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.

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 insatiable appetite for energy to support human brain function is mainly supplied by glucose oxidation (CMR_glc(ox)). But how much energy is consumed for signaling and nonsignaling processes in gray/white matter is highly debated. We examined this issue by combining metabolic measurements of gray/white matter and a theoretical calculation of bottom-up energy budget using biophysical properties of neuronal/glial cells in conjunction with species-exclusive electrophysiological and morphological data. We calculated a CMR_glc(ox)-derived budget and confirmed it with experimental results measured by PET, autoradiography, ¹³C-MRS, and electrophysiology. Several conserved principles were observed regarding the energy costs for brain’s signaling and nonsignaling components in both human and rat. The awake resting cortical signaling processes and mass-dependent nonsignaling processes, respectively, demand ∼70% and ∼30% of CMR_glc(ox). Inhibitory neurons and glia need 15–20% of CMR_glc(ox), with the rest demanded by excitatory neurons. Nonsignaling demands dominate in white matter, in near opposite contrast to gray matter demands. Comparison between ¹³C-MRS data and calculations suggests ∼1.2 Hz glutamatergic signaling rate in the awake human cortex, which is ∼4 times lower than signaling in the rat cortex. Top-down validated bottom-up budgets could allow computation of anatomy-based CMR_glc(ox) maps and accurate cellular level interpretation of brain metabolic imaging.

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.