Mathematics

Mathematical Modelling And Control Of Blood Glucose/Insulin Concentrations in An Insulin Dependent Diabetic Subject

Abstract

Mathematical models describing the variations in the plasma glucose and J insulin levels over time in an insulin – dependent diabetic person (IDD patient) were formulated. We showed that these models can correctly describe these variations when we solved them sirnuttaneously by andytical approach rather than the normal numerical approach employed for solving non-linear differential equations. The effect of the various parameters involved in the model were tested and it was shown that even though the body cell response to the plasn~ag lucose contributes to the determination of the plasma glucose level, the major determinants of the plasma insulin/glucose level are the pancreatic and liver cells respectively. Furthermore, a control process of the plasma glucose and insulin levels in the blood of an IDD patient was demonstrated. It was shown that insulin infirsion or > injection (intra-muscularly) correctly reduces the plasma glucose level to normal state. The dose of the insulin to be injected into a patient depends on the level of severity of this disease. Similarly, the quantity of the sugar (glucose) to be taken by the patient . and the time it tias to be taken, depends on the level of severity. It was noticed that due to wrong diagnosis, over dose of insutin into a patient can result to HYPOGLYCAEMIA and this usually complicatethe state of health of the patient. The peripheral cell response (body cell level of response to the glucose and insulin quantities in the blood)dorc not markedly determine the plasma glucose level but at’fects the length of time required to return this level to the basal state.



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