Is type 1 diabetes a chaotic phenomenon? - Ginoux, Jean-Marc; Ruskeepää, Heikki; Perc, Matjaž; Naeck, Roomila; Costanzo, Véronique Di; Bouchouicha, Moez; Fnaiech, Farhat; Sayadi, Mounir; Hamdi, Takoua (Chaos, solitons and fractals, 2018)
•Continuous glucose monitoring in 10 type 1 diabetes patients over a period of 14 days.•Phase space reconstruction from measured blood glucose variations for all patients.•Determination of the correlation dimension for all patients.•Determination of the maximal Lyapunov exponent and the Lyapunov time for all patients.•Showing that type 1 diabetes could indeed be a chaotic phenomenon. 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.