Detrended fluctuation analysis: A scale-free view on neuronal oscillations

Frontiers in Physiology

Volumn 3 NOV, Issue , 2012, Pages

  Hardstone, Richard ^a   Poil, Simon Shlomo ^a   Schiavone, Giuseppina ^a   Jansen, Rick ^a,b   Nikulin, Vadim V ^c   Mansvelder, Huibert D ^a   Linkenkaer Hansen, Klaus ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b VU UNIVERSITY MEDICAL CENTER   (Netherlands)

^c CHARITÉ UNIVERSITÄTSMEDIZIN BERLIN   (Germany)

Author keywords

Criticality; Detrended fluctuation analysis; Long range temporal correlations; Ongoing oscillations; Scale free dynamics

Indexed keywords

EID: 84870917484     PISSN: None     EISSN: 1664042X     Source Type: Journal    
DOI: 10.3389/fphys.2012.00450     Document Type: Article

References (55)

1. Axmacher,N., Mormann, F.,Fernández, G., Elger, C. E., and Fell, J. (2006). Memory formationbyneuronalsyn-chronization. Brain Res. Rev. 52, 170-182.
2. Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. Berlin: Springer.
3. Bassingthwaighte, J. B., Liebovitch,L. S., and West, B. J. (1994). Fractal Physiology. New York: Oxford University Press.
4. Beggs, J. M., and Plenz, D. (2003). Neu-ronal avalanches in neocortical circuits. J. Neurosci. 23, 11167-11177.
5. Beran, J. (1994). Statistics for Long-Memory Processes. New York: Chapman & Hall/CRC.
6. Berthouze, L., and Farmer, S. F. (2012). Adaptive time-varying detrended fluctuation analysis. J. Neurosci. Methods 209, 178-188.
7. Berthouze, L., James,L. M., and Farmer, S. F. (2010). Human EEG shows long-range temporal correlations of oscillation amplitude in Theta, Alpha and Beta bands across a wide age range. Clin. Neurophysiol. 121, 1187-1197.
8. Buzsáki,G. (2006).Rhythms of the Brain. Oxford: Oxford University Press.
9. Cassenaer, S., and Laurent, G. (2007). Hebbian STDP in mushroom bodies facilitates the synchronous flow of olfactory information in locusts. Nature 448, 709-713.
10. Castiglioni, P., Parati, G., Di Rienzo, M., Carabalona, R., Cividjan, A., and Quintin, L. (2010). Scale exponents of blood pressure and heart rate during autonomic blockade as assessed by detrended fluctuation analysis. J. Physiol. (Lond.) 589, 355-369.
11. Chen, Z., Ivanov, P. C., Hu, K., and Stanley, H. (2002). Effect of nonsta-tionarities on detrended fluctuation analysis. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65, 041107.
12. Eke, A., Hermán, P., Bassingthwaighte, J., Raymond, G., Percival, D., Cannon, M., et al. (2000). Physiological time series: distinguishing fractal noises from motions. Pflugers Arch. 439, 403.
13. Eke, A., Herman, P., Kocsis, L., and Kozak, L. (2002). Fractal characterization of complexity in temporal physiological signals. Physiol. Meas. 23, R1.
14. Frey, U., Maksym, G., and Suki, B. (2011). Temporal complexityinclin-ical manifestations of lung disease. J. Appl. Physiol. 110, 1723.
15. Ghosh, A., Rho, Y., McIntosh, A., Köt-ter, R., and Jirsa, V. (2008). Noise during rest enables the exploration of the brain's dynamic repertoire. PLoS Comput. Biol. 4, e1000196. doi:10.1371/journal.pcbi.1000196
16. Gilden, D. L. (2001). Cognitive emissions of 1/f noise. Psychol. Rev. 108, 33-56.
17. Goldberger, A. L., Amaral, L. A. N., Glass, L., Hausdorff, J. M., Ivanov, P. Ch., Mark, R. G., et al. (2000). Phys-ioBank, PhysioToolkit, and Phys-ioNet: componentsof anew research resource for complex physiologic signals. Circulation 101, E215-E220.
18. Goldberger, A. L., Amaral, L. A. N., Hausdorff, J. M., Ivanov, P. C., Peng, C. K., and Stanley, H. E. (2002). Fractal dynamics in physiology: alterations with disease and aging. Proc. Natl. Acad. Sci. U S A. 99, 1.
19. He, B. J., Zempel, J. M., Snyder, A. Z., and Raichle, M. E. (2010). The temporal structures and functional significance of scale-free brain activity. Neuron 66, 353-369.
20. Hohlefeld, F. U., Huebl, J., Huchzer-meyer, C., Schneider, G. H., Schö-necker, T., Kühn, A. A., et al. (2012). Long-range temporal correlations in the subthalamic nucleus of patients with Parkinson's disease. Eur. J. Neu-rosci.
21. Hu, K., Ivanov, P. C., Chen, Z., Carpena, P., and Stanley, H. E. (2001). Effect of trends on detrended fluctuation analysis. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64, 011114.
22. Kantelhardt, J. W., Koscielny-Bunde, E., Rego, H. H. A., Havlin, S., and Bunde, A. (2001). Detecting long-range correlations with detrended fluctuation analysis. Physica A 295, 441-454.
23. Kello, C. T., Brown, G. D. A., Ferrer-I-Cancho, R., Holden, J. G., Linkenkaer-Hansen, K., Rhodes, T., et al. (2010). Scaling lawsin cognitive sciences. Trends Cogn. Sci. (Regul. Ed.) 14, 223-232.
24. Kim, J. W., Shin, H. B., and Robinson, P. A. (2009). Quantitative study of the sleep onset period via detrended fluctuation analysis: normal vs. nar-coleptic subjects. Clin. Neurophysiol. 120, 1245-1251.
25. Kinouchi, O., and Copelli, M. (2006). Optimal dynamical range of excitable networks at criticality. Nat. Phys. 2, 348-351.
26. Leopold,D.A.,Murayama,Y.,and Logo-thetis, N. K. (2003). Very slow activity fluctuations in monkey visual cortex: implications for functional brain imaging. Cereb. Cortex 13, 422.
27. Linkenkaer-Hansen, K., Monto, S., Ryt-sala, H., Suominen, K., Isometsä, E., and Kähkönen, S. (2005). Breakdown of long-range temporal correlations in theta oscillations in patients with major depressive disorder. J. Neurosci. 25, 10131-10137.
28. Linkenkaer-Hansen,K.,Nikouline,V.V., Palva, J. M., and Ilmoniemi, R. J. (2001). Long-Range temporal correlations and scaling behavior in human brain oscillations. J. Neu-rosci. 21, 1370-1377.
29. Linkenkaer-Hansen, K., Nikulin, V. V., Palva, J. M., Kaila, K., and Ilmoniemi, R. J. (2004). Stimulus-induced change in long-range temporal correlations and scaling behaviour of sensorimotor oscillations. Eur. J. Neurosci. 19, 203-218.
30. Linkenkaer-Hansen, K., Smit, D. J. A., Barkil, A., Van Beijsterveldt, T. E. M., Brussaard, A. B., Boomsma, D. I., et al. (2007). Genetic contributions to long-range temporal correlations in ongoing oscillations. J. Neurosci. 27, 13882-13889.
31. Lisman, J. (2010). Working memory: the importance of theta and gamma oscillations. Curr. Biol. 20, R490-R492.
32. Mandelbrot, B. (1967). How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156, 636.
33. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. New York: Times Books.
34. Mandelbrot, B. B., and Wallis, J. R. (1969). Some long-run properties of geophysical records. Water Resour. Res. 5, 321-340.
35. Montez, T., Poil, S. S., Jones, B. F., Man-shanden, I., Verbunt, J., Van Dijk, B. W., et al. (2009). Altered temporal correlations in parietal alpha and prefrontal theta oscillations in early-stage Alzheimer disease. Proc. Natl. Acad. Sci. U.S.A. 106, 1614.
36. Monto, S., Palva, S., Voipio, J., and Palva, J. M. (2008). Very slow EEG fluctuations predict the dynamics of stimulus detection and oscillation amplitudes in humans. J. Neurosci. 28, 8268-8272.
37. Monto, S., Vanhatalo, S., Holmes, M. D., and Palva, J. M. (2007). Epileptogenic neocortical networks are revealed by abnormal temporal dynamics in seizure-free subdural EEG. Cereb. Cortex 17, 1386.
38. Nikulin, V. V., and Brismar, T. (2004). Long-range temporal correlations in alpha and beta oscillations: effect of arousal level and test-retest reliability. Clin. Neurophysiol. 115, 1896-1908.
39. Nikulin, V. V., and Brismar, T. (2005). Long-range temporal correlations in electroencephalographic oscillations: relation to topography, frequency band, age and gender. Neu-roscience 130, 549-558.
40. Nikulin, V. V., Jönsson, E. G., and Bris-mar, T. (2012). Attenuation of long range temporal correlations in the amplitude dynamics of alpha and beta neuronal oscillations in patients with schizophrenia. Neuroimage 61, 162-169.
41. Nikulin, V. V., Linkenkaer-Hansen, K., Nolte, G., Lemm, S., Müller, K. R., Ilmoniemi, R. J., et al. (2007). A novel mechanism for evoked responses in the human brain. Eur. J. Neurosci. 25, 3146-3154.
42. Parish, L., Worrell, G., Cranstoun, S., Stead, S., Pennell, P., and Litt, B. (2004). Long-range temporal correlations in epileptogenic and non-epileptogenic human hippocampus. Neuroscience 125, 1069-1076.
43. Peitgen, H. O., Jurgens, H., and Saupe, D. (1992). Chaos and Fractals: New Frontiers of Science. New York: Springer.
44. Peng, C., Havlin, S., Stanley, H., and Goldberger, A. (1995). Quantification of scaling exponents and crossover phenomena in nonsta-tionary heartbeat time series. Chaos 5, 82-87.
45. Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L. (1994). Mosaic organization of DNA nucleotides. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49, 1685.
46. Petermann, T., Thiagarajan, T. C., Lebedev, M. A., Nicolelis, M. A. L., Chialvo, D. R., and Plenz, D. (2009). Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proc. Natl. Acad. Sci. U.S.A. 106, 15921-15926.
47. Poil, S.-S., Hardstone, R., Mans-velder, H. D., and Linkenkaer-Hansen, K. (2012). Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation/inhibition in neu-ronal networks. J. Neurosci. 32, 9817-9823.
48. Poil, S. S., Jansen, R., Van Aerde, K., Timmerman, J., Brussaard, A. B., Mansvelder, H. D., et al. (2011). Fast network oscillations in vitro exhibit a slow decay of temporal auto-correlations. Eur. J. Neurosci. 34, 394-403.
49. Riley, M., Bonnette, S., Kuznetsov, N., Wallot, S., and Gao,J. (2012). A tutorial introduction to adaptive fractal analysis. Front. Physiol. 3:371. doi:10.3389/fphys.2012.00371
50. Smit, D. J. A., De Geus, E. J. C., Van De Nieuwenhuijzen, M. E., Van Beijsterveldt, C. E. M., Van Baal, G. C. M., Mansvelder, H. D., et al. (2011). Scale-free modulation of resting-state neuronal oscillations reflects prolonged brain maturation in humans. J. Neurosci. 31, 13128-13136.
51. Stam, C. (2005). Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin. Neurophys-iol. 116, 2266-2301.
52. Stead, M., Worrell, G., and Litt, B. (2005). Frequency and dependence of long range temporal correlations in human hippocampal energy fluctuations. Complexity 10, 35-44.
53. Turcotte, D. L. (1997). Fractals and Chaos in Geology and Geophysics. Cambridge: Cambridge University Press.
54. West, B. J. (2010). Frontiers: fractal physiology and the fractional calculus: a perspective. Front. Physiol. 1:12. doi:10.3389/fphys.2010.00012
55. Xu, Y., Ma, Q. D. Y., Schmitt, D. T., Bernaola-Galván, P., and Ivanov, P. C. (2011). Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals. Physica A 390, 4057-4072.