The maintenance of blood glucose homeostasis is complex and involves several key tissues. Most of these tissues are not easily accessible, making direct measurement of the physiological parameters involved in glucose metabolism difficult. The use of isotope tracer methodology and mathematical modeling allows indirect estimates of in vivo glucose metabolism through relatively noninvasive means. The purpose of this paper was to provide a mathematical synthesis of the models developed for describing glucose kinetics. As many of the models were developed using dogs, example data from the canine literature are presented. However, examples from the human and feline literature are also given in the absence of dog data. The glucose system is considered in both the steady and nonsteady states, and the models are examined by grouping them into schemes consisting of one, two, and three glucose compartments. Noncompartmental schemes are also considered briefly. 1. Introduction Glucose is a ubiquitous cellular fuel source for all mammalian tissues. As such, the regulation of glucose metabolism has been under extensive investigation for the past century. In healthy animals, several biological mechanisms ensure that the rate of appearance of glucose in the bloodstream tightly matches that of glucose uptake by tissues, resulting in relatively constant blood glucose concentrations irrespective of physiological condition. These control mechanisms are predominantly dictated by the energy status of the animal. In postabsorptive and fasting periods the body largely relies on endogenous glucose production via liver glycogenolysis or gluconeogenesis to maintain glucose homeostasis. In the postprandial period (or fed state) glucose uptake and utilization by tissues is increased in response to the absorption of glucose in the small intestine, giving rise to the subsequent stabilization of blood glucose concentrations. Both production and uptake are principally hormonally regulated by glucagon and insulin, but substrate availability, circulating free fatty acids (FFAs), and catecholamines (released in response to stress and/or exercise) also impact glucose metabolism. Dysregulation of glucose homeostasis, as seen in metabolic diseases including obesity and diabetes, has become a worldwide epidemic in humans [1] and companion animals [2]. These diseases share the common feature of progressive insulin resistance and hyperglycemia. The rat has been used extensively as a model for studying the etiology of these diseases (reviewed by [3]). However, the dog provides a model more
References
[1]
J. E. Shaw, R. A. Sicree, and P. Z. Zimmet, “Global estimates of the prevalence of diabetes for 2010 and 2030,” Diabetes Research and Clinical Practice, vol. 87, no. 1, pp. 4–14, 2010.
[2]
J. S. Rand, L. M. Fleeman, H. A. Farrow, D. J. Appleton, and R. Lederer, “Canine and feline diabetes mellitus: nature or nurture?” Journal of Nutrition, vol. 134, no. 8, pp. 2072S–2080S, 2004.
[3]
D. A. Rees and J. C. Alcolado, “Animal models of diabetes mellitus,” Diabetic Medicine, vol. 22, no. 4, pp. 359–370, 2005.
[4]
R. R. Wolfe and D. L. Chinkes, Isotope Tracers in Metabolic Research, John Wiley & Sons, Hoboken, NJ, USA, 2005.
[5]
E. Nyman, C. Br？nnmark, R. Palmér et al., “A hierarchical whole-body modeling approach elucidates the link between in vitro insulin signaling and in vivo glucose homeostasis,” Journal of Biological Chemistry, vol. 286, no. 29, pp. 26028–26041, 2011.
[6]
H. Kang, K. Han, and M. Choi, “Mathematical model for glucose regulation in the whole-body system,” Islets, vol. 4, pp. 84–93, 2012.
[7]
T. R. Strack, P. Poussier, E. B. Marliss, and A. M. Albisser, “Glucose turnover after a mixed meal in dogs: glucoregulation without change in arterial glycemia,” American Journal of Physiology, vol. 266, no. 3, pp. R889–R895, 1994.
[8]
E. Bailhache, K. Ouguerram, C. Gayet et al., “An insulin-resistant hypertriglyceridaemic normotensive obese dog model: assessment of insulin resistance by the euglycaemic hyperinsulinaemic clamp in combination with the stable isotope technique,” Journal of Animal Physiology and Animal Nutrition, vol. 87, no. 3-4, pp. 86–95, 2003.
[9]
S. P. Kim, M. Ellmerer, G. W. van Citters, and R. N. Bergman, “Primacy of hepatic insulin resistance in the development of the metabolic syndrome induced by an isocaloric moderate-fat diet in the dog,” Diabetes, vol. 52, no. 10, pp. 2453–2460, 2003.
[10]
M. J. Christopher, C. Rantzau, G. M. Ward, and F. P. Alford, “Impact of variable insulinemia and glycemia on in vivo glycolysis and glucose storage in dogs,” American Journal of Physiology, vol. 266, no. 1, pp. E62–E71, 1994.
[11]
N. Altszuler, A. Barkai, and C. Bjerknes, “Glucose turnover values in the dog obtained with various species of labeled glucose,” American Journal of Physiology, vol. 229, no. 6, pp. 1662–1667, 1975.
[12]
J. M. Weber, T. J. Roberts, R. Vock, E. R. Weibel, and C. R. Taylor, “Design of the oxygen and substrate pathways. III. Partitioning energy provision from carbohydrates,” Journal of Experimental Biology, vol. 199, no. 8, pp. 1659–1666, 1996.
[13]
M. J. Christopher, Z. P. Chen, C. Rantzau, B. E. Kemp, and F. P. Alford, “Skeletal muscle basal AMP-activated protein kinase activity is chronically elevated in alloxan-diabetic dogs: impact of exercise,” Journal of Applied Physiology, vol. 95, no. 4, pp. 1523–1530, 2003.
[14]
C. Rantzau, M. Christopher, and F. P. Alford, “Contrasting effects of exercise, AICAR, and increased fatty acid supply on in vivo and skeletal muscle glucose metabolism,” Journal of Applied Physiology, vol. 104, no. 2, pp. 363–370, 2008.
[15]
M. J. Christopher, C. Rantzau, G. McConell, B. E. Kemp, and F. P. Alford, “Prevailing hyperglycemia is critical in the regulation of glucose metabolism during exercise in poorly controlled alloxan-diabetic dogs,” Journal of Applied Physiology, vol. 98, no. 3, pp. 930–939, 2005.
[16]
I. R. Hsu, E. Zuniga, and R. N. Bergman, “Pulsatile changes in free fatty acids augment hepatic glucose production and preserves peripheral glucose homeostasis,” American Journal of Physiology, vol. 299, no. 1, pp. E131–E136, 2010.
[17]
R. Steele, “Influences of glucose loading and of injected insulin on hepatic glucose output,” Annals of the New York Academy of Sciences, vol. 82, pp. 420–430, 1959.
[18]
W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Hoboken, NJ, USA, 10th edition, 2012.
[19]
R. N. Bergman, Y. Z. Ider, C. R. Bowden, and C. Cobelli, “Quantitative estimation of insulin sensitivity,” The American Journal of Physiology, vol. 236, no. 6, pp. E667–E677, 1979.
[20]
C. Cobelli, G. Pacini, G. Toffolo, and L. Sacca, “Estimation of insulin sensitivity and glucose clearance from minimal model: new insights from labeled IVGTT,” American Journal of Physiology, vol. 250, no. 5, pp. E591–E598, 1986.
[21]
V. W. Bolie, “Coefficients of normal blood glucose regulation,” Journal of Applied Physiology, vol. 16, pp. 783–788, 1961.
[22]
N. P. Balakrishnan, G. P. Rangaiah, and L. Samavedham, “Review and analysis of blood glucose (BG) models for type 1 diabetic patients,” Industrial and Engineering Chemical Research, vol. 50, pp. 12041–12066, 2011.
[23]
M. Hoenig, K. Thomaseth, J. Brandao, M. Waldron, and D. C. Ferguson, “Assessment and mathematical modeling of glucose turnover and insulin sensitivity in lean and obese cats,” Domestic Animal Endocrinology, vol. 31, no. 4, pp. 373–389, 2006.
[24]
V. Ionut, E. L. Kirkman, and R. N. Bergman, “Investigation of the effect of acepromazine on intravenous glucose tolerance tests in dogs,” American Journal of Veterinary Research, vol. 65, no. 8, pp. 1124–1127, 2004.
[25]
K. R. Verkest, L. M. Fleeman, J. S. Rand, and J. M. Morton, “Evaluation of beta-cell sensitivity to glucose and first-phase insulin secretion in obese dogs,” American Journal of Veterinary Research, vol. 72, no. 3, pp. 357–366, 2011.
[26]
K. J. Kaiyala, R. L. Prigeon, S. E. Kahn, S. C. Woods, D. Porte, and M. W. Schwartz, “Reduced β-cell function contributes to impaired glucose tolerance in dogs made obese by high-fat feeding,” American Journal of Physiology, vol. 277, no. 4, pp. E659–E667, 1999.
[27]
S. D. Mittelman, G. W. van Citters, S. P. Kim et al., “Longitudinal compensation for fat-induced insulin resistance includes reduced insulin clearance and enhanced β-cell response,” Diabetes, vol. 49, no. 12, pp. 2116–2125, 2000.
[28]
N. Hofer-Inteeworn, D. L. Panciera, W. E. Monroe et al., “Effect of hypothyroidism on insulin sensitivity and glucose tolerance in dogs,” American Journal of Veterinary Research, vol. 73, pp. 529–538, 2012.
[29]
J. Radziuk, K. H. Norwich, and M. Vranic, “Experimental validation of measurements of glucose turnover in nonsteady state,” Journal of Physiology, vol. 234, pp. E84–E93, 1978.
[30]
R. A. Shipley and R. E. Clark, Tracer Methods For In Vivo Kinetics, Academic Press, New York, NY, USA, 1972.
[31]
C. Cobelli, P. Vicini, G. Toffolo, and A. Caumo, “The hot IVGTT minimal models: simultaneous assessment of disposal indices and hepatic glucose release,” in The Minimal Model Approach and Determinants of Glucose Tolerance, R. N. Bergman and J. C. Lovejoy, Eds., Louisiana State University Press, Baton Rouge, La, USA, 1997.
[32]
G. M. Steil, K. Rebrin, S. D. Mittelman, and R. N. Bergman, “Role of portal insulin delivery in the disappearance of intravenous glucose and assessment of insulin sensitivity,” Diabetes, vol. 47, no. 5, pp. 714–720, 1998.
[33]
A. Caumo and C. Cobelli, “Hepatic glucose production during the labeled IVGTT: estimation by deconvolution with a new minimal model,” American Journal of Physiology, vol. 264, no. 5, pp. E829–E841, 1993.
[34]
P. Vicini, A. Caumo, and C. Cobelli, “The hot IVGTT two-compartment minimal model: indexes of glucose effectiveness and insulin sensitivity,” American Journal of Physiology, vol. 273, no. 5, pp. E1024–E1032, 1997.
[35]
K. M. Krudys, M. G. Dodds, S. M. Nissen, and P. Vicini, “Integrated model of hepatic and peripheral glucose regulation for estimation of endogenous glucose production during the hot IVGTT,” American Journal of Physiology, vol. 288, no. 5, pp. E1038–E1046, 2005.
[36]
C. Cobelli, G. Toffolo, and E. Ferrannini, “A model of glucose kinetics and their control by insulin, compartmental and noncompartmental approaches,” Mathematical Biosciences, vol. 72, no. 2, pp. 291–315, 1984.
[37]
J. H. M. Thornley and J. France, Mathematical Models in Agriculture, CAB International, Wallingford, Oxon, UK, 2nd edition, 2007.
[38]
O. P. McGuinness and A. Mari, “Assessment of insulin action on glucose uptake and production during a euglycemic-hyperinsulinemic clamp in dog: a new kinetic analysis,” Metabolism, vol. 46, no. 10, pp. 1116–1127, 1997.
[39]
M. F. Saad, R. L. Anderson, A. Laws et al., “A comparison between the minimal model and the glucose clamp in the assessment of insulin sensitivity across the spectrum of glucose tolerance,” Diabetes, vol. 43, no. 9, pp. 1114–1121, 1994.
