Comparison Analysis: Granger Causality and New Causality and Their Applications to Motor Imagery

Source Causal Connectivity Noninvasively Predicting Surgical Outcomes of Drug-Refractory Epilepsy

AIMS

Drug-refractory epilepsy (DRE) refers to the failure of controlling seizures with adequate trials of two tolerated and appropriately chosen anti-seizure medications (ASMs). For patients with DRE, surgical intervention becomes the most effective and viable treatment, but its success rate is unsatisfactory at only approximately 50%. Predicting surgical outcomes in advance can provide additional guidance to clinicians. Despite the high accuracy of invasive methods, they inevitably carry the risk of post-operative infection and complications. Herein, to noninvasively predict surgical outcomes of DRE, we propose the "source causal connectivity" framework.

METHODS

In this framework, sLORETA, an EEG source imaging technique, was first used to inversely reconstruct intracranial neuronal electrical activity. Then, full convergent cross mapping (FCCM), a robust causal measure was introduced to calculate the causal connectivity between remodeled neuronal signals within epileptogenic zones (EZs). After that, statistical tests were performed to find out if there was a significant difference between the successful and failed surgical groups. Finally, a model for surgical outcome prediction was developed by combining causal network features with machine learning.

RESULTS

A total of 39 seizures with 205 ictal EEG segments were included in this prospective study. Experimental results exhibit that source causal connectivity in α-frequency band (8~13 Hz) gains the most significant differences between the surgical success and failure groups, with a p-value of 5.00e-05 and Cohen's d effect size of 0.68. All machine learning models can achieve an average accuracy of higher than 85%. Among them, the SVM classifier with Gaussian kernel function and Bayesian optimization demonstrates the highest accuracy of 90.73%, with a PPV of 87.91%, an NPV of 92.98%, a sensitivity of 90.91%, a specificity of 90.60%, and an F1-score of 89.39%.

CONCLUSION

Our results demonstrate that the source causal network of EZ is a reliable biomarker for predicting DRE surgical outcomes. The findings promote noninvasive precision medicine for DRE.

A Human-Machine Joint Learning Framework to Boost Endogenous BCI Training

Brain-computer interfaces (BCIs) provide a direct pathway from the brain to external devices and have demonstrated great potential for assistive and rehabilitation technologies. Endogenous BCIs based on electroencephalogram (EEG) signals, such as motor imagery (MI) BCIs, can provide some level of control. However, mastering spontaneous BCI control requires the users to generate discriminative and stable brain signal patterns by imagery, which is challenging and is usually achieved over a very long training time (weeks/months). Here, we propose a human-machine joint learning framework to boost the learning process in endogenous BCIs, by guiding the user to generate brain signals toward an optimal distribution estimated by the decoder, given the historical brain signals of the user. To this end, we first model the human-machine joint learning process in a uniform formulation. Then a human-machine joint learning framework is proposed: 1) for the human side, we model the learning process in a sequential trial-and-error scenario and propose a novel "copy/new" feedback paradigm to help shape the signal generation of the subject toward the optimal distribution and 2) for the machine side, we propose a novel adaptive learning algorithm to learn an optimal signal distribution along with the subject's learning process. Specifically, the decoder reweighs the brain signals generated by the subject to focus more on "good" samples to cope with the learning process of the subject. Online and psuedo-online BCI experiments with 18 healthy subjects demonstrated the advantages of the proposed joint learning process over coadaptive approaches in both learning efficiency and effectiveness.

Causal Brain Network in Clinically-Annotated Epileptogenic Zone Predicts Surgical Outcomes of Drug-Resistant Epilepsy

OBJECTIVE

Patients with drug-resistant epilepsy (DRE) are commonly treated using neurosurgery, while its success rate is limited with approximately 50%. Predicting surgical outcomes is currently a prominent topic. The DRE is recognized as a network disorder involving a seizure triggering mechanism within epileptogenic zone (EZ); however, a systematic exploration of the EZ causal network remains lacking.

METHODS

This paper will advance DRE study by: 1) developing a novel causal coupling algorithm, "full convergent cross mapping (FCCM)" to improve the quantization performance; 2) characterizing the DRE's multi-frequency epileptogenic network by FCCM calculation of ictal iEEG; 3) predicting surgical outcomes using network features and machine learning. Numerical validations demonstrate the FCCM's superior quantization in terms of nonlinearity, accuracy, and stability. A multicenter cohort containing 22 DRE patients with 81 seizures is included.

RESULT

Based on the Mann-Whitney-U-test, coupling strength of the epileptogenic network in successful surgeries is significantly higher than that of the failed group, with the most significant difference observed in -iEEG network (). Other clinical covariates are also considered and all the -iEEG networks demonstrate consistent differences comparing successful and failed groups, with and for lesional and non-lesional DRE, , , and for three clinical centers CHFU, JHU and NIH. Using FCCM features and 10-fold cross validation, the SVM achieves the highest accuracy of 87.65% in predicting surgical outcomes.

CONCLUSION

The epileptogenic causal network is a reliable biomarker for estimating DRE's surgical outcomes.

SIGNIFICANCE

The proposed approach is promising to facilitate DRE precision medicine.

Detection of quadratic phase coupling by cross-bicoherence and spectral Granger causality in bifrequencies interactions

Quadratic Phase Coupling (QPC) serves as an essential statistical instrument for evaluating nonlinear synchronization within multivariate time series data, especially in signal processing and neuroscience fields. This study explores the precision of QPC detection using numerical estimates derived from cross-bicoherence and bivariate Granger causality within a straightforward, yet noisy, instantaneous multiplier model. It further assesses the impact of accidental statistically significant bifrequency interactions, introducing new metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling. Ratios nearing 1 signify a high degree of accuracy in detecting QPC. The coupling strength between interacting channels is identified as a key element that introduces nonlinearities, influencing the signal-to-noise ratio in the output channel. The model is tested across 59 experimental conditions of simulated recordings, with each condition evaluated against six coupling strength values, covering a wide range of carrier frequencies to examine a broad spectrum of scenarios. The findings demonstrate that the bispectral method outperforms bivariate Granger causality, particularly in identifying specific QPC under conditions of very weak couplings and in the presence of noise. The detection of specific QPC is crucial for neuroscience applications aimed at better understanding the temporal and spatial coordination between different brain regions.

Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

This article addresses the problem of estimating brain effective connectivity from electroencephalogram (EEG) signals using a Granger causality (GC) characterized on state-space models, extended from the conventional vector autoregressive (VAR) process. The scheme involves two main steps: model estimation and model inference to estimate brain connectivity. The model estimation performs a subspace identification and active source selection based on group-norm regularized least-squares. The model inference relies on the concept of state-space GC that requires solving a Riccati equation for the covariance of estimation error. We verify the performance on simulated datasets that represent realistic human brain activities under several conditions, including percentages and location of active sources, and the number of EEG electrodes. Our model's accuracy in estimating connectivity is compared with a two-stage approach using source reconstructions and a VAR-based Granger analysis. Our method achieved better performances than the two-stage approach under the assumptions that the true source dynamics are sparse and generated from state-space models. When the method was applied to a real EEG SSVEP dataset, the temporal lobe was found to be a mediating connection between the temporal and occipital areas, which agreed with findings in previous studies.

Constructing Time-varying Directed EEG network by Multivariate Nonparametric Dynamical Granger Causality

Time-varying directed electroencephalography (EEG) network is the potential tool for studying the dynamical causality among brain areas at a millisecond level; which conduces to understanding how our brain effectively adapts to information processing, giving inspiration to causality- and brain-inspired machine learning. Currently, its construction still mainly relies on the parametric approach such as multivariate adaptive autoregressive (MVAAR), represented by the most widely used adaptive directed transfer function (ADTF). Restricted by the model assumption, the corresponding performance largely depends on the MVAAR modeling which usually encounters difficulty in fitting complex spectral features. In this study, we proposed to construct EEG directed network with multivariate nonparametric dynamical Granger causality (mndGC) method that infers the causality of a network, instead, in a data-driven way directly and therefore avoids the trap in the model-dependent parametric approach. Comparisons between mndGC and ADTF were conducted both with simulation and real data application. Simulation study demonstrated the superiority of mndGC both in noise resistance and capturing the instantaneous directed network changes. When applying to the real motor imagery (MI) data set, distinguishable network characters between left- and right-hand MI during different MI stages were better revealed by mndGC. Our study extends the nonparametric causality exploration and provides practical suggestions for the time-varying directed EEG network analysis.

Motor Impairment in Stroke Patients is Associated with Network Properties During Consecutive Motor Imagery

OBJECTIVE

Our study aimed to predict the Fugl-Meyer assessment (FMA) upper limb using network properties during motor imagery using electroencephalography (EEG) signals.

METHODS

The subjects performed a finger tapping imagery task according to consecutive cues. We measured the weighted phase lag index (wPLI) as functional connectivity and directed transfer function (DTF) as causal connectivity in healthy controls and stroke patients. The network properties based on the wPLI and DTF were calculated. We predicted the FMA upper limb using partial least squares regression.

RESULTS

A higher DTF in the mu band was observed in stroke patients than in healthy controls. Notably, the difference in local properties at node F3 was negatively correlated with motor impairment in stroke patients. Finally, using significant network properties based on the wPLI and DTF, we predicted motor impairments using the FMA upper limb with a root-mean-square error of 1.68 (R² = 0.97). This outperformed the state-of-the-art predictors.

CONCLUSION

These findings demonstrate that network properties based on functional and causal connectivity were highly associated with motor function in stroke patients.

SIGNIFICANCE

Our network properties can help calculate the predictor of motor impairments in stroke rehabilitation and provide insight into the neural correlates related to motor function based on EEG after reorganization induced by stroke.

Sparse Granger Causality Analysis Model Based on Sensors Correlation for Emotion Recognition Classification in Electroencephalography

In recent years, affective computing based on electroencephalogram (EEG) data has attracted increased attention. As a classic EEG feature extraction model, Granger causality analysis has been widely used in emotion classification models, which construct a brain network by calculating the causal relationships between EEG sensors and select the key EEG features. Traditional EEG Granger causality analysis uses the L₂ norm to extract features from the data, and so the results are susceptible to EEG artifacts. Recently, several researchers have proposed Granger causality analysis models based on the least absolute shrinkage and selection operator (LASSO) and the L_1/2 norm to solve this problem. However, the conventional sparse Granger causality analysis model assumes that the connections between each sensor have the same prior probability. This paper shows that if the correlation between the EEG data from each sensor can be added to the Granger causality network as prior knowledge, the EEG feature selection ability and emotional classification ability of the sparse Granger causality model can be enhanced. Based on this idea, we propose a new emotional computing model, named the sparse Granger causality analysis model based on sensor correlation (SC-SGA). SC-SGA integrates the correlation between sensors as prior knowledge into the Granger causality analysis based on the L_1/2 norm framework for feature extraction, and uses L₂ norm logistic regression as the emotional classification algorithm. We report the results of experiments using two real EEG emotion datasets. These results demonstrate that the emotion classification accuracy of the SC-SGA model is better than that of existing models by 2.46–21.81%.

Deep Learning-Based Approaches for Decoding Motor Intent From Peripheral Nerve Signals

Previous literature shows that deep learning is an effective tool to decode the motor intent from neural signals obtained from different parts of the nervous system. However, deep neural networks are often computationally complex and not feasible to work in real-time. Here we investigate different approaches' advantages and disadvantages to enhance the deep learning-based motor decoding paradigm's efficiency and inform its future implementation in real-time. Our data are recorded from the amputee's residual peripheral nerves. While the primary analysis is offline, the nerve data is cut using a sliding window to create a “pseudo-online” dataset that resembles the conditions in a real-time paradigm. First, a comprehensive collection of feature extraction techniques is applied to reduce the input data dimensionality, which later helps substantially lower the motor decoder's complexity, making it feasible for translation to a real-time paradigm. Next, we investigate two different strategies for deploying deep learning models: a one-step (1S) approach when big input data are available and a two-step (2S) when input data are limited. This research predicts five individual finger movements and four combinations of the fingers. The 1S approach using a recurrent neural network (RNN) to concurrently predict all fingers' trajectories generally gives better prediction results than all the machine learning algorithms that do the same task. This result reaffirms that deep learning is more advantageous than classic machine learning methods for handling a large dataset. However, when training on a smaller input data set in the 2S approach, which includes a classification stage to identify active fingers before predicting their trajectories, machine learning techniques offer a simpler implementation while ensuring comparably good decoding outcomes to the deep learning ones. In the classification step, either machine learning or deep learning models achieve the accuracy and F1 score of 0.99. Thanks to the classification step, in the regression step, both types of models result in a comparable mean squared error (MSE) and variance accounted for (VAF) scores as those of the 1S approach. Our study outlines the trade-offs to inform the future implementation of real-time, low-latency, and high accuracy deep learning-based motor decoder for clinical applications.

Analysis of corticomuscular connectivity during walking using vine copula

Corticomuscular connectivity plays an important role in the neural control of human motion. This study recorded electroencephalography (EEG) and surface electromyography (sEMG) signals from subjects performing specific tasks (walking on level ground and on stairs) based on metronome instructions. This study presents a novel method based on vine copula to jointly model EEG and sEMG signals. The advantage of vine copula is its applicability in the construction of dependency structures to describe the connectivity between the cortex and muscles during different movements. A corticomuscular function network was also constructed by analyzing the dependence of each channel sample. The successfully constructed network shows information transmission between different divisions of the cortex, between muscles, and between the cortex and muscles when the body performs lower limb movements. Additionally, it highlights the potential of the vine copula concept used in this study, indicating that significant changes in the corticomuscular network under lower limb movements can be quantified by effective connectivity values.

State Transitions During Discrimination Learning in the Gerbil Auditory Cortex Analyzed by Network Causality Metrics

This work studies the evolution of cortical networks during the transition from escape strategy to avoidance strategy in auditory discrimination learning in Mongolian gerbils trained by the well-established two-way active avoidance learning paradigm. The animals were implanted with electrode arrays centered on the surface of the primary auditory cortex and electrocorticogram (ECoG) recordings were made during performance of an auditory Go/NoGo discrimination task. Our experiments confirm previous results on a sudden behavioral change from the initial naïve state to an avoidance strategy as learning progresses. We employed two causality metrics using Granger Causality (GC) and New Causality (NC) to quantify changes in the causality flow between ECoG channels as the animals switched to avoidance strategy. We found that the number of channel pairs with inverse causal interaction significantly increased after the animal acquired successful discrimination, which indicates structural changes in the cortical networks as a result of learning. A suitable graph-theoretical model is developed to interpret the findings in terms of cortical networks evolving during cognitive state transitions. Structural changes lead to changes in the dynamics of neural populations, which are described as phase transitions in the network graph model with small-world connections. Overall, our findings underscore the importance of functional reorganization in sensory cortical areas as a possible neural contributor to behavioral changes.

An EEG channel selection method for motor imagery based brain-computer interface and neurofeedback using Granger causality

Motor imagery (MI) brain-computer interface (BCI) and neurofeedback (NF) with electroencephalogram (EEG) signals are commonly used for motor function improvement in healthy subjects and to restore neurological functions in stroke patients. Generally, in order to decrease noisy and redundant information in unrelated EEG channels, channel selection methods are used which provide feasible BCI and NF implementations with better performances. Our assumption is that there are causal interactions between the channels of EEG signal in MI tasks that are repeated in different trials of a BCI and NF experiment. Therefore, a novel method for EEG channel selection is proposed which is based on Granger causality (GC) analysis. Additionally, the machine-learning approach is used to cluster independent component analysis (ICA) components of the EEG signal into artifact and normal EEG clusters. After channel selection, using the common spatial pattern (CSP) and regularized CSP (RCSP), features are extracted and with the k-nearest neighbor (k-NN), support vector machine (SVM) and linear discriminant analysis (LDA) classifiers, MI tasks are classified into left and right hand MI. The goal of this study is to achieve a method resulting in lower EEG channels with higher classification performance in MI-based BCI and NF by causal constraint. The proposed method based on GC, with only eight selected channels, results in 93.03% accuracy, 92.93% sensitivity, and 93.12% specificity, with RCSP feature extractor and best classifier for each subject, after being applied on Physionet MI dataset, which is increased by 3.95%, 3.73%, and 4.13%, in comparison with correlation-based channel selection method.

An Efficient Entropy-Based Causal Discovery Method for Linear Structural Equation Models With IID Noise Variables

The discovery of causal relationships from the observational data is an important task. To identify the unique causal structure belonging to a Markov equivalence class, a number of algorithms, such as the linear non-Gaussian acyclic model (LiNGAM), have been proposed. However, two challenges remain to be met: 1) these algorithms fail to work on the data which follow linear structural equation model with Gaussian noise and 2) they misjudge the causal direction when the data contain additional measurement errors. In this paper, we propose an entropy-based two-phase iterative algorithm for arbitrary distribution data with additional measurement errors under some mild assumptions. In the first phase of the algorithm, based on the property that entropy can measure the amount of information behind the data with arbitrary distribution, we design a general approach for the identification of exogenous variable on both Gaussian and non-Gaussian data, and we give the corresponding theoretical derivation. In the second phase, to eliminate the effects of measurement errors, we revise the value of the exogenous variable by removing its measurement error and further use the revised value to remove its effect on the remaining variables. Experimental results on real-world causal structures are presented to demonstrate the effectiveness and stability of our method. We also apply the proposed algorithm on the mobile-base-station data with measurement errors, and the results further prove the effectiveness of our algorithm.

Directed EEG neural network analysis by LAPPS (p≤1) Penalized sparse Granger approach

The conventional multivariate Granger Analysis (GA) of directed interactions has been widely applied in brain network construction based on EEG recordings as well as fMRI. Nevertheless, EEG is usually inevitably contaminated by strong noise, which may cause network distortion due to the L2-norm used in GAs for directed network recovery. The Lp (p ≤1) norm has been shown to be more robust to outliers as compared to LASSO and L2-GAs. Motivated to construct the sparse brain networks under strong noise condition, we hereby introduce a new approach for GA analysis, termed LAPPS (Least Absolute LP (0<p<1) Penalized Solution). LAPPS utilizes the L1-loss function for the residual error to alleviate the effect of outliers, and another Lp-penalty term (p=0.5) to obtain the sparse connections while suppressing the spurious linkages in the networks. The simulation results reveal that LAPPS obtained the best performance under various noise conditions. In a real EEG data test when subjects performed the left and right hand Motor Imagery (MI) for brain network estimation, LAPPS also obtained a sparse network pattern with the hub at the contralateral brain primary motor areas consistent with the physiological basis of MI.

Time-Frequency-Domain Copula-Based Granger Causality and Application to Corticomuscular Coupling in Stroke

The corticomuscular coupling (CMC) characterization between the motor cortex and muscles during motion control is a valid biomarker of motor system function after stroke, which can improve clinical decision-making. However, traditional CMC analysis is mainly based on the coherence method that can’t determine the coupling direction, whereas Granger Causality (GC) is limited in identifying linear cause–effect relationship. In this paper, a time-frequency domain copula-based GC (copula-GC) method is proposed to assess CMC characteristic. The 32-channel electroencephalogram (EEG) signals over brain scalp and electromyography (EMG) signals from upper limb were recorded during controlling and maintaining steady-state force output for five stroke patients and five healthy controls. Then, the time-frequency copula-GC analysis was applied to evaluate the CMC strength in both directions. Experimental results show that the CMC strength of descending direction is greater than that of ascending direction in the time domain for healthy controls. With the increase of grip strength, the bi-directional CMC strength has an increasing trend. Meanwhile, the bi-directional CMC strength of right hand is larger than that of left hand. In addition, the bi-directional CMC strength of stroke patients is lower than that of healthy controls. In the frequency domain, the strongest CMC is observed at the beta frequency band. Additionally, the CMC strength of descending direction is slightly larger than that of ascending direction in healthy controls, while the CMC strength of descending direction is lower than that of ascending direction in stroke patients. We suggest that the proposed time-frequency domain analysis approach based on copula-GC can effectively detect complex functional coupling between cortical oscillations and muscle activities, and provide a potential quantitative analysis measure for motion control and rehabilitation evaluation.

Prediction of epilepsy seizure from multi-channel electroencephalogram by effective connectivity analysis using Granger causality and directed transfer function methods

Epilepsy is a chronic disorder, which causes strange perceptions, muscle spasms, sometimes seizures, and loss of awareness, associated with abnormal neuronal activity in the brain. The goal of this study is to investigate how effective connectivity (EC) changes effect on unexpected seizures prediction, as this will authorize the patients to play it safe and avoid risk. We approve the hypothesis that EC variables near seizure change significantly so seizure can be predicted in accordance with this variation. We introduce two time-variant coefficients based on standard deviation of EC on Freiburg EEG dataset by using directed transfer function and Granger causality methods and compare index changes over the course of time in five different frequency bands. Comparison of the multivariate and bivariate analysis of factors is implemented in this investigation. The performance based on the suggested methods shows the seizure occurrence period is approximately 50 min that is expected onset stated in, the maximum value of sensitivity approaching ~ 80%, and 0.33 FP/h is the false prediction rate. The findings revealed that greater accuracy and sensitivity are obtained by the designed system in comparison with the results of other works in the same condition. Even though these results still are not sufficient for clinical applications. Based on the conclusions, it can generally be observed that the greater results by DTF method are in the gamma and beta frequency bands.

Shortcomings/Limitations of Blockwise Granger Causality and Advances of Blockwise New Causality

Multivariate blockwise Granger causality (BGC) is used to reflect causal interactions among blocks of multivariate time series. In particular, spectral BGC and conditional spectral BGC are used to disclose blockwise causal flow among different brain areas in various frequencies. In this paper, we demonstrate that: 1) BGC in time domain may not necessarily disclose true causality and 2) due to the use of the transfer function or its inverse matrix and partial information of the multivariate linear regression model, both of spectral BGC and conditional spectral BGC have shortcomings and/or limitations, which may inevitably lead to misinterpretation. We then, in time and frequency domains, develop two new multivariate blockwise causality methods for the linear regression model called blockwise new causality (BNC) and spectral BNC, respectively. By several examples, we confirm that BNC measures are more reasonable and sensitive to reflect true causality or trend of true causality than BGC or conditional BGC. Finally, for electroencephalograph data from an epilepsy patient, we analyze event-related potential causality and demonstrate that both of the BGC and BNC methods show significant causality flow in frequency domain, but the spectral BNC method yields satisfactory and convincing results, which are consistent with an event-related time-frequency power spectrum activity. The spectral BGC method is shown to generate misleading results. Thus, we deeply believe that our new blockwise causality definitions as well as our previous NC definitions may have wide applications to reflect true causality among two blocks of time series or two univariate time series in economics, neuroscience, and engineering.