Submitted on April 7, 2006
Accepted on July 25, 2006
Long-range negative correlation of glucose dynamics in humans and its breakdown in diabetes mellitus
Hitomi Ogata1, Kumpei Tokuyama1, Shoichiro Nagasaka2, Akihiko Ando3, Ikuyo Kusaka3, Naoko Sato3, Akiko Goto3, Shun Ishibashi3, Ken Kiyono4, Zbigniew R Struzik4, and Yoshiharu Yamamoto5*
1 Graduate School of Comprehensive Human Sciences, University of Tsukuba, Tsukuba-shi, Ibaraki, Japan
2 United States
3 Division of Endocrinology and Metabolism, Department of Medicine, Jichi Medical School, Yakushiji, Tochigi, Japan
4 Educational Physiology Laboratory, Graduate School of Education, The University of Tokyo, Hongo, Tokyo, Japan
5 Educational Physiology Laboratory, Graduate School of Education, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
* To whom correspondence should be addressed. E-mail: yamamoto{at}p.u-tokyo.ac.jp.
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 non-diabetic subjects and 15 diabetic patients. The DFA exponent 
= 1.25 ± 0.29 for healthy individuals in the "long-range" (> 2 hour) regime is shown to be significantly (p < 0.01) smaller than the reference "uncorrelated" value of = 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 = 1.65 ± 0.30 is significantly (p < 0.05) higher than that in non-diabetic 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.
