title: A computational model of the human glucose-insulin regulatory system.
abstract: OBJECTIVE
  A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The proposed method for the estimation of parameters for a system of ordinary differential equations (ODEs) that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test (GTT) in physiological studies is presented. The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.
  
  
  METHODS
  Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals (SSR) function, which quantifies the difference between theoretical model predictions and GTT's experimental observations. Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.
  
  
  RESULTS
  Based on the Ackerman's published data, we estimated the key parameters by applying R-based iterative computer programs. As a result, the theoretically simulated curves perfectly matched the experimental data points. Our model showed that the estimated parameters, computed frequency and period values, were proven a good indicator of diabetes.
  
  
  CONCLUSIONS
  The present paper introduces a computational algorithm to biomedical problems, particularly to endocrinology and metabolism fields, which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier. The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.
authors.affiliation: Division of Biostatistics, Department of Information Sciences, City of Hope National Medical Center, Duarte, CA 91010-3000, USA ; Division of Hematopoietic Stem Cell and Leukemia Research, City of Hope National Medical Center, Duarte, CA 91010-3000, USA.
authors.forename: Keh-Dong
authors.initials: KD
authors.lastname: Shiang
authors.forename: Fouad
authors.initials: F
authors.lastname: Kandeel
keywords: Coupled ordinary differential equations; cost function; glucose tolerance test; multiple shooting method; parameters estimation; sum of squared residuals
references.citation: Diabetes Care. 2005 May;28(5):1231-9
references.pmid: 15855600
references.citation: Am J Physiol. 1986 May;250(5 Pt 1):E591-8
references.pmid: 3518490
references.citation: Biomed Eng Online. 2005 Jan 11;4:4
references.pmid: 15644138
references.citation: Diabetes. 1970 Sep;19(9):644-55
references.pmid: 5469118
references.citation: Diabetes. 2004 Apr;53(4):955-62
references.pmid: 15047610
references.citation: Am J Physiol. 1979 Jun;236(6):E667-77
references.pmid: 443421
references.citation: Biomed Eng Online. 2006 Jun 29;5:43
references.pmid: 16808835
references.citation: Comput Methods Programs Biomed. 1986 Oct;23(2):113-22
references.pmid: 3640682
references.citation: Diabet Med. 1991 Nov;8(9):822-32
references.pmid: 1837509
references.citation: Comput Methods Programs Biomed. 2000 Jul;62(3):249-57
references.pmid: 10837910
references.citation: Curr Opin Clin Nutr Metab Care. 2002 Sep;5(5):495-501
references.pmid: 12172472
references.citation: Diabetologia. 1985 Jul;28(7):412-9
references.pmid: 3899825
references.citation: J Clin Endocrinol Metab. 2005 Jun;90(6):3387-91
references.pmid: 15784705
references.citation: Diabetes. 2001 Apr;50(4):710-9
references.pmid: 11289033
references.citation: Diabetes. 1993 Feb;42(2):250-6
references.pmid: 8425661
references.citation: Bull Math Biophys. 1965;27:Suppl:21-37
references.pmid: 5884133
references.citation: Comput Biomed Res. 1970 Apr;3(2):146-65
references.pmid: 5431933
references.citation: Comput Methods Programs Biomed. 2009 May;94(2):118-42
references.pmid: 19157629
references.citation: Diabetes. 2002 Feb;51 Suppl 1:S258-61
references.pmid: 11815489
references.citation: Diabetes. 1970 Jun;19(6):445-9
references.pmid: 5421367
references.citation: Comput Biol Med. 2007 May;37(5):611-27
references.pmid: 16867301
references.citation: Comput Biol Med. 2005 Dec;35(10):862-74
references.pmid: 16310011
references.citation: J R Soc Interface. 2008 Oct 6;5(27):1119-35
references.pmid: 18611843
references.citation: Diabetes. 1973 Feb;22(2):94-103
references.pmid: 4687648
references.citation: Diabetologia. 1996 Aug;39(8):997-1000
references.pmid: 8858225
references.citation: Diabetes. 1980 Dec;29(12):979-90
references.pmid: 7002673
references.citation: J Appl Physiol. 1961 Sep;16:783-8
references.pmid: 13870789
references.citation: Endocr Rev. 1985 Winter;6(1):45-86
references.pmid: 3884329
references.citation: Am J Physiol. 1998 Mar;274(3):E573-6
references.pmid: 9530143
references.citation: Comput Biol Med. 2008 Feb;38(2):185-95
references.pmid: 17991459
references.citation: Diabetes. 1988 Feb;37(2):223-31
references.pmid: 3292317
references.citation: Diabetes Care. 2004 Jun;27(6):1487-95
references.pmid: 15161807
references.citation: Am J Physiol. 1993 May;264(5 Pt 1):E829-41
references.pmid: 8498505
references.citation: J Clin Endocrinol Metab. 2000 Jul;85(7):2402-10
references.pmid: 10902785
references.citation: Diabetes Metab. 2000 Apr;26(2):148-51
references.pmid: 10804331
references.citation: Diabetes Care. 1987 Mar-Apr;10(2):225-37
references.pmid: 3582083