Estimation of insulin secretion, glucose uptake by tissues, and liver handling of glucose using a mathematical model of glucose-insulin homeostasis in lean and obese mice

Michael Brenner; Sakineh Esmaeili Mohsen Abadi; Ramin Balouchzadeh; H Felix Lee; Hoo Sang Ko; Michael Johns; Nehal Malik; Joshua J Lee; Guim Kwon

doi:10.1016/j.heliyon.2017.e00310

Estimation of insulin secretion, glucose uptake by tissues, and liver handling of glucose using a mathematical model of glucose-insulin homeostasis in lean and obese mice

Heliyon. 2017 Jun 7;3(6):e00310. doi: 10.1016/j.heliyon.2017.e00310. eCollection 2017 Jun.

Authors

Michael Brenner¹, Sakineh Esmaeili Mohsen Abadi¹, Ramin Balouchzadeh¹, H Felix Lee¹, Hoo Sang Ko¹, Michael Johns², Nehal Malik², Joshua J Lee³, Guim Kwon³

Affiliations

¹ Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026, United States.
² Department of Biological Sciences, Southern Illinois University Edwardsville, Edwardsville, IL 62026, United States.
³ School of Pharmacy, Southern Illinois University Edwardsville, Edwardsville, IL 62026, United States.

Abstract

Destruction of the insulin-producing β-cells is the key determinant of diabetes mellitus regardless of their types. Due to their anatomical location within the islets of Langerhans scattered throughout the pancreas, it is difficult to monitor β-cell function and mass clinically. To this end, we propose to use a mathematical model of glucose-insulin homeostasis to estimate insulin secretion, glucose uptake by tissues, and hepatic handling of glucose. We applied the mathematical model by Lombarte et al. (2013) to compare various rate constants representing glucose-insulin homeostasis between lean (11% fat)- and high fat diet (HFD; 45% fat)-fed mice. Mice fed HFD (n = 12) for 3 months showed significantly higher body weights (49.97 ± 0.52 g vs. 29.86 ± 0.46 g), fasting blood glucose levels (213.08 ± 10.35 mg/dl vs. 121.91 ± 2.26 mg/dl), and glucose intolerance compared to mice fed lean diet (n = 12). Mice were injected with 1 g/kg glucose intraperitoneally and blood glucose levels were measured at various intervals for 120 min. We performed simulation using Arena™ software based on the mathematical model and estimated the rate constants (9 parameters) for various terms in the differential equations using OptQuest™. The simulated data fit accurately to the observed data for both lean and obese mice, validating the use of the mathematical model in mice at different stages of diabetes progression. Among 9 parameters, 5 parameters including basal insulin, k₂ (rate constant for insulin-dependent glucose uptake to tissues), k₃ (rate constant for insulin-independent glucose uptake to tissues), k₄ (rate constant for liver glucose transfer), and I_pi (rate constant for insulin concentration where liver switches from glucose release to uptake) were significantly different between lean- and HFD-fed mice. Basal blood insulin levels, k₃, and I_pi were significantly elevated but k₂ and k₄ were reduced in mice fed a HFD compared to those fed a lean diet. Non-invasive assessment of the key components of glucose-insulin homeostasis including insulin secretion, glucose uptake by tissues, and hepatic handling of glucose may be helpful for individualized drug therapy and designing a customized control algorithm for the artificial pancreas.

Keywords: Mathematical bioscience.