Complexity and multifractality of neuronal noise in mouse and human hippocampal epileptiform dynamics

Epileptic network identification: insights from dynamic mode decomposition of sEEG data

Objective.For medically-refractory epilepsy patients, stereoelectroencephalography (sEEG) is a surgical method using intracranial electrode recordings to identify brain networks participating in early seizure organization and propagation (i.e. the epileptogenic zone, EZ). If identified, surgical EZ treatment via resection, ablation or neuromodulation can lead to seizure-freedom. To date, quantification of sEEG data, including its visualization and interpretation, remains a clinical and computational challenge. Given elusiveness of physical laws or governing equations modelling complex brain dynamics, data science offers unique insight into identifying unknown patterns within high-dimensional sEEG data. We apply here an unsupervised data-driven algorithm, dynamic mode decomposition (DMD), to sEEG recordings from five focal epilepsy patients (three with temporal lobe, and two with cingulate epilepsy), who underwent subsequent resective or ablative surgery and became seizure free.Approach.DMD obtains a linear approximation of nonlinear data dynamics, generating coherent structures ('modes') defining important signal features, used to extract frequencies, growth rates and spatial structures. DMD was adapted to produce dynamic modal maps (DMMs) across frequency sub-bands, capturing onset and evolution of epileptiform dynamics in sEEG data. Additionally, we developed a static estimate of EZ-localized electrode contacts, termed the higher-frequency mode-based norm index (MNI). DMM and MNI maps for representative patient seizures were validated against clinical sEEG results and seizure-free outcomes following surgery.Main results.DMD was most informative at higher frequencies, i.e. gamma (including high-gamma) and beta range, successfully identifying EZ contacts. Combined interpretation of DMM/MNI plots best identified spatiotemporal evolution of mode-specific network changes, with strong concordance to sEEG results and outcomes across all five patients. The method identified network attenuation in other contacts not implicated in the EZ.Significance.This is the first application of DMD to sEEG data analysis, supporting integration of neuroengineering, mathematical and machine learning methods into traditional workflows for sEEG review and epilepsy surgical decision-making.

On Multiscaling of Parkinsonian Rest Tremor Signals and Their Classification

Self-similar stochastic processes and broad probability distributions are ubiquitous in nature and in many man-made systems. The brain is a particularly interesting example of (natural) complex system where those features play a pivotal role. In fact, the controversial yet experimentally validated "criticality hypothesis" explaining the functioning of the brain implies the presence of scaling laws for correlations. Recently, we have analyzed a collection of rest tremor velocity signals recorded from patients affected by Parkinson's disease, with the aim of determining and hence exploiting the presence of scaling laws. Our results show that multiple scaling laws are required in order to describe the dynamics of such signals, stressing the complexity of the underlying generating mechanism. We successively extracted numeric features by using the multifractal detrended fluctuation analysis procedure. We found that such features can be effective for discriminating classes of signals recorded in different experimental conditions. Notably, we show that the use of medication (L-DOPA) can be recognized with high accuracy.

Fractal Geometry Meets Computational Intelligence: Future Perspectives

Characterizations in terms of fractals are typically employed for systems with complex and multiscale descriptions. A prominent example of such systems is provided by the human brain, which can be idealized as a complex dynamical system made of many interacting subunits. The human brain can be modeled in terms of observable variables together with their spatio-temporal-functional relations. Computational intelligence is a research field bridging many nature-inspired computational methods, such as artificial neural networks, fuzzy systems, and evolutionary and swarm intelligence optimization techniques. Typical problems faced by means of computational intelligence methods include those of recognition, such as classification and prediction. Although historically conceived to operate in some vector space, such methods have been recently extended to the so-called nongeometric spaces, considering labeled graphs as the most general example of such patterns. Here, we suggest that fractal analysis and computational intelligence methods can be exploited together in neuroscience research. Fractal characterizations can be used to (i) assess scale-invariant properties and (ii) offer numeric, feature-based representations to complement the usually more complex pattern structures encountered in neurosciences. Computational intelligence methods could be used to exploit such fractal characterizations, considering also the possibility to perform data-driven analysis of nongeometric input spaces, therby overcoming the intrinsic limits related to Euclidean geometry.

Morphology and Fractal-Based Classifications of Neurons and Microglia in Two and Three Dimensions

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than do neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well-described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has substantially contributed to classifying functional categories, where, in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions, including hyper-ramification. This chapter provides a review of the intimate relationships between neurons and microglia, by introducing 2D and 3D fractal analysis methodology and its applications in neuron-microglia function in health and disease.

Regional Hurst Exponent Reflects Impulsivity-Related Alterations in Fronto-Hippocampal Pathways Within the Waiting Impulsivity Network

In general, the Hurst exponent. is used as a measure of long-term memory of time series. In previous neuroimaging studies, H has been introduced as one important parameter to define resting-state networks, reflecting upon global scale-free properties emerging from a network. H has been examined in the waiting impulsivity (WI) network in an earlier study. We found that alterations of H in the anterior cingulate cortex (H^ACC) and the nucleus accumbens (H^NAcc) were lower in high impulsive (highIMP) compared to low impulsive (lowIMP) participants. Following up on those findings, we addressed the relation between altered fractality in H^ACC and H^NAcc and brain activation and neural network connectivity. To do so, brain activation maps were calculated, and network connectivity was determined using the Dynamic Causal Modeling (DCM) approach. Finally, 1–H scores were determined to quantify the alterations of H. This way, the focus of the analyses was placed on the potential effects of alterations of H on neural network activation and connectivity. Correlation analyses between the alterations of H^ACC/H^NAcc and activation maps and DCM estimates were performed. We found that the alterations of H predominantly correlated with fronto-hippocampal pathways and correlations were significant only in highIMP subjects. For example, alterations of H^ACC was associated with a decrease in neural activation in the right HC in combination with increased ACC-hippocampal connectivity. Alteration inH^NAcc, in return, was related to an increase in bilateral prefrontal activation in combination with increased fronto-hippocampal connectivity. The findings, that the WI network was related to H alteration in highIMP subjects indicated that impulse control was not reduced per se but lacked consistency. Additionally, H has been used to describe long-term memory processes before, e.g., in capital markets, energy future prices, and human memory. Thus, current findings supported the relation of H toward memory processing even when further prominent cognitive functions were involved.

Multifractal detrended fluctuation analysis of continuous neural time series in primate visual cortex

BACKGROUND

Local field potential (LFP) recordings have become an important tool to study the activity of populations of neurons. The functional activity of LFPs is usually compared with the activity of neighboring single spike neurons with sampling rates much higher than those of the continuous field potential channel (5 kHz). However, comparison of these signals generated with the lower sampling rate technique is important.

NEW METHOD

In this study, we provide an analysis of extracellular field potential time series using the sophisticated nonlinear multifractal detrended fluctuation analysis (MF-DFA). Using the MF-DFA, we demonstrate that the integral of the singularity spectrum is a powerful new method to measure the response tuning of spikes in the continuous field potential channel.

RESULTS

Results show that the spikes in the continuous channel at frequency ranges above the LFP component signals were consistently tuned similar to those in the spike channel. Our results also show that using a low-pass filter (<250 Hz), which is commonly applied as a preprocessing step to insulate LFPs from spikes, significantly influences the nonlinearity of the multifractal time series.

COMPARISON WITH EXISTING METHODS AND CONCLUSIONS

Our approach for inferring the tuning curve of spiking activity from the continuous channel has some advantages compared to conventional methods such as spike trains. The MF-DFA does not require any preprocessing of the raw signal data and makes no assumptions about the time series characteristics. This method is robust and can be applied to short time series of continuous raw signals.

Evidence of embodied social competence during conversation in high functioning children with autism spectrum disorder

Even high functioning children with Autism Spectrum Disorder (ASD) exhibit impairments that affect their ability to carry out and maintain effective social interactions in multiple contexts. One aspect of subtle nonverbal communication that might play a role in this impairment is the whole-body motor coordination that naturally arises between people during conversation. The current study aimed to measure the time-dependent, coordinated whole-body movements between children with ASD and a clinician during a conversational exchange using tools of nonlinear dynamics. Given the influence that subtle interpersonal coordination has on social interaction feelings, we expected there to be important associations between the dynamic motor movement measures introduced in the current study and the measures used traditionally to categorize ASD impairment (ADOS-2, joint attention and theory of mind). The study found that children with ASD coordinated their bodily movements with a clinician, that these movements were complex and that the complexity of the children’s movements matched that of the clinician’s movements. Importantly, the degree of this bodily coordination was related to higher social cognitive ability. This suggests children with ASD are embodying some degree of social competence during conversations. This study demonstrates the importance of further investigating the subtle but important bodily movement coordination that occurs during social interaction in children with ASD.

Discrimination and Characterization of Parkinsonian Rest Tremors by Analyzing Long-Term Correlations and Multifractal Signatures

GOAL

We analyze 48 signals of rest tremor velocity related to 12 distinct subjects affected by the Parkinson's disease. The subjects belong to two different groups, high- and low-amplitude rest tremors, with four and eight subjects, respectively. Each subject has been tested in four settings given by combining the use of deep brain stimulation and L-DOPA medication.

METHODS

We develop two main feature-based representations of the signals, which are obtained by considering 1) the long-term correlations and multifractal properties, and 2) the power spectra.

RESULTS

Our results show that, when medication is used, a qualitative change is observed in the related signals from anticorrelated to long term positively correlated. In addition, the medication effect yields statistically significant differences in both high- and low-amplitude tremor groups. We successively consider three different classification problems, involving the recognition of 1) the use of medication, 2) the use of deep brain stimulation, and 3) the membership to the high- and low-amplitude tremor groups. Classification results show that the best results are obtained with a parsimonious, two-dimensional (2-D) representation encoding the long-term correlations and multifractal properties of the signals.

CONCLUSIONS

Long-term correlations and multifractal signatures of time series provided an effective tool to analyze Parkinsonian rest tremor signals.

SIGNIFICANCE

The developed 2-D representation is a parsimonious and effective representation for rest tremor signals that could be adopted in clinical settings, even by considering resource-constrained scenarios.

Fractal analysis of heart graft acute rejection microscopic images

BACKGROUND

Endomyocardial biopsy to evaluate rejection in the transplanted heart is accepted at the "gold standard." The complexity of microscopic images suggested using digital methods for precise evaluating of acute rejection episodes with numerical representation. The aim of the present was study to characterize digitally acute rejection of the transplanted heart using complexity/fractal image analysis.

MATERIAL AND METHODS

Biopsy samples harvested form 40 adult recipients after orthotropic heart transplantation were collected and rejection grade was evaluated according to the International Society for Heart and Lung Transplantation (0, 1a, 1b, or 3a) at transverse and longitudinal sections. Fifteen representative digital microscope images from each grade were collected and analyzed after Sobel edge detection and binarization.

RESULTS

Only mean fractal dimension showed a progressive and significant increase and correlation based on rejection grade using longitudinal sections. Lacunarity and number of foreground pixels showed unequivocal results.

CONCLUSION

Mean fractal diameter could serve as auxiliary digital parameter for grading of acute rejection in the transplanted heart.

Distinguishing cognitive state with multifractal complexity of hippocampal interspike interval sequences

Fractality, represented as self-similar repeating patterns, is ubiquitous in nature and the brain. Dynamic patterns of hippocampal spike trains are known to exhibit multifractal properties during working memory processing; however, it is unclear whether the multifractal properties inherent to hippocampal spike trains reflect active cognitive processing. To examine this possibility, hippocampal neuronal ensembles were recorded from rats before, during and after a spatial working memory task following administration of tetrahydrocannabinol (THC), a memory-impairing component of cannabis. Multifractal detrended fluctuation analysis was performed on hippocampal interspike interval sequences to determine characteristics of monofractal long-range temporal correlations (LRTCs), quantified by the Hurst exponent, and the degree/magnitude of multifractal complexity, quantified by the width of the singularity spectrum. Our results demonstrate that multifractal firing patterns of hippocampal spike trains are a marker of functional memory processing, as they are more complex during the working memory task and significantly reduced following administration of memory impairing THC doses. Conversely, LRTCs are largest during resting state recordings, therefore reflecting different information compared to multifractality. In order to deepen conceptual understanding of multifractal complexity and LRTCs, these measures were compared to classical methods using hippocampal frequency content and firing variability measures. These results showed that LRTCs, multifractality, and theta rhythm represent independent processes, while delta rhythm correlated with multifractality. Taken together, these results provide a novel perspective on memory function by demonstrating that the multifractal nature of spike trains reflects hippocampal microcircuit activity that can be used to detect and quantify cognitive, physiological, and pathological states.

Complexity of Multi-Channel Electroencephalogram Signal Analysis in Childhood Absence Epilepsy

Absence epilepsy is an important epileptic syndrome in children. Multiscale entropy (MSE), an entropy-based method to measure dynamic complexity at multiple temporal scales, is helpful to disclose the information of brain connectivity. This study investigated the complexity of electroencephalogram (EEG) signals using MSE in children with absence epilepsy. In this research, EEG signals from 19 channels of the entire brain in 21 children aged 5-12 years with absence epilepsy were analyzed. The EEG signals of pre-ictal (before seizure) and ictal states (during seizure) were analyzed by sample entropy (SamEn) and MSE methods. Variations of complexity index (CI), which was calculated from MSE, from the pre-ictal to the ictal states were also analyzed. The entropy values in the pre-ictal state were significantly higher than those in the ictal state. The MSE revealed more differences in analysis compared to the SamEn. The occurrence of absence seizures decreased the CI in all channels. Changes in CI were also significantly greater in the frontal and central parts of the brain, indicating fronto-central cortical involvement of “cortico-thalamo-cortical network” in the occurrence of generalized spike and wave discharges during absence seizures. Moreover, higher sampling frequency was more sensitive in detecting functional changes in the ictal state. There was significantly higher correlation in ictal states in the same patient in different seizures but there were great differences in CI among different patients, indicating that CI changes were consistent in different absence seizures in the same patient but not from patient to patient. This implies that the brain stays in a homogeneous activation state during the absence seizures. In conclusion, MSE analysis is better than SamEn analysis to analyze complexity of EEG, and CI can be used to investigate the functional brain changes during absence seizures.

Multifractal analysis of information processing in hippocampal neural ensembles during working memory under Δ⁹-tetrahydrocannabinol administration

BACKGROUND

Multifractal analysis quantifies the time-scale-invariant properties in data by describing the structure of variability over time. By applying this analysis to hippocampal interspike interval sequences recorded during performance of a working memory task, a measure of long-range temporal correlations and multifractal dynamics can reveal single neuron correlates of information processing.

NEW METHOD

Wavelet leaders-based multifractal analysis (WLMA) was applied to hippocampal interspike intervals recorded during a working memory task. WLMA can be used to identify neurons likely to exhibit information processing relevant to operation of brain-computer interfaces and nonlinear neuronal models.

RESULTS

Neurons involved in memory processing ("Functional Cell Types" or FCTs) showed a greater degree of multifractal firing properties than neurons without task-relevant firing characteristics. In addition, previously unidentified FCTs were revealed because multifractal analysis suggested further functional classification. The cannabinoid type-1 receptor (CB1R) partial agonist, tetrahydrocannabinol (THC), selectively reduced multifractal dynamics in FCT neurons compared to non-FCT neurons.

COMPARISON WITH EXISTING METHODS

WLMA is an objective tool for quantifying the memory-correlated complexity represented by FCTs that reveals additional information compared to classification of FCTs using traditional z-scores to identify neuronal correlates of behavioral events.

CONCLUSION

z-Score-based FCT classification provides limited information about the dynamical range of neuronal activity characterized by WLMA. Increased complexity, as measured with multifractal analysis, may be a marker of functional involvement in memory processing. The level of multifractal attributes can be used to differentially emphasize neural signals to improve computational models and algorithms underlying brain-computer interfaces.

Fractal dimension of EEG activity senses neuronal impairment in acute stroke

The brain is a self-organizing system which displays self-similarities at different spatial and temporal scales. Thus, the complexity of its dynamics, associated to efficient processing and functional advantages, is expected to be captured by a measure of its scale-free (fractal) properties. Under the hypothesis that the fractal dimension (FD) of the electroencephalographic signal (EEG) is optimally sensitive to the neuronal dysfunction secondary to a brain lesion, we tested the FD's ability in assessing two key processes in acute stroke: the clinical impairment and the recovery prognosis. Resting EEG was collected in 36 patients 4-10 days after a unilateral ischemic stroke in the middle cerebral artery territory and 19 healthy controls. National Health Institute Stroke Scale (NIHss) was collected at T0 and 6 months later. Highuchi FD, its inter-hemispheric asymmetry (FDasy) and spectral band powers were calculated for EEG signals. FD was smaller in patients than in controls (1.447±0.092 vs 1.525±0.105) and its reduction was paired to a worse acute clinical status. FD decrease was associated to alpha increase and beta decrease of oscillatory activity power. Larger FDasy in acute phase was paired to a worse clinical recovery at six months. FD in our patients captured the loss of complexity reflecting the global system dysfunction resulting from the structural damage. This decrease seems to reveal the intimate nature of structure-function unity, where the regional neural multi-scale self-similar activity is impaired by the anatomical lesion. This picture is coherent with neuronal activity complexity decrease paired to a reduced repertoire of functional abilities. FDasy result highlights the functional relevance of the balance between homologous brain structures' activities in stroke recovery.

Fractal dimension of EEG activity senses neuronal impairment in acute stroke

The brain is a self-organizing system which displays self-similarities at different spatial and temporal scales. Thus, the complexity of its dynamics, associated to efficient processing and functional advantages, is expected to be captured by a measure of its scale-free (fractal) properties. Under the hypothesis that the fractal dimension (FD) of the electroencephalographic signal (EEG) is optimally sensitive to the neuronal dysfunction secondary to a brain lesion, we tested the FD's ability in assessing two key processes in acute stroke: the clinical impairment and the recovery prognosis. Resting EEG was collected in 36 patients 4-10 days after a unilateral ischemic stroke in the middle cerebral artery territory and 19 healthy controls. National Health Institute Stroke Scale (NIHss) was collected at T0 and 6 months later. Highuchi FD, its inter-hemispheric asymmetry (FDasy) and spectral band powers were calculated for EEG signals. FD was smaller in patients than in controls (1.447±0.092 vs 1.525±0.105) and its reduction was paired to a worse acute clinical status. FD decrease was associated to alpha increase and beta decrease of oscillatory activity power. Larger FDasy in acute phase was paired to a worse clinical recovery at six months. FD in our patients captured the loss of complexity reflecting the global system dysfunction resulting from the structural damage. This decrease seems to reveal the intimate nature of structure-function unity, where the regional neural multi-scale self-similar activity is impaired by the anatomical lesion. This picture is coherent with neuronal activity complexity decrease paired to a reduced repertoire of functional abilities. FDasy result highlights the functional relevance of the balance between homologous brain structures' activities in stroke recovery.