Page 452 - Handbook of Biomechatronics

446 Graham Brooker

maximum. The slow secretion is generated by new insulin secretory gran-
ules and is proportional to the glucose concentration.

SR tðÞ ¼ mF tðÞ (8)
where SR is the secretion rate and F is the ready realizable insulin
described by

_
FtðÞ ¼ mF tðÞ + YG, tÞ
ð
with initial conditions F(0) ¼ F 0 , where F 0 is the amount of insulin released
immediately after the glucose stimulus. Y(G,t) is the provision of new insulin
that depends on the glucose level
1
_
ð
ð
ð
YG, tÞ ¼ ½ YG, tÞ YG, ∞ފ
T
where Y(0) ¼ 0 and

0 if GtðÞ < h
YG, ∞Þ ¼
ð
½
β GtðÞ hŠ if GtðÞ h
These rather complex subsystem models can be integrated into a complete
model of the glucose-insulin control system as shown in Fig. 25.
For conventional physical systems, equations can be developed from first
principles to accurately describe their behavior, whereas maximal models of
physiological processes rely on the interpretation of measurements. Those
issues notwithstanding, complex models provide answers to “what if” ques-
tions in a teaching environment and more importantly to assess control algo-
rithms and different insulin diffusion techniques. This method is sufficiently
advanced that the FDA has accepted in silico trials using maximal models as a
substitute to preclinical animal studies (Cobelli et al., 2009).

5.2 Closed-Loop Control
Control schemes can be open or closed loop, both of which aim to keep
blood glucose within a desired range by compensating for disturbances using
insulin. Typically, open-loop methods do not use real-time data to make
their decisions whereas the closed-loop system exploits real-time measure-
ments correlated with the control variable to react to disturbances.
A completely open-loop system would rely on fixed basal insulin admin-
istration throughout the day with additional boluses at meal times, based on
patient characteristics without glucose measurements. Such a control system