Peter Herman

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.

Physiological time series: distinguishing fractal noises from motions

Abstract. Many physiological signals appear fractal, in having self-similarity over a large range of their power spectral densities. They are analogous to one of two classes of discretely sampled pure fractal time signals, fractional Gaussian noise (fGn) or fractional Brownian motion (fBm). The fGn series are the successive differences between elements of a fBm series; they are stationary and are completely characterized by two parameters, σ2, the variance, and H, the Hurst coefficient. Such efficient characterization of physiological signals is valuable since H defines the autocorrelation and the fractal dimension of the time series. Estimation of H from Fourier analysis is inaccurate, so more robust methods are needed. Dispersional analysis (Disp) is good for noise signals while bridge detrended scaled windowed variance analysis (bdSWV) is good for motion signals. Signals whose slopes of their power spectral densities lie near the border between fGn and fBm are difficult to classify. A new method using signal summation conversion (SSC), wherein an fGn is converted to an fBm or an fBm to a summed fBm and bdSWV then applied, greatly improves the classification and the reliability of Ĥ, the estimates of H, for the times series. Applying these methods to laser-Doppler blood cell perfusion signals obtained from the brain cortex of anesthetized rats gave Ĥ of 0.24±0.02 (SD, n=8) and defined the signal as a fractional Brownian motion. The implication is that the flow signal is the summation (motion) of a set of local velocities from neighboring vessels that are negatively correlated, as if induced by local resistance fluctuations.

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.

Energetics of neuronal signaling and fMRI activity

Energetics of resting and evoked fMRI signals were related to localized ensemble firing rates (ν) measured by electrophysiology in rats. Two different unstimulated, or baseline, states were established by anesthesia. Halothane and α-chloralose established baseline states of high and low energy, respectively, in which forepaw stimulation excited the contralateral primary somatosensory cortex (S1). With α-chloralose, forepaw stimulation induced strong and reproducible fMRI activations in the contralateral S1, where the ensemble firing was dominated by slow signaling neurons (SSN; ν range of 1–13 Hz). Under halothane, weaker and less reproducible fMRI activations were observed in the contralateral S1 and elsewhere in the cortex, but ensemble activity in S1 was dominated by rapid signaling neurons (RSN; ν range of 13–40 Hz). For both baseline states, the RSN activity (i.e., higher frequencies, including the γ band) did not vary upon stimulation, whereas the SSN activity (i.e., α band and lower frequencies) did change. In the high energy baseline state, a large majority of total oxidative energy [cerebral metabolic rate of oxygen consumption (CMRO2)] was devoted to RSN activity, whereas in the low energy baseline state, it was roughly divided between SSN and RSN activities. We hypothesize that in the high energy baseline state, the evoked changes in fMRI activation in areas beyond S1 are supported by rich intracortical interactions represented by RSN. We discuss implications for interpreting fMRI data where stimulus-specific ΔCMRO2 is generally small compared with baseline CMRO2.

Remote Effects of Focal Hippocampal Seizures on the Rat Neocortex

Seizures have both local and remote effects on nervous system function. Whereas propagated seizures are known to disrupt cerebral activity, little work has been done on remote network effects of seizures that do not propagate. Human focal temporal lobe seizures demonstrate remote changes including slow waves on electroencephalography (EEG) and decreased cerebral blood flow (CBF) in the neocortex. Ictal neocortical slow waves have been interpreted as seizure propagation; however, we hypothesize that they reflect a depressed cortical state resembling sleep or coma. To investigate this hypothesis, we performed multimodal studies of partial and secondarily generalized limbic seizures in rats. Video/EEG monitoring of spontaneous seizures revealed slow waves in the frontal cortex during behaviorally mild partial seizures, contrasted with fast polyspike activity during convulsive generalized seizures. Seizures induced by hippocampal stimulation produced a similar pattern, and were used to perform functional magnetic resonance imaging weighted for blood oxygenation and blood volume, demonstrating increased signals in hippocampus, thalamus and septum, but decreases in orbitofrontal, cingulate, and retrosplenial cortex during partial seizures, and increases in all of these regions during propagated seizures. Combining these results with neuronal recordings and CBF measurements, we related neocortical slow waves to reduced neuronal activity and cerebral metabolism during partial seizures, but found increased neuronal activity and metabolism during propagated seizures. These findings suggest that ictal neocortical slow waves represent an altered cortical state of depressed function, not propagated seizure activity. This remote effect of partial seizures may cause impaired cerebral functions, including loss of consciousness.

Oxidative Neuroenergetics in Event-Related Paradigms

Energetic basis of neural activity provides a solid foundation for noninvasive neuroimaging with calibrated functional magnetic resonance imaging (fMRI). Calculating dynamic changes in cerebral oxidative energy utilization (CMRO2) is limited by uncertainties about whether or not the conventional blood oxygenation level-dependent (BOLD) model can be applied transiently using multimodal measurements of blood flow (CBF) and volume (CBV) that affect the BOLD signal. A prerequisite for dynamic calibrated fMRI is testing the linearity of multimodal signals within a temporal regimen, as assessed by signal strength (i.e., both intensity and width). If each hyperemic component (BOLD, CBV, CBF) is demonstrated to be linear with neural activity under various experimental conditions, then the respective transfer functions generated by deconvolution with neural activity should be time invariant and thus could potentially be used for calculating CMRO2 transients. Hyperemic components were investigated at 11.7 T in α-chloralose-anesthetized rats and combined with electrophysiological recordings of local field potential (LFP) and multiunit activity (MUA) from the cortex during forepaw stimulation, in which stimulus number and frequency were varied. Although relationships between neural activity and stimulus features ranged from linear to nonlinear, associations between hyperemic components and neural activity were linear. Specific to each hyperemic component, a universal transfer function (with LFP or MUA) yielded predictions in agreement with experimental measurements. The results identified a component of the BOLD signal that can be attributed to significant changes in CMRO2, even for temporal events separated by <200 ms.

Relative Changes in Cerebral Blood Flow and Neuronal Activity in Local Microdomains during Generalized Seizures

There is broad agreement that generalized tonic–clonic seizures (GTCS) and normal somatosensory stimulation are associated with increases in regional CBF. However, the data regarding CBF changes during absence seizures are controversial. Electrophysiologic studies in WAG/Rij rats, an established animal model of absence seizures, have shown spike-wave discharges (SWD) that are largest in the perioral somatosensory cortex while sparing the visual cortex. Recent functional magnetic resonance imaging (fMRI) studies in the same model have also shown localized increases in fMRI signals in the perioral somatosensory cortex during SWD. Because fMRI signals are only indirectly related to neuronal activity, the authors directly measured CBF and neuronal activity from specific microdomains of the WAG/Rij cortex using a specially designed probe combining laser-Doppler flowmetry and extracellular microelectrode recordings under fentanyl/haloperidol anesthesia. Using this approach, parallel increases in neuronal activity and CBF were observed during SWD in the whisker somatosensory (barrel) cortex, whereas the visual cortex showed no significant changes. For comparison, these measurements were repeated during somatosensory (whisker) stimulation, and bicuculline-induced GTCS in the same animals. Interestingly, whisker stimulation increased neuronal activity and CBF in the barrel cortex more than during SWD. During GTCS, much larger increases that included both the somatosensory and visual cortex were observed. Thus, SWD in this model produce parallel localized increases in neuronal activity and CBF with similar distribution to somatosensory stimulation, whereas GTCS produce larger and more widespread changes. The normal response to somatosensory stimulation appears to be poised between two abnormal responses produced by two physiologically different types of seizures.

Decreased Subcortical Cholinergic Arousal in Focal Seizures

Impaired consciousness in temporal lobe seizures has a major negative impact on quality of life. The prevailing view holds that this disorder impairs consciousness by seizure spread to the bilateral temporal lobes. We propose instead that seizures invade subcortical regions and depress arousal, causing impairment through decreases rather than through increases in activity. Using functional magnetic resonance imaging in a rodent model, we found increased activity in regions known to depress cortical function, including lateral septum and anterior hypothalamus. Importantly, we found suppression of intralaminar thalamic and brainstem arousal systems and suppression of the cortex. At a cellular level, we found reduced firing of identified cholinergic neurons in the brainstem pedunculopontine tegmental nucleus and basal forebrain. Finally, we used enzyme-based amperometry to demonstrate reduced cholinergic neurotransmission in both cortex and thalamus. Decreased subcortical arousal is a critical mechanism for loss of consciousness in focal temporal lobe seizures.

Neural Progenitor Cells Regulate Capillary Blood Flow in the Postnatal Subventricular Zone

In the postnatal subventricular zone (SVZ), S phase entry of neural progenitor cells (NPCs) correlates with a local increase in blood flow. However, the cellular mechanism controlling this hemodynamic response remains unknown. We show that a subpopulation of SVZ cells, astrocyte-like cells or B-cells, sends projections ensheathing pericytes on SVZ capillaries in young mice. We examined whether calcium increases in pericytes or B-cells led to a vascular response in acute slices using the P2Y2/4 receptor (P2Y2/4R) agonist UTP, electrical stimulation, or transgenic mice expressing exogenous Gq-coupled receptors (MrgA1) in B-cells. UTP increased calcium in pericytes leading to capillary constrictions. Electrical stimulation induced calcium propagation in SVZ cells followed by capillary constrictions involving purinergic receptors. In transgenic mice, selective calcium increases in B-cells induced P2Y2/4R-dependent capillary constrictions, suggesting that B-cells release ATP activating purinergic receptors on pericytes. Interestingly, in the presence of a P2Y2/4R blocker, dilation was observed. Intraventricular UTP injection transiently decreased blood flow monitored in vivo using laser Doppler flowmetry. Using neonatal electroporation, we expressed MrgA1 in slow cycling radial glia-derived B1 cells, i.e., NPCs. Intraventricular injection of an MrgA1 ligand increased blood flow in the SVZ. Thus, upon intracellular calcium increases B-cells/NPCs release ATP and vasodilating factors that activate purinergic receptors on pericytes triggering a vascular response and blood flow increase in vivo. Considering that NPCs receive signals from other SVZ cells, these findings further suggest that NPCs act as transducers of neurometabolic coupling in the SVZ.

Frequency‐dependent tactile responses in rat brain measured by functional MRI

We measured frequency‐dependent functional MRI (fMRI) activations (at 11.7 T) in the somatosensory cortex with whisker and forepaw stimuli in the same α‐chloralose anesthetized rats. Whisker and forepaw stimuli were attained by computer‐controlled pulses of air puffs and electrical currents, respectively. Air puffs deflected (±2 mm) the chosen whisker(s) in the right snout in the rostral to caudal direction, and electrical currents (2 mA amplitude, 0.3 ms duration) stimulated the left forepaw with subcutaneous copper electrodes placed between the second and fourth digits. In the same subject, unimodal stimulation of whisker and forepaw gave rise to significant blood oxygen level‐dependent (BOLD) signal increases in corresponding contralateral somatosensory areas of whisker barrel field (S1BF) and forelimb (S1FL), respectively, with no significant spatial overlap between these regions. The BOLD responses in S1BF and S1FL regions were found to be differentially variable with frequency of each stimulus type. In the S1BF, a linear increase in the BOLD response was observed with whisker stimulation frequency of up to ∼12 Hz, beyond which the response seemed to saturate (and/or slightly attenuate) up to the maximum frequency studied (i.e. 30 Hz). In the S1FL, the magnitude of the BOLD response was largest at forepaw stimulation frequency between 1.5 and 3 Hz, beyond which the response diminished with little or no activity at frequencies higher than 20 Hz. The volume of tissue activated by each stimulus type followed a similar pattern to that of the stimulation frequency dependence. These results of bimodal whisker and forepaw stimuli in the same subject may provide a framework to study interactions of different tactile modules, with both fMRI and neurophysiology (i.e. inside and outside the magnet). Copyright