Characterizing Fractal Genetic Variation in the Human Genome from the Hapmap Project

Characterization of antiseizure medications effects on the EEG neurodynamic by fractal dimension

Objectives

An important challenge in epilepsy is to define biomarkers of response to treatment. Many electroencephalography (EEG) methods and indices have been developed mainly using linear methods, e.g., spectral power and individual alpha frequency peak (IAF). However, brain activity is complex and non-linear, hence there is a need to explore EEG neurodynamics using nonlinear approaches. Here, we use the Fractal Dimension (FD), a measure of whole brain signal complexity, to measure the response to anti-seizure therapy in patients with Focal Epilepsy (FE) and compare it with linear methods.

Materials

Twenty-five drug-responder (DR) patients with focal epilepsy were studied before (t1, named DR-t1) and after (t2, named DR-t2) the introduction of the anti-seizure medications (ASMs). DR-t1 and DR-t2 EEG results were compared against 40 age-matched healthy controls (HC).

Methods

EEG data were investigated from two different angles: frequency domain-spectral properties in δ, θ, α, β, and γ bands and the IAF peak, and time-domain-FD as a signature of the nonlinear complexity of the EEG signals. Those features were compared among the three groups.

Results

The δ power differed between DR patients pre and post-ASM and HC (DR-t1 vs. HC, p < 0.01 and DR-t2 vs. HC, p < 0.01). The θ power differed between DR-t1 and DR-t2 (p = 0.015) and between DR-t1 and HC (p = 0.01). The α power, similar to the δ, differed between DR patients pre and post-ASM and HC (DR-t1 vs. HC, p < 0.01 and DR-t2 vs. HC, p < 0.01). The IAF value was lower for DR-t1 than DR-t2 (p = 0.048) and HC (p = 0.042). The FD value was lower in DR-t1 than in DR-t2 (p = 0.015) and HC (p = 0.011). Finally, Bayes Factor analysis showed that FD was 195 times more likely to separate DR-t1 from DR-t2 than IAF and 231 times than θ.

Discussion

FD measured in baseline EEG signals is a non-linear brain measure of complexity more sensitive than EEG power or IAF in detecting a response to ASMs. This likely reflects the non-oscillatory nature of neural activity, which FD better describes.

Conclusion

Our work suggests that FD is a promising measure to monitor the response to ASMs in FE.

Brain Dynamics Complexity as a Signature of Cognitive Decline in Parkinson's Disease

BACKGROUND

Higuchi's fractal dimension (FD) captures brain dynamics complexity and may be a promising method to analyze resting-state functional magnetic resonance imaging (fMRI) data and detect the neuronal interaction complexity underlying Parkinson's disease (PD) cognitive decline.

OBJECTIVES

The aim was to compare FD with a more established index of spontaneous neural activity, the fractional amplitude of low-frequency fluctuations (fALFF), and identify through machine learning (ML) models which method could best distinguish across PD-cognitive states, ranging from normal cognition (PD-NC), mild cognitive impairment (PD-MCI) to dementia (PDD). Finally, the aim was to explore correlations between fALFF and FD with clinical and cognitive PD features.

METHODS

Among 118 PD patients age-, sex-, and education matched with 35 healthy controls, 52 were classified with PD-NC, 46 with PD-MCI, and 20 with PDD based on an extensive cognitive and clinical evaluation. fALFF and FD metrics were computed on rs-fMRI data and used to train ML models.

RESULTS

FD outperformed fALFF metrics in differentiating between PD-cognitive states, reaching an overall accuracy of 78% (vs. 62%). PD showed increased neuronal dynamics complexity within the sensorimotor network, central executive network (CEN), and default mode network (DMN), paralleled by a reduction in spontaneous neuronal activity within the CEN and DMN, whose increased complexity was strongly linked to the presence of dementia. Further, we found that some DMN critical hubs correlated with worse cognitive performance and disease severity.

CONCLUSIONS

Our study indicates that PD-cognitive decline is characterized by an altered spontaneous neuronal activity and increased temporal complexity, involving the CEN and DMN, possibly reflecting an increased segregation of these networks. Therefore, we propose FD as a prognostic biomarker of PD-cognitive decline. © 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

Fractal Dimension as a discriminative feature for high accuracy classification in motor imagery EEG-based brain-computer interface

BACKGROUND AND OBJECTIVE

The brain-computer interface (BCI) technology acquires human brain electrical signals, which can be effectively and successfully used to control external devices, potentially supporting subjects suffering from motor impairments in the interaction with the environment. To this aim, BCI systems must correctly decode and interpret neurophysiological signals reflecting the intention of the subjects to move. Therefore, the accurate classification of single events in motor tasks represents a fundamental challenge in ensuring efficient communication and control between users and BCIs. Movement-associated changes in electroencephalographic (EEG) sensorimotor rhythms, such as event-related desynchronization (ERD), are well-known features of discriminating motor tasks. Fractal dimension (FD) can be used to evaluate the complexity and self-similarity in brain signals, potentially providing complementary information to frequency-based signal features.

METHODS

In the present work, we introduce FD as a novel feature for subject-independent event classification, and we test several machine learning (ML) models in behavioural tasks of motor imagery (MI) and motor execution (ME).

RESULTS

Our results show that FD improves the classification accuracy of ML compared to ERD. Furthermore, unilateral hand movements have higher classification accuracy than bilateral movements in both MI and ME tasks.

CONCLUSIONS

These results provide further insights into subject-independent event classification in BCI systems and demonstrate the potential of FD as a discriminative feature for EEG signals.

Fractal Time Series: Background, Estimation Methods, and Performances

Over the past 40 years, from its classical application in the characterization of geometrical objects, fractal analysis has been progressively applied to study time series in several different disciplines. In neuroscience, starting from identifying the fractal properties of neuronal and brain architecture, attention has shifted to evaluating brain signals in the time domain. Classical linear methods applied to analyzing neurophysiological signals can lead to classifying irregular components as noise, with a potential loss of information. Thus, characterizing fractal properties, namely, self-similarity, scale invariance, and fractal dimension (FD), can provide relevant information on these signals in physiological and pathological conditions. Several methods have been proposed to estimate the fractal properties of these neurophysiological signals. However, the effects of signal characteristics (e.g., its stationarity) and other signal parameters, such as sampling frequency, amplitude, and noise level, have partially been tested. In this chapter, we first outline the main properties of fractals in the domain of space (fractal geometry) and time (fractal time series). Then, after providing an overview of the available methods to estimate the FD, we test them on synthetic time series (STS) with different sampling frequencies, signal amplitudes, and noise levels. Finally, we describe and discuss the performances of each method and the effect of signal parameters on the accuracy of FD estimation.