Abstract
BackgroundFrequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans. Dimensional analysis of the model is up to now not available.MethodsA formal dimensional analysis of MINMOD was carried out and the degree of freedom of MINMOD was examined. Through re-expressing all state variable and parameters in terms of their reference scales, MINMOD was transformed into a dimensionless format. Previously defined physiological indices including insulin sensitivity, glucose effectiveness, and first and second phase insulin responses were re-examined in this new formulation. Further, the parameter estimation from FSIVGTT was implemented using both the dimensional and the dimensionless formulations of MINMOD, and the performances were compared utilizing Monte Carlo simulation as well as real human FSIVGTT data.ResultsThe degree of freedom (DOF) of MINMOD was found to be 7. The model was maximally simplified in the dimensionless formulation that normalizes the variation in glucose and insulin during FSIVGTT. In the new formulation, the disposition index (Dl), a composite parameter known to be important in diabetes pathology, was naturally defined as one of the dimensionless parameters in the system. The numerical simulation using the dimensionless formulation led to a 1.5–5 fold gain in speed, and significantly improved accuracy and robustness in parameter estimation compared to the dimensional implementation.ConclusionDimensional analysis of MINMOD led to simplification of the model, direct identification of the important composite factors in the dynamics of glucose metabolic control, and better simulations algorithms.
Highlights
Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans
First formulated and introduced by Richard Bergman and colleagues, it describes the kinetics of plasma glucose and insulin during a Frequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT), and allows dissection of the composite effects of insulin secretion and insulin sensitivity on glucose tolerance and risk for diabetes [1,2,3]
Dimensional analysis of MINMOD The dimensions of the state variables and parameters The mathematical structure of MINMOD consists of two first-order ordinary differential equations (ODE) for glucose disappearance and one first-order ODE for insulin kinetics
Summary
Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans. The minimal model of glucose regulation, MINMOD, is one such model. First formulated and introduced by Richard Bergman and colleagues, it describes the kinetics of plasma glucose and insulin during a Frequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT), and allows dissection of the composite effects of insulin secretion and insulin sensitivity on glucose tolerance and risk for diabetes [1,2,3]. The model was termed as "minimal" for it was the least complex mathematical representation that is capable of accounting for the observed dynamic relationship between insulin and glucose disappearance [1,2]. The regulation of plasma glucose concentration G(t) was formulated to be [1,2,3]: dG(t) dt
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