title: Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm.
abstract: BACKGROUND
  Frequently 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.
  
  
  METHODS
  A 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.
  
  
  RESULTS
  The 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.
  
  
  CONCLUSIONS
  Dimensional 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.
authors.affiliation: Max McGee National Research Center for Juvenile Diabetes & Human and Molecular Genetics Center, Medical College of Wisconsin, Children's Research Institute, Children's Hospital of Wisconsin, Milwaukee, Wl 53226, USA. anittala@mcw.edu
authors.forename: Aparna
authors.initials: A
authors.lastname: Nittala
authors.forename: Soumitra
authors.initials: S
authors.lastname: Ghosh
authors.forename: Darko
authors.initials: D
authors.lastname: Stefanovski
authors.forename: Richard
authors.initials: R
authors.lastname: Bergman
authors.forename: Xujing
authors.initials: X
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D001786:Blood Glucose / Q000032:analysis* / Q000378:metabolism*; D003198:Computer Simulation; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D005246:Feedback / Q000502:physiology; D005951:Glucose Tolerance Test / Q000379:methods*; D006706:Homeostasis / Q000502:physiology; D006801:Humans; D007328:Insulin / Q000097:blood*; D008954:Models, Biological; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
chemical_list: D001786:Blood Glucose; D007328:Insulin