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 (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.

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 (⌬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 (⌬D) were measured by echo wall tracking; carotid compliance coefficient (CC) was defined as ⌬D/⌬P and distensibility coefficient as 2⌬D/DD · ⌬P. , with no significant changes afterward. CC and DC were inversely proportional to age (rϭϪ0.49 and Ϫ0.62, respectively, PϽ0.001). 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.

Encoding continuous sensory variables requires sustained synaptic signalling. At several sensory synapses, rapid vesicle supply is achieved via highly mobile vesicles and specialized ribbon structures, but how this is achieved at central synapses without ribbons is unclear. Here we examine vesicle mobility at excitatory cerebellar mossy fibre synapses which sustain transmission over a broad frequency bandwidth. Fluorescent recovery after photobleaching in slices from VGLUT1Venus knock-in mice reveal 75% of VGLUT1-containing vesicles have a high mobility, comparable to that at ribbon synapses. Experimentally constrained models establish hydrodynamic interactions and vesicle collisions are major determinants of vesicle mobility in crowded presynaptic terminals. Moreover, models incorporating 3D reconstructions of vesicle clouds near active zones (AZs) predict the measured releasable pool size and replenishment rate from the reserve pool. They also show that while vesicle reloading at AZs is not diffusion-limited at the onset of release, diffusion limits vesicle reloading during sustained high-frequency signalling.DOI: http://dx.doi.org/10.7554/eLife.15133.001