The human brain has been described as a complex system. Its study by means of neurophysiological signals has revealed the presence of linear and nonlinear interactions. In this context, entropy metrics have been used to uncover brain behavior in the presence and absence of neurological disturbances. Entropy mapping is of great interest for the study of progressive neurodegenerative diseases such as Alzheimer’s disease. The aim of this study was to characterize the dynamics of brain oscillations in such disease by means of entropy and amplitude of low frequency oscillations from Bold signals of the default network and the executive control network in Alzheimer’s patients and healthy individuals, using a database extracted from the Open Access Imaging Studies series. The results revealed higher discriminative power of entropy by permutations compared to low-frequency fluctuation amplitude and fractional amplitude of low-frequency fluctuations. Increased entropy by permutations was obtained in regions of the default network and the executive control network in patients. The posterior cingulate cortex and the precuneus showed differential characteristics when assessing entropy by permutations in both groups. There were no findings when correlating metrics with clinical scales. The results demonstrated that entropy by permutations allows characterizing brain function in Alzheimer’s patients, and also reveals information about nonlinear interactions complementary to the characteristics obtained by calculating the amplitude of low frequency oscillations.

1. World Health Organization. The global dementia observatory reference guide world health organization [Internet]. Geneva, Switzerland; 2018. Available from: https://apps.who.int/iris/bitstream/handle/ 10665/272669/WHO-MSD-MER-18.1-eng.pdf

2. Takeuchi Y, Ariza-Araujo Y, Prada S. P3-349: Prevalence estimates of dementia in Colombia (2005–2020): Transitions and stage of disease. Alzheimer’s & Dementia 2014; 10(4S): 758.

3. doi: 10.1016/j.jalz.2014.05.1442.

4. Prada SI, Takeuchi Y, Ariza Y. Costo monetario del tratamiento de la enfermedad deAlzheimer en Colombia (Spanish) [Monetary cost of treatment of Alzheimer’s disease in Colombia]. Acta Neurológica Colombiana 2014; 30(4).

5. Busche MA, Hyman BT. Synergy between amyloid-β and tau in Alzheimer’s disease. Nature Neuroscience 2020; 23(10): 1183–1193.

6. Vermunt L, Sikkes SAM, van den Houtet A, et al. Duration of preclinical, prodromal, and dementia stages of Alzheimer’s disease in relation to age, sex, and APOE genotype. Alzheimer’s & Dementia 2019; 15(7): 888–898. doi: 10.1016/j.jalz.2019.04.001

7. Dickerson BC, Agosta F, Filippi M. fMRI in Neurodegenerative diseases: From scientific insights to clinical applications. In: fMRI techniques and protocols. New York: Humana Press; 2016. p. 699–739. doi: 10.1007/978-1-4939-5611-1_23.

8. Agosta F, Pievani M, Geroldi C, et al. Resting state fMRI in Alzheimer’s disease: Beyond the default mode network. Neurobiology of Aging 2012; 33(8): 1564–1578.

9. doi: 10.1016/j.neurobiolaging.2011.06.007.

10. Badhwar AP, Tam A, Dansereau C, et al. Resting-state network dysfunction in Alzheimer’s disease: A systematic review and meta-analysis. Alzheimer’s & Dementia: Diagnosis, Assessment & Disease Monitoring 2017; 8(1): 73–85.

11. doi: 10.1016/j.dadm.2017.03.007

12. Weiler M, Aya F, Lilian FPM, et al. Default mode, executive function, and language functional connectivity networks are compromised in mild Alzheimer’s disease. Current Alzheimer Research 2014; 11(3): 274–282.

13. doi: 10.2174/1567205011666140131114716.

14. Zhao Q, Lu H, Metmer H, et al. Evaluating functional connectivity of executive control network and frontoparietal network in Alzheimer’s disease. Brain Research 2018; 1678: 262–272.

15. doi: 10.1016/j.brainres.2017.10.025

16. Dennis EL, Thompson PM. Functional brain connectivity using fMRI in aging and Alzheimer’s disease. Neuropsychology Review 2014; 24(1): 49–62. doi: 10.1007/s11065-014-9249-6

17. Lv H, Wang Z, Tong E, et al. Resting-state functional MRI: Everything at Nonexperts have always wanted to know. American Journal of Neuroradiology 2018; 39(8): 1390–1399.

18. doi: 10.3174/ajnr.A5527

19. Yang L, Yan Y, Wang Y, et al. Gradual disturbances of the amplitude of low-frequency fluctuations (ALFF) and fractional ALFF in Alzheimer spectrum. Frontiers in Neuroscience 2018; 12: 975.

20. doi: 10.3389/fnins.2018.00975.

21. Poldrack PA. The role of fMRI in Cognitive Neuroscience: Where do we stand? Current Opinion in Neurobiology 2008; 18(2): 223–227.

22. doi: 10.1016/j.conb.2008.07.006

23. Timme NM, Lapish C. A tutorial for information theory in neuroscience. eNeuro 2018; 5(3).

24. doi: 10.1523/ENEURO.0052-18.2018

25. Moguilner S, García AM, Sanz Perl Y, et al. Dynamic brain fluctuations outperform connectivity measures and mirror pathophysiological profiles across dementia subtypes: A multicenter study. Neuroimage 2021; 225: 117522.

26. doi: 10.1016/j.neuroimage.2020.117522

27. Yang A, Tsai SJ, Lin C, et al. A strategy to reduce bias of entropy estimates in resting-state fMRI signals. Frontiers in Neuroscience 2008; 12: 398.

28. doi: 10.3389/fnins.2018.00398

29. Bandt C, Pompe B. Permutation entropy: A natural complexity measure for time series. Physical Review Letters 2001; 88(17).

30. Wang B, Niu Y, Miao L, et al. Decreased complexity in Alzheimer’s disease: Resting-state fMRI evidence of Brain entropy mapping. Frontiers in Aging Neuroscience 2017; 9. doi: 10.3389/fnagi.2017.00378.

31. Sun J, Wang B, Niu Y, et al. Complexity analysis of EEG, MEG, and fMRI in mild cognitive impairment and Alzheimer’s disease: A review. Entropy 2020; 22(2). doi: 10.3390/e22020239.

32. LaMontagne PJ, Benzinger TLS, Morris JC, et al. OASIS-3: Longitudinal neuroimaging, clinical, and cognitive dataset for normal aging and Alzheimer disease. MedRxiv 2019; 2–37.

33. doi: 10.1101/2019.12.13.19014902

34. O’Bryant SE, Waring SC, Cullum CM, et al. Staging dementia using clinical dementia rating scale sum of boxes scores: A Texas Alzheimer’s research consortium study. Archives of Neurology 2008; 65(8): 1091–1095. doi: 10.1001/archneur.65.8.1091.

35. OASIS. OASIS-3: Imaging methods & data dictionary [Intrnet]. 2018. Available from: https://www.oasis-brains.org/files/OASIS-3_Imaging_Data_Dictionary_v1.8.pdf.

36. Whitfield-Gabrieli S, Nieto-Castanon A. Conn: A functional connectivity toolbox for correlated and anticorrelated brain networks. Brain Connectivity 2012; 2(3): 125–141. doi: 10.10 89/brain.2012.0073.

37. Shirer WR, Ryali S, Rykhlevskaia E, et al. Decoding subject-driven cognitive states with whole-brain connectivity patterns. Cerebral Cortex 2011; 22(10): 158–165. doi: 10.1093/cercor/bhr099.

38. Yan C, Wang X, Zuo X, et al. DPABI: Data processing & analysis for (resting-state) brain imaging. Neuroinformatics 2016; 14(3): 339–351. doi: 10.1007/s12021-016-9299-4

39. Zuo X, Di Martinoa A, Kelly C, et al. The oscillating brain: complex and reliable. Neuroimage 2010; 49(2): 1432–1445.

40. doi: 10.1016/j.neuroimage.2009.09.037

41. Riedl M, Müller A, Wessel N. Practical considerations of permutation entropy: A tutorial review. European Physical Journal: Special Topics 2013; 222(2): 249–262. doi: 10.1140/epjst/e2013-01862-7.

42. Glerean E, Pan RK, Salmi J, et al. Reorganization of functionally connected brain subnetworks in high-functioning autism. Human Brain Mapping 2015; 37: 1066–1079. doi: 10.1002/hbm.23084.

43. Hentschke H, Stüttgen MC. Computation of measures of effect size for neuroscience data sets. European Journal of Neuroscience 2011; 34(12): 1887–1894.

44. doi: 10.1111/j.1460-9568.2011.07902.x.

45. Yokoi T, Watanabe H, Yamaguchi H, et al. Involvement of the precuneus/posterior cingulate cortex is significant for the development of Alzheimer’s disease: A PET (THK5351, PiB) and resting fMRI study. Frontiers in Aging Neuroscience 2018; 10.

46. doi: 10.3389/fnagi.2018.00304.

47. Dillen KNH, Jacobs HIL, Kukolja J, et al. Aberrant functional connectivity differentiates rerosplenial cortex from posterior cingulate cortex in prodromal Alzheimer’s disease. Neurobiology of Aging 2016; 44: 114–126.

48. doi: 10.1016/j.neurobiolaging.2016.04.010.

49. Koch W, Teipel S, Mueller S, et al. Diagnostic power of default mode network resting state fMRI in the detection of Alzheimer’s disease. Neurobiology of Aging 2012; 33(3): 466–478.

50. doi: 10.1016/j.neurobiolaging.2 010.04.013.

51. Lee P, Chou K, Chung C, et al. Posterior cingulate cortex network predicts Alzheimer’s disease progression. Frontiers in Aging Neuroscience 2020; 12. 608667. doi: 10.3389/fnagi.2020.608667.

52. Li C, Li Y, Zheng L, et al. Abnormal brain network connectivity in a triple-network model of Alzheimer’s disease. Journal of Alzheimer’s Disease 2019; 69(1): 237–252. doi: 10.3233/JAD-181097.

53. Jagust W. Imaging the evolution and pathophysiology of Alzheimer disease. Nature Reviews Neuroscience 2018; 19(11): 687–700.

54. doi: 10.1038/s41583-018-0067-3.

55. Zheng H, Onoda K, Nagai A, et al. Reduced dynamic complexity of BOLD signals differentiates mild cognitive impairment from normal aging. Frontiers in Aging Neuroscience 2020; 12: 90. doi: 10.3389/fnagi.2020.00090.

56. Grieder M, Wang DJJ, Dierks T, et al. Default mode network complexity and cognitive decline in mild Alzheimer’s disease. Frontiers in Neuroscience 2018; 12: 770. doi: 10.3389/fnins.2018.00770.

57. Boccardi V, Comanducci C, Baroni M, et al. Of energy and entropy: The ineluctable impact of aging in old age dementia. International Journal of Molecular Sciences 2017; 18(12): 2672.

58. doi: 10.3390/ijms18122672.

59. Wang Z. Brain entropy mapping in healthy aging and Alzheimer’s disease. Frontiers in Aging Neuroscience 2020; 12: 372. doi: 10.3389/fnagi.2020.596122

60. Tagliazucchi E, Balenzuela P, Fraiman D, et al. Criticality in large-scale brain fMRI dynamics unveiled by a novel point process analysis. Frontiers in Physiology 2012; 3: 15.

61. doi: 10.3389/fphys.2012.00015.

62. Haimovici A, Tagliazucchi E, Balenzuela P, et al. Brain organization into resting state networks emerges at criticality on a model of the human connectome. Physical Review Letters 2013; 110(17): 178101. doi: 10.1103/PhysRevLett.110.178101.

63. Song D, Chang D, Zhang J, et al. Associations of brain entropy (BEN) to cerebral blood flow and fractional amplitude of low-frequency fluctuations in the resting brain. Brain Imaging and Behavior 2019; 13(5): 1486–1495.

64. doi: 10.1007/s11682-018-9963-4.

65. Mera-Jiménez L, Ochoa-Gómez JF. Convolutional neural networks for the classification of independent rs-fMRI components. TecnoLógicas 2021; 24(50): 97–115.

66. Liégeois R, Li J, Kong R, et al. Resting brain dynamics at different timescales capture distinct aspects of human behavior. Nature Communications 2019; 10(1): 1–9. doi: 10.1038/s41467-019-10317-7.