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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| Veröffentlicht in: | Chaos, solitons and fractals Jg. 111; S. 198 - 205 |
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01.06.2018
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| Abstract | •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. |
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| AbstractList | 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. •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. |
| Author | Sayadi, Mounir Fnaiech, Farhat Ginoux, Jean-Marc Perc, Matjaž Naeck, Roomila Bouchouicha, Moez Ruskeepää, Heikki Costanzo, Véronique Di Hamdi, Takoua |
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| Cites_doi | 10.1016/0013-4694(57)90088-3 10.1142/S0218127498001637 10.1103/PhysRevA.33.1134 10.1111/j.1469-8986.1979.tb02991.x 10.1177/193229680800200223 10.1007/BF01053745 10.1142/S0218127498001418 10.1089/dia.2014.0378 10.1373/clinchem.2010.148841 10.1016/0375-9601(85)90444-X 10.1001/archpsyc.1968.01740030024004 10.1016/S1262-3636(12)71538-0 10.1016/0167-2789(92)90100-2 10.1136/jcp.2007.049205 10.1002/(SICI)1096-9136(199807)15:7<539::AID-DIA668>3.0.CO;2-S 10.1103/PhysRevLett.45.712 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 10.1016/0167-2789(83)90298-1 10.1016/S1262-3636(07)70023-X 10.1103/PhysRevA.45.3403 10.2337/diacare.27.5.1047 10.1016/0375-9601(94)90991-1 10.1088/0143-0807/26/1/021 10.1007/BFb0091924 10.1038/261459a0 10.1103/PhysRevLett.68.427 |
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| Keywords | Chaos Diabetes Correlation dimension Lyapunov exponent Delay coordinate embedding Blood glucose variations |
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| SubjectTerms | 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 |
| Title | Is type 1 diabetes a chaotic phenomenon? |
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