Is type 1 diabetes a chaotic phenomenon?

Jean-Marc Ginoux (1) , Heikki Ruskeepää , Matjaž Perc (2) , Roomila Naeck , Véronique Di Costanzo , Moez Bouchouicha (1) , Farhat Fnaiech (3) , Mounir Sayadi , Takoua Hamdi (3)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 Faculty of Natural Sciences and Mathematics [Maribor]
3 Université de Tunis

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 hours and 14 days, i.e., 20,160 data point. 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-minutes sleep-dream cycle. We hope that our results will prove to be useful to characterize and predict blood glucose variations.

Domaines: Dynamique Chaotique [nlin.CD]; Endocrinologie et métabolisme; Analyse numérique [math.NA]

Jean-Marc Ginoux, Heikki Ruskeepää, Matjaž Perc, Roomila Naeck, Véronique Di Costanzo, et al.. Is type 1 diabetes a chaotic phenomenon?. Chaos, Solitons & Fractals, 2018, 111, pp.198-205. ⟨10.1016/j.chaos.2018.03.033⟩. ⟨hal-02194779⟩