Page 451 - Handbook of Biomechatronics

The Artificial Pancreas 445

parallel with a glucose subsystem that represents all tissues producing, distrib-
uting, or metabolizing glucose. When the system is perturbed the concen-
trations of glucose, G(t) and insulin I(t) can each be considered in terms of a
known input and a noisy output and modeled independently. Cobelli
describes seven coarse models of increasing complexity to explain blood glu-
cose concentration using blood insulin as a known input. The differential
equations describing the simplest of these glucose models is

_ 0 0
Q tðÞ ¼ NHGB Q tðÞ, I tðÞð Þ R d QtðÞ, I tðÞÞ + D δ tðÞ
ð
1
0 0
_ I tðÞ ¼ k 3 I tðÞ + k 2 ItðÞ I b Š
½
(7)
QtðÞ
GtðÞ ¼
V
For initial conditions
Q 0ðÞ ¼ Q b
0
I 0ðÞ ¼ 0
where Q is the blood glucose mass with Q b being the basal value, I is the
blood insulin concentration with I b being the basal value. I (t) is the above
0
basal remote insulin, D is the glucose dose, and V is the glucose distribution
volume. k 2 and k 3 are rate parameters and NHGB is the net hepatic glucose
0
balance that depends on the blood glucose and the remote insulin I .
0 0
NHGB Q tðÞ, I tðÞð Þ ¼ NHGB 0 k 5 + k 6 I tðފQtðÞ
½
and R d is the rate of glucose disappearance from the peripheral tissues, which
0
is also a function of blood glucose and remote insulin I .
0 0
R d QtðÞ, I tðÞð Þ ¼ R d0 + k 1 + k 4 I tðފQtðÞ
½
Various nonlinear insulin models have been described. However, their
parameterization is complicated because it is only possible to measure the
posthepatic insulin concentration that is smaller than the pancreatic secretion
levels. To overcome this, the C-peptide secretion that is equivalent in con-
centration to the insulin secretion and is not extracted by the liver, is mea-
sured as a proxy.
The insulin secretion model can be described by fast and slow compo-
nents. The first phase secretion has a 2-min turnover and is probably from
previously primed insulin secretory granules. It exerts derivative control as it
is proportional to the rate of increase of glucose from the basal up to the