László Kocsis

Fractal characterization of complexity in temporal physiological signals

This review first gives an overview on the concept of fractal geometry with definitions and explanations of the most fundamental properties of fractal structures and processes like self-similarity, power law scaling relationship, scale invariance, scaling range and fractal dimensions. Having laid down the grounds of the basics in terminology and mathematical formalism, the authors systematically introduce the concept and methods of monofractal time series analysis. They argue that fractal time series analysis cannot be done in a conscious, reliable manner without having a model capable of capturing the essential features of physiological signals with regard to their fractal analysis. They advocate the use of a simple, yet adequate, dichotomous model of fractional Gaussian noise (fGn) and fractional Brownian motion (fBm). They demonstrate the importance of incorporating a step of signal classification according to the fGn/fBm model prior to fractal analysis by showing that missing out on signal class can result in completely meaningless fractal estimates. Limitation and precision of various fractal tools are thoroughly described and discussed using results of numerical experiments on ideal monofractal signals. Steps of a reliable fractal analysis are explained. Finally, the main applications of fractal time series analysis in biomedical research are reviewed and critically evaluated.

The modified Beer-Lambert law revisited.

The modified Beer-Lambert law (MBLL) is the basis of continuous-wave near-infrared tissue spectroscopy (cwNIRS). The differential form of MBLL (dMBLL) states that the change in light attenuation is proportional to the changes in the concentrations of tissue chromophores, mainly oxy- and deoxyhaemoglobin. If attenuation changes are measured at two or more wavelengths, concentration changes can be calculated. The dMBLL is based on two assumptions: (1) the absorption of the tissue changes homogeneously, and (2) the scattering loss is constant. It is known that absorption changes are usually inhomogeneous, and therefore dMBLL underestimates the changes in concentrations (partial volume effect) and every calculated value is influenced by the change in the concentration of other chromophores (cross-talk between chromophores). However, the error introduced by the second assumption (cross-talk of scattering changes) has not been assessed previously. An analytically treatable special case (semi-infinite, homogeneous medium, with optical properties of the cerebral cortex) is utilized here to estimate its order of magnitude. We show that the per cent change of the transport scattering coefficient and that of the absorption coefficient have an approximately equal effect on the changes of attenuation, and a 1% increase in scattering increases the estimated concentration changes by about 0.5 microM.

Maturation of Cardiovagal Autonomic Function From Childhood to Young Adult Age

Background—Cardiovagal autonomic control declines with age in adult subjects, which is related in part to increasing stiffness of the barosensory vessel wall. It is not known, however, whether autonomic function changes with age in children. Methods and Results—We studied 137 healthy subjects divided into 4 age groups: group 1, 7 to 14 years; group 2, 11 to 14 years; group 3, 15 to 18 years; and group 4, 19 to 22 years. Brachial artery pressure was measured by sphygmomanometry and continuous radial artery pressure and carotid artery pulse pressure (&Dgr;P) by applanation tonometry. The R-R interval was derived from the ECG. Autonomic function was assessed by spontaneous sequence and frequency-domain indices, which indicate the extent of coupling between fluctuations in heart rate and systolic pressure. Carotid artery diastolic diameter (DD) and pulsatile distension (&Dgr;D) were measured by echo wall tracking; carotid compliance coefficient (CC) was defined as &Dgr;D/&Dgr;P and distensibility coefficient as 2&Dgr;D/DD · &Dgr;P. From group 1 to group 3, spontaneous indices increased significantly (18.1±1.7 versus 33.3±4.0; 14.4±1.1 versus 25.5±22; 12.9±1.1 versus 20.8±2.0; and 6.4±0.6 versus 16.2±1.4 ms/mm Hg [mean±SEM] for Seq+, Seq−, LF&agr;, and LFgain, respectively), with no significant changes afterward. CC and DC were inversely proportional to age (r=−0.49 and −0.62, respectively, P<0.001). The efficiency of neural integrative mechanisms, estimated as the ratio of spontaneous indices and CC, more than doubled from group 1 to group 3. Spontaneous indices were linearly related to measures of cardiac vagal activity. Conclusions—The increase in spontaneous indices from early childhood to adolescence, despite gradual stiffening of the carotid artery, may indicate improved cardiovagal autonomic function, which is most likely a result of maturation of neural mechanisms, attaining peak level at adolescence.

Prediction of the main cortical areas and connections involved in the tactile function of the visual cortex by network analysis.

We explored the cortical pathways from the primary somatosensory cortex to the primary visual cortex (V1) by analysing connectional data in the macaque monkey using graph‐theoretical tools. Cluster analysis revealed the close relationship of the dorsal visual stream and the sensorimotor cortex. It was shown that prefrontal area 46 and parietal areas VIP and 7a occupy a central position between the different clusters in the visuo‐tactile network. Among these structures all the shortest paths from primary somatosensory cortex (3a, 1 and 2) to V1 pass through VIP and then reach V1 via MT, V3 and PO. Comparison of the input and output fields suggested a larger specificity for the 3a/1‐VIP‐MT/V3‐V1 pathways among the alternative routes. A reinforcement learning algorithm was used to evaluate the importance of the aforementioned pathways. The results suggest a higher role for V3 in relaying more direct sensorimotor information to V1. Analysing cliques, which identify areas with the strongest coupling in the network, supported the role of VIP, MT and V3 in visuo‐tactile integration. These findings indicate that areas 3a, 1, VIP, MT and V3 play a major role in shaping the tactile information reaching V1 in both sighted and blind subjects. Our observations greatly support the findings of the experimental studies and provide a deeper insight into the network architecture underlying visuo‐tactile integration in the primate cerebral cortex.

Static and dynamic changes in carotid artery diameter in humans during and after strenuous exercise

Arterial baroreflex function is altered by dynamic exercise, but it is not clear to what extent baroreflex changes are due to altered transduction of pressure into deformation of the barosensory vessel wall. In this study we measured changes in mean common carotid artery diameter and the pulsatile pressure: diameter ratio (PDR) during and after dynamic exercise. Ten young, healthy subjects performed a graded exercise protocol to exhaustion on a bicycle ergometer. Carotid dimensions were measured with an ultrasound wall‐tracking system; central arterial pressure was measured with the use of radial tonometry and the generalized transfer function; baroreflex sensitivity (BRS) was assessed in the post‐exercise period by spectral analysis and the sequence method. Data are given as means ±s.e.m. Mean carotid artery diameter increased during exercise as compared with control levels, but carotid distension amplitude did not change. PDR was reduced from 27.3 ± 2.7 to 13.7 ± 1.0 μm mmHg−1. Immediately after stopping exercise, the carotid artery constricted and PDR remained reduced. At 60 min post‐exercise, the carotid artery dilated and the PDR increased above control levels (33.9 ± 1.4 μm mmHg−1). The post‐exercise changes in PDR were closely paralleled by those in BRS (0.74 ≤r≤ 0.83, P < 0.05). These changes in mean carotid diameter and PDR suggest that the mean baroreceptor activity level increases during exercise, with reduced dynamic sensitivity; at the end of exercise baroreceptors are suddenly unloaded, then at 1 h post‐exercise, baroreceptor activity increases again with increasing dynamic sensitivity. The close correlation between PDR and BRS observed at post‐exercise underlies the significance of mechanical factors in arterial baroreflex control.

Inverse-orthostasis may induce elevation of blood pressure due to sympathetic activation.

Microgravity and simulated microgravity may cause cardiovascular deconditioning, but mechanisms of instantaneous responses to inverse-orthostasis are not studied. Hence, we investigated transient and steady state cardiovascular changes by combining the tilt technique with cardiovascular telemetry. Normotensive and NO-deprived hypertensive Wistar rats were used to analyze responses of mean arterial blood pressure, heart rate, contractility, spontaneous baroreflex sensitivity (sBRS), and autonomic balance. Inverse-orthostasis tests were carried out by 45° head-down tilting (repeated 3 × 5 mins “R”, or sustained for 120 mins “S”). In normotensive rats, horizontal control blood pressure was R111.3 ± 1.7/S110.4 ± 2.3 mm Hg and heart rate was R385.2 ± 5.9/S371.1 ± 6.1 BPM. Head-down tilt induced an increase in blood pressure by R5.9/S10.6 mm Hg, while heart rate, contractility, sBRS, and autonomic balance did not change. The hypertensive response was sustained, could be prevented by prazosin (10 mg/kgbw), and augmented by subanesthetic doses of chloralose (26 and 43 mg/kgbw). In NO-suppressed hypertension, control blood pressure and heart rate were R132.4 ± 2.9/S130.0 ± 4.1 mm Hg and R339.2 ± 7.9/S307.2 ± 23.6 BPM, respectively. Head-down tilt further increased blood pressure by R5.1/S10.5 mm Hg. These data demonstrate that conscious rats respond to inverse-orthostasis by sustained elevation of blood pressure independent of NO synthesis. This response is neither due to increased contractility and altered sBRS, nor due to non-specific stress, but probably due to sympathetic activation elicited by gravity-related reflexes, which increase peripheral resistance.

Fractal Characterization of Complexity in Dynamic Signals: Application to Cerebral Hemodynamics

We introduce the concept of spatial and temporal complexity with emphasis on how its fractal characterization for 1D, 2D or 3D hemodynamic brain signals can be carried out. Using high-resolution experimental data sets acquired in animal and human brain by noninvasive methods - such as laser Doppler flowmetry, laser speckle, near infrared, or functional magnetic resonance imaging - the spatiotemporal complexity of cerebral hemodynamics is demonstrated. It is characterized by spontaneous, seemingly random (that is disorderly) fluctuation of the hemodynamic signals. Fractal analysis, however, proved that these fluctuations are correlated according to the special order of self-similarity. The degree of correlation can be assessed quantitatively either in the temporal or the frequency domain respectively by the Hurst exponent (H) and the spectral index (beta). The values of H for parenchymal regions of white and gray matter of the rat brain cortex are distinctly different. In human studies, the values of beta were instrumental in identifying age-related stiffening of cerebral vasculature and their potential vulnerability in watershed areas of the brain cortex such as in borderline regions between frontal and temporal lobes. Biological complexity seems to be present within a restricted range of H or beta values which may have medical significance because outlying values can indicate a state of pathology.