A mathematical model of insulin secretion

Diabetes mellitus is a chronic state of excessive blood glucose levels (hyperglycaemia), which may result from many environmental and genetic factors, often acting jointly. The major regulator of glucose concentration in the blood is insulin. It is known that about 50% of the insulin is taken up by the liver on passing through it after secretion from the pancreas. The precise value of this fractional uptake is not known, so the prehepatic insulin secretion rates cannot be readily estimated from the plasma insulin concentration levels. By utilizing the equimolar secretion of insulin and connecting peptide (C-peptide) from the pancreas, a noninvasive method has been formulated. This was based on a compartmental model which involved the pancreas, liver, and plasma. The resulting differential equation yielded a gamma variate solution which could be readily linearized. The model was then tested on 56 normal (51 nonobese and 5 obese) subjects, and three groups of subjects with diabetes who could be labelled as mild, moderate, and severe (based on the fasting plasma glucose concentration) with 83, 88, and 64 subjects respectively. We have focused on the human patient environment of the clinician to produce a distinct model which gave a consistent pattern within all four groups with good fits between observed and theoretical values of the plasma insulin levels. The consequent rates for insulin secretion were consistent across the groups and were clinically meaningful.