This is a particularly important chapter on the method of lowering blood glucose in diabetic patients by automated infusion of insulin. Herein, we first review the functions of the pancreas in Section 3.2. Then in Section 3.4, we provide an overview of the current treatment methods for insulin-dependent diabetes involving subcutaneous insulin injection or continuous infusion of insulin. Section 3.5 presents noninvasive insulin delivery systems. Thereafter from Section 3.6 onwards we present our work on the automated insulin infusion regulation system.
Figure 3.22 shows an overview of the insulin release system. In this system, there are two sensors, namely noninvasive glucose sensor and insulin sensor. These sensors provide the instant glucose and insulin concentrations to the respective computation sub-systems. In turn, the glucose-insulin kinetics system response parameters computer derives the required amount of insulin the human biological system requires after a meal.
Firstly, the blood glucose response computer involves the governing differential equation model for glucose response (y) to glucose bolus ingestion Gδ(t). The solutions of this equation are provided for (1) underdamped response (for normal subject), (2) overdamped response (for diabetic patient), and (3) critical-damped response (for at-risk subject) The controller in Figure 3.22 is constructed based on the formulation of these equations. It calculates the values of the model parameters for underdamping, critical damping and overdamping scenarios based on the glucose concentration response y(t).
Next, the insulin response computer deals with the insulin concentration response x(t) to glucose bolus ingestion. We have the differential equations for x′ for underdamped, overdamped and critically damped responses, and their solutions for x(t). This controller is constructed based on the formulation of these equations.
Then the glucose-insulin kinetics system response parameters computer calculates the values of the model parameters α, β, γ, and δ for underdamp, critical, and overdamp scenarios based on the insulin concentration x(t) response caused by the glucose input impulse y(t). The controller will then also calculate the nondimensional physiological indices and determine if the patient is normal, at-risk, or diabetic It will determine the insulin amount required at that moment, and the send a signal for the amount of insulin required in the blood-pool.
In the next Section 3.7, we discuss the design of the insulin infusion controller. The key function of the controller in our system is to bring the blood glucose concentration down as soon as possible, but prevent hypoglycemia within a sample period of 2 hours. Therein, we have presented the performances of three common control techniques for the insulin infusion system: proportional-derivative (PD) control, proportional-integral (PI) control, and proportional-integral-derivative (PID) control.
In Section 3.8, we are presenting the performances of the PD, PI, and PID controllers for some specific subjects. Based on Figure 3.33, Figure 3.34, we can observe that the PD controller is outperforming the PI and PID controllers, as the amount of undershoots (under the reference blood glucose level) by PD controller is not as frequent as with the other two controllers.
So then in Section 3.9, on the derivation of insulin response in the blood pool, we are presenting the remodeled glucose-insulin dynamic system. The central idea here is that when the system shows an overdamped response of a diabetic subject, the insulin infusion is put in, by which the system shows an underdamped response of the subject.
Now based on the governing differential equations in Chapter 2, we derive the glucose and insulin responses to the application of an insulin impulse p(t) = Iδ(t) where I is the amplitude of insulin impulse and δ(t) is the finite delta function. Figure 3.38 shows the blood glucose responses before and after release of the insulin pulse. In this figure,
- (i)
the initial glucose (overdamped) response y(t) = (G/ω)e−Atsinh ωt is caused after a meal,
- (ii)
then insulin infusion p(t) = I (kPy(t) + kDy′(t)) is provided, resulting in
- (iii)
.
All this is very effectively conveyed in Figure 3.40, the final block diagram of the insulin infusion system, wherein the only sensor used is the noninvasive blood glucose sensor. In this figure, based on the blood glucose sensor, the initial glucose response y(t) is obtained as: y(t) = (G/ω)e−Atsinh ωt, after a meal. Then, this leads to insulin infusion impulse p(t) release into the gastrointestinal (GI) tract, as given by: p(t) = I (kPy(t) + kDy′(t)). The resulting normalized blood glucose concentration is obtained as: .
We have thereby demonstrated that we can bring down the blood glucose concentration within 2 hours for the subjects who were determined as diabetic. This is the effectiveness of our control system model for lowering the glucose concentration by application of insulin infusion based on the glucose response.
