Blood glucose concentration is regulated primarily by the controlled release of insulin in the pancreas. Discuss
Blood glucose concentration is regulated primarily by the controlled release of insulin in the pancreas. However, patients with Type I diabetes mellitus are incapable of producing insulin and therefore require shots of insulin to be administered several times a day to regulate the blood glucose concentration. Assuming that we are on a project to develop a miniaturized implantable insulin pump that is automatic. We will do some preliminary design work to determine the performance characteristics of such a device. As we have discussed in the class, we will need one mathematical model to describe the effect of insulin on glucose and a second mathematical model to describe the effect of a meal on the glucose concentration. We will use Bergman\’s minimal model (Bergman et al., 1981), described the three differential equations: where and represent the deviation in blood glucose and insulin concentrations, respectively, is proportional to the insulin concentration in a \”remote\” compartment. The inputs are , (input of glucose due to a meal – considered a disturbance here), and , the manipulated insulin infusion rate. The blood parameters include , , , and (which represents the blood volume). and are the \”basal\” (baseline) values of blood glucose and insulin concentration. For the purpose of control system design, a linearized state-space representation with the state variables =, =, and =, input variables =- and = (glucose disturbance due to meal input) and the output variable = can be derived out of the above non-linear model. Some typical values for the above constants are as follows:=4.5 mmol/liter=4.5 mU/liter=12 liters = 0 /min = 0.025/min = 0.0000013 mU/liter=5/54 /min The corresponding transfer functions will be (you will have two transfer functions corresponding to the two inputs): and The transfer function relates the output to the input ; the transfer function relates the output to the input .
