1. FRACTALS IN NEUROSCIENCE Bio and Brain Engineering in KAIST, Son HyunJin

2. Contents Part1 What is Fractal Fractal Properties Fractal Dimension Fractal in Neuroscience Part2 Fractal Analysis in Neuroimaging Fractal Analysis in Neurological Disease Fractal Analysis of Brain Tumor Fractal Analysis of Time Series

3. Part 1 General Principles and Basic Neurosciences Di Ieva A et al, Fractals in the neurosciences, part I: general principles and basic neurosciences. Neuroscientist, 2014

4. What is Fractal?

5. Fractal Properties Iteration Irregularity Non-integer fractal dimension Scaling

6. Fractal Properties Iteration Irregularity Non-integer fractal dimension Scaling Self-similarity : Any portion of the object would appear identical to the whole object

7. Fractal Dimension

9. Box-counting method

10. Fractal Dimension Box-counting method

11. Fractal in Neuroscience  Mandelbrot (1983)  Smith (1994)  Nowadays, modern neurosciences admit the prevalence of fractal properties in the brain at various levels  FD correlates with the increase in morphological complexity and neuronal maturity DeFelipe J. The evolution of the brain, the human nature of cortical circuits, and the intellectual creativity. Front Neuroanat 5:1–16. 2011

12. Fractal in Neuroscience Fernández E, Jelinek HF. Use of fractal theory in neuroscience: methods, advantages, and potential problems. Methods 24(4):309–21. 2001

13. Fractal in Neuroscience Pirici D, Mogoantă L, et al, Fractal analysis of astrocytes in stroke and dementia. Rom J Morphol Embryol 50(3):381–90. 2009

14. Fractal in Neuroscience Slope = D

15. Part 2 Clinical Applications and Future Perspectives Di Ieva A et al, Fractals in the neurosciences, Part II, Clinical Applications and Future Perspectives Neuroscientist, 2015

16. Fractal Analysis in Neuroimaging Zhang L et al, Quantifying degeneration of white matter in normal aging using fractal dimension. Neurobiol Aging 28(10):1543–55. 2007

17. Fractal Analysis in Neuroimaging Rajagopalan V et al, Brain white matter shape changes in amyotrophic lateral sclerosis (ALS): a fractal dimension study. PLoS One, 2013

18. Sandu AL et al, Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia. Comput Med Imaging Graph, 2008 Schizophrenia Fractal Analysis in Neurological Disease

19. Arteriovenous Malformations(AVMs) Fractal Analysis in Neurological Disease Reishofer G et al, Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations. PLoS One, 2012

20. Fractal Analysis of brain tumor Di Ieva A et al, Three-dimensional susceptibility-weighted imaging at 7 T using fractal-based quantitative analysis to grade gliomas. Neuroradiology, 2013 Di Ieva A et al, Fractal analysis of the susceptibility weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7 T magnetic resonance during a period of four weeks. World Neurosurg, 2012

21. Fractal Analysis of brain tumor Di Ieva A et al, Three-dimensional susceptibility-weighted imaging at 7 T using fractal-based quantitative analysis to grade gliomas. Neuroradiology, 2013 Di Ieva A et al, Fractal analysis of the susceptibility weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7 T magnetic resonance during a period of four weeks. World Neurosurg, 2012

22. Fractal Analysis of brain tumor Morphology of tumor contours determines the dynamic behavior of growth by means of the scale invariances of their complex structures. Cell colony contours. Contours of a C6 cell line at different culture times. Local width function Brú A et al, The universal dynamics of tumor growth. Biophys J 85(5):2948–61. 2003

23. Fractal Analysis of brain tumor “Fractal analysis is potentially valid tool for proving microvascular fingerprinting” Di Ieva A, et al, Computer-assisted and fractal-based morphometric assessment of microvascularity in histological specimens of gliomas. Sci Rep 2:429–38. 2012

24.  Geometric complexity in space  Correlation FD in phase space of dynamic system using time-delay method  Using FFT in frequency domain for stationary series  FD in time domain using Higuchi’s method Fractal Analysis of Time series Fractal Dimension

25. Fractal Analysis of Time series Klonowski W, From conformons to human brains: an informal overview of nonlinear dynamics and its applications in biomedicine. Nonlinear Biomed Phys 1:5. 2007

26. Fractal Analysis of Time series Bardasano JL et al, New device against non-thermal effects from mobile telephones. Environmentalist 25:257–63. 2005 Klonowski W, From conformons to human brains: an informal overview of nonlinear dynamics and its applications in biomedicine. Nonlinear Biomed Phys 1:5. 2007

27. Fractal Analysis of Time series Lorazepam and benzodiadepines in general tend to increase beta rhythm and this increase has a consequent effect on FD. FD variations are highly correlated with variations in beta band. Michail E et al, Benzodiazepine administration effect on EEG fractal dimension: results and causalities. Conf Proc IEEE Eng Med Biol Soc, 2010

28. Our world is not linear. Fractal is powerful model to research!

29. Thank you :)