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Is type 1 diabetes a chaotic phenomenon?

Author

Listed:
  • Ginoux, Jean-Marc
  • Ruskeepää, Heikki
  • Perc, Matjaž
  • Naeck, Roomila
  • Costanzo, Véronique Di
  • Bouchouicha, Moez
  • Fnaiech, Farhat
  • Sayadi, Mounir
  • Hamdi, Takoua

Abstract

A database of ten type 1 diabetes patients wearing a continuous glucose monitoring device has enabled to record their blood glucose continuous variations every minute all day long during fourteen consecutive days. These recordings represent, for each patient, a time series consisting of 1 value of glycaemia per minute during 24 h and 14 days, i.e., 20,160 data points. Thus, while using numerical methods, these time series have been anonymously analyzed. Nevertheless, because of the stochastic inputs induced by daily activities of any human being, it has not been possible to discriminate chaos from noise. So, we have decided to keep only the 14 nights of these ten patients. Then, the determination of the time delay and embedding dimension according to the delay coordinate embedding method has allowed us to estimate for each patient the correlation dimension and the maximal Lyapunov exponent. This has led us to show that type 1 diabetes could indeed be a chaotic phenomenon. Once this result has been confirmed by the determinism test, we have computed the Lyapunov time and found that the limit of predictability of this phenomenon is nearly equal to half the 90 min sleep-dream cycle. We hope that our results will prove to be useful to characterize and predict blood glucose variations.

Suggested Citation

  • Ginoux, Jean-Marc & Ruskeepää, Heikki & Perc, Matjaž & Naeck, Roomila & Costanzo, Véronique Di & Bouchouicha, Moez & Fnaiech, Farhat & Sayadi, Mounir & Hamdi, Takoua, 2018. "Is type 1 diabetes a chaotic phenomenon?," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 198-205.
    • Handle: RePEc:eee:chsofr:v:111:y:2018:i:c:p:198-205
    DOI: 10.1016/j.chaos.2018.03.033
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    Citations

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    Cited by:

    1. Trobia, José & de Souza, Silvio L.T. & dos Santos, Margarete A. & Szezech, José D. & Batista, Antonio M. & Borges, Rafael R. & Pereira, Leandro da S. & Protachevicz, Paulo R. & Caldas, Iberê L. & Iaro, 2022. "On the dynamical behaviour of a glucose-insulin model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Yang, Chuanzuo & Luan, Guoming & Liu, Zhao & Wang, Qingyun, 2019. "Dynamical analysis of epileptic characteristics based on recurrence quantification of SEEG recordings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 507-515.
    3. Liu, Shang & Li, Peiyu, 2020. "Nonlinear analysis of pedestrian flow Reynolds number in video scenes," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Dutta, Maitreyee & Roy, Binoy Krishna, 2020. "A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. Wei, Zhouchao & Zhu, Bin & Yang, Jing & Perc, Matjaž & Slavinec, Mitja, 2019. "Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 265-281.

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