We study a system consisting of two coupled phase oscillators in the presence of noise. This system is
used as a model for the cardiorespiratory interaction in wakefulness and anaesthesia. We show that longrange
correlated noise produces transitions between epochs with different n:m synchronisation ratios, as
observed in the cardiovascular system. Also, we see that, the smaller the noise (specially the one acting
on the slower oscillator), the bigger the synchronisation time, exactly as happens in anaesthesia compared
with wakefulness. The dependence of the synchronisation time on the couplings, in the presence of noise,
is studied; such dependence is softened by low-frequency noise. We show that the coupling from the slow
oscillator to the fast one (respiration to heart) plays a more important role in synchronisation. Finally, we
see that the isolines with same synchronisation time seem to be a linear combination of the two couplings.
We present a model of the cardiovascular system (CVS) based on a system of coupled oscillators. Using this
approach we can describe several complex physiological phenomena that can have a range of applications. For
instance, heart rate variability (HRV), can have a new deterministic explanation. The intrinsic dynamics of the
HRV is controlled by deterministic couplings between the physiological oscillators in our model and without
the need to introduce external noise as is commonly done. This new result provides potential applications not
only for physiological systems but also for the design of very precise electronic generators where the frequency
stability is crucial. Another important phenomenon is that of oscillation death. We show that in our CVS
model the mechanism leading to the quenching of the oscillations can be controlled, not only by the coupling
parameter, but by a more general scheme. In fact, we propose that a change in the relative current state
of the cardiovascular oscillators can lead to a cease of the oscillations without actually changing the strength
of the coupling among them. We performed real experiments using electronic oscillators and show them to
match the theoretical and numerical predictions. We discuss the relevance of the studied phenomena to real
cardiovascular systems regimes, including the explanation of certain pathologies, and the possible applications
in medical practice.
We address the problem of interactions between the phase of cardiac and respiration oscillatory components.
The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian
processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction
of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the
strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and
stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical
with original one.
Heart rate variability (HRV) measures cycle-to-cycle correlations in the instantaneous oscillation period of the
heart. In this paper it is shown that a simple model process, consisting of a sum of uncoupled sinusoidal oscillators
with slightly different frequencies, has a HRV spectrum with a 1/f scaling over a range of frequencies. This implies
that the appearance of 1/f HRV spectra in experiments should not be considered evidence of oscillator coupling
or other more complex dynamics. The origin of the 1/f scaling in the model is examined analytically, and its
dependence upon the sampling of low-amplitude fluctuations of the process is highlighted.
The backscattered intensity from low-intensity laser illumination of the skin in the area of vascular plexus is investigated in vivo. The exposure of blood to low power laser light in the absorption range of haemoglobin leads to increasing intensity of the backscattered light. Theoretical evaluation using an existing optical model of erythrocyte aggregation has suggests that the fragmentation of erythrocyte aggregates is the most probable mechanism leading to the enhanced backscattering.
The electrical activity of the heart (ECG), respiratory function and
electric activity of the brain (EEG) were simultaneously recorded in
conscious, healthy humans. Instantaneous frequencies of the heart
beat, respiration and α-waves were then determined from
30-minutes recordings. The instantaneous cardiac frequency was
defined as the inverse value of the time interval between two
consecutive R-peaks. The instantaneous respiratory frequency was
obtained from recordings of the excursions of thorax by application
of the Hilbert transform. To obtain the instantaneous frequency of
α-waves, the EEG signal recorded from the forehead was first
analysed using the wavelet transform. Then the frequency band
corresponding to α-waves was extracted and the Hilbert
transform applied. Synchronization analysis was performed and the
direction of coupling was ascertained, using pairs of instantaneous
frequencies in each case. It is shown that the systems are weakly
bidirectionally coupled. It was confirmed that, in conscious healthy
humans, respiration drives cardiac activity. We also demonstrate
from these analyses that α-activity drives both respiration
and cardiac activity.
Preliminary results are reported from a research project analysing
congestive heart failure in terms a stochastic coupled-oscillator
model of the cardiovascular system. Measurements of blood flow by
laser Doppler flowmetry (LDF) have been processed by use of the
wavelet transform to separate its oscillatory components, which
number at least five. Particular attention was concentrated on the
frequency content near 0.01 Hz, which is known to be associated
with endothelial function. The LDF was carried out in conjunction
with iontophoretically administered acetylcholine (ACh) and sodium
nitroprusside (SNP) in order to evaluate endothelial reactivity.
Measurements were made on 17 congestive heart failure (CHF)
patients (a) on first diagnosis, and (b) again several weeks later
after their treatment with a β-blocker had been stabilised.
The results of these two sets of measurements are being compared
with each other, and with data from an age and sex-matched group
of healthy controls. It is confirmed that endothelial reactivity
is reduced in CHF patients, as compared to healthy controls, and
it is found that one effect of the Beta-blocker is to ameliorate the loss of endothelial function in CHF. The implications of these results are discussed.
The human cardiovascular system is a complex system with the pumping activity of the heart as the main generator of oscillations. Besides the heartbeat there are several other oscillatory components which determine its dynamics. Their nonlinear nature and a weak coupling between them both require special treatment while studying this system. A particular characteristic of the oscillatory components is their frequency fluctuations in time. Consequently, their interactions also fluctuate in time.
Therefore the wavelet transform is applied to trace the oscillatory components in time, and specific quantitative measures are introduced to quantify the contribution of each of the oscillatory components involved on the time scale of up to three minutes. Oscillatory components are then analysed from signals obtained by simultaneous measurements of blood flow in the microcirculation, ECG, respiration and blood pressure. Based on quantitative evaluation of the oscillatory components related to (I) the heart beat (0.6-2Hz), (II) respiration (0.145-0.6Hz), (III) intrinsic myogenic activity (0.052-0.145Hz), (IV) sympathetic activity (0.021-0.052Hz), (V, VI) endothelial related activity (0.0095-0.021Hz, 0.005 - 0.0095 Hz), 30-minutes recording taken on 109 healthy subjects, 75 patients with diabetes, and 82 patients after acute myocardial infarction (AMI) were analysed.
Classification of the effect of ageing, diabetes and AMI from blood flow signals simultaneously recorded in the skin of four extremities, the heart rate and heart rate variability from R-R intervals will be presented and discussed.
The intensity of light backscattered when low-power laser radiation is incident on the skin is investigated under in vivo conditions. The exposure of blood to low-power laser light in the absorption range of haemoglobin leads an increased intensity of the backscattered light. The theoretical calculation using the existing optical model of erythrocyte aggregation has suggest that the fragmentation of erythrocyte aggregates is it most probable mechanism leading to the enhanced backscattering.
The human cardiovascular system (CVS), responsible for the delivery of nutrients and removal of waste products to/from the entire body, is a highly complex system involving many control mechanisms. Signals derived from the CVS are inherently difficult to analyse because they are noisy, time-varying, and of necessarily limited duration. The application of techniques drawn from nonlinear science has, however, yielded many insights into the nature of the CVS, and has provided strong evidence for a large degree of determinism in the way it functions. Yet there is compelling evidence that random fluctuations (noise) also play an essential role. There are at least five oscillatory processes of widely differing frequency involved in the blood distribution. The evidence for them, and their probable physiological origins, are discussed. Interactions between some of the processes can give rise to modulation and synchronization phenomena, very similar to those observed in classical oscillators in many areas of physics. The extent to which the CVS can be modelled as a stochastic nonlinear dynamical system is reviewed, and future research directions and possible applications based on this perception are considered.
The complexities exhibited by biological systems are highly intriguing. Their activity can span both micro and macroscopic scales simultaneously. Often noise plays an important role. So, the analysis of the dynamical properties of such systems poses a major challenge. In this paper we introduce an approach that is applicable within both the micro and macroscopic worlds, where a large number of oscillators acting on a similar time scale can be represented as an ensemble that, on the macroscopic scale, may be taken as a single oscillator. On the macroscopic scale they interact with other similar type of oscillators, but usually on widely different time scales. We use recently introduced nonlinear dynamics methods and methods derived from information theory, and extend their application to oscillations acting on micro and macroscopic scales at the same time. We demonstrate such interactions using numerical examples and real physiological data related to cardiac, respiratory and brain activities.
We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.