Advances in Neurobiology

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...

The chapter presents three new fractal indices (fractal fragmentation index, fractal tentacularity index, and fractal anisotropy index) and normalized Kolmogorov complexity with proven applicability in geographic research, developed by the authors, and the possibility of their future use in neuroscience. The research demonstrates the relevance of fractal analysis in different fields and the basic concepts and principles of fractal geometry being sufficient for the development of models relevant to the studied reality...

The concept of fractal was popularized by Mandelbrot as a tool to tame the geometrical structure of objects with infinite hierarchical depth. The key aspect of fractals is the use of simple parsimonious rules and initial conditions, which when applied recursively can generate unbounded complexity. Fractals are structures ubiquitous in nature, being present in coast lines, bacteria colonies, trees, and physiological time series. However, within the field of cognitive science, the core question is not which phenomena can generate fractal structures, but whether human or animal minds can represent recursive processes, and if so in which domains...

People are continually exposed to the rich complexity generated by the repetition of fractal patterns at different size scales. Fractals are prevalent in natural scenery and also in patterns generated by artists and mathematicians. In this chapter, we will investigate the powerful significance of fractals for the human senses. In particular, we propose that fractals with mid-range complexity play a unique role in our visual experiences because the visual system has adapted to these prevalent natural patterns...

In parallel to medical applications, exploring how neurons interact with the artificial interface of implants in the human body can be used to learn about their fundamental behavior. For both fundamental and applied research, it is important to determine the conditions that encourage neurons to maintain their natural behavior during these interactions. Whereas previous biocompatibility studies have focused on the material properties of the neuron-implant interface, here we discuss the concept of fractal resonance - the possibility that favorable connectivity properties might emerge by matching the fractal geometry of the implant surface to that of the neurons...

Imagine a world in which damaged parts of the body - an arm, an eye, and ultimately a region of the brain - can be replaced by artificial implants capable of restoring or even enhancing human performance. The associated improvements in the quality of human life would revolutionize the medical world and produce sweeping changes across society. In this chapter, we discuss several approaches to the fabrication of fractal electronics designed to interface with neural networks. We consider two fundamental functions - stimulating electrical signals in the neural networks and sensing the location of the signals as they pass through the network...

Visual patterns reflect the anatomical and cognitive background underlying process governing how we perceive information, influenced by stimulus characteristics and our own visual perception. These patterns are both spatially complex and display self-similarity seen in fractal geometry at different scales, making them challenging to measure using the traditional topological dimensions used in Euclidean geometry.However, methods for measuring eye gaze patterns using fractals have shown success in quantifying geometric complexity, matchability, and implementation into machine learning methods...

MATLAB is one of the software platforms most widely used for scientific computation. MATLAB includes a large set of functions, packages, and toolboxes that make it simple and fast to obtain complex mathematical and statistical computations for many applications. In this chapter, we review some tools available in MATLAB for performing fractal analyses on typical neuroscientific data in a practical way. We provide detailed examples of how to calculate the fractal dimension of 1D, 2D, and 3D data in MATLAB. Furthermore, we review other software packages for fractal analysis...

To explore questions asked in neuroscience, neuroscientists rely heavily on the tools available. One such toolset is ImageJ, open-source, free, biological digital image analysis software. Open-source software has matured alongside of fractal analysis in neuroscience, and today ImageJ is not a niche but a foundation relied on by a substantial number of neuroscientists for work in diverse fields including fractal analysis. This is largely owing to two features of open-source software leveraged in ImageJ and vital to vigorous neuroscience: customizability and collaboration...

After the previous sections on "Fractals: What and Why?," the last section of this book covers the software tools necessary to perform computational fractal-based analysis, with special emphasis on its applications into the neurosciences. The use of ImageJ and MATLAB, as well as other software packages, is reviewed. The current and future applications of fractal modeling in bioengineering and biotechnology are discussed as well. Perspectives on the translation of merging fractals with artificial intelligence-based methods with the final aim of pattern discrimination in neurological diseases by means of a unified fractal model of the brain are also given...

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...

Autism spectrum disorder is an increasingly prevalent and debilitating neurodevelopmental condition and an electroencephalogram (EEG) diagnostic challenge. Despite large amounts of electrophysiological research over many decades, an EEG biomarker for autism spectrum disorder (ASD) has not been found. We hypothesized that reductions in complex dynamical system behaviour in the human central nervous system as part of the macroscale neuronal function during cognitive processes might be detectable in whole EEG for higher-risk ASD adults...

In this chapter, we review the research that has applied fractal measures to the study of the most common psychological disorders, that is, affective and anxiety disorders. Early studies focused on heart rate, but diverse measures have also been examined, from variations in subjective mood, or hand movements, to electroencephalogram or magnetoencephalogram data. In general, abnormal fractal dynamics in different physiological and behavioural outcomes have been observed in mental disorders. Despite the disparity of variables measured, fractal analysis has shown high sensitivity in discriminating patients from healthy controls...

Research has shown that relying only on self-reports for diagnosing psychiatric disorders does not yield accurate results at all times. The advances of technology as well as artificial intelligence and other machine learning algorithms have allowed the introduction of point of care testing (POCT) including EEG characterization and correlations with possible psychopathology. Nonlinear methods of EEG analysis have significant advantages over linear methods. Empirical mode decomposition (EMD) is a reliable nonlinear method of EEG pre-processing...

Depression is currently one of the most complicated public health problems with the rising number of patients, increasing partly due to pandemics, but also due to increased existential insecurities and complicated aetiology of disease. Besides the tsunami of mental health issues, there are limitations imposed by ambiguous clinical rules of assessment of the symptoms and obsolete and inefficient standard therapy approaches. Here we are summarizing the neuroimaging results pointing out the actual complexity of the disease and novel attempts to detect depression that are evidence-based, mostly related to electrophysiology...

The neuronal ongoing electrical activity in the brain network, the neurodynamics, reflects the structure and functionality of generating neuronal pools. The activity of neurons due to their excitatory and inhibitory projections is associated with specific brain functions. Here, the purpose was to investigate if the local ongoing electrical activity exhibits its characteristic spectral and fractal features in wakefulness and sleep across and within subjects. Moreover, we aimed to show that measures typical of complex systems catch physiological features missed by linear spectral analyses...

The conscious perception of pain is the result of dynamic interactions of neural activities from local brain regions to distributed brain networks. Mapping out the networks of functional connections between brain regions that form and disperse when an experimental participant received nociceptive stimulations allow to characterize the pattern of network connections related to the pain experience.Although the pattern of intra- and inter-areal connections across the brain are incredibly complex, they appear also largely scale free, with "fractal" connectivity properties reproducing at short and long-time scales...

The neuroplasticity potential is reduced with aging and impairs during neurodegenerative diseases and brain and visual system injuries. This limits the brain's capacity to repair the structure and dynamics of its activity after lesions. Maximization of neuroplasticity is necessary to provide the maximal CNS response to therapeutic intervention and adaptive reorganization of neuronal networks in patients with degenerative pathology and traumatic injury to restore the functional activity of the brain and retina...

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...

Brain tumor detection is crucial for clinical diagnosis and efficient therapy. In this work, we propose a hybrid approach for brain tumor classification based on both fractal geometry features and deep learning. In our proposed framework, we adopt the concept of fractal geometry to generate a "percolation" image with the aim of highlighting important spatial properties in brain images. Then both the original and the percolation images are provided as input to a convolutional neural network to detect the tumor...