Sample size determination in the laser-Doppler measurements of skin blood flow.

Pre-study calculations of the required sample size are vital to a large majority of studies. Using the method based on the Monte-Carlo simulations, we have illustrated how the sample size is related to the statistic power value, the significance level, the variability of observations and the minor magnitude of the effect of interest under study. If the study has been already completed, one should not perform any 'post hoc' power calculations. In this case, calculation of confidence intervals is a better choice. We assessed the confidence intervals given in a number of publications where microcirculation is studied by LDF techniques using different protocols. We have found that types I and II errors are frequently encountered in the LDF studies, which is a consequence of an inappropriate sample size.

Assessment of cardiac time intervals by wavelet transform of the impedance cardiogram.

BACKGROUND: Impedance cardiography (ICG) is an inexpensive, noninvasive technique for estimating hemodynamic parameters. ICG can be used to obtain the ejection fraction of the left atrium and to monitor systolic time intervals. Traditional ICG technique does not enable unambiguous detection of the left ventricle ejection time (LVET) and the time relationships between specific marker points. OBJECTIVE: This work aims to approbate a new approach for ICG signal processing using wavelet transform (WT) and to investigate the possibilities of this approach for determination of the parameters which are related to the stroke volume (SV), in particular LVET. METHODS: Thoracic tetrapolar polyrheocardiography method for simultaneous registration of ECG, ICG and phonocardiograms has been used. A control group consisted of eight healthy men aged 20-25 years. In addition, four patients with essential hypertension participated in the study. Wavelet representation of the ICG data produced local maxima in a two dimensional distribution of the wavelet coefficient. Each extremum point was characterized by the amplitude, scale and time, which determine SV. RESULTS: LVET was defined as the scale corresponding to the E-wave maximum related to the systolic phase of the cardiac cycle. Also, we defined the initial systolic time interval (ISTI) as the time interval between R peak in the ECG and E-wave maximum on the wavelet plane. During functional test LVET and ISTI values defined by WT demonstrated a proper hemodynamic response to loading for the control group and patients with essential hypertension. CONCLUSION: The proposed approach demonstrates the ability of ICG-WT technique for adequate assessment of SV parameters, including cardiac time intervals.

Hindered Energy Cascade in Highly Helical Isotropic Turbulence.

The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that helicity can play a significant role in turbulent systems, e.g., supporting the generation of large-scale magnetic fields, but its impact on the energy cascade to small scales has never been observed. We suggest, for the first time, a generalized phenomenology for isotropic turbulence with an arbitrary spectral distribution of the helicity. We discuss various scenarios of direct turbulent cascades with new helicity effect, which can be interpreted as a hindering of the spectral energy transfer. Therefore, the energy is accumulated and redistributed so that the efficiency of nonlinear interactions will be sufficient to provide a constant energy flux. We confirm our phenomenology by high Reynolds number numerical simulations based on a shell model of helical turbulence. The energy in our model is injected at a certain large scale only, whereas the source of helicity is distributed over all scales. In particular, we found that the helical bottleneck effect can appear in the inertial interval of the energy spectrum.

Non-Kolmogorov cascade of helicity-driven turbulence.

We solve the Navier-Stokes equations with two simultaneous forcings. One forcing is applied at a given large scale and it injects energy. The other forcing is applied at all scales belonging to the inertial range and it injects helicity. In this way we can vary the degree of turbulence helicity from nonhelical to maximally helical. We find that increasing the rate of helicity injection does not change the energy flux. On the other hand, the level of total energy is strongly increased and the energy spectrum gets steeper. The energy spectrum spans from a Kolmogorov scaling law k^{-5/3} for a nonhelical turbulence, to a non-Kolmogorov scaling law k^{-7/3} for a maximally helical turbulence. In the latter case we find that the characteristic time of the turbulence is not the turnover time but a time based on the helicity injection rate. We also analyze the results in terms of helical modes decomposition. For a maximally helical turbulence one type of helical mode is found to be much more energetic than the other one, by several orders of magnitude. The energy cascade of the most energetic type of helical mode results from the sum of two fluxes. One flux is negative and can be understood in terms of a decimated model. This negative flux, however, is not sufficient to lead an inverse energy cascade. Indeed, the other flux involving the least energetic type of helical mode is positive and the largest. The least energetic type of helical mode is then essential and cannot be neglected.

Wavelet-analysis of skin temperature oscillations during local heating for revealing endothelial dysfunction.

Skin microvessels have proven to be a model to investigate the mechanisms of vascular disease; in particular, endothelial dysfunction. To analyze skin blood flow, high-resolution thermometry can be used because low-amplitude skin temperature oscillations are caused by changes in the tone of skin vessels. The aim of our study was to test the possibilities of wavelet analysis of skin temperature (WAST) for the diagnosis of impaired regulation of microvascular tone in patients with type 2 diabetes. A local heating functional test was used for the assessment of microvascular tone regulation. A control group consisted of healthy male and female volunteers (n=5 each), aged 39.1±5.3years. A group of patients with type 2 diabetes comprised thirteen people, seven men and six women, aged 36 to 51years old (43.2±3.4years). The diagnosis of diabetes was made according to the criteria of the World Health Organization (WHO). The mean disease duration was 7.36±0.88years. Skin temperature oscillations, reflecting intrinsic myogenic activity (0.05-0.14Hz), neurogenic factors (0.02-0.05Hz) and endothelial activity (0.0095-0.02Hz) increase greatly during local heating for healthy subjects. In the group of patients with type 2 diabetes, no statistically significant differences in the amplitudes in the endothelial range were observed. Relative changes in the oscillation amplitudes in patients with type 2 diabetes were markedly lower compared to the control group. The latter indicates that the WAST method enables assessment of the state of vascular tone and the effects of mechanisms responsible for regulation of blood flow in the microvasculature.

Systematic bias in the calculation of spectral density from a three-dimensional spatial grid.

The energy spectral density E(k), where k is the spatial wave number, is a well-known diagnostic of homogeneous turbulence and magnetohydrodynamic turbulence. However, in most of the curves plotted by different authors, some systematic kinks can be observed at k=9, 15, and 19. We claim that these kinks have no physical meaning and are in fact the signature of the method that is used to estimate E(k) from a three-dimensional spatial grid. In this paper we give another method in order to get rid of the spurious kinks and to estimate E(k) much more accurately.

Turbulent viscosity and turbulent magnetic diffusivity in a decaying spin-down flow of liquid sodium.

The free decay of a strong flow of liquid sodium (at Reynolds number defined via the maximal mean velocity and the radius of the channel cross section up to Re≈3×10(60) and the corresponding magnetic Reynolds number up to Rm≈30) generated by the sudden stop of a rapidly rotating toroidal channel is studied experimentally. The toroidal and poloidal components of velocity are measured using a potential probe. We describe the onset of motion, the evolution of strongly anisotropic fluctuations, and the homogenization and decay of turbulence in the final period. We analyze the statistical characteristics of velocity fields in relation to the behavior of effective magnetic diffusivity estimated from measurements of the phase shift between the induced and applied magnetic fields. For the late (self-similar) decay of turbulent flow, turbulent viscosity is shown to be dependent on the root-mean-square velocity pulsations and can be expressed as νt∼νRe1.3. The behavior of turbulent magnetic diffusivity depends on the magnetic Reynolds number defined in terms of the root-mean-square velocity pulsations. At low magnetic Reynolds numbers (Rmrms<1), turbulent magnetic diffusivity grows rapidly with increasing velocity pulsations (ηt∼ηRmrms2). If the magnetic Reynolds number exceeds unity, the behavior of turbulent magnetic diffusivity becomes similar to the behavior of turbulent viscosity. The highest values of turbulent magnetic diffusivity are achieved at the end of braking, which corresponds to the transient stage of a strongly anisotropic turbulent flow in which the poloidal velocity oscillations prevail.

Cascades and dissipation ratio in rotating magnetohydrodynamic turbulence at low magnetic Prandtl number.

A phenomenology of isotropic magnetohydrodynamic (MHD) turbulence subject to both rotation and applied magnetic field is presented. It is assumed that the triple correlation decay time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and the Alfvén wave period. For Pm=1 it leads to four kinds of piecewise spectra, depending on four parameters: injection rate of energy, magnetic diffusivity, rotation rate, and applied field. With a shell model of MHD turbulence (including rotation and applied magnetic field), spectra for Pm ≤ 1 are presented, together with the ratio between magnetic and viscous dissipations.

Direct measurement of effective magnetic diffusivity in turbulent flow of liquid sodium.

The first direct measurements of effective magnetic diffusivity in turbulent flow of electroconductive fluids (the so-called ß effect) under the magnetic Reynolds number Rm≫1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re≈3×10(6), which corresponds to the magnetic Reynolds number Rm≈30. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal deviation of magnetic diffusivity from its laminar value reaches about 50%.

Dynamo action in Möbius flow.

We demonstrate that flows of conducting fluid along a Möbius strip and related surfaces are hydromagnetic dynamos, i.e., they can produce an exponentially growing magnetic field from an infinitesimal seed. The critical magnetic Reynolds number in one of our models is as low as about 16. Together with other attractive features, this makes this flow an interesting candidate for a laboratory dynamo experiment.

Mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow.

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean-field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-type dynamo. In view of this application the second-order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.

Large- and small-scale interactions and quenching in an alpha2-dynamo.

The evolution of the large-scale magnetic field in a turbulent flow of conducting fluid is considered in the framework of a multiscale alpha2-dynamo model, which includes the poloidal and the toroidal components for the large-scale magnetic field and a shell model for the small-scale magnetohydrodynamical turbulence. The conjugation of the mean-field description for the large-scale field and the shell formalism for the small-scale turbulence is based on strict conformity to the conservation laws. The model displays a substantial magnetic contribution to the alpha effect. It was shown that a large-scale magnetic field can be generated by current helicity even solely. The alpha quenching and the role of the magnetic Prandtl number (Pm) are studied. We have determined the dynamic nature of the saturation mechanism of dynamo action. Any simultaneous cross correlation of alpha and large-scale magnetic field energy EB is negligible, whereas coupling between alpha and EB becomes substantial for moderate time lags. An unexpected result is the behavior of the large-scale magnetic energy with variation of the magnetic Prandtl number. Diminishing of Pm does not have an inevitable ill effect on the magnetic field generation. The most efficient large-scale dynamo operates under relatively low Prandtl numbers--then the small-scale dynamo is suppressed and the decrease of Pm can lead even to superequipartition of the large-scale magnetic field (i.e., EB>Eu). In contrast, the growth of Pm does not promote the large-scale magnetic field generation. A growing counteraction of the magnetic alpha effect reduces the level of mean large-scale magnetic energy at the saturated state.

Screw dynamo in a time-dependent pipe flow.

The kinematic dynamo problem is investigated for the flow of a conducting fluid in a cylindrical, periodic tube with conducting walls. The methods used are an eigenvalue analysis of the steady regime, and the three-dimensional solution of the time-dependent induction equation. The configuration and parameters considered here are close to those of a dynamo experiment planned in Perm, which will use a torus-shaped channel. We find growth of an initial magnetic field by more than three orders of magnitude. A marked field growth can be obtained if the braking time is less than 0.2 s and only one diverter is used in the channel. The structure of the seed field has a strong impact on the field amplification factor. Generation properties can be improved by adding ferromagnetic particles to the fluid in order to increase its relative permeability, but this will not be necessary for the success of the dynamo experiment. For higher magnetic Reynolds numbers, the nontrivial evolution of different magnetic modes limits the value of simple "optimistic" and "pessimistic" estimates.