Using what is accessible to measure that which is not: necessity of model of system.

Understanding the in vivo functioning of endocrine-metabolic systems requires the quantitative knowledge of system parameters like production/utilization of substrales, secretion/degradation of hormones, and substrate-hormone signaling. Unfortunately, these system parameters are not directly accessible and an indirect measurement approach is needed based on a model of the system. We review first the principals of the model of system methodology focusing on compartmental and input-output modeling. Then, the model of system methodology is applied to the measurement of nonaccessible parameters/variables of the glucose system like glucose fluxes, insulin fluxes, and glucose-insulin signaling.

[1]  L Finkelstein,et al.  Validation of simple and complex models in physiology and medicine. , 1984, The American journal of physiology.

[2]  J J DiStefano,et al.  Optimized blood sampling protocols and sequential design of kinetic experiments. , 1981, The American journal of physiology.

[3]  C. Cobelli,et al.  V-A and A-V modes in whole body and regional kinetics: domain of validity from a physiological model. , 1992, The American journal of physiology.

[4]  A. Signore,et al.  Immunotherapy with ciamexon in the non obese diabetic (NOD) mouse. , 1992, Hormone and metabolic research = Hormon- und Stoffwechselforschung = Hormones et metabolisme.

[5]  Malcolm Rowland,et al.  Clinical pharmacokinetics : concepts and applications , 1989 .

[6]  Claudio Cobelli,et al.  Undermodeling affects minimal model indexes: insights from a two-compartment model. , 1999, American journal of physiology. Endocrinology and metabolism.

[7]  K. Polonsky,et al.  Peripheral insulin parallels changes in insulin secretion more closely than C-peptide after bolus intravenous glucose administration. , 1988, The Journal of clinical endocrinology and metabolism.

[8]  Bruce H. Frank,et al.  Use of biosynthetic human C-peptide in the measurement of insulin secretion rates in normal volunteers and type I diabetic patients. , 1986, The Journal of clinical investigation.

[9]  Eric Walter,et al.  Identifiability of parametric models , 1987 .

[10]  C. Cobelli,et al.  4 In vivo glucose transport in human skeletal muscle: tools, problems and perspectives , 1993 .

[11]  K. M. Erickson,et al.  Prehepatic insulin production in man: kinetic analysis using peripheral connecting peptide behavior. , 1980, The Journal of clinical endocrinology and metabolism.

[12]  B H Frank,et al.  Quantitative study of insulin secretion and clearance in normal and obese subjects. , 1988, The Journal of clinical investigation.

[13]  K. Polonsky,et al.  Insulin Secretion and Clearance: Comparison After Oral and Intravenous Glucose , 1987, Diabetes.

[14]  Jones Ea,et al.  Use of Kinetic Analysis and Mathematical Modeling in the Study of Metabolic Pathways in Vivo: Applications to Hepatic Organic Anion Metabolism , 1979 .

[15]  Claudio Cobelli,et al.  Identifiability results on some constrained compartmental systems , 1979 .

[16]  C. Cobelli,et al.  Glucose turnover in presence of changing glucose concentrations: error analysis for glucose disappearance. , 1995, The American journal of physiology.

[17]  M. Reivich,et al.  THE [14C]DEOXYGLUCOSE METHOD FOR THE MEASUREMENT OF LOCAL CEREBRAL GLUCOSE UTILIZATION: THEORY, PROCEDURE, AND NORMAL VALUES IN THE CONSCIOUS AND ANESTHETIZED ALBINO RAT 1 , 1977, Journal of neurochemistry.

[18]  If the minimal model is too minimal, who suffers more: SG or SI? , 1997, Diabetologia.

[19]  P Vicini,et al.  Estimation of endogenous glucose production after a glucose perturbation by nonparametric stochastic deconvolution. , 1997, Computer methods and programs in biomedicine.

[20]  J. Sturis,et al.  Entrainment of pulsatile insulin secretion by oscillatory glucose infusion. , 1991, The Journal of clinical investigation.

[21]  D. Finegood,et al.  Reduced glucose effectiveness associated with reduced insulin release: an artifact of the minimal-model method. , 1996, The American journal of physiology.

[22]  C. Cobelli,et al.  Modeling glucose metabolism in man: theory and practice. , 1990, Hormone and metabolic research. Supplement series.

[23]  J. P. Norton,et al.  An investigation of the sources of nonuniqueness in deterministic identifiability , 1982 .

[24]  C Cobelli,et al.  Non-steady state: error analysis of Steele's model and developments for glucose kinetics. , 1987, The American journal of physiology.

[25]  C. Bradshaw,et al.  Posthepatic rate of appearance of insulin: measurement and validation in the nonsteady state. , 1992, The American journal of physiology.

[26]  R N Bergman,et al.  Role of Glucose Effectiveness in the Determination of Glucose Tolerance , 1996, Diabetes Care.

[27]  K. Polonsky,et al.  Twenty-four-hour profiles and pulsatile patterns of insulin secretion in normal and obese subjects. , 1988, The Journal of clinical investigation.

[28]  M. Byrne,et al.  Insulin secretion and clearance during low-dose graded glucose infusion. , 1995, The American journal of physiology.

[29]  E. H. Twizell.  The mathematical modeling of metabolic and endocrine systems: E.R. Carson, C. Cobelli and L. Finkelstein John Wiley and Sons, Chichester, Sussex, UK, 394 pp., £45.15, 1983 , 1984 .

[30]  R. Steele,et al.  Measurement of size and turnover rate of body glucose pool by the isotope dilution method. , 1956, The American journal of physiology.

[31]  C. Cobelli,et al.  Qualitative experiment design in physiological system identification , 1992, IEEE Control Systems.

[32]  J J DiStefano,et al.  Noncompartmental vs. compartmental analysis: some bases for choice. , 1982, The American journal of physiology.

[33]  C Cobelli,et al.  Assessment of insulin action and glucose effectiveness in diabetic and nondiabetic humans. , 1994, The Journal of clinical investigation.

[34]  C. Cobelli,et al.  Models to Measure Hepatic Glucose Release in Nonsteady State: A General Validation Strategy Based on Dual-Tracer Administration and Convolution , 1994 .

[35]  J J DiStefano,et al.  Comprehensive kinetics of triiodothyronine production, distribution, and metabolism in blood and tissue pools of the rat using optimized blood-sampling protocols. , 1982, Endocrinology.

[36]  Jeppe Sturis,et al.  Estimation of Insulin Secretion Rates from C-Peptide Levels: Comparison of Individual and Standard Kinetic Parameters for C-Peptide Clearance , 1992, Diabetes.

[37]  C Cobelli,et al.  Optimal design of sampling schedules for studying glucose kinetics with tracers. , 1989, The American journal of physiology.

[38]  K. Polonsky,et al.  Ingestion of a mixed meal does not affect the metabolic clearance rate of biosynthetic human C-peptide. , 1986, The Journal of clinical endocrinology and metabolism.

[39]  C. Cobelli,et al.  A stochastic deconvolution method to reconstruct insulin secretion rate after a glucose stimulus , 1996, IEEE Transactions on Biomedical Engineering.

[40]  J. Jacquez.  Compartmental analysis in biology and medicine , 1985 .

[41]  J. S. Robertson,et al.  Compartmental distribution of radiotracers , 1983 .

[42]  Claudio Cobelli,et al.  A model of glucose kinetics and their control by insulin, compartmental and noncompartmental approaches , 1984 .

[43]  Claudio Cobelli,et al.  Roles of Glucose Transport and Glucose Phosphorylation in Muscle Insulin Resistance of NIDDM , 1996, Diabetes.

[44]  P Vicini,et al.  The hot but not the cold minimal model allows precise assessment of insulin sensitivity in NIDDM subjects. , 1996, The American journal of physiology.

[45]  Joseph J. DiStefano,et al.  Complete parameter bounds and quasiidentifiability conditions for a class of unidentifiable linear systems , 1983 .

[46]  C. Cobelli,et al.  A minimal input-output configuration for a priori identifiability of a compartmental model of leucine metabolism , 1993, IEEE Transactions on Biomedical Engineering.

[47]  C. Cobelli,et al.  Direct assessment of liver glycogen storage by 13C nuclear magnetic resonance spectroscopy and regulation of glucose homeostasis after a mixed meal in normal subjects. , 1996, The Journal of clinical investigation.

[48]  Claudio Cobelli,et al.  Structural Identifiability of Nonlinear Systems: Algorithms Based on Differential Ideals , 1994 .

[49]  J J DiStefano,et al.  Multiexponential, multicompartmental, and noncompartmental modeling. II. Data analysis and statistical considerations. , 1984, The American journal of physiology.

[50]  Giuseppe De Nicolao,et al.  Nonparametric input estimation in physiological systems: Problems, methods, and case studies , 1997, Autom..

[51]  J. Jacquez.  Theory of production rate calculations in steady and non-steady states and its application to glucose metabolism. , 1992, The American journal of physiology.

[52]  C. Cobelli,et al.  A model to measure insulin effects on glucose transport and phosphorylation in muscle: a three-tracer study. , 1996, The American journal of physiology.

[53]  S. Grundy,et al.  Lipoprotein Kinetics and Modeling , 1982 .

[54]  B H Frank,et al.  Dose-dependent effects of oral and intravenous glucose on insulin secretion and clearance in normal humans. , 1988, The American journal of physiology.

[55]  C Cobelli,et al.  The kinetics of insulin in man. II. Role of the liver. , 1987, Diabetes/metabolism reviews.

[56]  M. Quon,et al.  Non-Insulin-Mediated Glucose Disappearance in Subjects With IDDM: Discordance Between Experimental Results and Minimal Model Analysis , 1994, Diabetes.

[57]  E. Hoffman,et al.  Tomographic measurement of local cerebral glucose metabolic rate in humans with (F‐18)2‐fluoro‐2‐deoxy‐D‐glucose: Validation of method , 1979, Annals of neurology.

[58]  C. Cobelli,et al.  A reduced sampling schedule for estimating the parameters of the glucose minimal model from a labeled IVGTT , 1991, IEEE Transactions on Biomedical Engineering.

[59]  A Rescigno,et al.  Estimation of average times of residence, recycle and interconversion of blood-borne compounds using tracer methods. , 1973, The Journal of clinical endocrinology and metabolism.

[60]  C Cobelli,et al.  Estimation of insulin sensitivity and glucose clearance from minimal model: new insights from labeled IVGTT. , 1986, The American journal of physiology.

[61]  Claudio Cobelli.  Modeling and identification of endocrine-metabolic systems. theoretical aspects and their importance in practice , 1984 .

[62]  Richard M Watanabe,et al.  A Comparison Between the Minimal Model and the Glucose Clamp in the Assessment of Insulin Sensitivity Across the Spectrum of Glucose Tolerance , 1994, Diabetes.

[63]  C Cobelli,et al.  SAAM II: Simulation, Analysis, and Modeling Software for tracer and pharmacokinetic studies. , 1998, Metabolism: clinical and experimental.

[64]  C Cobelli,et al.  Estimation of β-Cell Sensitivity From Intravenous Glucose Tolerance Test C-Peptide Data: Knowledge of the Kinetics Avoids Errors in Modeling the Secretion , 1995, Diabetes.

[65]  W. G. Hoover.  molecular dynamics , 1986, Catalysis from A to Z.

[66]  C Cobelli,et al.  Minimal Models of Glucose Disappearance: Lessons from the Labelled IVGTT , 1991, Diabetic medicine : a journal of the British Diabetic Association.

[67]  C Cobelli,et al.  Tracer-to-tracee ratio for analysis of stable isotope tracer data: link with radioactive kinetic formalism. , 1992, The American journal of physiology.

[68]  Simon C Watkins,et al.  The effect of non-insulin-dependent diabetes mellitus and obesity on glucose transport and phosphorylation in skeletal muscle. , 1996, The Journal of clinical investigation.

[69]  Claudio Cobelli,et al.  Theoretical Aspects and Practical Strategies for the Identification of Unidentifiable Compartmental Systems , 1985 .

[70]  C Cobelli,et al.  Stable-Label Intravenous Glucose Tolerance Test Minimal Model , 1989, Diabetes.

[71]  R N Bergman,et al.  Estimation of Endogenous Glucose Production During Hyperinsulinemic-Euglycemic Glucose Clamps: Comparison of Unlabeled and Labeled Exogenous Glucose Infusates , 1987, Diabetes.

[72]  C. Cobelli,et al.  Global identifiability of linear compartmental models-a computer algebra algorithm , 1998, IEEE Transactions on Biomedical Engineering.

[73]  R. Bergman,et al.  Differences Between the Tolbutamide-Boosted and the Insulin-Modified Minimal Model Protocols , 1997, Diabetes.

[74]  C. Cobelli,et al.  Glucose effectiveness and insulin sensitivity from the minimal models: consequences of undermodeling assessed by Monte Carlo simulation , 1999, IEEE Transactions on Biomedical Engineering.

[75]  H. Yki-Järvinen,et al.  Kinetics of glucose disposal in whole body and across the forearm in man. , 1987, The Journal of clinical investigation.

[76]  C Cobelli,et al.  Hepatic glucose production during the labeled IVGTT: estimation by deconvolution with a new minimal model. , 1993, The American journal of physiology.

[77]  Y. Z. Ider,et al.  Quantitative estimation of insulin sensitivity. , 1979, The American journal of physiology.

[78]  Claudio Cobelli,et al.  Optimal equidose inputs and role of measurement error for estimating the parameters of a compartmental model of glucose kinetics from continuous- and discrete-time optimal samples , 1988 .

[79]  C. Cobelli,et al.  On optimality of the impulse input for linear system identification , 1988 .

[80]  R N Bergman,et al.  Reassessment of Glucose Effectiveness and Insulin Sensitivity From Minimal Model Analysis: A Theoretical Evaluation of the Single-Compartment Glucose Distribution Assumption , 1997, Diabetes.

[81]  Claudio Cobelli,et al.  The minimal model of glucose disappearance: optimal input studies , 1987 .

[82]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[83]  C. Cobelli,et al.  Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. , 1980, The American journal of physiology.

[84]  R N Bergman,et al.  Glucose effectiveness assessed under dynamic and steady state conditions. Comparability of uptake versus production components. , 1997, The Journal of clinical investigation.

[85]  J. DiStefano,et al.  Identifiability of Model Parameter , 1985 .

[86]  C Cobelli,et al.  Effect of insulin on the distribution and disposition of glucose in man. , 1985, The Journal of clinical investigation.

[87]  C Cobelli,et al.  The kinetics of insulin in man. I. General aspects. , 1987, Diabetes/metabolism reviews.

[88]  C. Cobelli,et al.  A Minimal Model of Insulin During Insulin Modified IVGTT: Assessment of Hepatic Insulin Extraction , 1997 .

[89]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[90]  Claudio Cobelli,et al.  Optimal Design of Multioutput Sampling Schedules - Software and Applications to Endocrine - Metabolic and Pharmacokinetic Models , 1985, IEEE Transactions on Biomedical Engineering.