities is presented. We discuss the smearing of the fine structure of the bicritical attractor and the Fourier spectra in the presence of noise, the self-similar structure of the Lyapunov charts on the parameter plane near the bicritical point, and the shift of the threshold of hyperchaos in dependence of the noise intensity.

Journal Article↗

PubMed2001

Loss of coherence in a system of globally coupled maps.

We study the formation of symmetric (i.e., equally sized) or nearly symmetric clusters in an ensemble of globally coupled, identical chaotic maps. It is shown that the loss of synchronization for the coherent state and the emergence of subgroups of oscillators with synchronized behavior are two distinct processes, and that the type of behavior that arises after the loss of total synchronization depends sensitively on the dynamics of the individual map. For our system of globally coupled logistic maps, symmetric two-cluster formation is found to proceed through a periodic state associated with the stabilization either of an asynchronous period-2 cycle or of an asynchronous period-4 cycle. With further reduction of the coupling strength, each of the principal clustering states undergoes additional bifurcations leading to cycles of higher periodicity or to quasiperiodic and chaotic dynamics. If desynchronization of the coherent chaotic state occurs before the formation of stable clusters becomes possible, high-dimensional chaotic motion is observed in the intermediate parameter interval.

Journal Article↗

PubMed2001

Cluster synchronization modes in an ensemble of coupled chaotic oscillators.

Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science and technology, is illustrated through concrete examples of coupled biological cell models.

Journal Article↗

PubMed2001

Chaotic dynamics from interspike intervals.

Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov exponent (LE) from point processes differ between the two models. We also consider the problem of estimating the second LE and the possibility to diagnose hyperchaotic behavior by processing spike trains. Since the second exponent is quite sensitive to the structure of the ISI series, we investigate the problem of its computation.

Journal Article↗

PubMed2001

Transcritical riddling in a system of coupled maps.

The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.

Journal Article↗

PubMed2000

Modeling the insulin-glucose feedback system: the significance of pulsatile insulin secretion.

A mathematical model of the insulin-glucose feedback regulation in man is used to examine the effects of an oscillatory supply of insulin compared to a constant supply at the same average rate. We show that interactions between the oscillatory insulin supply and the receptor dynamics can be of minute significance only. It is possible, however, to interpret seemingly conflicting results of clinical studies in terms of their different experimental conditions with respect to the hepatic glucose release. If this release is operating near an upper limit, an oscillatory insulin supply will be more efficient in lowering the blood glucose level than a constant supply. If the insulin level is high enough for the hepatic release of glucose to nearly vanish, the opposite effect is observed. For insulin concentrations close to the point of inflection of the insulin-glucose dose-response curve an oscillatory and a constant insulin infusion produce similar effects.

Blood Glucose↗

PubMed2000

The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens.

The rate of expansion of bacterial colonies of S. liquefaciens is investigated in terms of a mathematical model that combines biological as well as hydrodynamic processes. The relative importance of cell differentiation and production of an extracellular wetting agent to bacterial swarming is explored using a continuum representation. The model incorporates aspects of thin film flow with variable suspension viscosity, wetting, and cell differentiation. Experimental evidence suggests that the bacterial colony is highly sensitive to its environment and that a variety of mechanisms are exploited in order to proliferate on a variety of surfaces. It is found that a combination of effects are required to reproduce the variation of bacterial colony motility over a large range of nutrient availability and medium hardness.

Cell Division↗

PubMed2000

Dynamical system approach to phyllotaxis

This paper presents a bifurcation study of a model widely used to discuss phyllotactic patterns, i.e., leaf arrangements. Although stable patterns can be easily obtained by numerical simulations, a stability or bifurcation analysis is hindered by the fact that the model is defined by an algorithm and not a dynamical system, mainly because new active elements are added at each step, and thus the dimension of the "natural" phase space is not conserved. Here a construction is presented by which a well defined dynamical system can be obtained, and a bifurcation analysis can be carried out. Stable and unstable patterns are found by an analytical relation, in which the roles of different growth mechanisms determining the shape is clarified. Then bifurcations are studied, especially anomalous scenarios due to discontinuities embedded in the original model. Finally, an explicit formula for evaluation of the Jacobian, and thus the eigenvalues, is given. It is likely that problems of the above type often arise in biology, and especially in morphogenesis, where growing systems are modeled.

Journal Article↗