An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM), chemical diabetes (NIDDM), and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. FCAS modeling consists in fitting a power-law function to the bivariate lognormal distribution of the variables. The power-law exponent is estimated by principal component analysis (PCA). Analyses have shown that glucose disposal can be considered a fractal process, thereby implying a complex hierarchy of interacting scales and mechanisms in glucose handling. The first principal component represents quantitative glucose disposal, and the second component is compatible with insulin efficiency. PCA further retrieved distinct ongoing pathological processes within clinical groups of subjects. The IDDM insulin production defect had a high (absolute value) exponent of -3.5 that confirms a crude defect scanning the whole fractal hierarchy. Definite insulin resistance has been detected in clinically normal subjects with a low exponent of -0.5, thus suggesting a subtle and complex problem possibly due to aging or reduced physical activity. Insulin sensitivity was definitely impaired in the NIDDM clinical group with an exponent of -2.2, thereby suggesting poorly scheduled insulin feedback, possibly due to peripheral insensitivity. NIDDM appeared to result from aggravation of the subtle insensitivity seen in normal subjects. On the whole, the fractal model seemed to be capable of assessing the degree of complexity of a disease. It is concluded that future studies of diabetes using FCAS modeling ought to be undertaken on the basis of multiple-scale biological variables, thereby closely reflecting the complexity of glucose handling. It is further recommended that such analyses be undertaken with dynamic data to track down the precise timing of the various homeostatic disruptions. It would also be important to carry out this type of analysis on less known but equally complex disease processes. The results might point to important new research findings.
Power law; Fractals; Diabetes mellitus; insulin-dependent; Diabetes mellitus, non-insulin dependent; Nonlinear dynamics; Principal component analysis; Complex-adaptive-system modeling; Allometry
