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

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 Ipi (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 Ipi 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.

Tracking changes of the parameters of glucose-insulin homeostasis during the course of obesity in B6D2F1 mice

“…(2) of the mathematical model in the Methods section. In our previous study, the rate constant for insulin clearance was slightly elevated in HFD-fed mice as compared to lean diet-fed mice after three months of the respective diets although statistical significance was not reached [20]. The primary location of insulin clearance in the body is the liver [23].…”

“…We have previously observed that the rate constants for insulinindependent glucose uptake into tissues (k 3 ) were much higher in the HFD-fed mice than those in the lean diet-fed mice after 3 months of HFD feeding [20]. Increased body mass of the HFD-fed mice and perhaps increased number of glucose transporters that transport glucose into tissues in an insulin-independent manner due to expanded fat pads, blood volume (increased blood cells), etc.…”

“…Brief descriptions of various parameters and terms in the three equations are summarized below. More detailed mathematical analysis and parameter estimation and validation can be found in the articles [15,20]. Eq.…”

“…The search algorithm of OptQuest™ evaluated various combinations of the parameters and determined the best set that minimized the sum of squared errors between the observed and the simulated data. Out of 8 parameters, we fixed three parameters including the rate constant of glucose entering blood from peritoneal cavity (k 0 ), the rate constant of insulin clearance from blood (k 6 ), and the rate constant of glucose leaving peritoneal cavity (k a ) because these rate constants were not significantly different between lean and obese mice based on our previous studies [20].…”

Pancreas Hormones- Inspired Method

“…The role of the pancreas is that, releases the two most important hormones that control glucose homeostasis: insulin and glucagon. They produced in pancreatic-β cells, and pancreatic-α-cells respectively [27], [28], [24].When the blood glucose level is high β cells secrete insulin to help our cells in the process of glucose absorption. Whereas, α-cells secret Glucagon when blood glucose levels fall below normal.…”