The Fractal Geometry of the Brain

 

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

 

 

 

An aparitie	2016
Autor	Di Ieva
Dimensiuni	15.6 x 3.33 x 23.39 cm
Editura	Springer
Format	Hardcover
ISBN	9781493939930
Limba	Engleza
Nr pag	607