When modeling a system as complex as the brain, considerable simplifications are inevitable. The nature of these simplifications depends on the available experimental evidence, and the desired form of model predictions. A focus on the former often inspires models of networks of individual neurons, since properties of single cells are more easily measured than those of entire populations. However, if the goal is to describe the processes responsible for the electroencephalogram (EEG), such models can become unmanageable due to the large numbers of neurons involved. Mean-field models in which assemblies of neurons are represented by their average properties allow activity underlying the EEG to be captured in a tractable manner. The starting point of the results presented here is a recent physiologically-based mean-field model of the corticothalamic system, which includes populations of excitatory and inhibitory cortical neurons, and an excitatory population representing the thalamic relay nuclei, reciprocally connected with the cortex and the inhibitory thalamic reticular nucleus. The average firing rates of these populations depend nonlinearly on their membrane potentials, which are determined by afferent inputs after axonal propagation and dendritic and synaptic delays. It has been found that neuronal activity spreads in an approximately wavelike fashion across the cortex, which is modeled as a two-dimensional surface. On the basis of the literature, the EEG signal is assumed to be roughly proportional to the activity of cortical excitatory neurons, allowing physiological parameters to be extracted by inverse modeling of empirical EEG spectra. One objective of the present work is to characterize the statistical distributions of fitted model parameters in the healthy population. Variability of model parameters within and between individuals is assessed over time scales of minutes to more than a year, and compared with the variability of classical quantitative EEG (qEEG) parameters. These parameters are generally not normally distributed, and transformations toward the normal distribution are often used to facilitate statistical analysis. However, no single optimal transformation exists to render data distributions approximately normal. A uniformly applicable solution that not only yields data following the normal distribution as closely as possible, but also increases test-retest reliability, is described in Chapter 2. Specialized versions of this transformation have been known for some time in the statistical literature, but it has not previously found its way to the empirical sciences. Chapter 3 contains the study of intra-individual and inter-individual variability in model parameters, also providing a comparison of test-retest reliability with that of commonly used EEG spectral measures such as band powers and the frequency of the alpha peak. It is found that the combined model parameters provide a reliable characterization of an individual's EEG spectrum, where some parameters are more informative than others. Classical quantitative EEG measures are found to be somewhat more reproducible than model parameters. However, the latter have the advantage of providing direct connections with the underlying physiology. In addition, model parameters are complementary to classical measures in that they capture more information about spectral structure. Another conclusion from this work was that a few minutes of alert eyes-closed EEG already contain most of the individual variability likely to occur in this state on the scale of years. In Chapter 4, age trends in model parameters are investigated for a large sample of healthy subjects aged 6-86 years. Sex differences in parameter distributions and trends are considered in three age ranges, and related to the relevant literature. We also look at changes in inter-individual variance across age, and find that subjects are in many respects maximally different around adolescence. This study forms the basis for prospective comparisons with age trends in evoked response potentials (ERPs) and alpha peak morphology, besides providing a standard for the assessment of clinical data. It is the first study to report physiologically-based parameters for such a large sample of EEG data. The second main thrust of this work is toward incorporating the thalamocortical system and the basal ganglia in a unified framework. The basal ganglia are a group of gray matter structures reciprocally connected with the thalamus and cortex, both significantly influencing, and influenced by, their activity. Abnormalities in the basal ganglia are associated with various disorders, including schizophrenia, Huntington's disease, and Parkinson's disease. A model of the basal ganglia-thalamocortical system is presented in Chapter 5, and used to investigate changes in average firing rates often measured in parkinsonian patients and animal models of Parkinson's disease. Modeling results support the hypothesis that two pathways through the basal ganglia (the so-called direct and indirect pathways) are differentially affected by the dopamine depletion that is the hallmark of Parkinson's disease. However, alterations in other components of the system are also suggested by matching model predictions to experimental data. The dynamics of the model are explored in detail in Chapter 6. Electrophysiological aspects of Parkinson's disease include frequency reduction of the alpha peak, increased relative power at lower frequencies, and abnormal synchronized fluctuations in firing rates. It is shown that the same parameter variations that reproduce realistic changes in mean firing rates can also account for EEG frequency reduction by increasing the strength of the indirect pathway, which exerts an inhibitory effect on the cortex. Furthermore, even more strongly connected subcircuits in the indirect pathway can sustain limit cycle oscillations around 5 Hz, in accord with oscillations at this frequency often observed in tremulous patients. Additionally, oscillations around 20 Hz that are normally present in corticothalamic circuits can spread to the basal ganglia when both corticothalamic and indirect circuits have large gains. The model also accounts for changes in the responsiveness of the components of the basal ganglia-thalamocortical system, and increased synchronization upon dopamine depletion, which plausibly reflect the loss of specificity of neuronal signaling pathways in the parkinsonian basal ganglia. Thus, a parsimonious explanation is provided for many electrophysiological correlates of Parkinson's disease using a single set of parameter changes with respect to the healthy state. Overall, we conclude that mean-field models of brain electrophysiology possess a versatility that allows them to be usefully applied in a variety of scenarios. Such models allow information about underlying physiology to be extracted from the experimental EEG, complementing traditional measures that may be more statistically robust but do not provide a direct link with physiology. Furthermore, there is ample opportunity for future developments, extending the basic model to encompass different neuronal systems, connections, and mechanisms. The basal ganglia are an important addition, not only leading to unified explanations for many hitherto disparate phenomena, but also contributing to the validation of this form of modeling
