Mean-field analysis of basal ganglia and thalamocortical dynamics

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

Scalability of asynchronous networks is limited by one-to-one mapping between effective connectivity and correlations

Network models are routinely downscaled because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics is conserved, here we show that this is generally impossible already for second-order statistics. We argue that studies in computational biology need to make the scaling applied explicit, and that results should be verified where possible by full-scale simulations. We consider neuronal networks, where the importance of correlations in network dynamics is obvious because they directly interact with synaptic plasticity, the neuronal basis of learning, but the conclusions are generic. We derive conditions for the preservation of both mean activities and correlations under a change in numbers of neurons or synapses in the asynchronous regime typical of cortical networks. Analytical and simulation results are obtained for networks of binary and networks of leaky integrate-and-fire model neurons, randomly connected with or without delays. The structure of average pairwise correlations in such networks is determined by the effective population-level connectivity. We show that in the absence of symmetries or zeros in the population-level connectivity or correlations, the converse is also true. This is in line with earlier work on inferring connectivity from correlations, but implies that such network reconstruction should be possible for a larger class of networks than hitherto considered. When changing in-degrees, effective connectivity and hence correlation structure can be maintained by an appropriate scaling of the synaptic weights, but only over a limited range of in-degrees determined by the extrinsic variance. Our results show that the reducibility of asynchronous networks is fundamentally limited

Fundamental activity constraints lead to specific interpretations of the connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.Comment: J. Schuecker and M. Schmidt contributed equally to this wor

Construction of a multi-scale spiking model of macaque visual cortex

Understanding the relationship between structure and dynamics of the mammalian cortex is a key challenge of neuroscience. So far, it has been tackled in two ways: by modeling neurons or small circuits in great detail, and through large-scale models representing each area with a small number of differential equations. To bridge the gap between these two approaches, we construct a spiking network model extending earlier work on the cortical microcircuit by Potjans & Diesmann (2014) to all 32 areas of the macaque visual cortex in the parcellation of Felleman & Van Essen (1991). The model takes into account spe- cific neuronal densities and laminar thicknesses of the individual areas. The connectivity of the model combines recently updated binary tracing data from the CoCoMac database (Stephan et al., 2001) with quantitative tracing data providing connection densities (Markov et al., 2014a) and laminar connection patterns (Stephan et al., 2001; Markov et al., 2014b). We estimate missing data using structural regular- ities such as the exponential decay of connection densities with distance between areas (Ercsey-Ravasz et al., 2013) and a fit of laminar patterns versus logarithmic ratios of neuron densities. The model integrates a large body of knowledge on the structure of macaque visual cortex into a consistent framework that allows for progressive refinement

Usage and Scaling of an Open-Source Spiking Multi-Area Model of Monkey Cortex

We are entering an age of `big' computational neuroscience, in which neural network models are increasing in size and in numbers of underlying data sets. Consolidating the zoo of models into large-scale models simultaneously consistent with a wide range of data is only possible through the effort of large teams, which can be spread across multiple research institutions. To ensure that computational neuroscientists can build on each other's work, it is important to make models publicly available as well-documented code. This chapter describes such an open-source model, which relates the connectivity structure of all vision-related cortical areas of the macaque monkey with their resting-state dynamics. We give a brief overview of how to use the executable model specification, which employs NEST as simulation engine, and show its runtime scaling. The solutions found serve as an example for organizing the workflow of future models from the raw experimental data to the visualization of the results, expose the challenges, and give guidance for the construction of ICT infrastructure for neuroscience

Reconciliation of weak pairwise spike-train correlations and highly coherent local field potentials across space

Chronic and acute implants of multi-electrode arrays that cover several mm$^2$ of neural tissue provide simultaneous access to population signals like extracellular potentials and the spiking activity of 100 or more individual neurons. While the recorded data may uncover principles of brain function, its interpretation calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Such models can facilitate the search of mechanisms underlying observed spatiotemporal activity patterns in cortex. Multi-layer spiking neuron network models of local cortical circuits covering ~1 mm$^2$ have been developed, integrating experimentally obtained neuron-type specific connectivity data and reproducing features of in-vivo spiking statistics. With forward models, local field potentials (LFPs) can be computed from the simulated spiking activity. To account for the spatial scale of common neural recordings, we extend a local network and LFP model to 4x4 mm$^2$. The upscaling preserves the neuron densities, and introduces distance-dependent connection probabilities and delays. As detailed experimental connectivity data is partially lacking, we address this uncertainty in model parameters by testing parameter combinations within biologically plausible bounds. Based on model predictions of spiking activity and LFPs, we find that the upscaling procedure preserves the overall spiking statistics of the original model and reproduces asynchronous irregular spiking across populations and weak pairwise spike-train correlations observed in sensory cortex. In contrast with the weak spike-train correlations, the correlation of LFP signals is strong and distance-dependent, compatible with experimental observations. Enhanced spatial coherence in the low-gamma band may explain the recent experimental report of an apparent band-pass filter effect in the spatial reach of the LFP.Comment: 44 pages, 9 figures, 5 table