A. Bandrivskyy

Wavelet Phase Coherence Analysis: Application to Skin Temperature and Blood Flow

The technique of wavelet phase coherence analysis is introduced and used to explore relationships between oscillations on blood flow and temperature in the skin of 10 healthy subjects. Their skin temperature and blood flow were continuously recorded: under basal conditions for 30 min; during local cooling of the skin with an ice-pack for 20 min: and 30 min thereafter. The group mean basal skin temperature of 33.4°C was decreased to 29.2°C during the cooling period, and had recovered to 32.1°C by the end of the recording. The wavelet transform was used to obtain the time–frequency content of the two signals, and their coherence. It is shown that cooling increases coherence to a statistically significant extent in two frequency intervals, around 0.007 and 0.1 Hz, suggesting that these oscillatory components are involved in the regulation of skin temperature when cold is applied as a stress.

Reconstruction of stochastic nonlinear dynamical models from trajectory measurements

An algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. The strengths of the algorithm are illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. The efficiency and accuracy of the algorithm are further demonstrated by inferring a model for a system of five globally and locally coupled noisy oscillators.

Wavelet analysis of blood flow dynamics:effect on the individual oscillatory components of iontophoresis with pharmacologically neutral electrolytes

Iontophoresis currents are used in the transcutaneous delivery of vasoactive substances for noninvasive assessment of skin vascular properties. The blood flow rate can be recorded by laser Doppler flowmetry (LDF), its average value and the amplitudes of its oscillatory components being used to evaluate the effect of the drugs. Because non-drug-specific, current-induced, vasodilation could confound the interpretation of the response, we have investigated the effect of currents of both polarities on the spectral components of the LDF signal in the absence of vasoactive substances. It was recorded for healthy volunteers with both high conductance (5 mol/l NaCl) and low conductance (deionized water) electrolytes. The oscillatory components were analysed by wavelet transform within 0.0095-1.6 Hz, divided into five sub-intervals. Only cathodal iontophoresis with deionized water increased the oscillatory energy and amplitude. It did so at all frequencies, but none of the sub-intervals associated with vasodilation (0.0095-0.145 Hz) was selectively affected compared to the others.

Noise-induced shift of singularities in the pattern of optimal paths

We analyse the non-equilibrium distribution in dissipative dynamical systems at finite noise intensities. The effect of finite noise is described in terms of topological changes in the pattern of optimal paths. Theoretical predictions are in good agreement with the numerical results.

Fast Monte Carlo Simulations and Singularities in the Probability Distributions of Nonequilibrium Systems.

A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of nonequilibrium systems. Results for the quasistationary probability distribution in two model systems are compared with the asymptotically exact theory in the limit of extremely small noise intensity. Singularities of the nonequilibrium distributions are revealed by the simulations.

Role of transdermal potential difference during iontophoretic drug delivery

Potential differences have been measured during transdermal iontophoresis in order to establish the effect of voltage, as opposed to current, on cutaneous blood flow. It is known that, even in the absence of drugs, the iontophoresis current can sometimes produce increased blood flow. The role of voltage in this process is studied through single-ended measurements (between electrode and body) of the potential difference during iontophoresis with 100-/spl mu/A, 20-s current pulses through deionized water, saturated 20.4% NaCl solution, 1 % acetylcholine, and 1 % sodium nitroprusside. It is found that the voltage needed to deliver the current varied by orders of magnitudes less than the differences in the conductance of these different electrolytes, and it is concluded that, at least for the present current protocol, the voltage as such is not an important factor in increasing the blood flow.

Time-Varying Cardiovascular Oscillations

Signals derived from the human cardiovascular system (CVS) are exceptionally complex, being time-varying, noisy, and of necessarily limited duration. Yet an appropriate analysis of them may be expected to yield detailed information about the dynamics of the underlying physiological processes. A new approach to the analysis and modelhng of CVS signals is proposed. It combines decomposition of the signals into principal modes and a novel method of parameter identification in nonlinear stochastic systems based on Bayesian inference. The scheme is tested on a noisy Van der Pol oscillator, for which it yields rapid convergence and correct inference of the known parameters. Preliminary applications to CVS data are discussed.

Inference of systems with delay and applications to cardiovascular dynamics

A Bayesian inference technique, able to encompass stochastic nonlinear systems, is described. It is applicable to differential equations with delay and enables values of model parameters, delay, and noise intensity to be inferred from measured time series. The procedure is demonstrated on a very simple one-dimensional model system, and then applied to inference of parameters in the Mackey-Glass model of the respiratory control system based on measurements of ventilation in a healthy subject. It is concluded that the technique offers a promising tool for investigating cardiovascular interactions.

Cardiovascular oscillations: in search of a nonlinear parametric model

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.

Stochastic Dynamics of Anæsthesia

Recent developments in the analysis of synchronization and directionality of couplings for noisy nonlinear oscillators are being applied to study the complex interactions between cardiac and respiratory oscillations, and brain waves (especially delta and gamma), during anaesthesia. It is found that marked changes occur in the inter‐oscillator interactions during anaesthesia in both rats and humans. These could form a new basis for measurement of depth of anaesthesia. The new EC programme BRACCIA will explore and quantify causal relationships between the oscillatory processes for the different stages of anaesthesia and consciousness.