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Description:
Reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. Will bring an understanding of fractals to clinicians and researchers also if they do not have a mathematical background, and will serve as a good tool for teaching the translational applications of computational models to students and scholars of different disciplines. This comprehensive collection is organized in four parts: (1) Basics of fractal analysis; (2) Applications of fractals to the basic neurosciences; (3) Applications of fractals to the clinical neurosciences; (4) Analysis software, modeling and methodology.
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Table of Contents:
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Part I: Introduction to Fractal Geometry and Its Applications to Neurosciences
Chapter 1: The Fractal Geometry of?the?Brain: An?Overview
1. 1 From the?Fractal Geometry of?Nature to?Fractal Analysis in?Biomedicine
1. 2 From Euclid to?the?Fractal Metrology
1. 3 The Fractal Geometry of?the?Brain
1. 4 Fractal Dimension and?Neurosciences
References
Chapter 2: Box-Counting Fractal Analysis: A?Primer for?the?Clinician
2. 1 Fractal Analysis: What Does It Measure?
2. 2 How Is a?DF Calculated?
2.
2. 1 Practical Points
2.
2.
1. 1 Statistical Self-Similarity
2.
2.
1. 2 DF and?Density
2.
2.
1. 3 The DF in?Neuroscience
2. 3 Box Counting
2.
3. 1 Sampling, S, and?N in?Box Counting
2.
3. 2 Methodological Issues in?Box Counting
2.
3.
2. 1 Regression Lines
2.
3.
2. 2 Sampling Size, Location, and?Rotational Orientation Bias
2.
3.
2. 3 Box-Counting Solutions
2. 4 Lacunarity
2.
4. 1 Calculating Lacunarity
2.
4. 2 Understanding the?DB and??
2.
4.
2. 1 Pattern Idiosyncrasies
2.
4.
2. 2 Applying Lacunarity
2. 5 Grayscale Volumes and?Box Counting
2. 6 Multifractal Analysis
2.
6. 1 Reading the?Dq Curve
2.
6. 2 Reading the??(?) Curve
2.
6. 3 Applying Multifractal Analysis
2. 7 Subscanning
2. 8 The Validity of?2D Patterns from?4-Dimensional Reality
2.
8. 1 Control and?Calibration
2. 9 Conclusion
References
Chapter 3: Tenets and?Methods of?Fractal Analysis (1/f Noise)
3. 1 Tenets and?Methods of?Fractal Analysis (1/f Noise)
3. 2 Statistical Terms: Parameter, Estimator, Estimate
3. 3 Properties of?1/f Noise: Self-Similarity and?Long Memory
3.
3. 1 Memory
3.
3. 2 Stationarity
3. 4 Fractal Parameters
3.
4. 1 Hurst Coefficient
3.
4. 2 Scaling Exponent (?)
3.
4. 3 Power Spectra
3.
4. 4 Power Exponent
3.
4. 5 Differencing Parameter (d)
3. 5 Estimators of?Fractal Parameters
3. 6 Identification of?Fractal Noise in?Empirical Settings
3. 7 Summary
References
Chapter 4: Tenets, Methods, and?Applications of?Multifractal Analysis in?Neurosciences
4. 1 Introduction
4. 2 Tenets of?Multifractal Analysis
4. 3 Methods of?Multifractal Analysis
4.
3. 1 Time Domain Methods
4.
3.
1. 1 Generalized Fractal Dimensions and?Multifractal Spectrum
4.
3.
1. 2 The ?Sandbox? or Cumulative Mass Method
4.
3.
1. 3 The Large-Deviation Multifractal Spectrum
4.
3.
1. 4 Multifractal Detrended Fluctuation Analysis: MDFA
4.
3.
1. 5 Multifractal Detrended Moving Average: MDMA
4.
3. 2 Time-Frequency Domain Methods
4.
3.
2. 1 Wavelet Transform Modulus Maxima: WTMM
4.
3.
2. 2 Wavelet Leaders-Based Multifractal Analysis: WLMA
4.
3.
2. 3 Multifractional Brownian Motion: mBm
4. 4 Applications of?Multifractal Analysis
4.
4. 1 Electroencephalogram Signal: EEG
4.
4. 2 Brain Imaging
4. 5 Conclusion
References
Part II: Fractals in Neuroanatomy and Basic Neurosciences
Chapter 5: Fractals in?Neuroanatomy and?Basic Neurosciences: An?Overview
5. 1 What About the?Brain?
5. 2 Fractals, Neurons, and?Microglia
5. 3 Brains and?Trees
5. 4 Increase of?the?Fractal Dimension from??Too Smooth to?Too Folded? Human Brains
5. 5 Neuronal Networks
References
Chapter 6: Morphology and?Fractal-Based Classifications of?Neurons and?Microglia
6. 1 A Brief Introduction to?Neurons and?Microglia
6.
1. 1 Neuronal and?Microglial Morphology in?Context
6. 2 Fractal Analysis of?Neurons
6.
2. 1 Fractal Analysis of?Dendritic Arbors
6.
2. 2 Methodological Issues
6.
2.
2. 1 Complementary Methods
6.
2.
2. 2 3D Analysis
6. 3 Microglia
6. 4 Future Directions
References
Chapter 7: The Morphology of?the?Brain Neurons: Box-?Counting Method in?Quantitative Analysis of
7. 1 Introduction
7. 2 Starting from?the?Fractal Geometry Toward?the?Fractal Analysis
7.
2. 1 Fractal Geometry in?2D Space
7.
2. 2 Self-Similarity and?Scaling
7.
2. 3 Fractal Analysis
7. 3 Box-Counting Method
7.
3. 1 Application on?2D Digital Image
7.
3. 2 The Software for?Box-Counting
7. 4 Material
7. 5 Box-Counting Methodology
7.
5. 1 Image Size and?Resolution
7.
5. 2 Image Rotation
7.
5. 3 Image Representation
7. 6 Discussion
References
Chapter 8: Neuronal Fractal Dynamics
8. 1 Synapse Formation from?the?Perspective of?Molecular and?Cellular Biology
8. 2 Fractal Time-Space in?the?Dynamic Process of?Synapse Formation
Appendix
8.
2. 1 Entropy and?Dynamics of?Synapse Formation in?Fractal Time-Space
References
Chapter 9: Does a?Self-Similarity Logic Shape the?Organization of?the?Nervous System?
9. 1 Introduction
9. 2 Structural Self-Similarity of?the?Nervous System
9.
2. 1 Cell Level: Complex Geometry of?Neurons and?Glial Cells
9.
2. 2 Tissue Level
9.
2.
2. 1 Central Nervous System
9.
2.
2. 2 Peripheral Nervous System
9. 3 A Self-Similarity Logic Drives the?Functional Features of?the?CNS
9.
3. 1 Interaction-Dominant Dynamics in?the?CNS
9.
3.
1. 1 The Concept of??Fringe?
9.
3.
1. 2 The Concept of??Lateral Inhibition?
9.
3. 2 Remodeling Processes in?the?Nervous System
9. 4 Concluding Remarks: A?Place for?Self-Similarity in?a?Global Model of?the?Nervous System?
References
Chapter 10: Fractality of?Cranial Sutures
10. 1 Biology of?Skull Suture Development
10. 2 Fundamental Principle of?Fractal Structure Formation: ?The Same Rule Appears on?Different S
10. 3 Models of?Skull Suture Development
10.
3. 1 Eden Collision Model
10.
3. 2 Partial Differential Equation (PDE)-Based Model and?the?Koch Curve
10.
3. 3 Mechanics-Based Model and?DLA
10. 4 Future Directions
10.
4. 1 Other Classes of?Models That Generate Fractal Structures
10.
4. 2 Experimental Verification of?Theoretical Models
10.
4. 3 Fractal Suture Analysis and?Craniosynostosis in?a?Clinical Setting
References
Chapter 11: The Fractal Geometry of?the?Human Brain: An?Evolutionary Perspective
11. 1 Introduction
11. 2 Principles of?Brain Evolution
11.
2. 1 Evolution of?the?Cerebral Cortex
11.
2. 2 Mechanisms of?Cortical Folding
11.
2. 3 Scaling of?the?Primate Neocortex
11. 3 Fractal Geometry of?Convoluted Brains
11.
3. 1 Principles of?Scaling
11.
3. 2 Fractal Scaling of?the?Neocortex
11. 4 Fractal Principles of?Neural Wiring
11.
4. 1 Neocortical Wiring
11.
4. 2 Neural Network Communication
11.
4. 3 Limits to?Information Processing
11. 5 Concluding Remarks
References
Part III: Fractals in Clinical Neurosciences
Chapter 12: Fractal Analysis in?Clinical Neurosciences: An?Overview
12. 1 Clinical Neurology and?Cerebrovascular System
12. 2 Neuroimaging
12. 3 Neurohistology, Neuropathology, and?Neuro-oncology
12. 4 Fractal-Based Time-Series Analysis in?Neurosciences
12. 5 Cognitive Sciences, Neuropsychology, and?Psychiatry
12. 6 Limitations of?Application of?Fractal Analysis into?Clinical Neurosciences
12.
6. 1 The ?Black Box?
References
Chapter 13: Fractal Analysis in?Neurological Diseases
13. 1 Geometric Fractal Analysis Applied to?Neuroscience
13. 2 Use of?Dynamic Fractal Analysis in?Neurology
13. 3 Diagnostic Precision of?Fractal Dimension
13.
3. 1 Depression and?Schizophrenia
13.
3. 2 Alzheimer?s Disease and?Autism
13.
3. 3 Epilepsy
13.
3. 4 Neural Loss in?Retinal Tissue
13.
3. 5 Brain Tumors
13. 4 Conclusion and?Future Perspectives
References
Chapter 14: Fractal Dimension Studies of?the?Brain Shape in?Aging and?Neurodegenerative Diseases
14. 1 Introduction
14.
1. 1 Anatomical Shape Features of?Interest
14.
1. 2 Fractal Dimension Methods
14. 2 Fractal Dimension Studies of?the?Brain Shape
14.
2. 1 Aging
14.
2. 2 Alzheimer?s Disease
14.
2. 3 Amyotrophic Lateral Sclerosis
14.
2. 4 Epilepsy
14.
2. 5 Multiple Sclerosis
14.
2. 6 Multiple System Atrophy
14.
2. 7 Stroke
14. 3 Discussion
References
Chapter 15: Fractal Analysis in?Neurodegenerative Diseases
15. 1 Alzheimer?s Disease and?Vascular Dementia
15.
1. 1 Fractal Dimension: A?Classifier for?the?AD Pathology
15.
1. 2 Imaging and?Fractal Analysis in?AD
15. 2 Other Neurodegenerative Diseases
15. 3 Conclusion
References
Chapter 16: Fractal Analysis of?the?Cerebrovascular System Physiopathology
16. 1 Introduction
16. 2 Cerebral Autoregulation as?a?Feedback Loop
16. 3 Variability and?Complexity
16. 4 Methodology of?Variation and?Fractal Analysis
16. 5 Hurst Coefficient HbdSWV
16. 6 Spectral Index ?
16. 7 Spectral Exponent ?
16. 8 Fractal Analysis of?Human CBF
16. 9 Decomplexification
16. 10 Frequency-Dependent CBF Variability
16. 11 Conclusions
References
Chapter 17: Fractals and?Chaos in?the?Hemodynamics of?Intracranial Aneurysms
17. 1 Introduction
17. 2 Fractal Patterns in?Time-Dependent Flows
17. 3 Basic Concepts Demonstrated on?a?Simplified 2D Case
17. 4 Measuring Chaotic Quantities from?Residence Times
17. 5 Appearance of?Chaotic Flow Inside?Intracranial Aneurysms
17. 6 Concluding Remarks
References
Chapter 18: Fractal-Based Analysis of?Arteriovenous Malformations (AVMs)
18. 1 Introduction
18. 2 Neuroimaging of?AVMs
18. 3 AVMs? Angioarchitecture Morphometrics
18. 4 Computational Fractal-Based Analyses of?AVMs
18.
4. 1 AVMs? Fractal Dimension
18.
4. 2 Fractal Dimension of?the?Nidus and?Its Relevance in?Radiosurgery
18. 5 Limitations
18. 6 Computational Techniques for?the?Automatic Nidus Identification
18. 7 Conclusion
References
Chapter 19: Fractals in?Neuroimaging
19. 1 Introduction
19. 2 Fractals in?Brain Magnetic Resonance Image Classification
19. 3 Other Applications of?Fractal Analysis in?Neuroimaging
19. 4 Conclusion and?Future Perspective
Appendix: Fractal Analysis Techniques
Range-Scale-Based Hurst Exponent
Detrended Fluctuation Analysis
Generalized Hurst Exponent
References
Chapter 20: Computational Fractal-Based Analysis of?MR Susceptibility-Weighted Imaging (SWI) in?Ne
20. 1 Introduction
20. 2 Technical Aspects of?SW Imaging
20. 3 SWI in?Neuro-oncology
20.
3. 1 Morphometrics and?Fractal-Based Analysis of?SWI in?Brain Tumors
20. 4 Future Perspective of?SWI in?Neurotraumatology
20. 5 Limitations
20. 6 Conclusion
References
Chapter 21: Texture Estimation for?Abnormal Tissue Segmentation in?Brain MRI
21. 1 Introduction
21. 2 Background Review
21.
2. 1 Fractal (PTPSA) Texture Feature Extraction
21.
2. 2 Multi-fractal Brownian Motion (mBm) Process and?Feature Extraction
21. 3 Methodology
21.
3. 1 Preprocessing
21.
3. 2 Feature Extraction, Fusion, Ranking, and?Selection
21.
3. 3 Classification with?Random Forest
21. 4 Results and?Discussion
21. 5 Conclusion and?Future Work
References
Chapter 22: Tumor Growth in?the?Brain: Complexity and?Fractality
22. 1 Introduction
22. 2 Fractal Dimension and?Brain Tumors
22. 3 The Scaling Analysis Approach
22. 4 Data Time-Like Series, Visibility Graphs, and?Complex Networks
22. 5 Conclusions and?Future Prospects
References
Chapter 23: Histological Fractal-Based Classification of?Brain Tumors
23. 1 Introduction
23. 2 Fractal Morphometry of?Tissue Complexity
23.
2. 1 Fractal Dimension Estimation
23.
2. 2 Related Work
23. 3 Automated Histopathological Image Analysis
23.
3. 1 Image Preparation
23.
3. 2 Pre-processing and?Focal Regions Segmentation
23.
3. 3 Feature Extraction and?Classification
23.
3. 4 Qualitative Enhancement and?Grading Results
23. 4 Characterizing Tissue via Fractal Properties
23. 5 Quasi-fractal Texture Representation
23. 6 Multi-fractality Analysis
23.
6. 1 Assessing Fractal Texture Heterogeneity
23.
6. 2 Performance Under Tissue Distribution Variation
23. 7 Diagnostic Challenges and?Future Perspectives
23. 8 Conclusion
References
Chapter 24: Computational Fractal-Based Analysis of?Brain Tumor Microvascular Networks
24. 1 Introduction
24. 2 Brain Tumors and?Vascularization
24.
2. 1 Immunohistochemistry (IHC)
24. 3 Morphometrics of?Microvascularity
24.
3. 1 Euclidean-Based Parameters
24.
3. 2 Image Analysis
24. 4 Fractal-Based Morphometric Analyses of?Microvessels
24.
4. 1 Microvascular Fractal Dimension (mvFD)
24.
4. 2 Local Fractal Dimension and?Local Box-Counting Dimension
24. 5 Fractal-Based Analysis of?the?Angio-Space in?Brain Pathology
24. 6 Limitations
24. 7 Future Perspectives and?Conclusion
References
Chapter 25: Fractal Analysis of?Electroencephalographic Time Series (EEG Signals)
25. 1 Introduction
25. 2 Nonlinearity and?Nonstationarity
25. 3 Fractal Analysis of?EEG
25. 4 Examples of?Application of?Fractal Analysis to?EEG Signals
25.
4. 1 Seasonal Affective Disorder: Artifacts in?EEG May Be?Important for?Diagnosis
25.
4. 2 Sleep Staging: One May Analyze Raw EEG Data Without?Artifact Elimination
25.
4. 3 Influence of?Electromagnetic Fields: Comparing Qualitative Features of?Df(t)
25.
4. 4 Epileptic Seizures and?Epileptic-Like Seizures in?Economic Organisms
25.
4. 5 Psychiatry: Assessing Effects of?Electroconvulsive Therapy
25.
4. 6 Anesthesiology: Monitoring the?Depth of?Anesthesia
25. 5 Conclusions
References
Chapter 26: On Multiscaling of?Parkinsonian Rest Tremor Signals and?Their Classification
26. 1 Introduction
26. 2 Multifractal Detrended Fluctuation Analysis for?Nonstationary Time Series
26. 3 Evidence of?Multiscaling in?Parkinsonian Rest Tremor Velocity Signals
26. 4 Concluding Remarks and?Future Research Perspectives
References
Chapter 27: Fractals and?Electromyograms
27. 1 Introduction
27. 2 Surface Electromyogram (sEMG)
27.
2. 1 Generation of?sEMG
27.
2. 2 Factors That Influence sEMG
27. 3 Fractal Analysis of?sEMG
27.
3. 1 Self-Similarity of?sEMG
27. 4 Method to?Determine Fractal Dimension
27. 5 Computation of?Fractal Dimension Using Higuchi?s Algorithm
27. 6 Relation of?FD to?sEMG
27. 7 Age-Related Decrease in?Fractal Dimension of?Surface Electromyogram
27. 8 Summary
References
Chapter 28: Fractal Analysis in?Neuro-ophthalmology
28. 1 Eye and?Nervous System
28. 2 Retinal Microvascular Networks and?Ophthalmopathies
28. 3 Our Experience: Neuro-ophthalmological Disorders
28.
3. 1 Optic Neuritis Versus?Nonarteritic Anterior Ischemic Optic Neuropathy: Retinal Microvascular
28.
3.
1. 1 Patients
28.
3.
1. 2 Image Analysis
Entropy, D1
28.
3.
1. 3 Statistical Analysis
28.
3.
1. 4 Results
28.
3. 2 Sjogren?s Syndrome: Corneal Nerve Plexus
28.
3.
2. 1 Patients
28.
3.
2. 2 Image Analysis
Geometric Complexity, D0
28.
3.
2. 3 Statistical Tests
28.
3.
2. 4 Results
28. 4 Discussion
References
Chapter 29: Fractals in?Affective and?Anxiety Disorders
29. 1 Introduction
29. 2 Fractals and?Affective Disorders
29. 3 Fractals and?Anxiety Disorders
29. 4 Fractals in?Affective and?Anxiety Disorders Treatments
29. 5 Conclusions
References
Chapter 30: Fractal Fluency: An?Intimate Relationship Between the?Brain and?Processing of?Fracta
30. 1 Introduction: The?Complexity of?Biophilic Fractals
30. 2 Fractal Fluency
30. 3 Enhanced Performance and?Fractal Aesthetics
30. 4 Conclusion: The?Brave New World of?Neuro-Aesthetics
References
Part IV: Computational Fractal-Based Neurosciences
Chapter 31: Computational Fractal-Based Neurosciences: An?Overview
31. 1 How to?Compute Fractals in?Clinical Neurosciences
31. 2 Fractals in?Bioengineering and?Artificial Intelligence
31. 3 Conclusive Remarks: Towards?a?Unified Fractal Model of?the?Brain?
Chapter 32: ImageJ in?Computational Fractal-Based Neuroscience: Pattern Extraction and?Translation
32. 1 Introduction
32. 2 What Is ImageJ?
32.
2. 1 Removing Barriers with?Free, Open-Source Software
32.
2. 2 Shaping Computational Fractal-Based Neuroscience
32.
2.
2. 1 Making Fractal Analysis Accessible and?Customizable
32. 3 Where Does IJ Fit in?Fractal-Based Neuroscience Today?
32. 4 Pattern Extraction
32.
4. 1 Pattern Types
32.
4. 2 Extraction Methods
32.
4.
2. 1 Built-in Functions
32.
4.
2. 2 Tracing Plug-Ins
32.
4.
2. 3 Thresholding
32.
4.
2. 4 Customized Pattern Extraction Methods
32. 5 Conclusion
References
Chapter 33: Fractal Analysis in?MATLAB: A?Tutorial for?Neuroscientists
33. 1 MATLAB Packages and?Toolboxes for?Fractal Analysis
33. 2 MATLAB Examples: Fractal Dimension Computation for?1D, 2D, and?3D Sets
33.
2. 1 EEG Fractal Dimension
33.
2. 2 Brain MRI Fractal Dimension of?the?Gray Matter with?FracLab
33.
2. 3 Fractal Dimension Computation of?an?MRI Volume of?the?Brain White Matter with?a?Boxcoun
33. 3 Other Software and?Online Resources for?Fractal Analysis
33. 4 Conclusions
References
Chapter 34: Methodology to?Increase the?Computational Speed to?Obtain the?Fractal Dimension Usin
34. 1 An Introduction to?GPU Programming
34.
1. 1 NVIDIA CUDA
34.
1. 2 OpenCL
34. 2 Previous Work
34. 3 Box-Counting Algorithm
34. 4 GPU Implementation
34. 5 Results
34.
5. 1 Hardware and?Test Models
34.
5. 2 Implementation Results
34. 6 Discussion, Conclusions, and?Future Work
References
Chapter 35: Fractal Electronics as?a?Generic Interface to?Neurons
35. 1 Introduction
35. 2 Fabrication of?the?Fractal Interconnects
35. 3 Functionality of?the?Fractal Interconnects
35. 4 The Biophilic Interface
35. 5 Conclusions
References
Chapter 36: Fractal Geometry Meets Computational Intelligence: Future Perspectives
36. 1 Introduction
36. 2 Fractal Analysis and?Brain Complexity
36. 3 Computational Intelligence Methods and?the?Challenge of?Processing Non-geometric Input Space
36. 4 On the?Interplay Between?Fractal Analysis and?CI Methods
36. 5 Future Perspectives and?Concluding Remarks
References
Erratum to: The Fractal Geometry of the Brain
Index
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