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At least 289 records · Page 16Linked to original sources
PubMed1994

Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis.

We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seen in vivo, including immunostimulation of tumor growth, "sneaking through" of the tumor, and formation of a tumor "dormant state". The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measured in vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.

Animals↗
PubMedDate not supplied

Heart rate variability in the human transplanted heart: nonlinear dynamics and QT vs RR-QT alterations during exercise suggest a return of neurocardiac regulation in long-term recovery.

RATIONALE: Functional reinnervation of the transplanted human heart by the autonomic nervous system has not been demonstrated. A lack of autonomic control of the transplanted allograft is reflected by an increased resting heart rate, a sluggish heart rate response to dynamical exercise and a reduced heart rate variability. Recent evidence suggests that a measure of deterministic chaos in the heartbeat interval series (point correlation dimension, PD2i) is superior to the conventional power spectrum or other stochastic measures in detecting changes in the mechanism underlying heartbeat generation. METHODS: The PD2i is based on the presumption that the variability is determined and patterned, whereas the stochastic measures all assume that the variability is around a stationary mean and is noise. The PD2i reconstructs the degrees of freedom (number of independent variables) in the system that generates the time series examined, and does this irrespective of whether the system is stochastic or deterministic and is stationary in time. RESULTS: PD2i was determined for heartbeat intervals (RR, ECG digitized at 1200 Hz; supine posture) of 23 heart transplant recipients (HTR: 9 adults, 14 children; 0.04-7.7 years after transplantation) and 21 healthy control subjects (CTL; 13 adults, 8 children). The PD2i (+/-SD) averaged 5.4 +/- 0.7 for the CTL adults and 5.4 +/- 0.6 for the CTL children. Mean PD2i was reduced after transplantation to 1.1 +/- 0.1 in 6 HTRs recorded within 1 year after surgery; in one HTR recorded 2 weeks after surgery the mean PD2i was 3.7. Between 1 to 2 years PD2i was found increased in 2 of 3 subjects and between 2 to 8 years it was increased in 13 of 13, but not to control levels. In normal hearts the QT subinterval of each heartbeat cycle is associated with inotropy and the RR-QT remainder with chronotropy (i.e., the dyastolic interval during which RR is primarily regulated). To examine more closely the residual and returning heartbeat dynamics of the HTR subjects, these subinterval series were examined during mild exercise (40 to 90 Watts) and its recovery. In recent HTRs, resting QT and RR-QT were moderately reduced and modulated by exercise and recovery, but with an approximate 100 beat latency. In long-term (7-8 years) HTR subjects there was a rapid and larger response to exercise/recovery, but compared to normal the range was smaller and the complexity of the subinterval trajectories in time was simpler. CONCLUSIONS: Recurrence of low-dimensional deterministic dynamics after transplantation suggests recovery of neurocardiac control attributable to 1) reorganization of the viable intrinsic cardiac nervous system, 2) reinnervation by the extrinsic autonomic nervous system, or 3) both.

Adult↗
PubMed2000

Nonlinear Dynamics in the Progression of Atherosclerotic Fatty Streaks: Morphometric Analysis.

Atherosclerotic lesions are heterogeneous in terms of their cellular and lipid composition. While heterogeneity can be the result of stochastic noise, an alternate hypothesis is that the differences observed among individual lesions arise from deterministic chaos. Five New Zealand white rabbits were fed a diet containing 0.15% cholesterol for 6 months. Segments of the aorta were fixed in formalin, stained en bloc with Nile red (NR) and filipin (F), and en face fluorescence microscopy was used to map the distribution of lipids in fatty streaks (FS). The smallest lesions detected stained only with filipin. Larger lesions stained with both Nile red and filipin and two distinct regions of Nile red staining, NR-orange (rich in polar lipids) and NR-yellow (rich in neutral lipids) were observed. Digital overlays revealed a "nested" arrangement of F, NR-orange, and NR-yellow. The lesions also showed marked heterogeneity in their lipid composition. Thus, although initially similar, as FS increased in size, their composition became divergent, suggesting that the ultimate composition of a FS was highly sensitive to its initial composition. Sensitivity to initial condition is one of the hallmarks of deterministic systems. To determine if FS were self-similar, another hallmark of deterministic chaos, the borders of the different regions defined by NR and F staining were subjected to fractal analysis. For each lesion, the borders of the F, NR-orange, and NR-yellow regions were found to be fractal. Return maps were constructed for the differently stained regions. Analysis of the entire 104-lesion data set showed that although the data could be described by a four-parameter logistic model, the population was not chaotic. However, return maps drawn for the maxima of the NR-orange stained regions demonstrated chaos. Taken together, the data suggest that deterministic chaos plays a role in the evolution of atheromatous disease but, in common with most biologic systems, as the lesions progress, chaotic behavior is dampened.

Journal Article↗
PubMed1994

Stereotyped human behavior: a nonlinear dynamical analysis.

Some forms of stereotyped human behavior seem to occur randomly in time. A dynamical analysis of several topographies demonstrates that while such stereotypies have the spectral characteristics of random noise, the rate at which each subject exhibits his/her stereotypy is to some extent predictable and, unlike uncorrelated noise, prediction accuracy declines with increasing prediction interval. Rhythmic stereotypies appear to be more predictable than nonrhythmic topographies but both show a similar decline in prediction accuracy. Furthermore, the distribution of interresponse times exhibits self-similar behavior. These results point to a deterministic, rather than stochastic, origin for the variability of observed rates of stereotyped behaviors.

Adolescent↗
PubMed1988

Oscillations and chaos in epidemics: a nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark.

Using traditional spectral analysis and recently developed non-linear methods, we analyze the incidence of six childhood diseases in Copenhagen, Denmark. In three cases, measles, mumps, rubella, the dynamics suggest low dimensional chaos. Outbreaks of chicken pox, on the other hand, conform to an annual cycle with noise superimposed. The remaining diseases, pertussis and scarlet fever, remain problematic. The real epidemics are compared with the output of a Monte Carlo analog of the SEIR model for childhood infections. For measles, mumps, rubella, and chicken pox, we find substantial agreement between the model simulations and the data.

Child↗
PubMed1990

Nonlinear dynamic behavior of cardiac oscillators.

By studying a mathematical model of the effects of brief current impulses on the oscillation of cardiac cells, we have simulated the phase transition curves of the oscillators. This has permitted discussions of the interactions of two coupled sinus oscillators and the periodic stimulation of one ventricular oscillator. The results have been compared with findings from the normal electrocardiogram and applied to explain the mechanisms of some arrhythmias.

Arrhythmias, Cardiac↗
PubMed2004

Tamoxifen treatment failure in cancer and the nonlinear dynamics of TGFbeta.

The process of cancer invasion involves a complex interplay between cell-cell and cell-medium adhesion, proteolytic enzyme secretion, cell birth and death processes, random and directed motility, and immune response, as well as many other factors. The growth factor TGF beta is known to have a complex effect on this process. It inhibits mitosis and promotes apoptosis in a concentration-dependent manner in vitro, and it is for this reason that its secretion is thought to be helpful in inhibiting tumour growth. However, recent in vitro and in vivo results have shown a significant effect of this growth factor in promoting the sensitivity of malignantly transformed cells to gradients of extracellular matrix proteins--an effect which tends to increase invasiveness. The drug tamoxifen has been demonstrated to be therapeutically effective in the treatment of patients with breast cancer; however, it is known also that many patients become resistant to the effect of this drug after a few years, and the reasons for this remain controversial. In this work we take our established model of cancer invasion (J. Theor. Biol. 216(1) (2002) 85), and extend it to include the effect of TGF beta. In so doing we demonstrate that a tamoxifen-stimulated upregulation of the secretion of TGF beta may give rise to a tumour which has a smaller number of cells but which has a greater invasiveness, greater metastatic potential, and a tumour histology which is known to correlate with a poorer prognosis. These data suggest that tamoxifen-stimulated secretion of TGF beta might explain treatment failure in some patients.

Anticarcinogenic Agents↗
PubMed1998

From bacteriophage lambda to nonlinear dynamics.

Thirty years ago, Waclaw and myself were working on the same organism and had the same type of interest. Since that happy time, our trajectories have diverged so much that I am afraid any paper I might offer for his jubilee would seem completely strange and irrelevant to him and as well to his colleagues. For this reason, I decided rather to offer Waclaw, as a modest present, a product of my recent work which I consider, perhaps presumptuously, as an 'oeuvre d'art' (of course, this qualification is not supposed to apply to this paper as a whole, just to the figure). Please note above the expressions 'divergent trajectories' and 'strange'; we will meet them again below in a different context.

Bacteriophage lambda↗
PubMedDate not supplied

Nonlinear dynamics of regulation of bacterial trp operon: model analysis of integrated effects of repression, feedback inhibition, and attenuation.

The trp operon encodes the five genes for the enzymes required to convert chorismate to tryptophan, and its switching on and off is controlled by both feedback repression and attenuation in response to different levels of tryptophan in the cell. Repression of the operon occurs when tryptophan concentration is high, and attenuation fine-tunes the transcription level at a lower cellular concentration of tryptophan. An extended mathematical model is established in this study to describe the switching on and off of the trp operon by considering the integrated effects of repression and attenuation. The influences of cell growth rate on the biosynthesis of tryptophan, stability and dynamic behavior of the trp operon are investigated. Sustained oscillations of tryptophan levels are predicted from the regulated turning on and off of the trp operon. It is interesting to note that during such oscillations the regulation of transcription displays a kind of "on" and "off" state in terms of gene expression, indicating the existence of a genetic circuit or switch in the regulation of the trp operon. Time lags between transcription and translation are also predicted and may explain the occurrence of such oscillation phenomenon.

Down-Regulation↗
PubMed2005

Nonlinear dynamics of confined polymer melts with attractive walls.

A scaling model is presented to analyze the reversible strain-hardening phenomenon in end-tethered polymer clay nanocomposites (Krishnamoorti, R.; Giannelis, E. P. Langmuir 2001, 17, 1448). It is assumed that for attractive clay-polymer interactions a fraction of the polymer chains that span the space between opposite clay plates get adsorbed on them, thereby bridging the plates. Under large amplitude oscillatory shear, such bridges are stretched, and this results in the strain-hardening behavior. The onset of strain hardening is predicted to be dependent only on the average distance separating the two plates and is independent of the frequency of the oscillations and the polymer molecular weight.

Journal Article↗
PubMed2002

Nonlinear dynamics of ice-wedge networks and resulting sensitivity to severe cooling events.

Patterns of subsurface wedges of ice that form along cooling-induced tension fractures, expressed at the ground surface by ridges or troughs spaced 10 30 m apart, are ubiquitous in polar lowlands. Fossilized ice wedges, which are widespread at lower latitudes, have been used to infer the duration and mean temperature of cold periods within Proterozoic and Quaternary climates, and recent climate trends have been inferred from fracture frequency in active ice wedges. Here we present simulations from a numerical model for the evolution of ice-wedge networks over a range of climate scenarios, based on the interactions between thermal tensile stress, fracture and ice wedges. We find that short-lived periods of severe cooling permanently alter the spacing between ice wedges as well as their fracture frequency. This affects the rate at which the widths of ice wedges increase as well as the network's response to subsequent climate change. We conclude that wedge spacing and width in ice-wedge networks mainly reflect infrequent episodes of rapidly falling ground temperatures rather than mean conditions.

Journal Article↗