On the Influence of Amplitude on the Connectivity between Phases

In recent studies, functional connectivities have been reported to display characteristics of complex networks that have been suggested to concur with those of the underlying structural, i.e., anatomical, networks. Do functional networks always agree with structural ones? In all generality, this question can be answered with “no”: for instance, a fully synchronized state would imply isotropic homogeneous functional connections irrespective of the “real” underlying structure. A proper inference of structure from function and vice versa requires more than a sole focus on phase synchronization. We show that functional connectivity critically depends on amplitude variations, which implies that, in general, phase patterns should be analyzed in conjunction with the corresponding amplitude. We discuss this issue by comparing the phase synchronization patterns of interconnected Wilson–Cowan models vis-à-vis Kuramoto networks of phase oscillators. For the interconnected Wilson–Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators’ amplitudes. In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics. Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large

Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others

Pallidal low‐frequency activity in dystonia after cessation of long‐term deep brain stimulation

Objective: This study investigates the association between pallidal low-frequency activity and motor sign severity in dystonia after chronic deep brain stimulation for several months. Methods: Local field potentials were recorded in 9 dystonia patients at 5 timepoints (T1–T5) during an OFF-stimulation period of 5 to 7 hours in parallel with clinical assessment using Burke-Fahn-Marsden Dystonia Rating Scale. A linear mixed effects model was used to investigate the potential association of motor signs with local field potential activity in the low frequency (3–12 Hz) and beta range (13–30 Hz). Results: A significant association of Burke-Fahn-Marsden Dystonia Rating Scale scores with low-frequency activity (3–12 Hz; b = 4.4; standard error = 1.5, degrees of freedom = 43, P = 0.006, 95% confidence interval, 1.3–7.5), but not beta activity (13–30 Hz) was revealed within participants across timepoints. Conclusion: Low-frequency activity is associated with dystonic motor sign severity, even months after chronic deep brain stimulation. Our findings corroborate the pathophysiological role of low-frequency activity in dystonia and highlight the potential utility as a biomarker for adaptive neuromodulation

Subthalamic nucleus phase-amplitude coupling correlates with motor impairment in Parkinson's disease

Objective High-amplitude beta band oscillations within the subthalamic nucleus are frequently associated with Parkinson’s disease but it is unclear how they might lead to motor impairments. Here we investigate a likely pathological coupling between the phase of beta band oscillations and the amplitude of high-frequency oscillations around 300Hz. Methods We analysed an extensive data set comprising resting-state recordings obtained from deep brain stimulation electrodes in 33 patients before and/or after taking dopaminergic medication. We correlated mean values of spectral power and phase-amplitude coupling with severity of hemibody bradykinesia/rigidity. In addition, we used simultaneously recorded magneto-encephalography to look at functional interactions between the subthalamic nucleus and ipsilateral motor cortex. Results We analysed an extensive data set comprising resting-state recordings obtained from deep brain stimulation electrodes in 33 patients before and/or after taking dopaminergic medication. We correlated mean values of spectral power and phase-amplitude coupling with severity of hemibody bradykinesia/rigidity. In addition, we used simultaneously recorded magneto-encephalography to look at functional interactions between the subthalamic nucleus and ipsilateral motor cortex. Conclusions We speculate that the beta band might impede pro-kinetic high-frequency activity patterns when phase-amplitude coupling is prominent. Furthermore, results provide evidence for a functional subdivision of the beta band into low and high frequencies. Significance Our findings contribute to the interpretation of oscillatory activity within the cortico-basal ganglia circuit

A Comparative Analysis of Extra-Embryonic Endoderm Cell Lines

Prior to gastrulation in the mouse, all endodermal cells arise from the primitive endoderm of the blastocyst stage embryo. Primitive endoderm and its derivatives are generally referred to as extra-embryonic endoderm (ExEn) because the majority of these cells contribute to extra-embryonic lineages encompassing the visceral endoderm (VE) and the parietal endoderm (PE). During gastrulation, the definitive endoderm (DE) forms by ingression of cells from the epiblast. The DE comprises most of the cells of the gut and its accessory organs. Despite their different origins and fates, there is a surprising amount of overlap in marker expression between the ExEn and DE, making it difficult to distinguish between these cell types by marker analysis. This is significant for two main reasons. First, because endodermal organs, such as the liver and pancreas, play important physiological roles in adult animals, much experimental effort has been directed in recent years toward the establishment of protocols for the efficient derivation of endodermal cell types in vitro. Conversely, factors secreted by the VE play pivotal roles that cannot be attributed to the DE in early axis formation, heart formation and the patterning of the anterior nervous system. Thus, efforts in both of these areas have been hampered by a lack of markers that clearly distinguish between ExEn and DE. To further understand the ExEn we have undertaken a comparative analysis of three ExEn-like cell lines (END2, PYS2 and XEN). PYS2 cells are derived from embryonal carcinomas (EC) of 129 strain mice and have been characterized as parietal endoderm-like [1], END2 cells are derived from P19 ECs and described as visceral endoderm-like, while XEN cells are derived from blastocyst stage embryos and are described as primitive endoderm-like. Our analysis suggests that none of these cell lines represent a bona fide single in vivo lineage. Both PYS2 and XEN cells represent mixed populations expressing markers for several ExEn lineages. Conversely END2 cells, which were previously characterized as VE-like, fail to express many markers that are widely expressed in the VE, but instead express markers for only a subset of the VE, the anterior visceral endoderm. In addition END2 cells also express markers for the PE. We extended these observations with microarray analysis which was used to probe and refine previously published data sets of genes proposed to distinguish between DE and VE. Finally, genome-wide pathway analysis revealed that SMAD-independent TGFbeta signaling through a TAK1/p38/JNK or TAK1/NLK pathway may represent one mode of intracellular signaling shared by all three of these lines, and suggests that factors downstream of these pathways may mediate some functions of the ExEn. These studies represent the first step in the development of XEN cells as a powerful molecular genetic tool to study the endodermal signals that mediate the important developmental functions of the extra-embryonic endoderm. Our data refine our current knowledge of markers that distinguish various subtypes of endoderm. In addition, pathway analysis suggests that the ExEn may mediate some of its functions through a non-classical MAP Kinase signaling pathway downstream of TAK1

A systematic review of local field potential physiomarkers in Parkinson’s disease: from clinical correlations to adaptive deep brain stimulation algorithms

Deep brain stimulation (DBS) treatment has proven effective in suppressing symptoms of rigidity, bradykinesia, and tremor in Parkinson’s disease. Still, patients may suffer from disabling fluctuations in motor and non-motor symptom severity during the day. Conventional DBS treatment consists of continuous stimulation but can potentially be further optimised by adapting stimulation settings to the presence or absence of symptoms through closed-loop control. This critically relies on the use of ‘physiomarkers’ extracted from (neuro)physiological signals. Ideal physiomarkers for adaptive DBS (aDBS) are indicative of symptom severity, detectable in every patient, and technically suitable for implementation. In the last decades, much effort has been put into the detection of local field potential (LFP) physiomarkers and in their use in clinical practice. We conducted a research synthesis of the correlations that have been reported between LFP signal features and one or more specific PD motor symptoms. Features based on the spectral beta band (~ 13 to 30 Hz) explained ~ 17% of individual variability in bradykinesia and rigidity symptom severity. Limitations of beta band oscillations as physiomarker are discussed, and strategies for further improvement of aDBS are explored

A systematic review of local field potential physiomarkers in Parkinson's disease: from clinical correlations to adaptive deep brain stimulation algorithms

Deep brain stimulation (DBS) treatment has proven effective in suppressing symptoms of rigidity, bradykinesia, and tremor in Parkinson's disease. Still, patients may suffer from disabling fluctuations in motor and non-motor symptom severity during the day. Conventional DBS treatment consists of continuous stimulation but can potentially be further optimised by adapting stimulation settings to the presence or absence of symptoms through closed-loop control. This critically relies on the use of 'physiomarkers' extracted from (neuro)physiological signals. Ideal physiomarkers for adaptive DBS (aDBS) are indicative of symptom severity, detectable in every patient, and technically suitable for implementation. In the last decades, much effort has been put into the detection of local field potential (LFP) physiomarkers and in their use in clinical practice. We conducted a research synthesis of the correlations that have been reported between LFP signal features and one or more specific PD motor symptoms. Features based on the spectral beta band (~ 13 to 30 Hz) explained ~ 17% of individual variability in bradykinesia and rigidity symptom severity. Limitations of beta band oscillations as physiomarker are discussed, and strategies for further improvement of aDBS are explored

Bayesian model reduction and empirical Bayes for group (DCM) studies

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.ISSN:1053-8119ISSN:1095-957