Judul: Simulation of Modified Minimal Model for Glucose and Insulin Mechanism in Type 2 Diabetes and Healthy Humans
Abstrak: Bergman minimal model is Mathematics model which is invented by Richard N. Bergman in 1979. That model consists of three compartments to predict glucose effectiveness (SG) and insulin sensitivity (SI) from the intravenous glucose tolerance test (IVGTT) data in a period of time. A lot of modifications from bergman minimal model have been made with the purpose to increase the accuracy and to handle process complexity in glucose-insulin mechanism system. Minimal model can be used in health to diagnose, to prevent, and to treat diabetes patients. In this research, mathematics model is modified based on the assumption that insulin enters the plasma insulin compartment at a rate proportional to the product of time and the glucose concentration above a basal plasma glucose concentration. If the plasma glucose concentration drops below the basal plasma glucose concentration, so insulin rate which enters the plasma glucose compartment is zero. Insulin is cleaned from the plasma insulin compartment at a rate proportional to the amount of insulin in the plasma insulin compartment. This model is also modified based on the assumption that the insulin decay rate is not always a first order process and function identification from insulin infusion rate. Modified minimal model that is obtained in this research consists of three ordinary diferensial equations. The first and second diferensial equations state that the influence of insulin to speed up glucose absorption, whereas the third diferensial equation states that the influence of glucose to increase insulin secretion. The accuracy of modified minimal model working is tested by comparing the simulation result of modified minimal model with the simulation result by Zheng and Zhao and the experiment result from the previous study which is done by Jiaxu et al. The simulation from that ordinary diferensial equation is accomplished using ode45. In general, modified minimal model is applied to healthy humans and type 2 diabetes patients which is then divided into four conditions based on the amount of exogenous insulin infusion that is applied in MATLAB (Matrix Laboratory). On the first condition, model simulation in healthy humans without giving insulin infusion. That simulation result shows that after giving glucose injection to the body, glucose reaches higher concentration and returns to basal condition within one hour. When giving glucose injection, the signal is sent to pancreas, β cells in islands of langerhans reacts by producing insulin hormone. This condition is signed with the increase of insulin concentration in the body. After that, insulin concentration decreases and forms little peak. Insulin hormone functions to process glucose so that it can be absorbed by body cells. Within one hour insulin concentration will return to basal level because there is no glucose that should be processed anymore. It presents that pancreas responsiveness is excellent, in which β cells are able to secrete enough insulin to keep blood glucose concentration in normal condition. On the second condition, that is model simulation in healthy humans by giving exogenous insulin infusion on the 20th minute for 5 minutes as much as 30 mU kg-1 body weight. Glucose concentration of healthy humans will return quickly to
Keyword: modified minimal model, glucose,, insulin, type 2 diabetes