Mathematical modeling in glucose metabolism and insulin secretion

Current Opinion in Clinical Nutrition and Metabolic Care

Volumn 5, Issue 5, 2002, Pages 495-501

  Mari, Andrea ^a,b  

^a CNR   (Italy)

^b Istituto di Ingeneria Biomedica del CNR   (Italy)

Author keywords

cell function; Glucose kinetics; Insulin secretion; Insulin sensitivity; Mathematical models

Indexed keywords

GLUCOSE; INSULIN;

ENDOCRINE FUNCTION; GLUCOSE METABOLISM; HORMONAL REGULATION; HUMAN; INSULIN RELEASE; INSULIN SENSITIVITY; MATHEMATICAL MODEL; METABOLIC REGULATION; NON INSULIN DEPENDENT DIABETES MELLITUS; PANCREAS ISLET BETA CELL; REVIEW; ANIMAL; ANIMAL MODEL; BIOLOGICAL MODEL; CYTOLOGY; GLUCOSE BLOOD LEVEL; GLUCOSE TOLERANCE TEST; MATHEMATICS; METABOLISM; PANCREAS ISLET; SECRETION;

ANIMALS; BLOOD GLUCOSE; GLUCOSE TOLERANCE TEST; HUMANS; INSULIN; ISLETS OF LANGERHANS; MATHEMATICS; MODELS, ANIMAL; MODELS, BIOLOGICAL;

EID: 0036725442     PISSN: 13631950     EISSN: None     Source Type: Journal    
DOI: 10.1097/00075197-200209000-00007     Document Type: Review

References (55)

1. Ferrannini E, Mari A. How to measure insulin sensitivity. J Hypertens 1998; 16:895-906.
2. Radziuk J. Insulin sensitivity and its measurement: structural commonalities among the methods. J Clin Endocrinol Metab 2000; 85:4426-4433.
3. Bergman RN, Lovejoy JC. The minimal model approach and determinants of glucose tolerance. Baton Rouge: Louisiana State University Press; 1997.
4. Caumo A, Cobelli C. Minimal model estimate of glucose effectiveness: role of the minimal model volume and of the second hidden compartment. Am J Physiol Endocrinol Metab 1998; 274:E573-E576.
5. Cobelli C, Bettini F, Caumo A, Quon MJ. Overestimation of minimal model glucose effectiveness in presence of insulin response is due to undermodeling. Am J Physiol Endocrinol Metab 1998; 275:E1031-E1036.
6. Caumo A, Vicini P, Zachwieja JJ, et al. Undermodeling affects minimal model indexes: insights from a two-compartment model. Am J Physiol Endocrinol Metab 1999; 276:E1171-E1193.
7. Regittnig W, Trajanoski Z, Leis HJ, et al. Plasma and interstitial glucose dynamics after intravenous glucose injection: evaluation of the single-compartment glucose distribution assumption in the minimal models. Diabetes 1999; 48:1070-1081.
8. Vicini P, Caumo A, Cobelli C. Glucose effectiveness and insulin sensitivity from the minimal models: consequences of undermodeling assessed by Monte Carlo simulation. IEEE Trans Biomed Eng 1999; 46:130-137.
9. Vicini P, Caumo A, Cobelli C. The hot IVGTT two-compartment minimal model: indexes of glucose effectiveness and insulin sensitivity. Am J Physiol Endocrinol Metab 1997; 273:E829-EE841.
10. I underestimation: improved accuracy by a Bayesian two-compartment model. Am J Physiol Endocrinol Metab 1999; 277:E481-E488.
11. Natalucci S, Boemi M, Fumelli P, et al. One- and two-compartment minimal models detect similar alterations of glucose metabolism indexes in hypertension. Metabolism 2000; 49:1529-1536.
12. Hovorka R, Bannister P, Eckland DJ, et al. Reproducibility and comparability of insulin sensitivity indices measured by stable-label intravenous glucose tolerance test. Diabet Med 1998; 15:234-246.
13. Vicini P, Zachwieja JJ, Yarasheski KE, et al. Glucose production during an IVGTT by deconvolution: validation with the tracer-to-tracee clamp technique. Am J Physiol Endocrinol Metab 1999; 276:E285-E294.
14. Ward GM, Walters JM, Barton J, et al. Physiologic modeling of the intravenous glucose tolerance test in type 2 diabetes: a new approach to the insulin compartment. Metabolism 2001; 50:512-519.
15. Godsland IF, Walton C. Maximizing the success rate of minimal model insulin sensitivity measurement in humans: the importance of basal glucose levels. Clin Sci (Lond) 2001; 101:1-9.
16. Steimer J, Vozeh S, Racine-Poon A, et al. The population approach: rationale, methods, and applications in clinical pharmacology and drug development. In: Welling P, Balant H, editors. Handbook of experimental pharmacology, vol. 110, Pharmacokinetics of drugs. New York: Springer; 1994.
17. Vicini P, Cobelli C. The iterative two-stage population approach to IVGTT minimal modeling: improved precision with reduced sampling: intravenous glucose tolerance test. Am J Physiol Endocrinol Metab 2001; 280:E179-E186. A useful application of the Bayesian approach to improve the minimal model parameter estimates with a reduced IVGTT sampling schedule.
18. I=0 problem in NIDDM subjects: nonzero Bayesian estimates with credible confidence intervals. Am J Physiol Endocrinol Metab 2002; 282:E564-E573. A useful application of the Bayesian approach to overcome the problem of negative insulin sensitivity estimates in type 2 diabetes.
19. Caumo A, Bergman RN, Cobelli C. Insulin sensitivity from meal tolerance tests in normal subjects: a minimal model index. J Clin Endocrinol Metab 2000; 85:4396-4402.
20. Breda E, Cavaghan MK, Toffolo G, et al. Oral glucose tolerance test minimal model indexes of beta-cell function and insulin sensitivity. Diabetes 2001; 50:150-158. This paper presents the OGTT version of the meal minimal model index of insulin sensitivity and new model-based indices of β-cell function obtained from the OGTT.
21. Mari A, Pacini G, Murphy E, et al. A model-based method for assessing insulin sensitivity from the oral glucose tolerance test. Diabetes Care 2001; 24:539-548. In this work a new model-based formula for insulin sensitivity from the OGTT is developed and validated against the glucose clamp across a wide spectrum of insulin sensitivity.
22. Matsuda M, DeFronzo RA. Insulin sensitivity indices obtained from oral glucose tolerance testing: comparison with the euglycemic insulin clamp. Diabetes Care 1999; 22:1462-1470.
23. Stumvoll M, Mitrakou A, Pimenta W, et al. Use of the oral glucose tolerance test to assess insulin release and insulin sensitivity. Diabetes Care 2000; 23:295-301.
24. Stumvoll M, Van Haeften T, Fritsche A, Gerich J. Oral glucose tolerance test indexes for insulin sensitivity and secretion based on various availabilities of sampling times. Diabetes Care 2001; 24:796-797.
25. Mari A. Assessment of insulin sensitivity and secretion with the labelled intravenous glucose tolerance test: improved modelling analysis. Diabetologia 1998; 41:1029-1039.
26. Natali A, Gastaldelli A, Camastra S, et al. Dose-response characteristics of insulin action on glucose metabolism: a non-steady-state approach. Am J Physiol Endocrinol Metab 2000; 278:E794-E801.
27. Hovorka R, Shojaee-Moradie F, Carrol PV, et al. Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT. Am J Physiol Endocrinol Metab 2002; 282:E992-E1007. This paper presents a new variant of the two-compartment minimal model with which the effects of insulin on glucose transport are evaluated from a double-label IVGTT.
28. De Gaetano A, Arino O. Mathematical modelling of the intravenous glucose tolerance test. J Math Biol 2000; 40:136-168.
29. Tolic IM, Mosekilde E, Sturis J. Modeling the insulin-glucose feedback system: the significance of pulsatile insulin secretion. J Theor Biol 2000; 207:361-375.
30. Engelborghs K, Lemaire V, Belair J, Roose D. Numerical bifurcation analysis of delay differential equations arising from physiological modeling. J Math Biol 2001; 42:361-385.
31. Lenbury Y, Ruktamatakul S, Amornsamarnkul S. Modeling insulin kinetics: responses to a single oral glucose administration or ambulatory-fed conditions. Biosystems 2001; 59:15-25.
32. Li J, Kuang Y, Li B. Analysis of IVGTT glucose-insulin interaction models with time delay. Discrete Continuous Dyn Syst B 2001; 1:103-124.
33. Topp B, Promislow K, deVries G, et al. A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes. J Theor Biol 2000; 206:605-619.
34. Hovorka R, Jones RH. How to measure insulin secretion. Diabetes Metab Rev 1994; 10:91-117.
35. Pacini G. Mathematical models of insulin secretion in physiological and clinical investigations. Comput Methods Programs Biomed 1994; 41:269-285.
36. Breda E, Cobelli C. Insulin secretion rate during glucose stimuli: alternative analyses of C-peptide data. Ann Biomed Eng 2001; 29:692-700.
37. Pillonetto G, Sparacino G, Cobelli C. Reconstructing insulin secretion rate after a glucose stimulus by an improved stochastic deconvolution method. IEEE Trans Biomed Eng 2001; 48:1352-1354.
38. Van Cauter E, Mestrez F, Sturis J, Polonsky KS. Estimation of insulin secretion rates from C-peptide levels: comparison of individual and standard kinetic parameters for C-peptide clearance. Diabetes 1992; 41:368-377.
39. Hovorka R, Koukkou E, Southerden D, et al. Measuring pre-hepatic insulin secretion using a population model of C-peptide kinetics: accuracy and required sampling schedule. Diabetologia 1998; 41:548-554.
40. Watanabe RM, Steil GM, Bergman RN. Critical evaluation of the combined model approach for estimation of prehepatic insulin secretion. Am J Physiol Endocrinol Metab 1998; 274:E172-E183.
41. Kjems LL, Christiansen E, Volund A, et al. Validation of methods for measurement of insulin secretion in humans in vivo. Diabetes 2000; 49:580-588.
42. Watanabe RM, Bergman RN. Accurate measurement of endogenous insulin secretion does not require separate assessment of C-peptide kinetics. Diabetes 2000; 49:373-382.
43. Kjems LL, Volund A, Madsbad S. Quantification of beta-cell function during IVGTT in type II and non-diabetic subjects: assessment of insulin secretion by mathematical methods. Diabetologia 2001; 44:1339-1348. This paper gives a balanced account of the performance of the combined model for insulin secretion.
44. Tura A, Ludvik B, Nolan JJ, et al. Insulin and C-peptide secretion and kinetics in humans: direct and model-based measurements during OGTT. Am J Physiol Endocrinol Metab 2001; 281:E966-E974. An interesting comparison between the combined model of insulin and C-peptide kinetics and the splanchnic catheterization method for the calculation of insulin secretion.
45. Nesher R, Cerasi E. Modeling phasic insulin release: immediate and time-dependent effects of glucose. Diabetes 2002; 51 (Suppl 1):S53-S59. An updated and thoughtful discussion on the essential characteristics of insulin secretion, with reference to a classical β-cell model and to recent molecular biology research.
46. Hovorka R, Chassin L, Luzio SD, et al. Pancreatic β-cell responsiveness during meal tolerance test: model assessment in normal subjects and subjects with newly diagnosed noninsulin-dependent diabetes mellitus. J Clin Endocrinot Metab 1998; 83:744-750.
47. Toffolo G, Cefalu WT, Cobelli C. Beta-cell function during insulin-modified intravenous glucose tolerance test successfully assessed by the C-peptide minimal model. Metabolism 1999; 48:1162-1166.
48. Cretti A, Lehtovirta M, Bonora E, et al. Assessment of beta-cell function during the oral glucose tolerance test by a minimal model of insulin secretion. Eur J Clin Invest 2001; 31:405-416. Description of an index of β-cell function derived from the OGTT. The index is tested in more than 50 individuals of different characteristics, and with various protocols.
49. Toffolo G, Breda E, Cavaghan MK, et al. Quantitative indexes of beta-cell function during graded up&down glucose infusion from C-peptide minimal models. Am J Physiol Endocrinol Metab 2001; 280:E2-E10. First application of a β-cell function model to the analysis of a meal-like glucose infusion test.
50. Breda E, Toffolo G, Polonsky KS, Cobelli C. Insulin release in impaired glucose tolerance: oral minimal model predicts normal sensitivity to glucose but defective response times. Diabetes 2002; 51 (Suppl 1):S227-S233.
51. Mari A, Camastra S, Toschi E, et al. A model for glucose control of insulin secretion during 24 h of free living. Diabetes 2001; 50 (Suppl 1):S164-S168. First description of a model for the assessment of β-cell function from a multiple-meal test. Evidence is presented that the simplest β-cell models are insufficient for this test.
52. Mari A, Tura A, Gastaldelli A, Ferrannini E. Assessing insulin secretion by modeling in multiple-meal tests: role of potentiation. Diabetes 2002; 51 (Suppl 1):S221-S226. This paper develops the previous β-cell model for multiple-meal tests by accounting for potentiation of insulin secretion, which, interestingly, is found impaired in type 2 diabetes.
53. Bertram R, Sherman A. Dynamical complexity and temporal plasticity in pancreatic beta-cells. J Biosci 2000; 25:197-209.
54. Aslanidi OV, Mornev OA, Skyggebjerg O, et al. Excitation wave propagation as a possible mechanism for signal transmission in pancreatic islets of Langerhans. Biophys J 2001; 80:1195-1209.
55. Giugliano M, Bove M, Grattarola M. Insulin release at the molecular level: metabolic-electrophysiological modeling of the pancreatic beta-cells. IEEE Trans Biomed Eng 2000; 47:611-623.