Closed Loop Control of a Nonlinear Glucose-Insulin
Regulatory System Considering Practical Delays
The blood glucose level
of a normal human being is within the range of 70-120mg/dl. In diabetic
patients, the glucose levels are high due to improper functioning of the pancreas.
It is necessary to maintain the plasma glucose concentration in the diabetic patient
within the normal range by injecting an appropriate amount of insulin. The
plasma glucose is typically measured using a glucose sensor. A model based
control strategy needs to be implemented to determine the amount of insulin to
be injected to the patient.
In this work, a
mathematical model representing ultradian oscillatory
nature of the glucose and insulin secretions in a normal human being is
considered. This model includes various physiological delays resulting in a set
of delay differential equations. The model was modified to consider the effects
of hyperglycemia, external glucose sensor characteristics and injected insulin
kinetics to make it resemble the glucose-insulin regulatory system in the
diabetic patients. A delay approximation method was applied for the delay terms
in the model and a set of ordinary differential equations were formed. An observer
was designed and implemented to measure the state estimates of the model. An extended
Kalman filter was implemented to estimate the state
variables. These state estimates were then used in the control algorithm. A
sensitivity analysis of the parameters in the model was also carried out. The
continuous closed loop control algorithm calculates the amount of insulin to be
injected to the patient to maintain the blood glucose levels within the normal
range. A model predictive control algorithm with constraints was implemented to
measure the rate at which the insulin should be injected. This value is then
fed to the infusion pump and the drug is delivered accordingly. Thus, the
control strategy implemented in this work can be considered as a step towards
the development of an artificial pancreas.