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.
Table of Contents:
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 Λ
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 ƒ(α) 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 (α)
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 ß
16. 7 Spectral Exponent α
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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