Fractal Analysis in Clinical Neurosciences: An Overview.

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and astrocytes) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the pattern representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, neuro-ophthalmology, and cognitive neurosciences, with special emphasis on the translation of the fractal dimension and other fractal parameters as clinical biomarkers useful from bench to bedside.

The Fractal Geometry of the Brain: AnOverview.

The first chapter of this book introduces some history, philosophy, and basic concepts of fractal geometry and discusses how the neurosciences can benefit from applying computational fractal-based analysis. Further, it compares fractal with Euclidean approaches to analyzing and quantifying the brain in its entire physiopathological spectrum and presents an overview of the first section of this book as well.

Fractal Dimension Analysis in Neurological Disorders: An Overview.

Fractal analysis has emerged as a powerful tool for characterizing irregular and complex patterns found in the nervous system. This characterization is typically applied by estimating the fractal dimension (FD), a scalar index that describes the topological complexity of the irregular components of the nervous system, both at the macroscopic and microscopic levels, that may be viewed as geometric fractals. Moreover, temporal properties of neurophysiological signals can also be interpreted as dynamic fractals. Given its sensitivity for detecting changes in brain morphology, FD has been explored as a clinically relevant marker of brain damage in several neuropsychiatric conditions as well as in normal and pathological cerebral aging. In this sense, evidence is accumulating for decreases in FD in Alzheimer's disease, frontotemporal dementia, Parkinson's disease, multiple sclerosis, and many other neurological disorders. In addition, it is becoming increasingly clear that fractal analysis in the field of clinical neurology opens the possibility of detecting structural alterations in the early stages of the disease, which highlights FD as a potential diagnostic and prognostic tool in clinical practice.

Fractals in Neuroanatomy and Basic Neurosciences: An Overview.

The introduction of fractal geometry to the neurosciences has been a major paradigm shift over the last decades as it has helped overcome approximations and limitations that occur when Euclidean and reductionist approaches are used to analyze neurons or the entire brain. Fractal geometry allows for quantitative analysis and description of the geometric complexity of the brain, from its single units to the neuronal networks.As illustrated in the second section of this book, fractal analysis provides a quantitative tool for the study of the morphology of brain cells (i.e., neurons and microglia) and its components (e.g., dendritic trees, synapses), as well as the brain structure itself (cortex, functional modules, neuronal networks). The self-similar logic which generates and shapes the different hierarchical systems of the brain and even some structures related to its "container," that is, the cranial sutures on the skull, is widely discussed in the following chapters, with a link between the applications of fractal analysis to the neuroanatomy and basic neurosciences to the clinical applications discussed in the third section.

Fractals, Pattern Recognition, Memetics, and AI: A Personal Journal in the Computational Neurosurgery.

In this chapter, the personal journey of the author in many countries, including Italy, Germany, Austria, the United Kingdom, Switzerland, the United States, Canada, and Australia, is summarized, aimed to merge different translational fields (such as neurosurgery and the clinical neurosciences in general, biomedical engineering, mathematics, computer science, and cognitive sciences) and lay the foundations of a new field defined computational neurosurgery, with fractals, pattern recognition, memetics, and artificial intelligence as the common key words of the journey.

Fractals in Neuroimaging.

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging.

Fractal Dimension Studies of the Brain Shape in Aging and Neurodegenerative Diseases.

The fractal dimension is a morphometric measure that has been used to investigate the changes of brain shape complexity in aging and neurodegenerative diseases. This chapter reviews fractal dimension studies in aging and neurodegenerative disorders in the literature. Research has shown that the fractal dimension of the left cerebral hemisphere increases until adolescence and then decreases with aging, while the fractal dimension of the right hemisphere continues to increase until adulthood. Studies in neurodegenerative diseases demonstrated a decline in the fractal dimension of the gray matter and white matter in Alzheimer's disease, amyotrophic lateral sclerosis, and spinocerebellar ataxia. In multiple sclerosis, the white matter fractal dimension decreases, but conversely, the fractal dimension of the gray matter increases at specific stages of disease. There is also a decline in the gray matter fractal dimension in frontotemporal dementia and multiple system atrophy of the cerebellar type and in the white matter fractal dimension in epilepsy and stroke. Region-specific changes in fractal dimension have also been found in Huntington's disease and Parkinson's disease. Associations were found between the fractal dimension and clinical scores, showing the potential of the fractal dimension as a marker to monitor brain shape changes in normal or pathological processes and predict cognitive or motor function.

Computational Fractal-Based Analysis of MR Susceptibility-Weighted Imaging (SWI) in Neuro-Oncology and Neurotraumatology.

Susceptibility-weighted imaging (SWI) is a magnetic resonance imaging (MRI) technique able to depict the magnetic susceptibility produced by different substances, such as deoxyhemoglobin, calcium, and iron. The main application of SWI in clinical neuroimaging is detecting microbleedings and venous vasculature. Quantitative analyses of SWI have been developed over the last few years, aimed to offer new parameters, which could be used as neuroimaging biomarkers. Each technique has shown pros and cons, but no gold standard exists yet. The fractal dimension (FD) has been investigated as a novel potential objective parameter for monitoring intratumoral space-filling properties of SWI patterns. We showed that SWI patterns found in different tumors or different glioma grades can be represented by a gradient in the fractal dimension, thereby enabling each tumor to be assigned a specific SWI fingerprint. Such results were especially relevant in the differentiation of low-grade versus high-grade gliomas, as well as from high-grade gliomas versus lymphomas.Therefore, FD has been suggested as a potential image biomarker to analyze intrinsic neoplastic architecture in order to improve the differential diagnosis within clinical neuroimaging, determine appropriate therapy, and improve outcome in patients.These promising preliminary findings could be extended into the field of neurotraumatology, by means of the application of computational fractal-based analysis for the qualitative and quantitative imaging of microbleedings in traumatic brain injury patients. In consideration of some evidences showing that SWI signals are correlated with trauma clinical severity, FD might offer some objective prognostic biomarkers.In conclusion, fractal-based morphometrics of SWI could be further investigated to be used in a complementary way with other techniques, in order to form a holistic understanding of the temporal evolution of brain tumors and follow-up response to treatment, with several further applications in other fields, such as neurotraumatology and cerebrovascular neurosurgery as well.

Fractal-Based Analysis of Arteriovenous Malformations (AVMs).

Arteriovenous malformations (AVMs) are cerebrovascular lesions consisting of a pathologic tangle of the vessels characterized by a core termed the nidus, which is the "nest" where the fistulous connections occur. AVMs can cause headache, stroke, and/or seizures. Their treatment can be challenging requiring surgery, endovascular embolization, and/or radiosurgery as well. AVMs' morphology varies greatly among patients, and there is still a lack of standardization of angioarchitectural parameters, which can be used as morphometric parameters as well as potential clinical biomarkers (e.g., related to prognosis).In search of new diagnostic and prognostic neuroimaging biomarkers of AVMs, computational fractal-based models have been proposed for describing and quantifying the angioarchitecture of the nidus. In fact, the fractal dimension (FD) can be used to quantify AVMs' branching pattern. Higher FD values are related to AVMs characterized by an increased number and tortuosity of the intranidal vessels or to an increasing angioarchitectural complexity as a whole. Moreover, FD has been investigated in relation to the outcome after Gamma Knife radiosurgery, and an inverse relationship between FD and AVM obliteration was found.Taken altogether, FD is able to quantify in a single and objective value what neuroradiologists describe in qualitative and/or semiquantitative way, thus confirming FD as a reliable morphometric neuroimaging biomarker of AVMs and as a potential surrogate imaging biomarker. Moreover, computational fractal-based techniques are under investigation for the automatic segmentation and extraction of the edges of the nidus in neuroimaging, which can be relevant for surgery and/or radiosurgery planning.

Fractal-Based Analysis of Histological Features of Brain Tumors.

The structural complexity of brain tumor tissue represents a major challenge for effective histopathological diagnosis. Tumor vasculature is known to be heterogeneous, and mixtures of patterns are usually present. Therefore, extracting key descriptive features for accurate quantification is not a straightforward task. Several steps are involved in the texture analysis process where tissue heterogeneity contributes to the variability of the results. One of the interesting aspects of the brain lies in its fractal nature. Many regions within the brain tissue yield similar statistical properties at different scales of magnification. Fractal-based analysis of the histological features of brain tumors can reveal the underlying complexity of tissue structure and angiostructure, also providing an indication of tissue abnormality development. It can further be used to quantify the chaotic signature of disease to distinguish between different temporal tumor stages and histopathological grades.Brain meningioma subtype classifications' improvement from histopathological images is the main focus of this chapter. Meningioma tissue texture exhibits a wide range of histological patterns whereby a single slide may show a combination of multiple patterns. Distinctive fractal patterns quantified in a multiresolution manner would be for better spatial relationship representation. Fractal features extracted from textural tissue patterns can be useful in characterizing meningioma tumors in terms of subtype classification, a challenging problem compared to histological grading, and furthermore can provide an objective measure for quantifying subtle features within subtypes that are hard to discriminate.

Computational Fractal-Based Analysis of Brain Tumor Microvascular Networks.

Brain parenchyma microvasculature is set in disarray in the presence of tumors, and malignant brain tumors are among the most vascularized neoplasms in humans. As microvessels can be easily identified in histologic specimens, quantification of microvascularity can be used alone or in combination with other histological features to increase the understanding of the dynamic behavior, diagnosis, and prognosis of brain tumors. Different brain tumors, and even subtypes of the same tumor, show specific microvascular patterns, as a kind of "microvascular fingerprint," which is particular to each histotype. Reliable morphometric parameters are required for the qualitative and quantitative characterization of the neoplastic angioarchitecture, although the lack of standardization of a technique able to quantify the microvascular patterns in an objective way has limited the "morphometric approach" in neuro-oncology.In this chapter, we focus on the importance of computational-based morphometrics, for the objective description of tumoral microvascular fingerprinting. By also introducing the concept of "angio-space," which is the tumoral space occupied by the microvessels, we here present fractal analysis as the most reliable computational tool able to offer objective parameters for the description of the microvascular networks.The spectrum of different angioarchitectural configurations can be quantified by means of Euclidean and fractal-based parameters in a multiparametric analysis, aimed to offer surrogate biomarkers of cancer. Such parameters are here described from the methodological point of view (i.e., feature extraction) as well as from the clinical perspective (i.e., relation to underlying physiology), in order to offer new computational parameters to the clinicians with the final goal of improving diagnostic and prognostic power of patients affected by brain tumors.

Analyzing Eye Paths Using Fractals.

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. This success is due to the inherent capabilities that fractals possess when reducing dimensionality using Hilbert curves, measuring temporal complexity using the Higuchi fractal dimension (HFD), and determining geometric complexity using the Minkowski-Bouligand dimension.Understanding the many applications of fractals when measuring and analyzing eye gaze patterns can extend the current growing body of knowledge by identifying markers tied to neurological pathology. Additionally, in future work, fractals can facilitate defining imaging modalities in eye tracking diagnostics by exploiting their capability to acquire multiscale information, including complementary functions, structures, and dynamics.

Computational and Translational Fractal-Based Analysis in the Translational Neurosciences: An Overview.

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. Moreover, some new translational applications of fractal analysis to the neurosciences are presented, including eye tracking analysis, cognitive neuroscience, and music.

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.

Fractals in the Neurosciences: A Translational Geographical Approach.

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. Also, the research highlighted the need to continue interdisciplinary research based on known fractal indicators, as well as the development of new analysis methods with the translational potential between fields.

A Deep Learning Framework for Skull Stripping in Brain MRI.

Skull-stripping, an important pre-processing step in neuroimage computing, involves the automated removal of non-brain anatomy (such as the skull, eyes, and ears) from brain images to facilitate brain segmentation and analysis. Manual segmentation is still practiced, but it is time-consuming and highly dependent on the expertise of clinicians or image analysts. Prior studies have developed various skull-stripping algorithms that perform well on brains with mild or no structural abnormalities. Nonetheless, they were not able to address the issue for brains with significant morphological changes, such as those caused by brain tumors, particularly when the tumors are located near the skull's border. In such cases, a portion of the normal brain may be stripped, or the reverse may occur during skull stripping. To address this limitation, we propose to use a novel deep learning framework based on nnUNet for skull stripping in brain MRI. Two publicly available datasets were used to evaluate the proposed method, including a normal brain MRI dataset - The Neurofeedback Skull-stripped Repository (NFBS), and a brain tumor MRI dataset - The Cancer Genome Atlas (TCGA). The method proposed in the study performed better than six other current methods, namely BSE, ROBEX, UNet, SC-UNet, MV-UNet, and 3D U-Net. The proposed method achieved an average Dice coefficient of 0.9960, a sensitivity of 0.9999, and a specificity of 0.9996 on the NFBS dataset, and an average Dice coefficient of 0.9296, a sensitivity of 0.9288, a specificity of 0.9866 and an accuracy of 0.9762 on the TCGA brain tumor dataset.

Domain-Specific Pre-training Improves Confidence in Whole Slide Image Classification.

Whole Slide Images (WSIs) or histopathology images are used in digital pathology. WSIs pose great challenges to deep learning models for clinical diagnosis, owing to their size and lack of pixel-level annotations. With the recent advancements in computational pathology, newer multiple-instance learning-based models have been proposed. Multiple-instance learning for WSIs necessitates creating patches and uses the encoding of these patches for diagnosis. These models use generic pre-trained models (ResNet-50 pre-trained on ImageNet) for patch encoding. The recently proposed KimiaNet, a DenseNet121 model pre-trained on TCGA slides, is a domain-specific pre-trained model. This paper shows the effect of domain-specific pre-training on WSI classification. To investigate the effect of domain-specific pre-training, we considered the current state-of-the-art multiple-instance learning models, 1) CLAM, an attention-based model, and 2) TransMIL, a self-attention-based model, and evaluated the models' confidence and predictive performance in detecting primary brain tumors - gliomas. Domain-specific pre-training improves the confidence of the models and also achieves a new state-of-the-art performance of WSI-based glioma subtype classification, showing a high clinical applicability in assisting glioma diagnosis. We will publicly share our code and experimental results at https://github.com/soham-chitnis10/WSI-domain-specific.

Connectomics as a prognostic tool of functional outcome in glioma surgery of the supplementary motor area: illustrative case.

BACKGROUND: The supplementary motor area (SMA) is essential in facilitating the commencement and coordination of complex self-initiated movements. Its complex functional connectivity poses a great risk for postoperative neurological deterioration. SMA syndrome can occur after tumor resection and comprises hemiakinesia and akinetic mutism (often, but unpredictably temporary). Although awake surgery is preferred for mapping and monitoring eloquent areas, connectomics is emerging as a novel technique to tailor neurosurgical approaches and predict functional prognosis, as illustrated in this case. OBSERVATIONS: The authors report on a patient presenting with recurrent oligodendroglioma after subtotal resection 7 years earlier. After extensive neuropsychological and neuroradiological assessment (including connectomics), awake surgery was indicated. No intraoperative deficits were recorded; however, the patient presented with postoperative right-sided akinesia and mutism. Postoperative neuroimaging demonstrated the connectome overlapping the preoperative one, and indeed, neurological symptoms resolved after 3 days. LESSONS: Comparison of the pre- and postoperative connectome can be used to objectively evaluate surgical outcomes and assess patient prognosis. To the best of the authors' knowledge, this is the first case demonstrating the feasibility of quantitative functional connectivity analysis as a prognostic tool for neurological improvement after surgery. A better understanding of brain networks is instrumental for improving diagnosis, prognosis, and treatment of neuro-oncological patients.

Radiomics and Machine Learning in Brain Tumors and Their Habitat: A Systematic Review.

Radiomics is a rapidly evolving field that involves extracting and analysing quantitative features from medical images, such as computed tomography or magnetic resonance images. Radiomics has shown promise in brain tumor diagnosis and patient-prognosis prediction by providing more detailed and objective information about tumors' features than can be obtained from the visual inspection of the images alone. Radiomics data can be analyzed to determine their correlation with a tumor's genetic status and grade, as well as in the assessment of its recurrence vs. therapeutic response, among other features. In consideration of the multi-parametric and high-dimensional space of features extracted by radiomics, machine learning can further improve tumor diagnosis, treatment response, and patients' prognoses. There is a growing recognition that tumors and their microenvironments (habitats) mutually influence each other-tumor cells can alter the microenvironment to increase their growth and survival. At the same time, habitats can also influence the behavior of tumor cells. In this systematic review, we investigate the current limitations and future developments in radiomics and machine learning in analysing brain tumors and their habitats.

The E3 Ubiquitin Ligase SCF Cyclin F Promotes Sequestosome-1/p62 Insolubility and Foci Formation and is Dysregulated in ALS and FTD Pathogenesis.

Amyotrophic lateral sclerosis (ALS)- and frontotemporal dementia (FTD)-linked mutations in CCNF have been shown to cause dysregulation to protein homeostasis. CCNF encodes for cyclin F, which is part of the cyclin F-E3 ligase complex SCFcyclinF known to ubiquitylate substrates for proteasomal degradation. In this study, we identified a function of cyclin F to regulate substrate solubility and show how cyclin F mechanistically underlies ALS and FTD disease pathogenesis. We demonstrated that ALS and FTD-associated protein sequestosome-1/p62 (p62) was a canonical substrate of cyclin F which was ubiquitylated by the SCFcyclinF complex. We found that SCFcyclin F ubiquitylated p62 at lysine(K)281, and that K281 regulated the propensity of p62 to aggregate. Further, cyclin F expression promoted the aggregation of p62 into the insoluble fraction, which corresponded to an increased number of p62 foci. Notably, ALS and FTD-linked mutant cyclin F p.S621G aberrantly ubiquitylated p62, dysregulated p62 solubility in neuronal-like cells, patient-derived fibroblasts and induced pluripotent stem cells and dysregulated p62 foci formation. Consistently, motor neurons from patient spinal cord tissue exhibited increased p62 ubiquitylation. We suggest that the p.S621G mutation impairs the functions of cyclin F to promote p62 foci formation and shift p62 into the insoluble fraction, which may be associated to aberrant mutant cyclin F-mediated ubiquitylation of p62. Given that p62 dysregulation is common across the ALS and FTD spectrum, our study provides insights into p62 regulation and demonstrates that ALS and FTD-linked cyclin F mutant p.S621G can drive p62 pathogenesis associated with ALS and FTD.