The fractal brain: scale-invariance in structure and dynamics

Fractals in Neuropsychology and Cognitive Neuroscience

The fractal dimension of cognition refers to the idea that the cognitive processes of the human brain exhibit fractal properties. This means that certain patterns of cognitive activity, such as visual perception, memory, language, or problem-solving, can be described using the mathematical concept of fractal dimension.The idea that cognition is fractal has been proposed by some researchers as a way to understand the complex, self-similar nature of the human brain. However, it's a relatively new idea and is still under investigation, so it's not yet clear to what extent cognitive processes exhibit fractal properties or what implications this might have for our understanding of the brain and clinical practice. Indeed, the mission of the "fractal neuroscience" field is to define the characteristics of fractality in human cognition in order to differently characterize the emergence of brain disorders.

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Multifractal long-range dependence pattern of functional magnetic resonance imaging in the human brain at rest

Long-range dependence is a prevalent phenomenon in various biological systems that characterizes the long-memory effect of temporal fluctuations. While recent research suggests that functional magnetic resonance imaging signal has fractal property, it remains unknown about the multifractal long-range dependence pattern of resting-state functional magnetic resonance imaging signals. The current study adopted the multifractal detrended fluctuation analysis on highly sampled resting-state functional magnetic resonance imaging scans to investigate long-range dependence profile associated with the whole-brain voxels as specific functional networks. Our findings revealed the long-range dependence's multifractal properties. Moreover, long-term persistent fluctuations are found for all stations with stronger persistency in whole-brain regions. Subsets with large fluctuations contribute more to the multifractal spectrum in the whole brain. Additionally, we found that the preprocessing with band-pass filtering provided significantly higher reliability for estimating long-range dependence. Our validation analysis confirmed that the optimal pipeline of long-range dependence analysis should include band-pass filtering and removal of daily temporal dependence. Furthermore, multifractal long-range dependence characteristics in healthy control and schizophrenia are different significantly. This work has provided an analytical pipeline for the multifractal long-range dependence in the resting-state functional magnetic resonance imaging signal. The findings suggest differential long-memory effects in the intrinsic functional networks, which may offer a neural marker finding for understanding brain function and pathology.

Sharp detection of oscillation packets in rich time-frequency representations of neural signals

Brain oscillations most often occur in bursts, called oscillation packets, which span a finite extent in time and frequency. Recent studies have shown that these packets portray a much more dynamic picture of synchronization and transient communication between sites than previously thought. To understand their nature and statistical properties, techniques are needed to objectively detect oscillation packets and to quantify their temporal and frequency extent, as well as their magnitude. There are various methods to detect bursts of oscillations. The simplest ones divide the signal into band limited sub-components, quantifying the strength of the resulting components. These methods cannot by themselves cope with broadband transients that look like genuine oscillations when restricted to a narrow band. The most successful detection methods rely on time-frequency representations, which can readily show broadband transients and harmonics. However, the performance of such methods is conditioned by the ability of the representation to localize packets simultaneously in time and frequency, and by the capabilities of packet detection techniques, whose current state of the art is limited to extraction of bounding boxes. Here, we focus on the second problem, introducing two detection methods that use concepts derived from clustering and topographic prominence. These methods are able to delineate the packets' precise contour in the time-frequency plane. We validate the new approaches using both synthetic and real data recorded in humans and animals and rely on a super-resolution time-frequency representation, namely the superlets, as input to the detection algorithms. In addition, we define robust tests for benchmarking and compare the new methods to previous techniques. Results indicate that the two methods we introduce shine in low signal-to-noise ratio conditions, where they only miss a fraction of packets undetected by previous methods. Finally, algorithms that delineate precisely the border of spectral features and their subcomponents offer far more valuable information than simple rectangular bounding boxes (time and frequency span) and can provide a solid foundation to investigate neural oscillations' dynamics.

Fluctuations in Upper and Lower Body Movement during Walking in Normal Pressure Hydrocephalus and Parkinson's Disease Assessed by Motion Capture with a Smartphone Application, TDPT-GT

We aimed to capture the fluctuations in the dynamics of body positions and find the characteristics of them in patients with idiopathic normal pressure hydrocephalus (iNPH) and Parkinson's disease (PD). With the motion-capture application (TDPT-GT) generating 30 Hz coordinates at 27 points on the body, walking in a circle 1 m in diameter was recorded for 23 of iNPH, 23 of PD, and 92 controls. For 128 frames of calculated distances from the navel to the other points, after the Fourier transforms, the slopes (the representatives of fractality) were obtained from the graph plotting the power spectral density against the frequency in log-log coordinates. Differences in the average slopes were tested by one-way ANOVA and multiple comparisons between every two groups. A decrease in the absolute slope value indicates a departure from the 1/f noise characteristic observed in healthy variations. Significant differences in the patient groups and controls were found in all body positions, where patients always showed smaller absolute values. Our system could measure the whole body's movement and temporal variations during walking. The impaired fluctuations of body movement in the upper and lower body may contribute to gait and balance disorders in patients.

Fast updating feedback from piriform cortex to the olfactory bulb relays multimodal reward contingency signals during rule-reversal

While animals readily adjust their behavior to adapt to relevant changes in the environment, the neural pathways enabling these changes remain largely unknown. Here, using multiphoton imaging, we investigated whether feedback from the piriform cortex to the olfactory bulb supports such behavioral flexibility. To this end, we engaged head-fixed mice in a multimodal rule-reversal task guided by olfactory and auditory cues. Both odor and, surprisingly, the sound cues triggered cortical bulbar feedback responses which preceded the behavioral report. Responses to the same sensory cue were strongly modulated upon changes in stimulus-reward contingency (rule reversals). The re-shaping of individual bouton responses occurred within seconds of the rule-reversal events and was correlated with changes in the behavior. Optogenetic perturbation of cortical feedback within the bulb disrupted the behavioral performance. Our results indicate that the piriform-to-olfactory bulb feedback carries reward contingency signals and is rapidly re-formatted according to changes in the behavioral context.

Multifractality in Surface Potential for Cancer Diagnosis

Recent advances in high-resolution biomedical imaging have improved cancer diagnosis, focusing on morphological, electrical, and biochemical properties of cells and tissues, scaling from cell clusters down to the molecular level. Multiscale imaging revealed high complexity that requires advanced data processing methods of multifractal analysis. We performed label-free multiscale imaging of surface potential variations in human ovarian cancer cells using Kelvin probe force microscopy (KPFM). An improvement in the differentiation between nonmalignant and cancerous cells by multifractal analysis using adaptive versus median threshold for image binarization was demonstrated. The results reveal the multifractality of cancer cells as a new biomarker for cancer diagnosis.

Inter-individual variability during neurodevelopment: an investigation of linear and nonlinear resting-state EEG features in an age-homogenous group of infants

Electroencephalography measures are of interest in developmental neuroscience as potentially reliable clinical markers of brain function. Features extracted from electroencephalography are most often averaged across individuals in a population with a particular condition and compared statistically to the mean of a typically developing group, or a group with a different condition, to define whether a feature is representative of the populations as a whole. However, there can be large variability within a population, and electroencephalography features often change dramatically with age, making comparisons difficult. Combined with often low numbers of trials and low signal-to-noise ratios in pediatric populations, establishing biomarkers can be difficult in practice. One approach is to identify electroencephalography features that are less variable between individuals and are relatively stable in a healthy population during development. To identify such features in resting-state electroencephalography, which can be readily measured in many populations, we introduce an innovative application of statistical measures of variance for the analysis of resting-state electroencephalography data. Using these statistical measures, we quantified electroencephalography features commonly used to measure brain development-including power, connectivity, phase-amplitude coupling, entropy, and fractal dimension-according to their intersubject variability. Results from 51 6-month-old infants revealed that the complexity measures, including fractal dimension and entropy, followed by connectivity were the least variable features across participants. This stability was found to be greatest in the right parietotemporal region for both complexity feature, but no significant region of interest was found for connectivity feature. This study deepens our understanding of physiological patterns of electroencephalography data in developing brains, provides an example of how statistical measures can be used to analyze variability in resting-state electroencephalography in a homogeneous group of healthy infants, contributes to the establishment of robust electroencephalography biomarkers of neurodevelopment through the application of variance analyses, and reveals that nonlinear measures may be most relevant biomarkers of neurodevelopment.