Page 304 - Glucose Monitoring Devices

Closed-loop glycemic control algorithms 311

which is equivalent to
K
r i;k ¼ D u i;k
The objective of the model predictive iterative learning control (MPILC) algo-
rithm is to minimize the term
sp
e i;k ¼ y y i;k
i
sp K
which can be rewritten as. e i;k ¼ y i y i;k 1 D y i;k
sp K
Hence, y and y i;k 1 are known, while D y i;k can be predicted using the afore-
i
mentioned ARX model. The MPILC optimization problem isthen
N
X 2 2
min q 1 ,e þ q 2 ,r
V N ¼ iþj;k iþj;k
r i;k ;.;r iþN;k
j¼0
subject to:
sp K
e iþj;k ¼ y y iþj;k 1 D y iþj;k
iþj
K
r iþj;k ¼ D u iþj;k for j˛I 0:N
1 K 1 K
A q D y iþj;k ¼ B q D u iþj d;k
where q 1 and q 2 are penalty weights for the deviation of the error and the input
moves and N is the prediction/control horizon. Additional constraints on the inputs
and controlled outputs may be readily incorporated into the optimization problem.

Adaptive weights through glycemic risk index
Variations in the glycemic measurements can alter the precedence for insulin infu-
sion. The fluctuating importance of insulin infusion can be reflected in the varying
weights of the MPC objective function. Manipulating the penalty weights of the
objective function based on the glucose measurements can vary the necessity for
insulin infusion. The weights of the objective function can be modified through
a glycemic risk index (GRI) that relates the glucose measurement to the weight
on the glucose tracking error (Fig. 15.2). The glycemic risk index disproportionally
increases the penalty weights as the CGM measurements deviate from the desired
set-point target, which in this case is considered to be 110 mg/dL. The asymmetry
of the GRI is due to the fact that hypoglycemia is associated with severe immediate
and short-term adverse effects, such as coma or death, the penalty on the set-point
tracking error should be increased rapidlyinresponseto decreasingglucose mea-
surements. Uncontrolled T1DM leads to prolonged hyperglycemia that can cause
more long-term ailments like micro- (i.e., neuropathy, retinopathy, and nephropa-
thy) and/or macrovascular (i.e., myocardial infarction and stroke) complications,
and premature mortality. Therefore the GRI increases steadily in response to
hyperglycemia. The GRI weight can be used to adjust the penalty weight for the