The influence of filtering and downsampling on the estimation of transfer entropy

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros-cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks.

Benchmarking Transfer Entropy Methods for the Study of Linear and Nonlinear Cardio-Respiratory Interactions

Transfer entropy (TE) has been used to identify and quantify interactions between physiological systems. Different methods exist to estimate TE, but there is no consensus about which one performs best in specific applications. In this study, five methods (linear, k-nearest neighbors, fixed-binning with ranking, kernel density estimation and adaptive partitioning) were compared. The comparison was made on three simulation models (linear, nonlinear and linear + nonlinear dynamics). From the simulations, it was found that the best method to quantify the different interactions was adaptive partitioning. This method was then applied on data from a polysomnography study, specifically on the ECG and the respiratory signals (nasal airflow and respiratory effort around the thorax). The hypothesis that the linear and nonlinear components of cardio-respiratory interactions during light and deep sleep change with the sleep stage, was tested. Significant differences, after performing surrogate analysis, indicate an increased TE during deep sleep. However, these differences were found to be dependent on the type of respiratory signal and sampling frequency. These results highlight the importance of selecting the appropriate signals, estimation method and surrogate analysis for the study of linear and nonlinear cardio-respiratory interactions.

Clinical factors associated with rapid treatment of sepsis

PURPOSE

To understand what clinical presenting features of sepsis patients are historically associated with rapid treatment involving antibiotics and fluids, as appropriate.

DESIGN

This was a retrospective, observational cohort study using a machine-learning model with an embedded feature selection mechanism (gradient boosting machine).

METHODS

For adult patients (age ≥ 18 years) who were admitted through Emergency Department (ED) meeting clinical criteria of severe sepsis from 11/2007 to 05/2018 at an urban tertiary academic medical center, we developed gradient boosting models (GBMs) using a total of 760 original and derived variables, including demographic variables, laboratory values, vital signs, infection diagnosis present on admission, and historical comorbidities. We identified the most impactful factors having strong association with rapid treatment, and further applied the Shapley Additive exPlanation (SHAP) values to examine the marginal effects for each factor.

RESULTS

For the subgroups with or without fluid bolus treatment component, the models achieved high accuracy of area-under-receiver-operating-curve of 0.91 [95% CI, 0.86-0.95] and 0.84 [95% CI, 0.81-0.86], and sensitivity of 0.81[95% CI, 0.72-0.87] and 0.91 [95% CI, 0.81-0.97], respectively. We identified the 20 most impactful factors associated with rapid treatment for each subgroup. In the non-hypotensive subgroup, initial physiological values were the most impactful to the model, while in the fluid bolus subgroup, value minima and maxima tended to be the most impactful.

CONCLUSION

These machine learning methods identified factors associated with rapid treatment of severe sepsis patients from a large volume of high-dimensional clinical data. The results provide insight into differences in the rapid provision of treatment among patients with sepsis.

Revisiting the global workspace orchestrating the hierarchical organization of the human brain

A central challenge in neuroscience is how the brain organizes the information necessary to orchestrate behaviour. Arguably, this whole-brain orchestration is carried out by a core subset of integrative brain regions, a 'global workspace', but its constitutive regions remain unclear. We quantified the global workspace as the common regions across seven tasks as well as rest, in a common 'functional rich club'. To identify this functional rich club, we determined the information flow between brain regions by means of a normalized directed transfer entropy framework applied to multimodal neuroimaging data from 1,003 healthy participants and validated in participants with retest data. This revealed a set of regions orchestrating information from perceptual, long-term memory, evaluative and attentional systems. We confirmed the causal significance and robustness of our results by systematically lesioning a generative whole-brain model. Overall, this framework describes a complex choreography of the functional hierarchical organization of the human brain.

Measuring spectrally-resolved information transfer

Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in the computation of transfer entropy and entirely avoids filtering of the original signals. The approach thereby avoids well-known problems due to phase shifts or the ineffectiveness of filtering in the information theoretic setting. We also show that measuring frequency-resolved information transfer is a partial information decomposition problem that cannot be fully resolved to date and discuss the implications of this issue. Last, we evaluate the performance of our algorithm on simulated data and apply it to human magnetoencephalography (MEG) recordings and to local field potential recordings in the ferret. In human MEG we demonstrate top-down information flow in temporal cortex from very high frequencies (above 100Hz) to both similarly high frequencies and to frequencies around 20Hz, i.e. a complex spectral configuration of cortical information transmission that has not been described before. In the ferret we show that the prefrontal cortex sends information at low frequencies (4-8 Hz) to early visual cortex (V1), while V1 receives the information at high frequencies (> 125 Hz).

What Can Local Transfer Entropy Tell Us about Phase-Amplitude Coupling in Electrophysiological Signals?

Modulation of the amplitude of high-frequency cortical field activity locked to changes in the phase of a slower brain rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining traction in neuroscience because of several reports on its appearance in normal and pathological brain processes in humans as well as across different mammalian species. This has led to the suggestion that PAC may be an intrinsic brain process that facilitates brain inter-area communication across different spatiotemporal scales. Several methods have been proposed to measure the PAC process, but few of these enable detailed study of its time course. It appears that no studies have reported details of PAC dynamics including its possible directional delay characteristic. Here, we study and characterize the use of a novel information theoretic measure that may address this limitation: local transfer entropy. We use both simulated and actual intracranial electroencephalographic data. In both cases, we observe initial indications that local transfer entropy can be used to detect the onset and offset of modulation process periods revealed by mutual information estimated phase-amplitude coupling (MIPAC). We review our results in the context of current theories about PAC in brain electrical activity, and discuss technical issues that must be addressed to see local transfer entropy more widely applied to PAC analysis. The current work sets the foundations for further use of local transfer entropy for estimating PAC process dynamics, and extends and complements our previous work on using local mutual information to compute PAC (MIPAC).

Effective brain connectivity for fNIRS data analysis based on multi-delays symbolic phase transfer entropy

OBJECTIVE

Recently, effective connectivity (EC) calculation methods for functional near-infrared spectroscopy (fNIRS) data mainly face two problems: the first problem is that noise can seriously affect the EC calculation and even lead to false connectivity; the second problem is that it ignores the various real neurotransmission delays between the brain region, and instead uses a fixed delay coefficient for calculation.

APPROACH

To overcome these two issues, a delay symbolic phase transfer entropy (dSPTE) is proposed by developing traditional transfer entropy (TE) to estimate EC for fNIRS. Firstly, the phase time sequence was obtained from the original sequence by the Hilbert transform and state-space reconstruction was realized using a uniform embedding scheme. Then, a symbolization technique was applied based on a neural-gas algorithm to improve its noise robustness. Finally, the EC was calculated on multiple time delay scales to match different inter-region neurotransmission delays.

MAIN RESULTS

A linear AR model, a nonlinear model and a multivariate hybrid model were introduced to simulate the performance of dSPTE, and the results showed that the accuracy of dSPTE was the highest, up to 74.27%, and specificity was 100% which means no false connectivity. The results confirmed that the dSPTE method realized better noise robustness, higher accuracy, and correct identification even if there was a long delay between series. Finally, we applied dSPTE to fNIRS dataset to analyse the EC during the finger-tapping task, the results showed that EC strength of task state significantly increased compared with the resting state.

SIGNIFICANCE

The proposed dSPTE method is a promising way to measure the EC for fNIRS. It incorporates the phase information TE with a symbolic process for fNIRS analysis for the first time. It has been confirmed to be noise robust and suitable for the complex network with different coupling delays.

A Data-Driven Measure of Effective Connectivity Based on Renyi's α-Entropy

Transfer entropy (TE) is a model-free effective connectivity measure based on information theory. It has been increasingly used in neuroscience because of its ability to detect unknown non-linear interactions, which makes it well suited for exploratory brain effective connectivity analyses. Like all information theoretic quantities, TE is defined regarding the probability distributions of the system under study, which in practice are unknown and must be estimated from data. Commonly used methods for TE estimation rely on a local approximation of the probability distributions from nearest neighbor distances, or on symbolization schemes that then allow the probabilities to be estimated from the symbols' relative frequencies. However, probability estimation is a challenging problem, and avoiding this intermediate step in TE computation is desirable. In this work, we propose a novel TE estimator using functionals defined on positive definite and infinitely divisible kernels matrices that approximate Renyi's entropy measures of order α. Our data-driven approach estimates TE directly from data, sidestepping the need for probability distribution estimation. Also, the proposed estimator encompasses the well-known definition of TE as a sum of Shannon entropies in the limiting case when α → 1. We tested our proposal on a simulation framework consisting of two linear models, based on autoregressive approaches and a linear coupling function, respectively, and on the public electroencephalogram (EEG) database BCI Competition IV, obtained under a motor imagery paradigm. For the synthetic data, the proposed kernel-based TE estimation method satisfactorily identifies the causal interactions present in the data. Also, it displays robustness to varying noise levels and data sizes, and to the presence of multiple interaction delays in the same connected network. Obtained results for the motor imagery task show that our approach codes discriminant spatiotemporal patterns for the left and right-hand motor imagination tasks, with classification performances that compare favorably to the state-of-the-art.

Modernizing the Bradford Hill criteria for assessing causal relationships in observational data

Perhaps no other topic in risk analysis is more difficult, more controversial, or more important to risk management policy analysts and decision-makers than how to draw valid, correctly qualified causal conclusions from observational data. Statistical methods can readily quantify associations between observed variables using measures such as relative risk (RR) ratios, odds ratios (OR), slope coefficients for exposure or treatment variables in regression models, and quantities derived from these measures. Textbooks of epidemiology explain how to calculate population attributable fractions, attributable risks, burden-of-disease estimates, and probabilities of causation from relative risk (RR) ratios. Despite their suggestive names, these association-based measures have no necessary connection to causation if the associations on which they are based arise from bias, confounding, p-hacking, coincident historical trends, or other noncausal sources. But policy analysts and decision makers need something more: trustworthy predictions - and, later, evaluations - of the changes in outcomes caused by changes in policy variables. This concept of manipulative causation differs from the more familiar concepts of associational and attributive causation most widely used in epidemiology. Drawing on modern literature on causal discovery and inference principles and algorithms for drawing limited but useful causal conclusions from observational data, we propose seven criteria for assessing consistency of data with a manipulative causal exposure-response relationship - mutual information, directed dependence, internal and external consistency, coherent causal explanation of biological plausibility, causal mediation confirmation, and refutation of non-causal explanations - and discuss to what extent it is now possible to automate discovery of manipulative causal dependencies and quantification of causal effects from observational data. We compare our proposed principles for causal discovery and inference to the traditional Bradford Hill considerations from 1965. Understanding how old and new principles are related can clarify and enrich both.

Predictive entrainment of natural speech through two fronto-motor top-down channels

Natural communication between interlocutors is enabled by the ability to predict upcoming speech in a given context. Previously we showed that these predictions rely on a fronto-motor top-down control of low-frequency oscillations in auditory-temporal brain areas that track intelligible speech. However, a comprehensive spatio-temporal characterisation of this effect is still missing. Here, we applied transfer entropy to source-localised MEG data during continuous speech perception. First, at low frequencies (1-4 Hz, brain delta phase to speech delta phase), predictive effects start in left fronto-motor regions and progress to right temporal regions. Second, at higher frequencies (14-18 Hz, brain beta power to speech delta phase), predictive patterns show a transition from left inferior frontal gyrus via left precentral gyrus to left primary auditory areas. Our results suggest a progression of prediction processes from higher-order to early sensory areas in at least two different frequency channels.