Long-range negative correlation of glucose dynamics in humans and its breakdown in diabetes mellitus

Abstract

Diurnal fluctuations in glucose levels continuously monitored during normal daily life are investigated using an extended random walk analysis, referred to as detrended fluctuation analysis (DFA), in 12 nondiabetic subjects and 15 diabetic patients. The DFA exponent alpha = 1.25 +/- 0.29 for healthy individuals in the "long-range" (>2 h) regime is shown to be significantly (P < 0.01) smaller than the reference "uncorrelated" value of alpha = 1.5, suggesting that the instantaneous net effects of the dynamical balance of glucose flux and reflux, causing temporal changes in glucose concentration, are long-range negatively correlated. By contrast, in diabetic patients, the DFA exponent alpha = 1.65 +/- 0.30 is significantly (P < 0.05) higher than that in nondiabetic subjects, evidencing a breakdown of the long-range negative correlation. It is suggested that the emergence of such positive long-range glucose correlations in diabetic patients-indicating that the net effects of the flux and reflux persist for many hours-likely reflects pathogenic mechanisms of diabetes, i.e., the lack of long-term stability of blood glucose and that the long-range negatively correlated glucose dynamics are functional in maintaining normal glucose homeostasis.

Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

“…The results are presented in the format of mean value plus-minus standard deviation. 12 Ogata et al [17] There is a qualitative correspondence between these two investigations since both show that the difference is not significant for  1 (p=0.278 for our data) but it is significant for  2 (p=0.0004 for our data). However, values of indices  1 and  2 for our data are larger than in Ogata et al's study [17].…”

“…Here we follow an established numerical scheme [17]. A general calculation scheme for DFA index  has been published [12,19] of the error between piece-wise two-line fitting and F(n) has been used to determine the crossover point n c .…”

“…To consider long term prediction (usually defined as beyond one hour [4,17]) and dynamic behaviour, we decomposed the glucose time series into two parts. One part is a trend, and another part corresponds to meal time (prandial) events.…”

“…1, d). For a comparison to the previous investigation by Ogata et al [17], results of both type 1 and type 2 diabetes groups were combined. The results are presented in the format of mean value plus-minus standard deviation.…”

“…DFA leads to a scaling index, , which is less than 1 for a stationary process and greater than 1 for nonstationary [12]. Ogata et al [17] showed that DFA is able to discriminate healthy and diabetic groups and they concluded that glucose profiles show negative long-range correlation for healthy individuals and positive long-range correlation for diabetic patients (largely treated with insulin).…”