Is type 1 diabetes a chaotic phenomenon?

•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 tim...

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Bibliographic Details
Published in:Chaos, solitons and fractals Vol. 111; pp. 198 - 205
Main Authors: Ginoux, Jean-Marc, Ruskeepää, Heikki, Perc, Matjaž, Naeck, Roomila, Costanzo, Véronique Di, Bouchouicha, Moez, Fnaiech, Farhat, Sayadi, Mounir, Hamdi, Takoua
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.06.2018
Elsevier
Subjects:
Blood glucose variations
Chaos
Chaotic Dynamics
Correlation dimension
Delay coordinate embedding
Diabetes
Endocrinology and metabolism
Human health and pathology
Life Sciences
Lyapunov exponent
Mathematics
Nonlinear Sciences
Numerical Analysis
Chaos
Diabetes
Correlation dimension
Lyapunov exponent
Delay coordinate embedding
Blood glucose variations
ISSN:0960-0779, 1873-2887
Online Access:Get full text
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Summary:•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.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2018.03.033