The rostro-caudal gradient in the prefrontal cortex and its modulation by subthalamic deep brain stimulation in Parkinson's disease.

Deep brain stimulation of the subthalamic nucleus (STN-DBS) alleviates motor symptoms in Parkinson's disease (PD) but also affects the prefrontal cortex (PFC), potentially leading to cognitive side effects. The present study tested alterations within the rostro-caudal hierarchy of neural processing in the PFC induced by STN-DBS in PD. Granger-causality analyses of fast functional near-infrared spectroscopy (fNIRS) measurements were used to infer directed functional connectivity from intrinsic PFC activity in 24 PD patients treated with STN-DBS. Functional connectivity was assessed ON stimulation, in steady-state OFF stimulation and immediately after the stimulator was switched ON again. Results revealed that STN-DBS significantly enhanced the rostro-caudal hierarchical organization of the PFC in patients who had undergone implantation early in the course of the disease, whereas it attenuated the rostro-caudal hierarchy in late-implanted patients. Most crucially, this systematic network effect of STN-DBS was reproducible in the second ON stimulation measurement. Supplemental analyses demonstrated the significance of prefrontal networks for cognitive functions in patients and matched healthy controls. These findings show that the modulation of prefrontal functional networks by STN-DBS is dependent on the disease duration before DBS implantation and suggest a neurophysiological mechanism underlying the side effects on prefrontally-guided cognitive functions observed under STN-DBS.

Controversies on the network theory of epilepsy: Debates held during the ICTALS 2019 conference.

Debates on six controversial topics on the network theory of epilepsy were held during two debate sessions, as part of the International Conference for Technology and Analysis of Seizures, 2019 (ICTALS 2019) convened at the University of Exeter, UK, September 2-5 2019. The debate topics were (1) From pathologic to physiologic: is the epileptic network part of an existing large-scale brain network? (2) Are micro scale recordings pertinent for defining the epileptic network? (3) From seconds to years: do we need all temporal scales to define an epileptic network? (4) Is it necessary to fully define the epileptic network to control it? (5) Is controlling seizures sufficient to control the epileptic network? (6) Does the epileptic network want to be controlled? This article, written by the organizing committee for the debate sessions and the debaters, summarizes the arguments presented during the debates on these six topics.

On the Validity of Neural Mass Models.

Modeling the dynamics of neural masses is a common approach in the study of neural populations. Various models have been proven useful to describe a plenitude of empirical observations including self-sustained local oscillations and patterns of distant synchronization. We discuss the extent to which mass models really resemble the mean dynamics of a neural population. In particular, we question the validity of neural mass models if the population under study comprises a mixture of excitatory and inhibitory neurons that are densely (inter-)connected. Starting from a network of noisy leaky integrate-and-fire neurons, we formulated two different population dynamics that both fall into the category of seminal Freeman neural mass models. The derivations contained several mean-field assumptions and time scale separation(s) between membrane and synapse dynamics. Our comparison of these neural mass models with the averaged dynamics of the population reveals bounds in the fraction of excitatory/inhibitory neuron as well as overall network degree for a mass model to provide adequate estimates. For substantial parameter ranges, our models fail to mimic the neural network's dynamics proper, be that in de-synchronized or in (high-frequency) synchronized states. Only around the onset of low-frequency synchronization our models provide proper estimates of the mean potential dynamics. While this shows their potential for, e.g., studying resting state dynamics obtained by encephalography with focus on the transition region, we must accept that predicting the more general dynamic outcome of a neural network via its mass dynamics requires great care.

The impact of physiological noise on hemodynamic-derived estimates of directed functional connectivity.

Measuring the strength of directed functional interactions between brain regions is fundamental to understand neural networks. Functional near-infrared spectroscopy (fNIRS) is a suitable method to map directed interactions between brain regions but is based on the neurovascular coupling. It, thus, relies on vasomotor reactivity and is potentially biased by non-neural physiological noise. To investigate the impact of physiological noise on fNIRS-based estimates of directed functional connectivity within the rostro-caudal hierarchical organization of the prefrontal cortex (PFC), we systematically assessed the effects of pathological perturbations of vasomotor reactivity and of externally triggered arterial blood pressure (aBP) fluctuations. Fifteen patients with unilateral stenosis of the internal carotid artery (ICA) underwent multi-channel fNIRS during rest and during metronomic breathing, inducing aBP oscillations at 0.1 Hz. Comparisons between the healthy and pathological hemispheres served as quasi-experimental manipulation of the neurovascular system's capability for vasomotor reactivity. Comparisons between rest and breathing served as experimental manipulation of two different levels of physiological noise that were expected to differ between healthy and pathological hemispheres. In the hemisphere affected by ICA stenosis, the rostro-caudal hierarchical organization of the PFC was compromised reflecting the pathological effect on the vascular and neural level. Breathing-induced aBP oscillations biased the magnitude of directed interactions in the PFC, but could be adjusted using either the aBP time series (intra-individual approach) or the aBP-induced fNIRS signal variance (inter-individual approach). Multi-channel fNIRS, hence, provides a sound basis for analyses of directed functional connectivity as potential bias due to physiological noise can be effectively controlled for.

Analytical approach to network inference: Investigating degree distribution.

When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is analytically analyzed. Moreover, an analytic formula of the density of the biased vertex degree distribution is found. In the inverse problem, we find a reliable procedure to reconstruct analytically the density of the vertex degree distribution of any network based on the inferred network and estimates for the false positive and false negative errors based on, e.g., simulation studies.

Seizure prediction - ready for a new era.

Epilepsy is a common disorder characterized by recurrent seizures. An overwhelming majority of people with epilepsy regard the unpredictability of seizures as a major issue. More than 30 years of international effort have been devoted to the prediction of seizures, aiming to remove the burden of unpredictability and to couple novel, time-specific treatment to seizure prediction technology. A highly influential review published in 2007 concluded that insufficient evidence indicated that seizures could be predicted. Since then, several advances have been made, including successful prospective seizure prediction using intracranial EEG in a small number of people in a trial of a real-time seizure prediction device. In this Review, we examine advances in the field, including EEG databases, seizure prediction competitions, the prospective trial mentioned and advances in our understanding of the mechanisms of seizures. We argue that these advances, together with statistical evaluations, set the stage for a resurgence in efforts towards the development of seizure prediction methodologies. We propose new avenues of investigation involving a synergy between mechanisms, models, data, devices and algorithms and refine the existing guidelines for the development of seizure prediction technology to instigate development of a solution that removes the burden of the unpredictability of seizures.

Improving network inference: The impact of false positive and false negative conclusions about the presence or absence of links.

BACKGROUND: A reliable inference of networks from data is of key interest in the Neurosciences. Several methods have been suggested in the literature to reliably determine links in a network. To decide about the presence of links, these techniques rely on statistical inference, typically controlling the number of false positives, paying little attention to false negatives. NEW METHOD: In this paper, by means of a comprehensive simulation study, we analyse the influence of false positive and false negative conclusions about the presence or absence of links in a network on the network topology. We show that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. We propose to run careful simulation studies prior to making potentially erroneous conclusion about the network topology. RESULTS: Our analysis shows that optimal values to balance false positive and false negative conclusions about links depend on the network topology and characteristic of interest. COMPARISON WITH EXISTING METHODS: Existing methods rely on a choice of the rate for false positive conclusions. They aim to be sure about individual links rather than the entire network. The rate of false negative conclusions is typically not investigated. CONCLUSIONS: Our investigation shows that the balance of false positive and false negative conclusions about links in a network has to be tuned for any network topology that is to be estimated. Moreover, within the same network topology, the results are qualitatively the same for each network characteristic, but the actual values leading to reliable estimates of the characteristics are different.

Detection of time-, frequency- and direction-resolved communication within brain networks.

Electroencephalography (EEG) records fast-changing neuronal signalling and communication and thus can offer a deep understanding of cognitive processes. However, traditional data analyses which employ the Fast-Fourier Transform (FFT) have been of limited use as they do not allow time- and frequency-resolved tracking of brain activity and detection of directional connectivity. Here, we applied advanced qEEG tools using autoregressive (AR) modelling, alongside traditional approaches, to murine data sets from common research scenarios: (a) the effect of age on resting EEG; (b) drug actions on non-rapid eye movement (NREM) sleep EEG (pharmaco-EEG); and (c) dynamic EEG profiles during correct vs incorrect spontaneous alternation responses in the Y-maze. AR analyses of short data strips reliably detected age- and drug-induced spectral EEG changes, while renormalized partial directed coherence (rPDC) reported direction- and time-resolved connectivity dynamics in mice. Our approach allows for the first time inference of behaviour- and stage-dependent data in a time- and frequency-resolved manner, and offers insights into brain networks that underlie working memory processing beyond what can be achieved with traditional methods.

Modeling Prion-Like Processing of Tau Protein in Alzheimer's Disease for Pharmaceutical Development.

Following our discovery of a fragment from the repeat domain of tau protein as a structural constituent of the PHF-core in Alzheimer's disease (AD), we developed an assay that captured several key features of the aggregation process. Tau-tau binding through the core tau fragment could be blocked by the same diaminophenothiazines found to dissolve proteolytically stable PHFs isolated from AD brain. We found that the PHF-core tau fragment is inherently capable of auto-catalytic self-propagation in vitro, or "prion-like processing", that has now been demonstrated for several neurodegenerative disorders. Here we review the findings that led to the first clinical trials to test tau aggregation inhibitor therapy in AD as a way to block this cascade. Although further trials are still needed, the results to date suggest that a treatment targeting the prion-like processing of tau protein may have a role in both prevention and treatment of AD.

Networks: On the relation of bi- and multivariate measures.

A reliable inference of networks from observations of the nodes' dynamics is a major challenge in physics. Interdependence measures such as a the correlation coefficient or more advanced methods based on, e.g., analytic phases of signals are employed. For several of these interdependence measures, multivariate counterparts exist that promise to enable distinguishing direct and indirect connections. Here, we demonstrate analytically how bivariate measures relate to the respective multivariate ones; this knowledge will in turn be used to demonstrate the implications of thresholded bivariate measures for network inference. Particularly, we show, that random networks are falsely identified as small-world networks if observations thereof are treated by bivariate methods. We will employ the correlation coefficient as an example for such an interdependence measure. The results can be readily transferred to all interdependence measures partializing for information of thirds in their multivariate counterparts.

Assessing parameter identifiability for dynamic causal modeling of fMRI data.

Deterministic dynamic causal modeling (DCM) for fMRI data is a sophisticated approach to analyse effective connectivity in terms of directed interactions between brain regions of interest. To date it is difficult to know if acquired fMRI data will yield precise estimation of DCM parameters. Focusing on parameter identifiability, an important prerequisite for research questions on directed connectivity, we present an approach inferring if parameters of an envisaged DCM are identifiable based on information from fMRI data. With the freely available "attention to motion" dataset, we investigate identifiability of two DCMs and show how different imaging specifications impact on identifiability. We used the profile likelihood, which has successfully been applied in systems biology, to assess the identifiability of parameters in a DCM with specified scanning parameters. Parameters are identifiable when minima of the profile likelihood as well as finite confidence intervals for the parameters exist. Intermediate epoch duration, shorter TR and longer session duration generally increased the information content in the data and thus improved identifiability. Irrespective of biological factors such as size and location of a region, attention should be paid to densely interconnected regions in a DCM, as those seem to be prone to non-identifiability. Our approach, available in the DCMident toolbox, enables to judge if the parameters of an envisaged DCM are sufficiently determined by underlying data without priors as opposed to primarily reflecting the Bayesian priors in a SPM-DCM. Assessments with the DCMident toolbox prior to a study will lead to improved identifiability of the parameters and thus might prevent suboptimal data acquisition. Thus, the toolbox can be used as a preprocessing step to provide immediate statements on parameter identifiability.

Network inference in the presence of latent confounders: the role of instantaneous causalities.

BACKGROUND: Detecting causal interactions in multivariate systems, in terms of Granger-causality, is of major interest in the Neurosciences. Typically, it is almost impossible to observe all components of the system. Missing certain components can lead to the appearance of spurious interactions. The aim of this study is to demonstrate the effect of this and to demonstrate that distinction between latent confounders and volume conduction is possible in some cases. NEW METHOD: Our new method uses a combination of renormalised partial directed coherence and analysis of the (partial) covariance matrix of residual noise process to detect instantaneous, spurious interactions. Sub-network analyses are performed to infer the true network structure of the underlying system. RESULTS: We provide evidence that it is possible to distinguish between instantaneous interactions that occur as a result of a latent confounder and those that occur as a result of volume conduction. COMPARISON WITH EXISTING METHODS: Our novel approach demonstrates to what extent inference of unobserved important processes as well as the distinction between latent confounders and volume conduction is possible. We suggest a combination of measures of Granger-causality and covariance selection models to achieve this numerically. CONCLUSIONS: Sub-network analyses enable a much more precise and correct inference of the true underlying network structure in some cases. From this it is possible to distinguish between unobserved processes and volume conduction. Our approach is straightforwardly adaptable to various measures of Granger-causality emphasising its ubiquitous successful applicability.

Assessing the strength of directed influences among neural signals: an approach to noisy data.

BACKGROUND: Measurements in the neurosciences are afflicted with observational noise. Granger-causality inference typically does not take this effect into account. We demonstrate that this leads to false positives conclusions and spurious causalities. NEW METHOD: State space modelling provides a convenient framework to obtain reliable estimates for Granger-causality. Despite its previous application in several studies, the analytical derivation of the statistics for parameter estimation in the state space model was missing. This prevented a rigorous evaluation of the results. RESULTS: In this manuscript we derive the statistics for parameter estimation in the state space model. We demonstrate in an extensive simulation study that our novel approach outperforms standard approaches and avoids false positive conclusions about Granger-causality. COMPARISON WITH EXISTING METHODS: In comparison with the naive application of Granger-causality inference, we demonstrate the superiority of our novel approach. The wide-spread applicability of our procedure provides a statistical framework for future studies. The application to mice electroencephalogram data demonstrates the immediate applicability of our approach. CONCLUSIONS: The analytical derivation of the statistics presented in this manuscript enables a rigorous evaluation of the results of Granger causal network inference. It is noteworthy that the statistics can be readily applied to various measures for Granger causality and other approaches that are based on vector autoregressive models.

Electrical stimulation for cortical mapping reduces the density of high frequency oscillations.

BACKGROUND: High frequency oscillations (HFOs, 80-500 Hz) are EEG biomarkers for epileptogenic areas. HFOs are also indicators of disease activity as HFO rates increase after reduction of antiepileptic medication. Electrical stimulation (ES) can be used for diagnostic purposes as well as therapy in patients with refractory epilepsy. This study investigates the occurrence and changes of HFOs during ES in patients with refractory epilepsy. OBJECTIVE: Analysis of the effects of ES using intracranial ES on the occurrence of epileptic HFOs. METHODS: Patients underwent ES for diagnostic purposes. Ripples (80-200 Hz) and fast ripples (200-500 Hz) were visually marked in a baseline EEG segment prior to ES, after each period of ES as well as after the end of ES. In patients in whom ES triggered a seizure a pre- and postictal segment was marked. Rates of HFOs were compared for the different time periods using a Spearman's correlation and Wilcoxon rank sum test (p<0.05). RESULTS: 12 patients with 911 EEG channels were analyzed. Ripple (r=-0.42, p<0.001) as well as fast ripple (r=-0.21, p<0.001) rates decreased significantly over the course of stimulation. This phenomenon was not focal over the seizure onset or neighboring contacts but even observed over distant contacts. CONCLUSIONS: ES resulted in a gradual decrease of HFO-Rates over time. The decrease of HFOs was not limited to SOZ areas. If HFOs are considered as markers of disease activity the reduction in HFO-rates as a result of intracranial ES has to be interpreted as a reduction of disease activity.

Spatial mapping of dynamic cerebral autoregulation by multichannel near-infrared spectroscopy in high-grade carotid artery disease.

The exact spatial distribution of impaired cerebral autoregulation in carotid artery disease is unknown. In this pilot study, we present a new approach of multichannel near-infrared spectroscopy (mcNIRS) for non-invasive spatial mapping of dynamic autoregulation in carotid artery disease. In 15 patients with unilateral severe carotid artery stenosis or occlusion, cortical hemodynamics in the bilateral frontal cortex were assessed from changes in oxyhemoglobin concentration using 52-channel NIRS (spatial resolution ∼2 cm). Dynamic autoregulation was graded by the phase shift between respiratory-induced 0.1 Hz oscillations of blood pressure and oxyhemoglobin. Ten of 15 patients showed regular phase values in the expected (patho) physiological range.Five patients had clearly outlying irregular phase values mostly due to artifacts. In patients with a regular phase pattern, a significant side-to-side difference of dynamic autoregulation was observed for the cortical border zone area between the middle and anterior cerebral artery (p < 0.05). In conclusion, dynamic cerebral autoregulation can be spatially assessed from slow hemodynamic oscillations with mcNIRS. In high-grade carotid artery disease,cortical dynamic autoregulation is affected mostly in the vascular border zone. Spatial mapping of dynamic autoregulation may serve as a powerful tool for identifying brain regions at specific risks for hemodynamic infarction.

Statistical evaluation of forecasts.

Reliable forecasts of extreme but rare events, such as earthquakes, financial crashes, and epileptic seizures, would render interventions and precautions possible. Therefore, forecasting methods have been developed which intend to raise an alarm if an extreme event is about to occur. In order to statistically validate the performance of a prediction system, it must be compared to the performance of a random predictor, which raises alarms independent of the events. Such a random predictor can be obtained by bootstrapping or analytically. We propose an analytic statistical framework which, in contrast to conventional methods, allows for validating independently the sensitivity and specificity of a forecasting method. Moreover, our method accounts for the periods during which an event has to remain absent or occur after a respective forecast.

Optimized spectral estimation for nonlinear synchronizing systems.

In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.

Differentiation of specific ripple patterns helps to identify epileptogenic areas for surgical procedures.

OBJECTIVE: High frequency oscillations (HFOs) at 80-500 Hz are promising markers of epileptic areas. Several retrospective studies reported that surgical removal of areas generating HFOs was associated with a good seizure outcome. Recent reports suggested that ripple (80-200 Hz) HFO patterns co-existed with different background EEG activities. We hypothesized that the coexisting background EEG pattern may distinguish physiological from epileptic ripples. METHODS: Rates of HFOs were analyzed in intracranial EEG recordings of 22 patients. Additionally, ripple patterns were classified for each channel depending either as coexisting with a flat or oscillatory background activity. A multi-variate analysis was performed to determine whether removal of areas showing the above EEG markers correlated with seizure outcome. RESULTS: Removal of areas generating high rates of 'fast ripples (>200 Hz)' and 'ripples on a flat background activity' showed a significant correlation with a seizure-free outcome. In contrast, removal of high rates of 'ripples' or 'ripple patterns in a continuously oscillating background' was not significantly associated with seizure outcome. CONCLUSION: Ripples occurring in an oscillatory background activity may be suggestive of physiological activity, while those on a flat background reflect epileptic activity. SIGNIFICANCE: Consideration of coexisting background patterns may improve the delineation of the epileptogenic areas using ripple oscillations.

Detection of preclinical neural dysfunction from functional connectivity graphs derived from task fMRI. An example from degeneration.

The early, preferably pre-clinical, identification of neurodegenerative diseases is important as treatment will be most successful before substantial neuronal loss. Here, we reasoned that functional brain changes as measured using functional magnetic resonance imaging (fMRI) will precede neurodegeneration. Three independent cohorts of patients with the genetic mutation leading to Huntington's Disease (HD) but without any clinical symptoms and matched controls performed three different fMRI tasks: Sequential finger tapping engaged the motor system, which is primarily affected by HD, whereas a working-memory task and a task aiming to induce irritation represented the range of low- and high-level cognitive functions also affected by HD. Each diagnostic group of every cohort included 11-16 subjects. After segmentation into 76 cortical and 14 subcortical regions, we extracted functional connectivity patterns through pairwise correlation between the signals in the regions. The resulting coefficients were directly embedded as input to a pattern classifier aiming to separate controls from gene mutation carriers. Alternatively, graph-theory measures such as degree and clustering coefficient were used as features for the discrimination. Classification accuracy never outperformed the accuracy of a grouping based on parameter estimates from a general-linear model approach or a grouping based on features extracted from anatomical images as reported in a previous analysis. Despite good within-subject stability between two runs of the same task, a high between-subject variability led to chance-level accuracy. These results indicate that standard graph-metrics are insufficient to detect subtle disease related changes when within-group variability is high. Developing methods that reduce variability related to noise should be the focus of future studies.

Block-bootstrapping for noisy data.

BACKGROUND: Statistical inference of signals is key to understand fundamental processes in the neurosciences. It is essential to distinguish true from random effects. To this end, statistical concepts of confidence intervals, significance levels and hypothesis tests are employed. Bootstrap-based approaches complement the analytical approaches, replacing the latter whenever these are not possible. NEW METHOD: Block-bootstrap was introduced as an adaption of the ordinary bootstrap for serially correlated data. For block-bootstrap, the signals are cut into independent blocks, yielding independent samples. The key parameter for block-bootstrapping is the block length. In the presence of noise, naïve approaches to block-bootstrapping fail. Here, we present an approach based on block-bootstrapping which can cope even with high noise levels. This method naturally leads to an algorithm of block-bootstrapping that is immediately applicable to observed signals. RESULTS: While naïve block-bootstrapping easily results in a misestimation of the block length, and therefore in an over-estimation of the confidence bounds by 50%, our new approach provides an optimal determination of these, still keeping the coverage correct. COMPARISON WITH EXISTING METHODS: In several applications bootstrapping replaces analytical statistics. Block-bootstrapping is applied to serially correlated signals. Noise, ubiquitous in the neurosciences, is typically neglected. Our new approach not only explicitly includes the presence of (observational) noise in the statistics but also outperforms conventional methods and reduces the number of false-positive conclusions. CONCLUSIONS: The presence of noise has impacts on statistical inference. Our ready-to-apply method enables a rigorous statistical assessment based on block-bootstrapping for noisy serially correlated data.