  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.
