Page 450 - Handbook of Biomechatronics

444 Graham Brooker

venous blood for glucose level analysis and could provide a continuous mea-
sure of insulin requirements. However, although the IV route is ideal it is not
practical and despite delayed absorption of insulin and in reading glucose
levels provided by subcutaneous operation, it has become the method of
choice for closed-loop operation (Leiva-Hidalgo, 2011).

5.1 Modeling
The development of adequate closed-loop control systems relies on com-
prehensive in vitro models of the interaction between insulin and glucose
in diverse environments. According to Cobelli, two mechanistic physiolog-
ically based models have been developed. Minimal (coarse) models describe
key components of system functionality and provide insight into glucose
metabolism and insulin control in both healthy and diabetic patients. Max-
imal (fine grain) models include all available knowledge about system func-
tionality and are thus capable of accurately simulating glucose-insulin
systems in diabetics, making it possible to create accurate simulation scenar-
ios to evaluate closed-loop treatments (Cobelli et al., 2009).
The simplest coarse models are obtained using an oral glucose tolerance
test (OGTT) to provide a step change in glucose levels and then observing
the blood glucose and insulin concentrations. The following differential
equations were obtained using IV administration of glucose.

_
GtðÞ ¼ a 1 GtðÞ a 2 ItðÞ + JtðÞ
(6)
_ ItðÞ ¼ a 3 GtðÞ a 4 ItðÞ
where G and I are the blood glucose and insulin concentrations respectively
and J is the glucose input that can be either a glucose injection providing a
step input or the more gradual absorption after a meal. The parameters a 1 to
a 4 are used to tune the response It assumes that the glucose use is a linear
function of both the glucose and insulin concentrations and that insulin
secretion is proportional to glucose concentration. This model is too simple
as the relationship between insulin secretion rate and glucose concentration
is nonlinear and very complex. In addition, the model does not consider the
complex interactive control of hepatic glucose production and uptake of
glucose and insulin.
Later models isolated the various contributions by opening the loop and
decomposing the closed-loop system into two independent subsystems that
are linked together by measured variables. In this case, an insulin subsystem
represents all tissues that secrete, distribute, or degrade insulin running in